25\\), then two spiders at the midpoints of opposite outer edges can contain the fly, each blocking two vertices. The third spider can catch the fly by making its way to the central vertex, cornering the fly on one of the four central edges. If \\(r=25\\), then the fly cannot definitely escape, though it's not guaranteed it gets caught, either. Regardless, our answer is \\(c=25\\).\n\n\\(\\boxed{25}\\)"},"answer":{"kind":"string","value":"25"},"metadata":{"kind":"string","value":"{\n \"competition\": \"us_comps\",\n \"dataset\": \"Ours\",\n \"posts\": null,\n \"source\": \"OMOSoln2.md\"\n}"},"problem":{"kind":"string","value":"A fly is being chased by three spiders on the edges of a regular octahedron. The fly has a speed of \\(50\\) meters per second, while each of the spiders has a speed of \\(r\\) meters per second. The spiders choose the (distinct) starting positions of all the bugs, with the requirement that the fly must begin at a vertex. Each bug knows the position of each other bug at all times, and the goal of the spiders is for at least one of them to catch the fly. What is the maximum \\(c\\) so that for any \\(r
id
stringlengths 6
15
| solution
stringlengths 8
36.1k
| answer
stringlengths 0
543
⌀ | metadata
dict | problem
stringlengths 15
7.84k
| tags
listlengths 1
56
| idea
stringlengths 29
420
| problem_embedding
listlengths 2.56k
2.56k
|
|---|---|---|---|---|---|---|---|
ours_461
|
By definition, a point on a parabola is equidistant to the focus and the directrix. Since \(F_{1} F_{2}=1\), and \(F_{2}\) lies on \(\mathcal{P}_{1}\), the distance from \(F_{2}\) to \(\ell_{1}\) is 1, and similarly, the distance from \(F_{1}\) to \(\ell_{2}\) is 1. Since \(F_{1} F_{2}\) is parallel to both directrices (which are distinct), both points must lie halfway between these two lines. Without loss of generality, assume that \(\ell_{1}: y=1\), \(\ell_{2}: y=-1\), \(F_{1}=\left(\frac{1}{2}, 0\right)\), \(F_{2}=\left(-\frac{1}{2}, 0\right)\). A point of intersection \(P=(x, y)\) must satisfy both \(\left(x-\frac{1}{2}\right)^{2}+y^{2}=(y-1)^{2}\) and \(\left(x+\frac{1}{2}\right)^{2}+y^{2}=(y+1)^{2}\). Solving this system of equations gives \((x, y)= \pm\left(\frac{\sqrt{3}}{2}, \frac{\sqrt{3}}{4}\right)\), so \(A B^{2}=\left(\sqrt{3}\right)^{2}+\left(\frac{\sqrt{3}}{2}\right)^{2}=\frac{15}{4}\), and our answer is \(1504\).
\(\boxed{1504}\)
|
1504
|
{
"competition": "us_comps",
"dataset": "Ours",
"posts": null,
"source": "OMOFall17Solns.md"
}
|
Let \(\mathcal{P}_{1}\) and \(\mathcal{P}_{2}\) be two parabolas with distinct directrices \(\ell_{1}\) and \(\ell_{2}\) and distinct foci \(F_{1}\) and \(F_{2}\) respectively. It is known that \(F_{1} F_{2}\) is parallel to both \(\ell_{1}\) and \(\ell_{2}\), \(F_{1}\) lies on \(\mathcal{P}_{2}\), and \(F_{2}\) lies on \(\mathcal{P}_{1}\). The two parabolas intersect at distinct points \(A\) and \(B\). Given that \(F_{1} F_{2}=1\), the value of \(A B^{2}\) can be expressed as \(\frac{m}{n}\) for relatively prime positive integers \(m\) and \(n\). Find \(100m+n\).
|
[
"/Mathematics/Geometry/CoordinateGeometry/AnalyticGeometry",
"/Mathematics/Geometry/CoordinateGeometry/Cartesian",
"/Mathematics/Geometry/CoordinateGeometry/CartesianCoordinateSystem",
"/Mathematics/Geometry/CoordinateGeometry/CartesianCoordinates",
"/Mathematics/Geometry/Curves/AlgebraicCurves",
"/Mathematics/Geometry/Curves/PlaneCurves",
"/Mathematics/Geometry/Distance/Point-LineDistance2-Dimensional",
"/Mathematics/Geometry/Distance/Point-PointDistance2-Dimensional",
"/Mathematics/Geometry/PlaneGeometry/PlaneCurves"
] |
Use the symmetry that the foci lie midway between the parallel directrices to coordinate‑place the problem and apply the parabola definition.
|
[
-0.000056803226470947266,
-0.039215087890625,
0.0143585205078125,
-0.0182342529296875,
-0.00005263090133666992,
0.011474609375,
-0.0001900196075439453,
0.009246826171875,
0.002902984619140625,
-0.0108184814453125,
0.0277252197265625,
0.0284423828125,
-0.0011472702026367188,
0.00905609130859375,
-0.020477294921875,
-0.01751708984375,
-0.028594970703125,
-0.0162506103515625,
0.03155517578125,
-0.0005283355712890625,
-0.01552581787109375,
0.01023101806640625,
-0.07391357421875,
0.00969696044921875,
-0.0011014938354492188,
-0.0189666748046875,
-0.00255584716796875,
-0.0186004638671875,
0.0027561187744140625,
0.015716552734375,
-0.0083465576171875,
0.00899505615234375,
0.00200653076171875,
-0.0259246826171875,
0.001613616943359375,
-0.00930023193359375,
-0.013671875,
0.00005263090133666992,
-0.023681640625,
-0.0099029541015625,
0.0089111328125,
-0.00919342041015625,
0.01100921630859375,
0.00983428955078125,
0.010833740234375,
0.01395416259765625,
-0.0009832382202148438,
-0.0025997161865234375,
-0.00818634033203125,
-0.00836181640625,
-0.0012197494506835938,
0.0015611648559570312,
-0.01453399658203125,
-0.011474609375,
-0.0350341796875,
-0.060791015625,
-0.0411376953125,
0.0023345947265625,
-0.0391845703125,
-0.01302337646484375,
0.0002512931823730469,
-0.0318603515625,
0.001293182373046875,
-0.0200958251953125,
-0.0011091232299804688,
-0.01010894775390625,
-0.0012388229370117188,
-0.0194091796875,
0.016876220703125,
-0.0213775634765625,
0.0220184326171875,
0.003978729248046875,
0.01357269287109375,
-0.006053924560546875,
0.0009660720825195312,
-0.0194854736328125,
-0.0045013427734375,
0.0018177032470703125,
0.014739990234375,
-0.0013332366943359375,
0.001979827880859375,
0.01096343994140625,
0.0178680419921875,
-0.07452392578125,
0.01009368896484375,
0.00705718994140625,
0.0023193359375,
0.0102081298828125,
0.0166473388671875,
-0.0118865966796875,
-0.00757598876953125,
0.03179931640625,
-0.0265045166015625,
-0.01496124267578125,
-0.004520416259765625,
-0.0045623779296875,
-0.0034313201904296875,
-0.0010614395141601562,
-0.008331298828125,
-0.00031280517578125,
-0.017181396484375,
-0.018280029296875,
-0.004825592041015625,
-0.020782470703125,
-0.00823211669921875,
-0.01015472412109375,
0.005916595458984375,
-0.0133819580078125,
0.00507354736328125,
-0.00014901161193847656,
0.01983642578125,
0.0204315185546875,
0.033294677734375,
0.006290435791015625,
0.017425537109375,
-0.01212310791015625,
0.036468505859375,
0.040802001953125,
0.0032024383544921875,
-0.02191162109375,
-0.002613067626953125,
0.019439697265625,
0.004009246826171875,
0.0024166107177734375,
-0.0007643699645996094,
0.0213470458984375,
-0.0018672943115234375,
-0.032135009765625,
-0.0192108154296875,
0.00885772705078125,
0.01020050048828125,
0.00180816650390625,
-0.046905517578125,
-0.030792236328125,
-0.0279541015625,
0.032012939453125,
-0.01503753662109375,
0.002685546875,
0.041656494140625,
-0.0213470458984375,
-0.0106201171875,
-0.00775146484375,
0.01457977294921875,
-0.0570068359375,
-0.00617218017578125,
-0.03253173828125,
-0.003612518310546875,
-0.020721435546875,
0.01482391357421875,
-0.00557708740234375,
-0.0003600120544433594,
-0.0057220458984375,
0.018218994140625,
0.005542755126953125,
-0.0151214599609375,
0.00508880615234375,
0.0003254413604736328,
0.0012502670288085938,
0.01393890380859375,
-0.0011749267578125,
0.00605010986328125,
-0.0102081298828125,
0.006618499755859375,
-0.00698089599609375,
-0.0050506591796875,
0.0037250518798828125,
-0.0198822021484375,
-0.005886077880859375,
-0.0168304443359375,
0.01861572265625,
0.003711700439453125,
-0.01091766357421875,
-0.00637054443359375,
0.00441741943359375,
-0.00970458984375,
0.00550079345703125,
-0.0021114349365234375,
-0.00916290283203125,
0.0019025802612304688,
0.017974853515625,
0.002079010009765625,
-0.0201263427734375,
0.006343841552734375,
0.021148681640625,
0.0028591156005859375,
-0.0289306640625,
-0.0005078315734863281,
0.0248260498046875,
0.03546142578125,
0.00824737548828125,
-0.0017576217651367188,
-0.0406494140625,
-0.01160430908203125,
0.002834320068359375,
-0.013885498046875,
-0.0283050537109375,
-0.03375244140625,
0.012908935546875,
-0.00921630859375,
0.026580810546875,
-0.0323486328125,
-0.030426025390625,
-0.004261016845703125,
0.0020771026611328125,
0.005413055419921875,
0.0207061767578125,
0.01033782958984375,
-0.0143585205078125,
-0.005992889404296875,
0.0028018951416015625,
0.020355224609375,
0.006381988525390625,
-0.011138916015625,
0.0197601318359375,
-0.01398468017578125,
-0.01000213623046875,
-0.017486572265625,
-0.0002834796905517578,
0.006832122802734375,
0.01702880859375,
0.0013074874877929688,
0.004978179931640625,
-0.01500701904296875,
-0.0163116455078125,
-0.0018777847290039062,
-0.020538330078125,
0.0183868408203125,
-0.001773834228515625,
0.016357421875,
-0.0037593841552734375,
0.029022216796875,
0.0038661956787109375,
-0.006183624267578125,
-0.00771331787109375,
-0.0291748046875,
-0.0030078887939453125,
-0.03265380859375,
0.022216796875,
-0.00301361083984375,
0.0152740478515625,
0.0008106231689453125,
-0.00040531158447265625,
-0.00838470458984375,
0.0028839111328125,
-0.0027923583984375,
-0.004405975341796875,
0.0128326416015625,
-0.0017490386962890625,
0.0222015380859375,
-0.01290130615234375,
-0.0129241943359375,
0.006511688232421875,
0.0092620849609375,
-0.0065765380859375,
-0.0033435821533203125,
0.0049896240234375,
0.0004756450653076172,
-0.02838134765625,
-0.01053619384765625,
0.0056915283203125,
-0.0155029296875,
-0.0167083740234375,
0.003879547119140625,
-0.008056640625,
0.004543304443359375,
0.06640625,
0.0050811767578125,
0.02288818359375,
0.00827789306640625,
-0.0279083251953125,
0.06109619140625,
-0.0292816162109375,
0.0047149658203125,
0.0059967041015625,
-0.0173797607421875,
-0.01013946533203125,
-0.00746917724609375,
0.0009245872497558594,
0.0158538818359375,
-0.01540374755859375,
0.0017099380493164062,
-0.0300750732421875,
-0.036224365234375,
0.023895263671875,
-0.0182647705078125,
0.00505828857421875,
-0.0027942657470703125,
-0.0007925033569335938,
-0.01413726806640625,
-0.005138397216796875,
0.002506256103515625,
-0.019073486328125,
-0.011138916015625,
-0.01122283935546875,
0.04547119140625,
0.047210693359375,
0.006206512451171875,
0.0118560791015625,
-0.00928497314453125,
-0.0030269622802734375,
0.01910400390625,
-0.0099639892578125,
0.007076263427734375,
-0.01209259033203125,
0.00830078125,
0.045684814453125,
0.034576416015625,
0.000492095947265625,
-0.0109405517578125,
-0.025726318359375,
-0.003284454345703125,
-0.0035343170166015625,
-0.01206207275390625,
-0.014678955078125,
-0.0049285888671875,
-0.04412841796875,
-0.0038051605224609375,
0.00791168212890625,
0.01532745361328125,
0.021636962890625,
-0.004451751708984375,
0.019012451171875,
0.02740478515625,
-0.0026569366455078125,
0.036651611328125,
-0.017669677734375,
0.01387786865234375,
-0.00482940673828125,
-0.04681396484375,
0.01678466796875,
0.0237274169921875,
0.00658416748046875,
-0.0052490234375,
-0.0015544891357421875,
-0.01107025146484375,
0.0018634796142578125,
-0.0142974853515625,
-0.0015668869018554688,
-0.0028972625732421875,
-0.00885772705078125,
0.02032470703125,
0.0008082389831542969,
0.0204315185546875,
-0.0592041015625,
-0.01275634765625,
-0.004711151123046875,
-0.02618408203125,
-0.0255279541015625,
-0.0546875,
-0.0114288330078125,
0.039306640625,
0.0028228759765625,
0.0236358642578125,
-0.0040283203125,
-0.01183319091796875,
0.016448974609375,
-0.0014753341674804688,
-0.0019741058349609375,
0.01126861572265625,
0.039215087890625,
-0.0029144287109375,
-0.0291595458984375,
0.01226806640625,
0.0291595458984375,
-0.00664520263671875,
-0.0052032470703125,
-0.0286102294921875,
-0.0009322166442871094,
-0.0270538330078125,
0.0093994140625,
-0.020416259765625,
0.01264190673828125,
-0.00665283203125,
0.01171112060546875,
0.01090240478515625,
0.023468017578125,
0.00864410400390625,
-0.00797271728515625,
-0.01409149169921875,
0.0026683807373046875,
-0.003326416015625,
0.0096893310546875,
-0.003696441650390625,
0.01073455810546875,
-0.0164947509765625,
-0.006504058837890625,
0.0011653900146484375,
-0.020294189453125,
-0.04058837890625,
-0.0005216598510742188,
-0.0084991455078125,
-0.0218353271484375,
-0.01070404052734375,
0.017852783203125,
-0.0293731689453125,
-0.02276611328125,
-0.0087890625,
0.0182647705078125,
0.032867431640625,
0.007457733154296875,
-0.03759765625,
-0.0194549560546875,
-0.0185546875,
-0.00202178955078125,
0.01244354248046875,
-0.01174163818359375,
0.004642486572265625,
-0.01117706298828125,
-0.00039958953857421875,
-0.01084136962890625,
-0.004360198974609375,
0.01922607421875,
-0.00173187255859375,
-0.019866943359375,
0.007781982421875,
0.0226593017578125,
0.004058837890625,
0.05072021484375,
-0.01039886474609375,
0.00888824462890625,
0.0029296875,
-0.01230621337890625,
0.00600433349609375,
0.0232086181640625,
0.004459381103515625,
0.0347900390625,
-0.002643585205078125,
0.052001953125,
-0.017822265625,
-0.0007195472717285156,
-0.0014133453369140625,
-0.004802703857421875,
0.01311492919921875,
0.02142333984375,
0.0190277099609375,
-0.00762939453125,
0.0175323486328125,
-0.0167694091796875,
0.0198516845703125,
0.028900146484375,
-0.007015228271484375,
-0.0243377685546875,
0.00780487060546875,
-0.0041046142578125,
0.00006121397018432617,
-0.014556884765625,
-0.004245758056640625,
0.0222625732421875,
-0.042572021484375,
0.04156494140625,
-0.0181884765625,
0.02838134765625,
0.035369873046875,
-0.030029296875,
0.022430419921875,
0.035736083984375,
-0.0052032470703125,
-0.0004532337188720703,
-0.039825439453125,
0.01555633544921875,
-0.0176239013671875,
0.0251922607421875,
-0.022979736328125,
0.0021381378173828125,
-0.020751953125,
-0.00004494190216064453,
-0.006694793701171875,
-0.005779266357421875,
0.0210113525390625,
0.0189208984375,
0.010162353515625,
-0.0192718505859375,
-0.0017118453979492188,
-0.0142669677734375,
-0.016265869140625,
0.00959014892578125,
0.01250457763671875,
-0.003467559814453125,
-0.01503753662109375,
0.002925872802734375,
-0.02508544921875,
-0.032012939453125,
0.0137176513671875,
-0.06976318359375,
0.0279998779296875,
0.037261962890625,
0.01317596435546875,
0.004619598388671875,
-0.00301361083984375,
-0.0291900634765625,
0.0177459716796875,
0.03533935546875,
-0.047149658203125,
-0.0233306884765625,
-0.00798797607421875,
-0.0032901763916015625,
0.0176849365234375,
-0.003322601318359375,
-0.0005087852478027344,
-0.0216064453125,
0.0102386474609375,
0.001300811767578125,
-0.007549285888671875,
0.00984954833984375,
-0.0245361328125,
-0.0012464523315429688,
0.0233612060546875,
0.011444091796875,
0.02484130859375,
-0.0031871795654296875,
-0.00289154052734375,
0.004974365234375,
0.0263824462890625,
-0.0279998779296875,
0.0214385986328125,
0.00412750244140625,
0.0031681060791015625,
-0.046173095703125,
-0.0217437744140625,
0.0305328369140625,
-0.040069580078125,
0.0193939208984375,
-0.015777587890625,
-0.052032470703125,
0.0264892578125,
0.0021114349365234375,
0.0108642578125,
-0.0330810546875,
0.0025482177734375,
0.0020503997802734375,
0.00444793701171875,
-0.029632568359375,
-0.06610107421875,
0.024871826171875,
0.00923919677734375,
-0.00342559814453125,
0.01000213623046875,
-0.021575927734375,
0.027740478515625,
-0.01035308837890625,
-0.0166778564453125,
-0.0014286041259765625,
-0.00885009765625,
-0.00847625732421875,
-0.005031585693359375,
-0.0213165283203125,
-0.01035308837890625,
0.00991058349609375,
-0.020294189453125,
-0.0001310110092163086,
0.022979736328125,
0.0136566162109375,
-0.0031185150146484375,
0.034332275390625,
-0.0234222412109375,
0.0167083740234375,
-0.0181121826171875,
-0.02716064453125,
-0.0185699462890625,
0.018280029296875,
-0.00731658935546875,
-0.004070281982421875,
0.038238525390625,
-0.0478515625,
0.004779815673828125,
-0.0168914794921875,
0.0196075439453125,
-0.01059722900390625,
0.01131439208984375,
-0.041534423828125,
-0.01399993896484375,
-0.006500244140625,
-0.041259765625,
0.01457977294921875,
0.0205535888671875,
0.0235748291015625,
-0.00357818603515625,
-0.001583099365234375,
0.00003421306610107422,
-0.00487518310546875,
0.03704833984375,
0.0188446044921875,
-0.007747650146484375,
-0.019012451171875,
-0.01425933837890625,
-0.0082550048828125,
-0.0217742919921875,
-0.035430908203125,
0.0027618408203125,
0.0142059326171875,
0.0177764892578125,
0.011077880859375,
-0.01995849609375,
-0.021514892578125,
0.00740814208984375,
0.0133056640625,
-0.01219940185546875,
0.0195159912109375,
0.03131103515625,
0.0093994140625,
0.042327880859375,
0.01214599609375,
-0.000766754150390625,
0.0004093647003173828,
-0.05633544921875,
-0.0006051063537597656,
-0.00917816162109375,
0.04486083984375,
0.024932861328125,
0.007572174072265625,
0.0006318092346191406,
-0.01338958740234375,
-0.0238800048828125,
0.0052947998046875,
-0.0103912353515625,
-0.029022216796875,
0.0014848709106445312,
-0.033447265625,
-0.029998779296875,
0.0135498046875,
-0.008087158203125,
0.00021016597747802734,
-0.01137542724609375,
0.0343017578125,
0.0200958251953125,
-0.0013303756713867188,
0.0148773193359375,
-0.03399658203125,
0.0006322860717773438,
-0.020660400390625,
-0.024078369140625,
-0.03692626953125,
0.0005230903625488281,
-0.015411376953125,
0.0030498504638671875,
-0.0242767333984375,
0.006923675537109375,
0.017303466796875,
0.039581298828125,
0.007427215576171875,
0.0275421142578125,
0.0106353759765625,
0.0265350341796875,
-0.032440185546875,
-0.0178070068359375,
0.00911712646484375,
-0.0258026123046875,
-0.0239410400390625,
-0.04150390625,
0.009002685546875,
-0.01531219482421875,
0.0002129077911376953,
0.01491546630859375,
0.0090179443359375,
0.0272064208984375,
-0.004016876220703125,
-0.00023925304412841797,
-0.0008869171142578125,
0.0390625,
0.0149688720703125,
0.005084991455078125,
-0.013885498046875,
0.01311492919921875,
0.0295562744140625,
-0.026153564453125,
0.0099945068359375,
-0.016632080078125,
-0.0189361572265625,
0.024688720703125,
0.01873779296875,
0.01212310791015625,
0.002399444580078125,
-0.011993408203125,
0.0032787322998046875,
-0.00829315185546875,
-0.021881103515625,
0.008819580078125,
-0.0238037109375,
0.014251708984375,
-0.0171356201171875,
-0.01041412353515625,
0.01316070556640625,
0.036834716796875,
-0.02777099609375,
-0.0052642822265625,
-0.0152435302734375,
-0.036712646484375,
-0.013458251953125,
0.003444671630859375,
0.0093231201171875,
0.0014190673828125,
0.01480865478515625,
-0.048583984375,
-0.00974273681640625,
0.02423095703125,
-0.0033111572265625,
0.020904541015625,
-0.0106201171875,
-0.032958984375,
-0.0027790069580078125,
-0.003505706787109375,
-0.030120849609375,
0.035247802734375,
0.0117340087890625,
-0.016754150390625,
-0.009307861328125,
0.007266998291015625,
0.0328369140625,
-0.0246734619140625,
-0.01016998291015625,
-0.06591796875,
-0.050079345703125,
-0.0150146484375,
0.0146026611328125,
-0.0255279541015625,
0.0033969879150390625,
0.0186004638671875,
-0.0244293212890625,
0.0169677734375,
-0.00665283203125,
-0.0274200439453125,
0.000980377197265625,
-0.030548095703125,
-0.0272216796875,
0.01593017578125,
0.0207977294921875,
0.00679779052734375,
-0.01212310791015625,
-0.036834716796875,
0.03924560546875,
-0.04669189453125,
-0.0019311904907226562,
0.01486968994140625,
-0.03271484375,
0.0047149658203125,
-0.00370025634765625,
0.002384185791015625,
-0.0198974609375,
0.0166015625,
0.0277099609375,
0.0199432373046875,
-0.036651611328125,
0.005146026611328125,
-0.006511688232421875,
0.00627899169921875,
0.0197601318359375,
-0.0037250518798828125,
0.006580352783203125,
-0.013763427734375,
0.01375579833984375,
0.0347900390625,
0.003459930419921875,
-0.004283905029296875,
-0.0369873046875,
-0.01367950439453125,
0.00624847412109375,
-0.020538330078125,
-0.03985595703125,
-0.015533447265625,
0.01323699951171875,
-0.0304718017578125,
0.0186767578125,
-0.0203399658203125,
0.0306854248046875,
0.002361297607421875,
-0.04132080078125,
-0.0224609375,
-0.0200347900390625,
-0.031890869140625,
0.03240966796875,
-0.01470184326171875,
-0.008575439453125,
-0.016143798828125,
-0.037353515625,
0.0041351318359375,
0.00046634674072265625,
-0.039520263671875,
-0.00007170438766479492,
0.034698486328125,
-0.010711669921875,
-0.0269775390625,
0.042266845703125,
-0.02349853515625,
0.0010128021240234375,
-0.0199737548828125,
0.0168914794921875,
0.0158538818359375,
0.0347900390625,
0.0006532669067382812,
-0.00537109375,
0.040374755859375,
0.01122283935546875,
0.0146636962890625,
-0.0267791748046875,
-0.01262664794921875,
0.01544189453125,
0.0025882720947265625,
-0.0121917724609375,
-0.00357818603515625,
-0.00197601318359375,
0.00521087646484375,
-0.020904541015625,
-0.0005364418029785156,
0.00621795654296875,
0.03875732421875,
-0.017242431640625,
0.01534271240234375,
-0.0037403106689453125,
0.00970458984375,
0.01348114013671875,
-0.0012483596801757812,
-0.0074920654296875,
-0.0267333984375,
-0.0237274169921875,
0.0156097412109375,
-0.01499176025390625,
0.01654052734375,
0.024658203125,
0.00984954833984375,
0.02301025390625,
-0.029205322265625,
-0.0230560302734375,
-0.024200439453125,
-0.004596710205078125,
-0.024993896484375,
-0.020599365234375,
0.002399444580078125,
0.000675201416015625,
0.0167694091796875,
0.0194091796875,
-0.0008854866027832031,
-0.0051116943359375,
0.0106964111328125,
-0.0086669921875,
-0.009857177734375,
-0.006137847900390625,
-0.0210418701171875,
0.0121917724609375,
-0.019500732421875,
0.007602691650390625,
0.017791748046875,
-0.01334381103515625,
0.0218505859375,
0.0157623291015625,
0.00983428955078125,
0.0035686492919921875,
0.0029048919677734375,
0.0477294921875,
0.048614501953125,
0.019775390625,
0.026092529296875,
-0.0015411376953125,
-0.020477294921875,
0.0241851806640625,
-0.0189666748046875,
0.01348114013671875,
0.01280975341796875,
0.005214691162109375,
-0.01367950439453125,
-0.01119232177734375,
0.0230865478515625,
-0.057861328125,
0.0171661376953125,
-0.01617431640625,
-0.01409149169921875,
-0.00597381591796875,
-0.0010013580322265625,
0.004322052001953125,
0.00974273681640625,
-0.00392913818359375,
0.023284912109375,
0.0011730194091796875,
-0.0185089111328125,
-0.0008254051208496094,
0.0220184326171875,
0.0224761962890625,
-0.029510498046875,
0.0101470947265625,
0.05218505859375,
0.02117919921875,
0.00787353515625,
-0.019073486328125,
-0.0172271728515625,
-0.0025577545166015625,
-0.00981903076171875,
-0.015472412109375,
0.0240936279296875,
0.006587982177734375,
0.00867462158203125,
-0.01471710205078125,
-0.00255584716796875,
0.01209259033203125,
-0.0266265869140625,
-0.04376220703125,
0.0205230712890625,
-0.024627685546875,
-0.004589080810546875,
-0.00897979736328125,
0.01486968994140625,
-0.003681182861328125,
-0.0281219482421875,
-0.017974853515625,
0.0009813308715820312,
0.0034580230712890625,
-0.00937652587890625,
-0.036773681640625,
0.01470184326171875,
0.018157958984375,
0.01432037353515625,
0.037994384765625,
-0.0236358642578125,
0.00482177734375,
-0.00670623779296875,
-0.01013946533203125,
-0.004352569580078125,
-0.0195159912109375,
0.01287841796875,
-0.006877899169921875,
-0.0244293212890625,
-0.00968170166015625,
0.0259857177734375,
0.024871826171875,
-0.0001291036605834961,
-0.02362060546875,
0.00748443603515625,
-0.038116455078125,
0.012237548828125,
0.0008645057678222656,
-0.046539306640625,
-0.00015628337860107422,
0.0279541015625,
0.018646240234375,
-0.01195526123046875,
0.023590087890625,
0.00045299530029296875,
0.0164642333984375,
-0.020965576171875,
-0.029693603515625,
0.0247955322265625,
0.0044708251953125,
0.005527496337890625,
0.0173187255859375,
0.01922607421875,
0.03814697265625,
0.016387939453125,
-0.016632080078125,
0.007457733154296875,
0.0164794921875,
-0.021942138671875,
0.020263671875,
-0.01428985595703125,
0.00754547119140625,
0.012939453125,
-0.019866943359375,
-0.007045745849609375,
-0.0033092498779296875,
0.018341064453125,
0.037017822265625,
-0.0017271041870117188,
0.0191497802734375,
-0.015899658203125,
0.0272216796875,
-0.0242767333984375,
-0.01015472412109375,
-0.03515625,
0.00450897216796875,
0.0197601318359375,
0.006656646728515625,
-0.00608062744140625,
0.0016117095947265625,
0.028594970703125,
-0.0286407470703125,
-0.005947113037109375,
-0.038970947265625,
-0.00847625732421875,
0.0263519287109375,
0.00891876220703125,
0.017303466796875,
-0.03125,
0.02203369140625,
-0.028289794921875,
-0.0133514404296875,
0.00788116455078125,
0.0162506103515625,
-0.01259613037109375,
0.00218963623046875,
0.01611328125,
0.00299835205078125,
0.03985595703125,
-0.022064208984375,
-0.01375579833984375,
0.01548004150390625,
-0.0260009765625,
0.0030269622802734375,
-0.0266876220703125,
0.0195770263671875,
-0.018585205078125,
-0.034210205078125,
0.00693511962890625,
-0.02374267578125,
-0.040130615234375,
0.005611419677734375,
-0.0062255859375,
0.005649566650390625,
0.01316070556640625,
-0.0152740478515625,
0.0193939208984375,
0.0243682861328125,
0.0003039836883544922,
-0.0127410888671875,
-0.0137481689453125,
0.012176513671875,
-0.0065155029296875,
0.022796630859375,
0.021942138671875,
0.0235595703125,
-0.01456451416015625,
0.012451171875,
-0.0306854248046875,
-0.0015125274658203125,
-0.01910400390625,
-0.0211029052734375,
0.0019588470458984375,
-0.04302978515625,
0.006526947021484375,
-0.026580810546875,
-0.005214691162109375,
-0.02655029296875,
-0.0220947265625,
0.044189453125,
0.0057830810546875,
0.007411956787109375,
0.0105133056640625,
-0.0246429443359375,
-0.01126861572265625,
-0.0084075927734375,
-0.0171661376953125,
0.0019397735595703125,
0.01157379150390625,
-0.0135498046875,
-0.01219940185546875,
0.00789642333984375,
0.0308990478515625,
-0.0269317626953125,
0.0097808837890625,
0.0038814544677734375,
-0.0080718994140625,
0.01239013671875,
-0.051116943359375,
0.004779815673828125,
0.01568603515625,
-0.02130126953125,
-0.006805419921875,
0.038421630859375,
-0.015625,
0.0209197998046875,
0.01262664794921875,
0.0008230209350585938,
0.01494598388671875,
0.023773193359375,
0.0234375,
-0.040283203125,
0.002288818359375,
0.012664794921875,
-0.0209808349609375,
0.0245819091796875,
0.00380706787109375,
0.0111236572265625,
0.004852294921875,
0.030609130859375,
-0.024383544921875,
-0.02734375,
0.00812530517578125,
-0.005237579345703125,
0.0248565673828125,
0.0011911392211914062,
0.0018177032470703125,
-0.01036834716796875,
0.01479339599609375,
-0.012603759765625,
0.004566192626953125,
-0.01239013671875,
-0.0300140380859375,
0.0155181884765625,
0.0245513916015625,
0.0208892822265625,
-0.04559326171875,
0.016876220703125,
0.0182952880859375,
0.000823974609375,
-0.020416259765625,
-0.01006317138671875,
-0.00005984306335449219,
0.0060882568359375,
-0.0092926025390625,
0.0137176513671875,
0.0165863037109375,
0.01471710205078125,
0.0400390625,
-0.01058197021484375,
0.005062103271484375,
-0.001194000244140625,
-0.005096435546875,
0.0012989044189453125,
-0.0046539306640625,
-0.032196044921875,
0.0267486572265625,
-0.00812530517578125,
-0.0007734298706054688,
-0.02197265625,
-0.0308990478515625,
-0.005855560302734375,
0.0189971923828125,
0.00910186767578125,
0.007965087890625,
-0.013916015625,
-0.00894927978515625,
-0.048614501953125,
-0.0146026611328125,
-0.002895355224609375,
0.0413818359375,
0.037261962890625,
-0.004634857177734375,
0.0377197265625,
0.0198516845703125,
-0.017608642578125,
0.0201263427734375,
-0.0093841552734375,
-0.013031005859375,
0.035186767578125,
-0.0156707763671875,
0.06256103515625,
-0.01074981689453125,
-0.023101806640625,
-0.00667572021484375,
0.005237579345703125,
0.0255889892578125,
-0.0085601806640625,
0.017669677734375,
-0.01568603515625,
-0.01062774658203125,
-0.0016431808471679688,
-0.044525146484375,
0.016204833984375,
-0.00884246826171875,
-0.0406494140625,
-0.0170440673828125,
0.01557159423828125,
0.01059722900390625,
0.007129669189453125,
-0.028411865234375,
-0.007457733154296875,
-0.006504058837890625,
0.0236968994140625,
-0.029266357421875,
-0.01236724853515625,
-0.0178070068359375,
-0.0078125,
-0.005889892578125,
-0.031890869140625,
-0.025665283203125,
-0.01026153564453125,
0.006702423095703125,
0.025848388671875,
-0.031005859375,
-0.01299285888671875,
0.0017566680908203125,
0.019744873046875,
-0.032623291015625,
0.00623321533203125,
0.006763458251953125,
-0.01526641845703125,
0.0274505615234375,
0.00592803955078125,
0.00714111328125,
0.0419921875,
0.00919342041015625,
-0.0025424957275390625,
-0.02728271484375,
0.00855255126953125,
-0.006649017333984375,
0.03515625,
0.005725860595703125,
-0.0295562744140625,
0.022491455078125,
-0.005733489990234375,
-0.0243682861328125,
0.019683837890625,
-0.02020263671875,
-0.03497314453125,
0.0132598876953125,
0.0048065185546875,
0.0103302001953125,
-0.0007638931274414062,
-0.01070404052734375,
-0.01117706298828125,
0.003871917724609375,
-0.021331787109375,
-0.0042877197265625,
-0.0245513916015625,
0.0029964447021484375,
0.022552490234375,
-0.01654052734375,
-0.011138916015625,
-0.01367950439453125,
0.01474761962890625,
-0.009246826171875,
0.042999267578125,
0.00873565673828125,
0.0075225830078125,
0.018707275390625,
-0.031524658203125,
0.022186279296875,
-0.0086669921875,
0.0223388671875,
0.008575439453125,
0.00677490234375,
0.003955841064453125,
-0.00328826904296875,
-0.0237579345703125,
0.048675537109375,
-0.00676727294921875,
0.03851318359375,
0.01305389404296875,
0.00018417835235595703,
0.017822265625,
-0.0198211669921875,
0.05572509765625,
0.0120697021484375,
0.043609619140625,
0.016815185546875,
0.022216796875,
-0.007598876953125,
0.03363037109375,
-0.016876220703125,
-0.00957489013671875,
-0.012908935546875,
0.0010652542114257812,
0.0071563720703125,
0.033111572265625,
-0.037841796875,
0.0005917549133300781,
0.0142974853515625,
-0.00991058349609375,
0.0301361083984375,
0.026824951171875,
-0.01824951171875,
0.0178985595703125,
-0.0498046875,
0.0158843994140625,
0.0165252685546875,
0.0027294158935546875,
0.0001990795135498047,
0.00862884521484375,
0.0087432861328125,
-0.00787353515625,
0.00957489013671875,
-0.03533935546875,
0.022674560546875,
0.0131072998046875,
-0.0016317367553710938,
-0.031524658203125,
-0.0149078369140625,
-0.0005426406860351562,
0.0017442703247070312,
-0.000033855438232421875,
-0.011627197265625,
0.05780029296875,
-0.017333984375,
-0.0156097412109375,
-0.006855010986328125,
-0.006557464599609375,
0.003513336181640625,
0.033355712890625,
0.0050811767578125,
-0.0235137939453125,
-0.019561767578125,
-0.04449462890625,
0.0087432861328125,
-0.00977325439453125,
-0.006496429443359375,
0.0093994140625,
0.033843994140625,
-0.01334381103515625,
-0.036529541015625,
-0.009735107421875,
-0.02398681640625,
-0.0275115966796875,
-0.0012378692626953125,
-0.0045928955078125,
-0.01111602783203125,
0.003170013427734375,
-0.002033233642578125,
0.023345947265625,
0.0073394775390625,
0.0308990478515625,
-0.01033782958984375,
0.0094146728515625,
0.0292816162109375,
-0.02545166015625,
0.0025959014892578125,
-0.0025653839111328125,
0.0178070068359375,
0.044189453125,
0.02740478515625,
-0.0296630859375,
-0.01085662841796875,
0.00844573974609375,
-0.0178070068359375,
-0.0296783447265625,
0.003803253173828125,
0.019317626953125,
0.01325225830078125,
0.0168609619140625,
0.0443115234375,
0.006923675537109375,
-0.025390625,
0.0036296844482421875,
-0.0262908935546875,
-0.0286712646484375,
0.005950927734375,
0.00234222412109375,
-0.0235443115234375,
0.01385498046875,
0.01200103759765625,
-0.0225067138671875,
-0.0213470458984375,
-0.015106201171875,
0.004917144775390625,
-0.028594970703125,
-0.005859375,
0.0235748291015625,
-0.0088348388671875,
-0.0006299018859863281,
0.01081085205078125,
0.0201263427734375,
0.005786895751953125,
0.02093505859375,
-0.00907135009765625,
-0.01387786865234375,
-0.014312744140625,
0.006084442138671875,
0.00038886070251464844,
-0.006923675537109375,
0.016510009765625,
0.01251983642578125,
-0.04803466796875,
0.006153106689453125,
-0.017730712890625,
-0.035675048828125,
0.01277923583984375,
-0.00812530517578125,
0.01352691650390625,
0.03277587890625,
-0.044189453125,
0.01134490966796875,
0.00467681884765625,
0.006580352783203125,
0.012969970703125,
-0.01435089111328125,
0.01074981689453125,
0.0139007568359375,
0.00531768798828125,
-0.0291748046875,
0.048431396484375,
0.0257568359375,
-0.0171661376953125,
-0.0019521713256835938,
-0.0253753662109375,
-0.0102996826171875,
-0.0260009765625,
-0.0033245086669921875,
-0.005863189697265625,
0.01399993896484375,
0.003482818603515625,
-0.0211181640625,
0.00801849365234375,
-0.017303466796875,
0.00176239013671875,
0.0110015869140625,
-0.00884246826171875,
-0.01306915283203125,
-0.003246307373046875,
-0.025390625,
0.004413604736328125,
-0.0108642578125,
-0.0120849609375,
0.0025787353515625,
0.0157470703125,
-0.014923095703125,
0.0249481201171875,
0.003589630126953125,
-0.01546478271484375,
-0.00745391845703125,
-0.009674072265625,
-0.033966064453125,
0.002834320068359375,
0.01039886474609375,
-0.003864288330078125,
-0.037872314453125,
-0.0183258056640625,
-0.0017137527465820312,
-0.00725555419921875,
0.0310211181640625,
0.00753021240234375,
-0.01947021484375,
0.0181427001953125,
-0.013092041015625,
-0.0031452178955078125,
-0.01425933837890625,
-0.00678253173828125,
-0.00665283203125,
0.005176544189453125,
-0.0254974365234375,
0.020782470703125,
-0.034210205078125,
-0.0196990966796875,
-0.018890380859375,
-0.005401611328125,
0.00860595703125,
0.007663726806640625,
-0.0081329345703125,
-0.02362060546875,
-0.0084075927734375,
-0.003917694091796875,
0.0016260147094726562,
-0.0174713134765625,
-0.017974853515625,
-0.0174560546875,
-0.014434814453125,
0.0015401840209960938,
-0.01128387451171875,
0.022491455078125,
-0.0083160400390625,
0.0208587646484375,
-0.01702880859375,
0.0219879150390625,
0.016876220703125,
0.014404296875,
-0.0170135498046875,
-0.022674560546875,
-0.00897216796875,
0.040069580078125,
0.0011844635009765625,
-0.01038360595703125,
-0.0022068023681640625,
0.039093017578125,
0.030914306640625,
-0.007354736328125,
-0.010467529296875,
0.026214599609375,
-0.019500732421875,
0.03228759765625,
-0.0054473876953125,
0.0233917236328125,
0.0067138671875,
-0.01012420654296875,
0.02703857421875,
-0.0079345703125,
-0.04248046875,
-0.00585174560546875,
-0.00928497314453125,
-0.00033974647521972656,
0.028656005859375,
0.039215087890625,
-0.0012140274047851562,
0.00970458984375,
0.0238189697265625,
0.037933349609375,
-0.01419830322265625,
0.00807952880859375,
-0.010650634765625,
-0.030609130859375,
-0.0156402587890625,
0.0051422119140625,
-0.019439697265625,
0.0301971435546875,
-0.019989013671875,
0.0026454925537109375,
-0.03350830078125,
-0.0227813720703125,
0.00885772705078125,
-0.00977325439453125,
0.00026869773864746094,
-0.007633209228515625,
-0.01088714599609375,
0.01715087890625,
0.01198577880859375,
0.0134429931640625,
0.01244354248046875,
-0.006069183349609375,
-0.04473876953125,
0.010833740234375,
0.0009655952453613281,
0.01165008544921875,
0.0238800048828125,
-0.044952392578125,
0.005126953125,
0.002460479736328125,
-0.0300750732421875,
0.01447296142578125,
0.02825927734375,
0.018890380859375,
-0.00023615360260009766,
0.009490966796875,
-0.055389404296875,
-0.007328033447265625,
-0.01187896728515625,
0.01629638671875,
-0.008544921875,
0.0139617919921875,
-0.029754638671875,
0.006069183349609375,
0.0235137939453125,
-0.045562744140625,
0.02972412109375,
-0.0138397216796875,
-0.00930023193359375,
-0.01348876953125,
-0.0222015380859375,
0.00762939453125,
-0.00760650634765625,
-0.005283355712890625,
0.01129913330078125,
0.0033779144287109375,
-0.0268707275390625,
0.018157958984375,
0.0016336441040039062,
-0.01084136962890625,
-0.00409698486328125,
-0.0192718505859375,
-0.0032138824462890625,
0.0221099853515625,
0.014007568359375,
-0.006343841552734375,
-0.024261474609375,
-0.0033550262451171875,
0.00759124755859375,
0.0019321441650390625,
0.004146575927734375,
0.005908966064453125,
-0.00954437255859375,
0.01419830322265625,
0.01505279541015625,
-0.0005698204040527344,
0.0012664794921875,
0.041351318359375,
0.0211334228515625,
0.045379638671875,
-0.002979278564453125,
0.0251312255859375,
-0.01087188720703125,
-0.0269775390625,
-0.041229248046875,
-0.002132415771484375,
0.0072784423828125,
-0.01806640625,
0.004734039306640625,
0.0018253326416015625,
0.0033779144287109375,
0.003841400146484375,
0.0234527587890625,
0.006072998046875,
0.00951385498046875,
-0.00977325439453125,
0.0247650146484375,
-0.0225830078125,
0.03466796875,
0.0293731689453125,
-0.00713348388671875,
-0.00661468505859375,
0.00342559814453125,
0.01099395751953125,
-0.00896453857421875,
0.015838623046875,
0.017242431640625,
-0.00717926025390625,
-0.01490020751953125,
0.039306640625,
-0.0266876220703125,
0.0006732940673828125,
-0.017303466796875,
0.00470733642578125,
0.0306854248046875,
-0.006031036376953125,
0.00675201416015625,
-0.0190582275390625,
0.01385498046875,
-0.0257415771484375,
-0.005474090576171875,
0.0104217529296875,
0.0262298583984375,
-0.02008056640625,
0.003299713134765625,
0.005466461181640625,
-0.0157318115234375,
0.0160369873046875,
-0.0260162353515625,
0.0298919677734375,
0.0202789306640625,
-0.01250457763671875,
0.002288818359375,
-0.005828857421875,
0.00389862060546875,
-0.0137786865234375,
-0.0197601318359375,
0.002437591552734375,
0.0301971435546875,
0.0120391845703125,
-0.0277099609375,
-0.0026531219482421875,
0.0008745193481445312,
0.01003265380859375,
-0.01316070556640625,
-0.002643585205078125,
0.019317626953125,
0.003376007080078125,
0.0196380615234375,
0.0098419189453125,
-0.039306640625,
0.01468658447265625,
-0.0225677490234375,
-0.0139923095703125,
-0.0162506103515625,
0.02789306640625,
0.02545166015625,
0.01029205322265625,
0.028564453125,
-0.0242919921875,
-0.022186279296875,
0.0345458984375,
0.0138397216796875,
0.00020813941955566406,
0.0294342041015625,
0.0196380615234375,
-0.062164306640625,
-0.0136871337890625,
0.0117340087890625,
-0.00444793701171875,
0.002323150634765625,
0.0036296844482421875,
-0.0026149749755859375,
0.01284027099609375,
-0.0233001708984375,
-0.01898193359375,
0.0030059814453125,
-0.01203155517578125,
0.01322174072265625,
0.00948333740234375,
-0.01788330078125,
-0.026611328125,
0.03497314453125,
-0.0121307373046875,
0.004734039306640625,
0.0017271041870117188,
0.00986480712890625,
-0.00231170654296875,
-0.0160980224609375,
-0.0013837814331054688,
0.020263671875,
-0.025360107421875,
0.0149688720703125,
0.00864410400390625,
0.02252197265625,
-0.005809783935546875,
0.0013132095336914062,
-0.00928497314453125,
-0.032073974609375,
-0.0004296302795410156,
-0.01238250732421875,
-0.00579833984375,
0.0006055831909179688,
0.01143646240234375,
0.0157928466796875,
-0.01436614990234375,
-0.032684326171875,
0.0186767578125,
-0.006748199462890625,
-0.035369873046875,
0.019439697265625,
-0.00746917724609375,
-0.027435302734375,
0.0014410018920898438,
0.0340576171875,
-0.01490020751953125,
-0.059326171875,
-0.0168304443359375,
0.0007386207580566406,
0.0185089111328125,
0.0210113525390625,
0.0240631103515625,
0.0010900497436523438,
-0.0263519287109375,
0.0156402587890625,
0.02447509765625,
0.0050506591796875,
0.0179901123046875,
0.0061492919921875,
-0.0157623291015625,
0.0168609619140625,
-0.0115814208984375,
0.007282257080078125,
0.033111572265625,
-0.017730712890625,
0.006549835205078125,
0.0248260498046875,
-0.03131103515625,
0.016387939453125,
-0.03564453125,
0.0019702911376953125,
0.004161834716796875,
-0.0399169921875,
0.005451202392578125,
-0.004436492919921875,
-0.006290435791015625,
0.0132598876953125,
0.00030922889709472656,
0.0018939971923828125,
-0.0058746337890625,
0.0189666748046875,
0.018035888671875,
0.012664794921875,
-0.00414276123046875,
0.01482391357421875,
0.01250457763671875,
-0.00226593017578125,
0.01381683349609375,
-0.00623321533203125,
0.004520416259765625,
0.032745361328125,
0.016082763671875,
0.0274505615234375,
0.01136016845703125,
0.005100250244140625,
0.0272369384765625,
-0.00040435791015625,
0.00580596923828125,
-0.01434326171875,
-0.018524169921875,
-0.005947113037109375,
-0.01073455810546875,
0.0196685791015625,
0.01568603515625,
0.005123138427734375,
-0.0306243896484375,
-0.005931854248046875,
-0.0085601806640625,
0.0194091796875,
0.01222991943359375,
0.0129547119140625,
0.030517578125,
0.00490570068359375,
0.0103607177734375,
-0.005985260009765625,
-0.018951416015625,
0.020599365234375,
-0.0026721954345703125,
-0.0093841552734375,
0.0163116455078125,
0.0230255126953125,
-0.04608154296875,
-0.0237274169921875,
0.0185089111328125,
-0.02313232421875,
0.0033321380615234375,
0.015960693359375,
-0.0158843994140625,
-0.02008056640625,
0.019256591796875,
-0.00591278076171875,
-0.00731658935546875,
-0.0007729530334472656,
0.00897216796875,
0.0046844482421875,
-0.0119171142578125,
0.01531982421875,
-0.01055908203125,
0.016357421875,
-0.037017822265625,
0.04522705078125,
-0.004734039306640625,
0.011932373046875,
-0.0017833709716796875,
0.00991058349609375,
-0.00439453125,
0.011993408203125,
0.02252197265625,
-0.0030002593994140625,
0.0005421638488769531,
0.0230865478515625,
-0.003314971923828125,
0.0156707763671875,
-0.041046142578125,
0.0015201568603515625,
0.006267547607421875,
0.01434326171875,
0.01459503173828125,
-0.0142974853515625,
0.007282257080078125,
-0.0125885009765625,
-0.0081024169921875,
0.021148681640625,
0.0021419525146484375,
-0.0007419586181640625,
0.0183868408203125,
-0.0311737060546875,
-0.0404052734375,
-0.0006494522094726562,
0.003932952880859375,
-0.016754150390625,
-0.002506256103515625,
-0.005634307861328125,
0.017242431640625,
-0.011810302734375,
0.0014801025390625,
0.0099029541015625,
0.00012385845184326172,
-0.002201080322265625,
-0.0212249755859375,
-0.01372528076171875,
-0.03076171875,
-0.016021728515625,
-0.02655029296875,
-0.04840087890625,
-0.01146697998046875,
-0.01473236083984375,
0.0281524658203125,
-0.019989013671875,
-0.023773193359375,
0.01007080078125,
-0.003337860107421875,
0.0006728172302246094,
-0.031524658203125,
0.00638580322265625,
-0.00966644287109375,
0.0103302001953125,
-0.0288238525390625,
-0.0229034423828125,
-0.00665283203125,
0.0092926025390625,
0.024993896484375,
0.0083160400390625,
0.004985809326171875,
0.0008111000061035156,
0.034454345703125,
-0.004909515380859375,
-0.0039043426513671875,
0.0156097412109375,
0.004642486572265625,
-0.00921630859375,
0.00399017333984375,
0.0193328857421875,
-0.02264404296875,
-0.0112457275390625,
-0.020721435546875,
-0.01270294189453125,
-0.0107574462890625,
0.0196533203125,
0.0073394775390625,
0.0067901611328125,
0.02142333984375,
-0.024749755859375,
-0.01419830322265625,
0.01265716552734375,
-0.0323486328125,
0.01413726806640625,
-0.0205230712890625,
-0.005054473876953125,
-0.01181793212890625,
-0.001483917236328125,
0.00649261474609375,
0.006809234619140625,
-0.0052337646484375,
0.01438140869140625,
-0.0104522705078125,
0.02655029296875,
-0.0013704299926757812,
-0.01282501220703125,
0.0285186767578125,
0.0445556640625,
-0.04742431640625,
0.0218963623046875,
0.005939483642578125,
-0.0157012939453125,
0.00449371337890625,
-0.005794525146484375,
-0.00531005859375,
0.00489044189453125,
-0.0130157470703125,
0.036102294921875,
0.004566192626953125,
0.0104217529296875,
0.016998291015625,
-0.003265380859375,
0.03558349609375,
-0.016326904296875,
-0.0161590576171875,
-0.00927734375,
-0.01073455810546875,
0.0016765594482421875,
-0.0257568359375,
0.003452301025390625,
-0.006107330322265625,
0.015899658203125,
-0.016937255859375,
0.01073455810546875,
0.0025043487548828125,
0.0110931396484375,
-0.030670166015625,
-0.002323150634765625,
-0.01910400390625,
0.00856781005859375,
-0.0280914306640625,
-0.005229949951171875,
-0.022064208984375,
0.0257568359375,
-0.039093017578125,
0.037261962890625,
0.01465606689453125,
-0.021026611328125,
-0.01543426513671875,
-0.031707763671875,
-0.00495147705078125,
0.01230621337890625,
0.0033168792724609375,
-0.004810333251953125,
0.0081634521484375,
-0.01230621337890625,
0.007198333740234375,
-0.00878143310546875,
0.024505615234375,
-0.01448822021484375,
-0.0140533447265625,
0.0110321044921875,
0.046875,
0.017608642578125,
-0.0245513916015625,
-0.0166015625,
0.0118255615234375,
-0.0009565353393554688,
-0.01157379150390625,
0.006900787353515625,
0.01044464111328125,
-0.0009222030639648438,
-0.0018482208251953125,
-0.011138916015625,
0.0005784034729003906,
0.0272674560546875,
-0.0011587142944335938,
0.0191802978515625,
-0.0195770263671875,
0.0004978179931640625,
-0.023681640625,
-0.037261962890625,
0.0203704833984375,
-0.004055023193359375,
0.0252227783203125,
-0.0012426376342773438,
0.022674560546875,
-0.0136871337890625,
-0.005584716796875,
-0.0211639404296875,
-0.001438140869140625,
-0.05767822265625,
-0.0132904052734375,
0.007335662841796875,
0.01111602783203125,
0.0048370361328125,
-0.0184783935546875,
-0.0015039443969726562,
-0.0011310577392578125,
-0.02496337890625,
0.01245880126953125,
-0.0130615234375,
0.029388427734375,
-0.0186004638671875,
0.00127410888671875,
0.0377197265625,
-0.00597381591796875,
-0.01824951171875,
-0.023773193359375,
0.0194091796875,
-0.043853759765625,
-0.0018796920776367188,
0.02972412109375,
-0.033355712890625,
0.0279693603515625,
0.00555419921875,
-0.01030731201171875,
-0.00274658203125,
0.03692626953125,
-0.0174560546875,
-0.0120086669921875,
0.01168060302734375,
-0.004146575927734375,
0.009368896484375,
0.0034942626953125,
0.031585693359375,
-0.00756072998046875,
-0.007167816162109375,
0.01025390625,
0.01212310791015625,
0.008544921875,
0.029052734375,
0.00677490234375,
0.005771636962890625,
-0.00614166259765625,
0.0379638671875,
-0.02838134765625,
-0.02667236328125,
0.02984619140625,
-0.0055389404296875,
0.03399658203125,
-0.00357818603515625,
-0.019561767578125,
0.016082763671875,
-0.022705078125,
-0.017242431640625,
0.00572967529296875,
-0.0220489501953125,
-0.048736572265625,
-0.0213470458984375,
-0.0027790069580078125,
-0.01442718505859375,
0.01152801513671875,
-0.005764007568359375,
-0.0077972412109375,
0.01403045654296875,
-0.0088653564453125,
0.003509521484375,
0.036407470703125,
-0.0199127197265625,
0.03289794921875,
0.032470703125,
0.01364898681640625,
-0.007579803466796875,
-0.0202178955078125,
0.005023956298828125,
0.0007138252258300781,
-0.0071868896484375,
0.0179290771484375,
-0.0142974853515625,
-0.004367828369140625,
-0.01293182373046875,
0.0145416259765625,
-0.00423431396484375,
0.0017175674438476562,
0.04779052734375,
0.024505615234375,
0.010406494140625,
0.0005345344543457031,
-0.0181884765625,
-0.0249176025390625,
0.0197601318359375,
-0.005252838134765625,
-0.009765625,
-0.0182342529296875,
0.00815582275390625,
0.01033782958984375,
-0.01543426513671875,
0.032684326171875,
0.0229034423828125,
0.01244354248046875,
0.0042877197265625,
0.039276123046875,
0.0152435302734375,
0.0026988983154296875,
-0.021392822265625,
0.01324462890625,
-0.01403045654296875,
0.0008969306945800781,
-0.006656646728515625,
-0.0179901123046875,
-0.0210418701171875,
0.02520751953125,
0.01207733154296875,
0.01511383056640625,
0.0112152099609375,
0.00311279296875,
0.00146484375,
-0.02838134765625,
0.01080322265625,
-0.017486572265625,
-0.00844573974609375,
0.031463623046875,
-0.0201873779296875,
-0.004398345947265625,
0.0239410400390625,
0.01393890380859375,
-0.034210205078125,
-0.012725830078125,
-0.002727508544921875,
-0.00927734375,
0.00626373291015625,
0.015838623046875,
0.0000014901161193847656,
0.00981903076171875,
0.01561737060546875,
0.060272216796875,
-0.01160430908203125,
-0.01122283935546875,
0.0169830322265625,
-0.0206298828125,
-0.0161895751953125,
-0.005352020263671875,
0.0091552734375,
0.0010356903076171875,
-0.00717926025390625,
-0.0256500244140625,
0.02276611328125,
-0.0184173583984375,
0.01337432861328125,
0.01322174072265625,
-0.0257110595703125,
0.015716552734375,
0.0479736328125,
0.0098724365234375,
-0.043731689453125,
0.00283050537109375,
0.004138946533203125,
-0.0098114013671875,
0.0173187255859375,
0.01332855224609375,
0.00732421875,
-0.0100860595703125,
0.0372314453125,
-0.003086090087890625,
0.0181884765625,
0.007175445556640625,
-0.0047760009765625,
-0.004795074462890625,
0.032806396484375,
0.0029392242431640625,
-0.02410888671875,
0.01128387451171875,
-0.0205230712890625,
0.034210205078125,
0.001575469970703125,
0.0122833251953125,
-0.014984130859375,
-0.00788116455078125,
0.0021266937255859375,
0.040771484375,
0.0228424072265625,
-0.01544952392578125,
0.01457977294921875,
0.0191802978515625,
-0.024200439453125,
0.0245208740234375,
-0.0103607177734375,
0.014068603515625,
0.021392822265625,
-0.022552490234375,
-0.0063934326171875,
0.049041748046875,
0.0056304931640625,
-0.01030731201171875,
-0.059112548828125,
-0.010498046875,
0.0177459716796875,
-0.0223388671875,
-0.0204010009765625,
-0.0281219482421875,
-0.03485107421875,
0.0173492431640625,
-0.003997802734375,
-0.02923583984375,
0.0269317626953125,
0.0158538818359375,
-0.0031490325927734375,
0.032196044921875,
-0.004665374755859375,
-0.00617218017578125,
0.002056121826171875,
-0.018280029296875,
0.0088653564453125,
-0.0015382766723632812,
0.02935791015625,
0.01511383056640625,
-0.0029850006103515625,
-0.0006279945373535156,
0.029083251953125,
-0.00032401084899902344,
0.017822265625,
0.01358795166015625,
0.0178680419921875,
-0.00847625732421875,
0.0207366943359375,
0.00861358642578125,
-0.04742431640625,
-0.00235748291015625,
-0.0196990966796875,
0.0222320556640625,
0.012054443359375,
-0.00275421142578125,
0.004199981689453125,
-0.0026702880859375,
-0.016998291015625,
-0.00884246826171875,
-0.0233612060546875,
-0.029296875,
0.00010198354721069336,
0.0155029296875,
0.0008096694946289062,
0.00797271728515625,
-0.0117340087890625,
-0.0201568603515625,
-0.01364898681640625,
-0.01155853271484375,
-0.0186004638671875,
-0.0142364501953125,
-0.0120391845703125,
-0.00400543212890625,
0.0156097412109375,
0.0031833648681640625,
-0.00811004638671875,
0.0191192626953125,
-0.01337432861328125,
0.0190277099609375,
-0.03515625,
-0.0208892822265625,
0.0205535888671875,
0.0108642578125,
0.004940032958984375,
0.00933837890625,
0.0164947509765625,
-0.011810302734375,
0.0079498291015625,
-0.0115966796875,
0.00264739990234375,
0.01409149169921875,
0.0224151611328125,
0.029541015625,
-0.021942138671875,
-0.01555633544921875,
0.002452850341796875,
-0.016143798828125,
0.0279998779296875,
-0.004840850830078125,
0.025390625,
-0.005184173583984375,
0.0017824172973632812,
-0.033538818359375,
-0.0007886886596679688,
-0.0165863037109375,
0.01163482666015625,
0.010650634765625,
-0.006237030029296875,
-0.007110595703125,
-0.0038623809814453125,
-0.037445068359375,
0.004611968994140625,
-0.004093170166015625,
0.012908935546875,
0.0247955322265625,
0.0018663406372070312,
-0.029632568359375,
-0.000213623046875,
-0.01465606689453125,
-0.007534027099609375,
0.0234222412109375,
0.006725311279296875,
-0.0082550048828125,
-0.026763916015625,
0.0185394287109375,
0.004299163818359375,
-0.0167236328125,
-0.0161895751953125,
-0.01306915283203125,
-0.00005918741226196289,
0.016876220703125,
0.0007534027099609375,
0.0015039443969726562,
-0.0086669921875,
-0.020721435546875,
0.0010271072387695312,
0.0174560546875,
-0.00041556358337402344,
-0.00400543212890625,
0.02923583984375,
0.000904083251953125,
0.002109527587890625,
-0.00774383544921875,
-0.0047760009765625,
0.027587890625,
0.011474609375,
-0.01099395751953125,
-0.005512237548828125,
0.0113983154296875,
0.033111572265625,
0.0126800537109375,
-0.0008678436279296875,
0.0232391357421875,
0.0189361572265625,
-0.013153076171875,
-0.005496978759765625,
0.031463623046875,
0.03570556640625,
0.0205535888671875,
0.012176513671875,
-0.00228118896484375,
0.0165863037109375,
0.027984619140625,
0.01849365234375,
-0.041046142578125,
-0.022857666015625,
-0.031463623046875,
-0.004241943359375,
-0.00353240966796875,
-0.0012264251708984375,
-0.0087738037109375,
-0.034759521484375,
0.01415252685546875,
-0.01100921630859375,
-0.037994384765625,
-0.02850341796875,
-0.030609130859375,
0.030242919921875,
0.02178955078125,
-0.0186309814453125,
0.00940704345703125,
-0.018585205078125,
-0.03179931640625,
0.0182647705078125,
-0.000008940696716308594,
-0.005229949951171875,
0.01067352294921875,
0.0109710693359375,
0.04302978515625,
0.006420135498046875,
-0.007312774658203125,
-0.015777587890625,
-0.025848388671875,
0.00722503662109375,
-0.0195465087890625,
-0.018829345703125,
0.01125335693359375,
-0.010894775390625,
-0.01441192626953125,
0.01104736328125,
-0.0113372802734375,
0.01261138916015625,
0.00554656982421875,
0.00962066650390625,
-0.005428314208984375,
0.0002906322479248047,
0.01152801513671875,
-0.0498046875,
-0.01210784912109375,
0.0019474029541015625,
-0.00879669189453125,
0.020782470703125,
-0.00839996337890625,
0.0119171142578125,
-0.0305938720703125,
-0.017852783203125,
-0.0193634033203125,
-0.0254058837890625,
-0.010040283203125,
-0.016876220703125,
-0.0148773193359375,
0.0219879150390625,
-0.0255279541015625,
0.0085296630859375,
-0.00336456298828125,
-0.0081024169921875,
0.0009412765502929688,
-0.0172882080078125,
0.02056884765625,
-0.01251983642578125,
0.002124786376953125,
0.017578125,
-0.0230560302734375,
0.02191162109375,
0.0225830078125,
0.049591064453125,
-0.00139617919921875,
0.00311279296875,
0.034027099609375,
0.00420379638671875,
0.010467529296875,
0.0435791015625,
-0.0404052734375,
-0.0006527900695800781,
0.0054779052734375,
0.0234222412109375,
0.002933502197265625,
-0.026763916015625,
0.0186614990234375,
0.01116943359375,
0.047210693359375,
0.023834228515625,
-0.014312744140625,
0.00934600830078125,
-0.0049591064453125,
0.009368896484375,
-0.036956787109375,
-0.01018524169921875,
-0.012786865234375,
0.048248291015625,
0.01898193359375,
0.0167083740234375,
-0.004177093505859375,
-0.00994110107421875,
-0.014251708984375,
0.01549530029296875,
-0.02227783203125,
0.01983642578125,
-0.0102996826171875,
-0.01232147216796875,
0.034942626953125,
-0.007198333740234375,
-0.00251007080078125,
0.01390838623046875,
-0.00226593017578125,
-0.00646209716796875,
0.005565643310546875,
-0.023712158203125,
-0.01062774658203125,
0.0186767578125,
0.003429412841796875,
-0.005138397216796875,
-0.0008592605590820312,
-0.026123046875,
-0.01036834716796875,
-0.012481689453125,
-0.036865234375,
0.01050567626953125,
-0.00836944580078125,
-0.018890380859375,
0.025299072265625,
-0.0289306640625,
0.02630615234375,
0.007381439208984375,
-0.011138916015625,
-0.0113372802734375,
0.0281524658203125,
-0.0007343292236328125,
-0.019622802734375,
0.031280517578125,
-0.01499176025390625,
0.00695037841796875,
0.018707275390625,
0.01047515869140625,
-0.0119171142578125,
0.055572509765625,
-0.015655517578125,
-0.006023406982421875,
0.0247802734375,
-0.01424407958984375,
-0.055023193359375,
0.0204315185546875,
-0.0162811279296875,
0.0131072998046875,
0.00310516357421875,
-0.0096893310546875,
0.032257080078125,
0.0013523101806640625,
-0.0084381103515625,
-0.0048980712890625,
-0.0221099853515625,
0.0301666259765625,
0.03759765625,
0.01544952392578125,
-0.0261688232421875,
0.01366424560546875,
-0.039276123046875,
0.0108642578125,
-0.01227569580078125,
-0.048095703125,
-0.0088653564453125,
0.005466461181640625,
-0.0113525390625,
0.0124053955078125,
0.00713348388671875,
-0.01415252685546875,
0.0164337158203125,
0.01751708984375,
-0.017547607421875,
0.023834228515625,
-0.023284912109375,
0.0301361083984375,
-0.0201873779296875,
-0.0027675628662109375,
-0.043701171875,
-0.01134490966796875,
-0.0017719268798828125,
-0.005504608154296875,
0.0040740966796875,
-0.04486083984375,
-0.0228424072265625,
-0.0227508544921875,
0.011260986328125,
-0.006359100341796875,
0.0175018310546875,
-0.0195770263671875,
0.0040435791015625,
-0.0103302001953125,
0.0026493072509765625,
0.016754150390625,
-0.0179901123046875,
-0.027618408203125,
-0.0208740234375,
0.034576416015625,
-0.0157623291015625,
-0.0217437744140625,
0.0017108917236328125,
-0.02508544921875,
-0.0013494491577148438,
0.0184326171875,
0.0181427001953125,
0.0028095245361328125,
-0.01219940185546875,
0.004638671875,
-0.027618408203125,
-0.004192352294921875,
0.0506591796875,
-0.01806640625,
-0.01390838623046875,
0.0031681060791015625,
0.0015382766723632812,
-0.0022068023681640625,
0.00064849853515625,
0.01425933837890625,
-0.00876617431640625,
-0.040191650390625,
0.022369384765625,
0.0022068023681640625,
-0.0018157958984375,
-0.004207611083984375,
0.00749969482421875,
0.00757598876953125,
-0.004619598388671875,
-0.0183563232421875,
-0.002597808837890625,
0.0168609619140625,
0.020782470703125,
-0.021881103515625,
0.0151519775390625,
-0.0006103515625,
0.018768310546875,
-0.01395416259765625,
0.013580322265625,
-0.0260772705078125,
-0.005645751953125,
0.03369140625,
-0.02532958984375,
-0.00373077392578125,
0.0107574462890625,
0.01849365234375,
0.037933349609375,
-0.01861572265625,
0.003345489501953125,
-0.0081024169921875,
0.026580810546875,
-0.0111236572265625,
0.01412200927734375,
-0.001979827880859375,
0.0028934478759765625,
-0.00405120849609375
] |
ours_462
|
I claim that
\[
f(n)=\sum_{d \mid n} \sum_{i=0}^{\infty} \frac{\varphi(d)}{2^{i d}}
\]
Consider all of the possible ways to write a nonnegative integer \( k \) in the form \( i d \) with \( d \) a divisor of \( n \). Then \(\frac{1}{2^{k}}\) appears for each \( d \) that is a divisor of \( k \) and a divisor of \( n \), so it appears for every divisor of \(\operatorname{gcd}(k, n)\). Then the sum of the coefficients of \(\frac{1}{2^{k}}\) is
\[
\sum_{d \mid \operatorname{gcd}(k, n)} \varphi(d)=\operatorname{gcd}(k, n)
\]
Thus, this representation of \( f \) works. Then
\[
f(n)=\sum_{d \mid n} \sum_{i=0}^{\infty} \frac{\varphi(d)}{2^{i d}}=\sum_{d \mid n} \frac{2^{d} \varphi(d)}{2^{d}-1}
\]
so the answer is \( 12321+v_{2}(\varphi(12321))=12324 \). Observe that \( g \) is unique by Möbius inversion.
\(\boxed{12324}\)
|
12324
|
{
"competition": "us_comps",
"dataset": "Ours",
"posts": null,
"source": "OMOFall17Solns.md"
}
|
For a positive integer \( n \), define \( f(n)=\sum_{i=0}^{\infty} \frac{\operatorname{gcd}(i, n)}{2^{i}} \) and let \( g: \mathbb{N} \rightarrow \mathbb{Q} \) be a function such that \(\sum_{d \mid n} g(d)=f(n)\) for all positive integers \( n \). Given that \( g(12321)=\frac{p}{q} \) for relatively prime integers \( p \) and \( q \), find \( v_{2}(p) \).
|
[
"/Mathematics/NumberTheory/Divisors/Divides",
"/Mathematics/NumberTheory/Divisors/Divisor",
"/Mathematics/NumberTheory/GeneralNumberTheory/ElementaryNumberTheory",
"/Mathematics/NumberTheory/GeneralNumberTheory/HigherArithmetic",
"/Mathematics/NumberTheory/GeneralNumberTheory/NumberTheory",
"/Mathematics/NumberTheory/NumberTheoreticFunctions/GreatestCommonDivisor",
"/Mathematics/NumberTheory/NumberTheoreticFunctions/TotientFunction"
] |
Express the series as a divisor sum using the identity \(\sum_{d\mid \gcd(k,n)}\varphi(d)=\gcd(k,n)\).
|
[
0.0000998377799987793,
0.02032470703125,
0.035247802734375,
0.016510009765625,
0.0003330707550048828,
-0.00911712646484375,
0.04327392578125,
-0.0086212158203125,
0.01457977294921875,
-0.01416778564453125,
0.035400390625,
-0.035552978515625,
-0.0017194747924804688,
0.0267333984375,
-0.008270263671875,
-0.0113983154296875,
0.04937744140625,
-0.0104217529296875,
-0.00571441650390625,
-0.0069427490234375,
-0.0163726806640625,
0.052978515625,
-0.0219573974609375,
0.032958984375,
-0.044281005859375,
-0.020355224609375,
-0.0231475830078125,
-0.0231170654296875,
0.0233154296875,
0.0263519287109375,
0.00556182861328125,
-0.0005507469177246094,
-0.005306243896484375,
-0.027435302734375,
-0.00027298927307128906,
-0.030181884765625,
-0.0195159912109375,
-0.005001068115234375,
-0.037261962890625,
0.0028095245361328125,
0.021820068359375,
0.020172119140625,
0.01103973388671875,
0.0233001708984375,
-0.00817108154296875,
0.0134429931640625,
0.002460479736328125,
0.029937744140625,
-0.039398193359375,
0.0017881393432617188,
-0.008392333984375,
0.00428009033203125,
-0.0229644775390625,
-0.01556396484375,
-0.00943756103515625,
-0.07757568359375,
0.00887298583984375,
0.010986328125,
0.0198516845703125,
-0.0205230712890625,
-0.01024627685546875,
0.01090240478515625,
-0.0167999267578125,
-0.00954437255859375,
-0.004489898681640625,
-0.0008921623229980469,
0.01076507568359375,
0.028900146484375,
0.00818634033203125,
-0.00983428955078125,
0.036773681640625,
0.026031494140625,
-0.01010894775390625,
0.027435302734375,
0.0012693405151367188,
-0.0176239013671875,
-0.006103515625,
0.00925445556640625,
0.0210723876953125,
-0.0037593841552734375,
0.0229034423828125,
-0.0024127960205078125,
0.0231170654296875,
-0.0156707763671875,
0.0237884521484375,
-0.01110076904296875,
0.0301361083984375,
-0.007778167724609375,
0.017120361328125,
0.010986328125,
0.01457977294921875,
0.0019464492797851562,
0.02093505859375,
-0.035064697265625,
-0.00348663330078125,
0.0038509368896484375,
0.004230499267578125,
-0.005390167236328125,
-0.019378662109375,
0.0035247802734375,
-0.01885986328125,
0.0097503662109375,
0.0026988983154296875,
0.0006399154663085938,
-0.07135009765625,
-0.0276031494140625,
-0.01509857177734375,
-0.01023101806640625,
-0.01904296875,
-0.00809478759765625,
0.0073394775390625,
-0.01287841796875,
0.037689208984375,
0.0213470458984375,
-0.00826263427734375,
-0.0214691162109375,
0.0112152099609375,
0.01861572265625,
0.01959228515625,
0.0169677734375,
-0.002223968505859375,
0.004383087158203125,
0.0026874542236328125,
0.04290771484375,
-0.00984954833984375,
-0.005809783935546875,
0.0035114288330078125,
-0.018310546875,
-0.0190582275390625,
0.007152557373046875,
-0.00006288290023803711,
0.0121612548828125,
-0.0202789306640625,
-0.0262603759765625,
-0.01312255859375,
0.0311279296875,
-0.032562255859375,
-0.0154266357421875,
0.00038123130798339844,
0.002849578857421875,
-0.00771331787109375,
-0.012451171875,
0.0036678314208984375,
-0.0000883936882019043,
-0.01328277587890625,
0.0303955078125,
0.00443267822265625,
-0.025787353515625,
0.00743865966796875,
-0.0158843994140625,
0.00400543212890625,
0.0149383544921875,
0.01715087890625,
-0.0015420913696289062,
0.0035266876220703125,
0.0057525634765625,
0.0111236572265625,
0.002605438232421875,
-0.00481414794921875,
-0.007175445556640625,
-0.004245758056640625,
0.00652313232421875,
0.011322021484375,
0.00289154052734375,
-0.0003066062927246094,
-0.004184722900390625,
0.012481689453125,
-0.0013580322265625,
-0.026641845703125,
-0.0208587646484375,
-0.0006256103515625,
-0.007572174072265625,
0.0003707408905029297,
-0.01092529296875,
0.004955291748046875,
0.007251739501953125,
-0.014068603515625,
0.00978851318359375,
-0.0036945343017578125,
0.0063323974609375,
-0.0008597373962402344,
-0.002964019775390625,
0.018218994140625,
0.0041046142578125,
0.01715087890625,
-0.01129913330078125,
-0.0106201171875,
-0.0154876708984375,
0.01849365234375,
-0.00284576416015625,
0.0160064697265625,
0.0190277099609375,
-0.00514984130859375,
0.005138397216796875,
-0.030792236328125,
0.01047515869140625,
-0.00655364990234375,
0.0033588409423828125,
0.02447509765625,
0.00594329833984375,
-0.00428009033203125,
0.01837158203125,
-0.00994873046875,
0.00847625732421875,
-0.00859832763671875,
-0.004974365234375,
0.0030460357666015625,
-0.0031528472900390625,
0.00201416015625,
-0.0024204254150390625,
0.0175323486328125,
-0.0172119140625,
-0.01476287841796875,
-0.04736328125,
-0.0016632080078125,
0.00004315376281738281,
-0.0184783935546875,
-0.00396728515625,
0.006404876708984375,
-0.043548583984375,
-0.016204833984375,
0.02117919921875,
0.004974365234375,
-0.0023040771484375,
-0.007564544677734375,
-0.00855255126953125,
0.01947021484375,
0.0128631591796875,
-0.0147552490234375,
0.01068878173828125,
0.017242431640625,
0.0189056396484375,
-0.0372314453125,
-0.005413055419921875,
-0.0007343292236328125,
0.006092071533203125,
-0.026397705078125,
-0.0141143798828125,
0.037139892578125,
0.0170745849609375,
-0.0038890838623046875,
-0.0160064697265625,
0.014556884765625,
-0.004100799560546875,
-0.011016845703125,
0.006732940673828125,
-0.0022754669189453125,
-0.00688934326171875,
-0.0162811279296875,
-0.027252197265625,
-0.009735107421875,
-0.01041412353515625,
-0.0295257568359375,
0.0006470680236816406,
0.009033203125,
-0.006473541259765625,
0.001148223876953125,
-0.0360107421875,
-0.0251617431640625,
-0.007709503173828125,
0.004261016845703125,
-0.045318603515625,
0.004573822021484375,
0.00519561767578125,
0.007411956787109375,
0.00267791748046875,
0.0092926025390625,
0.00353240966796875,
0.02154541015625,
0.0146942138671875,
0.0411376953125,
-0.0164031982421875,
-0.0012722015380859375,
-0.0114898681640625,
0.00960540771484375,
-0.01904296875,
0.0011444091796875,
0.00514984130859375,
-0.0005068778991699219,
0.01274871826171875,
0.0090484619140625,
-0.01332855224609375,
-0.0209503173828125,
0.0137176513671875,
-0.004901885986328125,
0.00926971435546875,
0.0160980224609375,
-0.029998779296875,
-0.01629638671875,
0.023956298828125,
-0.01113128662109375,
-0.01172637939453125,
0.0010080337524414062,
-0.01346588134765625,
0.06640625,
-0.010009765625,
0.0016279220581054688,
0.0152587890625,
-0.017974853515625,
-0.005725860595703125,
0.0144195556640625,
0.0237579345703125,
-0.017913818359375,
-0.0006690025329589844,
0.0306243896484375,
0.0104217529296875,
-0.00957489013671875,
0.0048065185546875,
-0.039459228515625,
-0.0294952392578125,
0.0030975341796875,
-0.0272674560546875,
-0.0084686279296875,
0.0021953582763671875,
-0.01325225830078125,
-0.044708251953125,
-0.00920867919921875,
0.0021800994873046875,
-0.0136260986328125,
-0.0215911865234375,
0.0021228790283203125,
0.0203704833984375,
-0.01788330078125,
0.0131683349609375,
-0.006927490234375,
0.0181732177734375,
0.023162841796875,
-0.01447296142578125,
-0.036834716796875,
-0.00878143310546875,
-0.04547119140625,
0.00864410400390625,
-0.0003104209899902344,
-0.016571044921875,
-0.004383087158203125,
-0.004878997802734375,
-0.0004992485046386719,
0.0011749267578125,
0.01415252685546875,
-0.008056640625,
0.0006747245788574219,
-0.003238677978515625,
0.029083251953125,
-0.0223388671875,
-0.048095703125,
0.01153564453125,
0.0270843505859375,
-0.001983642578125,
-0.0081024169921875,
-0.0200347900390625,
0.039825439453125,
0.01261138916015625,
0.0155487060546875,
0.0147247314453125,
-0.04095458984375,
0.02496337890625,
-0.0198822021484375,
0.00787353515625,
0.004444122314453125,
0.0190887451171875,
0.003246307373046875,
-0.034027099609375,
-0.00237274169921875,
0.01030731201171875,
0.0030689239501953125,
-0.0281524658203125,
-0.004299163818359375,
0.0222015380859375,
-0.0521240234375,
0.01084136962890625,
0.0005159378051757812,
-0.011383056640625,
0.0197601318359375,
-0.038818359375,
-0.0416259765625,
-0.003997802734375,
0.023712158203125,
0.0012922286987304688,
0.0098876953125,
0.02728271484375,
0.0012426376342773438,
0.037841796875,
0.00696563720703125,
0.06591796875,
-0.026763916015625,
-0.00516510009765625,
0.000530242919921875,
-0.042236328125,
-0.031829833984375,
0.00873565673828125,
-0.0178680419921875,
0.00013780593872070312,
0.012908935546875,
0.0171966552734375,
-0.0438232421875,
0.00510406494140625,
-0.00428009033203125,
0.043487548828125,
0.05438232421875,
0.0004024505615234375,
-0.0169830322265625,
-0.0008921623229980469,
-0.034912109375,
0.0298919677734375,
0.0173797607421875,
0.0033168792724609375,
-0.01148223876953125,
-0.005268096923828125,
0.0020656585693359375,
-0.01125335693359375,
-0.00958251953125,
0.01508331298828125,
0.0196533203125,
-0.00647735595703125,
0.0102081298828125,
0.00246429443359375,
0.031280517578125,
-0.01421356201171875,
-0.036956787109375,
0.0108642578125,
-0.0025634765625,
-0.0290985107421875,
0.01519775390625,
-0.00009310245513916016,
-0.007030487060546875,
-0.01393890380859375,
-0.0170440673828125,
0.03607177734375,
-0.019378662109375,
-0.01275634765625,
0.005672454833984375,
-0.0290985107421875,
0.01397705078125,
-0.00281524658203125,
0.00608062744140625,
0.0364990234375,
0.01216888427734375,
0.0235137939453125,
-0.006122589111328125,
0.004055023193359375,
0.017425537109375,
-0.010467529296875,
0.000759124755859375,
-0.0157318115234375,
-0.055572509765625,
0.026214599609375,
0.017242431640625,
0.00812530517578125,
-0.031646728515625,
-0.0021839141845703125,
-0.0085296630859375,
-0.002490997314453125,
-0.0007014274597167969,
-0.007476806640625,
0.011322021484375,
0.0005674362182617188,
0.0029315948486328125,
0.00018227100372314453,
0.018585205078125,
-0.03179931640625,
-0.007488250732421875,
0.00873565673828125,
-0.0215606689453125,
-0.00910186767578125,
-0.0223846435546875,
0.0032863616943359375,
-0.017303466796875,
0.002079010009765625,
-0.0111541748046875,
0.01416015625,
0.005374908447265625,
-0.03582763671875,
-0.0008707046508789062,
-0.0276031494140625,
-0.0450439453125,
0.0306243896484375,
-0.01490020751953125,
0.0281524658203125,
-0.0043792724609375,
-0.031341552734375,
0.0189361572265625,
-0.0263671875,
0.0202178955078125,
0.0175933837890625,
-0.004474639892578125,
0.0090179443359375,
0.001346588134765625,
0.0244903564453125,
0.02154541015625,
0.0162506103515625,
0.007656097412109375,
0.0692138671875,
-0.0291748046875,
-0.0291290283203125,
-0.0265960693359375,
-0.02001953125,
-0.031341552734375,
0.007904052734375,
-0.0182037353515625,
0.0005273818969726562,
-0.004955291748046875,
-0.0234375,
0.00737762451171875,
0.042510986328125,
-0.00865936279296875,
-0.003543853759765625,
0.015869140625,
0.022125244140625,
-0.0037860870361328125,
0.00569915771484375,
-0.005016326904296875,
0.0146484375,
-0.00884246826171875,
-0.0113677978515625,
0.022674560546875,
-0.0240325927734375,
-0.036407470703125,
0.00962066650390625,
0.0263671875,
-0.010498046875,
-0.0147705078125,
0.0217132568359375,
0.018035888671875,
-0.00836944580078125,
0.00983428955078125,
0.0284423828125,
0.01519012451171875,
-0.01611328125,
0.0074005126953125,
-0.0014810562133789062,
-0.0191802978515625,
-0.004547119140625,
0.0037250518798828125,
0.0002980232238769531,
-0.060394287109375,
-0.0189208984375,
0.0143890380859375,
-0.037322998046875,
-0.004772186279296875,
0.0244293212890625,
0.0033817291259765625,
-0.015960693359375,
-0.0003247261047363281,
-0.00756072998046875,
-0.0189971923828125,
-0.02960205078125,
0.00333404541015625,
0.031890869140625,
-0.00751495361328125,
-0.0015802383422851562,
0.006195068359375,
-0.01708984375,
-0.00909423828125,
0.00830841064453125,
-0.0047454833984375,
0.046722412109375,
0.01169586181640625,
0.00897979736328125,
-0.007610321044921875,
-0.0296478271484375,
0.03387451171875,
0.01416015625,
0.0172576904296875,
-0.01261138916015625,
0.007511138916015625,
0.0007386207580566406,
0.00362396240234375,
0.017730712890625,
-0.00908660888671875,
-0.0406494140625,
-0.002262115478515625,
0.005828857421875,
0.002166748046875,
-0.023956298828125,
0.0016717910766601562,
-0.02301025390625,
-0.0106048583984375,
0.02923583984375,
0.01043701171875,
-0.0124969482421875,
0.04095458984375,
0.005992889404296875,
-0.0005784034729003906,
-0.036468505859375,
0.040283203125,
0.01442718505859375,
0.032806396484375,
0.01136016845703125,
0.0101776123046875,
-0.0003209114074707031,
-0.00473785400390625,
-0.01019287109375,
-0.0171051025390625,
0.0026073455810546875,
-0.000507354736328125,
-0.0216827392578125,
-0.009918212890625,
-0.0124969482421875,
-0.00870513916015625,
-0.00823211669921875,
0.005054473876953125,
-0.0104827880859375,
-0.045501708984375,
0.006122589111328125,
0.0163421630859375,
0.01029205322265625,
0.01461029052734375,
0.00873565673828125,
-0.026092529296875,
-0.0184478759765625,
0.0231170654296875,
-0.0225830078125,
0.006072998046875,
0.011749267578125,
0.0127105712890625,
0.0132598876953125,
0.0167694091796875,
-0.00415802001953125,
0.015228271484375,
-0.031463623046875,
0.0017261505126953125,
0.0023937225341796875,
-0.01568603515625,
0.01678466796875,
-0.029541015625,
-0.01959228515625,
0.00135040283203125,
0.00835418701171875,
0.01143646240234375,
0.038970947265625,
-0.035308837890625,
-0.01010894775390625,
0.0328369140625,
-0.01605224609375,
0.0118560791015625,
0.0125579833984375,
-0.01381683349609375,
0.00969696044921875,
-0.026702880859375,
-0.01088714599609375,
0.037628173828125,
0.020843505859375,
0.005207061767578125,
-0.060546875,
-0.01018524169921875,
0.0207977294921875,
0.007389068603515625,
-0.03472900390625,
-0.0198822021484375,
0.0193023681640625,
-0.004489898681640625,
-0.00722503662109375,
-0.004924774169921875,
-0.006622314453125,
0.028228759765625,
0.005725860595703125,
0.030914306640625,
-0.050933837890625,
0.00788116455078125,
-0.0199432373046875,
0.00720977783203125,
0.0160369873046875,
0.0199737548828125,
-0.014251708984375,
-0.01140594482421875,
0.0024166107177734375,
0.01016998291015625,
-0.01023101806640625,
0.017608642578125,
-0.0233154296875,
0.0029296875,
-0.041717529296875,
0.0147705078125,
0.005008697509765625,
-0.0032196044921875,
-0.032745361328125,
-0.01184844970703125,
0.003875732421875,
0.00342559814453125,
0.032501220703125,
0.025238037109375,
0.006679534912109375,
0.044281005859375,
-0.0015821456909179688,
0.0228424072265625,
0.026336669921875,
0.00007855892181396484,
-0.0043792724609375,
-0.0269775390625,
-0.0141448974609375,
-0.01253509521484375,
0.035888671875,
-0.00714111328125,
0.0022869110107421875,
-0.00682830810546875,
-0.01058197021484375,
0.00013709068298339844,
-0.019256591796875,
-0.042633056640625,
-0.001678466796875,
0.0152740478515625,
-0.0009794235229492188,
0.00014519691467285156,
0.02203369140625,
-0.002826690673828125,
-0.036285400390625,
-0.0182647705078125,
0.01302337646484375,
0.0131988525390625,
0.006168365478515625,
-0.007320404052734375,
-0.0017719268798828125,
-0.0286102294921875,
-0.00856781005859375,
0.0001628398895263672,
0.01442718505859375,
0.0159149169921875,
0.002437591552734375,
0.025054931640625,
-0.0071868896484375,
-0.0253448486328125,
0.02899169921875,
-0.051361083984375,
-0.014678955078125,
0.01297760009765625,
0.011444091796875,
-0.006793975830078125,
-0.0010709762573242188,
-0.0220489501953125,
0.00835418701171875,
-0.0290374755859375,
-0.0134735107421875,
0.0103759765625,
-0.035186767578125,
-0.0423583984375,
-0.01837158203125,
0.01287841796875,
-0.00838470458984375,
0.0097198486328125,
-0.005916595458984375,
0.057586669921875,
-0.02862548828125,
0.01172637939453125,
0.0073089599609375,
0.0169219970703125,
0.027679443359375,
-0.034423828125,
-0.0001983642578125,
0.00516510009765625,
-0.009307861328125,
0.0090484619140625,
0.0212860107421875,
0.0095672607421875,
-0.081787109375,
-0.0010423660278320312,
0.0164031982421875,
0.03173828125,
-0.034210205078125,
-0.00974273681640625,
-0.00235748291015625,
-0.0372314453125,
-0.00907135009765625,
-0.0220947265625,
-0.012054443359375,
-0.026031494140625,
-0.001155853271484375,
-0.0084228515625,
-0.047210693359375,
-0.031158447265625,
0.0294952392578125,
-0.00004982948303222656,
0.00487518310546875,
-0.0006680488586425781,
-0.00015544891357421875,
0.0164794921875,
0.017730712890625,
-0.007709503173828125,
0.0018777847290039062,
0.0419921875,
-0.0268096923828125,
0.0362548828125,
-0.0184783935546875,
0.0274200439453125,
0.01061248779296875,
-0.0015516281127929688,
-0.005542755126953125,
-0.01442718505859375,
-0.03887939453125,
0.017669677734375,
-0.00289154052734375,
0.025909423828125,
0.0005059242248535156,
0.021881103515625,
-0.0021991729736328125,
-0.0167388916015625,
0.032318115234375,
0.0000756382942199707,
0.001857757568359375,
-0.0013427734375,
0.0272674560546875,
0.01027679443359375,
-0.01421356201171875,
-0.0019931793212890625,
0.0274810791015625,
-0.0013713836669921875,
-0.01641845703125,
0.0180511474609375,
-0.0112457275390625,
-0.00490570068359375,
-0.0037078857421875,
0.007801055908203125,
-0.0200653076171875,
0.00804901123046875,
0.031494140625,
0.0265350341796875,
-0.0228271484375,
0.0018930435180664062,
0.0089263916015625,
-0.0145263671875,
0.024932861328125,
-0.010589599609375,
0.0048065185546875,
-0.00461578369140625,
-0.0112152099609375,
-0.01922607421875,
-0.003635406494140625,
0.0164642333984375,
0.0120086669921875,
0.0033435821533203125,
-0.00023305416107177734,
0.02960205078125,
0.0306396484375,
-0.01293182373046875,
0.0270233154296875,
0.00782012939453125,
0.0223541259765625,
-0.004085540771484375,
0.0031452178955078125,
0.002315521240234375,
-0.004055023193359375,
0.0029048919677734375,
0.0208587646484375,
0.02716064453125,
-0.0312347412109375,
-0.004894256591796875,
-0.0304107666015625,
-0.0296783447265625,
-0.0009784698486328125,
0.0194244384765625,
0.01172637939453125,
0.01276397705078125,
0.017578125,
-0.03558349609375,
0.0005974769592285156,
0.0010938644409179688,
0.0181732177734375,
0.0035724639892578125,
0.0222320556640625,
-0.0030841827392578125,
-0.0246429443359375,
0.0169677734375,
-0.04888916015625,
0.00508880615234375,
-0.0014982223510742188,
-0.01511383056640625,
0.0012826919555664062,
-0.024749755859375,
-0.0180511474609375,
0.0266265869140625,
0.0022945404052734375,
0.048309326171875,
0.0168304443359375,
0.02606201171875,
0.0204925537109375,
-0.02020263671875,
0.0005202293395996094,
0.0041351318359375,
-0.00034928321838378906,
0.0235748291015625,
0.0430908203125,
-0.00127410888671875,
-0.038238525390625,
-0.0152435302734375,
0.0066986083984375,
-0.0230865478515625,
-0.026397705078125,
0.01016998291015625,
0.0252838134765625,
-0.02105712890625,
-0.0209197998046875,
-0.01235198974609375,
0.01430511474609375,
0.003673553466796875,
-0.0025272369384765625,
0.0294189453125,
0.01525115966796875,
-0.003726959228515625,
-0.006534576416015625,
-0.01499176025390625,
-0.0399169921875,
-0.00574493408203125,
0.01441192626953125,
0.032440185546875,
0.00971221923828125,
-0.0131378173828125,
-0.0115203857421875,
-0.02349853515625,
0.0202484130859375,
0.0230255126953125,
-0.0110931396484375,
-0.00322723388671875,
0.0282440185546875,
0.00914764404296875,
0.024200439453125,
-0.050628662109375,
-0.0162200927734375,
0.006885528564453125,
0.0029582977294921875,
0.030975341796875,
0.02960205078125,
0.024932861328125,
0.00665283203125,
0.00943756103515625,
0.00766754150390625,
0.008758544921875,
0.015899658203125,
-0.015899658203125,
-0.01497650146484375,
-0.035888671875,
0.004299163818359375,
-0.02423095703125,
0.037750244140625,
-0.01123809814453125,
-0.0022411346435546875,
0.0264129638671875,
0.0341796875,
0.02191162109375,
0.006740570068359375,
0.000110626220703125,
0.006237030029296875,
0.005260467529296875,
0.007129669189453125,
0.026641845703125,
0.0322265625,
-0.002300262451171875,
-0.007549285888671875,
0.0007276535034179688,
-0.001987457275390625,
-0.042999267578125,
-0.0233306884765625,
0.0071868896484375,
0.00150299072265625,
0.0010356903076171875,
0.01568603515625,
-0.0292510986328125,
-0.006298065185546875,
-0.01384735107421875,
-0.0225982666015625,
-0.006961822509765625,
-0.0278472900390625,
0.00469970703125,
-0.0072174072265625,
-0.056671142578125,
0.01031494140625,
0.015045166015625,
0.0311431884765625,
-0.019989013671875,
0.00391387939453125,
0.020782470703125,
0.031280517578125,
-0.0167236328125,
0.0005316734313964844,
-0.0162506103515625,
-0.0284576416015625,
-0.01526641845703125,
0.0191192626953125,
-0.01641845703125,
0.00714874267578125,
0.045562744140625,
-0.0003414154052734375,
-0.032073974609375,
0.033416748046875,
0.000027894973754882812,
-0.01396942138671875,
-0.0038166046142578125,
0.0188140869140625,
0.03765869140625,
-0.0207366943359375,
0.0205535888671875,
-0.01415252685546875,
-0.0170745849609375,
0.0142822265625,
0.0034942626953125,
0.016387939453125,
-0.00920867919921875,
-0.002643585205078125,
-0.0228424072265625,
-0.02093505859375,
0.02606201171875,
0.0244903564453125,
-0.05889892578125,
-0.0027599334716796875,
-0.0306549072265625,
-0.0023174285888671875,
0.01194000244140625,
0.0144805908203125,
0.01157379150390625,
-0.00501251220703125,
-0.01316070556640625,
0.0260467529296875,
-0.01529693603515625,
0.00797271728515625,
0.0106964111328125,
-0.004535675048828125,
-0.035430908203125,
-0.004642486572265625,
0.020355224609375,
0.0131378173828125,
-0.04638671875,
0.0233612060546875,
-0.00450897216796875,
0.0222320556640625,
-0.03802490234375,
-0.03375244140625,
-0.004947662353515625,
0.01505279541015625,
-0.01392364501953125,
-0.015533447265625,
0.04443359375,
-0.0114898681640625,
-0.01221466064453125,
-0.0225677490234375,
0.02740478515625,
0.0035400390625,
-0.0215911865234375,
-0.0101470947265625,
0.00666046142578125,
0.003795623779296875,
0.03277587890625,
-0.01393890380859375,
0.00496673583984375,
0.01334381103515625,
0.004730224609375,
0.0146636962890625,
0.0144805908203125,
-0.011077880859375,
0.018798828125,
0.0010967254638671875,
-0.016265869140625,
0.0016088485717773438,
0.04022216796875,
0.018402099609375,
-0.0072784423828125,
-0.007503509521484375,
0.0017719268798828125,
0.01238250732421875,
0.02978515625,
-0.037506103515625,
0.0249786376953125,
0.045623779296875,
-0.0107421875,
-0.00838470458984375,
0.0036144256591796875,
-0.0322265625,
0.005062103271484375,
-0.0026226043701171875,
-0.0287322998046875,
0.01605224609375,
0.00151824951171875,
0.01117706298828125,
-0.03668212890625,
0.04425048828125,
0.03662109375,
-0.01160430908203125,
0.0286102294921875,
0.0087127685546875,
0.0288543701171875,
0.0067291259765625,
-0.0136871337890625,
-0.00870513916015625,
-0.0207061767578125,
-0.020660400390625,
-0.05169677734375,
0.006153106689453125,
0.035797119140625,
-0.0110626220703125,
0.001739501953125,
-0.0002989768981933594,
-0.00018680095672607422,
-0.031402587890625,
-0.007747650146484375,
0.013336181640625,
0.0018033981323242188,
-0.0018482208251953125,
-0.006580352783203125,
0.0146942138671875,
-0.00658416748046875,
-0.007030487060546875,
0.0085906982421875,
0.01165771484375,
0.00891876220703125,
0.029632568359375,
0.006008148193359375,
0.0125579833984375,
0.00611114501953125,
-0.0010480880737304688,
0.0180206298828125,
0.0144805908203125,
-0.032745361328125,
-0.0022907257080078125,
-0.0150604248046875,
0.010162353515625,
0.01363372802734375,
0.02801513671875,
-0.004001617431640625,
-0.0018520355224609375,
-0.0350341796875,
-0.0305023193359375,
-0.01751708984375,
-0.0205535888671875,
-0.0101776123046875,
0.041748046875,
0.0209808349609375,
0.0015048980712890625,
0.00554656982421875,
0.0232696533203125,
-0.0165557861328125,
-0.002155303955078125,
0.0006256103515625,
0.006076812744140625,
0.0163726806640625,
0.00643157958984375,
0.0181732177734375,
-0.0185546875,
0.025543212890625,
-0.000354766845703125,
-0.0153656005859375,
0.01824951171875,
0.00725555419921875,
-0.023345947265625,
-0.000004887580871582031,
0.01544952392578125,
-0.016510009765625,
-0.038848876953125,
-0.0120849609375,
-0.0051116943359375,
-0.007537841796875,
-0.0233612060546875,
0.03619384765625,
-0.007843017578125,
-0.0248565673828125,
0.0311431884765625,
-0.03558349609375,
-0.010009765625,
-0.0305633544921875,
-0.0010728836059570312,
-0.0007371902465820312,
-0.004276275634765625,
0.004657745361328125,
-0.02435302734375,
-0.002147674560546875,
-0.01311492919921875,
-0.003131866455078125,
0.0241241455078125,
-0.0145263671875,
0.01242828369140625,
-0.000812530517578125,
0.0007047653198242188,
-0.02728271484375,
-0.0087127685546875,
-0.0347900390625,
-0.0249176025390625,
0.0218963623046875,
-0.01300811767578125,
-0.0167083740234375,
0.0360107421875,
0.0028514862060546875,
-0.00466156005859375,
-0.01007080078125,
-0.00273895263671875,
-0.0154571533203125,
0.039276123046875,
0.002712249755859375,
-0.00861358642578125,
0.00254058837890625,
0.00482940673828125,
0.0023021697998046875,
-0.0296478271484375,
-0.005413055419921875,
0.0262603759765625,
-0.0183868408203125,
-0.0160064697265625,
-0.0273895263671875,
0.0020847320556640625,
0.0239410400390625,
-0.006908416748046875,
-0.0281829833984375,
-0.020660400390625,
0.0175628662109375,
-0.0185546875,
-0.0172882080078125,
-0.0218505859375,
-0.0262451171875,
-0.01605224609375,
-0.0011301040649414062,
0.001422882080078125,
-0.01177215576171875,
0.0197906494140625,
-0.0034027099609375,
0.011199951171875,
-0.002590179443359375,
0.0289154052734375,
-0.00267791748046875,
-0.0460205078125,
-0.00011265277862548828,
-0.007213592529296875,
0.00807952880859375,
-0.00933074951171875,
0.0054473876953125,
-0.026153564453125,
0.009552001953125,
-0.01448822021484375,
0.01519775390625,
-0.0072479248046875,
-0.0053558349609375,
-0.0017786026000976562,
-0.042694091796875,
0.030670166015625,
0.016571044921875,
0.031707763671875,
0.017974853515625,
-0.0208892822265625,
-0.0026149749755859375,
0.028900146484375,
-0.020111083984375,
-0.070068359375,
-0.001483917236328125,
0.022369384765625,
-0.015380859375,
0.035552978515625,
-0.015777587890625,
0.037841796875,
-0.018280029296875,
0.006259918212890625,
0.032501220703125,
-0.025848388671875,
-0.059600830078125,
0.01331329345703125,
-0.026580810546875,
0.01739501953125,
0.005802154541015625,
-0.0151214599609375,
-0.018341064453125,
0.01641845703125,
-0.00783538818359375,
-0.029022216796875,
0.00925445556640625,
-0.0098724365234375,
0.01285552978515625,
0.001678466796875,
-0.0273284912109375,
0.01434326171875,
-0.0213470458984375,
0.00817108154296875,
0.01490020751953125,
-0.0161895751953125,
0.0032444000244140625,
0.00791168212890625,
-0.0249176025390625,
0.0187225341796875,
0.002300262451171875,
0.00131988525390625,
-0.0175018310546875,
0.0243682861328125,
-0.0006642341613769531,
0.0014562606811523438,
-0.0232391357421875,
0.005084991455078125,
0.0066680908203125,
-0.0168914794921875,
-0.0203857421875,
0.01422882080078125,
0.0301971435546875,
-0.004123687744140625,
-0.047698974609375,
-0.0091552734375,
-0.01340484619140625,
0.031280517578125,
-0.0369873046875,
0.00841522216796875,
0.00057220458984375,
0.020294189453125,
-0.0160675048828125,
-0.002750396728515625,
-0.0001195669174194336,
-0.00548553466796875,
-0.0094757080078125,
0.003261566162109375,
-0.00421905517578125,
0.0008912086486816406,
-0.01378631591796875,
-0.028167724609375,
-0.0107421875,
-0.005542755126953125,
0.0078582763671875,
-0.0198974609375,
0.032379150390625,
0.00897216796875,
-0.006237030029296875,
-0.01119232177734375,
-0.01314544677734375,
0.0170440673828125,
0.01309967041015625,
0.0090179443359375,
0.00514984130859375,
0.0135650634765625,
0.0003311634063720703,
-0.002254486083984375,
-0.03717041015625,
0.004302978515625,
-0.01702880859375,
0.028076171875,
0.004695892333984375,
0.02032470703125,
0.0056304931640625,
0.0021915435791015625,
-0.032257080078125,
0.01024627685546875,
-0.05316162109375,
-0.01142120361328125,
0.0002713203430175781,
-0.01422119140625,
-0.032562255859375,
0.00623321533203125,
0.006526947021484375,
0.04083251953125,
0.0010156631469726562,
0.0303802490234375,
0.040130615234375,
-0.0193634033203125,
-0.018707275390625,
0.01551055908203125,
-0.0205230712890625,
0.028594970703125,
0.01143646240234375,
-0.024017333984375,
-0.019073486328125,
0.029510498046875,
0.053009033203125,
-0.0175933837890625,
0.01171112060546875,
0.01183319091796875,
0.010467529296875,
0.0254058837890625,
0.0033855438232421875,
-0.01168060302734375,
0.010711669921875,
0.01421356201171875,
0.005146026611328125,
0.02392578125,
0.0216217041015625,
-0.0075836181640625,
0.013458251953125,
-0.0123443603515625,
0.00998687744140625,
0.005214691162109375,
0.007411956787109375,
0.02740478515625,
-0.00609588623046875,
0.006267547607421875,
-0.039306640625,
-0.001613616943359375,
-0.023193359375,
-0.0014972686767578125,
-0.0009131431579589844,
-0.019287109375,
-0.010040283203125,
0.0080718994140625,
0.0088043212890625,
0.038909912109375,
-0.0179290771484375,
-0.0203399658203125,
-0.01113128662109375,
-0.027069091796875,
0.0277099609375,
0.010894775390625,
-0.0197906494140625,
0.016510009765625,
0.0244293212890625,
-0.022369384765625,
0.0082855224609375,
0.006198883056640625,
-0.0302734375,
0.0322265625,
-0.0293731689453125,
-0.0022754669189453125,
-0.0005178451538085938,
-0.0193939208984375,
-0.025482177734375,
0.022796630859375,
0.0163726806640625,
0.0184173583984375,
0.010528564453125,
0.0162353515625,
0.008209228515625,
-0.01410675048828125,
0.0264892578125,
0.01383209228515625,
0.0234832763671875,
-0.0271453857421875,
0.0085601806640625,
0.00832366943359375,
0.006748199462890625,
-0.040191650390625,
-0.00676727294921875,
-0.00945281982421875,
0.0084381103515625,
-0.01708984375,
0.02001953125,
0.012786865234375,
0.0212554931640625,
-0.0127105712890625,
0.0204620361328125,
0.00782012939453125,
0.001811981201171875,
-0.001190185546875,
-0.013336181640625,
0.04351806640625,
0.00464630126953125,
-0.0094451904296875,
-0.01160430908203125,
-0.016082763671875,
-0.0148773193359375,
-0.0098876953125,
0.0007152557373046875,
-0.0213775634765625,
0.0186004638671875,
-0.0017757415771484375,
0.055450439453125,
0.01496124267578125,
-0.02008056640625,
0.0066070556640625,
0.00966644287109375,
0.009246826171875,
-0.0249176025390625,
-0.0037059783935546875,
0.01123809814453125,
0.03173828125,
-0.01264190673828125,
-0.006710052490234375,
-0.0225372314453125,
-0.029754638671875,
0.011627197265625,
0.05401611328125,
0.027130126953125,
0.0230712890625,
-0.01554107666015625,
0.04217529296875,
-0.0086212158203125,
0.0022430419921875,
-0.0374755859375,
0.0247802734375,
-0.00545501708984375,
0.0086212158203125,
0.029266357421875,
-0.004451751708984375,
-0.02520751953125,
0.026092529296875,
0.020416259765625,
-0.0119476318359375,
0.0159912109375,
0.01259613037109375,
0.0204620361328125,
0.0005383491516113281,
-0.015716552734375,
-0.00897979736328125,
-0.0182952880859375,
0.00795745849609375,
0.0088653564453125,
-0.0174407958984375,
0.0020313262939453125,
0.004352569580078125,
0.0194549560546875,
0.0247650146484375,
-0.0173187255859375,
0.006206512451171875,
0.02398681640625,
-0.01495361328125,
-0.0108795166015625,
-0.025787353515625,
-0.01393890380859375,
-0.04083251953125,
0.038970947265625,
-0.01776123046875,
0.049957275390625,
0.020751953125,
-0.0404052734375,
-0.0209197998046875,
-0.016448974609375,
-0.0050811767578125,
0.0384521484375,
-0.0185546875,
0.01433563232421875,
-0.02423095703125,
0.019927978515625,
-0.019561767578125,
0.002872467041015625,
0.00876617431640625,
-0.00618743896484375,
0.000125885009765625,
0.01397705078125,
0.00827789306640625,
0.0278167724609375,
0.004364013671875,
-0.038421630859375,
-0.0016841888427734375,
-0.003509521484375,
-0.018768310546875,
0.026641845703125,
-0.0170135498046875,
0.028533935546875,
0.0037174224853515625,
-0.01432037353515625,
0.0008282661437988281,
0.004833221435546875,
-0.0364990234375,
-0.0006809234619140625,
-0.0208892822265625,
0.0062255859375,
-0.0005664825439453125,
0.0166778564453125,
0.00022161006927490234,
0.00437164306640625,
0.000545501708984375,
0.0108795166015625,
-0.0216064453125,
0.0008168220520019531,
-0.01383209228515625,
0.0008230209350585938,
0.00634765625,
0.0004799365997314453,
0.0299835205078125,
-0.026885986328125,
0.0190887451171875,
-0.01131439208984375,
-0.01214599609375,
0.0301361083984375,
0.004337310791015625,
0.009552001953125,
-0.005802154541015625,
0.004817962646484375,
0.00518798828125,
-0.00989532470703125,
-0.014190673828125,
-0.039337158203125,
0.0018558502197265625,
-0.0096893310546875,
0.0156707763671875,
-0.0322265625,
-0.0144195556640625,
0.0007495880126953125,
0.039215087890625,
-0.0210113525390625,
0.01392364501953125,
-0.00713348388671875,
0.0195159912109375,
0.018157958984375,
0.01300048828125,
0.007343292236328125,
-0.0012226104736328125,
-0.00833892822265625,
0.003536224365234375,
-0.00421142578125,
0.007083892822265625,
0.0179443359375,
0.01128387451171875,
0.0093536376953125,
-0.007305145263671875,
-0.006381988525390625,
-0.02703857421875,
-0.00989532470703125,
-0.029571533203125,
0.019989013671875,
-0.002765655517578125,
0.0035533905029296875,
-0.01137542724609375,
-0.01361846923828125,
0.03448486328125,
-0.005481719970703125,
-0.00661468505859375,
0.0139617919921875,
0.00007998943328857422,
0.00021183490753173828,
-0.0030059814453125,
-0.01406097412109375,
-0.019561767578125,
0.0103302001953125,
-0.01113128662109375,
0.005817413330078125,
0.04937744140625,
-0.035919189453125,
-0.005146026611328125,
-0.0270843505859375,
-0.0157470703125,
-0.01175689697265625,
0.01934814453125,
0.0382080078125,
0.0015430450439453125,
-0.0036258697509765625,
-0.0099639892578125,
0.00830078125,
-0.0239715576171875,
0.03936767578125,
-0.00852203369140625,
0.01300811767578125,
0.01448822021484375,
0.015289306640625,
0.03216552734375,
-0.005908966064453125,
0.00643157958984375,
0.002529144287109375,
-0.004886627197265625,
0.0016536712646484375,
-0.018280029296875,
0.04248046875,
0.01490020751953125,
-0.0185394287109375,
0.0185699462890625,
-0.019287109375,
-0.01145172119140625,
0.0307464599609375,
-0.006015777587890625,
-0.01393890380859375,
0.01215362548828125,
-0.01277923583984375,
-0.015533447265625,
-0.0002968311309814453,
0.005474090576171875,
-0.0035648345947265625,
0.00453948974609375,
-0.0180206298828125,
-0.00543212890625,
0.02886962890625,
-0.0528564453125,
-0.03619384765625,
0.0272369384765625,
0.0224609375,
0.023590087890625,
0.01280975341796875,
0.01543426513671875,
-0.009429931640625,
0.0294189453125,
0.006908416748046875,
0.01291656494140625,
0.0056915283203125,
-0.0173797607421875,
-0.00337982177734375,
0.00853729248046875,
-0.0108642578125,
-0.016143798828125,
0.01541900634765625,
0.00814056396484375,
0.02655029296875,
0.0161895751953125,
-0.022735595703125,
0.016357421875,
0.000492095947265625,
-0.0252227783203125,
-0.01129913330078125,
0.00502777099609375,
-0.034637451171875,
-0.0114593505859375,
-0.008544921875,
0.0220184326171875,
0.00606536865234375,
0.01227569580078125,
-0.0031871795654296875,
0.006816864013671875,
-0.017547607421875,
0.01349639892578125,
0.0035076141357421875,
-0.0350341796875,
0.00728607177734375,
-0.0030879974365234375,
-0.0207977294921875,
-0.003040313720703125,
0.0234222412109375,
0.02191162109375,
0.0074615478515625,
0.0010633468627929688,
0.040771484375,
-0.034423828125,
0.0009765625,
0.0175628662109375,
0.0256805419921875,
-0.00384521484375,
0.0051116943359375,
-0.0092010498046875,
-0.03143310546875,
0.00571441650390625,
-0.0025005340576171875,
-0.008880615234375,
0.020721435546875,
-0.0230712890625,
0.0211181640625,
0.0120697021484375,
-0.01690673828125,
-0.003406524658203125,
-0.0261077880859375,
-0.0251922607421875,
0.0156707763671875,
0.0008335113525390625,
-0.022979736328125,
-0.0081329345703125,
0.00844573974609375,
-0.0010814666748046875,
0.0205078125,
0.0178680419921875,
0.002838134765625,
-0.031341552734375,
0.01117706298828125,
0.0025348663330078125,
0.025360107421875,
-0.00702667236328125,
0.0069122314453125,
-0.005123138427734375,
0.01788330078125,
-0.0013723373413085938,
-0.014129638671875,
0.00350189208984375,
0.00899505615234375,
0.00482940673828125,
0.011932373046875,
-0.0010347366333007812,
0.021514892578125,
-0.046112060546875,
-0.006832122802734375,
-0.02374267578125,
-0.0254974365234375,
0.0076904296875,
0.01232147216796875,
0.01418304443359375,
-0.0174102783203125,
-0.019012451171875,
-0.0157928466796875,
-0.0033817291259765625,
-0.0110931396484375,
0.029327392578125,
0.0272674560546875,
0.0123748779296875,
0.027191162109375,
-0.01311492919921875,
0.0294952392578125,
-0.00458526611328125,
-0.043731689453125,
0.0118408203125,
0.00623321533203125,
-0.03875732421875,
-0.00711822509765625,
0.02789306640625,
0.0151824951171875,
-0.039764404296875,
0.006374359130859375,
-0.0246734619140625,
-0.0076446533203125,
0.0133209228515625,
0.006793975830078125,
-0.012969970703125,
-0.0214996337890625,
-0.0161590576171875,
-0.0188751220703125,
0.034210205078125,
0.0301666259765625,
-0.0023517608642578125,
0.032196044921875,
-0.017547607421875,
0.0159759521484375,
0.00514984130859375,
-0.0323486328125,
-0.01149749755859375,
0.0343017578125,
0.0263519287109375,
0.004528045654296875,
0.0293731689453125,
0.01457977294921875,
0.0156097412109375,
0.005573272705078125,
-0.0059814453125,
-0.024505615234375,
-0.0200958251953125,
-0.01395416259765625,
0.015716552734375,
-0.0026397705078125,
-0.0043182373046875,
0.0185394287109375,
0.01422882080078125,
-0.0065765380859375,
-0.0008673667907714844,
-0.0221099853515625,
0.0068817138671875,
0.0018548965454101562,
-0.006130218505859375,
0.005893707275390625,
-0.0182037353515625,
0.0489501953125,
0.01251983642578125,
-0.00334930419921875,
0.005481719970703125,
0.0242156982421875,
-0.0096588134765625,
0.0003681182861328125,
-0.00667572021484375,
-0.006961822509765625,
0.017242431640625,
-0.02227783203125,
-0.0231170654296875,
0.020721435546875,
0.004138946533203125,
-0.037200927734375,
-0.0081329345703125,
-0.0001468658447265625,
0.033660888671875,
0.0008988380432128906,
-0.00917816162109375,
-0.0105438232421875,
-0.018035888671875,
-0.00489044189453125,
-0.00574493408203125,
-0.00579833984375,
0.04803466796875,
-0.00008767843246459961,
0.062255859375,
-0.00260162353515625,
-0.03179931640625,
0.01027679443359375,
-0.0009026527404785156,
-0.01486968994140625,
-0.004734039306640625,
-0.01021575927734375,
0.00266265869140625,
0.0046844482421875,
0.02325439453125,
-0.04229736328125,
0.003482818603515625,
0.0250091552734375,
-0.00870513916015625,
-0.00832366943359375,
-0.007373809814453125,
-0.005077362060546875,
-0.0008940696716308594,
0.01343536376953125,
0.0027980804443359375,
-0.01229095458984375,
0.0005321502685546875,
-0.016693115234375,
0.012542724609375,
-0.0005106925964355469,
-0.0088958740234375,
0.012939453125,
-0.00799560546875,
0.00994110107421875,
-0.03021240234375,
0.0224151611328125,
-0.01343536376953125,
0.007659912109375,
0.00997161865234375,
-0.005901336669921875,
-0.0207977294921875,
0.013031005859375,
-0.00518798828125,
0.00839996337890625,
-0.01062774658203125,
-0.01157379150390625,
0.002620697021484375,
0.01611328125,
0.01505279541015625,
-0.0199737548828125,
0.023406982421875,
0.0244598388671875,
-0.01044464111328125,
-0.006927490234375,
0.0064544677734375,
-0.00757598876953125,
-0.0149078369140625,
0.00637054443359375,
0.0157470703125,
0.01444244384765625,
0.0220947265625,
-0.0073089599609375,
0.004364013671875,
0.01149749755859375,
0.003726959228515625,
0.046478271484375,
-0.0171661376953125,
-0.0017375946044921875,
-0.026519775390625,
-0.002124786376953125,
0.0308837890625,
-0.018341064453125,
-0.01044464111328125,
-0.037933349609375,
-0.001056671142578125,
-0.024078369140625,
0.0023937225341796875,
-0.0023059844970703125,
0.0243988037109375,
-0.005489349365234375,
-0.0194854736328125,
-0.010345458984375,
-0.00506591796875,
0.031707763671875,
-0.01160430908203125,
-0.05712890625,
-0.0233001708984375,
-0.0175933837890625,
0.034332275390625,
0.00273895263671875,
0.01282501220703125,
-0.040130615234375,
0.0013132095336914062,
0.015899658203125,
-0.0183563232421875,
0.0283660888671875,
0.01096343994140625,
0.00963592529296875,
0.0073089599609375,
-0.0292816162109375,
0.01332855224609375,
0.0189666748046875,
-0.0086517333984375,
0.0180511474609375,
-0.01010894775390625,
0.010772705078125,
-0.006114959716796875,
0.00922393798828125,
-0.00893402099609375,
-0.0087738037109375,
0.017333984375,
0.0104827880859375,
-0.020538330078125,
0.0218353271484375,
-0.00980377197265625,
0.007205963134765625,
-0.01383209228515625,
-0.0117950439453125,
-0.00848388671875,
-0.0018377304077148438,
0.0006995201110839844,
0.0165252685546875,
-0.007312774658203125,
0.017242431640625,
0.0001270771026611328,
-0.03155517578125,
-0.0294952392578125,
0.0059967041015625,
0.0012073516845703125,
0.01806640625,
-0.005130767822265625,
0.0098114013671875,
-0.0011281967163085938,
0.0012388229370117188,
-0.020904541015625,
-0.040985107421875,
-0.0280609130859375,
-0.0198211669921875,
-0.0110931396484375,
0.024932861328125,
-0.0276641845703125,
-0.0177764892578125,
-0.005992889404296875,
0.00855255126953125,
-0.0008592605590820312,
0.011627197265625,
-0.0009016990661621094,
0.0200347900390625,
-0.038238525390625,
0.016754150390625,
0.017181396484375,
0.0257720947265625,
-0.0157470703125,
0.007663726806640625,
-0.04254150390625,
-0.01026153564453125,
-0.0286407470703125,
0.021942138671875,
-0.03515625,
0.018341064453125,
0.0063018798828125,
-0.02581787109375,
0.0249481201171875,
0.0181427001953125,
-0.047515869140625,
0.03131103515625,
-0.01151275634765625,
0.0211334228515625,
0.00901031494140625,
0.007534027099609375,
0.00823211669921875,
0.03070068359375,
-0.039581298828125,
-0.0028839111328125,
0.01041412353515625,
0.0272979736328125,
-0.0112762451171875,
0.003139495849609375,
-0.00121307373046875,
-0.02032470703125,
0.04248046875,
0.03399658203125,
-0.01073455810546875,
0.0114898681640625,
-0.0323486328125,
0.00817108154296875,
-0.0213623046875,
-0.032958984375,
0.0202484130859375,
-0.010009765625,
-0.0027408599853515625,
-0.024383544921875,
0.01515960693359375,
-0.0174407958984375,
-0.004467010498046875,
-0.0251312255859375,
-0.01105499267578125,
-0.0146484375,
-0.006626129150390625,
0.0017757415771484375,
-0.02020263671875,
0.0010461807250976562,
0.0288543701171875,
-0.0167236328125,
-0.006168365478515625,
0.0224609375,
0.030914306640625,
0.012725830078125,
0.002964019775390625,
-0.0012073516845703125,
0.022857666015625,
0.0175018310546875,
-0.0297088623046875,
-0.0099945068359375,
0.008331298828125,
-0.004550933837890625,
0.007843017578125,
-0.026763916015625,
-0.006938934326171875,
0.0217437744140625,
0.0120391845703125,
0.0310516357421875,
0.041015625,
0.029327392578125,
0.0011377334594726562,
0.00930023193359375,
-0.004344940185546875,
-0.01161956787109375,
-0.015594482421875,
0.01406097412109375,
-0.0167083740234375,
-0.00868988037109375,
0.0171051025390625,
-0.0013256072998046875,
0.00605010986328125,
-0.018707275390625,
-0.023284912109375,
-0.0094146728515625,
0.0238037109375,
-0.034881591796875,
-0.032135009765625,
-0.0223388671875,
-0.0109710693359375,
0.0178375244140625,
0.00724029541015625,
-0.015899658203125,
0.000812530517578125,
0.01194000244140625,
0.018829345703125,
-0.029510498046875,
0.0567626953125,
0.004116058349609375,
-0.006103515625,
-0.038787841796875,
0.016204833984375,
0.0034332275390625,
0.0321044921875,
0.0002987384796142578,
-0.020965576171875,
-0.049285888671875,
0.00421905517578125,
0.02520751953125,
-0.0355224609375,
-0.01324462890625,
0.00469970703125,
-0.00914764404296875,
0.027099609375,
0.022491455078125,
-0.0081939697265625,
-0.0179290771484375,
-0.0230865478515625,
0.0161285400390625,
-0.01386260986328125,
-0.00738525390625,
0.0029964447021484375,
0.0179290771484375,
0.01629638671875,
0.0108489990234375,
0.0035533905029296875,
-0.033721923828125,
0.0101165771484375,
-0.020111083984375,
0.01611328125,
-0.0064239501953125,
0.025146484375,
0.0270843505859375,
-0.0260162353515625,
0.0538330078125,
0.0118255615234375,
0.018280029296875,
-0.00408172607421875,
-0.004573822021484375,
-0.0006971359252929688,
0.00833892822265625,
0.0161285400390625,
-0.0175323486328125,
0.00044345855712890625,
-0.00555419921875,
0.0077362060546875,
0.0028057098388671875,
0.035919189453125,
-0.004230499267578125,
0.030731201171875,
0.00841522216796875,
0.0046234130859375,
0.0146026611328125,
-0.007343292236328125,
-0.00738525390625,
-0.00783538818359375,
0.0019893646240234375,
-0.021392822265625,
-0.003997802734375,
-0.0010080337524414062,
0.0179290771484375,
0.01212310791015625,
0.0169677734375,
-0.0026226043701171875,
0.0264739990234375,
-0.014404296875,
-0.0125579833984375,
0.0016679763793945312,
-0.0006036758422851562,
0.006500244140625,
0.0174407958984375,
-0.004528045654296875,
-0.02862548828125,
-0.00417327880859375,
0.00037598609924316406,
0.01325225830078125,
-0.0014896392822265625,
-0.008270263671875,
-0.01001739501953125,
-0.0002237558364868164,
0.000736236572265625,
-0.022735595703125,
-0.0250396728515625,
-0.006134033203125,
-0.012542724609375,
-0.0245208740234375,
-0.0080413818359375,
-0.0216064453125,
-0.01020050048828125,
0.009552001953125,
0.0016050338745117188,
-0.028106689453125,
-0.02862548828125,
0.027984619140625,
0.049072265625,
-0.01404571533203125,
-0.001834869384765625,
0.026702880859375,
0.007843017578125,
0.00395965576171875,
-0.0103302001953125,
0.0186767578125,
-0.0555419921875,
0.0160369873046875,
0.017242431640625,
-0.0013322830200195312,
0.0034122467041015625,
0.018157958984375,
0.0252227783203125,
-0.0301666259765625,
0.0223846435546875,
-0.00739288330078125,
0.0257415771484375,
0.00843048095703125,
0.0091400146484375,
-0.03472900390625,
0.005275726318359375,
-0.001903533935546875,
-0.0282135009765625,
-0.0015878677368164062,
0.0170440673828125,
-0.0012521743774414062,
-0.043731689453125,
0.0367431640625,
0.01395416259765625,
-0.0096893310546875,
-0.03045654296875,
-0.007625579833984375,
0.01611328125,
-0.0088348388671875,
0.01190185546875,
0.0175018310546875,
-0.00433349609375,
0.047454833984375,
-0.0063629150390625,
0.006748199462890625,
-0.0292205810546875,
-0.0208892822265625,
-0.0242156982421875,
-0.01531219482421875,
-0.0070343017578125,
-0.0161590576171875,
0.007038116455078125,
-0.0123748779296875,
0.01102447509765625,
-0.04071044921875,
-0.011810302734375,
0.020782470703125,
0.0068511962890625,
0.035247802734375,
0.0193939208984375,
0.0162200927734375,
0.01166534423828125,
-0.00998687744140625,
-0.01459503173828125,
-0.01136016845703125,
-0.02166748046875,
0.0088043212890625,
-0.00827789306640625,
0.041015625,
-0.010955810546875,
0.038299560546875,
-0.0267333984375,
-0.003570556640625,
-0.0295257568359375,
-0.0213470458984375,
-0.007793426513671875,
-0.002246856689453125,
0.0173187255859375,
-0.016021728515625,
-0.03607177734375,
0.0006818771362304688,
0.0001804828643798828,
-0.018218994140625,
0.032135009765625,
-0.0294342041015625,
0.0020465850830078125,
-0.005889892578125,
-0.029876708984375,
-0.0236968994140625,
0.0139312744140625,
0.0347900390625,
-0.0008521080017089844,
0.0103912353515625,
0.014862060546875,
0.028167724609375,
0.02880859375,
-0.018402099609375,
0.01471710205078125,
0.01119232177734375,
-0.0260009765625,
0.00946807861328125,
-0.0174560546875,
0.004207611083984375,
0.0059661865234375,
0.00640106201171875,
-0.0240020751953125,
-0.00003045797348022461,
-0.0404052734375,
0.01122283935546875,
-0.0159149169921875,
-0.01336669921875,
-0.00702667236328125,
-0.0239410400390625,
-0.0032749176025390625,
0.0157623291015625,
0.01428985595703125,
-0.00566864013671875,
0.052642822265625,
-0.034576416015625,
0.0015001296997070312,
-0.00621795654296875,
0.0232696533203125,
0.0200347900390625,
-0.004199981689453125,
-0.01119232177734375,
0.009033203125,
0.006008148193359375,
0.0031108856201171875,
0.007205963134765625,
0.0060882568359375,
-0.037872314453125,
-0.005405426025390625,
0.01425933837890625,
-0.0038623809814453125,
-0.01776123046875,
0.00652313232421875,
0.0289764404296875,
-0.0164337158203125,
-0.004154205322265625,
0.028411865234375,
-0.002742767333984375,
-0.00933074951171875,
-0.01708984375,
-0.0306396484375,
-0.00461578369140625,
-0.0006403923034667969,
0.0234527587890625,
-0.00536346435546875,
0.007129669189453125,
-0.00626373291015625,
-0.00899505615234375,
-0.000022590160369873047,
0.013946533203125,
-0.0181121826171875,
0.00920867919921875,
-0.01226806640625,
-0.01476287841796875,
-0.01280975341796875,
0.019195556640625,
-0.01263427734375,
-0.03076171875,
0.018157958984375,
0.005939483642578125,
-0.01213836669921875,
-0.00897216796875,
-0.00002568960189819336,
-0.016632080078125,
-0.005767822265625,
0.0225830078125,
-0.0222015380859375,
-0.004467010498046875,
0.00742340087890625,
-0.0093231201171875,
-0.002887725830078125,
0.010101318359375,
0.0288848876953125,
-0.03680419921875,
-0.02484130859375,
-0.024810791015625,
-0.0018320083618164062,
0.0159454345703125,
0.01041412353515625,
-0.0252532958984375,
-0.0253753662109375,
-0.00043487548828125,
-0.00896453857421875,
-0.0151519775390625,
0.010284423828125,
-0.036285400390625,
-0.004695892333984375,
0.0196075439453125,
0.01273345947265625,
0.021942138671875,
-0.0209808349609375,
0.0338134765625,
-0.00180816650390625,
-0.005340576171875,
-0.0225982666015625,
0.00846099853515625,
0.0027370452880859375,
-0.00867462158203125,
-0.0191497802734375,
-0.015289306640625,
-0.006011962890625,
0.0360107421875,
-0.00008589029312133789,
-0.03704833984375,
0.0423583984375,
0.008453369140625,
0.026214599609375,
0.045166015625,
-0.027740478515625,
0.00952911376953125,
-0.022552490234375,
0.027191162109375,
-0.009246826171875,
-0.00316619873046875,
0.018768310546875,
-0.006153106689453125,
0.0129852294921875,
0.016998291015625,
-0.0152587890625,
-0.0034809112548828125,
-0.00394439697265625,
0.026641845703125,
0.0010967254638671875,
0.00567626953125,
-0.01442718505859375,
0.023162841796875,
0.04718017578125,
-0.0003459453582763672,
0.01387786865234375,
-0.005161285400390625,
0.0009908676147460938,
0.00875091552734375,
-0.0127716064453125,
0.022186279296875,
-0.00725555419921875,
-0.0211029052734375,
0.01470947265625,
-0.0169677734375,
-0.02801513671875,
0.04522705078125,
-0.002445220947265625,
-0.0274200439453125,
0.004787445068359375,
-0.0244140625,
-0.01314544677734375,
-0.005950927734375,
0.0181732177734375,
-0.026611328125,
-0.00926971435546875,
0.01044464111328125,
-0.0031147003173828125,
-0.041961669921875,
-0.00023865699768066406,
0.01399993896484375,
-0.01505279541015625,
0.0151519775390625,
0.015838623046875,
0.0007901191711425781,
0.0287017822265625,
-0.034912109375,
0.01517486572265625,
0.01187896728515625,
0.0423583984375,
-0.011199951171875,
-0.015594482421875,
0.017791748046875,
-0.018768310546875,
-0.0014247894287109375,
0.031585693359375,
0.01316070556640625,
0.0274658203125,
0.0309295654296875,
-0.00673675537109375,
-0.003170013427734375,
-0.0211029052734375,
0.0256500244140625,
0.0081634521484375,
-0.0103912353515625,
-0.0127105712890625,
0.0188140869140625,
0.032196044921875,
-0.0065765380859375,
-0.0109100341796875,
-0.007152557373046875,
0.0205230712890625,
-0.007305145263671875,
-0.0200042724609375,
-0.023468017578125,
0.05560302734375,
0.01212310791015625,
-0.0162353515625,
-0.01407623291015625,
-0.0227813720703125,
0.027923583984375,
-0.048370361328125,
0.0014858245849609375,
0.057647705078125,
0.007171630859375,
-0.0239715576171875,
0.007396697998046875,
-0.033935546875,
0.00322723388671875,
-0.004428863525390625,
0.002620697021484375,
-0.018798828125,
0.0031528472900390625,
0.0350341796875,
-0.0206298828125,
0.01355743408203125,
-0.00443267822265625,
-0.024505615234375,
-0.027557373046875,
0.01352691650390625,
0.007511138916015625,
0.00787353515625,
-0.03851318359375,
-0.039764404296875,
-0.00902557373046875,
0.01715087890625,
-0.0002455711364746094,
-0.005077362060546875,
-0.00020968914031982422,
-0.01441192626953125,
-0.0004973411560058594,
0.0016117095947265625,
0.01195526123046875,
-0.01403045654296875,
-0.0287933349609375,
0.0012912750244140625,
0.0143585205078125,
-0.0010747909545898438,
-0.027587890625,
0.02423095703125,
-0.0078125,
-0.021392822265625,
-0.0206451416015625,
-0.0060882568359375,
-0.01885986328125,
-0.0202789306640625,
-0.021881103515625,
0.0224609375,
-0.0006895065307617188,
0.0213775634765625,
0.0061798095703125,
-0.013092041015625,
0.0206756591796875,
-0.0190277099609375,
-0.0027599334716796875,
-0.00395965576171875,
-0.0225372314453125,
0.014801025390625,
-0.0271453857421875,
0.01397705078125,
0.0138397216796875,
0.0077667236328125,
-0.00597381591796875,
-0.004337310791015625,
0.00820159912109375,
-0.005767822265625,
-0.0014190673828125,
0.01226043701171875,
-0.00374603271484375,
0.005695343017578125,
0.00736236572265625,
-0.00634765625,
0.015106201171875,
-0.00211334228515625,
-0.001674652099609375,
0.00336456298828125,
-0.006084442138671875,
-0.0156402587890625,
0.0199127197265625,
0.024505615234375,
0.0175628662109375,
0.019775390625,
-0.0273590087890625,
-0.00847625732421875,
-0.0311431884765625,
-0.01959228515625,
0.018280029296875,
0.021331787109375,
0.0013742446899414062,
-0.01053619384765625,
-0.0121612548828125,
0.02154541015625,
0.0114898681640625
] |
ours_463
|
Solution. Note that the second condition is equivalent to
\[
bc+ca+ab+1=abc.
\]
Then
\[
\begin{aligned}
abc-(a+2b-3c) & = bc+ca+ab-a-2b+3c+1 \\
& = \frac{1}{2}(a+b+c)^{2}-\frac{1}{2}a^{2}-\frac{1}{2}b^{2}-\frac{1}{2}c^{2}-a-2b+3c+1 \\
& = \frac{1}{2}(a+b+c)^{2}-\frac{1}{2}a^{2}+3a-\frac{1}{2}b^{2}+2b-\frac{1}{2}c^{2}+7c-4(a+b+c)+1 \\
& = 56-\frac{1}{2}(a-3)^{2}-\frac{1}{2}(b-2)^{2}-\frac{1}{2}(c-7)^{2} \\
& \leq 56.
\end{aligned}
\]
Equality holds when \((a, b, c) = (3, 2, 7)\).
Thus, the largest possible value is \(\boxed{56}\).
|
56
|
{
"competition": "us_comps",
"dataset": "Ours",
"posts": null,
"source": "OMOFall17Solns.md"
}
|
Let \( a, b, c \) be real nonzero numbers such that \( a+b+c=12 \) and
\[
\frac{1}{a}+\frac{1}{b}+\frac{1}{c}+\frac{1}{abc}=1.
\]
Compute the largest possible value of \( abc-(a+2b-3c) \).
|
[
"/Mathematics/Algebra/AlgebraicEquations/AlgebraicExpression",
"/Mathematics/Algebra/AlgebraicEquations/SimultaneousEquations",
"/Mathematics/Algebra/GeneralAlgebra/AffineEquation",
"/Mathematics/Algebra/GeneralAlgebra/Algebra",
"/Mathematics/Algebra/Sums/Sum",
"/Mathematics/RecreationalMathematics/Puzzles/Puzzle"
] |
Replace abc using the second condition and complete squares given the fixed sum a+b+c=12 to bound the expression.
|
[
-0.0000890493392944336,
0.003963470458984375,
0.037750244140625,
0.0233001708984375,
-0.00039458274841308594,
0.019683837890625,
-0.0216827392578125,
0.041015625,
-0.0017576217651367188,
-0.0513916015625,
0.0180511474609375,
-0.0242919921875,
-0.01004791259765625,
0.0178680419921875,
-0.023406982421875,
0.0059356689453125,
-0.01279449462890625,
-0.008148193359375,
0.05560302734375,
-0.0025119781494140625,
-0.010833740234375,
-0.026031494140625,
-0.04241943359375,
0.01245880126953125,
-0.0176849365234375,
0.0190277099609375,
-0.00994110107421875,
-0.01320648193359375,
0.0213470458984375,
0.00015926361083984375,
-0.0173797607421875,
-0.03753662109375,
-0.021392822265625,
-0.036865234375,
-0.003093719482421875,
0.00818634033203125,
0.00928497314453125,
-0.00707244873046875,
-0.0286712646484375,
-0.04620361328125,
-0.010040283203125,
0.0364990234375,
-0.019775390625,
0.017486572265625,
-0.059814453125,
0.0230865478515625,
-0.0095367431640625,
-0.007965087890625,
-0.02197265625,
0.01004791259765625,
0.001094818115234375,
0.00850677490234375,
0.02593994140625,
-0.0014028549194335938,
-0.02947998046875,
-0.0506591796875,
0.00702667236328125,
0.00019061565399169922,
-0.00537109375,
0.0066680908203125,
0.000014424324035644531,
-0.01139068603515625,
0.0253448486328125,
-0.01032257080078125,
-0.0002608299255371094,
-0.003997802734375,
-0.0035495758056640625,
-0.0253753662109375,
-0.0007634162902832031,
0.0021381378173828125,
0.031585693359375,
-0.029937744140625,
-0.004016876220703125,
0.03399658203125,
0.031219482421875,
-0.0094451904296875,
-0.0059356689453125,
0.01168060302734375,
-0.00013697147369384766,
0.01253509521484375,
0.0082550048828125,
0.0034618377685546875,
-0.006420135498046875,
-0.006275177001953125,
0.0275726318359375,
-0.007114410400390625,
-0.04254150390625,
0.0195465087890625,
-0.006900787353515625,
-0.0130615234375,
-0.00566864013671875,
0.01629638671875,
-0.0244903564453125,
-0.0031032562255859375,
0.0026187896728515625,
0.01302337646484375,
-0.0031223297119140625,
-0.0040130615234375,
-0.00897216796875,
0.006175994873046875,
-0.0160064697265625,
-0.003093719482421875,
0.03131103515625,
-0.01374053955078125,
-0.03887939453125,
-0.01287841796875,
-0.00464630126953125,
0.00275421142578125,
-0.0051116943359375,
-0.03094482421875,
0.01947021484375,
-0.01111602783203125,
-0.0061492919921875,
-0.007709503173828125,
-0.0133056640625,
-0.006649017333984375,
0.0083465576171875,
-0.0278778076171875,
-0.013336181640625,
0.037353515625,
-0.006610870361328125,
0.0119171142578125,
0.00698089599609375,
0.0237274169921875,
-0.00783538818359375,
0.00853729248046875,
0.01512908935546875,
-0.023223876953125,
-0.006267547607421875,
-0.0111846923828125,
0.0030975341796875,
-0.006214141845703125,
-0.05523681640625,
-0.0308074951171875,
-0.08306884765625,
-0.00922393798828125,
0.0186004638671875,
0.01009368896484375,
-0.0107574462890625,
-0.0086822509765625,
0.007228851318359375,
-0.014678955078125,
0.00830078125,
0.017913818359375,
-0.021270751953125,
-0.0423583984375,
0.01239013671875,
-0.01418304443359375,
-0.01081085205078125,
-0.0074005126953125,
-0.0045318603515625,
-0.00572967529296875,
0.00634765625,
-0.00846099853515625,
0.01271820068359375,
0.00908660888671875,
0.017730712890625,
0.02618408203125,
-0.022186279296875,
-0.01464080810546875,
-0.002777099609375,
-0.006015777587890625,
-0.0016803741455078125,
0.0015001296997070312,
0.0157012939453125,
-0.01169586181640625,
0.0040740966796875,
-0.0186920166015625,
-0.007068634033203125,
-0.00814056396484375,
0.006809234619140625,
0.01947021484375,
0.0029048919677734375,
-0.002475738525390625,
-0.01690673828125,
0.005283355712890625,
-0.0238037109375,
-0.007965087890625,
-0.012786865234375,
-0.00809478759765625,
-0.01387786865234375,
-0.0220794677734375,
-0.0002715587615966797,
-0.00916290283203125,
0.01439666748046875,
0.0008215904235839844,
0.0023708343505859375,
0.00794219970703125,
0.027496337890625,
0.00919342041015625,
-0.038177490234375,
0.01055145263671875,
0.01074981689453125,
-0.01259613037109375,
0.0249481201171875,
-0.007030487060546875,
-0.035125732421875,
-0.0026302337646484375,
0.004459381103515625,
-0.0004420280456542969,
-0.0013971328735351562,
-0.008209228515625,
0.0186767578125,
0.005329132080078125,
0.0021038055419921875,
0.00383758544921875,
0.008514404296875,
-0.0075225830078125,
-0.00505828857421875,
0.016693115234375,
-0.0022754669189453125,
0.036407470703125,
0.004505157470703125,
-0.0304412841796875,
-0.0173797607421875,
0.00872039794921875,
-0.01178741455078125,
-0.00742340087890625,
0.01090240478515625,
0.0027408599853515625,
0.005580902099609375,
0.01025390625,
-0.0241546630859375,
-0.0031490325927734375,
-0.004627227783203125,
0.0227813720703125,
-0.0143585205078125,
0.0030345916748046875,
0.01560211181640625,
0.0077667236328125,
0.0025539398193359375,
-0.005886077880859375,
0.017364501953125,
-0.0085906982421875,
-0.0225830078125,
-0.003154754638671875,
-0.043914794921875,
-0.0059356689453125,
-0.01470184326171875,
-0.01207733154296875,
-0.0004930496215820312,
-0.03399658203125,
0.01806640625,
-0.0057830810546875,
0.007122039794921875,
-0.0015172958374023438,
0.019378662109375,
-0.013458251953125,
-0.005092620849609375,
-0.0275726318359375,
-0.04254150390625,
0.0068206787109375,
-0.0233917236328125,
-0.00768280029296875,
0.0017242431640625,
0.0004992485046386719,
0.007610321044921875,
0.01068115234375,
-0.0168914794921875,
0.03070068359375,
-0.005733489990234375,
-0.03857421875,
-0.01265716552734375,
-0.028656005859375,
-0.01074981689453125,
0.006378173828125,
0.02459716796875,
0.006290435791015625,
0.0178985595703125,
-0.01131439208984375,
0.0192413330078125,
-0.02044677734375,
-0.00016748905181884766,
0.0004401206970214844,
0.0164337158203125,
0.0264739990234375,
-0.006305694580078125,
0.0123291015625,
-0.0152130126953125,
0.00200653076171875,
0.0018968582153320312,
0.008544921875,
-0.00487518310546875,
-0.00591278076171875,
-0.0004467964172363281,
0.011199951171875,
0.032928466796875,
-0.026458740234375,
-0.0052947998046875,
0.00867462158203125,
-0.004650115966796875,
-0.0184478759765625,
-0.0111846923828125,
0.002208709716796875,
0.05615234375,
-0.00412750244140625,
-0.020050048828125,
0.0237579345703125,
0.030487060546875,
0.01776123046875,
0.0277252197265625,
0.0205230712890625,
-0.017059326171875,
0.0010099411010742188,
0.0055694580078125,
0.01800537109375,
0.0013275146484375,
-0.016448974609375,
0.00016987323760986328,
-0.005580902099609375,
0.0102996826171875,
-0.00494384765625,
-0.009674072265625,
-0.0157928466796875,
-0.048095703125,
-0.0426025390625,
-0.0034351348876953125,
0.0164337158203125,
-0.00754547119140625,
0.01023101806640625,
-0.00748443603515625,
-0.01268768310546875,
-0.005687713623046875,
0.0207061767578125,
-0.0012912750244140625,
-0.00484466552734375,
0.006259918212890625,
0.01503753662109375,
0.043121337890625,
0.06365966796875,
-0.05169677734375,
0.0013866424560546875,
-0.00047850608825683594,
-0.001163482666015625,
-0.016815185546875,
0.010406494140625,
-0.005397796630859375,
0.00853729248046875,
0.0013360977172851562,
0.00792694091796875,
0.0205535888671875,
-0.0158843994140625,
0.0158538818359375,
-0.00836181640625,
0.0162506103515625,
0.01409149169921875,
0.0011157989501953125,
0.004283905029296875,
0.00439453125,
-0.0292510986328125,
0.0192718505859375,
0.01447296142578125,
0.0224151611328125,
-0.01104736328125,
-0.01885986328125,
-0.01148223876953125,
-0.00443267822265625,
0.0027065277099609375,
0.00677490234375,
0.0141143798828125,
0.0213775634765625,
-0.01045989990234375,
-0.007152557373046875,
0.0049591064453125,
-0.018402099609375,
0.02008056640625,
-0.0200958251953125,
-0.0009045600891113281,
-0.03466796875,
0.00823974609375,
-0.0137176513671875,
0.01551055908203125,
0.01108551025390625,
-0.006923675537109375,
0.01250457763671875,
-0.0009140968322753906,
-0.0238800048828125,
0.032745361328125,
0.009674072265625,
-0.00848388671875,
-0.00922393798828125,
0.02618408203125,
-0.0267791748046875,
0.034942626953125,
0.01464080810546875,
-0.007259368896484375,
-0.0009541511535644531,
-0.006198883056640625,
-0.00440216064453125,
0.0163116455078125,
0.0012922286987304688,
-0.0016241073608398438,
-0.0003516674041748047,
0.006496429443359375,
-0.0211944580078125,
-0.08160400390625,
-0.001445770263671875,
0.031524658203125,
0.0140228271484375,
-0.01062774658203125,
-0.0310821533203125,
-0.0015869140625,
-0.032318115234375,
-0.0229034423828125,
0.0003829002380371094,
-0.0089111328125,
-0.021820068359375,
0.00438690185546875,
-0.0057830810546875,
-0.0151519775390625,
0.02520751953125,
-0.02130126953125,
-0.006168365478515625,
-0.00891876220703125,
-0.0130767822265625,
-0.0078582763671875,
0.020477294921875,
-0.0166168212890625,
-0.024932861328125,
-0.019866943359375,
-0.01474761962890625,
-0.0008478164672851562,
0.0367431640625,
-0.01548004150390625,
0.031494140625,
0.0135650634765625,
-0.0239105224609375,
0.0233154296875,
0.0207977294921875,
-0.017791748046875,
0.0252685546875,
-0.007625579833984375,
0.003772735595703125,
0.0208892822265625,
-0.009429931640625,
0.015289306640625,
0.009063720703125,
-0.01375579833984375,
-0.00402069091796875,
0.015167236328125,
0.01007080078125,
-0.005420684814453125,
-0.0013666152954101562,
0.0025234222412109375,
0.0098876953125,
0.01690673828125,
0.0460205078125,
0.031402587890625,
0.0043487548828125,
-0.01812744140625,
-0.01560211181640625,
-0.008087158203125,
0.02410888671875,
-0.032379150390625,
-0.046844482421875,
0.018035888671875,
0.051605224609375,
-0.019500732421875,
-0.00803375244140625,
-0.01715087890625,
0.007198333740234375,
0.003009796142578125,
-0.0018320083618164062,
0.01035308837890625,
-0.0177764892578125,
-0.0030689239501953125,
-0.036285400390625,
0.047149658203125,
0.005809783935546875,
0.0148162841796875,
0.0135498046875,
-0.051239013671875,
-0.0116424560546875,
-0.0142364501953125,
-0.0482177734375,
0.0220489501953125,
-0.00640869140625,
0.0194854736328125,
-0.02447509765625,
0.01824951171875,
0.0247344970703125,
-0.019989013671875,
-0.0290374755859375,
-0.0095977783203125,
-0.01496124267578125,
0.00559234619140625,
0.01702880859375,
-0.0002956390380859375,
-0.012237548828125,
0.002300262451171875,
0.023223876953125,
0.06182861328125,
-0.01021575927734375,
-0.03961181640625,
-0.0159759521484375,
-0.007266998291015625,
0.00881195068359375,
0.0177001953125,
-0.00885772705078125,
-0.0018310546875,
0.03326416015625,
-0.041412353515625,
0.0281829833984375,
0.01163482666015625,
0.0236968994140625,
-0.00717926025390625,
0.0143280029296875,
0.02386474609375,
0.00518035888671875,
0.0224761962890625,
0.0234832763671875,
0.0007915496826171875,
0.00399017333984375,
-0.03839111328125,
0.021331787109375,
-0.007904052734375,
0.0243988037109375,
-0.0171966552734375,
-0.0077056884765625,
0.017730712890625,
-0.038604736328125,
0.01702880859375,
0.043609619140625,
-0.0357666015625,
0.002407073974609375,
0.00659942626953125,
-0.0037822723388671875,
-0.00948333740234375,
0.02691650390625,
-0.0151519775390625,
-0.01343536376953125,
0.00530242919921875,
0.02178955078125,
0.01873779296875,
-0.036407470703125,
-0.0010528564453125,
-0.0214691162109375,
-0.021514892578125,
0.0175628662109375,
0.033721923828125,
-0.0183868408203125,
-0.022857666015625,
-0.0002453327178955078,
-0.0299530029296875,
-0.01763916015625,
0.017547607421875,
-0.00356292724609375,
-0.006961822509765625,
-0.0105133056640625,
0.01505279541015625,
0.022674560546875,
-0.005558013916015625,
0.00933074951171875,
-0.0087890625,
-0.0227508544921875,
-0.017974853515625,
0.019927978515625,
0.0203704833984375,
-0.016448974609375,
0.01499176025390625,
0.0240631103515625,
-0.0164642333984375,
0.032470703125,
0.0117950439453125,
-0.0143280029296875,
-0.0214080810546875,
0.0246124267578125,
-0.0279693603515625,
0.0023899078369140625,
-0.0360107421875,
-0.01136016845703125,
-0.025909423828125,
-0.00785064697265625,
0.0189056396484375,
-0.00797271728515625,
-0.0203857421875,
-0.01312255859375,
0.00727081298828125,
0.0190277099609375,
-0.02166748046875,
0.00501251220703125,
0.0234222412109375,
0.01363372802734375,
-0.0100555419921875,
-0.002925872802734375,
-0.0229034423828125,
-0.01470184326171875,
0.021636962890625,
-0.006855010986328125,
-0.0115814208984375,
-0.0200653076171875,
0.00551605224609375,
0.0008945465087890625,
0.006763458251953125,
-0.00785064697265625,
-0.03802490234375,
0.01076507568359375,
-0.0029964447021484375,
0.005664825439453125,
-0.01560211181640625,
0.026824951171875,
0.022430419921875,
-0.033905029296875,
0.0213623046875,
-0.002391815185546875,
0.028594970703125,
-0.0295562744140625,
-0.01495361328125,
-0.017181396484375,
-0.0210723876953125,
-0.00033402442932128906,
0.006122589111328125,
-0.0254058837890625,
0.01258087158203125,
0.01364898681640625,
0.0159912109375,
-0.020477294921875,
0.006214141845703125,
0.0066680908203125,
-0.00769805908203125,
-0.00420379638671875,
0.01373291015625,
-0.0273590087890625,
0.01953125,
-0.02569580078125,
-0.0196380615234375,
-0.01454925537109375,
-0.026123046875,
0.01148223876953125,
0.00223541259765625,
-0.0141143798828125,
0.0003497600555419922,
0.01427459716796875,
-0.0066070556640625,
-0.054168701171875,
0.0124664306640625,
-0.01445770263671875,
0.01490020751953125,
-0.0100555419921875,
-0.014404296875,
-0.00732421875,
-0.01184844970703125,
0.0184173583984375,
-0.06329345703125,
-0.037872314453125,
0.0008730888366699219,
-0.007503509521484375,
0.0018701553344726562,
0.01108551025390625,
0.0013332366943359375,
-0.0191497802734375,
-0.005413055419921875,
0.00708770751953125,
0.032562255859375,
0.01220703125,
0.019012451171875,
-0.024932861328125,
-0.037078857421875,
0.00958251953125,
0.0005326271057128906,
0.0136871337890625,
0.01256561279296875,
0.007671356201171875,
0.0233154296875,
0.005523681640625,
0.0015316009521484375,
-0.0018939971923828125,
-0.0274200439453125,
0.02337646484375,
-0.0015058517456054688,
0.0185699462890625,
-0.0298614501953125,
0.0050201416015625,
-0.020904541015625,
-0.0232086181640625,
0.018829345703125,
-0.0096282958984375,
0.00798797607421875,
0.0145263671875,
-0.001911163330078125,
0.02032470703125,
0.0176849365234375,
0.0209197998046875,
-0.0079498291015625,
0.005084991455078125,
0.0286102294921875,
0.0262603759765625,
0.0013637542724609375,
0.0188751220703125,
-0.007415771484375,
0.0009012222290039062,
-0.00728607177734375,
-0.0104522705078125,
0.00884246826171875,
0.00875091552734375,
-0.0216064453125,
0.007083892822265625,
-0.0010919570922851562,
0.0212860107421875,
-0.046478271484375,
0.00890350341796875,
-0.00830841064453125,
0.03204345703125,
-0.0197296142578125,
-0.01165771484375,
-0.006622314453125,
-0.0224761962890625,
0.0286102294921875,
-0.02691650390625,
0.0175018310546875,
-0.002887725830078125,
-0.0172576904296875,
-0.007808685302734375,
0.00702667236328125,
-0.0338134765625,
-0.004207611083984375,
0.00490570068359375,
-0.00150299072265625,
0.0171051025390625,
0.007617950439453125,
0.00470733642578125,
-0.00580596923828125,
-0.0283355712890625,
-0.006275177001953125,
0.049896240234375,
0.0170440673828125,
-0.01739501953125,
-0.04547119140625,
0.005462646484375,
0.00959014892578125,
-0.0150146484375,
0.0014543533325195312,
-0.0194244384765625,
0.0260162353515625,
0.006717681884765625,
-0.00921630859375,
-0.0196075439453125,
-0.049072265625,
-0.02734375,
-0.0173797607421875,
0.04302978515625,
-0.0138092041015625,
0.0169219970703125,
0.00937652587890625,
-0.03924560546875,
-0.03387451171875,
0.01776123046875,
-0.025146484375,
-0.006778717041015625,
-0.0137176513671875,
0.0123748779296875,
0.02252197265625,
-0.010223388671875,
-0.031951904296875,
-0.012420654296875,
-0.0185699462890625,
0.0068817138671875,
-0.00977325439453125,
0.0020294189453125,
0.004207611083984375,
-0.025634765625,
-0.01702880859375,
0.010101318359375,
-0.0097198486328125,
-0.0277252197265625,
0.003467559814453125,
-0.0380859375,
-0.036529541015625,
-0.0399169921875,
0.01045989990234375,
-0.027557373046875,
-0.03369140625,
0.0180206298828125,
-0.01430511474609375,
0.023529052734375,
-0.0183563232421875,
-0.0290679931640625,
0.0233154296875,
0.0277099609375,
-0.001247406005859375,
0.0162506103515625,
-0.006305694580078125,
0.004230499267578125,
0.0119171142578125,
0.0094757080078125,
0.005481719970703125,
-0.035003662109375,
0.021270751953125,
0.038055419921875,
-0.0131378173828125,
0.0082855224609375,
0.0026454925537109375,
-0.0078582763671875,
-0.0147857666015625,
-0.0151214599609375,
-0.031982421875,
-0.002399444580078125,
-0.032928466796875,
-0.01064300537109375,
-0.0247650146484375,
0.0201263427734375,
-0.00644683837890625,
-0.01326751708984375,
0.01271820068359375,
-0.019073486328125,
0.00537872314453125,
0.0027408599853515625,
0.0008654594421386719,
-0.0243072509765625,
0.0264129638671875,
0.02734375,
-0.0034847259521484375,
-0.0169219970703125,
-0.018768310546875,
0.03125,
-0.0144500732421875,
-0.00507354736328125,
0.00836181640625,
-0.018463134765625,
0.0003910064697265625,
-0.01338958740234375,
-0.0027904510498046875,
0.022705078125,
-0.0002732276916503906,
-0.0233154296875,
0.0172882080078125,
-0.006076812744140625,
0.004245758056640625,
0.020660400390625,
0.031097412109375,
0.0032520294189453125,
-0.007755279541015625,
-0.0377197265625,
-0.00275421142578125,
-0.0171661376953125,
0.02508544921875,
0.0105133056640625,
0.0102386474609375,
-0.01486968994140625,
0.00954437255859375,
-0.00800323486328125,
0.0128631591796875,
0.042022705078125,
0.0014934539794921875,
-0.01058197021484375,
-0.035491943359375,
-0.00525665283203125,
0.051971435546875,
-0.006015777587890625,
-0.0203094482421875,
-0.006214141845703125,
0.05670166015625,
-0.03912353515625,
0.018646240234375,
0.00217437744140625,
0.0341796875,
0.0213775634765625,
0.00983428955078125,
-0.01641845703125,
-0.00011020898818969727,
0.00814056396484375,
-0.0162506103515625,
0.0216827392578125,
-0.0222320556640625,
-0.011962890625,
-0.0008563995361328125,
0.006038665771484375,
-0.001678466796875,
0.036590576171875,
-0.0176849365234375,
0.00794219970703125,
-0.00699615478515625,
-0.005748748779296875,
0.0110626220703125,
0.017578125,
0.04034423828125,
0.0009627342224121094,
0.0301513671875,
0.029510498046875,
-0.034088134765625,
0.0214996337890625,
0.01282501220703125,
0.018035888671875,
0.01044464111328125,
0.032318115234375,
0.0013799667358398438,
0.028900146484375,
-0.01230621337890625,
-0.00812530517578125,
0.0140228271484375,
-0.017333984375,
0.005748748779296875,
0.01605224609375,
-0.00431060791015625,
0.02166748046875,
-0.01116180419921875,
0.0041961669921875,
-0.014068603515625,
0.0217132568359375,
-0.017333984375,
0.00867462158203125,
0.0203399658203125,
0.0022487640380859375,
-0.0159454345703125,
-0.021728515625,
-0.0017147064208984375,
-0.025848388671875,
0.01409149169921875,
0.00431060791015625,
0.0273590087890625,
-0.0029144287109375,
0.03955078125,
0.0186767578125,
0.02850341796875,
-0.0010366439819335938,
0.0032558441162109375,
0.0068359375,
0.0036792755126953125,
-0.04071044921875,
0.0430908203125,
0.0096588134765625,
-0.00292205810546875,
-0.01235198974609375,
-0.01549530029296875,
-0.0304718017578125,
-0.00017380714416503906,
0.03912353515625,
0.018829345703125,
-0.019073486328125,
0.025360107421875,
-0.01380157470703125,
0.0325927734375,
-0.017059326171875,
0.00971221923828125,
-0.017059326171875,
0.009063720703125,
-0.0148162841796875,
-0.03179931640625,
-0.01055908203125,
-0.004489898681640625,
0.01080322265625,
-0.002960205078125,
-0.0093841552734375,
0.00775909423828125,
0.00024175643920898438,
-0.006134033203125,
-0.02117919921875,
0.01165008544921875,
0.002132415771484375,
-0.00888824462890625,
-0.0029392242431640625,
0.003177642822265625,
0.022674560546875,
-0.00542449951171875,
-0.0153961181640625,
-0.0426025390625,
0.0029754638671875,
0.0032634735107421875,
-0.002948760986328125,
0.0064239501953125,
0.0104827880859375,
0.004077911376953125,
-0.016754150390625,
0.00392913818359375,
-0.0005893707275390625,
0.009857177734375,
0.01739501953125,
0.051666259765625,
0.007633209228515625,
-0.0281829833984375,
-0.0224456787109375,
-0.01000213623046875,
0.0033435821533203125,
-0.03472900390625,
-0.00010734796524047852,
-0.01558685302734375,
-0.0019378662109375,
0.0186920166015625,
0.034637451171875,
0.0161590576171875,
-0.037384033203125,
-0.0335693359375,
0.00907135009765625,
-0.0244598388671875,
-0.003276824951171875,
0.0135040283203125,
-0.000354766845703125,
-0.0010805130004882812,
0.005084991455078125,
-0.0006847381591796875,
0.0245208740234375,
0.0249786376953125,
-0.0229339599609375,
-0.0045318603515625,
-0.0213775634765625,
0.004734039306640625,
0.0112457275390625,
-0.0060577392578125,
-0.0038127899169921875,
-0.0313720703125,
-0.03265380859375,
-0.00432586669921875,
0.0156707763671875,
0.01100921630859375,
0.0166015625,
-0.00969696044921875,
-0.0062103271484375,
-0.0031948089599609375,
-0.00630950927734375,
0.01157379150390625,
-0.006092071533203125,
-0.019439697265625,
-0.00632476806640625,
0.02337646484375,
-0.0223388671875,
0.03326416015625,
-0.005908966064453125,
0.007904052734375,
-0.036163330078125,
0.0160064697265625,
0.0134735107421875,
0.0038204193115234375,
-0.01103973388671875,
0.0038433074951171875,
-0.0136260986328125,
0.013671875,
0.0012960433959960938,
0.0158538818359375,
0.015472412109375,
0.004604339599609375,
-0.0169677734375,
-0.01442718505859375,
-0.018341064453125,
-0.025726318359375,
0.017547607421875,
-0.00759124755859375,
-0.0186004638671875,
-0.0102386474609375,
-0.0015201568603515625,
0.0257415771484375,
0.0018100738525390625,
0.0033512115478515625,
0.00861358642578125,
-0.0015344619750976562,
-0.01097869873046875,
-0.0291900634765625,
0.004486083984375,
0.006214141845703125,
0.001583099365234375,
-0.01090240478515625,
0.01253509521484375,
0.01390838623046875,
-0.00510406494140625,
0.01497650146484375,
0.004405975341796875,
0.02227783203125,
0.010040283203125,
-0.00676727294921875,
-0.0023365020751953125,
0.0313720703125,
-0.011077880859375,
-0.016845703125,
0.00010448694229125977,
-0.0170135498046875,
0.027862548828125,
0.0227203369140625,
-0.0185394287109375,
-0.0028743743896484375,
0.00469970703125,
0.0302276611328125,
-0.049713134765625,
-0.043060302734375,
0.01004791259765625,
-0.03533935546875,
0.0250396728515625,
0.00946807861328125,
-0.0195159912109375,
-0.0308074951171875,
0.027740478515625,
0.0115966796875,
-0.00742340087890625,
0.0079498291015625,
-0.01898193359375,
0.0303802490234375,
0.052490234375,
0.0291290283203125,
-0.0183563232421875,
-0.0251007080078125,
-0.0074310302734375,
-0.018707275390625,
0.0058135986328125,
0.012481689453125,
0.003910064697265625,
-0.0018482208251953125,
0.015960693359375,
-0.0033969879150390625,
0.0252838134765625,
-0.0035533905029296875,
0.01238250732421875,
-0.02490234375,
0.005908966064453125,
0.0221405029296875,
0.0147552490234375,
-0.0232086181640625,
0.0013475418090820312,
-0.00701141357421875,
-0.006748199462890625,
0.003368377685546875,
-0.010589599609375,
0.01248931884765625,
-0.01396942138671875,
0.002529144287109375,
0.00870513916015625,
0.0295257568359375,
0.006984710693359375,
0.011322021484375,
-0.050140380859375,
-0.0224456787109375,
-0.0184173583984375,
0.013427734375,
0.0009899139404296875,
-0.007843017578125,
0.000006079673767089844,
-0.006206512451171875,
-0.005214691162109375,
-0.0293121337890625,
0.0158233642578125,
0.01019287109375,
-0.008758544921875,
-0.00959014892578125,
0.0162200927734375,
-0.023834228515625,
-0.006870269775390625,
-0.0002589225769042969,
-0.0177459716796875,
-0.0086822509765625,
0.0023784637451171875,
-0.0186767578125,
0.0123748779296875,
-0.01421356201171875,
0.021636962890625,
0.0129547119140625,
0.019073486328125,
-0.039306640625,
-0.0151519775390625,
0.0386962890625,
-0.032073974609375,
0.0020389556884765625,
-0.0024929046630859375,
0.01393890380859375,
-0.0111541748046875,
0.026275634765625,
0.00511932373046875,
-0.005100250244140625,
0.01345062255859375,
0.01369476318359375,
-0.0226593017578125,
-0.003047943115234375,
0.01549530029296875,
0.00954437255859375,
0.0008831024169921875,
-0.039764404296875,
0.0308074951171875,
0.0207977294921875,
-0.030029296875,
0.0193634033203125,
-0.0125885009765625,
0.0266571044921875,
-0.0156402587890625,
0.04949951171875,
-0.0099029541015625,
-0.0204315185546875,
0.0164642333984375,
0.0015020370483398438,
0.00664520263671875,
0.0088348388671875,
-0.0204925537109375,
-0.02044677734375,
0.0107879638671875,
-0.01183319091796875,
-0.01947021484375,
0.002685546875,
0.006984710693359375,
0.006946563720703125,
0.0147552490234375,
-0.0096435546875,
-0.0033130645751953125,
-0.0017061233520507812,
-0.0014562606811523438,
-0.0113525390625,
-0.00362396240234375,
0.028350830078125,
-0.03582763671875,
-0.0007257461547851562,
-0.0013027191162109375,
0.005016326904296875,
-0.0084991455078125,
-0.0017099380493164062,
-0.01373291015625,
0.0034027099609375,
0.00312042236328125,
-0.030181884765625,
-0.037567138671875,
-0.00383758544921875,
0.036468505859375,
0.003932952880859375,
0.0172271728515625,
0.02252197265625,
-0.043121337890625,
0.006923675537109375,
-0.0007758140563964844,
-0.0303802490234375,
0.0072479248046875,
-0.01947021484375,
0.00965118408203125,
-0.007137298583984375,
0.002376556396484375,
-0.00904083251953125,
-0.0078125,
0.00228118896484375,
-0.0013456344604492188,
-0.0172119140625,
-0.01042938232421875,
-0.0085601806640625,
-0.0118560791015625,
-0.0207061767578125,
0.0031986236572265625,
0.04791259765625,
0.0036869049072265625,
0.00269317626953125,
-0.0049591064453125,
0.03631591796875,
-0.006351470947265625,
0.02435302734375,
0.01192474365234375,
0.026702880859375,
0.0019512176513671875,
0.0295867919921875,
-0.0033473968505859375,
0.00971221923828125,
0.016387939453125,
-0.03228759765625,
-0.019683837890625,
-0.028350830078125,
0.0279541015625,
0.01137542724609375,
-0.03369140625,
0.0116729736328125,
-0.03167724609375,
0.02740478515625,
0.005573272705078125,
0.014434814453125,
-0.0030841827392578125,
-0.0144195556640625,
-0.0182342529296875,
-0.0182647705078125,
0.0167999267578125,
-0.0178985595703125,
0.02215576171875,
-0.039794921875,
-0.00859832763671875,
0.012969970703125,
-0.0090484619140625,
0.028472900390625,
0.0125732421875,
-0.0257110595703125,
0.033538818359375,
0.003971099853515625,
0.04449462890625,
-0.00484466552734375,
0.02301025390625,
-0.0041351318359375,
-0.0230712890625,
0.0171051025390625,
0.005107879638671875,
0.003955841064453125,
0.001049041748046875,
-0.0158538818359375,
0.0007419586181640625,
0.0079345703125,
-0.0166778564453125,
-0.00769805908203125,
0.0309295654296875,
-0.005096435546875,
0.0029697418212890625,
-0.0215911865234375,
0.0012836456298828125,
0.031402587890625,
0.00010210275650024414,
-0.0129241943359375,
0.025787353515625,
-0.0068511962890625,
-0.019073486328125,
0.02410888671875,
-0.0188446044921875,
0.024017333984375,
-0.0242919921875,
0.0008363723754882812,
0.04046630859375,
0.0192108154296875,
-0.00476837158203125,
-0.0253753662109375,
-0.023162841796875,
-0.003139495849609375,
-0.02618408203125,
-0.032257080078125,
0.01454925537109375,
-0.0162811279296875,
-0.0038051605224609375,
0.000019729137420654297,
0.0209503173828125,
0.005096435546875,
0.007091522216796875,
0.0239715576171875,
0.0250091552734375,
0.0189971923828125,
-0.00437164306640625,
0.017730712890625,
-0.01175689697265625,
0.00007539987564086914,
0.016998291015625,
0.024658203125,
-0.0171356201171875,
-0.0206146240234375,
-0.00382232666015625,
0.0180511474609375,
0.002223968505859375,
-0.011474609375,
-0.02191162109375,
0.01256561279296875,
0.0017032623291015625,
0.00865936279296875,
-0.0227508544921875,
0.0008745193481445312,
-0.01255035400390625,
0.015716552734375,
-0.0175628662109375,
0.0033817291259765625,
-0.0287628173828125,
-0.014801025390625,
-0.009735107421875,
0.040924072265625,
-0.045013427734375,
-0.021148681640625,
0.0004982948303222656,
0.004344940185546875,
-0.0355224609375,
0.01172637939453125,
0.01479339599609375,
-0.047882080078125,
0.0165557861328125,
-0.00626373291015625,
-0.0226287841796875,
0.02032470703125,
-0.01091766357421875,
0.0159912109375,
0.0277252197265625,
0.032440185546875,
0.0088958740234375,
0.023406982421875,
0.01348114013671875,
-0.0091400146484375,
-0.0117034912109375,
0.029632568359375,
0.0340576171875,
0.00824737548828125,
-0.0216522216796875,
0.00783538818359375,
0.0195770263671875,
-0.027740478515625,
-0.0245208740234375,
0.02801513671875,
-0.01103973388671875,
-0.01471710205078125,
0.0005483627319335938,
-0.01361083984375,
-0.022247314453125,
0.01442718505859375,
-0.002971649169921875,
0.0090179443359375,
-0.0306396484375,
0.0208740234375,
-0.01033782958984375,
-0.034942626953125,
-0.011962890625,
-0.0117034912109375,
-0.0010576248168945312,
0.00345611572265625,
0.00978851318359375,
-0.0099639892578125,
0.0015993118286132812,
0.007328033447265625,
-0.02105712890625,
0.00033926963806152344,
0.008697509765625,
-0.0184478759765625,
0.005039215087890625,
-0.0031280517578125,
-0.0039825439453125,
-0.00354766845703125,
0.00902557373046875,
0.0290679931640625,
0.03314208984375,
-0.00682830810546875,
0.000980377197265625,
-0.02825927734375,
0.0131378173828125,
0.014495849609375,
0.003948211669921875,
-0.0151519775390625,
0.0182647705078125,
0.00460052490234375,
-0.007030487060546875,
-0.033447265625,
0.0225067138671875,
-0.0333251953125,
0.01096343994140625,
0.009918212890625,
-0.01322174072265625,
0.022918701171875,
0.043792724609375,
0.035888671875,
-0.0285186767578125,
-0.0017766952514648438,
-0.019195556640625,
-0.021728515625,
0.0271453857421875,
-0.01305389404296875,
-0.01538848876953125,
-0.01045989990234375,
0.00009399652481079102,
-0.01202392578125,
-0.0011434555053710938,
-0.032470703125,
0.0026760101318359375,
0.0030841827392578125,
-0.00882720947265625,
0.01898193359375,
0.0305938720703125,
0.0220184326171875,
-0.0019426345825195312,
-0.004779815673828125,
0.01183319091796875,
-0.0154571533203125,
-0.0396728515625,
0.01293182373046875,
0.01322174072265625,
0.02020263671875,
-0.0158233642578125,
-0.029632568359375,
0.010650634765625,
-0.0173797607421875,
-0.00399017333984375,
-0.00553131103515625,
0.0189208984375,
0.01108551025390625,
-0.0286712646484375,
0.0192413330078125,
0.0084381103515625,
-0.00136566162109375,
-0.0322265625,
0.0073394775390625,
-0.004077911376953125,
0.0258026123046875,
0.04437255859375,
0.0020999908447265625,
-0.01285552978515625,
0.038482666015625,
0.02728271484375,
-0.0023822784423828125,
0.002300262451171875,
-0.0443115234375,
0.00908660888671875,
-0.017822265625,
0.016510009765625,
-0.007411956787109375,
0.02508544921875,
-0.0199737548828125,
-0.0015211105346679688,
-0.0181732177734375,
-0.011199951171875,
0.0037555694580078125,
0.044647216796875,
0.02587890625,
-0.005207061767578125,
-0.035125732421875,
-0.02655029296875,
0.0097808837890625,
0.0029926300048828125,
-0.00481414794921875,
-0.01190948486328125,
-0.017913818359375,
0.0137481689453125,
-0.00667572021484375,
0.049835205078125,
0.02069091796875,
-0.001850128173828125,
-0.0137939453125,
0.0078277587890625,
-0.0223388671875,
0.0234527587890625,
-0.0128021240234375,
0.0084381103515625,
0.011810302734375,
0.035308837890625,
-0.032012939453125,
0.0154266357421875,
0.011505126953125,
-0.006328582763671875,
-0.0308380126953125,
0.01142120361328125,
-0.01110076904296875,
-0.0182342529296875,
-0.0008358955383300781,
-0.019378662109375,
-0.0085906982421875,
0.00856781005859375,
-0.001216888427734375,
-0.0294342041015625,
-0.005466461181640625,
0.0184173583984375,
-0.036041259765625,
0.00689697265625,
-0.00396728515625,
0.03875732421875,
0.01274871826171875,
0.004840850830078125,
-0.00982666015625,
-0.02362060546875,
0.0006718635559082031,
0.00951385498046875,
-0.00037860870361328125,
-0.0135955810546875,
0.032196044921875,
0.0286865234375,
-0.0119171142578125,
0.016693115234375,
0.004886627197265625,
0.02142333984375,
-0.007686614990234375,
0.0274658203125,
-0.0139007568359375,
0.00620269775390625,
0.007305145263671875,
-0.00539398193359375,
0.013641357421875,
-0.0050201416015625,
0.0281524658203125,
0.01493072509765625,
-0.00811004638671875,
0.023406982421875,
-0.01186370849609375,
0.0263671875,
-0.01338958740234375,
-0.00298309326171875,
-0.005321502685546875,
0.0369873046875,
0.027923583984375,
-0.004932403564453125,
-0.0233917236328125,
0.0140380859375,
-0.024383544921875,
-0.01496124267578125,
-0.0171051025390625,
0.019744873046875,
0.00560760498046875,
0.035064697265625,
0.040863037109375,
-0.003879547119140625,
-0.01153564453125,
0.00545501708984375,
0.00815582275390625,
-0.034637451171875,
-0.014007568359375,
-0.0039005279541015625,
-0.005126953125,
0.01219940185546875,
0.01361846923828125,
-0.004512786865234375,
-0.0047149658203125,
-0.017333984375,
0.005344390869140625,
-0.0032100677490234375,
0.01345062255859375,
0.017852783203125,
-0.00853729248046875,
-0.01194000244140625,
0.038970947265625,
0.007038116455078125,
0.0015659332275390625,
-0.011505126953125,
0.033843994140625,
0.00868988037109375,
-0.005252838134765625,
-0.002597808837890625,
-0.0447998046875,
0.0241851806640625,
-0.00702667236328125,
0.04437255859375,
0.00783538818359375,
-0.004241943359375,
0.020843505859375,
0.0206756591796875,
0.0211181640625,
-0.046966552734375,
0.0109405517578125,
0.0165557861328125,
0.002643585205078125,
-0.0212860107421875,
0.01229095458984375,
0.0106658935546875,
0.00853729248046875,
-0.01824951171875,
-0.01332855224609375,
0.0007295608520507812,
0.01519775390625,
0.047607421875,
0.0243072509765625,
0.0149993896484375,
0.0306396484375,
0.031219482421875,
-0.00919342041015625,
-0.00009846687316894531,
-0.035858154296875,
-0.00931549072265625,
0.0030670166015625,
-0.005031585693359375,
-0.01183319091796875,
0.005466461181640625,
-0.02423095703125,
0.027496337890625,
0.0240020751953125,
-0.0005979537963867188,
-0.0011005401611328125,
-0.016387939453125,
-0.01546478271484375,
0.0033931732177734375,
0.01198577880859375,
-0.00743865966796875,
0.01220703125,
0.0150299072265625,
-0.0090179443359375,
0.031463623046875,
-0.01413726806640625,
-0.0151214599609375,
0.0092926025390625,
-0.017547607421875,
-0.0120391845703125,
-0.0047454833984375,
-0.0281524658203125,
0.0226287841796875,
-0.0007376670837402344,
0.004428863525390625,
-0.01532745361328125,
0.00003218650817871094,
-0.005672454833984375,
0.0023040771484375,
-0.023345947265625,
0.0274658203125,
0.005764007568359375,
0.0032520294189453125,
0.03857421875,
-0.002132415771484375,
0.003833770751953125,
-0.01490020751953125,
0.0258636474609375,
-0.018646240234375,
0.0110931396484375,
0.0276336669921875,
-0.01291656494140625,
0.0076446533203125,
0.0038089752197265625,
0.0007610321044921875,
0.016082763671875,
-0.018524169921875,
-0.0174102783203125,
-0.043609619140625,
-0.006313323974609375,
-0.00392913818359375,
-0.01334381103515625,
0.0048828125,
-0.0026454925537109375,
0.0004696846008300781,
0.00824737548828125,
0.0133514404296875,
-0.003284454345703125,
-0.0145416259765625,
0.00182342529296875,
0.016998291015625,
0.0146484375,
0.01282501220703125,
0.00778961181640625,
-0.0073394775390625,
0.0304718017578125,
0.0178375244140625,
0.00995635986328125,
0.005435943603515625,
-0.005794525146484375,
-0.024444580078125,
0.01727294921875,
-0.00498199462890625,
-0.0204620361328125,
-0.006641387939453125,
-0.0193023681640625,
0.0142059326171875,
0.00290679931640625,
0.006397247314453125,
-0.0032806396484375,
-0.00913238525390625,
0.02783203125,
0.01824951171875,
-0.012847900390625,
-0.01666259765625,
-0.0033473968505859375,
-0.0161285400390625,
-0.0019016265869140625,
0.00438690185546875,
0.036224365234375,
-0.0102386474609375,
-0.03399658203125,
0.0099334716796875,
-0.00989532470703125,
0.01041412353515625,
-0.01154327392578125,
-0.01049041748046875,
-0.0166168212890625,
0.0362548828125,
-0.01006317138671875,
-0.00662994384765625,
-0.0052642822265625,
-0.02972412109375,
-0.004802703857421875,
-0.027923583984375,
0.0109100341796875,
-0.01152801513671875,
-0.0181884765625,
0.00962066650390625,
-0.0251617431640625,
-0.0160064697265625,
0.01064300537109375,
0.0117950439453125,
-0.01226806640625,
-0.0091552734375,
0.01271820068359375,
-0.006626129150390625,
-0.036834716796875,
-0.0052490234375,
0.011505126953125,
0.028045654296875,
0.0078277587890625,
0.00249481201171875,
-0.059173583984375,
0.0169830322265625,
0.0201263427734375,
-0.029266357421875,
-0.00884246826171875,
-0.0241241455078125,
-0.0004138946533203125,
-0.01216888427734375,
-0.0110626220703125,
0.01313018798828125,
-0.041290283203125,
0.01305389404296875,
-0.019866943359375,
-0.023406982421875,
0.01129150390625,
0.0309600830078125,
-0.0145721435546875,
0.0003764629364013672,
-0.01464080810546875,
-0.002185821533203125,
0.043487548828125,
0.0182952880859375,
0.00458526611328125,
0.0216827392578125,
-0.020904541015625,
0.025848388671875,
0.0242156982421875,
-0.043731689453125,
-0.00019562244415283203,
0.0008916854858398438,
0.0284881591796875,
0.0130615234375,
0.005657196044921875,
-0.0389404296875,
-0.005809783935546875,
-0.00801849365234375,
-0.00341796875,
-0.0211944580078125,
0.0029544830322265625,
-0.0151824951171875,
0.0164642333984375,
0.0031986236572265625,
0.0036907196044921875,
-0.005527496337890625,
0.0102081298828125,
-0.021270751953125,
0.0017108917236328125,
0.0235137939453125,
0.0158233642578125,
-0.02117919921875,
0.04052734375,
-0.03900146484375,
-0.0022716522216796875,
0.0164031982421875,
-0.02581787109375,
0.0042877197265625,
-0.0103607177734375,
0.0224456787109375,
-0.003711700439453125,
0.0189361572265625,
0.0182342529296875,
0.00875091552734375,
-0.027191162109375,
-0.04345703125,
-0.0207672119140625,
0.0224151611328125,
0.0017633438110351562,
-0.0517578125,
0.02410888671875,
0.004039764404296875,
0.046905517578125,
-0.0190277099609375,
-0.0177154541015625,
0.0230560302734375,
0.00914764404296875,
0.018157958984375,
-0.0028934478759765625,
0.01248931884765625,
0.0577392578125,
0.01342010498046875,
0.02593994140625,
-0.0199737548828125,
-0.00576019287109375,
0.042266845703125,
0.0193023681640625,
-0.028900146484375,
-0.00292205810546875,
-0.0325927734375,
0.0020351409912109375,
-0.003246307373046875,
0.01140594482421875,
-0.0260162353515625,
0.027801513671875,
0.0008573532104492188,
0.003650665283203125,
-0.008056640625,
0.011962890625,
0.010986328125,
0.0180206298828125,
0.004787445068359375,
-0.00604248046875,
-0.012725830078125,
0.01361846923828125,
-0.0173187255859375,
0.015777587890625,
-0.0352783203125,
0.00768280029296875,
0.00960540771484375,
0.0229339599609375,
0.01079559326171875,
-0.039276123046875,
-0.00479888916015625,
-0.00531768798828125,
0.0091094970703125,
-0.027740478515625,
-0.00043964385986328125,
0.0027675628662109375,
0.01412200927734375,
0.005527496337890625,
0.01413726806640625,
-0.020263671875,
0.012054443359375,
-0.01483917236328125,
-0.00922393798828125,
0.037689208984375,
-0.0295257568359375,
-0.01324462890625,
0.033416748046875,
-0.01116180419921875,
-0.0025424957275390625,
0.00424957275390625,
0.002643585205078125,
0.01186370849609375,
-0.019866943359375,
-0.0169525146484375,
0.0251617431640625,
0.045989990234375,
0.02215576171875,
-0.0014848709106445312,
-0.006622314453125,
-0.01369476318359375,
0.0209808349609375,
0.00394439697265625,
0.01027679443359375,
0.002986907958984375,
0.00206756591796875,
0.0106658935546875,
-0.007354736328125,
0.028350830078125,
-0.032867431640625,
0.021484375,
-0.005306243896484375,
0.00860595703125,
-0.006412506103515625,
0.0274505615234375,
-0.0078582763671875,
-0.02215576171875,
-0.03582763671875,
0.007266998291015625,
0.0011272430419921875,
-0.037261962890625,
0.006931304931640625,
-0.0087432861328125,
-0.01485443115234375,
0.01447296142578125,
0.0124664306640625,
0.049957275390625,
0.0020732879638671875,
-0.0126800537109375,
-0.027740478515625,
0.00518798828125,
0.03192138671875,
-0.0036296844482421875,
-0.003910064697265625,
0.0124969482421875,
0.016998291015625,
-0.0264739990234375,
0.00978851318359375,
-0.0233612060546875,
-0.0223236083984375,
0.0056610107421875,
0.0177154541015625,
-0.0151824951171875,
0.006679534912109375,
0.004207611083984375,
-0.00653839111328125,
0.02374267578125,
0.0243072509765625,
0.02130126953125,
-0.01334381103515625,
-0.039520263671875,
-0.0057525634765625,
-0.0256500244140625,
0.005279541015625,
-0.0165252685546875,
0.0029296875,
-0.016448974609375,
-0.00244140625,
-0.00730133056640625,
0.01293182373046875,
-0.0013027191162109375,
-0.017669677734375,
-0.0009908676147460938,
0.032318115234375,
0.00832366943359375,
-0.0013370513916015625,
0.00196075439453125,
0.015777587890625,
-0.01534271240234375,
0.000820159912109375,
-0.013214111328125,
-0.0400390625,
-0.01364898681640625,
-0.0362548828125,
-0.0012035369873046875,
-0.0029754638671875,
-0.01812744140625,
0.010894775390625,
-0.01140594482421875,
-0.02392578125,
0.04058837890625,
-0.02191162109375,
0.0019130706787109375,
0.01788330078125,
-0.0155181884765625,
0.007709503173828125,
0.044036865234375,
-0.0208282470703125,
0.010009765625,
0.0012054443359375,
-0.0002086162567138672,
-0.008575439453125,
-0.01213836669921875,
0.0158538818359375,
-0.0202178955078125,
0.0014696121215820312,
-0.0147705078125,
0.01690673828125,
-0.0035686492919921875,
0.0235137939453125,
-0.0096282958984375,
0.008758544921875,
-0.0019741058349609375,
-0.00897979736328125,
0.022491455078125,
0.0013704299926757812,
0.0263214111328125,
0.0131683349609375,
-0.01148223876953125,
0.0082855224609375,
0.01264190673828125,
0.034271240234375,
0.0023746490478515625,
0.00751495361328125,
-0.033203125,
-0.01482391357421875,
0.036834716796875,
0.005016326904296875,
-0.0293731689453125,
-0.005283355712890625,
-0.00592041015625,
0.0231475830078125,
-0.014801025390625,
-0.0104217529296875,
0.053985595703125,
-0.029510498046875,
-0.0270538330078125,
0.00142669677734375,
0.00630950927734375,
-0.0135345458984375,
-0.0184173583984375,
-0.01119232177734375,
-0.0079498291015625,
-0.01416015625,
0.0139923095703125,
0.00942230224609375,
0.01280975341796875,
0.01087188720703125,
-0.0089263916015625,
-0.002941131591796875,
0.004840850830078125,
0.02789306640625,
0.00502777099609375,
0.017120361328125,
-0.0015096664428710938,
0.01497650146484375,
0.03155517578125,
0.000698089599609375,
0.018341064453125,
-0.0302581787109375,
-0.035919189453125,
-0.00324249267578125,
0.01287841796875,
-0.0002932548522949219,
0.03009033203125,
0.0367431640625,
0.01332855224609375,
-0.04486083984375,
0.0100860595703125,
-0.01153564453125,
0.02947998046875,
0.033538818359375,
0.0079803466796875,
-0.01380157470703125,
-0.0035076141357421875,
0.020599365234375,
0.0123443603515625,
-0.00823974609375,
0.00568389892578125,
-0.0150146484375,
-0.01519775390625,
0.0185546875,
-0.0028667449951171875,
-0.0197296142578125,
0.036773681640625,
-0.023162841796875,
0.007518768310546875,
-0.0088653564453125,
-0.017822265625,
0.00806427001953125,
-0.01873779296875,
0.00939178466796875,
0.0026454925537109375,
0.01227569580078125,
-0.0176544189453125,
-0.012542724609375,
0.03265380859375,
-0.0014858245849609375,
0.009429931640625,
-0.040130615234375,
0.005123138427734375,
0.024261474609375,
-0.0088653564453125,
0.045257568359375,
-0.02337646484375,
-0.0215606689453125,
0.005786895751953125,
0.00585174560546875,
0.00547027587890625,
-0.0023059844970703125,
0.00650787353515625,
0.01306915283203125,
-0.004062652587890625,
0.006793975830078125,
-0.0264129638671875,
0.004917144775390625,
-0.00284576416015625,
0.033233642578125,
-0.0211181640625,
0.0217742919921875,
0.01020050048828125,
-0.01331329345703125,
0.007579803466796875,
-0.0106048583984375,
0.018341064453125,
-0.0018320083618164062,
-0.0247039794921875,
-0.0080413818359375,
0.00931549072265625,
-0.004486083984375,
0.0187530517578125,
0.02899169921875,
-0.01788330078125,
0.045013427734375,
0.01001739501953125,
0.0165252685546875,
-0.0128173828125,
-0.002368927001953125,
-0.0170745849609375,
0.018829345703125,
0.0306854248046875,
-0.01529693603515625,
-0.0191650390625,
-0.01898193359375,
0.04095458984375,
-0.005107879638671875,
0.0225830078125,
0.00637054443359375,
-0.0015821456909179688,
0.01261138916015625,
0.011932373046875,
-0.020965576171875,
-0.0210723876953125,
-0.003856658935546875,
-0.006988525390625,
-0.002559661865234375,
-0.01367950439453125,
0.0087127685546875,
-0.003108978271484375,
-0.01654052734375,
-0.01384735107421875,
0.00833892822265625,
0.0001289844512939453,
0.01270294189453125,
0.0156707763671875,
-0.01203155517578125,
-0.004360198974609375,
0.029449462890625,
-0.0241546630859375,
-0.00983428955078125,
0.01483917236328125,
-0.02508544921875,
-0.032135009765625,
0.05340576171875,
0.00362396240234375,
0.01532745361328125,
-0.033050537109375,
-0.00608062744140625,
0.037750244140625,
0.022552490234375,
-0.033966064453125,
0.0136566162109375,
0.0258636474609375,
0.01428985595703125,
-0.014678955078125,
0.0186767578125,
-0.031402587890625,
0.00885009765625,
0.02740478515625,
0.0066375732421875,
-0.02978515625,
0.0008616447448730469,
-0.01404571533203125,
-0.0008730888366699219,
-0.000583648681640625,
-0.017608642578125,
0.032196044921875,
0.005588531494140625,
-0.018157958984375,
-0.01318359375,
0.0419921875,
-0.035247802734375,
0.018829345703125,
-0.0011529922485351562,
0.01081085205078125,
-0.010589599609375,
0.0263824462890625,
0.0194854736328125,
-0.003589630126953125,
0.0035076141357421875,
0.01490020751953125,
0.0243377685546875,
0.006771087646484375,
-0.00479888916015625,
0.01306915283203125,
0.0163116455078125,
-0.0034027099609375,
0.0179595947265625,
-0.034271240234375,
-0.01450347900390625,
-0.006038665771484375,
-0.0231781005859375,
0.00007301568984985352,
0.0015392303466796875,
-0.0216827392578125,
-0.02423095703125,
-0.0098724365234375,
0.02099609375,
-0.0137481689453125,
-0.0240020751953125,
0.01294708251953125,
-0.043853759765625,
0.021331787109375,
-0.01158905029296875,
-0.007068634033203125,
-0.0071563720703125,
0.020782470703125,
0.01093292236328125,
0.04547119140625,
-0.0178070068359375,
-0.027313232421875,
0.0226287841796875,
-0.0090484619140625,
-0.01171875,
-0.01372528076171875,
-0.0014448165893554688,
0.01251983642578125,
0.02752685546875,
0.002994537353515625,
0.002048492431640625,
-0.006542205810546875,
0.005290985107421875,
-0.0026836395263671875,
-0.039215087890625,
0.0026798248291015625,
-0.0073699951171875,
0.0179901123046875,
-0.039825439453125,
-0.0017404556274414062,
-0.0236663818359375,
0.0141448974609375,
-0.0262451171875,
0.021636962890625,
0.0071563720703125,
-0.00957489013671875,
0.009796142578125,
-0.0124969482421875,
0.0408935546875,
-0.018646240234375,
0.005275726318359375,
0.0151519775390625,
-0.01195526123046875,
0.024932861328125,
0.0086669921875,
-0.009368896484375,
0.0183563232421875,
-0.0010061264038085938,
-0.037506103515625,
-0.0016660690307617188,
0.0280914306640625,
-0.0283966064453125,
0.0104217529296875,
0.0018873214721679688,
-0.01605224609375,
0.011444091796875,
-0.0026378631591796875,
0.006984710693359375,
0.0038585662841796875,
0.024658203125,
0.01953125,
-0.0201568603515625,
0.0098724365234375,
0.01776123046875,
0.016937255859375,
0.01502227783203125,
0.01372528076171875,
-0.013519287109375,
0.0193634033203125,
-0.005950927734375,
0.0006880760192871094,
-0.0087127685546875,
-0.043304443359375,
-0.037567138671875,
0.0007519721984863281,
0.00458526611328125,
-0.00439453125,
-0.005718231201171875,
0.007709503173828125,
-0.033203125,
-0.0034637451171875,
-0.003200531005859375,
-0.010223388671875,
0.034149169921875,
0.0274505615234375,
0.033294677734375,
0.05255126953125,
0.025848388671875,
-0.0017147064208984375,
-0.0087890625,
0.057464599609375,
0.0149383544921875,
0.01123809814453125,
-0.01534271240234375,
-0.0225982666015625,
0.01364898681640625,
0.0014524459838867188,
0.0017871856689453125,
0.0031452178955078125,
0.004634857177734375,
0.033477783203125,
-0.0270538330078125,
0.0225982666015625,
0.01995849609375,
0.0155487060546875,
-0.003814697265625,
0.01338958740234375,
0.05377197265625,
0.0137786865234375,
-0.028778076171875,
-0.01244354248046875,
0.00785064697265625,
0.0207672119140625,
-0.005115509033203125,
0.007350921630859375,
-0.004077911376953125,
0.0117950439453125,
0.023040771484375,
0.050079345703125,
-0.00041103363037109375,
0.00440216064453125,
0.006015777587890625,
-0.041015625,
0.017364501953125,
0.005359649658203125,
-0.00908660888671875,
0.00824737548828125,
-0.0125732421875,
0.00644683837890625,
0.0010204315185546875,
-0.0251312255859375,
0.0005121231079101562,
0.0207977294921875,
-0.0280303955078125,
-0.0167694091796875,
0.0139312744140625,
0.04962158203125,
-0.0226593017578125,
0.00882720947265625,
-0.0006771087646484375,
-0.01294708251953125,
-0.008514404296875,
-0.00910186767578125,
0.039642333984375,
-0.026153564453125,
-0.029083251953125,
0.01332855224609375,
-0.01497650146484375,
-0.01329803466796875,
-0.0002434253692626953,
0.0035190582275390625,
0.0158843994140625,
-0.0148773193359375,
0.039794921875,
-0.0111083984375,
-0.01512908935546875,
0.0217132568359375,
-0.0242767333984375,
0.0196380615234375,
-0.00995635986328125,
0.034088134765625,
-0.0083160400390625,
0.006031036376953125,
0.0002827644348144531,
0.01425933837890625,
0.025909423828125,
0.01471710205078125,
-0.01384735107421875,
0.03277587890625,
0.024169921875,
0.0008783340454101562,
0.0219879150390625,
-0.0234222412109375,
0.00508880615234375,
0.032196044921875,
0.03192138671875,
0.02581787109375,
-0.054351806640625,
0.0140228271484375,
0.01220703125,
-0.0133819580078125,
0.055389404296875,
0.0059967041015625,
0.0026073455810546875,
0.01258087158203125,
-0.00997161865234375,
0.0019130706787109375,
0.040863037109375,
-0.0013589859008789062,
0.0245361328125,
0.05242919921875,
-0.0030727386474609375,
0.0021209716796875,
-0.0237579345703125,
0.0004520416259765625,
0.0213165283203125,
0.025390625,
0.0263824462890625,
0.0298309326171875,
0.00910186767578125,
0.0082244873046875,
0.017242431640625,
-0.03192138671875,
0.0188751220703125,
-0.00743865966796875,
0.01084136962890625,
0.00560760498046875,
-0.0341796875,
-0.0163726806640625,
0.0147552490234375,
0.0208587646484375,
-0.0289764404296875,
0.0030574798583984375,
-0.0153045654296875,
0.034149169921875,
0.0095367431640625,
0.0051422119140625,
0.033660888671875,
0.0036792755126953125,
-0.03216552734375,
0.05029296875,
0.0165557861328125,
0.040740966796875,
-0.029632568359375,
-0.0240936279296875,
0.0194549560546875,
0.036346435546875,
0.01334381103515625,
-0.0285797119140625,
0.019927978515625,
0.005779266357421875,
-0.0015325546264648438,
-0.0036106109619140625,
0.01442718505859375,
-0.002361297607421875,
0.0556640625,
-0.040863037109375,
-0.007099151611328125,
0.030517578125,
-0.026458740234375,
-0.029998779296875,
0.00936126708984375,
-0.0016002655029296875,
0.0268096923828125,
0.01340484619140625,
-0.005184173583984375,
0.0196533203125,
-0.005947113037109375,
-0.018341064453125,
-0.0220489501953125,
0.02655029296875,
0.0027904510498046875,
0.04498291015625,
0.00830841064453125,
-0.0203704833984375,
-0.046356201171875,
-0.0035247802734375,
0.026611328125,
-0.026275634765625,
-0.016326904296875,
0.015655517578125,
-0.0260162353515625,
-0.00997161865234375,
-0.00450897216796875,
-0.05010986328125,
-0.007137298583984375,
0.003383636474609375,
-0.0260772705078125,
-0.0003402233123779297,
0.01332855224609375,
0.01812744140625,
-0.0001647472381591797,
0.018310546875,
0.00418853759765625,
-0.00432586669921875,
0.00691986083984375,
-0.0178375244140625,
0.0038509368896484375,
-0.004009246826171875,
-0.0687255859375,
-0.0160980224609375,
-0.039794921875,
0.0017547607421875,
0.038818359375,
0.015625,
0.0099029541015625,
-0.0161590576171875,
0.00920867919921875,
0.03558349609375,
0.03277587890625,
-0.0097808837890625,
0.0014829635620117188,
-0.0173492431640625,
-0.054931640625,
0.006500244140625,
-0.022003173828125,
0.015167236328125,
0.016845703125,
-0.0330810546875,
0.020416259765625,
-0.022003173828125,
-0.004337310791015625,
-0.0035305023193359375,
-0.04278564453125,
-0.01142120361328125,
0.003665924072265625,
0.0026073455810546875,
-0.0352783203125,
0.006397247314453125,
0.022796630859375,
-0.0304718017578125,
-0.0025463104248046875,
-0.028350830078125,
0.044708251953125,
-0.0129547119140625,
0.0277252197265625,
0.018218994140625,
0.0006246566772460938,
-0.01153564453125,
-0.018218994140625,
0.0244598388671875,
-0.0054931640625,
-0.02960205078125,
-0.0110015869140625,
-0.0122222900390625,
0.00989532470703125,
0.031585693359375,
-0.0260772705078125,
0.0221710205078125,
0.0185394287109375,
-0.00539398193359375,
0.0280303955078125,
-0.0047607421875,
0.0081939697265625,
-0.007843017578125,
-0.0141754150390625,
-0.0140228271484375,
-0.0088348388671875,
-0.01154327392578125,
0.006755828857421875,
0.0097503662109375,
0.01824951171875,
-0.0012044906616210938,
-0.00897979736328125,
0.0086212158203125,
0.041107177734375,
-0.0220489501953125,
0.003734588623046875,
-0.0251617431640625,
-0.00914764404296875
] |
ours_464
|
Solution. Imagine another ant named Asset at the origin. If both Tessa and Asset move 3 steps and end up at the same point (without returning to the origin), then Tessa can return to the origin in 6 steps by retracing the steps of Asset. It suffices to consider the points that Tessa can reach in 3 steps and the number of ways to reach each of them.
The number of points to consider is enormous, but using symmetry can significantly simplify the calculation. There are only eight classes of lattice points that need to be considered, listed below in order of increasing distance from the origin. (Note: when a point \((a, b, c, d)\) is mentioned, all of its coordinate permutations are included.)
1. The points \(( \pm 1, \pm 1, \pm 1, \pm 1)\) and \(( \pm 2,0,0,0)\). (24 vertices of a 24-cell)
2. The points \(( \pm 2, \pm 2,0,0)\). (24 vertices of a larger 24-cell)
3. The points \(( \pm 3, \pm 1, \pm 1, \pm 1)\) and \(( \pm 2, \pm 2, \pm 2,0)\). (96 vertices of a rectified 24-cell)
4. The points \(( \pm 4,0,0,0)\) and \(( \pm 2, \pm 2, \pm 2, \pm 2)\). (24 vertices of an even larger 24-cell)
5. The points \(( \pm 3, \pm 3, \pm 1, \pm 1)\) and \(( \pm 4, \pm 2,0,0)\). (144 vertices of a runcinated 24-cell)
6. The points \(( \pm 4, \pm 2, \pm 2,0)\). (96 vertices of a larger rectified 24-cell)
7. The points \(( \pm 5, \pm 1, \pm 1, \pm 1), ( \pm 3, \pm 3, \pm 3, \pm 1)\), and \(( \pm 4, \pm 2, \pm 2, \pm 2)\). (192 vertices of a truncated 24-cell)
8. The points \(( \pm 6,0,0,0)\) and \(( \pm 3, \pm 3, \pm 3, \pm 3)\). (24 vertices of a yet even larger 24-cell)
We compute the number of ways for one to move from a given point in one class to any point in another class. The results are tabulated in the following table. (Rows are the originating class and columns are the destination class. Only the first four classes are relevant as movement origins as they are the only ones that can be reached in 2 steps from the origin.)
\[
\begin{array}{c|cccccccc}
& (1) & (2) & (3) & (4) & (5) & (6) & (7) & (8) \\
\hline
(1) & 8 & 6 & 8 & 1 & - & - & - & - \\
(2) & 6 & - & 12 & - & 6 & - & - & - \\
(3) & 2 & 3 & 6 & 2 & 6 & 3 & 2 & - \\
(4) & 1 & - & 8 & - & 6 & - & 8 & 1 \\
\end{array}
\]
From the table, we compute the number of ways to reach a class from a given point in class (1) in 2 steps:
\[
\begin{array}{c|cccccccc}
& (1) & (2) & (3) & (4) & (5) & (6) & (7) & (8) \\
\hline
& 117 & 72 & 192 & 24 & 90 & 24 & 24 & 1 \\
\end{array}
\]
There are two things to note: first, since class (1) contains 24 points and after 1 step Tessa and Asset can each end up on any one of them, we need to multiply 24 to the number of ways for each ant; second, if both ants end up in the same class, in only \(\frac{1}{N}\) of the cases do they actually end up on the same point, where \(N\) is the number of points in the class, so we need to divide this number for each class.
As a result, we compute the answer as:
\[
24^{2} \cdot\left(\frac{117^{2}}{24}+\frac{72^{2}}{24}+\frac{192^{2}}{96}+\frac{24^{2}}{24}+\frac{90^{2}}{144}+\frac{24^{2}}{96}+\frac{24^{2}}{192}+\frac{1^{2}}{24}\right)=725568
\]
\(\boxed{725568}\)
|
725568
|
{
"competition": "us_comps",
"dataset": "Ours",
"posts": null,
"source": "OMOFall17Solns.md"
}
|
Tessa the hyper-ant is at the origin of the four-dimensional Euclidean space \(\mathbb{R}^{4}\). For each step, she moves to another lattice point that is 2 units away from the point she is currently on. How many ways can she return to the origin for the first time after exactly 6 steps?
|
[
"/Mathematics/DiscreteMathematics/Combinatorics/Enumeration",
"/Mathematics/DiscreteMathematics/Combinatorics/GeneralCombinatorics",
"/Mathematics/DiscreteMathematics/Combinatorics/LatticePathsandPolygons",
"/Mathematics/DiscreteMathematics/PointLattices/IntegerLattice",
"/Mathematics/DiscreteMathematics/PointLattices/Lattice",
"/Mathematics/DiscreteMathematics/PointLattices/LatticePoint",
"/Mathematics/DiscreteMathematics/PointLattices/PointLattice",
"/Mathematics/Geometry/MultidimensionalGeometry/Four-DimensionalGeometry",
"/Mathematics/Geometry/MultidimensionalGeometry/Polytopes",
"/Mathematics/Geometry/Points/LatticePoint",
"/Mathematics/Geometry/Points/Point",
"/Mathematics/Geometry/Symmetry/RotationalSymmetry",
"/Mathematics/Geometry/Symmetry/Symmetric",
"/Mathematics/RecreationalMathematics/Puzzles/Puzzle"
] |
Reduce the 6‑step return to two independent 3‑step walks that must meet, then count meeting points using symmetry classes of lattice points.
|
[
-0.0000641942024230957,
-0.0096435546875,
0.0457763671875,
-0.031646728515625,
0.00006186962127685547,
0.0189056396484375,
0.005107879638671875,
-0.01422882080078125,
0.007038116455078125,
0.0352783203125,
0.0242767333984375,
0.0148162841796875,
-0.0003077983856201172,
0.03546142578125,
-0.00119781494140625,
-0.0108184814453125,
0.0023975372314453125,
0.033660888671875,
0.004642486572265625,
0.003643035888671875,
-0.01465606689453125,
-0.038848876953125,
-0.0183563232421875,
0.052154541015625,
-0.049346923828125,
-0.0071868896484375,
-0.015594482421875,
0.0204010009765625,
0.0228424072265625,
0.035064697265625,
-0.0311737060546875,
0.005367279052734375,
0.059906005859375,
0.03924560546875,
0.001827239990234375,
-0.0030879974365234375,
0.020111083984375,
-0.0010671615600585938,
-0.007526397705078125,
-0.040924072265625,
0.00836181640625,
-0.02435302734375,
0.01239013671875,
0.00862884521484375,
-0.0174560546875,
0.01543426513671875,
-0.01068115234375,
-0.0005421638488769531,
0.005279541015625,
-0.017822265625,
0.0029582977294921875,
0.0095062255859375,
-0.0241546630859375,
-0.0285491943359375,
-0.046417236328125,
-0.015655517578125,
-0.042999267578125,
-0.001983642578125,
-0.0267791748046875,
0.0090179443359375,
0.007732391357421875,
-0.02294921875,
0.005062103271484375,
-0.0172882080078125,
-0.0086517333984375,
-0.011444091796875,
0.016571044921875,
-0.01605224609375,
0.005168914794921875,
0.01166534423828125,
-0.0189208984375,
0.00783538818359375,
-0.0093841552734375,
0.03179931640625,
0.0151519775390625,
-0.005035400390625,
-0.0126495361328125,
0.0255889892578125,
-0.0037899017333984375,
0.00630950927734375,
0.0294647216796875,
-0.004886627197265625,
0.008941650390625,
-0.05133056640625,
-0.0005784034729003906,
0.0264892578125,
-0.01361083984375,
-0.00522613525390625,
0.02862548828125,
-0.0172271728515625,
-0.002452850341796875,
-0.0103302001953125,
-0.0083770751953125,
0.00728607177734375,
0.0014734268188476562,
0.021331787109375,
-0.0031890869140625,
-0.0096588134765625,
-0.0013341903686523438,
-0.0018215179443359375,
0.0157928466796875,
-0.0017375946044921875,
0.01427459716796875,
-0.004779815673828125,
-0.031463623046875,
-0.0205535888671875,
-0.01580810546875,
-0.0106964111328125,
0.0032787322998046875,
0.01447296142578125,
0.004192352294921875,
0.01165771484375,
0.007488250732421875,
0.034820556640625,
-0.0018434524536132812,
0.004207611083984375,
-0.026092529296875,
-0.004474639892578125,
0.00201416015625,
-0.0012655258178710938,
0.00662994384765625,
0.00838470458984375,
0.004070281982421875,
0.00600433349609375,
-0.007549285888671875,
-0.02313232421875,
-0.00510406494140625,
0.0037021636962890625,
-0.0158233642578125,
0.00891876220703125,
0.0008053779602050781,
0.007083892822265625,
-0.0174713134765625,
-0.0467529296875,
-0.026580810546875,
-0.0369873046875,
-0.0268096923828125,
-0.0116729736328125,
0.0081329345703125,
-0.0016374588012695312,
0.019439697265625,
-0.0187835693359375,
0.022491455078125,
-0.063232421875,
0.0025615692138671875,
0.00888824462890625,
0.0086212158203125,
-0.03375244140625,
0.013153076171875,
0.01383209228515625,
0.003513336181640625,
0.01387786865234375,
0.021270751953125,
0.01221466064453125,
-0.011505126953125,
-0.000293731689453125,
-0.0096588134765625,
-0.01320648193359375,
-0.00615692138671875,
0.010894775390625,
-0.0027141571044921875,
-0.00762939453125,
0.02606201171875,
0.062164306640625,
0.01654052734375,
0.0131988525390625,
0.0084381103515625,
-0.005558013916015625,
-0.00815582275390625,
0.02398681640625,
0.0083770751953125,
-0.030426025390625,
0.02105712890625,
-0.020904541015625,
-0.010650634765625,
0.015045166015625,
0.005584716796875,
0.015625,
-0.002239227294921875,
0.0148773193359375,
-0.00423431396484375,
-0.054412841796875,
0.0430908203125,
-0.0020275115966796875,
0.0310821533203125,
-0.0045318603515625,
0.0002307891845703125,
0.01096343994140625,
0.0156707763671875,
0.0186309814453125,
-0.03216552734375,
-0.0020732879638671875,
-0.005702972412109375,
0.0008540153503417969,
-0.00975799560546875,
-0.0165252685546875,
-0.0071563720703125,
-0.0006875991821289062,
0.030731201171875,
0.0156097412109375,
-0.0210723876953125,
-0.00032210350036621094,
0.01300048828125,
-0.00018310546875,
-0.01245880126953125,
-0.01459503173828125,
0.00441741943359375,
-0.0092620849609375,
0.01557159423828125,
-0.0013828277587890625,
-0.00173187255859375,
-0.006855010986328125,
-0.0181121826171875,
-0.0419921875,
-0.0007176399230957031,
-0.003170013427734375,
-0.00913238525390625,
-0.01154327392578125,
0.0249786376953125,
-0.00925445556640625,
0.028533935546875,
0.00231170654296875,
-0.004245758056640625,
0.0099945068359375,
-0.0274200439453125,
-0.0057373046875,
-0.0023593902587890625,
-0.00858306884765625,
0.0030517578125,
0.0140228271484375,
0.01409912109375,
-0.0014371871948242188,
-0.004024505615234375,
-0.01763916015625,
0.004207611083984375,
0.00206756591796875,
0.003833770751953125,
-0.02447509765625,
-0.0114288330078125,
0.00247955322265625,
0.017242431640625,
0.01311492919921875,
0.00585174560546875,
-0.01422119140625,
0.0121002197265625,
0.003814697265625,
0.0036487579345703125,
-0.002597808837890625,
-0.005344390869140625,
-0.018280029296875,
0.0015802383422851562,
0.01238250732421875,
-0.0027599334716796875,
-0.023345947265625,
-0.01178741455078125,
0.0023937225341796875,
-0.00876617431640625,
0.0065765380859375,
-0.00750732421875,
0.0113067626953125,
-0.0169830322265625,
0.032623291015625,
0.004058837890625,
0.0041961669921875,
0.000036835670471191406,
-0.0229644775390625,
0.0035533905029296875,
-0.01568603515625,
0.007709503173828125,
0.01021575927734375,
0.00441741943359375,
0.0178070068359375,
-0.00958251953125,
0.01114654541015625,
-0.007778167724609375,
-0.002452850341796875,
0.0111846923828125,
0.0033092498779296875,
0.0306396484375,
0.00310516357421875,
0.00702667236328125,
-0.019989013671875,
-0.002689361572265625,
0.007114410400390625,
0.0079345703125,
0.007358551025390625,
0.0007948875427246094,
-0.0063934326171875,
-0.020111083984375,
0.012725830078125,
0.005397796630859375,
-0.0122528076171875,
-0.0025177001953125,
0.0012121200561523438,
-0.0100555419921875,
-0.056854248046875,
0.0292205810546875,
0.011077880859375,
-0.00424957275390625,
-0.024444580078125,
0.01540374755859375,
-0.008514404296875,
0.00516510009765625,
0.031005859375,
0.0162811279296875,
0.0256805419921875,
0.0036525726318359375,
-0.00446319580078125,
-0.0225677490234375,
0.0188751220703125,
-0.0171966552734375,
0.0139312744140625,
0.00684356689453125,
-0.0184783935546875,
0.00576019287109375,
-0.0252227783203125,
-0.0013380050659179688,
0.01454925537109375,
-0.0146942138671875,
-0.0218658447265625,
0.0224761962890625,
-0.00969696044921875,
-0.01053619384765625,
0.0092620849609375,
0.0455322265625,
0.01453399658203125,
0.0224609375,
0.0006670951843261719,
-0.03436279296875,
-0.0084991455078125,
-0.03277587890625,
0.00921630859375,
-0.0024261474609375,
-0.006839752197265625,
-0.012359619140625,
-0.0138397216796875,
-0.017059326171875,
0.0260009765625,
0.002368927001953125,
0.017181396484375,
-0.0197601318359375,
0.0036563873291015625,
0.031463623046875,
-0.0084228515625,
-0.006916046142578125,
0.00023365020751953125,
-0.013519287109375,
-0.006866455078125,
0.00621795654296875,
0.006130218505859375,
-0.0209808349609375,
0.0177459716796875,
0.037567138671875,
-0.01322174072265625,
-0.035614013671875,
-0.0011663436889648438,
0.01395416259765625,
-0.01175689697265625,
-0.0025119781494140625,
0.01088714599609375,
0.0166473388671875,
-0.0007252693176269531,
-0.0010557174682617188,
-0.0202178955078125,
0.049652099609375,
0.013916015625,
-0.035430908203125,
0.0022068023681640625,
-0.048492431640625,
0.0100555419921875,
-0.0034770965576171875,
0.007625579833984375,
0.006023406982421875,
-0.002796173095703125,
-0.01128387451171875,
0.0018472671508789062,
0.052886962890625,
-0.01250457763671875,
-0.00226593017578125,
0.0014104843139648438,
0.0227508544921875,
0.032806396484375,
0.00783538818359375,
0.0006647109985351562,
-0.00572967529296875,
-0.004566192626953125,
-0.012664794921875,
-0.0282440185546875,
-0.05157470703125,
0.0174407958984375,
-0.0296173095703125,
-0.0124053955078125,
-0.00786590576171875,
0.014007568359375,
-0.033599853515625,
-0.01519012451171875,
0.002910614013671875,
0.0048370361328125,
0.01076507568359375,
0.0013885498046875,
0.01407623291015625,
0.00728607177734375,
0.00423431396484375,
0.0121612548828125,
-0.0162811279296875,
-0.0247650146484375,
0.01238250732421875,
-0.00647735595703125,
-0.01727294921875,
0.01110076904296875,
0.004398345947265625,
-0.0035915374755859375,
0.004852294921875,
-0.0083465576171875,
-0.01788330078125,
0.034393310546875,
0.0277557373046875,
0.018890380859375,
-0.00982666015625,
-0.01192474365234375,
-0.00557708740234375,
-0.01534271240234375,
-0.0020885467529296875,
-0.00365447998046875,
0.044189453125,
0.0183563232421875,
-0.029815673828125,
0.0364990234375,
-0.0203094482421875,
0.006435394287109375,
0.005680084228515625,
0.039337158203125,
0.0169525146484375,
0.05169677734375,
0.004718780517578125,
0.034637451171875,
0.04742431640625,
-0.0223541259765625,
-0.049346923828125,
0.00843048095703125,
-0.004001617431640625,
0.00450897216796875,
-0.015716552734375,
-0.0102996826171875,
-0.0093994140625,
0.00827789306640625,
0.04736328125,
0.013763427734375,
0.01303863525390625,
-0.02099609375,
-0.0003197193145751953,
-0.03289794921875,
-0.00222015380859375,
-0.0010004043579101562,
-0.0170745849609375,
0.037384033203125,
0.006412506103515625,
-0.00991058349609375,
-0.016998291015625,
-0.0063323974609375,
0.016693115234375,
-0.01493072509765625,
-0.03521728515625,
0.0125732421875,
-0.04132080078125,
0.0012865066528320312,
-0.0247802734375,
-0.038665771484375,
0.052001953125,
-0.050872802734375,
-0.01082611083984375,
-0.03070068359375,
-0.0113525390625,
0.003398895263671875,
-0.0064849853515625,
0.02276611328125,
0.047698974609375,
0.0008130073547363281,
0.0020599365234375,
-0.006038665771484375,
0.0215911865234375,
0.046905517578125,
0.0101470947265625,
0.057891845703125,
0.01043701171875,
-0.00612640380859375,
0.016845703125,
0.025115966796875,
0.034393310546875,
-0.0338134765625,
0.0207061767578125,
0.0013580322265625,
-0.0266876220703125,
-0.021331787109375,
-0.00940704345703125,
-0.0011911392211914062,
-0.00890350341796875,
-0.026123046875,
-0.0210418701171875,
0.016082763671875,
0.0218353271484375,
0.0276031494140625,
-0.0283355712890625,
0.03228759765625,
0.004230499267578125,
0.03436279296875,
0.067626953125,
0.004425048828125,
0.01416778564453125,
0.034454345703125,
0.006053924560546875,
-0.002185821533203125,
0.018280029296875,
-0.0198211669921875,
0.021331787109375,
0.0012235641479492188,
0.0115966796875,
0.00867462158203125,
-0.016448974609375,
-0.006313323974609375,
-0.0267486572265625,
0.02093505859375,
0.023895263671875,
0.009307861328125,
-0.01800537109375,
0.006256103515625,
-0.0079193115234375,
0.035003662109375,
-0.025421142578125,
-0.015167236328125,
0.0074615478515625,
-0.044769287109375,
-0.0191497802734375,
-0.00066375732421875,
0.010650634765625,
0.00733184814453125,
-0.0145263671875,
0.0016384124755859375,
0.0089263916015625,
0.006961822509765625,
-0.009918212890625,
-0.001056671142578125,
0.0367431640625,
-0.00658416748046875,
0.015472412109375,
0.015960693359375,
0.0170135498046875,
0.00626373291015625,
-0.05230712890625,
0.0007781982421875,
0.0004601478576660156,
0.002323150634765625,
-0.015899658203125,
0.0151824951171875,
0.006946563720703125,
0.0288848876953125,
-0.01666259765625,
-0.0009212493896484375,
-0.02587890625,
0.00548553466796875,
-0.0099945068359375,
-0.0288848876953125,
0.020416259765625,
0.031951904296875,
0.042724609375,
-0.0006022453308105469,
0.00925445556640625,
-0.0131378173828125,
-0.004974365234375,
-0.04852294921875,
-0.002017974853515625,
-0.019866943359375,
-0.0272216796875,
-0.0124053955078125,
-0.0153656005859375,
-0.0014858245849609375,
-0.01800537109375,
-0.0027980804443359375,
-0.0125274658203125,
-0.019775390625,
0.004657745361328125,
0.01910400390625,
-0.01727294921875,
0.034637451171875,
-0.01351165771484375,
-0.028472900390625,
0.01416778564453125,
0.0219268798828125,
0.0128173828125,
-0.0224456787109375,
-0.0220489501953125,
0.0447998046875,
-0.00785064697265625,
-0.0032596588134765625,
0.0007905960083007812,
-0.008087158203125,
0.00518035888671875,
-0.00560760498046875,
-0.0211181640625,
0.00891876220703125,
0.01540374755859375,
0.00015223026275634766,
-0.01064300537109375,
-0.0052947998046875,
0.02117919921875,
0.013671875,
-0.031402587890625,
0.027099609375,
0.0014238357543945312,
-0.031768798828125,
0.002124786376953125,
0.0231475830078125,
-0.02447509765625,
-0.005817413330078125,
0.06610107421875,
-0.01337432861328125,
-0.00862884521484375,
0.00342559814453125,
0.029754638671875,
-0.041412353515625,
-0.0259857177734375,
-0.01039886474609375,
-0.0041961669921875,
0.0253753662109375,
-0.009918212890625,
-0.03765869140625,
-0.0204620361328125,
0.022369384765625,
0.00846099853515625,
-0.01543426513671875,
-0.00884246826171875,
0.0022563934326171875,
0.061370849609375,
-0.004924774169921875,
0.0008993148803710938,
-0.006031036376953125,
-0.0482177734375,
0.0028934478759765625,
-0.017364501953125,
0.00807952880859375,
-0.0044708251953125,
-0.00939178466796875,
0.0211944580078125,
-0.0192108154296875,
0.0193634033203125,
0.037261962890625,
-0.0148468017578125,
-0.0064697265625,
-0.0404052734375,
0.0090484619140625,
-0.0231781005859375,
-0.015777587890625,
-0.039031982421875,
0.00519561767578125,
-0.0246429443359375,
0.00284576416015625,
-0.0010499954223632812,
0.00968170166015625,
0.010772705078125,
-0.0233154296875,
0.03594970703125,
0.017578125,
-0.0254058837890625,
0.0055389404296875,
-0.0064544677734375,
-0.034393310546875,
-0.0015478134155273438,
0.0011882781982421875,
-0.01702880859375,
-0.018096923828125,
0.0173797607421875,
-0.0189361572265625,
-0.020355224609375,
-0.005504608154296875,
-0.0008454322814941406,
-0.025970458984375,
0.010223388671875,
-0.00897979736328125,
0.01494598388671875,
-0.01336669921875,
0.0179443359375,
0.00933074951171875,
0.0268402099609375,
0.01296234130859375,
0.0283355712890625,
0.021240234375,
0.0163116455078125,
0.0406494140625,
0.011474609375,
0.01364898681640625,
-0.0009016990661621094,
0.0250396728515625,
-0.0228118896484375,
0.004810333251953125,
0.01265716552734375,
-0.0251007080078125,
-0.0165863037109375,
0.0149993896484375,
-0.0455322265625,
0.011688232421875,
0.032562255859375,
-0.0251312255859375,
0.0271759033203125,
-0.0005340576171875,
-0.02593994140625,
-0.03436279296875,
0.01097869873046875,
-0.00815582275390625,
-0.01503753662109375,
0.035614013671875,
-0.02252197265625,
-0.02581787109375,
0.0024547576904296875,
-0.038818359375,
0.0043487548828125,
-0.013214111328125,
-0.00543975830078125,
0.00672149658203125,
0.0443115234375,
0.022216796875,
0.0038356781005859375,
0.0212860107421875,
-0.0243072509765625,
-0.006221771240234375,
0.0260009765625,
-0.0076141357421875,
-0.036773681640625,
-0.027984619140625,
-0.00852203369140625,
-0.0212249755859375,
0.0013799667358398438,
0.00659942626953125,
-0.003688812255859375,
-0.0007576942443847656,
-0.04132080078125,
-0.062042236328125,
-0.00286865234375,
-0.027923583984375,
0.00421905517578125,
-0.0171356201171875,
0.0223236083984375,
0.03521728515625,
0.005146026611328125,
-0.0091552734375,
-0.017578125,
0.0194549560546875,
-0.0208740234375,
-0.0024242401123046875,
-0.0096435546875,
0.0162353515625,
0.042755126953125,
0.0190277099609375,
0.04327392578125,
-0.040283203125,
-0.0065460205078125,
0.0290069580078125,
-0.00035858154296875,
-0.014739990234375,
0.0009608268737792969,
0.0093841552734375,
-0.01148223876953125,
0.00876617431640625,
-0.0167694091796875,
-0.020355224609375,
0.01264190673828125,
0.01117706298828125,
-0.020904541015625,
0.029327392578125,
-0.0181732177734375,
-0.0194244384765625,
-0.06298828125,
-0.005519866943359375,
0.0226898193359375,
-0.0015964508056640625,
0.027008056640625,
-0.039947509765625,
-0.0589599609375,
-0.005641937255859375,
0.020172119140625,
-0.03338623046875,
0.022308349609375,
-0.01132965087890625,
-0.004970550537109375,
-0.0220947265625,
0.00432586669921875,
0.00244140625,
-0.004283905029296875,
-0.01678466796875,
-0.00992584228515625,
0.02105712890625,
-0.0066375732421875,
0.0257110595703125,
0.0264892578125,
-0.02825927734375,
0.0171051025390625,
-0.003879547119140625,
0.0193328857421875,
-0.0726318359375,
-0.0019063949584960938,
0.0216217041015625,
-0.045562744140625,
-0.006870269775390625,
0.0052032470703125,
0.01317596435546875,
0.039276123046875,
-0.0160675048828125,
-0.011505126953125,
0.023651123046875,
-0.0210113525390625,
-0.003269195556640625,
0.01064300537109375,
-0.0036334991455078125,
-0.030487060546875,
0.01514434814453125,
0.01202392578125,
-0.0035724639892578125,
-0.00299835205078125,
0.0220489501953125,
0.01424407958984375,
0.0438232421875,
-0.00634002685546875,
0.0301055908203125,
0.01274871826171875,
-0.0089111328125,
-0.0230560302734375,
0.02215576171875,
-0.0214996337890625,
-0.00860595703125,
0.01113128662109375,
0.016265869140625,
-0.016082763671875,
0.0230560302734375,
0.00666046142578125,
0.0149078369140625,
-0.01116180419921875,
0.0148773193359375,
0.0004718303680419922,
-0.020904541015625,
0.0070953369140625,
-0.0247955322265625,
-0.049224853515625,
0.0185699462890625,
-0.03076171875,
0.0006818771362304688,
0.0200042724609375,
0.02880859375,
-0.023284912109375,
-0.02532958984375,
0.0238189697265625,
-0.00493621826171875,
-0.01032257080078125,
0.0340576171875,
0.0025482177734375,
0.0191497802734375,
-0.0235595703125,
0.017822265625,
0.0263214111328125,
0.02105712890625,
-0.0340576171875,
-0.007678985595703125,
-0.007282257080078125,
-0.0328369140625,
0.0238494873046875,
-0.0220794677734375,
-0.0190887451171875,
0.011199951171875,
-0.001224517822265625,
-0.021636962890625,
-0.005138397216796875,
-0.0106048583984375,
0.003681182861328125,
0.028839111328125,
0.0149688720703125,
0.0246734619140625,
0.005802154541015625,
0.006542205810546875,
0.0020198822021484375,
-0.0289154052734375,
0.00911712646484375,
0.0197601318359375,
0.005672454833984375,
-0.02752685546875,
-0.003269195556640625,
-0.007488250732421875,
-0.01326751708984375,
-0.0191497802734375,
0.0235748291015625,
0.01425933837890625,
0.005191802978515625,
-0.0014896392822265625,
0.038848876953125,
0.0032825469970703125,
-0.0057373046875,
0.0009484291076660156,
0.001819610595703125,
-0.02471923828125,
-0.006359100341796875,
-0.034271240234375,
-0.005619049072265625,
-0.04095458984375,
-0.0611572265625,
0.01201629638671875,
-0.019500732421875,
0.039794921875,
-0.03155517578125,
-0.029754638671875,
-0.007701873779296875,
-0.0031414031982421875,
-0.005954742431640625,
-0.00856781005859375,
-0.00197601318359375,
-0.00936126708984375,
-0.010223388671875,
0.0246124267578125,
-0.0211944580078125,
0.0014934539794921875,
0.039794921875,
0.01995849609375,
-0.0136260986328125,
-0.0021152496337890625,
-0.00034737586975097656,
-0.003997802734375,
-0.010284423828125,
-0.0009279251098632812,
0.019134521484375,
0.0023632049560546875,
0.006805419921875,
0.01009368896484375,
-0.01215362548828125,
0.01184844970703125,
-0.006206512451171875,
0.013458251953125,
-0.004974365234375,
-0.0011615753173828125,
-0.0235443115234375,
0.0218048095703125,
-0.03729248046875,
-0.0411376953125,
0.0189361572265625,
-0.01152801513671875,
-0.004718780517578125,
-0.00829315185546875,
0.01126861572265625,
0.032501220703125,
0.005115509033203125,
0.0003516674041748047,
-0.0100860595703125,
-0.0222930908203125,
-0.010711669921875,
-0.019439697265625,
-0.028656005859375,
0.005832672119140625,
-0.037109375,
0.006443023681640625,
-0.012237548828125,
0.00605010986328125,
0.01488494873046875,
-0.0291290283203125,
0.007061004638671875,
0.004608154296875,
-0.022186279296875,
0.00031280517578125,
-0.01983642578125,
-0.01947021484375,
0.00786590576171875,
-0.0026683807373046875,
0.0039005279541015625,
-0.015625,
-0.0216064453125,
0.0416259765625,
0.0034332275390625,
-0.005615234375,
-0.009063720703125,
-0.00856781005859375,
-0.0228118896484375,
0.01497650146484375,
-0.0194091796875,
0.01293182373046875,
0.026702880859375,
-0.0010309219360351562,
-0.03326416015625,
-0.00205230712890625,
0.0067596435546875,
0.0188140869140625,
-0.0081939697265625,
-0.00955963134765625,
-0.0127716064453125,
-0.04425048828125,
0.0251617431640625,
0.01302337646484375,
0.007537841796875,
0.020172119140625,
-0.0191802978515625,
0.01314544677734375,
-0.02142333984375,
-0.02020263671875,
-0.0258941650390625,
0.0249176025390625,
0.00586700439453125,
-0.01861572265625,
0.01090240478515625,
-0.01242828369140625,
0.003162384033203125,
-0.0014095306396484375,
-0.00530242919921875,
-0.0239410400390625,
-0.01380157470703125,
0.0162353515625,
0.0006155967712402344,
0.033294677734375,
-0.00952911376953125,
0.01214599609375,
0.00011545419692993164,
-0.0230255126953125,
-0.029266357421875,
-0.0131988525390625,
0.01381683349609375,
-0.03778076171875,
-0.05548095703125,
-0.006256103515625,
0.003963470458984375,
-0.00621795654296875,
-0.00621795654296875,
-0.004619598388671875,
0.01145172119140625,
-0.0369873046875,
-0.0328369140625,
0.0286865234375,
0.01351165771484375,
0.0296478271484375,
-0.007694244384765625,
-0.04168701171875,
-0.0157012939453125,
0.01003265380859375,
0.01435089111328125,
0.0169830322265625,
-0.036651611328125,
0.0026683807373046875,
-0.0169525146484375,
0.00299072265625,
-0.0281524658203125,
0.03668212890625,
0.01934814453125,
-0.0164031982421875,
0.0232696533203125,
-0.05413818359375,
0.0002880096435546875,
-0.007358551025390625,
0.00557708740234375,
-0.0028228759765625,
-0.0272369384765625,
0.02886962890625,
-0.0146636962890625,
-0.033905029296875,
0.007720947265625,
-0.0020904541015625,
0.01320648193359375,
0.005222320556640625,
0.005435943603515625,
0.04229736328125,
0.00794219970703125,
0.0305633544921875,
-0.01299285888671875,
-0.0039825439453125,
0.021148681640625,
-0.0078887939453125,
-0.004322052001953125,
0.0213623046875,
0.013641357421875,
0.0399169921875,
-0.0411376953125,
0.032623291015625,
-0.01280975341796875,
-0.007076263427734375,
0.02606201171875,
0.00811767578125,
-0.00750732421875,
-0.01552581787109375,
-0.01377105712890625,
0.00872802734375,
-0.028656005859375,
0.006866455078125,
-0.01332855224609375,
-0.002918243408203125,
0.0208587646484375,
-0.00371551513671875,
0.022979736328125,
0.031585693359375,
0.006591796875,
0.025054931640625,
0.0005002021789550781,
0.024932861328125,
-0.0188140869140625,
0.0297393798828125,
0.023651123046875,
-0.0099639892578125,
0.043212890625,
0.019622802734375,
0.01042938232421875,
-0.004497528076171875,
0.0193634033203125,
0.01548004150390625,
-0.018890380859375,
0.005207061767578125,
-0.001312255859375,
0.00293731689453125,
0.0013675689697265625,
0.002838134765625,
-0.0009365081787109375,
-0.00806427001953125,
0.01837158203125,
0.01073455810546875,
0.0155029296875,
0.011077880859375,
0.015625,
0.030120849609375,
-0.0173187255859375,
-0.03729248046875,
-0.0011882781982421875,
-0.0054168701171875,
-0.012786865234375,
0.01190185546875,
0.004116058349609375,
-0.015716552734375,
0.019866943359375,
0.0004715919494628906,
0.0127716064453125,
0.00373077392578125,
-0.009613037109375,
0.0129241943359375,
-0.047515869140625,
0.0291748046875,
0.01378631591796875,
-0.01016998291015625,
0.0257720947265625,
0.0014886856079101562,
-0.002468109130859375,
-0.0226898193359375,
0.006805419921875,
-0.0204315185546875,
0.006317138671875,
0.0145111083984375,
-0.0276336669921875,
0.0034160614013671875,
-0.022003173828125,
-0.0034809112548828125,
-0.0005040168762207031,
0.0067596435546875,
0.0019092559814453125,
-0.0262298583984375,
-0.032440185546875,
0.06292724609375,
-0.04583740234375,
0.042205810546875,
-0.032684326171875,
-0.050994873046875,
0.012298583984375,
0.0084228515625,
0.0224609375,
0.00003814697265625,
-0.01190185546875,
0.0020046234130859375,
0.0006489753723144531,
0.011260986328125,
-0.0208892822265625,
-0.013092041015625,
-0.046295166015625,
0.0218963623046875,
-0.01947021484375,
-0.0343017578125,
-0.0288848876953125,
-0.02935791015625,
-0.00786590576171875,
-0.0009374618530273438,
-0.0035533905029296875,
0.003192901611328125,
0.01299285888671875,
0.005290985107421875,
-0.0161895751953125,
-0.01100921630859375,
-0.0120086669921875,
0.0169830322265625,
-0.007671356201171875,
-0.014129638671875,
0.0006108283996582031,
-0.01123809814453125,
0.03387451171875,
0.0184783935546875,
-0.0211029052734375,
-0.02685546875,
-0.024505615234375,
-0.0286102294921875,
0.0020751953125,
-0.00974273681640625,
-0.029693603515625,
-0.0146484375,
-0.006870269775390625,
0.027801513671875,
0.01336669921875,
-0.0253143310546875,
-0.0260772705078125,
0.01261138916015625,
0.0264739990234375,
0.013336181640625,
-0.0067901611328125,
0.0280609130859375,
0.005779266357421875,
0.00836181640625,
-0.03973388671875,
0.013275146484375,
-0.0122222900390625,
-0.0037479400634765625,
0.0294189453125,
0.00043392181396484375,
0.0246124267578125,
-0.01197052001953125,
0.008575439453125,
-0.01837158203125,
0.00992584228515625,
-0.041168212890625,
0.0025691986083984375,
0.020416259765625,
0.0013713836669921875,
0.0050506591796875,
-0.017974853515625,
-0.033203125,
-0.01294708251953125,
-0.0017004013061523438,
-0.0015153884887695312,
0.005558013916015625,
-0.0008392333984375,
-0.0042572021484375,
-0.027984619140625,
0.0160369873046875,
-0.036590576171875,
-0.012847900390625,
-0.00823974609375,
-0.007579803466796875,
-0.00634765625,
0.0435791015625,
0.007076263427734375,
0.0247344970703125,
0.00823211669921875,
-0.023162841796875,
0.003780364990234375,
0.027984619140625,
-0.006744384765625,
0.0008893013000488281,
-0.007904052734375,
-0.01074981689453125,
0.00005561113357543945,
0.02935791015625,
0.0107421875,
0.0234375,
-0.0227203369140625,
-0.003337860107421875,
0.0180511474609375,
-0.009857177734375,
-0.018890380859375,
-0.0079345703125,
-0.0007104873657226562,
0.011322021484375,
-0.0172576904296875,
-0.01276397705078125,
-0.0208282470703125,
-0.040008544921875,
-0.0019989013671875,
0.0237274169921875,
0.012115478515625,
0.00563812255859375,
0.0299224853515625,
0.0120849609375,
-0.016510009765625,
0.01258087158203125,
-0.0025997161865234375,
0.0229949951171875,
0.0221099853515625,
-0.00727081298828125,
0.00323486328125,
-0.018402099609375,
-0.01207733154296875,
0.031280517578125,
-0.0204925537109375,
-0.01873779296875,
-0.040557861328125,
-0.0037097930908203125,
-0.0176849365234375,
0.0338134765625,
-0.011810302734375,
-0.0017185211181640625,
-0.0131072998046875,
0.0159149169921875,
-0.007465362548828125,
-0.0030670166015625,
-0.01387786865234375,
-0.0159454345703125,
0.0017213821411132812,
-0.0244140625,
-0.01425933837890625,
0.0258636474609375,
-0.028350830078125,
0.01016998291015625,
0.0009503364562988281,
0.0014591217041015625,
0.004070281982421875,
-0.0173492431640625,
0.046478271484375,
0.0048675537109375,
-0.031890869140625,
-0.036163330078125,
-0.01284027099609375,
-0.016387939453125,
-0.019317626953125,
0.003509521484375,
0.041473388671875,
-0.00652313232421875,
-0.00347900390625,
0.01104736328125,
-0.01194000244140625,
-0.0130615234375,
-0.007373809814453125,
0.0280303955078125,
-0.0035400390625,
0.01277923583984375,
0.024566650390625,
0.0198974609375,
0.0003521442413330078,
0.0019321441650390625,
0.00014078617095947266,
-0.011322021484375,
0.00750732421875,
0.03253173828125,
-0.0224761962890625,
0.019744873046875,
0.0034351348876953125,
0.02447509765625,
0.017913818359375,
0.000675201416015625,
0.024566650390625,
-0.032958984375,
-0.012786865234375,
0.01381683349609375,
-0.033355712890625,
0.01154327392578125,
-0.00926971435546875,
0.028076171875,
-0.023284912109375,
0.027496337890625,
-0.0038127899169921875,
-0.0262908935546875,
-0.00949859619140625,
-0.01177978515625,
0.01025390625,
0.0263671875,
-0.004375457763671875,
0.03070068359375,
0.007068634033203125,
-0.0001862049102783203,
0.0309600830078125,
-0.025299072265625,
-0.0193023681640625,
-0.016937255859375,
0.01123809814453125,
-0.04754638671875,
-0.0184326171875,
0.016571044921875,
0.00395965576171875,
-0.000037729740142822266,
0.0222320556640625,
-0.0137176513671875,
0.00405120849609375,
0.006500244140625,
0.000021278858184814453,
0.003810882568359375,
0.01009368896484375,
0.0032634735107421875,
-0.004726409912109375,
-0.00983428955078125,
-0.0015439987182617188,
-0.051666259765625,
-0.01800537109375,
-0.01486968994140625,
-0.00002104043960571289,
0.0038433074951171875,
0.0234375,
0.01047515869140625,
0.0160064697265625,
0.0276947021484375,
0.007625579833984375,
-0.0219573974609375,
0.01309967041015625,
-0.01255035400390625,
-0.022552490234375,
0.01190185546875,
-0.00478363037109375,
-0.032745361328125,
-0.0038509368896484375,
0.0021762847900390625,
-0.00106048583984375,
-0.0088348388671875,
0.0208282470703125,
-0.01079559326171875,
-0.019927978515625,
0.005458831787109375,
0.03228759765625,
-0.005611419677734375,
-0.00684356689453125,
-0.00901031494140625,
0.0345458984375,
-0.036529541015625,
0.006275177001953125,
0.019775390625,
0.026031494140625,
-0.02386474609375,
-0.0360107421875,
-0.00722503662109375,
0.00411224365234375,
0.0080718994140625,
0.0120086669921875,
0.01471710205078125,
0.0022296905517578125,
0.0313720703125,
-0.003093719482421875,
0.01025390625,
-0.007144927978515625,
-0.01010894775390625,
0.00555419921875,
-0.0241546630859375,
-0.00823211669921875,
-0.020660400390625,
0.0006389617919921875,
-0.01480865478515625,
-0.0176239013671875,
-0.0098876953125,
0.0037136077880859375,
-0.0117340087890625,
0.01168060302734375,
0.01290130615234375,
0.0099334716796875,
-0.004497528076171875,
0.02301025390625,
-0.006500244140625,
-0.006008148193359375,
0.0054779052734375,
-0.01397705078125,
-0.005130767822265625,
0.00496673583984375,
0.00960540771484375,
-0.020599365234375,
0.0269775390625,
-0.01531219482421875,
-0.01033782958984375,
-0.004180908203125,
-0.01045989990234375,
-0.003604888916015625,
0.0150909423828125,
-0.00272369384765625,
-0.01195526123046875,
-0.013702392578125,
-0.02362060546875,
-0.0160675048828125,
0.005680084228515625,
-0.0037212371826171875,
0.0091094970703125,
-0.0141448974609375,
-0.0265960693359375,
-0.0186920166015625,
0.0033721923828125,
0.01467132568359375,
-0.003131866455078125,
-0.007061004638671875,
-0.01666259765625,
-0.01522064208984375,
0.015869140625,
0.01141357421875,
-0.012664794921875,
-0.022430419921875,
-0.01187896728515625,
0.0252838134765625,
-0.0011959075927734375,
0.0181884765625,
-0.02667236328125,
-0.0224456787109375,
0.034759521484375,
0.00682830810546875,
-0.0098876953125,
-0.00980377197265625,
0.0229339599609375,
0.02203369140625,
0.003589630126953125,
-0.00865936279296875,
0.0045623779296875,
0.0191192626953125,
0.007442474365234375,
0.053985595703125,
0.0311431884765625,
0.01085662841796875,
0.0016641616821289062,
-0.002292633056640625,
0.025909423828125,
-0.0009860992431640625,
0.03369140625,
0.02984619140625,
0.004413604736328125,
-0.0206451416015625,
-0.021514892578125,
0.01364898681640625,
0.01062774658203125,
0.00617218017578125,
-0.005405426025390625,
-0.005802154541015625,
-0.0185699462890625,
0.0284881591796875,
0.016937255859375,
-0.0343017578125,
0.026824951171875,
-0.004642486572265625,
0.00220489501953125,
-0.0000033974647521972656,
-0.0211639404296875,
0.00916290283203125,
-0.020172119140625,
-0.035736083984375,
0.0095367431640625,
0.004405975341796875,
0.00223541259765625,
-0.0031223297119140625,
-0.0023517608642578125,
-0.0096282958984375,
0.027130126953125,
-0.02838134765625,
-0.0195465087890625,
-0.0160980224609375,
0.0163726806640625,
0.0013074874877929688,
-0.0345458984375,
0.0021419525146484375,
-0.004528045654296875,
0.030120849609375,
0.0238037109375,
-0.032073974609375,
-0.0004410743713378906,
0.022796630859375,
-0.005374908447265625,
-0.0277252197265625,
-0.02923583984375,
0.0089569091796875,
0.034820556640625,
0.00914764404296875,
-0.0237884521484375,
0.0178375244140625,
-0.00554656982421875,
-0.020233154296875,
-0.0159454345703125,
-0.031829833984375,
-0.0248565673828125,
0.023223876953125,
0.0263214111328125,
-0.007572174072265625,
0.005367279052734375,
0.01385498046875,
-0.0019855499267578125,
-0.0208282470703125,
0.0162506103515625,
0.003665924072265625,
-0.0096588134765625,
-0.004199981689453125,
0.01861572265625,
0.0035343170166015625,
0.0184326171875,
0.003948211669921875,
0.03460693359375,
-0.00891876220703125,
0.001079559326171875,
0.003765106201171875,
-0.00246429443359375,
-0.0190277099609375,
-0.01468658447265625,
0.003108978271484375,
-0.007328033447265625,
-0.005645751953125,
-0.021820068359375,
0.0307159423828125,
-0.00786590576171875,
-0.0002084970474243164,
-0.01494598388671875,
0.0182342529296875,
0.035186767578125,
-0.01044464111328125,
-0.010223388671875,
0.0128326416015625,
0.0180511474609375,
0.01392364501953125,
-0.0003819465637207031,
0.007541656494140625,
-0.015411376953125,
0.00501251220703125,
0.00345611572265625,
0.013916015625,
0.01995849609375,
-0.021881103515625,
-0.01056671142578125,
0.0232696533203125,
0.0112457275390625,
0.016845703125,
-0.01385498046875,
0.01532745361328125,
-0.008148193359375,
0.0022945404052734375,
0.0241851806640625,
-0.01568603515625,
-0.0117645263671875,
0.0193939208984375,
-0.027435302734375,
-0.00827789306640625,
0.007476806640625,
-0.001766204833984375,
0.03265380859375,
-0.0081787109375,
0.0089111328125,
0.0141143798828125,
0.0038204193115234375,
-0.005767822265625,
0.0107574462890625,
0.019134521484375,
-0.00728607177734375,
0.005863189697265625,
0.041839599609375,
-0.00109100341796875,
-0.01137542724609375,
-0.00830841064453125,
0.016693115234375,
-0.0313720703125,
0.00643157958984375,
-0.001941680908203125,
-0.03289794921875,
-0.025177001953125,
0.04278564453125,
-0.019683837890625,
-0.015411376953125,
0.004329681396484375,
-0.0010042190551757812,
0.00722503662109375,
-0.02587890625,
-0.0171051025390625,
-0.005168914794921875,
0.034393310546875,
0.02423095703125,
0.047332763671875,
-0.0247955322265625,
0.0077362060546875,
0.0291595458984375,
0.0118865966796875,
-0.0065155029296875,
0.0099945068359375,
-0.0204010009765625,
0.008575439453125,
-0.015869140625,
0.002979278564453125,
0.0236663818359375,
0.0211181640625,
0.00554656982421875,
0.04180908203125,
-0.0010509490966796875,
-0.0265655517578125,
-0.00551605224609375,
-0.01181793212890625,
0.0251007080078125,
0.0025806427001953125,
0.004810333251953125,
-0.007175445556640625,
-0.04046630859375,
-0.020904541015625,
0.014007568359375,
-0.046478271484375,
-0.034332275390625,
0.0035610198974609375,
-0.002361297607421875,
0.01541900634765625,
-0.00522613525390625,
-0.0250244140625,
-0.0438232421875,
0.004207611083984375,
-0.00656890869140625,
-0.005374908447265625,
0.0103607177734375,
0.020172119140625,
0.0076751708984375,
0.027374267578125,
0.0185699462890625,
-0.0007734298706054688,
-0.026641845703125,
-0.0007529258728027344,
0.00435638427734375,
-0.019622802734375,
0.00695037841796875,
0.028289794921875,
-0.00554656982421875,
-0.03118896484375,
-0.00910186767578125,
0.00478363037109375,
0.0285797119140625,
0.05120849609375,
-0.00817108154296875,
0.0276947021484375,
0.033111572265625,
-0.033843994140625,
0.0017175674438476562,
-0.01428985595703125,
-0.0035152435302734375,
0.03106689453125,
-0.0140228271484375,
0.0164337158203125,
0.009002685546875,
0.029296875,
0.0287322998046875,
0.03155517578125,
0.0002472400665283203,
-0.01190948486328125,
-0.00415802001953125,
0.0281829833984375,
0.0013628005981445312,
-0.008636474609375,
0.02301025390625,
0.0006909370422363281,
0.00836181640625,
-0.001003265380859375,
-0.0005397796630859375,
-0.00872802734375,
0.02398681640625,
-0.01230621337890625,
0.04022216796875,
0.01168060302734375,
-0.02423095703125,
0.0031585693359375,
-0.02459716796875,
-0.0069427490234375,
-0.0096588134765625,
0.0029888153076171875,
-0.00846099853515625,
0.0090179443359375,
0.027130126953125,
0.006046295166015625,
0.01558685302734375,
0.01232147216796875,
-0.031097412109375,
-0.017852783203125,
0.0272216796875,
-0.003658294677734375,
0.0157012939453125,
0.0292816162109375,
-0.028411865234375,
0.01421356201171875,
0.010498046875,
-0.011627197265625,
0.012664794921875,
0.0153045654296875,
-0.005397796630859375,
-0.003650665283203125,
0.01071929931640625,
0.02874755859375,
-0.01212310791015625,
-0.014007568359375,
0.0123748779296875,
-0.0289459228515625,
-0.004444122314453125,
0.01451873779296875,
0.002407073974609375,
-0.006069183349609375,
-0.00020170211791992188,
0.0183868408203125,
-0.0019779205322265625,
-0.00399017333984375,
0.030242919921875,
-0.005107879638671875,
-0.01078033447265625,
-0.0076904296875,
0.007434844970703125,
-0.0193939208984375,
0.0147857666015625,
-0.0325927734375,
0.0096588134765625,
0.009552001953125,
-0.04437255859375,
-0.00722503662109375,
0.0243072509765625,
0.017547607421875,
-0.0272369384765625,
0.0008244514465332031,
0.0272064208984375,
-0.005054473876953125,
0.004505157470703125,
-0.0059661865234375,
0.0287017822265625,
0.037933349609375,
-0.01479339599609375,
-0.00919342041015625,
-0.0090179443359375,
-0.0193023681640625,
0.00571441650390625,
0.00897979736328125,
-0.0135498046875,
0.006427764892578125,
0.027191162109375,
0.02862548828125,
-0.01137542724609375,
-0.01554107666015625,
0.01513671875,
-0.010955810546875,
-0.01322174072265625,
0.00757598876953125,
-0.01134490966796875,
-0.03265380859375,
-0.0182647705078125,
0.01522064208984375,
-0.0166473388671875,
0.0295562744140625,
0.002971649169921875,
0.0019683837890625,
0.019439697265625,
-0.017974853515625,
0.0299835205078125,
-0.023284912109375,
-0.03228759765625,
0.01442718505859375,
0.007045745849609375,
0.044342041015625,
-0.00231170654296875,
-0.019775390625,
0.0172271728515625,
-0.035186767578125,
-0.01102447509765625,
0.0037441253662109375,
-0.03448486328125,
0.032806396484375,
0.01047515869140625,
-0.031982421875,
-0.0382080078125,
0.035919189453125,
0.01551055908203125,
-0.0001424551010131836,
-0.0032176971435546875,
-0.022705078125,
-0.002838134765625,
0.00772857666015625,
0.03326416015625,
-0.01461029052734375,
0.00444793701171875,
-0.02423095703125,
-0.00980377197265625,
-0.02545166015625,
-0.0297088623046875,
-0.020843505859375,
0.0263214111328125,
-0.03228759765625,
0.00817108154296875,
0.0253143310546875,
0.03448486328125,
-0.0034351348876953125,
-0.00994873046875,
0.0224761962890625,
-0.0201568603515625,
0.0181732177734375,
-0.0218963623046875,
-0.019256591796875,
0.017852783203125,
-0.0088958740234375,
-0.004833221435546875,
0.003040313720703125,
-0.034912109375,
-0.035003662109375,
-0.006626129150390625,
-0.0301361083984375,
-0.045745849609375,
0.021270751953125,
0.013031005859375,
0.0028285980224609375,
0.0191192626953125,
0.01983642578125,
-0.016021728515625,
0.0177459716796875,
0.0158843994140625,
0.007678985595703125,
0.00971221923828125,
-0.01488494873046875,
0.00769805908203125,
-0.010040283203125,
0.05804443359375,
-0.0162506103515625,
-0.0229949951171875,
-0.0037689208984375,
-0.01641845703125,
0.00177764892578125,
0.0258636474609375,
0.0210113525390625,
-0.0092315673828125,
0.004390716552734375,
0.005123138427734375,
-0.0004687309265136719,
0.01629638671875,
0.006427764892578125,
0.016754150390625,
0.003429412841796875,
0.019287109375,
-0.0162811279296875,
0.0177154541015625,
0.00830841064453125,
-0.00762176513671875,
0.0038433074951171875,
0.0019054412841796875,
-0.01512908935546875,
-0.01483154296875,
-0.031982421875,
0.003208160400390625,
-0.00492095947265625,
0.0015497207641601562,
0.01922607421875,
0.037567138671875,
0.02545166015625,
-0.006038665771484375,
0.0006532669067382812,
0.0019168853759765625,
-0.013916015625,
0.006992340087890625,
0.032562255859375,
-0.00807952880859375,
-0.006519317626953125,
-0.03717041015625,
0.0052490234375,
-0.02093505859375,
0.0166168212890625,
-0.0177154541015625,
0.018096923828125,
0.000446319580078125,
-0.01898193359375,
0.017852783203125,
-0.0070037841796875,
0.006977081298828125,
0.0227813720703125,
0.0255584716796875,
0.0211029052734375,
0.0160675048828125,
-0.006290435791015625,
-0.003513336181640625,
0.006988525390625,
-0.009521484375,
-0.004405975341796875,
0.005950927734375,
0.0279388427734375,
0.01541900634765625,
-0.023529052734375,
-0.004276275634765625,
-0.021728515625,
-0.036407470703125,
-0.005977630615234375,
0.022705078125,
0.0260467529296875,
-0.00609588623046875,
0.019775390625,
0.051055908203125,
0.0254058837890625,
-0.04107666015625,
-0.008331298828125,
-0.0309906005859375,
-0.011383056640625,
-0.01434326171875,
0.052886962890625,
-0.032989501953125,
0.00023496150970458984,
0.0213623046875,
-0.017913818359375,
-0.0142974853515625,
0.01318359375,
0.006988525390625,
0.016448974609375,
-0.007045745849609375,
-0.01374053955078125,
-0.020050048828125,
0.0065765380859375,
-0.01459503173828125,
-0.01654052734375,
0.00147247314453125,
-0.02496337890625,
0.01605224609375,
0.022491455078125,
-0.0016040802001953125,
0.0174102783203125,
-0.0007224082946777344,
0.0128021240234375,
0.01209259033203125,
-0.0014591217041015625,
-0.0140380859375,
0.01511383056640625,
-0.02825927734375,
0.024688720703125,
0.04443359375,
-0.006053924560546875,
0.00152587890625,
-0.0036563873291015625,
-0.03125,
-0.01555633544921875,
0.004650115966796875,
0.0295867919921875,
0.0233306884765625,
-0.0230255126953125,
0.01245880126953125,
0.006290435791015625,
0.033233642578125,
0.012176513671875,
-0.0186309814453125,
0.00096893310546875,
-0.057586669921875,
-0.0029697418212890625,
-0.0140838623046875,
-0.00917816162109375,
0.0138702392578125,
-0.04193115234375,
0.0134124755859375,
-0.00959014892578125,
-0.0004200935363769531,
0.021759033203125,
0.0465087890625,
0.022491455078125,
-0.0202789306640625,
-0.03009033203125,
0.01219940185546875,
0.0254669189453125,
-0.0123138427734375,
-0.011871337890625,
-0.006893157958984375,
0.01328277587890625,
0.034912109375,
0.0233306884765625,
0.034759521484375,
0.0240936279296875,
-0.024261474609375,
-0.005462646484375,
-0.02764892578125,
0.004283905029296875,
0.028656005859375,
-0.006237030029296875,
-0.034698486328125,
-0.001850128173828125,
0.0310821533203125,
0.0201873779296875,
-0.01319122314453125,
0.0006594657897949219,
0.009002685546875,
0.0010766983032226562,
0.0014171600341796875,
-0.00933074951171875,
0.00008225440979003906,
-0.0016450881958007812,
-0.001636505126953125,
-0.01265716552734375,
0.01030731201171875,
-0.01230621337890625,
-0.005828857421875,
-0.01296234130859375,
0.0224761962890625,
-0.0002999305725097656,
-0.00576019287109375,
0.00945281982421875,
-0.03155517578125,
0.045196533203125,
0.000213623046875,
-0.055511474609375,
0.0010271072387695312,
-0.00695037841796875,
0.0013322830200195312,
-0.041900634765625,
0.0084381103515625,
-0.0184173583984375,
-0.0121917724609375,
0.014862060546875,
0.0007791519165039062,
-0.02203369140625,
0.0226593017578125,
0.012908935546875,
-0.0172119140625,
-0.03448486328125,
0.01788330078125,
0.007022857666015625,
0.025482177734375,
0.007686614990234375,
-0.005756378173828125,
-0.01372528076171875,
0.01104736328125,
0.00475311279296875,
-0.029449462890625,
-0.00838470458984375,
0.03448486328125,
-0.01324462890625,
0.01470947265625,
0.0082550048828125,
0.00295257568359375,
-0.005619049072265625,
0.003734588623046875,
0.0200958251953125,
-0.00794219970703125,
0.004058837890625,
0.034454345703125,
0.004119873046875,
-0.0110321044921875,
-0.0151214599609375,
0.0262298583984375,
0.043365478515625,
0.0103302001953125,
-0.0065765380859375,
0.01247406005859375,
-0.0252227783203125,
-0.0007524490356445312,
0.0183258056640625,
0.0184783935546875,
0.01019287109375,
0.00800323486328125,
0.0038623809814453125,
-0.03472900390625,
0.0004718303680419922,
0.0124359130859375,
0.00457000732421875,
-0.0017375946044921875,
-0.02178955078125,
0.019256591796875,
-0.037811279296875,
-0.0091400146484375,
0.0198974609375,
-0.01213836669921875,
-0.00278472900390625,
-0.00988006591796875,
0.006732940673828125,
0.0015554428100585938,
-0.007549285888671875,
-0.0035610198974609375,
-0.0104217529296875,
0.0230865478515625,
0.033538818359375,
0.004474639892578125,
-0.013427734375,
0.0188446044921875,
-0.00699615478515625,
-0.0012331008911132812,
0.000614166259765625,
0.01824951171875,
0.0120391845703125,
0.027984619140625,
0.024139404296875,
0.01410675048828125,
-0.006031036376953125,
-0.006229400634765625,
-0.00952911376953125,
-0.0006718635559082031,
0.001377105712890625,
-0.0006308555603027344,
-0.005031585693359375,
0.01413726806640625,
0.007488250732421875,
-0.01013946533203125,
-0.033782958984375,
-0.00727081298828125,
0.0037364959716796875,
-0.00615692138671875,
-0.01490020751953125,
-0.033538818359375,
0.004253387451171875,
-0.07086181640625,
-0.015625,
0.0117950439453125,
0.00035858154296875,
0.026580810546875,
0.00031280517578125,
-0.01849365234375,
-0.007495880126953125,
0.02081298828125,
-0.0140380859375,
-0.0083160400390625,
-0.003993988037109375,
0.0323486328125,
0.00018298625946044922,
-0.004673004150390625,
0.00540924072265625,
-0.01317596435546875,
-0.032379150390625,
0.04278564453125,
-0.0019502639770507812,
0.025115966796875,
-0.0184478759765625,
-0.0018663406372070312,
0.011627197265625,
-0.004817962646484375,
-0.0311126708984375,
-0.0184326171875,
0.026824951171875,
-0.0164794921875,
-0.0268707275390625,
-0.0158843994140625,
0.026214599609375,
0.004001617431640625,
0.00531768798828125,
-0.0172271728515625,
0.0272216796875,
-0.0307464599609375,
0.00873565673828125,
0.0264129638671875,
-0.01031494140625,
-0.00411224365234375,
0.004741668701171875,
0.0203399658203125,
0.006938934326171875,
0.02691650390625,
-0.00502777099609375,
-0.0085601806640625,
-0.0161285400390625,
0.0029125213623046875,
-0.0032787322998046875,
-0.0040130615234375,
0.0258331298828125,
-0.047027587890625,
0.00502777099609375,
0.0111083984375,
-0.00923919677734375,
0.01922607421875,
0.0228729248046875,
-0.0013170242309570312,
-0.00029587745666503906,
-0.006378173828125,
0.0246734619140625,
0.0277557373046875,
0.00016939640045166016,
0.0213623046875,
-0.00884246826171875,
-0.00441741943359375,
0.0073394775390625,
-0.0338134765625,
-0.005096435546875,
0.0264129638671875,
-0.0128021240234375,
-0.0062103271484375,
0.00368499755859375,
0.0080108642578125,
-0.0056304931640625,
-0.0048370361328125,
-0.00247955322265625,
-0.019927978515625,
0.00945281982421875,
-0.00762939453125,
0.004436492919921875,
-0.003635406494140625,
-0.008209228515625,
-0.016845703125,
-0.01751708984375,
-0.00022041797637939453,
-0.023895263671875,
-0.0255889892578125,
-0.01529693603515625,
-0.01470947265625,
0.015625,
0.02081298828125,
-0.00823211669921875,
-0.0012912750244140625,
-0.0216522216796875,
-0.00598907470703125,
0.01401519775390625,
-0.0141754150390625,
0.00988006591796875,
-0.0156402587890625,
-0.0069580078125,
-0.0280914306640625,
-0.00560760498046875,
-0.0016088485717773438,
-0.043914794921875,
-0.00531005859375,
0.0077972412109375,
-0.0181121826171875,
0.003948211669921875,
-0.0170135498046875,
-0.0166015625,
-0.004665374755859375,
-0.00765228271484375,
0.023284912109375,
0.004688262939453125,
-0.0240936279296875,
-0.01244354248046875,
-0.009521484375,
0.0087432861328125,
-0.0074005126953125,
-0.00705718994140625,
0.00754547119140625,
0.035064697265625,
0.004657745361328125,
-0.00556182861328125,
-0.00559234619140625,
0.023193359375,
-0.024810791015625,
0.00003999471664428711,
0.007724761962890625,
0.00150299072265625,
-0.0077056884765625,
0.0115509033203125,
0.01503753662109375,
0.0015087127685546875,
0.007442474365234375,
0.0145263671875,
-0.027496337890625,
-0.0205230712890625,
-0.0260772705078125,
-0.034149169921875,
-0.006450653076171875,
-0.0200653076171875,
0.02374267578125,
-0.0194091796875,
-0.0308380126953125,
-0.020294189453125,
0.00823211669921875,
-0.046539306640625,
-0.00199127197265625,
0.054443359375,
0.00016927719116210938,
-0.0034389495849609375,
0.0115814208984375,
-0.042816162109375,
0.01580810546875,
0.0096282958984375,
0.02667236328125,
0.01174163818359375,
0.0175018310546875,
0.0031299591064453125,
0.00878143310546875,
0.004222869873046875,
-0.00200653076171875,
-0.01546478271484375,
-0.010345458984375,
0.0202484130859375,
-0.00955963134765625,
-0.0190582275390625,
-0.00299835205078125,
-0.014678955078125,
0.01044464111328125,
-0.02532958984375,
0.0270538330078125,
-0.0244140625,
-0.0086669921875,
0.0287017822265625,
0.0072784423828125,
0.026336669921875,
0.01739501953125,
-0.02105712890625,
-0.005161285400390625,
0.0102691650390625,
-0.00487518310546875,
-0.02410888671875,
-0.0189056396484375,
-0.00141143798828125,
0.004489898681640625,
-0.0128631591796875,
0.005786895751953125,
0.0292816162109375,
-0.00830078125,
0.01035308837890625,
-0.005702972412109375,
-0.01107025146484375,
0.005405426025390625,
-0.004627227783203125,
0.033782958984375,
-0.0034465789794921875,
0.00849151611328125,
-0.036407470703125,
-0.01224517822265625,
0.016571044921875,
0.0193634033203125,
-0.026153564453125,
0.006267547607421875,
-0.01519775390625,
-0.01367950439453125,
-0.01381683349609375,
0.024871826171875,
-0.0048065185546875,
-0.0109710693359375,
0.0244293212890625,
0.03387451171875,
0.00994110107421875,
0.035400390625,
0.002635955810546875,
0.0209503173828125,
0.003749847412109375,
0.0055999755859375,
-0.0164031982421875,
-0.00855255126953125,
0.007045745849609375,
-0.0160369873046875,
0.0423583984375,
0.0134735107421875,
-0.0163421630859375,
0.0189971923828125,
0.027618408203125,
-0.007244110107421875,
0.0011949539184570312,
-0.006015777587890625,
-0.0254058837890625,
-0.0116119384765625,
0.0154876708984375,
0.005023956298828125,
0.018310546875,
-0.00919342041015625,
-0.028839111328125,
0.0194549560546875,
0.00974273681640625,
0.01043701171875,
0.023651123046875,
-0.0119781494140625,
-0.018402099609375,
0.0253753662109375,
-0.0418701171875,
0.01470184326171875,
0.000827789306640625,
-0.00923919677734375,
-0.00643157958984375,
-0.00968170166015625,
-0.007114410400390625,
-0.01216888427734375,
-0.036163330078125,
-0.0217132568359375,
0.0019321441650390625,
0.0038967132568359375,
-0.0150909423828125,
-0.0291900634765625,
0.0194854736328125,
-0.00025391578674316406,
-0.03192138671875,
-0.004974365234375,
0.01216888427734375,
-0.011077880859375,
0.061370849609375,
0.0174560546875,
0.0180206298828125,
-0.0386962890625,
0.0036411285400390625,
-0.014434814453125,
-0.03558349609375,
-0.004093170166015625,
-0.00467681884765625,
-0.0264739990234375,
0.01038360595703125,
0.0009336471557617188,
0.0028972625732421875,
0.0239715576171875,
-0.0174102783203125,
0.0198516845703125,
0.0242462158203125,
0.0225830078125,
0.00533294677734375,
0.0191650390625,
-0.0132293701171875,
0.025543212890625,
0.005565643310546875,
-0.0253143310546875,
0.040283203125,
-0.005374908447265625,
-0.0218505859375,
0.006687164306640625,
-0.01047515869140625,
-0.032501220703125,
0.0029392242431640625,
0.032501220703125,
-0.01233673095703125,
-0.0098114013671875,
-0.020111083984375,
0.016204833984375,
-0.0090484619140625,
0.024810791015625,
0.0235595703125,
0.043853759765625,
0.007099151611328125,
0.0053558349609375,
-0.011688232421875,
-0.0028705596923828125,
0.003833770751953125,
0.015167236328125,
0.0030517578125,
0.033355712890625,
0.007678985595703125,
-0.00498199462890625,
0.00754547119140625,
0.005496978759765625,
-0.04132080078125,
0.005401611328125,
-0.0040740966796875,
0.01253509521484375,
-0.0017404556274414062,
-0.0284881591796875,
0.006137847900390625,
0.0174102783203125,
0.006961822509765625,
-0.001972198486328125,
0.004840850830078125,
0.0045928955078125,
-0.00818634033203125,
-0.016082763671875,
-0.00629425048828125,
-0.0081939697265625,
0.037445068359375,
0.00321197509765625,
-0.01763916015625,
-0.0016498565673828125,
-0.011627197265625,
-0.01727294921875,
-0.0229644775390625,
-0.030181884765625,
0.00775146484375,
0.00884246826171875,
-0.00025200843811035156,
-0.029144287109375,
-0.028656005859375,
-0.00701904296875,
-0.000614166259765625,
0.006748199462890625,
0.031524658203125,
0.00318145751953125,
-0.003971099853515625,
0.023406982421875,
-0.03106689453125,
0.0237884521484375,
-0.013824462890625,
-0.001743316650390625,
-0.00601959228515625,
-0.0035266876220703125,
0.008544921875,
-0.00437164306640625,
0.0150604248046875,
-0.01053619384765625,
-0.0083770751953125,
-0.0017185211181640625,
-0.040313720703125,
0.00836181640625,
0.005443572998046875,
0.018310546875,
0.040374755859375,
0.0227203369140625,
0.0509033203125,
0.00421905517578125,
-0.00966644287109375,
-0.0021800994873046875,
0.0230712890625,
-0.013885498046875,
0.009674072265625,
-0.014739990234375,
-0.01291656494140625,
-0.0118560791015625,
0.00879669189453125,
0.0090789794921875,
0.0038661956787109375,
-0.007434844970703125,
-0.0230865478515625,
-0.0275421142578125,
0.0290374755859375,
0.0307769775390625,
-0.01120758056640625,
0.00380706787109375,
0.04425048828125,
0.026580810546875
] |
ours_465
|
First, we show that no valid configuration can be rotated to obtain itself. The only way to place 2017 blue marbles to have rotational symmetry is if they are vertices of a regular 2017-gon, and the same goes for red and green. However, this requires all red marbles to be next to a green marble, which is not valid. Therefore, we can assume without loss of generality that the "first" position is a blue marble, which comprises \(\frac{1}{3}\) of all the ways.
The 2017 blue marbles will leave out 2017 gaps in between them. By considering how many gaps are filled with red marbles and how many are filled with green marbles, we get that
\[
N = 3 \cdot \sum_{i=1}^{2016} \binom{2017}{i} \binom{2016}{i-1} \binom{2016}{2016-i}
\]
Since \(\binom{2017}{i}\) is always divisible by 2017, \( N \) is divisible by 2017. Moreover, since \(\binom{2016}{i} \equiv (-1)^{i} \pmod{2017}\), we have
\[
\frac{N}{2017} = 3 \cdot \sum_{i=1}^{2016} \frac{1}{2017} \binom{2017}{i} \binom{2016}{i-1} \binom{2016}{2016-i} \equiv -\frac{3}{2017} \cdot \sum_{i=1}^{2016} \binom{2017}{i} \cdot (-1)^{2017} = -\frac{3}{2017} \left(2^{2017} - 2\right) \pmod{2017}
\]
It suffices to compute \( 2^{2017} \) modulo \( 2017^{2} \), which comes out to be 2793547. Therefore,
\[
\frac{N}{2017} \equiv -3 \cdot \frac{2793547 - 2}{2017} = -3 \cdot 1385 \equiv 3 \cdot 632 = 1896 \pmod{2017}
\]
Thus, \( m = 1 \) and \( r = 1896 \), and \( p m + r = 2017 + 1896 = 3913 \).
\(\boxed{3913}\)
|
3913
|
{
"competition": "us_comps",
"dataset": "Ours",
"posts": null,
"source": "OMOFall17Solns.md"
}
|
Let \( p = 2017 \) be a prime. Suppose that the number of ways to place \( p \) indistinguishable red marbles, \( p \) indistinguishable green marbles, and \( p \) indistinguishable blue marbles around a circle such that no red marble is next to a green marble and no blue marble is next to a blue marble is \( N \). (Rotations and reflections of the same configuration are considered distinct.) Given that \( N = p^{m} \cdot n \), where \( m \) is a nonnegative integer and \( n \) is not divisible by \( p \), and \( r \) is the remainder of \( n \) when divided by \( p \), compute \( p m + r \).
|
[
"/Mathematics/DiscreteMathematics/Combinatorics/BinomialCoefficients",
"/Mathematics/DiscreteMathematics/Combinatorics/CombinatorialIdentities",
"/Mathematics/DiscreteMathematics/Combinatorics/Enumeration",
"/Mathematics/DiscreteMathematics/Combinatorics/GeneralCombinatorics",
"/Mathematics/NumberTheory/Congruences/Congruence",
"/Mathematics/NumberTheory/Congruences/Congruent",
"/Mathematics/NumberTheory/Congruences/Mod",
"/Mathematics/NumberTheory/Congruences/ModularArithmetic",
"/Mathematics/NumberTheory/Congruences/Modulus",
"/Mathematics/NumberTheory/GeneralNumberTheory/ElementaryMethods",
"/Mathematics/NumberTheory/GeneralNumberTheory/ElementaryNumberTheory",
"/Mathematics/NumberTheory/GeneralNumberTheory/HigherArithmetic",
"/Mathematics/NumberTheory/GeneralNumberTheory/NumberTheory",
"/Mathematics/NumberTheory/PrimeNumbers/PrimeNumberProperties"
] |
Count configurations by placing blues first, then fill the gaps with reds and greens, noting each term contains a factor p from \(\binom{p}{i}\).
|
[
-0.000012218952178955078,
-0.045013427734375,
-0.0225677490234375,
0.0023899078369140625,
0.00007450580596923828,
0.045806884765625,
-0.0294342041015625,
-0.0029277801513671875,
0.01012420654296875,
0.003570556640625,
0.039642333984375,
-0.036163330078125,
0.0006256103515625,
-0.005725860595703125,
-0.04547119140625,
-0.0178375244140625,
0.00853729248046875,
-0.01457977294921875,
-0.002407073974609375,
-0.000942230224609375,
-0.0115509033203125,
-0.033233642578125,
-0.019866943359375,
0.0195770263671875,
0.00933837890625,
-0.0287322998046875,
-0.013519287109375,
0.027587890625,
0.012176513671875,
-0.0172271728515625,
-0.0174102783203125,
0.00841522216796875,
0.017242431640625,
-0.01629638671875,
-0.0004191398620605469,
0.00725555419921875,
-0.006809234619140625,
0.003414154052734375,
-0.00487518310546875,
-0.039398193359375,
-0.00926971435546875,
0.0494384765625,
0.0220947265625,
0.0218505859375,
-0.027679443359375,
-0.01096343994140625,
-0.0023517608642578125,
0.04461669921875,
-0.009796142578125,
0.00237274169921875,
0.00792694091796875,
0.0040435791015625,
-0.0280609130859375,
-0.00772857666015625,
-0.0270843505859375,
-0.062286376953125,
0.001659393310546875,
-0.00017380714416503906,
0.006923675537109375,
-0.0231475830078125,
0.003284454345703125,
-0.01548004150390625,
-0.006687164306640625,
-0.0177459716796875,
0.00433349609375,
0.0038604736328125,
0.00897979736328125,
0.00982666015625,
0.00732421875,
-0.02471923828125,
0.0162811279296875,
-0.040313720703125,
-0.0110931396484375,
0.05877685546875,
0.043365478515625,
-0.01439666748046875,
0.0009517669677734375,
0.02252197265625,
0.0005693435668945312,
0.01445770263671875,
-0.00823211669921875,
0.027069091796875,
0.00966644287109375,
-0.00555419921875,
0.0111236572265625,
0.017913818359375,
0.01058197021484375,
0.00656890869140625,
0.0099334716796875,
-0.0023708343505859375,
-0.0014238357543945312,
0.028472900390625,
0.01580810546875,
0.042327880859375,
0.00899505615234375,
-0.005157470703125,
-0.00015294551849365234,
-0.0032176971435546875,
-0.0212860107421875,
0.0008950233459472656,
0.007293701171875,
-0.0106964111328125,
-0.0045166015625,
-0.0028171539306640625,
-0.03839111328125,
-0.00962066650390625,
-0.01155853271484375,
0.01543426513671875,
-0.01247406005859375,
0.01468658447265625,
-0.0013055801391601562,
0.0026702880859375,
0.048187255859375,
0.0034313201904296875,
0.0108642578125,
-0.002529144287109375,
0.02197265625,
0.0008063316345214844,
-0.01123809814453125,
-0.0278167724609375,
-0.001674652099609375,
0.0134429931640625,
-0.0169830322265625,
0.006473541259765625,
0.01419830322265625,
-0.031890869140625,
-0.0033435821533203125,
0.004703521728515625,
0.021331787109375,
0.0152130126953125,
0.033203125,
-0.01270294189453125,
-0.003902435302734375,
-0.009796142578125,
-0.043731689453125,
-0.0155792236328125,
0.0091400146484375,
0.0069122314453125,
-0.0028858184814453125,
0.016357421875,
0.01126861572265625,
0.010284423828125,
-0.010101318359375,
-0.0091400146484375,
0.00370025634765625,
0.0301055908203125,
-0.0113372802734375,
-0.0119476318359375,
-0.0007314682006835938,
-0.0084991455078125,
-0.0237579345703125,
-0.027618408203125,
0.028656005859375,
0.0009551048278808594,
-0.01995849609375,
0.0007944107055664062,
-0.0037078857421875,
0.0166473388671875,
0.00728607177734375,
0.0005369186401367188,
0.00836181640625,
0.0023174285888671875,
-0.00797271728515625,
-0.002010345458984375,
0.006572723388671875,
-0.0016460418701171875,
0.01146697998046875,
0.01338958740234375,
0.01119232177734375,
0.02947998046875,
0.0256805419921875,
-0.01364898681640625,
-0.01078033447265625,
-0.0018606185913085938,
0.005157470703125,
-0.0196990966796875,
-0.00659942626953125,
0.0282135009765625,
-0.00505828857421875,
0.0240478515625,
0.004650115966796875,
-0.043212890625,
-0.0034275054931640625,
0.0010328292846679688,
-0.0059356689453125,
0.00421905517578125,
-0.00047326087951660156,
0.0023097991943359375,
0.01776123046875,
0.0099029541015625,
-0.00762939453125,
-0.0225982666015625,
-0.000331878662109375,
0.030792236328125,
-0.000934600830078125,
-0.005504608154296875,
-0.00759124755859375,
0.0311431884765625,
0.04962158203125,
0.0031585693359375,
-0.0008788108825683594,
0.01263427734375,
0.018524169921875,
-0.00540924072265625,
-0.0050201416015625,
0.007801055908203125,
0.0268096923828125,
0.0002903938293457031,
0.0033206939697265625,
-0.0089569091796875,
0.00296783447265625,
-0.01412200927734375,
-0.01708984375,
-0.0252227783203125,
-0.01467132568359375,
-0.0014486312866210938,
-0.019866943359375,
0.0034732818603515625,
0.0084991455078125,
-0.044952392578125,
0.006679534912109375,
0.0160369873046875,
-0.005222320556640625,
-0.019683837890625,
-0.0269622802734375,
-0.0031280517578125,
0.00826263427734375,
0.0173492431640625,
-0.00925445556640625,
0.0046539306640625,
-0.0188140869140625,
-0.0010051727294921875,
0.00130462646484375,
0.005695343017578125,
-0.0015850067138671875,
-0.007183074951171875,
0.0112762451171875,
-0.01023101806640625,
0.0161895751953125,
-0.0189208984375,
0.031951904296875,
-0.01739501953125,
0.00620269775390625,
0.006305694580078125,
-0.020965576171875,
0.0005350112915039062,
-0.0119781494140625,
-0.0036182403564453125,
0.0095672607421875,
-0.019622802734375,
-0.01947021484375,
0.010986328125,
0.0033130645751953125,
0.005878448486328125,
-0.0058441162109375,
-0.0051727294921875,
0.0196380615234375,
-0.00044846534729003906,
-0.01448822021484375,
-0.0038776397705078125,
-0.0142364501953125,
-0.02008056640625,
-0.0027561187744140625,
-0.02130126953125,
0.00545501708984375,
-0.0033016204833984375,
0.047088623046875,
-0.0171051025390625,
0.018035888671875,
-0.0188751220703125,
0.03594970703125,
-0.0263671875,
-0.0157470703125,
0.0177001953125,
0.0361328125,
-0.00019621849060058594,
-0.00310516357421875,
0.00748443603515625,
-0.008819580078125,
-0.0174560546875,
0.02056884765625,
-0.021331787109375,
-0.00926971435546875,
0.00260162353515625,
0.00922393798828125,
0.003200531005859375,
-0.01525115966796875,
-0.0032062530517578125,
-0.0178680419921875,
0.0017862319946289062,
-0.01056671142578125,
-0.00933074951171875,
-0.0088653564453125,
0.0081939697265625,
0.06842041015625,
-0.07025146484375,
0.005054473876953125,
0.02667236328125,
0.029083251953125,
-0.02490234375,
0.0258331298828125,
-0.007709503173828125,
0.013946533203125,
0.038604736328125,
-0.004535675048828125,
0.02142333984375,
-0.009368896484375,
-0.01551055908203125,
-0.0192108154296875,
0.01739501953125,
0.003932952880859375,
0.0020160675048828125,
0.004528045654296875,
-0.0016260147094726562,
-0.0186614990234375,
-0.020843505859375,
-0.01451873779296875,
0.0443115234375,
0.005649566650390625,
0.040191650390625,
0.028289794921875,
0.004245758056640625,
-0.0256805419921875,
-0.01235198974609375,
0.0242462158203125,
-0.01141357421875,
0.0207366943359375,
0.0157623291015625,
-0.0255584716796875,
0.01317596435546875,
-0.05303955078125,
-0.0173187255859375,
-0.00615692138671875,
-0.02667236328125,
-0.0118255615234375,
-0.0024204254150390625,
-0.0033168792724609375,
0.027923583984375,
0.01204681396484375,
-0.005931854248046875,
-0.007236480712890625,
0.015716552734375,
0.04241943359375,
-0.0229339599609375,
-0.00273895263671875,
0.023040771484375,
0.00919342041015625,
0.0184783935546875,
-0.005420684814453125,
-0.0277557373046875,
0.00453948974609375,
0.0138092041015625,
0.0004172325134277344,
0.031158447265625,
-0.00959014892578125,
0.01538848876953125,
-0.01299285888671875,
0.0201873779296875,
-0.0169219970703125,
0.0013837814331054688,
0.01311492919921875,
0.014984130859375,
0.004070281982421875,
0.001636505126953125,
0.0175018310546875,
-0.02508544921875,
-0.0158538818359375,
0.02386474609375,
-0.033599853515625,
-0.021697998046875,
-0.0163116455078125,
-0.021728515625,
0.02984619140625,
-0.029083251953125,
-0.0430908203125,
-0.016815185546875,
-0.00983428955078125,
0.0119781494140625,
0.00580596923828125,
-0.00677490234375,
-0.01045989990234375,
0.043121337890625,
-0.0252838134765625,
0.054351806640625,
-0.0257720947265625,
0.0023097991943359375,
0.0076904296875,
-0.015594482421875,
-0.039031982421875,
0.01168060302734375,
-0.0082244873046875,
-0.0014295578002929688,
-0.017059326171875,
0.015655517578125,
0.0300445556640625,
-0.047698974609375,
0.0027179718017578125,
0.005046844482421875,
0.0220794677734375,
-0.0242919921875,
0.0003426074981689453,
-0.00567626953125,
0.0032749176025390625,
-0.0214996337890625,
0.011749267578125,
0.00806427001953125,
-0.0206146240234375,
-0.0079498291015625,
-0.01111602783203125,
0.01425933837890625,
0.00811767578125,
0.0012025833129882812,
0.0002422332763671875,
-0.009857177734375,
0.03271484375,
-0.000012636184692382812,
0.00617218017578125,
0.0231475830078125,
-0.040802001953125,
0.0227508544921875,
-0.020721435546875,
-0.034759521484375,
0.00937652587890625,
-0.0056915283203125,
0.0278472900390625,
0.047943115234375,
-0.028289794921875,
0.0250091552734375,
-0.01261138916015625,
-0.01306915283203125,
0.00498199462890625,
-0.01343536376953125,
-0.00933074951171875,
0.0161590576171875,
0.02044677734375,
0.025390625,
-0.00418853759765625,
0.00942230224609375,
0.0028781890869140625,
0.0255889892578125,
0.0308380126953125,
-0.036285400390625,
-0.0015077590942382812,
-0.0020923614501953125,
-0.0084991455078125,
0.008697509765625,
0.008331298828125,
0.0227508544921875,
-0.03704833984375,
0.0061492919921875,
-0.01453399658203125,
-0.0125579833984375,
-0.01030731201171875,
0.007259368896484375,
0.004184722900390625,
0.037994384765625,
-0.0109100341796875,
-0.0257110595703125,
0.023223876953125,
-0.002349853515625,
0.0021953582763671875,
0.02099609375,
-0.00557708740234375,
0.01763916015625,
-0.0313720703125,
0.0040740966796875,
-0.01064300537109375,
0.00046539306640625,
0.0239410400390625,
-0.0034503936767578125,
-0.0190582275390625,
-0.02178955078125,
-0.0050201416015625,
-0.024139404296875,
-0.050872802734375,
0.019378662109375,
0.0175628662109375,
0.0240478515625,
0.01326751708984375,
-0.0092926025390625,
0.00981903076171875,
0.00872802734375,
-0.027557373046875,
0.03656005859375,
-0.006992340087890625,
0.0030002593994140625,
0.037750244140625,
0.0149078369140625,
-0.0139923095703125,
0.0219573974609375,
0.028656005859375,
0.0377197265625,
-0.031646728515625,
-0.01355743408203125,
-0.00606536865234375,
-0.01390838623046875,
-0.0110626220703125,
0.01375579833984375,
-0.0007748603820800781,
0.01413726806640625,
0.0125732421875,
-0.0235595703125,
-0.0018415451049804688,
0.029449462890625,
0.013458251953125,
-0.01399993896484375,
0.076171875,
-0.01003265380859375,
-0.01151275634765625,
-0.0209197998046875,
-0.0176849365234375,
0.041717529296875,
0.0209808349609375,
-0.03289794921875,
-0.004909515380859375,
0.0138702392578125,
0.0198516845703125,
-0.00652313232421875,
-0.0015087127685546875,
0.04571533203125,
-0.01873779296875,
0.037506103515625,
0.031768798828125,
0.01221466064453125,
0.0182647705078125,
0.0028858184814453125,
0.01141357421875,
-0.0076904296875,
-0.00972747802734375,
-0.0271453857421875,
0.003993988037109375,
-0.0032863616943359375,
0.003204345703125,
-0.0229339599609375,
-0.0367431640625,
0.024017333984375,
0.00582122802734375,
-0.0216522216796875,
-0.0001735687255859375,
0.0125885009765625,
0.00608062744140625,
-0.005535125732421875,
0.02734375,
-0.0034427642822265625,
-0.01432037353515625,
-0.007137298583984375,
-0.0068511962890625,
0.0211181640625,
-0.042144775390625,
0.0084381103515625,
-0.0074615478515625,
0.01276397705078125,
-0.0086822509765625,
-0.0123443603515625,
-0.01727294921875,
0.006565093994140625,
-0.03131103515625,
-0.007541656494140625,
-0.0220489501953125,
-0.01076507568359375,
0.034698486328125,
-0.01275634765625,
0.007476806640625,
-0.0005936622619628906,
0.0173797607421875,
0.0031414031982421875,
-0.031402587890625,
0.003177642822265625,
-0.012115478515625,
-0.0006494522094726562,
0.0167083740234375,
0.01605224609375,
-0.035308837890625,
-0.02630615234375,
0.009613037109375,
0.00287628173828125,
-0.0304107666015625,
-0.00713348388671875,
0.01152801513671875,
-0.00832366943359375,
0.0012760162353515625,
0.03985595703125,
0.00811004638671875,
0.033905029296875,
0.040191650390625,
-0.0025615692138671875,
0.0173797607421875,
0.027099609375,
0.015350341796875,
-0.0137786865234375,
-0.004474639892578125,
0.023773193359375,
0.00817108154296875,
0.03204345703125,
-0.01085662841796875,
-0.0178375244140625,
0.041473388671875,
-0.002349853515625,
0.01345062255859375,
-0.0179901123046875,
0.01250457763671875,
-0.024627685546875,
-0.025146484375,
0.016387939453125,
-0.01275634765625,
-0.0304107666015625,
0.01885986328125,
-0.00522613525390625,
0.0014247894287109375,
-0.01038360595703125,
-0.0033855438232421875,
-0.0159454345703125,
0.04248046875,
-0.0018148422241210938,
0.03466796875,
0.00708770751953125,
-0.0123748779296875,
-0.009063720703125,
0.006137847900390625,
-0.0208740234375,
-0.0161590576171875,
0.0172576904296875,
-0.0028533935546875,
0.00958251953125,
-0.00891876220703125,
-0.0080718994140625,
0.0267181396484375,
-0.03216552734375,
0.0293731689453125,
-0.02557373046875,
-0.033538818359375,
0.034637451171875,
-0.006732940673828125,
-0.0010890960693359375,
-0.0033626556396484375,
0.02825927734375,
0.013397216796875,
0.005970001220703125,
-0.0062255859375,
-0.0216217041015625,
-0.00592803955078125,
0.0301055908203125,
-0.005451202392578125,
-0.041259765625,
-0.042572021484375,
0.0164337158203125,
0.030303955078125,
0.0238800048828125,
-0.0218658447265625,
0.00786590576171875,
-0.00028896331787109375,
-0.043792724609375,
0.007259368896484375,
0.0036411285400390625,
0.01271820068359375,
-0.0088958740234375,
-0.003082275390625,
-0.0155792236328125,
0.006744384765625,
-0.01120758056640625,
0.00759124755859375,
0.006977081298828125,
-0.0194549560546875,
-0.006130218505859375,
-0.025054931640625,
0.0174102783203125,
-0.0289154052734375,
-0.001659393310546875,
0.033172607421875,
-0.0096282958984375,
0.0213470458984375,
-0.020172119140625,
0.006072998046875,
-0.02447509765625,
0.0198974609375,
-0.007476806640625,
0.0166015625,
-0.0005002021789550781,
0.0156402587890625,
-0.0020160675048828125,
0.02716064453125,
0.023223876953125,
0.03961181640625,
-0.0208282470703125,
0.0369873046875,
0.0159454345703125,
-0.005641937255859375,
-0.01076507568359375,
0.0185089111328125,
0.003963470458984375,
-0.006374359130859375,
0.00106048583984375,
0.017120361328125,
0.0003638267517089844,
-0.005580902099609375,
-0.03277587890625,
-0.004703521728515625,
-0.0208892822265625,
-0.01399993896484375,
-0.00394439697265625,
0.0162506103515625,
-0.032623291015625,
0.0004782676696777344,
0.0084228515625,
0.0117645263671875,
-0.011962890625,
0.0136260986328125,
0.019439697265625,
-0.0261993408203125,
0.00955963134765625,
-0.035552978515625,
-0.01276397705078125,
0.00858306884765625,
-0.0008502006530761719,
-0.013092041015625,
-0.01277923583984375,
0.0306549072265625,
0.0025787353515625,
0.0164337158203125,
0.0181732177734375,
-0.0037822723388671875,
0.032806396484375,
-0.01171875,
-0.0184783935546875,
0.0254364013671875,
0.006641387939453125,
-0.01502227783203125,
-0.04779052734375,
0.00366973876953125,
-0.02716064453125,
-0.0010194778442382812,
-0.0008392333984375,
0.01485443115234375,
0.002017974853515625,
-0.036529541015625,
-0.0307464599609375,
0.00494384765625,
-0.031707763671875,
-0.049072265625,
-0.005573272705078125,
0.02978515625,
0.0274505615234375,
0.03887939453125,
0.0111236572265625,
0.00860595703125,
0.0028514862060546875,
-0.009796142578125,
-0.0462646484375,
0.014251708984375,
0.030029296875,
0.045623779296875,
0.002643585205078125,
-0.005802154541015625,
-0.0068817138671875,
0.003322601318359375,
-0.010498046875,
0.0230712890625,
-0.0221405029296875,
-0.01367950439453125,
-0.0010004043579101562,
-0.01666259765625,
-0.0236968994140625,
0.0256195068359375,
-0.004016876220703125,
0.004405975341796875,
0.003353118896484375,
-0.01348114013671875,
-0.01377105712890625,
-0.006122589111328125,
0.0328369140625,
-0.007030487060546875,
0.0087890625,
0.0081939697265625,
-0.0272216796875,
-0.012237548828125,
-0.01374053955078125,
-0.05029296875,
0.029693603515625,
0.004688262939453125,
-0.042510986328125,
0.006954193115234375,
-0.00884246826171875,
-0.00963592529296875,
0.0325927734375,
-0.0098114013671875,
-0.0047760009765625,
-0.010467529296875,
-0.02276611328125,
0.00989532470703125,
-0.008270263671875,
0.03863525390625,
0.00731658935546875,
0.01485443115234375,
-0.0014009475708007812,
0.005626678466796875,
0.01617431640625,
0.005344390869140625,
-0.0238494873046875,
-0.007568359375,
-0.0025272369384765625,
0.0037174224853515625,
-0.01366424560546875,
-0.00734710693359375,
0.026702880859375,
0.00875091552734375,
-0.0008525848388671875,
0.0024662017822265625,
0.012115478515625,
-0.0289306640625,
-0.015533447265625,
0.0182647705078125,
0.005092620849609375,
0.00572967529296875,
-0.0264739990234375,
0.005523681640625,
-0.0168304443359375,
-0.025146484375,
0.000006020069122314453,
0.0183563232421875,
0.033782958984375,
0.00872039794921875,
0.040313720703125,
0.008758544921875,
0.0124664306640625,
-0.0208587646484375,
-0.0013399124145507812,
0.0036373138427734375,
0.0247039794921875,
0.0216064453125,
0.0016355514526367188,
-0.01654052734375,
0.005458831787109375,
-0.015350341796875,
-0.0038127899169921875,
-0.0087738037109375,
-0.010406494140625,
-0.019744873046875,
0.0173492431640625,
-0.02099609375,
-0.046356201171875,
0.01593017578125,
0.00040841102600097656,
-0.00077056884765625,
-0.0036144256591796875,
0.037261962890625,
-0.01438140869140625,
0.017669677734375,
-0.004974365234375,
0.0281829833984375,
-0.025848388671875,
-0.00007206201553344727,
-0.0107574462890625,
-0.02532958984375,
-0.001964569091796875,
-0.0235748291015625,
0.0187530517578125,
0.0184783935546875,
-0.0021114349365234375,
0.006439208984375,
-0.01325225830078125,
-0.0005345344543457031,
-0.0027599334716796875,
0.052886962890625,
-0.01837158203125,
-0.013824462890625,
0.00627899169921875,
-0.008758544921875,
-0.005420684814453125,
0.035003662109375,
0.0018815994262695312,
-0.003925323486328125,
-0.027587890625,
0.0133056640625,
0.00873565673828125,
0.00518035888671875,
0.01186370849609375,
0.0206298828125,
0.03155517578125,
-0.00612640380859375,
-0.0034160614013671875,
0.023193359375,
-0.0404052734375,
-0.02716064453125,
0.0200958251953125,
-0.03582763671875,
0.0056610107421875,
-0.00531768798828125,
-0.0242767333984375,
-0.033935546875,
-0.01387786865234375,
0.025604248046875,
0.00870513916015625,
0.0199737548828125,
-0.015777587890625,
0.020751953125,
-0.01078033447265625,
-0.01222991943359375,
-0.0248565673828125,
0.0214080810546875,
-0.045562744140625,
0.00824737548828125,
-0.000942230224609375,
-0.0048065185546875,
-0.0008449554443359375,
0.014801025390625,
-0.039154052734375,
-0.02435302734375,
-0.025909423828125,
-0.002689361572265625,
0.0140533447265625,
-0.002605438232421875,
-0.00824737548828125,
0.018402099609375,
-0.0016679763793945312,
-0.032135009765625,
0.00038504600524902344,
0.0175628662109375,
0.034881591796875,
0.032867431640625,
0.0260162353515625,
0.0125732421875,
-0.01132965087890625,
0.0284576416015625,
-0.0017757415771484375,
0.0335693359375,
-0.0084991455078125,
-0.004123687744140625,
-0.0222930908203125,
-0.003978729248046875,
0.020477294921875,
0.006412506103515625,
0.0240936279296875,
0.0095672607421875,
0.0272216796875,
-0.006107330322265625,
0.019134521484375,
0.0181427001953125,
-0.0013303756713867188,
0.01031494140625,
0.007762908935546875,
-0.0210113525390625,
0.0024204254150390625,
-0.0219268798828125,
-0.0243072509765625,
0.042083740234375,
0.0083465576171875,
-0.0032863616943359375,
0.01043701171875,
-0.0204925537109375,
-0.0288543701171875,
-0.01099395751953125,
-0.0264129638671875,
-0.030670166015625,
0.019195556640625,
-0.0024204254150390625,
-0.0145263671875,
0.009063720703125,
-0.007785797119140625,
-0.0136566162109375,
-0.01273345947265625,
0.01512908935546875,
0.01076507568359375,
0.0165557861328125,
-0.0244903564453125,
-0.010711669921875,
0.01465606689453125,
0.005146026611328125,
0.0361328125,
0.00910186767578125,
0.00836944580078125,
-0.016632080078125,
0.01268768310546875,
-0.00882720947265625,
-0.03961181640625,
-0.00033974647521972656,
0.002094268798828125,
-0.01355743408203125,
0.0225677490234375,
0.01450347900390625,
0.02374267578125,
-0.0138092041015625,
0.0147705078125,
-0.009124755859375,
-0.0161895751953125,
-0.03460693359375,
0.0303192138671875,
0.01467132568359375,
-0.031158447265625,
0.01422119140625,
0.0082244873046875,
0.003875732421875,
0.03558349609375,
-0.0198211669921875,
0.01560211181640625,
0.0199737548828125,
0.01253509521484375,
0.0281524658203125,
0.0309295654296875,
-0.0005640983581542969,
0.003231048583984375,
-0.0256195068359375,
0.009185791015625,
0.0252685546875,
-0.00909423828125,
0.0260772705078125,
-0.0008802413940429688,
-0.001155853271484375,
-0.02392578125,
0.0147705078125,
-0.0137939453125,
-0.055450439453125,
-0.01314544677734375,
-0.0210113525390625,
0.0282135009765625,
-0.0097198486328125,
0.0002713203430175781,
-0.01018524169921875,
0.021728515625,
-0.04156494140625,
0.01309967041015625,
0.0269622802734375,
0.013641357421875,
-0.0267486572265625,
-0.036590576171875,
-0.0226898193359375,
-0.004199981689453125,
-0.061370849609375,
0.0224151611328125,
0.048553466796875,
0.0167236328125,
0.00794219970703125,
-0.0179290771484375,
-0.004608154296875,
-0.0287017822265625,
-0.0154876708984375,
0.02099609375,
-0.0030345916748046875,
-0.0294647216796875,
-0.012847900390625,
-0.002346038818359375,
0.0037174224853515625,
-0.00989532470703125,
-0.005596160888671875,
-0.0163116455078125,
-0.05084228515625,
0.0021533966064453125,
0.0158233642578125,
-0.0077667236328125,
-0.013702392578125,
0.002185821533203125,
-0.0023479461669921875,
0.0013589859008789062,
-0.0211334228515625,
-0.026641845703125,
0.008758544921875,
0.029510498046875,
0.027496337890625,
-0.01116180419921875,
-0.0205078125,
-0.0203857421875,
0.03497314453125,
-0.01708984375,
0.00936126708984375,
-0.045135498046875,
0.0181884765625,
-0.0104217529296875,
-0.019317626953125,
0.01715087890625,
0.01172637939453125,
0.02874755859375,
-0.00492095947265625,
-0.00440216064453125,
-0.018768310546875,
-0.00875091552734375,
-0.00981903076171875,
0.0032215118408203125,
0.0072021484375,
-0.0209808349609375,
-0.0289154052734375,
-0.01102447509765625,
0.0091552734375,
-0.006114959716796875,
-0.044647216796875,
0.0009851455688476562,
-0.003139495849609375,
0.0155487060546875,
-0.0104827880859375,
-0.03692626953125,
0.01328277587890625,
-0.0294647216796875,
0.01085662841796875,
-0.0253143310546875,
0.0132293701171875,
0.00228118896484375,
0.01421356201171875,
-0.0144500732421875,
-0.029632568359375,
0.023101806640625,
0.01483154296875,
-0.0017948150634765625,
-0.041900634765625,
0.0203399658203125,
-0.000006556510925292969,
0.0007061958312988281,
0.0047760009765625,
-0.01666259765625,
-0.042999267578125,
0.03289794921875,
-0.0290374755859375,
-0.0122833251953125,
-0.0269927978515625,
0.0338134765625,
0.0001087188720703125,
0.021484375,
-0.043304443359375,
0.004955291748046875,
-0.045989990234375,
-0.011749267578125,
-0.0341796875,
-0.0014486312866210938,
0.01302337646484375,
0.03472900390625,
-0.00131988525390625,
0.0184783935546875,
0.0143890380859375,
-0.010986328125,
-0.01384735107421875,
-0.01097869873046875,
-0.027252197265625,
0.004802703857421875,
-0.0012769699096679688,
-0.00994873046875,
-0.00656890869140625,
-0.02880859375,
-0.0029964447021484375,
0.0132598876953125,
0.0035648345947265625,
-0.00428009033203125,
0.0205841064453125,
-0.03619384765625,
0.0126953125,
0.007602691650390625,
-0.01171112060546875,
-0.004863739013671875,
0.003551483154296875,
-0.02099609375,
0.007045745849609375,
-0.01198577880859375,
0.00521087646484375,
-0.0027332305908203125,
-0.0209808349609375,
0.046600341796875,
-0.027435302734375,
0.0034332275390625,
-0.006214141845703125,
-0.0141448974609375,
-0.0034160614013671875,
-0.0015516281127929688,
0.02471923828125,
0.012847900390625,
0.0001646280288696289,
-0.019989013671875,
0.0304412841796875,
-0.0092010498046875,
-0.0225677490234375,
0.004871368408203125,
0.003269195556640625,
0.0273590087890625,
-0.0306396484375,
0.021575927734375,
-0.02288818359375,
-0.016876220703125,
0.00507354736328125,
0.004291534423828125,
-0.022247314453125,
-0.004474639892578125,
0.0003733634948730469,
-0.03009033203125,
-0.037841796875,
0.0089569091796875,
-0.03131103515625,
0.0256195068359375,
0.0162506103515625,
0.0004413127899169922,
0.005908966064453125,
-0.004558563232421875,
-0.0099029541015625,
0.005191802978515625,
-0.02313232421875,
0.01174163818359375,
-0.03118896484375,
0.031097412109375,
0.0022830963134765625,
0.0009975433349609375,
-0.016082763671875,
-0.00951385498046875,
-0.040283203125,
0.0010166168212890625,
-0.01413726806640625,
-0.006694793701171875,
-0.0173187255859375,
0.017303466796875,
-0.0133056640625,
0.00013148784637451172,
-0.0242156982421875,
-0.0028228759765625,
0.00701141357421875,
0.030670166015625,
-0.01389312744140625,
0.0005092620849609375,
-0.0016145706176757812,
-0.028045654296875,
0.0004570484161376953,
-0.01103973388671875,
0.048736572265625,
-0.007450103759765625,
0.00780487060546875,
0.00804901123046875,
-0.01071929931640625,
-0.00507354736328125,
0.01317596435546875,
0.0205230712890625,
-0.0157623291015625,
-0.01114654541015625,
-0.0018148422241210938,
-0.01800537109375,
-0.041778564453125,
0.032562255859375,
0.0054779052734375,
0.0037689208984375,
0.024322509765625,
-0.0175933837890625,
-0.0078887939453125,
-0.026885986328125,
-0.03057861328125,
-0.0073394775390625,
0.0279388427734375,
0.01535797119140625,
-0.0120697021484375,
0.007625579833984375,
0.0021572113037109375,
0.004451751708984375,
0.01055908203125,
-0.0118865966796875,
0.0061187744140625,
-0.029296875,
-0.00568389892578125,
-0.0218353271484375,
-0.00243377685546875,
0.01387786865234375,
-0.00342559814453125,
0.05316162109375,
0.01006317138671875,
-0.007282257080078125,
-0.0220489501953125,
-0.038787841796875,
0.01904296875,
-0.00510406494140625,
-0.0303192138671875,
-0.036102294921875,
0.006061553955078125,
0.000995635986328125,
-0.03167724609375,
0.01465606689453125,
-0.036041259765625,
-0.0166015625,
-0.00943756103515625,
0.01033782958984375,
0.005947113037109375,
0.003131866455078125,
0.0004935264587402344,
0.005859375,
0.0211944580078125,
0.006679534912109375,
0.017425537109375,
-0.035186767578125,
-0.058868408203125,
0.006420135498046875,
0.0295257568359375,
0.00875091552734375,
-0.0082244873046875,
-0.0031566619873046875,
0.02899169921875,
0.004398345947265625,
-0.04522705078125,
-0.036865234375,
-0.00371551513671875,
-0.0003898143768310547,
-0.0033054351806640625,
-0.0164642333984375,
0.005252838134765625,
-0.015838623046875,
0.0036258697509765625,
0.018646240234375,
-0.009857177734375,
-0.01035308837890625,
0.006282806396484375,
0.0247039794921875,
0.003124237060546875,
0.021697998046875,
0.0166473388671875,
-0.00946807861328125,
0.01161956787109375,
-0.01401519775390625,
-0.0049285888671875,
-0.018157958984375,
-0.007137298583984375,
-0.004245758056640625,
0.02252197265625,
-0.01549530029296875,
0.0045166015625,
0.004863739013671875,
0.01299285888671875,
0.0057373046875,
0.04180908203125,
-0.0113525390625,
-0.01715087890625,
0.00489044189453125,
-0.02520751953125,
0.0016107559204101562,
-0.0091094970703125,
0.04638671875,
-0.015655517578125,
0.0012035369873046875,
-0.00327301025390625,
0.01039886474609375,
0.0077362060546875,
0.01224517822265625,
-0.003269195556640625,
0.01094818115234375,
-0.006885528564453125,
-0.01715087890625,
-0.025665283203125,
0.004016876220703125,
-0.01268768310546875,
0.01467132568359375,
0.037078857421875,
0.037994384765625,
-0.0145263671875,
-0.044586181640625,
0.002674102783203125,
0.04937744140625,
0.0012493133544921875,
-0.0137786865234375,
0.01174163818359375,
0.039031982421875,
-0.032470703125,
0.0239105224609375,
0.0006103515625,
-0.043853759765625,
0.019744873046875,
0.00502777099609375,
0.01806640625,
0.043548583984375,
-0.004535675048828125,
-0.01502227783203125,
0.008148193359375,
-0.018951416015625,
0.009796142578125,
0.002620697021484375,
-0.00836944580078125,
-0.037353515625,
-0.02520751953125,
-0.012054443359375,
-0.00627899169921875,
-0.0119171142578125,
0.0242156982421875,
-0.0030040740966796875,
0.0159759521484375,
0.00865936279296875,
-0.0209503173828125,
0.01280975341796875,
0.01715087890625,
0.0063323974609375,
0.0075225830078125,
-0.018951416015625,
-0.0026874542236328125,
-0.003070831298828125,
0.026458740234375,
-0.01398468017578125,
-0.00992584228515625,
-0.0299835205078125,
-0.01390838623046875,
-0.0258026123046875,
0.0002617835998535156,
-0.0016908645629882812,
0.02001953125,
0.0021877288818359375,
0.0155181884765625,
0.0031757354736328125,
-0.013458251953125,
0.0193328857421875,
-0.0191192626953125,
-0.002338409423828125,
0.022979736328125,
0.0216827392578125,
0.0230255126953125,
0.0186920166015625,
-0.00408172607421875,
0.0146942138671875,
0.020538330078125,
0.00084686279296875,
-0.005977630615234375,
0.0305328369140625,
-0.0015630722045898438,
0.0007081031799316406,
-0.02392578125,
-0.0160369873046875,
0.004810333251953125,
0.01544189453125,
-0.0311737060546875,
0.01800537109375,
0.0008716583251953125,
-0.0218048095703125,
-0.01006317138671875,
-0.007732391357421875,
0.0230865478515625,
-0.00945281982421875,
-0.0002620220184326172,
0.0021877288818359375,
0.022735595703125,
0.027679443359375,
-0.04620361328125,
0.0240020751953125,
0.0042266845703125,
0.0023212432861328125,
0.036224365234375,
0.0094146728515625,
-0.0290679931640625,
0.018768310546875,
-0.024169921875,
-0.019927978515625,
-0.024566650390625,
0.017730712890625,
-0.007343292236328125,
-0.0007295608520507812,
0.0001569986343383789,
0.01134490966796875,
0.0255126953125,
0.0295257568359375,
0.006595611572265625,
-0.0161285400390625,
-0.012054443359375,
0.00731658935546875,
-0.008209228515625,
0.00844573974609375,
0.030059814453125,
-0.0002675056457519531,
-0.027557373046875,
0.01471710205078125,
-0.01010894775390625,
-0.033111572265625,
-0.03179931640625,
0.001186370849609375,
0.0548095703125,
0.0049285888671875,
0.01812744140625,
0.022216796875,
-0.0112152099609375,
-0.0167236328125,
0.0180206298828125,
-0.0055389404296875,
-0.0028533935546875,
0.0234222412109375,
-0.005832672119140625,
-0.01406097412109375,
-0.0209808349609375,
0.0196533203125,
-0.0116119384765625,
-0.00556182861328125,
-0.029541015625,
-0.02496337890625,
0.02227783203125,
0.01328277587890625,
-0.0005674362182617188,
-0.00725555419921875,
0.0204620361328125,
0.0229644775390625,
0.0343017578125,
-0.01012420654296875,
0.00930023193359375,
-0.01052093505859375,
-0.0078125,
0.0087432861328125,
-0.020843505859375,
0.0020923614501953125,
0.04412841796875,
-0.008544921875,
0.0275421142578125,
-0.019683837890625,
-0.0209197998046875,
-0.00943756103515625,
0.034881591796875,
0.02459716796875,
0.01361083984375,
-0.0030364990234375,
-0.01922607421875,
-0.01953125,
-0.024932861328125,
0.005199432373046875,
0.00759124755859375,
-0.028594970703125,
-0.0111541748046875,
-0.01375579833984375,
0.0213165283203125,
-0.0020313262939453125,
0.0126495361328125,
-0.00013744831085205078,
-0.011138916015625,
-0.01055145263671875,
-0.011810302734375,
-0.0185699462890625,
0.038330078125,
-0.0031375885009765625,
-0.039398193359375,
-0.003986358642578125,
-0.01018524169921875,
-0.026123046875,
0.02642822265625,
0.00618743896484375,
0.003444671630859375,
0.0147552490234375,
-0.020721435546875,
-0.0238494873046875,
0.01158905029296875,
0.0023403167724609375,
0.0095977783203125,
-0.00971221923828125,
-0.00662994384765625,
0.0022373199462890625,
-0.005130767822265625,
-0.006206512451171875,
0.005794525146484375,
0.0277099609375,
0.010162353515625,
-0.0021877288818359375,
0.03900146484375,
-0.005283355712890625,
0.0252227783203125,
-0.022918701171875,
0.0152130126953125,
0.0262451171875,
0.00040435791015625,
0.03155517578125,
-0.01395416259765625,
0.03253173828125,
-0.005767822265625,
0.0095062255859375,
0.00788116455078125,
-0.01371002197265625,
0.0107269287109375,
-0.0175933837890625,
0.004085540771484375,
-0.025054931640625,
-0.021209716796875,
-0.007354736328125,
0.0107879638671875,
0.006610870361328125,
0.028900146484375,
-0.058837890625,
0.0096282958984375,
0.012542724609375,
-0.03851318359375,
-0.00008392333984375,
0.00823974609375,
0.0267486572265625,
0.012420654296875,
-0.0256195068359375,
-0.0025768280029296875,
-0.00214385986328125,
0.013671875,
0.00382232666015625,
0.0124053955078125,
0.021331787109375,
0.00031280517578125,
-0.0184173583984375,
0.0191497802734375,
0.00516510009765625,
-0.0246124267578125,
-0.0212554931640625,
-0.0199737548828125,
-0.03741455078125,
-0.0206298828125,
0.01415252685546875,
0.035888671875,
-0.0072784423828125,
0.00799560546875,
-0.0015420913696289062,
-0.0125579833984375,
-0.018524169921875,
0.0131072998046875,
0.0263824462890625,
-0.0367431640625,
-0.01383209228515625,
-0.006626129150390625,
0.00490570068359375,
0.03326416015625,
0.02813720703125,
0.0155792236328125,
0.0203857421875,
-0.0166473388671875,
0.01177978515625,
0.0024967193603515625,
-0.006290435791015625,
0.020843505859375,
-0.018096923828125,
0.0139312744140625,
0.0217132568359375,
0.004077911376953125,
-0.00910186767578125,
0.009246826171875,
-0.005565643310546875,
0.0167388916015625,
-0.0112762451171875,
-0.01641845703125,
-0.0134735107421875,
-0.005565643310546875,
0.01441192626953125,
-0.0304107666015625,
0.03216552734375,
0.036773681640625,
0.001132965087890625,
-0.004344940185546875,
0.004764556884765625,
0.04345703125,
0.01421356201171875,
-0.022247314453125,
0.004039764404296875,
-0.0088958740234375,
0.01708984375,
0.019683837890625,
-0.016204833984375,
-0.043243408203125,
0.0271453857421875,
-0.0270233154296875,
0.012237548828125,
0.02081298828125,
0.025665283203125,
0.00089263916015625,
0.000020444393157958984,
0.00677490234375,
-0.020538330078125,
0.0120697021484375,
-0.055694580078125,
0.0294036865234375,
0.0177001953125,
0.019561767578125,
0.01641845703125,
0.002376556396484375,
-0.00628662109375,
-0.0026988983154296875,
0.0188751220703125,
0.03961181640625,
-0.0294647216796875,
0.02215576171875,
-0.0235595703125,
0.01473236083984375,
-0.021759033203125,
0.01806640625,
0.005443572998046875,
0.0269622802734375,
0.033477783203125,
0.0093994140625,
-0.002773284912109375,
-0.0016632080078125,
0.0074005126953125,
0.01351165771484375,
0.0019073486328125,
-0.0199432373046875,
-0.01036834716796875,
-0.00890350341796875,
0.005672454833984375,
-0.00795745849609375,
0.014617919921875,
-0.0299072265625,
0.004055023193359375,
-0.0129547119140625,
0.0222015380859375,
0.0191497802734375,
-0.0014019012451171875,
-0.046905517578125,
-0.00788116455078125,
0.0091552734375,
0.040496826171875,
0.0015745162963867188,
0.02410888671875,
0.0080718994140625,
0.00196075439453125,
-0.0028057098388671875,
0.005573272705078125,
0.040283203125,
-0.01300048828125,
-0.0031833648681640625,
-0.0006456375122070312,
0.0221710205078125,
0.007411956787109375,
0.027313232421875,
0.028533935546875,
-0.0165863037109375,
0.047088623046875,
-0.01267242431640625,
0.0096588134765625,
-0.01485443115234375,
-0.01340484619140625,
-0.00698089599609375,
0.01458740234375,
-0.0235595703125,
-0.01029205322265625,
-0.0306396484375,
-0.00635528564453125,
0.0240936279296875,
-0.0236053466796875,
-0.0247039794921875,
-0.00811004638671875,
-0.0083160400390625,
0.01548004150390625,
0.034698486328125,
0.007080078125,
0.0003418922424316406,
-0.0224609375,
0.0015010833740234375,
-0.018341064453125,
0.015716552734375,
0.00557708740234375,
0.007625579833984375,
0.0025463104248046875,
-0.00861358642578125,
-0.01187896728515625,
0.030731201171875,
0.01169586181640625,
-0.0174713134765625,
0.0262603759765625,
-0.01537322998046875,
-0.004833221435546875,
0.021484375,
-0.01043701171875,
-0.0120086669921875,
-0.0174407958984375,
-0.033782958984375,
0.03277587890625,
-0.0128631591796875,
0.006763458251953125,
-0.00762939453125,
0.022857666015625,
-0.00525665283203125,
0.01389312744140625,
0.0029315948486328125,
0.0258026123046875,
0.0200653076171875,
0.00628662109375,
-0.03125,
-0.03741455078125,
0.006343841552734375,
-0.033050537109375,
-0.0233612060546875,
-0.002838134765625,
0.00765228271484375,
-0.019927978515625,
-0.007442474365234375,
-0.017364501953125,
0.016143798828125,
-0.023468017578125,
-0.0004165172576904297,
0.0230865478515625,
-0.0293426513671875,
0.0021343231201171875,
-0.006870269775390625,
-0.00125885009765625,
-0.015625,
-0.01450347900390625,
-0.0034236907958984375,
-0.00630950927734375,
0.032470703125,
-0.0135955810546875,
-0.0027599334716796875,
-0.0201416015625,
0.003093719482421875,
-0.0085296630859375,
-0.00704193115234375,
-0.0020084381103515625,
-0.01494598388671875,
0.0165252685546875,
0.02276611328125,
-0.0017414093017578125,
0.039154052734375,
0.0260162353515625,
-0.0032291412353515625,
-0.01641845703125,
-0.033203125,
0.0005292892456054688,
-0.0104217529296875,
0.01377105712890625,
0.0059967041015625,
-0.03106689453125,
-0.01568603515625,
-0.005931854248046875,
0.01117706298828125,
-0.002475738525390625,
-0.0163116455078125,
0.01535797119140625,
0.0015153884887695312,
0.01171112060546875,
-0.0204315185546875,
-0.01385498046875,
0.0128021240234375,
-0.0184326171875,
-0.034027099609375,
0.022613525390625,
-0.0060272216796875,
0.0033550262451171875,
-0.00797271728515625,
0.0192413330078125,
-0.00893402099609375,
0.015289306640625,
-0.025177001953125,
-0.0176239013671875,
0.0169219970703125,
0.0183563232421875,
-0.0085906982421875,
-0.0035457611083984375,
-0.00797271728515625,
0.017730712890625,
-0.00555419921875,
0.0229034423828125,
0.02813720703125,
-0.00197601318359375,
0.00836181640625,
0.0164642333984375,
-0.002086639404296875,
0.0246734619140625,
-0.00807952880859375,
0.042266845703125,
-0.0228729248046875,
-0.0167999267578125,
0.0192413330078125,
0.0144500732421875,
-0.00786590576171875,
-0.01470184326171875,
0.005924224853515625,
-0.018035888671875,
0.0128326416015625,
0.01123046875,
-0.00910186767578125,
0.02105712890625,
0.0010251998901367188,
-0.0089263916015625,
-0.014190673828125,
0.0162811279296875,
0.01190948486328125,
0.0008764266967773438,
0.012481689453125,
-0.0083465576171875,
0.0238494873046875,
-0.005584716796875,
-0.012725830078125,
0.03021240234375,
0.00466156005859375,
0.0036373138427734375,
-0.01195526123046875,
0.0015020370483398438,
-0.0178375244140625,
-0.019805908203125,
0.0010347366333007812,
0.01546478271484375,
0.0236053466796875,
-0.007106781005859375,
0.01361083984375,
0.00988006591796875,
0.0186767578125,
0.0031032562255859375,
0.01593017578125,
-0.01029205322265625,
-0.01047515869140625,
0.0196380615234375,
0.00604248046875,
0.0023345947265625,
0.0023193359375,
-0.0005526542663574219,
0.00760650634765625,
-0.011077880859375,
-0.0052032470703125,
0.0158233642578125,
-0.0292205810546875,
-0.0032939910888671875,
-0.012725830078125,
0.00579833984375,
0.040130615234375,
0.058685302734375,
0.041046142578125,
-0.011932373046875,
-0.0086212158203125,
-0.0008254051208496094,
0.0089263916015625,
0.0182342529296875,
0.032257080078125,
-0.0063018798828125,
-0.01113128662109375,
0.030975341796875,
-0.0065155029296875,
0.0173797607421875,
0.00916290283203125,
-0.007785797119140625,
-0.005886077880859375,
-0.01136016845703125,
-0.01343536376953125,
0.00882720947265625,
-0.0162811279296875,
-0.0181732177734375,
-0.002559661865234375,
0.0231781005859375,
-0.0011043548583984375,
-0.005413055419921875,
-0.03466796875,
-0.012939453125,
-0.0159759521484375,
0.032501220703125,
0.00643157958984375,
0.0458984375,
-0.0220794677734375,
-0.0172882080078125,
-0.0160980224609375,
-0.02099609375,
0.0401611328125,
0.026702880859375,
-0.00832366943359375,
0.0036449432373046875,
-0.0158843994140625,
0.009002685546875,
-0.0252532958984375,
-0.00621795654296875,
0.010498046875,
0.014678955078125,
0.042083740234375,
-0.035552978515625,
-0.032745361328125,
0.0306243896484375,
-0.0242462158203125,
0.004520416259765625,
0.0181121826171875,
0.0153961181640625,
-0.00811004638671875,
-0.01544189453125,
0.00983428955078125,
-0.0318603515625,
-0.0037250518798828125,
0.0008516311645507812,
0.006175994873046875,
0.0131683349609375,
-0.0220794677734375,
-0.0033130645751953125,
0.00363922119140625,
-0.0196685791015625,
-0.00875091552734375,
-0.02056884765625,
0.0015087127685546875,
-0.00699615478515625,
-0.0010395050048828125,
0.0005435943603515625,
0.004413604736328125,
0.039154052734375,
0.0031223297119140625,
-0.0159454345703125,
-0.0244903564453125,
-0.045654296875,
-0.0027942657470703125,
-0.01267242431640625,
0.01715087890625,
-0.04150390625,
-0.01444244384765625,
-0.00643157958984375,
-0.024688720703125,
-0.01123809814453125,
-0.015533447265625,
0.0079345703125,
0.023712158203125,
-0.0107574462890625,
0.0211944580078125,
0.0273895263671875,
0.0180816650390625,
-0.00026702880859375,
-0.017181396484375,
-0.022369384765625,
-0.0023899078369140625,
0.0031414031982421875,
0.01380157470703125,
-0.04815673828125,
0.002887725830078125,
0.006542205810546875,
-0.01221466064453125,
0.009368896484375,
0.00037860870361328125,
-0.00539398193359375,
0.0098876953125,
0.020172119140625,
-0.01071929931640625,
0.03179931640625,
0.06121826171875,
-0.0180206298828125,
0.0008978843688964844,
-0.032989501953125,
-0.010986328125,
0.01522064208984375,
0.01806640625,
0.0009179115295410156,
0.005329132080078125,
0.019866943359375,
0.00540924072265625,
0.0077056884765625,
0.0168914794921875,
0.004955291748046875,
0.0017309188842773438,
-0.0151824951171875,
-0.00995635986328125,
-0.02764892578125,
-0.021636962890625,
0.027587890625,
-0.007152557373046875,
0.005367279052734375,
0.03289794921875,
0.0059051513671875,
0.00018107891082763672,
-0.0272369384765625,
-0.0169525146484375,
0.0010929107666015625,
-0.002178192138671875,
0.002246856689453125,
-0.006805419921875,
0.024932861328125,
-0.04364013671875,
0.007411956787109375,
-0.01715087890625,
-0.000274658203125,
0.0296478271484375,
0.013397216796875,
0.04010009765625,
0.01202392578125,
0.0191802978515625,
0.01898193359375,
0.01486968994140625,
-0.0301361083984375,
0.02099609375,
-0.004535675048828125,
0.0128326416015625,
0.014190673828125,
-0.0074462890625,
0.00807952880859375,
0.0062713623046875,
-0.020538330078125,
-0.01322174072265625,
0.00305938720703125,
-0.0021800994873046875,
0.016571044921875,
-0.0038909912109375,
-0.0027217864990234375,
0.006221771240234375,
0.01776123046875,
0.0421142578125,
-0.005603790283203125,
-0.0035228729248046875,
0.0206146240234375,
0.023529052734375,
0.03985595703125,
-0.00850677490234375,
-0.0016574859619140625,
-0.0015926361083984375,
0.025543212890625,
-0.05255126953125,
0.004459381103515625,
-0.015655517578125,
-0.0021209716796875,
-0.00920867919921875,
-0.01079559326171875,
0.0072784423828125,
0.0017871856689453125,
0.0138702392578125,
-0.0031719207763671875,
-0.015838623046875,
0.03265380859375,
-0.0254974365234375,
-0.007122039794921875,
-0.047332763671875,
0.01303863525390625,
0.018524169921875,
0.030975341796875,
0.027374267578125,
-0.02606201171875,
-0.0063018798828125,
-0.00809478759765625,
-0.0182952880859375,
-0.0245819091796875,
0.0019283294677734375,
-0.01102447509765625,
0.005374908447265625,
0.005161285400390625,
0.0119781494140625,
-0.029296875,
0.02978515625,
0.0291595458984375,
0.020263671875,
-0.023223876953125,
-0.01206207275390625,
-0.004642486572265625,
-0.0003559589385986328,
-0.0242462158203125,
0.005947113037109375,
-0.005126953125,
-0.031951904296875,
-0.0262603759765625,
-0.00969696044921875,
-0.0190887451171875,
-0.011810302734375,
-0.002532958984375,
0.0035839080810546875,
-0.0082550048828125,
0.046539306640625,
0.0060272216796875,
0.02996826171875,
0.006389617919921875,
0.0185089111328125,
0.019744873046875,
0.028533935546875,
0.02825927734375,
0.0018444061279296875,
-0.00913238525390625,
0.011444091796875,
0.01081085205078125,
0.0032253265380859375,
0.0277557373046875,
0.00940704345703125,
0.0188140869140625,
-0.004512786865234375,
0.0193939208984375,
-0.03564453125,
-0.017364501953125,
-0.012298583984375,
-0.00004935264587402344,
0.0200347900390625,
-0.01262664794921875,
-0.01058197021484375,
0.015716552734375,
0.0204010009765625,
0.019134521484375,
0.0098114013671875,
0.0038318634033203125,
-0.0006046295166015625,
0.0186614990234375,
0.0021514892578125,
0.008544921875,
0.00991058349609375,
-0.02313232421875,
-0.0009555816650390625,
-0.0233306884765625,
-0.01296234130859375,
-0.0142822265625,
0.0312042236328125,
-0.003353118896484375,
-0.02301025390625,
-0.003215789794921875,
0.0272216796875,
-0.0002872943878173828,
0.006320953369140625,
-0.01678466796875,
0.00732421875,
-0.0213470458984375,
0.01003265380859375,
-0.0093841552734375,
-0.034454345703125,
-0.02783203125,
0.021392822265625,
0.0270233154296875,
0.001415252685546875,
0.0202484130859375,
-0.01531982421875,
-0.00782012939453125,
-0.0135345458984375,
-0.004596710205078125,
-0.009246826171875,
0.033599853515625,
0.00830078125,
-0.009918212890625,
0.002498626708984375,
-0.01258087158203125,
-0.035430908203125,
0.01546478271484375,
-0.029296875,
0.018280029296875,
0.00948333740234375,
0.01690673828125,
-0.03118896484375,
0.0028591156005859375,
0.00600433349609375,
0.0025691986083984375,
0.00858306884765625,
0.039886474609375,
-0.022552490234375,
0.01526641845703125,
-0.01202392578125,
-0.0003235340118408203,
-0.017181396484375,
-0.00975799560546875,
0.0170440673828125,
-0.02569580078125,
-0.027435302734375,
0.0017032623291015625,
0.012176513671875,
-0.0265655517578125,
0.01922607421875,
0.03765869140625,
-0.01360321044921875,
0.023193359375,
-0.015655517578125,
0.008026123046875,
-0.0247344970703125,
0.0139312744140625,
-0.007526397705078125,
-0.022125244140625,
0.00983428955078125,
0.002521514892578125,
0.042449951171875,
0.0218505859375,
-0.005077362060546875,
0.0179595947265625,
0.03973388671875,
-0.006565093994140625,
0.01407623291015625,
-0.0108184814453125,
0.002506256103515625,
-0.0177001953125,
0.0057525634765625,
0.011993408203125,
0.0074005126953125,
-0.0204010009765625,
0.025390625,
-0.00414276123046875,
-0.00701904296875,
0.015777587890625,
-0.0221405029296875,
0.0176544189453125,
-0.005680084228515625,
-0.006504058837890625,
-0.01065826416015625,
0.026397705078125,
-0.005039215087890625,
0.008270263671875,
0.011932373046875,
-0.026214599609375,
0.03546142578125,
-0.00433349609375,
0.0309600830078125,
0.0099639892578125,
0.0009427070617675781,
-0.00007939338684082031,
-0.03826904296875,
0.0008988380432128906,
0.043060302734375,
0.0089263916015625,
-0.02374267578125,
0.0256500244140625,
-0.01085662841796875,
-0.010406494140625,
-0.00412750244140625,
0.02227783203125,
0.0157318115234375,
0.002777099609375,
-0.01200103759765625,
0.00402069091796875,
0.00835418701171875,
-0.0010213851928710938,
-0.01947021484375,
0.00917816162109375,
-0.026123046875,
-0.01155853271484375,
0.033843994140625,
-0.0152740478515625,
0.016265869140625,
-0.0186004638671875,
0.00377655029296875,
-0.0009341239929199219,
-0.00011229515075683594,
0.0153045654296875,
-0.0117034912109375,
-0.0023136138916015625,
-0.00274658203125,
-0.01373291015625,
0.032196044921875,
0.0183868408203125,
0.0034084320068359375,
-0.00461578369140625,
0.01198577880859375,
-0.026153564453125,
0.0027065277099609375,
-0.006072998046875,
0.0162506103515625,
0.0163726806640625,
-0.01192474365234375,
-0.00786590576171875,
0.061492919921875,
-0.041229248046875,
0.021392822265625,
0.032562255859375,
0.00876617431640625,
0.010467529296875,
0.03167724609375,
-0.027069091796875,
0.019927978515625,
-0.0081939697265625,
-0.0286407470703125,
-0.027435302734375,
-0.0119476318359375,
-0.0028095245361328125,
0.0223236083984375,
-0.00917816162109375,
0.00899505615234375,
-0.0248870849609375,
-0.0273284912109375,
-0.0009737014770507812,
-0.01629638671875,
0.00255584716796875,
0.01097869873046875,
0.003749847412109375,
-0.01053619384765625,
0.004302978515625,
0.0257568359375,
0.00409698486328125,
-0.0046234130859375,
0.0064239501953125,
-0.00019741058349609375,
-0.0111236572265625,
0.046783447265625,
-0.0184783935546875,
0.006671905517578125,
-0.0247039794921875,
0.01355743408203125,
0.03131103515625,
0.006591796875,
-0.0166015625,
-0.0032291412353515625,
-0.01197052001953125,
-0.005401611328125,
-0.01265716552734375,
-0.031402587890625,
-0.01490020751953125,
0.0037364959716796875,
-0.0032787322998046875,
-0.00347137451171875,
0.007122039794921875,
0.004192352294921875,
-0.00826263427734375,
0.0127105712890625,
-0.004970550537109375,
-0.006763458251953125,
-0.010986328125,
0.025115966796875,
0.04351806640625,
-0.01239776611328125,
0.030426025390625,
-0.024566650390625,
0.002166748046875,
0.0289764404296875,
0.0014200210571289062,
-0.0133514404296875,
-0.00023555755615234375,
-0.01497650146484375,
0.005977630615234375,
-0.045562744140625,
0.01325225830078125,
0.00243377685546875,
-0.034332275390625,
0.017303466796875,
-0.0119781494140625,
0.032073974609375,
0.007343292236328125,
-0.01806640625,
-0.001720428466796875,
-0.01410675048828125,
-0.01080322265625,
0.027099609375,
0.00644683837890625,
0.0518798828125,
0.01383209228515625,
0.037200927734375,
0.0045318603515625,
-0.031768798828125,
0.00615692138671875,
-0.0176239013671875,
0.032257080078125,
0.0323486328125,
-0.02069091796875,
0.043670654296875,
-0.01242828369140625,
-0.0236663818359375,
0.0279541015625,
-0.004817962646484375,
-0.013153076171875,
0.02886962890625,
-0.004444122314453125,
-0.0038433074951171875,
-0.0009169578552246094,
0.011444091796875,
0.001544952392578125,
0.012542724609375,
-0.0028057098388671875,
-0.013427734375,
0.0003204345703125,
-0.01457977294921875,
0.014434814453125,
0.034637451171875,
0.033721923828125,
0.0450439453125,
-0.0296478271484375,
-0.0006289482116699219,
0.0292510986328125,
-0.0015306472778320312,
-0.00286865234375,
-0.01381683349609375,
-0.00821685791015625,
-0.0237579345703125,
0.00969696044921875,
-0.0009984970092773438,
0.0220947265625,
0.0262298583984375,
-0.0153656005859375,
0.034942626953125,
0.0140228271484375,
0.01198577880859375,
-0.031707763671875,
0.031707763671875,
0.03338623046875,
-0.0146026611328125,
0.01306915283203125,
0.010009765625,
-0.0027637481689453125,
0.0176544189453125,
-0.019561767578125,
-0.0237579345703125,
-0.01459503173828125,
0.0286712646484375,
-0.0270233154296875,
0.0159149169921875,
-0.00489044189453125,
-0.003772735595703125,
0.01206207275390625,
0.0254974365234375,
-0.007476806640625,
0.01409149169921875,
0.01401519775390625,
-0.02294921875,
-0.01363372802734375,
-0.0004558563232421875,
0.0401611328125,
-0.01418304443359375,
-0.0179595947265625,
-0.01555633544921875,
0.00039386749267578125,
0.0142059326171875,
-0.0169830322265625,
-0.003814697265625,
-0.008697509765625,
0.01153564453125,
0.006496429443359375,
-0.015869140625,
-0.003520965576171875,
0.023468017578125,
-0.030670166015625,
-0.02813720703125,
-0.0263519287109375,
-0.020416259765625,
0.03802490234375,
-0.00701141357421875,
-0.01739501953125,
0.041259765625,
-0.0250091552734375,
0.00035500526428222656,
-0.009613037109375,
-0.05206298828125,
-0.0157928466796875,
0.03387451171875,
0.038360595703125,
0.03533935546875,
0.01338958740234375,
0.002361297607421875,
-0.004688262939453125,
0.0175323486328125,
0.029022216796875,
-0.0022487640380859375,
0.017425537109375,
-0.01006317138671875,
-0.004070281982421875,
-0.0191650390625,
-0.031829833984375,
-0.0643310546875,
-0.0258026123046875,
-0.00579833984375,
0.007221221923828125,
0.0020351409912109375,
0.0026645660400390625,
-0.0247344970703125,
0.0023975372314453125,
-0.023468017578125,
0.0302276611328125,
0.046722412109375,
-0.040740966796875,
-0.0177001953125,
0.00337982177734375,
0.048187255859375,
-0.0217742919921875,
0.0074005126953125,
-0.0022258758544921875,
-0.0139923095703125,
-0.00201416015625,
-0.012237548828125,
-0.01482391357421875,
0.001697540283203125,
-0.027740478515625,
0.009429931640625,
0.0032958984375,
0.01470184326171875,
0.004169464111328125,
0.0190582275390625,
0.05767822265625,
-0.0212554931640625,
-0.0014867782592773438,
-0.01788330078125,
-0.0149993896484375,
0.00878143310546875,
-0.025604248046875,
0.04742431640625,
-0.0309295654296875,
0.0168609619140625,
-0.0036869049072265625,
0.057830810546875,
0.011199951171875,
-0.0204010009765625,
-0.00009882450103759766,
0.007076263427734375,
-0.007732391357421875,
-0.00423431396484375,
-0.0009326934814453125,
0.024627685546875,
0.01055908203125,
0.004100799560546875,
0.01103973388671875,
0.00823974609375,
0.0200653076171875,
0.0234527587890625,
-0.0103759765625,
0.016754150390625,
0.00928497314453125,
0.02911376953125,
-0.0228118896484375,
-0.00809478759765625,
-0.0119171142578125,
-0.0196075439453125,
0.00569915771484375,
0.023651123046875,
-0.017181396484375,
-0.00025200843811035156,
0.004314422607421875,
-0.007442474365234375,
0.03778076171875
] |
ours_466
|
The answer is \(7056\).
For convenience, we denote each square by its coordinates, with \((0,0)\) being the lower left corner of the Sacred subboard, and \((7,7)\) being the upper right corner. Moreover, we color a square black if its sum of coordinates is even and white otherwise (like a normal chessboard). Since a Holy Knight (HK) on a black square attacks only white squares and vice versa, it suffices to consider the number of ways for all the white squares to be attacked by HKs (on black squares) and square this number to get the answer.
We use the following two observations:
1. If a HK is placed on a black square \((x, y)\) where \(1 \leq x, y \leq 6\), then for its neighboring Sacred white squares to be attacked, there are two configurations: either there are two knights placed at \((x+2, y+2)\) and \((x-2, y-2)\) or \((x+2, y-2)\) and \((x-2, y+2)\), with one exception: if the HK is placed on \((1,1)\) (or \((6,6)\)), then the four neighbors can be covered by HKs on \((3,3),(-2,0)\), and \((0,-2)\) (or \((4,4),(9,7)\), and \((7,9)\)).
2. Suppose that \((x, y)\) is not yet attacked but all of \((x-1, y+3),(x, y+2),(x+1, y+1),(x+2, y),(x+3, y-1)\) are, then the square can only be attacked by an HK on \((x-2, y-1)\) or \((x-1, y-2)\).
With these two observations, we can consider various possibilities for arrangements. In particular, consider the HK that attacks \((3,4)\) (WLOG assume that the HK is below the main diagonal).
**Case 1:** The HK is on \((2,2)\). By Observation 1, there are two HKs on \((0,4)\) and \((4,0)\) or \((0,0)\) and \((4,4)\).
- **Case 1.1:** In the first possibility, for \((0,5)\) to be attacked without attacking other Sacred squares that are already attacked, an HK must be placed on \((-2,6)\), and similarly for \((5,0)\). This will cover all black squares on or below the line \(x+y=7\). By Observation 2, for \((4,5)\) to be attacked, an HK must be placed on \((6,6)\) or \((5,7)\), and for \((5,4)\) to be attacked, an HK must be placed on \((6,6)\) or \((7,5)\).
- **Case 1.1.1:** An HK is placed on \((6,6)\). By Observation 1, since HK cannot be placed on \((4,4)\) anymore, two HKs must be placed on \((4,8)\) and \((8,4)\). This takes care of all the Sacred white squares.
- **Case 1.1.2:** Two HKs are placed on \((5,7)\) and \((7,5)\). This leaves \((2,7),(4,7),(7,2),(7,4)\) unattacked. The only valid way is to place two HKs at \((3,9)\) and \((9,3)\) respectively.
- **Case 1.2:** In the second possibility, applying Observation 1 to \((4,4)\) shows that \((6,6)\) must contain an HK. As mentioned in the exception to Observation 1, the two squares \((6,7),(7,6)\) can be attacked by the same HK at \((8,8)\) or two different HKs at \((7,9)\) and \((9,7)\), and either way does not affect the other white Sacred squares. We need now to consider the unattacked squares above \(y-x=4\) and below \(x-y=4\). Applying Observation 2 to \((1,6)\) gives that one HK must be placed at \((-1,7)\) or \((0,8)\), and it is not difficult to see that another HK must be placed at \((1,9)\) or \((-2,6)\) respectively to cover the remaining squares on the upper-left corner. The same applies for the squares on the lower-right corner.
We have 2 ways from Case 1.1 and \(2 \cdot 2 \cdot 2=8\) ways from Case 1.2, for 10 ways in this case.
**Case 2:** The HK is on \((1,3)\). By Observation 1, there are two HKs on \((-1,5)\) and \((3,1)\) or \((-1,1)\) and \((3,5)\).
- **Case 2.1:** In the first possibility, by Observation 1 again on \((3,1)\), an HK must be placed on \((5,-1)\), and these HKs combined attack all the squares on or below the main diagonal. The rest is identical to Case 1.1.
- **Case 2.2:** In the second possibility, applying Observation 1 on \((3,5)\) gives that an HK must be placed on \((5,7)\). For \((6,7)\) to be attacked, an HK must be placed on \((7,9)\). This leaves a single square \((0,7)\) and all the squares below \(x-y=2\) unattacked. There are two ways to attack \((0,7)\) without attacking other Sacred squares: an HK at \((-2,8)\) or \((-1,9)\). For the lower-right corner, applying Observation 2 on \((4,1),(5,2),(6,3)\) gives that two HKs must be placed on \((5,-1)\) and \((7,1)\) or \((6,0)\) and \((8,2)\). In the former case, we still need to attack \((7,2)\) and \((7,4)\), which can only be done by an HK at \((9,3)\), and the latter case is symmetric to this case.
We have 2 ways from Case 2.1 and \(2 \cdot 2=4\) ways from Case 2.2, for 6 ways in this case.
**Case 3:** The HK is on \((4,2)\). By Observation 1, there are two HKs on \((2,4)\) and \((6,0)\) or \((2,0)\) and \((6,4)\).
- **Case 3.1:** In the first possibility, by Observation 1 on \((2,4)\) forces placement of another HK at \((0,6)\). There are two ways to attack the squares \((0,1)\) and \((1,0)\) (same as \((6,7)\) and \((7,6)\) in Case 1.2). There are two ways to attack each of the unattacked squares \((0,7)\) and \((7,0)\) (see Case 2.2). It now remains to consider the squares above \(x+y=10\). Applying Observation 2 on \((5,6)\) and \((6,5)\) gives two cases.
- **Case 3.1.1:** They are attacked by the same HK on \((7,7)\). Then to cover \((4,7),(6,7),(7,4),(7,6)\) we need to place two more HKs on \((5,9)\) and \((9,5)\).
- **Case 3.1.2:** They are attacked by two different HKs on \((6,8)\) and \((8,6)\). Then all the white Sacred squares are taken care of.
- **Case 3.2:** In the second possibility, Observation 1 on \((6,4)\) forces placement of another HK on \((8,6)\). For \((1,0)\) to be attacked, an HK must be placed on \((0,-2)\). The arrangement of remaining squares \((7,0)\) and all squares above \(y-x=2\) is symmetric to Case 2.2.
We have \(2 \cdot 2^{2} \cdot 2=16\) ways from Case 3.1 and 4 ways from Case 3.2, for 20 ways in this case.
**Case 4:** The HK is on \((1,5)\). By Observation 1, there are two HKs on \((-1,7)\) and \((3,3)\) or \((-1,3)\) and \((3,7)\).
- **Case 4.1:** In the first possibility, applying Observation 1 on \((3,3)\) forces an HK on \((5,1)\) and applying it again on \((5,1)\) forces an HK on \((7,-1)\). The rest is identical to Case 3.1 (after \((7,0)\) and \((0,7)\) are covered).
The total number of ways is \(10 + 6 + 20 + 20 = 56\). Since we only considered one color of squares, we square this number to account for both colors, giving us \(56^2 = 3136\).
Thus, the number of ways Rosabel can protect the Sanctity of Iris' chessboard is \(\boxed{7056}\).
|
7056
|
{
"competition": "us_comps",
"dataset": "Ours",
"posts": null,
"source": "OMOFall17Solns.md"
}
|
Iris has an infinite chessboard, in which an \(8 \times 8\) subboard is marked as Sacred. In order to preserve the Sanctity of this chessboard, her friend Rosabel wishes to place some indistinguishable Holy Knights on the chessboard (not necessarily within the Sacred subboard) such that:
- No two Holy Knights occupy the same square;
- Each Holy Knight attacks at least one Sacred square;
- Each Sacred square is attacked by exactly one Holy Knight.
In how many ways can Rosabel protect the Sanctity of Iris' chessboard? (A Holy Knight works in the same way as a knight piece in chess, that is, it attacks any square that is two squares away in one direction and one square away in a perpendicular direction. Note that a Holy Knight does not attack the square it is on.)
|
[
"/Mathematics/DiscreteMathematics/Combinatorics/Configurations",
"/Mathematics/DiscreteMathematics/Combinatorics/Enumeration",
"/Mathematics/DiscreteMathematics/Combinatorics/GeneralCombinatorics",
"/Mathematics/DiscreteMathematics/GeneralDiscreteMathematics/DiscreteMath",
"/Mathematics/DiscreteMathematics/GeneralDiscreteMathematics/DiscreteMathematics",
"/Mathematics/RecreationalMathematics/Puzzles/Puzzle"
] |
Use the chessboard coloring to separate the problem: knights on black squares must uniquely cover all white sacred squares, then square the count for both colors.
|
[
0.000059604644775390625,
-0.040252685546875,
0.0270538330078125,
-0.07635498046875,
0.0003256797790527344,
-0.01407623291015625,
0.0010690689086914062,
-0.031280517578125,
0.0154876708984375,
0.0005269050598144531,
0.004375457763671875,
-0.041015625,
-0.0019016265869140625,
0.02960205078125,
-0.018798828125,
-0.0367431640625,
0.010772705078125,
-0.00232696533203125,
-0.01995849609375,
-0.0008559226989746094,
-0.02252197265625,
-0.0535888671875,
-0.01076507568359375,
0.038421630859375,
0.038543701171875,
-0.025482177734375,
-0.0157928466796875,
0.037567138671875,
-0.002468109130859375,
0.023345947265625,
-0.040313720703125,
-0.038787841796875,
0.033447265625,
0.0292510986328125,
0.000782012939453125,
0.007167816162109375,
0.0665283203125,
0.001251220703125,
-0.004039764404296875,
-0.01446533203125,
-0.0028400421142578125,
-0.01617431640625,
-0.0027179718017578125,
0.0014753341674804688,
0.0000934600830078125,
0.0203094482421875,
0.0030651092529296875,
-0.005825042724609375,
-0.0070648193359375,
0.005001068115234375,
-0.01166534423828125,
0.01479339599609375,
0.028900146484375,
0.00138092041015625,
0.00917816162109375,
-0.0121002197265625,
-0.062744140625,
-0.0017232894897460938,
0.006801605224609375,
0.004405975341796875,
0.01026153564453125,
0.0226287841796875,
-0.042083740234375,
-0.0196990966796875,
-0.0034847259521484375,
-0.0004680156707763672,
-0.0136260986328125,
0.01100921630859375,
0.00257110595703125,
-0.003387451171875,
-0.02044677734375,
0.004123687744140625,
-0.0335693359375,
0.038330078125,
0.025115966796875,
-0.007312774658203125,
-0.015472412109375,
0.0207061767578125,
0.017364501953125,
0.01496124267578125,
0.01210784912109375,
-0.0017528533935546875,
-0.0021762847900390625,
-0.00341033935546875,
-0.00229644775390625,
0.0031585693359375,
0.0224456787109375,
-0.0032978057861328125,
0.006103515625,
-0.0019931793212890625,
0.007007598876953125,
0.031036376953125,
0.01393890380859375,
-0.009613037109375,
0.01096343994140625,
0.0226593017578125,
-0.0010862350463867188,
0.0085906982421875,
-0.002063751220703125,
-0.0038700103759765625,
0.0009098052978515625,
-0.0018024444580078125,
-0.0018835067749023438,
-0.003078460693359375,
-0.01049041748046875,
-0.00284576416015625,
-0.006984710693359375,
-0.01531982421875,
-0.02130126953125,
0.01727294921875,
0.0018901824951171875,
0.0176849365234375,
0.0195159912109375,
0.01316070556640625,
0.0006680488586425781,
-0.001628875732421875,
-0.005100250244140625,
-0.0030574798583984375,
-0.01074981689453125,
-0.0189056396484375,
-0.0020694732666015625,
-0.016387939453125,
0.01465606689453125,
0.00933074951171875,
0.0033969879150390625,
-0.032562255859375,
0.00542449951171875,
-0.021148681640625,
0.035675048828125,
0.019805908203125,
0.015289306640625,
-0.0071258544921875,
0.0171966552734375,
-0.00452423095703125,
-0.006103515625,
-0.0159454345703125,
-0.0066375732421875,
-0.01497650146484375,
0.0014524459838867188,
-0.015106201171875,
-0.0013427734375,
-0.01096343994140625,
-0.00002872943878173828,
-0.0265045166015625,
-0.01104736328125,
0.044158935546875,
0.012481689453125,
-0.0333251953125,
0.0169677734375,
0.01346588134765625,
0.01015472412109375,
-0.0132904052734375,
0.004730224609375,
-0.00034999847412109375,
-0.0064544677734375,
0.0232086181640625,
0.002819061279296875,
-0.01023101806640625,
0.003292083740234375,
-0.0032100677490234375,
-0.0047607421875,
0.006320953369140625,
-0.0147247314453125,
0.0517578125,
-0.0081329345703125,
0.01392364501953125,
0.00632476806640625,
-0.0035991668701171875,
-0.01233673095703125,
0.0034332275390625,
-0.00908660888671875,
-0.0121002197265625,
0.0154571533203125,
-0.0240631103515625,
0.020599365234375,
-0.006805419921875,
0.01091766357421875,
0.0287322998046875,
-0.004627227783203125,
0.02874755859375,
0.017852783203125,
-0.05389404296875,
0.014495849609375,
0.0183563232421875,
-0.0034580230712890625,
0.00988006591796875,
0.0067596435546875,
0.0032291412353515625,
0.01959228515625,
0.0185089111328125,
0.0008502006530761719,
0.01165008544921875,
-0.0207366943359375,
0.0093231201171875,
0.012664794921875,
-0.0172271728515625,
-0.018402099609375,
-0.0118560791015625,
0.037353515625,
-0.00942230224609375,
-0.03302001953125,
0.0013561248779296875,
0.035736083984375,
-0.01488494873046875,
0.026580810546875,
0.00922393798828125,
0.00641632080078125,
0.00014710426330566406,
-0.005382537841796875,
-0.00882720947265625,
-0.0199127197265625,
-0.0222015380859375,
0.004116058349609375,
-0.008636474609375,
0.0069427490234375,
-0.0007061958312988281,
-0.0122528076171875,
-0.0089874267578125,
0.043548583984375,
-0.040191650390625,
0.012420654296875,
-0.0026760101318359375,
-0.01568603515625,
-0.01358795166015625,
-0.028594970703125,
0.00579071044921875,
0.022216796875,
-0.01308441162109375,
0.0006422996520996094,
-0.005802154541015625,
-0.0087432861328125,
0.02178955078125,
-0.005832672119140625,
-0.004360198974609375,
-0.005115509033203125,
-0.0116424560546875,
-0.010528564453125,
-0.0278167724609375,
-0.006084442138671875,
0.01617431640625,
0.052001953125,
0.0174102783203125,
-0.01494598388671875,
0.007328033447265625,
-0.006000518798828125,
-0.0026607513427734375,
0.0193023681640625,
0.01235198974609375,
-0.015045166015625,
-0.01352691650390625,
-0.00800323486328125,
-0.013275146484375,
-0.01036834716796875,
-0.0148162841796875,
-0.01507568359375,
-0.0161285400390625,
-0.0023174285888671875,
0.02294921875,
-0.01044464111328125,
-0.04852294921875,
0.0023517608642578125,
-0.0266571044921875,
0.00762176513671875,
-0.00759124755859375,
-0.016632080078125,
-0.01410675048828125,
0.0055999755859375,
0.00493621826171875,
-0.0046539306640625,
0.01270294189453125,
0.0300750732421875,
0.0113983154296875,
-0.02923583984375,
0.00518035888671875,
0.0158538818359375,
-0.024261474609375,
-0.0274810791015625,
-0.01690673828125,
0.0216827392578125,
-0.0025577545166015625,
0.0014295578002929688,
-0.0499267578125,
-0.0264434814453125,
0.0027637481689453125,
0.027557373046875,
-0.020355224609375,
0.005462646484375,
0.0222930908203125,
0.01546478271484375,
0.01194000244140625,
0.007167816162109375,
0.00667572021484375,
-0.005825042724609375,
-0.016937255859375,
0.019622802734375,
-0.0439453125,
-0.0027313232421875,
-0.00977325439453125,
0.0105438232421875,
0.005054473876953125,
0.0011119842529296875,
-0.0009918212890625,
-0.006317138671875,
0.02685546875,
0.016204833984375,
0.0262908935546875,
-0.002422332763671875,
-0.0101318359375,
0.002727508544921875,
0.0180816650390625,
-0.007030487060546875,
-0.0011148452758789062,
-0.0095672607421875,
0.0021915435791015625,
-0.027252197265625,
-0.0017786026000976562,
0.0145416259765625,
0.00395965576171875,
-0.0110015869140625,
0.0107574462890625,
0.015411376953125,
0.0001424551010131836,
0.047882080078125,
0.01715087890625,
0.01129913330078125,
-0.0042266845703125,
0.01453399658203125,
0.0030841827392578125,
-0.0249786376953125,
0.046417236328125,
-0.061859130859375,
0.00865936279296875,
0.013946533203125,
0.006656646728515625,
-0.04010009765625,
0.0248870849609375,
0.00347137451171875,
0.0306854248046875,
0.0115203857421875,
-0.01442718505859375,
-0.022430419921875,
-0.01264190673828125,
0.01788330078125,
-0.0256500244140625,
0.01464080810546875,
0.0022182464599609375,
0.01122283935546875,
-0.0211181640625,
0.0156707763671875,
0.01505279541015625,
0.01302337646484375,
0.0023059844970703125,
0.005573272705078125,
-0.0043792724609375,
-0.043731689453125,
-0.003925323486328125,
0.006153106689453125,
-0.004459381103515625,
-0.047698974609375,
-0.0081024169921875,
-0.0031604766845703125,
0.0089111328125,
0.011810302734375,
0.0201263427734375,
0.01739501953125,
-0.0070037841796875,
-0.02801513671875,
0.0222930908203125,
-0.00945281982421875,
-0.0028285980224609375,
-0.0005774497985839844,
-0.02264404296875,
-0.01453399658203125,
-0.006771087646484375,
-0.0330810546875,
0.0234832763671875,
0.002178192138671875,
-0.009429931640625,
-0.001708984375,
-0.01035308837890625,
-0.00972747802734375,
0.053985595703125,
0.0115966796875,
0.0240325927734375,
-0.014801025390625,
-0.01160430908203125,
-0.03521728515625,
-0.0321044921875,
-0.0509033203125,
0.00279998779296875,
-0.00750732421875,
0.018707275390625,
-0.006542205810546875,
-0.003910064697265625,
0.00640869140625,
-0.046539306640625,
0.006816864013671875,
-0.01247406005859375,
0.029296875,
-0.016876220703125,
-0.03570556640625,
-0.0013446807861328125,
-0.003997802734375,
-0.01300811767578125,
-0.0171966552734375,
0.01294708251953125,
0.00811767578125,
0.01416778564453125,
0.00016224384307861328,
0.0012121200561523438,
0.0139007568359375,
0.02410888671875,
0.01201629638671875,
-0.0169525146484375,
-0.0297393798828125,
-0.02685546875,
0.00609588623046875,
-0.025909423828125,
-0.0234222412109375,
-0.02490234375,
0.0027828216552734375,
-0.0018167495727539062,
0.01544189453125,
0.01959228515625,
-0.0084075927734375,
-0.0210723876953125,
-0.0250244140625,
0.0040283203125,
0.0205078125,
0.0230865478515625,
0.0048828125,
0.01129150390625,
0.015106201171875,
0.0106658935546875,
0.002170562744140625,
0.04052734375,
-0.0008645057678222656,
-0.0035724639892578125,
-0.0214385986328125,
0.0099945068359375,
-0.047454833984375,
-0.01230621337890625,
-0.019500732421875,
-0.027557373046875,
0.031646728515625,
-0.03717041015625,
0.0026683807373046875,
0.0177001953125,
-0.02276611328125,
0.0124664306640625,
-0.0093841552734375,
0.0276641845703125,
0.001983642578125,
0.00548553466796875,
0.0211029052734375,
0.0207977294921875,
0.02374267578125,
-0.022613525390625,
-0.0263519287109375,
-0.00024330615997314453,
0.010162353515625,
0.004669189453125,
0.039886474609375,
0.026214599609375,
-0.0204315185546875,
-0.014617919921875,
-0.00951385498046875,
-0.00952911376953125,
0.020538330078125,
-0.0009899139404296875,
0.0158538818359375,
-0.0439453125,
0.01861572265625,
0.006473541259765625,
-0.00019562244415283203,
0.022735595703125,
0.04205322265625,
0.0093841552734375,
-0.0333251953125,
-0.0218505859375,
0.017547607421875,
0.014312744140625,
0.021453857421875,
0.03521728515625,
0.0028057098388671875,
-0.0183868408203125,
0.0162811279296875,
0.039886474609375,
-0.03045654296875,
-0.0236053466796875,
0.01202392578125,
0.05999755859375,
0.00867462158203125,
-0.0172576904296875,
-0.005298614501953125,
-0.00968170166015625,
0.013427734375,
0.007549285888671875,
-0.02978515625,
0.00858306884765625,
-0.0018663406372070312,
-0.031463623046875,
-0.01265716552734375,
0.0244903564453125,
0.02142333984375,
-0.00865936279296875,
0.031829833984375,
-0.02642822265625,
0.021026611328125,
-0.0091094970703125,
-0.0021305084228515625,
-0.003955841064453125,
-0.007106781005859375,
-0.01546478271484375,
0.0222625732421875,
-0.0018224716186523438,
0.0367431640625,
-0.0220794677734375,
-0.00664520263671875,
0.0174713134765625,
0.01220703125,
-0.026763916015625,
0.0005412101745605469,
0.0213470458984375,
-0.00637054443359375,
-0.00024700164794921875,
0.007572174072265625,
-0.0182952880859375,
0.0147857666015625,
0.022613525390625,
0.0031108856201171875,
0.00873565673828125,
0.0025157928466796875,
-0.01479339599609375,
0.0179443359375,
0.01300048828125,
-0.010223388671875,
-0.0406494140625,
0.0087432861328125,
0.00788116455078125,
-0.01206207275390625,
-0.0259857177734375,
0.024871826171875,
0.00650787353515625,
0.0101165771484375,
-0.01837158203125,
0.03472900390625,
0.01174163818359375,
-0.0186004638671875,
-0.01180267333984375,
0.004764556884765625,
-0.004650115966796875,
-0.00727081298828125,
-0.005130767822265625,
-0.0400390625,
-0.00453948974609375,
-0.0076141357421875,
0.00556182861328125,
-0.025482177734375,
-0.0164031982421875,
-0.053863525390625,
0.00528717041015625,
0.004718780517578125,
0.0447998046875,
0.03765869140625,
-0.01201629638671875,
0.0189971923828125,
-0.0169830322265625,
0.015869140625,
-0.005859375,
-0.004344940185546875,
-0.01690673828125,
0.00522613525390625,
-0.0185394287109375,
-0.01041412353515625,
0.01258087158203125,
-0.0208587646484375,
0.006206512451171875,
-0.0169677734375,
-0.030364990234375,
0.0049285888671875,
0.0236053466796875,
-0.01154327392578125,
-0.0064544677734375,
-0.00733184814453125,
-0.007221221923828125,
0.034515380859375,
-0.0081787109375,
0.0033206939697265625,
0.006557464599609375,
-0.004547119140625,
0.0201416015625,
0.0184783935546875,
0.01300811767578125,
-0.00980377197265625,
0.01053619384765625,
-0.01239013671875,
0.01129150390625,
-0.015289306640625,
-0.02532958984375,
-0.0016202926635742188,
-0.033905029296875,
0.001064300537109375,
0.0029735565185546875,
-0.01367950439453125,
-0.047027587890625,
0.0232391357421875,
0.007144927978515625,
0.00829315185546875,
0.005462646484375,
-0.0014095306396484375,
-0.02740478515625,
0.0011339187622070312,
0.0092315673828125,
0.044525146484375,
-0.01045989990234375,
-0.0238037109375,
-0.015228271484375,
0.01428985595703125,
-0.0246429443359375,
-0.02838134765625,
0.021331787109375,
0.038299560546875,
0.01248931884765625,
-0.00632476806640625,
0.00849151611328125,
0.002849578857421875,
-0.0223846435546875,
0.0233612060546875,
0.00569915771484375,
-0.0168609619140625,
0.006359100341796875,
0.0180511474609375,
-0.015655517578125,
0.020751953125,
0.01534271240234375,
0.01235198974609375,
0.005847930908203125,
0.0198822021484375,
-0.0004076957702636719,
0.01302337646484375,
0.003849029541015625,
0.0111083984375,
-0.00827789306640625,
0.019256591796875,
-0.0038356781005859375,
0.01171875,
-0.0074615478515625,
-0.0258941650390625,
-0.002285003662109375,
0.01500701904296875,
-0.00189208984375,
-0.0230255126953125,
-0.0207977294921875,
-0.0023345947265625,
-0.0033016204833984375,
0.016326904296875,
-0.00453948974609375,
0.002483367919921875,
-0.01529693603515625,
0.0225372314453125,
-0.00707244873046875,
-0.0008749961853027344,
-0.0065460205078125,
-0.0220184326171875,
-0.0235443115234375,
-0.01080322265625,
-0.01480865478515625,
0.0010662078857421875,
-0.0025043487548828125,
-0.0006542205810546875,
-0.00943756103515625,
-0.01284027099609375,
-0.03253173828125,
-0.01593017578125,
0.00852203369140625,
0.0016202926635742188,
-0.00579833984375,
0.00971221923828125,
0.0254058837890625,
-0.02484130859375,
0.0386962890625,
0.034271240234375,
-0.0187835693359375,
0.049346923828125,
-0.007106781005859375,
0.0225677490234375,
-0.00403594970703125,
0.0269012451171875,
-0.00800323486328125,
-0.005298614501953125,
-0.01320648193359375,
0.0111846923828125,
-0.00540924072265625,
-0.0135498046875,
0.01166534423828125,
-0.00777435302734375,
0.01178741455078125,
0.0018739700317382812,
0.020660400390625,
0.00547027587890625,
-0.0169677734375,
0.00848388671875,
0.04010009765625,
-0.035064697265625,
0.01549530029296875,
-0.037261962890625,
-0.0155181884765625,
-0.031890869140625,
0.018768310546875,
-0.00839996337890625,
0.00601959228515625,
0.00394439697265625,
-0.03143310546875,
-0.00011676549911499023,
0.0335693359375,
-0.006671905517578125,
0.0181121826171875,
-0.0194549560546875,
-0.0009012222290039062,
0.0007610321044921875,
0.01385498046875,
0.0166778564453125,
0.0011844635009765625,
0.00653839111328125,
-0.004718780517578125,
-0.0000807046890258789,
-0.0211944580078125,
-0.030975341796875,
0.017425537109375,
-0.0230255126953125,
-0.0127105712890625,
-0.002727508544921875,
0.0139007568359375,
-0.035003662109375,
-0.035003662109375,
0.01593017578125,
-0.023895263671875,
-0.013031005859375,
-0.000873565673828125,
-0.001495361328125,
0.0173797607421875,
-0.005016326904296875,
0.006992340087890625,
-0.00769805908203125,
0.0035400390625,
-0.0171356201171875,
0.019378662109375,
0.0287322998046875,
0.01461029052734375,
0.048095703125,
-0.01070404052734375,
0.01363372802734375,
-0.033599853515625,
0.00896453857421875,
-0.0116119384765625,
0.01070404052734375,
-0.0308837890625,
-0.0087890625,
0.025390625,
-0.0233917236328125,
0.0136566162109375,
-0.01287841796875,
-0.005535125732421875,
0.0066375732421875,
-0.00624847412109375,
-0.0021209716796875,
-0.001010894775390625,
0.0052490234375,
0.003696441650390625,
-0.013885498046875,
-0.0179290771484375,
0.044891357421875,
0.032989501953125,
0.008819580078125,
-0.002613067626953125,
-0.04010009765625,
-0.0094451904296875,
0.056732177734375,
-0.033447265625,
-0.00206756591796875,
-0.0178680419921875,
-0.013458251953125,
0.013153076171875,
-0.041351318359375,
-0.0213165283203125,
0.00832366943359375,
-0.0186767578125,
0.0113677978515625,
0.00971221923828125,
-0.000027894973754882812,
0.0102691650390625,
0.024322509765625,
-0.040252685546875,
-0.00555419921875,
-0.006717681884765625,
0.029693603515625,
-0.02471923828125,
0.011016845703125,
0.041229248046875,
-0.0225067138671875,
-0.02276611328125,
0.0006952285766601562,
0.028289794921875,
-0.003803253173828125,
-0.0153350830078125,
0.00045680999755859375,
-0.017913818359375,
-0.01220703125,
-0.014923095703125,
0.0204010009765625,
-0.047149658203125,
0.006053924560546875,
-0.030853271484375,
0.0012807846069335938,
0.029876708984375,
0.0011529922485351562,
0.04010009765625,
-0.0160064697265625,
0.006595611572265625,
-0.0179901123046875,
0.0216827392578125,
-0.0164794921875,
0.01018524169921875,
0.002895355224609375,
-0.0236358642578125,
0.023284912109375,
-0.004825592041015625,
0.006366729736328125,
0.00975799560546875,
-0.019927978515625,
0.0272369384765625,
0.030059814453125,
0.01309967041015625,
-0.023345947265625,
-0.00533294677734375,
0.0113983154296875,
0.0034847259521484375,
-0.0031833648681640625,
-0.01385498046875,
-0.005847930908203125,
0.0367431640625,
-0.0258636474609375,
-0.0302886962890625,
0.00287628173828125,
-0.0182647705078125,
0.0105133056640625,
-0.01497650146484375,
0.020233154296875,
0.015838623046875,
0.01082611083984375,
0.01442718505859375,
-0.0006470680236816406,
-0.0027103424072265625,
0.037109375,
-0.004932403564453125,
0.00829315185546875,
0.01500701904296875,
0.0186767578125,
-0.0277557373046875,
-0.0016031265258789062,
-0.0185089111328125,
-0.004913330078125,
-0.0296630859375,
-0.007080078125,
-0.0267486572265625,
-0.041259765625,
-0.0207672119140625,
-0.00679779052734375,
-0.01392364501953125,
-0.0037822723388671875,
0.035736083984375,
0.040924072265625,
-0.004726409912109375,
0.040283203125,
-0.008514404296875,
-0.0105133056640625,
0.0018224716186523438,
0.00595855712890625,
0.02996826171875,
-0.0016908645629882812,
-0.041595458984375,
-0.0262908935546875,
-0.00652313232421875,
0.043853759765625,
0.0008611679077148438,
-0.0306396484375,
0.0260162353515625,
0.0184326171875,
-0.0251922607421875,
0.029449462890625,
0.0203857421875,
-0.00994873046875,
-0.016265869140625,
0.01082611083984375,
-0.0033893585205078125,
0.02984619140625,
-0.0119476318359375,
0.0222320556640625,
-0.03228759765625,
-0.012603759765625,
-0.005176544189453125,
-0.0029544830322265625,
0.0032024383544921875,
0.005046844482421875,
0.00144195556640625,
-0.0107879638671875,
-0.003307342529296875,
0.0106353759765625,
0.01177215576171875,
-0.0018472671508789062,
0.003326416015625,
0.007568359375,
-0.010406494140625,
-0.038604736328125,
-0.006633758544921875,
0.002689361572265625,
0.0196075439453125,
0.00933837890625,
0.0101776123046875,
-0.0110321044921875,
-0.0012960433959960938,
0.00594329833984375,
-0.00635528564453125,
0.0170745849609375,
-0.02581787109375,
0.00910186767578125,
-0.00576019287109375,
-0.0018138885498046875,
-0.0040435791015625,
0.036895751953125,
0.0201416015625,
-0.00804901123046875,
0.003589630126953125,
0.0145111083984375,
0.028961181640625,
-0.01245880126953125,
-0.0052032470703125,
-0.02886962890625,
-0.02655029296875,
-0.027130126953125,
0.0217132568359375,
-0.001453399658203125,
0.00556182861328125,
0.015716552734375,
-0.0011358261108398438,
-0.00997161865234375,
0.004611968994140625,
-0.017822265625,
-0.0174407958984375,
0.0297393798828125,
0.0176544189453125,
-0.0226287841796875,
0.0204620361328125,
-0.0307769775390625,
0.0269927978515625,
0.0196990966796875,
-0.00978851318359375,
0.01097869873046875,
-0.016693115234375,
-0.03900146484375,
0.049774169921875,
-0.022918701171875,
-0.01910400390625,
0.01163482666015625,
-0.0078277587890625,
-0.0151214599609375,
0.0081787109375,
0.0316162109375,
0.006397247314453125,
-0.004138946533203125,
0.0013837814331054688,
-0.00787353515625,
0.006412506103515625,
0.0028438568115234375,
0.0286865234375,
-0.015899658203125,
-0.010345458984375,
0.005329132080078125,
0.027313232421875,
-0.003665924072265625,
0.01080322265625,
0.0095977783203125,
0.01399993896484375,
-0.0018262863159179688,
-0.01141357421875,
0.00982666015625,
-0.0203857421875,
0.00791168212890625,
-0.030181884765625,
-0.0029239654541015625,
0.021514892578125,
0.0260162353515625,
0.035491943359375,
0.023193359375,
-0.026519775390625,
0.004062652587890625,
0.0172882080078125,
0.03936767578125,
-0.005825042724609375,
-0.020751953125,
-0.0135955810546875,
0.02032470703125,
-0.007785797119140625,
0.01424407958984375,
-0.0217437744140625,
0.0025577545166015625,
-0.0034465789794921875,
0.021087646484375,
-0.007472991943359375,
0.003475189208984375,
0.00876617431640625,
0.009918212890625,
-0.0165252685546875,
0.0100860595703125,
0.00940704345703125,
0.01287841796875,
-0.0172882080078125,
-0.0035533905029296875,
-0.01904296875,
-0.0273284912109375,
0.0046234130859375,
-0.004642486572265625,
-0.0240325927734375,
0.0100250244140625,
-0.0029888153076171875,
-0.0234375,
0.02227783203125,
0.014617919921875,
0.03515625,
0.01313018798828125,
-0.0263519287109375,
-0.00916290283203125,
-0.0406494140625,
-0.00434112548828125,
0.01024627685546875,
-0.01010894775390625,
-0.0230560302734375,
-0.00921630859375,
-0.00470733642578125,
-0.019073486328125,
0.006610870361328125,
0.0256500244140625,
0.016632080078125,
0.0042266845703125,
-0.0445556640625,
-0.0078277587890625,
0.04132080078125,
-0.047698974609375,
-0.009124755859375,
0.009002685546875,
0.03173828125,
0.00173187255859375,
0.005889892578125,
-0.0045013427734375,
-0.001667022705078125,
-0.01568603515625,
-0.01043701171875,
0.02203369140625,
0.017608642578125,
-0.0030765533447265625,
-0.02496337890625,
-0.006381988525390625,
-0.0093231201171875,
0.007129669189453125,
-0.03228759765625,
-0.02838134765625,
-0.011993408203125,
-0.006519317626953125,
0.01174163818359375,
0.022064208984375,
0.00939178466796875,
0.00470733642578125,
0.0026416778564453125,
-0.00396728515625,
-0.01031494140625,
0.00487518310546875,
0.0189056396484375,
-0.01065826416015625,
-0.012359619140625,
-0.0146636962890625,
0.0157318115234375,
-0.031341552734375,
-0.02044677734375,
-0.0088348388671875,
-0.017242431640625,
-0.033203125,
-0.015838623046875,
0.0124359130859375,
0.01253509521484375,
0.0015115737915039062,
-0.0016164779663085938,
-0.0196380615234375,
0.031280517578125,
0.039093017578125,
0.005924224853515625,
0.0003693103790283203,
-0.0254669189453125,
0.026519775390625,
0.01245880126953125,
0.01102447509765625,
0.04290771484375,
-0.035797119140625,
0.01248931884765625,
-0.00289154052734375,
0.00482940673828125,
0.0117034912109375,
0.01141357421875,
0.02545166015625,
-0.0140228271484375,
-0.00006133317947387695,
-0.006534576416015625,
0.0228271484375,
-0.01453399658203125,
0.0036773681640625,
0.0015420913696289062,
0.00567626953125,
-0.040740966796875,
-0.0173187255859375,
0.02490234375,
0.0245513916015625,
0.01824951171875,
-0.01299285888671875,
0.01983642578125,
-0.00469970703125,
0.0013856887817382812,
0.0272369384765625,
-0.0235595703125,
-0.05718994140625,
0.0222930908203125,
-0.0298309326171875,
0.01422882080078125,
0.004474639892578125,
-0.004669189453125,
0.0067596435546875,
0.0091552734375,
-0.0037403106689453125,
-0.02545166015625,
0.01419830322265625,
-0.024200439453125,
0.0259552001953125,
0.03326416015625,
-0.056427001953125,
-0.01087188720703125,
-0.009033203125,
-0.0215606689453125,
0.005878448486328125,
0.01141357421875,
0.04400634765625,
-0.001983642578125,
-0.044891357421875,
0.0187530517578125,
-0.033050537109375,
-0.0011348724365234375,
-0.050079345703125,
-0.00637054443359375,
0.0155792236328125,
-0.0027713775634765625,
0.04473876953125,
-0.0157318115234375,
-0.0091705322265625,
-0.00693511962890625,
0.0233154296875,
-0.00974273681640625,
-0.0061492919921875,
-0.00449371337890625,
0.0016069412231445312,
0.033782958984375,
-0.0191650390625,
-0.02545166015625,
-0.008087158203125,
-0.0150299072265625,
0.023162841796875,
-0.0038814544677734375,
-0.03607177734375,
-0.01169586181640625,
0.0016355514526367188,
-0.0024852752685546875,
0.0127105712890625,
0.0221405029296875,
-0.016510009765625,
-0.0211944580078125,
0.02813720703125,
0.01641845703125,
-0.00948333740234375,
0.0267791748046875,
0.007511138916015625,
0.0166778564453125,
0.027191162109375,
0.016693115234375,
0.0194549560546875,
-0.0260162353515625,
0.0202789306640625,
-0.0206756591796875,
-0.007167816162109375,
-0.0177154541015625,
-0.0032024383544921875,
0.036468505859375,
-0.0138397216796875,
0.0148468017578125,
-0.0236968994140625,
0.005985260009765625,
0.003536224365234375,
-0.0186004638671875,
-0.00922393798828125,
-0.004150390625,
0.0062713623046875,
0.019317626953125,
-0.0261688232421875,
-0.0077056884765625,
-0.022216796875,
-0.017120361328125,
-0.014984130859375,
-0.00098419189453125,
0.0036334991455078125,
0.0292205810546875,
0.046417236328125,
-0.01555633544921875,
-0.006595611572265625,
-0.04608154296875,
-0.0209808349609375,
-0.01045989990234375,
-0.002269744873046875,
-0.029052734375,
-0.00390625,
-0.002166748046875,
0.0013885498046875,
0.01629638671875,
-0.00595855712890625,
-0.01332855224609375,
0.027191162109375,
0.00275421142578125,
-0.0014858245849609375,
-0.01346588134765625,
-0.0185089111328125,
-0.0280303955078125,
0.000058770179748535156,
0.03515625,
-0.027740478515625,
0.01171112060546875,
-0.019500732421875,
0.007465362548828125,
0.0250244140625,
0.0155029296875,
0.00563812255859375,
-0.008544921875,
-0.037750244140625,
0.012603759765625,
-0.02215576171875,
0.0141754150390625,
0.0001392364501953125,
0.00771331787109375,
0.00556182861328125,
-0.0061798095703125,
0.0268402099609375,
-0.0220489501953125,
-0.0030517578125,
0.00328826904296875,
0.0114898681640625,
-0.0276947021484375,
0.00200653076171875,
0.011505126953125,
0.004058837890625,
-0.024261474609375,
-0.0006823539733886719,
0.013641357421875,
0.005214691162109375,
-0.003177642822265625,
-0.01183319091796875,
0.0188446044921875,
-0.0183868408203125,
0.01210784912109375,
-0.0307769775390625,
0.0151824951171875,
0.004268646240234375,
-0.0170135498046875,
-0.0012655258178710938,
-0.030242919921875,
-0.0083160400390625,
-0.0003504753112792969,
-0.01548004150390625,
0.00449371337890625,
0.0142059326171875,
-0.01128387451171875,
-0.00994873046875,
-0.021820068359375,
-0.01486968994140625,
-0.001220703125,
0.0036754608154296875,
0.002475738525390625,
-0.0266265869140625,
0.023651123046875,
-0.0211944580078125,
0.007549285888671875,
-0.0067138671875,
0.025115966796875,
-0.0082244873046875,
0.01094818115234375,
-0.0171051025390625,
-0.00464630126953125,
-0.0283966064453125,
0.036041259765625,
0.0012712478637695312,
-0.018768310546875,
-0.0256805419921875,
-0.046539306640625,
-0.0029754638671875,
0.039520263671875,
-0.0256500244140625,
-0.020050048828125,
0.00592041015625,
0.0299835205078125,
0.0204925537109375,
-0.002536773681640625,
0.029205322265625,
-0.0179595947265625,
-0.0194549560546875,
0.02630615234375,
0.0021419525146484375,
-0.031158447265625,
-0.046234130859375,
0.0077362060546875,
0.01511383056640625,
0.0294189453125,
0.0229644775390625,
0.006038665771484375,
0.0151214599609375,
0.022430419921875,
0.01433563232421875,
0.01116180419921875,
0.0093841552734375,
-0.00882720947265625,
-0.023040771484375,
0.0113525390625,
-0.00838470458984375,
0.035308837890625,
0.0186767578125,
-0.00473785400390625,
0.0015344619750976562,
-0.00812530517578125,
-0.03173828125,
0.034088134765625,
-0.00394439697265625,
-0.00936126708984375,
-0.0103607177734375,
0.012359619140625,
-0.0112762451171875,
0.011810302734375,
-0.0030269622802734375,
-0.01181793212890625,
0.0316162109375,
0.007099151611328125,
-0.026031494140625,
0.0033206939697265625,
-0.023406982421875,
0.0079803466796875,
-0.00689697265625,
-0.01885986328125,
0.043426513671875,
-0.0017690658569335938,
-0.0021877288818359375,
0.0150909423828125,
0.012847900390625,
0.0140838623046875,
-0.0096588134765625,
0.0098876953125,
-0.00061798095703125,
0.01947021484375,
0.0203704833984375,
0.0065765380859375,
-0.0216522216796875,
-0.02716064453125,
-0.0153045654296875,
0.002628326416015625,
0.05340576171875,
0.0157470703125,
0.0131988525390625,
0.00925445556640625,
0.002655029296875,
-0.0218505859375,
-0.048004150390625,
-0.022308349609375,
0.0266265869140625,
0.014739990234375,
0.0036716461181640625,
0.0421142578125,
-0.0171661376953125,
0.034698486328125,
-0.0184478759765625,
0.00833892822265625,
-0.00727081298828125,
0.0071258544921875,
-0.01102447509765625,
0.0027103424072265625,
-0.0081634521484375,
0.00461578369140625,
0.00032639503479003906,
0.000020563602447509766,
-0.03875732421875,
-0.01224517822265625,
0.0223236083984375,
-0.0278778076171875,
-0.0268707275390625,
-0.00634765625,
0.0174560546875,
0.01324462890625,
-0.0008282661437988281,
-0.011810302734375,
-0.0252532958984375,
-0.028900146484375,
0.0068359375,
0.0176544189453125,
0.00940704345703125,
-0.004116058349609375,
-0.03216552734375,
-0.029815673828125,
-0.006755828857421875,
-0.006195068359375,
0.00211334228515625,
0.006488800048828125,
-0.0177764892578125,
-0.0050201416015625,
0.004108428955078125,
0.00390625,
0.0301666259765625,
-0.01751708984375,
-0.006023406982421875,
-0.0268402099609375,
0.0008807182312011719,
-0.0269317626953125,
0.007595062255859375,
-0.0308685302734375,
-0.026031494140625,
0.032501220703125,
-0.037261962890625,
0.0072784423828125,
0.0123138427734375,
-0.005931854248046875,
0.0212554931640625,
0.01528167724609375,
0.0119171142578125,
-0.0295867919921875,
0.0035648345947265625,
0.0027980804443359375,
-0.0124664306640625,
-0.0046539306640625,
0.00012421607971191406,
-0.0023193359375,
-0.0256500244140625,
-0.016693115234375,
-0.00960540771484375,
0.01091766357421875,
-0.00605010986328125,
0.00629425048828125,
-0.00146484375,
-0.01149749755859375,
-0.0345458984375,
-0.0241241455078125,
0.003551483154296875,
-0.011810302734375,
-0.049041748046875,
0.01187896728515625,
-0.00432586669921875,
0.051239013671875,
0.015045166015625,
-0.01421356201171875,
-0.034393310546875,
0.006679534912109375,
-0.017669677734375,
-0.0234222412109375,
-0.0302886962890625,
-0.0123291015625,
-0.0277252197265625,
0.018096923828125,
0.044647216796875,
-0.01202392578125,
-0.035308837890625,
0.003246307373046875,
0.0243682861328125,
-0.0095062255859375,
-0.003814697265625,
-0.0146636962890625,
-0.0256805419921875,
0.01079559326171875,
-0.0104217529296875,
0.004497528076171875,
-0.0075836181640625,
-0.0213165283203125,
0.0298004150390625,
0.024627685546875,
-0.028778076171875,
0.01055908203125,
-0.02301025390625,
0.01080322265625,
0.0035114288330078125,
0.004199981689453125,
0.01324462890625,
-0.00011640787124633789,
-0.0043182373046875,
0.007625579833984375,
-0.035125732421875,
0.005565643310546875,
0.026458740234375,
-0.022979736328125,
-0.052947998046875,
-0.0256805419921875,
0.0032978057861328125,
0.0035800933837890625,
-0.0014820098876953125,
0.018463134765625,
-0.005153656005859375,
-0.0215606689453125,
0.00836944580078125,
0.00843048095703125,
-0.01325225830078125,
0.004058837890625,
0.0092620849609375,
-0.0257568359375,
0.00667572021484375,
-0.0218505859375,
0.0237884521484375,
0.027191162109375,
-0.0269622802734375,
-0.0195465087890625,
0.00110626220703125,
-0.0055694580078125,
-0.005977630615234375,
0.004547119140625,
-0.007144927978515625,
-0.006526947021484375,
-0.01126861572265625,
-0.0224609375,
-0.0007200241088867188,
-0.0093841552734375,
0.009552001953125,
0.00151824951171875,
-0.0004057884216308594,
-0.0143280029296875,
-0.00029349327087402344,
-0.021209716796875,
-0.0135650634765625,
0.00620269775390625,
0.025665283203125,
0.0242462158203125,
-0.01068115234375,
0.0203704833984375,
0.0141448974609375,
0.022918701171875,
0.046722412109375,
-0.041717529296875,
0.00383758544921875,
-0.0152435302734375,
-0.005519866943359375,
0.004009246826171875,
-0.01488494873046875,
-0.0194549560546875,
0.002758026123046875,
-0.0254669189453125,
-0.01554107666015625,
-0.02301025390625,
-0.0006198883056640625,
0.00922393798828125,
0.01042938232421875,
-0.011688232421875,
-0.0017919540405273438,
-0.00402069091796875,
-0.01493072509765625,
-0.0277862548828125,
-0.0181884765625,
0.0311737060546875,
0.0081939697265625,
0.0235748291015625,
0.01080322265625,
-0.0099945068359375,
0.0007686614990234375,
-0.037994384765625,
-0.01506805419921875,
0.043914794921875,
-0.00923919677734375,
0.00572967529296875,
-0.00315093994140625,
-0.010589599609375,
0.005580902099609375,
0.00682830810546875,
0.0178070068359375,
0.0030574798583984375,
0.00815582275390625,
-0.0203857421875,
-0.046478271484375,
-0.0279998779296875,
0.0003783702850341797,
0.0195159912109375,
-0.0185546875,
0.04876708984375,
0.0014886856079101562,
0.004856109619140625,
0.01422119140625,
0.0085601806640625,
-0.013092041015625,
0.0112152099609375,
-0.019500732421875,
-0.0189666748046875,
0.035308837890625,
0.0258941650390625,
0.042266845703125,
-0.032806396484375,
-0.0105438232421875,
-0.02471923828125,
-0.018951416015625,
0.051544189453125,
0.004642486572265625,
-0.001834869384765625,
-0.0005273818969726562,
0.00017189979553222656,
-0.0128936767578125,
0.006351470947265625,
-0.00788116455078125,
-0.003589630126953125,
0.006687164306640625,
0.021209716796875,
0.045623779296875,
-0.01059722900390625,
0.03179931640625,
-0.03680419921875,
0.055206298828125,
-0.00653076171875,
0.032470703125,
-0.0028400421142578125,
0.0043792724609375,
0.01403045654296875,
-0.00618743896484375,
-0.007106781005859375,
-0.03082275390625,
0.015289306640625,
-0.0308685302734375,
-0.01224517822265625,
0.005519866943359375,
-0.0036678314208984375,
-0.01465606689453125,
0.01459503173828125,
0.0162506103515625,
-0.0272369384765625,
-0.00852203369140625,
-0.0210418701171875,
0.0202178955078125,
-0.0091705322265625,
-0.006496429443359375,
0.0129852294921875,
0.00691986083984375,
-0.015960693359375,
-0.0036678314208984375,
0.0005717277526855469,
0.01161956787109375,
-0.00732421875,
0.01325225830078125,
-0.0158233642578125,
-0.0166473388671875,
0.0092010498046875,
-0.010772705078125,
0.016082763671875,
0.026641845703125,
0.0360107421875,
0.0140838623046875,
0.0199432373046875,
-0.03009033203125,
0.01873779296875,
0.0196990966796875,
0.01104736328125,
-0.0050506591796875,
-0.0026397705078125,
0.01261138916015625,
-0.036712646484375,
-0.0060882568359375,
0.032440185546875,
-0.0175018310546875,
0.024993896484375,
0.0274658203125,
-0.028961181640625,
-0.03717041015625,
-0.0229034423828125,
0.025390625,
-0.031219482421875,
0.0261688232421875,
0.0267333984375,
0.0067138671875,
-0.03094482421875,
0.0212554931640625,
0.00884246826171875,
-0.022674560546875,
-0.0269775390625,
0.04779052734375,
-0.02947998046875,
-0.027313232421875,
-0.016357421875,
-0.006191253662109375,
0.03338623046875,
0.0166015625,
-0.029998779296875,
-0.0267181396484375,
0.0021343231201171875,
-0.0210723876953125,
0.03179931640625,
0.0020236968994140625,
0.01213836669921875,
-0.0015230178833007812,
0.0210113525390625,
-0.007579803466796875,
0.0019588470458984375,
-0.01064300537109375,
0.0020198822021484375,
0.00357818603515625,
-0.014892578125,
-0.02679443359375,
-0.0006394386291503906,
-0.0011196136474609375,
0.0298919677734375,
0.0092010498046875,
-0.006725311279296875,
-0.0267181396484375,
0.01335906982421875,
0.01503753662109375,
0.00815582275390625,
0.0217132568359375,
-0.0222320556640625,
0.0027523040771484375,
-0.00200653076171875,
-0.01094818115234375,
0.0204315185546875,
0.02899169921875,
-0.0093231201171875,
-0.01181793212890625,
0.0369873046875,
-0.004650115966796875,
-0.040313720703125,
0.0156097412109375,
0.005512237548828125,
0.0090789794921875,
-0.0309906005859375,
0.0007166862487792969,
-0.0036411285400390625,
0.0390625,
-0.01702880859375,
-0.037750244140625,
-0.007411956787109375,
0.04547119140625,
0.008514404296875,
-0.03265380859375,
0.0119171142578125,
-0.007793426513671875,
0.002475738525390625,
0.0006608963012695312,
-0.003345489501953125,
0.0073699951171875,
-0.01088714599609375,
0.035980224609375,
0.0021343231201171875,
-0.006237030029296875,
-0.02374267578125,
-0.038970947265625,
-0.01267242431640625,
0.0115814208984375,
-0.0126190185546875,
-0.0015277862548828125,
0.00370025634765625,
0.007266998291015625,
-0.01013946533203125,
-0.042816162109375,
0.0159454345703125,
-0.0230712890625,
0.0104522705078125,
0.0302276611328125,
0.015106201171875,
0.01239013671875,
-0.0063629150390625,
-0.0224761962890625,
-0.0170745849609375,
-0.00044417381286621094,
-0.02545166015625,
-0.008941650390625,
0.005428314208984375,
0.0041961669921875,
0.00960540771484375,
0.00817108154296875,
-0.007579803466796875,
0.015289306640625,
0.0191192626953125,
-0.0350341796875,
-0.0012617111206054688,
0.00363922119140625,
-0.00534820556640625,
0.00799560546875,
0.0010023117065429688,
0.0216064453125,
-0.01202392578125,
0.004436492919921875,
0.01224517822265625,
0.0190582275390625,
0.026275634765625,
0.0031719207763671875,
0.0289764404296875,
-0.0233001708984375,
0.0073699951171875,
0.004444122314453125,
-0.02197265625,
0.021881103515625,
0.0165557861328125,
0.0016603469848632812,
0.0015659332275390625,
0.01198577880859375,
-0.0187530517578125,
0.014312744140625,
-0.0023670196533203125,
0.000934600830078125,
0.018463134765625,
-0.0177154541015625,
0.00007432699203491211,
0.039886474609375,
-0.004261016845703125,
0.008453369140625,
0.027008056640625,
-0.030303955078125,
-0.0268707275390625,
-0.035125732421875,
-0.0251617431640625,
-0.0025615692138671875,
-0.0007853507995605469,
0.031768798828125,
-0.004058837890625,
-0.0131988525390625,
0.042755126953125,
0.005550384521484375,
-0.0176849365234375,
-0.01140594482421875,
-0.0443115234375,
-0.00942230224609375,
0.0063934326171875,
-0.00649261474609375,
-0.0123291015625,
0.0287628173828125,
-0.0175018310546875,
0.031341552734375,
0.033111572265625,
-0.0046234130859375,
-0.0182342529296875,
0.0027923583984375,
-0.0390625,
-0.0007581710815429688,
0.00289154052734375,
0.007293701171875,
0.0278167724609375,
0.016815185546875,
-0.04595947265625,
-0.02215576171875,
-0.010894775390625,
-0.0166015625,
-0.0105438232421875,
0.0167388916015625,
0.031341552734375,
0.0099029541015625,
-0.0248870849609375,
0.007457733154296875,
0.029632568359375,
0.0271453857421875,
-0.01055908203125,
-0.0133056640625,
-0.0113525390625,
0.018463134765625,
-0.00742340087890625,
0.0019207000732421875,
-0.0188140869140625,
0.01507568359375,
-0.006103515625,
0.011383056640625,
0.0220794677734375,
0.019775390625,
0.0032138824462890625,
0.0053253173828125,
-0.0014705657958984375,
0.0265960693359375,
0.010711669921875,
0.005828857421875,
0.0030364990234375,
0.0021839141845703125,
-0.0189666748046875,
-0.0048065185546875,
-0.01222991943359375,
-0.031402587890625,
0.0196380615234375,
0.01548004150390625,
-0.0239715576171875,
-0.0137176513671875,
0.003833770751953125,
-0.0010595321655273438,
0.0205535888671875,
-0.005584716796875,
0.008514404296875,
0.00664520263671875,
0.01763916015625,
0.0122833251953125,
0.03741455078125,
-0.0007061958312988281,
-0.00382232666015625,
-0.00763702392578125,
0.025665283203125,
0.0175628662109375,
-0.0012378692626953125,
-0.01416778564453125,
0.0119781494140625,
0.004329681396484375,
0.005565643310546875,
-0.0032978057861328125,
-0.02557373046875,
-0.0130767822265625,
0.0252227783203125,
-0.00911712646484375,
0.0340576171875,
0.0177154541015625,
0.056365966796875,
-0.030853271484375,
-0.0251007080078125,
0.00952911376953125,
0.006191253662109375,
-0.022491455078125,
0.00809478759765625,
0.005405426025390625,
-0.0105438232421875,
-0.0226898193359375,
0.0179443359375,
-0.02752685546875,
-0.0301055908203125,
-0.01104736328125,
0.008209228515625,
0.007602691650390625,
0.0037746429443359375,
-0.002971649169921875,
-0.0017576217651367188,
-0.0167388916015625,
-0.00406646728515625,
-0.03948974609375,
-0.00399017333984375,
-0.0084228515625,
-0.0119171142578125,
-0.00235748291015625,
-0.00972747802734375,
0.002330780029296875,
-0.005184173583984375,
0.024078369140625,
0.003643035888671875,
-0.01451873779296875,
-0.007793426513671875,
-0.0018014907836914062,
-0.04522705078125,
-0.050140380859375,
0.003742218017578125,
-0.0198822021484375,
-0.01519775390625,
0.0191650390625,
-0.01346588134765625,
0.0125274658203125,
0.036346435546875,
0.035430908203125,
-0.021270751953125,
-0.037994384765625,
-0.01348114013671875,
-0.0014314651489257812,
-0.0013570785522460938,
0.0194244384765625,
-0.036956787109375,
-0.031982421875,
0.0011262893676757812,
-0.00975799560546875,
0.0005426406860351562,
0.01456451416015625,
-0.0157470703125,
0.0273895263671875,
-0.020294189453125,
-0.0008063316345214844,
0.02569580078125,
0.006488800048828125,
-0.01090240478515625,
-0.0128173828125,
-0.00913238525390625,
0.02471923828125,
0.006473541259765625,
0.03387451171875,
-0.0269775390625,
0.0018482208251953125,
-0.00836944580078125,
0.0006923675537109375,
0.00762176513671875,
0.007610321044921875,
-0.0208740234375,
-0.0083770751953125,
-0.043609619140625,
0.00734710693359375,
0.0202484130859375,
0.027862548828125,
0.005077362060546875,
-0.031890869140625,
-0.004302978515625,
0.0190887451171875,
0.004810333251953125,
0.0191497802734375,
0.0185699462890625,
-0.04327392578125,
-0.0145263671875,
0.00720977783203125,
-0.030029296875,
0.02081298828125,
0.007312774658203125,
-0.005123138427734375,
-0.0167388916015625,
-0.0010433197021484375,
-0.00600433349609375,
-0.0248260498046875,
-0.02685546875,
-0.02569580078125,
-0.016357421875,
0.01157379150390625,
0.024658203125,
-0.0177001953125,
-0.0037994384765625,
0.0098419189453125,
-0.0097503662109375,
-0.0186767578125,
-0.0094757080078125,
-0.00792694091796875,
0.006908416748046875,
0.0196685791015625,
0.0010728836059570312,
0.0219573974609375,
0.0172576904296875,
0.0218658447265625,
-0.0145416259765625,
0.00399017333984375,
0.005123138427734375,
-0.01267242431640625,
0.01422119140625,
0.014984130859375,
-0.015228271484375,
0.0218048095703125,
-0.020477294921875,
-0.0130767822265625,
-0.008026123046875,
0.0016956329345703125,
-0.0166015625,
-0.0015354156494140625,
0.00682830810546875,
-0.0238494873046875,
-0.0065460205078125,
0.0025501251220703125,
0.021575927734375,
0.041046142578125,
0.00710296630859375,
-0.044647216796875,
-0.016815185546875,
0.0069122314453125,
-0.0018835067749023438,
0.010955810546875,
0.0276641845703125,
0.02899169921875,
0.00830078125,
0.0195465087890625,
-0.0333251953125,
0.005779266357421875,
0.0447998046875,
-0.0244903564453125,
-0.004413604736328125,
-0.0177459716796875,
-0.021026611328125,
-0.00426483154296875,
-0.0079803466796875,
-0.039520263671875,
0.0307769775390625,
-0.004932403564453125,
-0.0028820037841796875,
-0.007434844970703125,
-0.029144287109375,
0.00775909423828125,
-0.00791168212890625,
-0.015838623046875,
-0.00205230712890625,
0.01190948486328125,
0.050079345703125,
0.042724609375,
-0.0267791748046875,
0.0007448196411132812,
-0.0027675628662109375,
-0.00849151611328125,
-0.0293731689453125,
-0.017547607421875,
0.01276397705078125,
0.0108795166015625,
-0.004299163818359375,
0.037506103515625,
-0.0234375,
0.0181121826171875,
-0.00711822509765625,
-0.0023365020751953125,
0.0286712646484375,
-0.0048065185546875,
-0.00008046627044677734,
0.0003495216369628906,
0.00555419921875,
0.0113983154296875,
0.0114593505859375,
-0.0005183219909667969,
-0.01763916015625,
0.0181427001953125,
0.0025806427001953125,
-0.0207366943359375,
-0.049591064453125,
-0.0017309188842773438,
0.01123809814453125,
0.016021728515625,
0.045928955078125,
0.0102996826171875,
-0.045806884765625,
0.0186309814453125,
-0.00302886962890625,
0.04473876953125,
0.01473236083984375,
-0.01049041748046875,
-0.021240234375,
0.00922393798828125,
-0.00804901123046875,
-0.0019435882568359375,
0.0015554428100585938,
-0.018035888671875,
-0.006839752197265625,
-0.042510986328125,
-0.01349639892578125,
-0.007762908935546875,
-0.0030975341796875,
0.0247039794921875,
0.007144927978515625,
0.00788116455078125,
0.0139617919921875,
-0.0097198486328125,
-0.0007200241088867188,
-0.002895355224609375,
0.037628173828125,
0.0294952392578125,
-0.0095977783203125,
-0.0074005126953125,
0.03839111328125,
0.00792694091796875,
0.017822265625,
0.0107879638671875,
0.004993438720703125,
-0.0016326904296875,
0.0265350341796875,
-0.0223236083984375,
-0.0158843994140625,
-0.0226593017578125,
0.042572021484375,
-0.01273345947265625,
0.0026378631591796875,
-0.015655517578125,
-0.00850677490234375,
0.0095062255859375,
-0.0035610198974609375,
-0.0084075927734375,
0.0035572052001953125,
0.0234832763671875,
-0.021270751953125,
-0.0225372314453125,
-0.0119476318359375,
-0.0127105712890625,
0.024810791015625,
-0.039215087890625,
0.0219879150390625,
0.0023403167724609375,
-0.002948760986328125,
-0.0181427001953125,
0.0001499652862548828,
-0.0193634033203125,
0.010589599609375,
0.0311737060546875,
0.01092529296875,
-0.0170745849609375,
0.01995849609375,
-0.0260162353515625,
0.037506103515625,
0.00022971630096435547,
0.0068206787109375,
0.01413726806640625,
0.021942138671875,
0.02178955078125,
0.0010061264038085938,
-0.01557159423828125,
-0.0078125,
0.037811279296875,
0.007476806640625,
0.004871368408203125,
-0.0184478759765625,
0.0460205078125,
-0.020355224609375,
-0.00299835205078125,
-0.0220184326171875,
-0.0011348724365234375,
-0.0002741813659667969,
-0.0218048095703125,
0.01435089111328125,
-0.00331878662109375,
-0.01482391357421875,
0.026214599609375,
0.00833892822265625,
0.01450347900390625,
0.025390625,
-0.02264404296875,
-0.0211944580078125,
-0.01873779296875,
0.0281982421875,
-0.01097869873046875,
0.007244110107421875,
0.019927978515625,
-0.054229736328125,
0.00824737548828125,
-0.003448486328125,
0.0028839111328125,
-0.0012750625610351562,
0.0286865234375,
0.003101348876953125,
-0.0029735565185546875,
-0.0112457275390625,
0.004154205322265625,
-0.0008101463317871094,
-0.003925323486328125,
0.0011043548583984375,
-0.013458251953125,
-0.0031280517578125,
0.026153564453125,
0.01436614990234375,
0.02783203125,
0.0287322998046875,
-0.005916595458984375,
0.01108551025390625,
-0.002696990966796875,
0.001918792724609375,
-0.040283203125,
0.01206207275390625,
-0.0175933837890625,
-0.031890869140625,
0.019256591796875,
-0.002773284912109375,
0.0106964111328125,
0.025054931640625,
0.004543304443359375,
0.0076751708984375,
-0.031768798828125,
-0.00482177734375,
-0.01495361328125,
-0.003353118896484375,
0.00765228271484375,
0.011810302734375,
-0.00551605224609375,
0.0036220550537109375,
0.006999969482421875,
-0.031402587890625,
0.01221466064453125,
0.0151214599609375,
0.01294708251953125,
0.007274627685546875,
-0.0173492431640625,
0.0015268325805664062,
-0.01361083984375,
-0.0201263427734375,
-0.0184478759765625,
-0.0015697479248046875,
-0.012542724609375,
-0.0323486328125,
0.00821685791015625,
0.01148223876953125,
0.0012540817260742188,
-0.00867462158203125,
-0.0017862319946289062,
0.00191497802734375,
0.0296173095703125,
0.005695343017578125,
0.00284576416015625,
0.01425933837890625,
-0.00963592529296875,
0.003810882568359375,
0.036956787109375,
-0.007266998291015625,
-0.05029296875,
0.006866455078125,
-0.0079803466796875,
0.0193023681640625,
-0.024810791015625,
-0.0211944580078125,
-0.0038814544677734375,
-0.0114898681640625,
0.0223541259765625,
0.0029392242431640625,
0.0015649795532226562,
-0.01236724853515625,
-0.02056884765625,
0.030914306640625,
-0.031829833984375,
0.0268402099609375,
0.02337646484375,
-0.02093505859375,
0.0189971923828125,
-0.048065185546875,
-0.0440673828125,
-0.0379638671875,
-0.00792694091796875,
-0.00716400146484375,
-0.0238189697265625,
0.0247650146484375,
0.01216888427734375,
0.01318359375,
-0.039459228515625,
-0.006351470947265625,
-0.01419830322265625,
0.01055145263671875,
0.00928497314453125,
-0.0004360675811767578,
-0.02850341796875,
0.039459228515625,
0.0021839141845703125,
0.0265350341796875,
-0.051361083984375,
0.005214691162109375,
0.0006499290466308594,
0.0038204193115234375,
0.021636962890625,
0.0016813278198242188,
0.003932952880859375,
-0.044677734375,
0.015899658203125,
0.01320648193359375,
-0.018829345703125,
-0.0133514404296875,
-0.006320953369140625,
-0.00251007080078125,
-0.01019287109375,
-0.000004649162292480469,
-0.003993988037109375,
-0.01393890380859375,
0.0147552490234375,
0.022491455078125,
0.0223541259765625,
0.0101318359375,
-0.0035076141357421875,
0.0017337799072265625,
-0.0021209716796875,
0.0128021240234375,
0.0133209228515625,
-0.00412750244140625,
0.010101318359375,
-0.02520751953125,
-0.0215911865234375,
-0.02392578125,
0.012237548828125,
-0.0258331298828125,
-0.01513671875,
-0.0003399848937988281,
-0.0031642913818359375,
-0.0155029296875,
0.005878448486328125,
-0.0014019012451171875,
-0.00013947486877441406,
0.0000978708267211914,
-0.01389312744140625,
-0.01509857177734375,
0.008758544921875,
0.0005488395690917969,
-0.0080718994140625,
-0.0204925537109375,
-0.0288238525390625,
-0.017669677734375,
-0.0204315185546875,
-0.01396942138671875,
0.03314208984375,
-0.0215911865234375,
0.025238037109375,
-0.005710601806640625,
0.048065185546875,
0.002033233642578125,
-0.00965118408203125,
0.02386474609375,
-0.0192108154296875,
0.024078369140625,
0.0177459716796875,
-0.030242919921875,
0.003765106201171875,
0.0168609619140625,
-0.01397705078125,
0.004520416259765625,
-0.018218994140625,
-0.00081634521484375,
0.07275390625,
-0.0133514404296875,
-0.0207672119140625,
-0.00414276123046875,
-0.0013427734375,
-0.004764556884765625,
-0.0191192626953125,
-0.0025806427001953125,
-0.0041961669921875,
-0.0180511474609375,
-0.039825439453125,
0.003662109375,
-0.015289306640625,
0.0023212432861328125,
0.0292205810546875,
-0.0146942138671875,
-0.00614166259765625,
0.03399658203125,
-0.034881591796875,
-0.0040740966796875,
-0.0018329620361328125,
-0.03155517578125,
0.0308074951171875,
-0.0234527587890625,
-0.0003018379211425781,
0.0092620849609375,
0.03277587890625,
-0.038726806640625,
0.028076171875,
-0.0028820037841796875,
-0.0232391357421875,
-0.0209808349609375,
0.0234375,
0.01544952392578125,
-0.0047760009765625,
0.00746917724609375,
-0.016845703125,
-0.0094146728515625,
0.06378173828125,
-0.039947509765625,
0.00400543212890625,
-0.0293426513671875,
-0.006805419921875,
-0.016357421875,
-0.03515625,
-0.0162506103515625,
0.01177215576171875,
0.025360107421875,
0.0242767333984375,
-0.01461029052734375,
-0.003711700439453125,
-0.0194854736328125,
0.0030193328857421875,
0.0014171600341796875,
-0.0308990478515625,
0.04345703125,
0.0013685226440429688,
-0.0164642333984375,
-0.010284423828125,
0.0119476318359375,
0.0019550323486328125,
0.0011444091796875,
-0.0009279251098632812,
-0.0007562637329101562,
-0.0003228187561035156,
0.033416748046875,
0.0035552978515625,
-0.0335693359375,
0.037200927734375,
0.0309906005859375,
-0.0203094482421875,
-0.0209197998046875,
-0.0318603515625,
0.037567138671875,
-0.0189056396484375,
-0.012969970703125,
0.05010986328125,
0.03912353515625,
-0.016448974609375,
0.0103302001953125,
-0.00788116455078125,
-0.004840850830078125,
-0.0007147789001464844,
0.0237274169921875,
0.01094818115234375,
0.005626678466796875,
0.020233154296875,
-0.01219940185546875,
0.0184326171875,
0.00968170166015625,
0.004657745361328125,
-0.0220794677734375,
-0.013824462890625,
-0.033203125,
0.034637451171875,
-0.0189056396484375,
-0.02532958984375,
0.0223541259765625,
-0.00301361083984375,
-0.028076171875,
-0.01082611083984375,
-0.0181884765625,
-0.04705810546875,
0.0130767822265625,
0.0028896331787109375,
0.01102447509765625,
0.004161834716796875,
-0.029937744140625,
-0.0183563232421875,
-0.0225372314453125,
0.0255584716796875,
0.0020465850830078125,
-0.028045654296875,
-0.01239776611328125,
0.006748199462890625,
0.00946807861328125,
-0.005260467529296875,
-0.0110931396484375,
-0.03643798828125,
-0.038116455078125,
-0.01203155517578125,
0.022125244140625,
-0.00782012939453125,
0.0233001708984375,
0.0010471343994140625,
0.052459716796875,
-0.0251312255859375,
0.0265655517578125,
0.0113983154296875,
-0.0149383544921875,
0.0203857421875,
0.01100921630859375,
-0.02349853515625,
-0.001979827880859375,
-0.0027866363525390625,
0.00026345252990722656,
0.00870513916015625,
-0.00047397613525390625,
-0.0270233154296875,
0.02392578125,
0.01338958740234375,
-0.031463623046875,
-0.025421142578125,
0.0017690658569335938,
-0.01515960693359375,
0.00957489013671875,
0.0225677490234375,
0.012054443359375,
0.0194854736328125,
0.01291656494140625,
-0.006427764892578125,
-0.0259552001953125,
-0.0120391845703125,
0.0276336669921875,
0.0184478759765625,
-0.0184478759765625,
-0.017791748046875,
-0.004947662353515625,
-0.02056884765625,
-0.0177764892578125,
0.0122833251953125,
0.00983428955078125,
-0.0022182464599609375,
0.00913238525390625,
-0.01445770263671875,
0.01119232177734375
] |
ours_467
|
Solution. Choosing the numbers \(0, 1, 1, 1, 1\) gives a sum of four. It's not possible to have a sum less than four, as that would imply at least two of the numbers are \(0\), and \(0\) is not relatively prime to itself. Therefore, the smallest possible sum is \(\boxed{4}\).
|
4
|
{
"competition": "us_comps",
"dataset": "Ours",
"posts": null,
"source": "OMOFall18Solns.md"
}
|
Leonhard has five cards. Each card has a nonnegative integer written on it, and any two cards show relatively prime numbers. Compute the smallest possible value of the sum of the numbers on Leonhard's cards.
Note: Two integers are relatively prime if no positive integer other than 1 divides both numbers.
|
[
"/Mathematics/NumberTheory/Divisors/Coprime",
"/Mathematics/NumberTheory/Divisors/RelativelyPrime",
"/Mathematics/NumberTheory/GeneralNumberTheory/ElementaryMethods",
"/Mathematics/NumberTheory/GeneralNumberTheory/ElementaryNumberTheory",
"/Mathematics/NumberTheory/GeneralNumberTheory/NumberTheory",
"/Mathematics/NumberTheory/Integers/Integer",
"/Mathematics/NumberTheory/Integers/NonnegativeInteger",
"/Mathematics/NumberTheory/Integers/WholeNumber",
"/Mathematics/NumberTheory/PrimeNumbers/PrimeNumberProperties"
] |
Use one zero (the only number that can be 0) and fill the other cards with 1's, since any two 1's are relatively prime and two zeros would violate the condition.
|
[
0.0005369186401367188,
-0.01032257080078125,
0.031982421875,
0.043060302734375,
0.002239227294921875,
-0.0081024169921875,
0.01015472412109375,
-0.0259246826171875,
0.020660400390625,
-0.0023975372314453125,
-0.031494140625,
-0.048065185546875,
-0.004146575927734375,
-0.0219879150390625,
-0.046661376953125,
0.0074005126953125,
0.022491455078125,
-0.0006766319274902344,
-0.0036411285400390625,
-0.00304412841796875,
-0.01082611083984375,
-0.00015938282012939453,
-0.040252685546875,
0.008880615234375,
-0.0175628662109375,
-0.0230712890625,
-0.0216827392578125,
0.0022106170654296875,
0.0198974609375,
0.0250396728515625,
-0.003509521484375,
-0.020294189453125,
-0.00927734375,
-0.03277587890625,
-0.00009590387344360352,
0.011932373046875,
0.028778076171875,
0.0006451606750488281,
-0.011016845703125,
-0.044830322265625,
-0.00879669189453125,
0.01404571533203125,
0.0036525726318359375,
-0.0032901763916015625,
-0.03857421875,
0.005458831787109375,
-0.0008368492126464844,
0.0377197265625,
-0.025390625,
-0.0012454986572265625,
-0.0022106170654296875,
0.0073394775390625,
0.012939453125,
-0.004302978515625,
-0.032318115234375,
-0.0372314453125,
0.0021038055419921875,
0.0057220458984375,
-0.0177764892578125,
-0.00882720947265625,
-0.00670623779296875,
-0.009033203125,
0.006137847900390625,
-0.0059051513671875,
0.00008511543273925781,
-0.00614166259765625,
0.01428985595703125,
-0.035430908203125,
0.0062408447265625,
-0.0261993408203125,
0.006000518798828125,
-0.01580810546875,
-0.01499176025390625,
0.0196685791015625,
0.018890380859375,
-0.00272369384765625,
-0.00530242919921875,
0.002349853515625,
-0.0225982666015625,
0.0160369873046875,
0.026397705078125,
0.0175933837890625,
0.007709503173828125,
0.031768798828125,
-0.007266998291015625,
0.004505157470703125,
-0.007480621337890625,
-0.0030612945556640625,
0.0241851806640625,
0.0093231201171875,
-0.006160736083984375,
-0.005207061767578125,
0.00787353515625,
-0.0076904296875,
-0.003925323486328125,
-0.01161956787109375,
0.01299285888671875,
-0.00009697675704956055,
-0.008270263671875,
0.0081787109375,
0.00066375732421875,
-0.00403594970703125,
0.03131103515625,
-0.0287628173828125,
-0.025390625,
0.00640106201171875,
-0.0276947021484375,
0.0013217926025390625,
-0.01500701904296875,
0.0021839141845703125,
0.006561279296875,
0.006366729736328125,
0.0227203369140625,
-0.006458282470703125,
0.0141754150390625,
-0.012420654296875,
0.05096435546875,
-0.0204620361328125,
-0.0028076171875,
-0.02386474609375,
0.00193023681640625,
0.0211639404296875,
-0.00070953369140625,
0.00490570068359375,
-0.0132293701171875,
-0.034637451171875,
-0.0022125244140625,
-0.0189208984375,
-0.039215087890625,
0.01543426513671875,
0.0343017578125,
-0.005702972412109375,
-0.0302886962890625,
0.0022563934326171875,
-0.04888916015625,
-0.0022602081298828125,
-0.006710052490234375,
0.003139495849609375,
0.0015916824340820312,
-0.002178192138671875,
0.004833221435546875,
-0.01983642578125,
-0.00762176513671875,
0.0266876220703125,
0.004886627197265625,
0.03228759765625,
0.007293701171875,
-0.043609619140625,
0.01473236083984375,
-0.00041556358337402344,
0.017242431640625,
-0.0211944580078125,
-0.0005173683166503906,
-0.0151519775390625,
-0.0202178955078125,
0.01274871826171875,
0.009124755859375,
0.0063629150390625,
0.001377105712890625,
0.0033168792724609375,
0.005947113037109375,
-0.00730133056640625,
-0.0208587646484375,
-0.01271820068359375,
0.00322723388671875,
-0.008026123046875,
-0.0017747879028320312,
0.005401611328125,
-0.0004830360412597656,
0.01165771484375,
0.00768280029296875,
0.0072174072265625,
-0.01012420654296875,
-0.00537872314453125,
-0.0209503173828125,
0.0021953582763671875,
-0.004852294921875,
0.03302001953125,
0.0010395050048828125,
0.0396728515625,
-0.00994873046875,
-0.005023956298828125,
0.0377197265625,
-0.0159912109375,
0.016815185546875,
0.00008362531661987305,
0.00405120849609375,
-0.0013532638549804688,
0.014556884765625,
0.00970458984375,
-0.0021724700927734375,
-0.025299072265625,
-0.01056671142578125,
0.00737762451171875,
0.0015134811401367188,
0.00811004638671875,
-0.0016384124755859375,
0.006366729736328125,
0.0179290771484375,
0.01641845703125,
-0.0103302001953125,
0.010345458984375,
-0.0109100341796875,
0.00963592529296875,
0.0122528076171875,
-0.01219940185546875,
0.00616455078125,
0.0027027130126953125,
0.006938934326171875,
0.01517486572265625,
-0.0195770263671875,
0.0006704330444335938,
-0.01026153564453125,
0.0163726806640625,
-0.0041351318359375,
0.0004754066467285156,
0.0089263916015625,
0.0018987655639648438,
-0.0010290145874023438,
-0.08795166015625,
0.004852294921875,
0.01580810546875,
0.0191497802734375,
-0.0005388259887695312,
-0.010650634765625,
-0.0092010498046875,
0.01126861572265625,
-0.0157318115234375,
0.00414276123046875,
-0.0012693405151367188,
-0.00555419921875,
0.013824462890625,
-0.0027828216552734375,
-0.0030460357666015625,
0.0010662078857421875,
-0.003528594970703125,
-0.02325439453125,
-0.01300811767578125,
0.025421142578125,
0.0031337738037109375,
0.07586669921875,
-0.005008697509765625,
0.01464080810546875,
0.0006809234619140625,
-0.018096923828125,
-0.005321502685546875,
0.00016701221466064453,
-0.0062255859375,
-0.007480621337890625,
-0.01340484619140625,
-0.0164031982421875,
0.00579071044921875,
0.0072784423828125,
-0.01390838623046875,
0.00727081298828125,
0.00452423095703125,
0.005321502685546875,
0.0023288726806640625,
-0.0053253173828125,
-0.03729248046875,
-0.00439453125,
-0.046875,
-0.007297515869140625,
-0.0007467269897460938,
0.0199432373046875,
0.0313720703125,
0.043731689453125,
0.0021533966064453125,
0.0010061264038085938,
-0.01708984375,
0.0220184326171875,
-0.015106201171875,
-0.01367950439453125,
0.0035552978515625,
0.026123046875,
0.00583648681640625,
0.0003170967102050781,
0.0029010772705078125,
0.005130767822265625,
0.0210418701171875,
-0.0020236968994140625,
-0.00926971435546875,
-0.01477813720703125,
0.023468017578125,
0.0040740966796875,
-0.0185546875,
0.012115478515625,
-0.0296630859375,
0.01262664794921875,
0.0182342529296875,
-0.0042877197265625,
-0.004150390625,
0.00943756103515625,
0.0125732421875,
0.037017822265625,
-0.0303802490234375,
0.0142822265625,
-0.004825592041015625,
0.0262451171875,
-0.01538848876953125,
0.023895263671875,
-0.01386260986328125,
0.00225830078125,
0.0257110595703125,
0.0099639892578125,
0.020721435546875,
0.01953125,
-0.003894805908203125,
0.0204925537109375,
-0.01381683349609375,
-0.000652313232421875,
0.002811431884765625,
0.0269775390625,
-0.004467010498046875,
-0.021453857421875,
-0.02984619140625,
-0.006710052490234375,
0.0156097412109375,
-0.0019702911376953125,
-0.030059814453125,
0.01898193359375,
0.0027332305908203125,
-0.0345458984375,
0.012237548828125,
0.0219879150390625,
-0.00140380859375,
0.0146636962890625,
-0.0018901824951171875,
-0.01244354248046875,
0.0219879150390625,
-0.04150390625,
0.00547027587890625,
0.017303466796875,
-0.0222320556640625,
-0.0201263427734375,
0.0016107559204101562,
-0.0200042724609375,
-0.00020766258239746094,
0.0017480850219726562,
0.02032470703125,
-0.0046539306640625,
-0.0012674331665039062,
-0.005161285400390625,
0.03741455078125,
-0.0010585784912109375,
0.01462554931640625,
-0.04376220703125,
0.0033206939697265625,
-0.017486572265625,
-0.0225830078125,
-0.0160980224609375,
0.0220947265625,
0.051177978515625,
0.0008368492126464844,
-0.03289794921875,
-0.0010213851928710938,
-0.0022220611572265625,
0.0003769397735595703,
0.0173187255859375,
0.0231475830078125,
0.024932861328125,
-0.0247344970703125,
-0.0171051025390625,
-0.0203399658203125,
0.0018415451049804688,
-0.0266265869140625,
0.009185791015625,
0.00997161865234375,
-0.03466796875,
-0.0194854736328125,
-0.014007568359375,
0.0156097412109375,
-0.0003719329833984375,
-0.042816162109375,
-0.042327880859375,
-0.0161285400390625,
0.00019598007202148438,
0.0007605552673339844,
-0.0014696121215820312,
0.00946807861328125,
0.00968170166015625,
0.04461669921875,
0.005832672119140625,
-0.005474090576171875,
-0.0097198486328125,
0.003643035888671875,
0.0224761962890625,
-0.02587890625,
0.003993988037109375,
0.0008096694946289062,
0.006572723388671875,
0.0063018798828125,
0.01265716552734375,
-0.0150146484375,
0.03765869140625,
-0.0355224609375,
-0.00220489501953125,
0.0156707763671875,
0.0333251953125,
-0.0033721923828125,
-0.0102386474609375,
-0.00946044921875,
-0.0235137939453125,
0.0183563232421875,
0.0011224746704101562,
0.0114593505859375,
0.004581451416015625,
0.0234222412109375,
0.012664794921875,
-0.049285888671875,
-0.026641845703125,
0.0200347900390625,
0.00652313232421875,
-0.0009675025939941406,
-0.00331878662109375,
-0.0177459716796875,
-0.0162200927734375,
-0.0102691650390625,
-0.01873779296875,
-0.005035400390625,
0.0167999267578125,
-0.024383544921875,
0.0012350082397460938,
-0.015289306640625,
0.0027370452880859375,
0.01480865478515625,
-0.004070281982421875,
0.016845703125,
0.03411865234375,
0.013458251953125,
0.0390625,
0.0006375312805175781,
0.0118408203125,
0.01654052734375,
-0.00677490234375,
0.0185394287109375,
0.009979248046875,
-0.0209503173828125,
0.00655364990234375,
-0.007049560546875,
0.0070343017578125,
-0.005336761474609375,
-0.006633758544921875,
-0.0211029052734375,
0.0083160400390625,
0.00423431396484375,
0.007640838623046875,
0.00035953521728515625,
-0.014892578125,
0.0006532669067382812,
0.01092529296875,
-0.00791168212890625,
-0.040008544921875,
-0.0017910003662109375,
-0.008880615234375,
-0.004863739013671875,
0.0184478759765625,
0.0161285400390625,
-0.0287322998046875,
-0.0284576416015625,
-0.003570556640625,
-0.00826263427734375,
-0.0125885009765625,
0.0006608963012695312,
0.02960205078125,
0.006099700927734375,
0.0158538818359375,
0.0025081634521484375,
0.004169464111328125,
0.054107666015625,
0.0052947998046875,
-0.01140594482421875,
0.0345458984375,
-0.0020046234130859375,
-0.0193328857421875,
0.054779052734375,
0.021759033203125,
0.044708251953125,
-0.0006656646728515625,
0.0024871826171875,
-0.0321044921875,
-0.0005769729614257812,
-0.0103302001953125,
0.02471923828125,
0.0013713836669921875,
0.018280029296875,
0.02667236328125,
0.01435089111328125,
0.01348876953125,
-0.0200958251953125,
0.01010894775390625,
0.01120758056640625,
-0.0506591796875,
-0.048065185546875,
-0.005397796630859375,
-0.008148193359375,
-0.00724029541015625,
0.0004634857177734375,
0.0126190185546875,
0.0091400146484375,
-0.00009590387344360352,
-0.039276123046875,
0.0286102294921875,
-0.0176849365234375,
0.01111602783203125,
0.00963592529296875,
0.0216827392578125,
-0.0047149658203125,
0.0030384063720703125,
0.0093231201171875,
0.0011205673217773438,
-0.01186370849609375,
0.024383544921875,
-0.043853759765625,
-0.01312255859375,
-0.025115966796875,
0.039398193359375,
-0.0199432373046875,
-0.006824493408203125,
0.0224151611328125,
-0.01513671875,
0.002780914306640625,
0.043487548828125,
0.0259857177734375,
0.024322509765625,
0.0182647705078125,
0.0108489990234375,
-0.020355224609375,
0.023284912109375,
0.004924774169921875,
-0.01546478271484375,
-0.0152435302734375,
0.04315185546875,
0.00829315185546875,
-0.04486083984375,
0.0233917236328125,
0.003398895263671875,
-0.0157470703125,
0.001804351806640625,
-0.00894927978515625,
0.01093292236328125,
-0.01160430908203125,
0.0233306884765625,
-0.0038814544677734375,
-0.0103759765625,
-0.05474853515625,
-0.00926971435546875,
-0.0035228729248046875,
0.0013895034790039062,
0.0220489501953125,
0.00799560546875,
0.0148468017578125,
-0.01220703125,
-0.023590087890625,
-0.00588226318359375,
-0.022674560546875,
0.0307159423828125,
0.002346038818359375,
-0.01739501953125,
-0.0281982421875,
-0.0255126953125,
0.0085906982421875,
-0.0119781494140625,
-0.00412750244140625,
-0.0002455711364746094,
-0.012420654296875,
-0.0021800994873046875,
-0.006687164306640625,
0.0101776123046875,
-0.046875,
0.0028514862060546875,
0.007038116455078125,
0.01496124267578125,
-0.0312347412109375,
-0.005809783935546875,
-0.029937744140625,
-0.03472900390625,
-0.020355224609375,
0.0147552490234375,
-0.01434326171875,
0.02227783203125,
-0.00852203369140625,
-0.00698089599609375,
0.0295562744140625,
-0.0125274658203125,
-0.0217437744140625,
-0.0022373199462890625,
0.0077972412109375,
0.0167083740234375,
0.004116058349609375,
-0.03887939453125,
0.0230255126953125,
0.0243682861328125,
0.0234375,
-0.0128631591796875,
0.0029277801513671875,
0.034698486328125,
0.007144927978515625,
0.01983642578125,
-0.009735107421875,
0.007762908935546875,
-0.005107879638671875,
0.00595855712890625,
0.023223876953125,
0.01543426513671875,
0.014007568359375,
-0.0177154541015625,
0.011871337890625,
0.033721923828125,
-0.009765625,
-0.001697540283203125,
-0.052276611328125,
-0.0241241455078125,
-0.001071929931640625,
0.005859375,
-0.00038504600524902344,
-0.01275634765625,
-0.0233001708984375,
-0.0248565673828125,
0.036529541015625,
0.00016105175018310547,
0.018524169921875,
-0.0122528076171875,
0.0217132568359375,
-0.00839996337890625,
-0.0372314453125,
0.02081298828125,
-0.02313232421875,
-0.01447296142578125,
-0.0035152435302734375,
-0.0099334716796875,
-0.01751708984375,
0.0098419189453125,
-0.0203399658203125,
-0.01047515869140625,
-0.0010023117065429688,
-0.0233154296875,
0.0232391357421875,
-0.0197601318359375,
0.030029296875,
-0.001148223876953125,
-0.01277923583984375,
0.0250244140625,
-0.04437255859375,
0.00016450881958007812,
0.0162353515625,
-0.0005750656127929688,
0.0276336669921875,
0.01511383056640625,
0.018096923828125,
-0.0016527175903320312,
-0.0006737709045410156,
-0.01349639892578125,
0.028076171875,
0.0313720703125,
-0.0155792236328125,
0.021240234375,
-0.01490020751953125,
0.0208740234375,
-0.0118560791015625,
0.00797271728515625,
0.0124053955078125,
-0.0237884521484375,
0.01224517822265625,
-0.0196685791015625,
-0.0182952880859375,
0.0411376953125,
-0.005344390869140625,
-0.038909912109375,
-0.0122222900390625,
-0.0200042724609375,
-0.00687408447265625,
0.018890380859375,
0.00502777099609375,
0.032958984375,
-0.008087158203125,
-0.030670166015625,
-0.000431060791015625,
0.0164031982421875,
0.0170745849609375,
-0.0093231201171875,
0.01215362548828125,
0.04620361328125,
-0.0138092041015625,
0.0179595947265625,
0.00957489013671875,
-0.001605987548828125,
0.01288604736328125,
-0.0122528076171875,
0.0214080810546875,
0.0027370452880859375,
-0.00908660888671875,
-0.0124359130859375,
-0.0038890838623046875,
-0.0224761962890625,
-0.024383544921875,
0.0006470680236816406,
0.00879669189453125,
-0.0173797607421875,
-0.0226898193359375,
-0.006618499755859375,
-0.0255584716796875,
0.0076141357421875,
-0.002468109130859375,
-0.007049560546875,
-0.01078033447265625,
0.00910186767578125,
-0.01172637939453125,
-0.03643798828125,
0.01441192626953125,
0.0080108642578125,
0.0184326171875,
-0.0164337158203125,
-0.006557464599609375,
0.0023975372314453125,
-0.0259246826171875,
0.0061492919921875,
-0.00714874267578125,
-0.0016660690307617188,
-0.006214141845703125,
-0.00922393798828125,
-0.00409698486328125,
-0.013702392578125,
0.0240936279296875,
0.031280517578125,
0.0350341796875,
-0.0283355712890625,
-0.004222869873046875,
0.0097503662109375,
-0.0100250244140625,
-0.0274658203125,
-0.016204833984375,
-0.007297515869140625,
-0.006244659423828125,
-0.0271759033203125,
-0.01313018798828125,
0.016265869140625,
-0.005077362060546875,
0.0211639404296875,
0.005588531494140625,
-0.0014209747314453125,
-0.00347900390625,
0.005474090576171875,
0.003047943115234375,
-0.0245819091796875,
-0.0169677734375,
0.0295867919921875,
-0.006664276123046875,
-0.0162200927734375,
-0.025360107421875,
0.00399017333984375,
-0.0224609375,
0.00998687744140625,
-0.04827880859375,
-0.0142822265625,
0.0272369384765625,
0.0304718017578125,
0.016326904296875,
-0.00493621826171875,
-0.0155487060546875,
-0.0169219970703125,
-0.00817108154296875,
-0.0065765380859375,
-0.0010347366333007812,
-0.004047393798828125,
-0.0261077880859375,
-0.05291748046875,
-0.008941650390625,
-0.053192138671875,
0.03106689453125,
-0.00908660888671875,
0.019378662109375,
0.0038089752197265625,
0.01486968994140625,
-0.0043182373046875,
0.04180908203125,
-0.03350830078125,
0.01047515869140625,
0.017364501953125,
-0.00237274169921875,
0.0031871795654296875,
-0.00502777099609375,
0.02294921875,
0.01242828369140625,
-0.0083160400390625,
-0.015167236328125,
0.02056884765625,
0.007312774658203125,
0.00322723388671875,
-0.00844573974609375,
0.036834716796875,
0.0249176025390625,
0.03192138671875,
0.000042378902435302734,
0.00658416748046875,
0.0009560585021972656,
-0.0009427070617675781,
0.003353118896484375,
0.018524169921875,
0.00855255126953125,
-0.01262664794921875,
0.0025272369384765625,
0.00611114501953125,
0.0218353271484375,
0.0244598388671875,
-0.0309295654296875,
-0.0030975341796875,
-0.01336669921875,
0.00623321533203125,
0.0089874267578125,
0.010955810546875,
0.00881195068359375,
-0.02301025390625,
-0.015411376953125,
-0.006099700927734375,
-0.03021240234375,
-0.044219970703125,
0.018890380859375,
0.0059967041015625,
-0.01187896728515625,
0.0169525146484375,
0.037261962890625,
-0.031982421875,
0.0030269622802734375,
-0.00789642333984375,
-0.0027332305908203125,
-0.0143890380859375,
-0.039215087890625,
0.01480865478515625,
-0.0263824462890625,
-0.0535888671875,
0.014984130859375,
-0.030975341796875,
-0.0183868408203125,
0.0138702392578125,
-0.0177154541015625,
0.03460693359375,
0.028350830078125,
-0.029541015625,
0.05975341796875,
0.039215087890625,
-0.0103912353515625,
0.036163330078125,
-0.02667236328125,
-0.004199981689453125,
-0.0052490234375,
-0.025146484375,
0.0156402587890625,
0.02996826171875,
0.01318359375,
0.004505157470703125,
0.027099609375,
-0.006450653076171875,
-0.007904052734375,
-0.027984619140625,
0.0141754150390625,
0.0170135498046875,
0.00015294551849365234,
-0.0118255615234375,
-0.005046844482421875,
-0.00995635986328125,
-0.0264739990234375,
0.031494140625,
-0.0254364013671875,
0.006198883056640625,
0.0018520355224609375,
0.01276397705078125,
0.0027713775634765625,
0.01019287109375,
0.0115814208984375,
0.02435302734375,
-0.01898193359375,
0.00354766845703125,
0.01202392578125,
0.060516357421875,
0.024658203125,
0.0019702911376953125,
0.0203094482421875,
-0.0280303955078125,
-0.007427215576171875,
0.0168609619140625,
-0.0264129638671875,
-0.0007071495056152344,
0.043487548828125,
-0.0196685791015625,
-0.04364013671875,
0.02825927734375,
0.01142120361328125,
0.0110931396484375,
-0.018035888671875,
-0.0134735107421875,
-0.016754150390625,
-0.01202392578125,
-0.0263214111328125,
-0.01776123046875,
0.00229644775390625,
-0.0002961158752441406,
-0.00815582275390625,
-0.003978729248046875,
0.021148681640625,
-0.0271759033203125,
0.0007376670837402344,
0.0300140380859375,
0.0153045654296875,
-0.03643798828125,
-0.006374359130859375,
-0.002292633056640625,
0.002826690673828125,
0.00882720947265625,
0.0158538818359375,
-0.0281829833984375,
0.0287017822265625,
0.018157958984375,
0.0146026611328125,
-0.01763916015625,
-0.0028858184814453125,
-0.00455474853515625,
0.0103302001953125,
-0.0253753662109375,
-0.00943756103515625,
0.003314971923828125,
-0.021759033203125,
-0.00194549560546875,
-0.02056884765625,
0.006023406982421875,
-0.0206298828125,
0.001636505126953125,
-0.01067352294921875,
-0.018157958984375,
-0.007472991943359375,
-0.01496124267578125,
0.0193328857421875,
-0.0182647705078125,
0.02484130859375,
0.00838470458984375,
0.00597381591796875,
-0.005084991455078125,
-0.00815582275390625,
-0.00362396240234375,
0.024139404296875,
-0.0154876708984375,
-0.0198822021484375,
0.003650665283203125,
0.03076171875,
0.0279998779296875,
0.0163116455078125,
-0.0013017654418945312,
0.0090484619140625,
-0.040496826171875,
0.0179290771484375,
-0.00702667236328125,
0.0006418228149414062,
-0.01250457763671875,
-0.005039215087890625,
0.03314208984375,
-0.0093231201171875,
0.01751708984375,
-0.032073974609375,
0.01422882080078125,
-0.00986480712890625,
0.0287628173828125,
-0.0138397216796875,
-0.034393310546875,
-0.0275726318359375,
0.00955963134765625,
0.04241943359375,
0.0187225341796875,
0.03363037109375,
0.0123138427734375,
0.0089111328125,
0.0186004638671875,
0.0275115966796875,
-0.0008311271667480469,
-0.07275390625,
-0.019073486328125,
-0.00572967529296875,
-0.00952911376953125,
0.0201263427734375,
-0.0008211135864257812,
-0.01500701904296875,
-0.033416748046875,
0.050567626953125,
-0.007625579833984375,
-0.0212860107421875,
-0.02154541015625,
0.0157623291015625,
0.018707275390625,
-0.03790283203125,
0.0012645721435546875,
-0.0192718505859375,
-0.01157379150390625,
0.039398193359375,
0.005035400390625,
-0.016845703125,
0.00820159912109375,
-0.0015554428100585938,
-0.0165252685546875,
-0.004657745361328125,
0.0198211669921875,
0.02410888671875,
-0.0107574462890625,
0.00652313232421875,
0.0009098052978515625,
-0.01232147216796875,
0.0247650146484375,
-0.01522064208984375,
-0.004627227783203125,
-0.0005679130554199219,
0.01020050048828125,
0.0184783935546875,
0.01511383056640625,
-0.0181427001953125,
-0.00514984130859375,
-0.033935546875,
-0.017913818359375,
0.0496826171875,
-0.01296234130859375,
-0.010528564453125,
-0.0203857421875,
0.0322265625,
-0.0198974609375,
-0.0272979736328125,
-0.026214599609375,
-0.007312774658203125,
0.0024509429931640625,
-0.005298614501953125,
-0.00995635986328125,
-0.0036163330078125,
0.0413818359375,
0.019287109375,
-0.01296234130859375,
-0.010498046875,
0.0223846435546875,
-0.00708770751953125,
0.0164642333984375,
0.006633758544921875,
0.010833740234375,
-0.03271484375,
0.007244110107421875,
-0.01375579833984375,
-0.0046234130859375,
0.0066680908203125,
0.0357666015625,
-0.0167083740234375,
0.03607177734375,
0.017578125,
-0.0237274169921875,
-0.002460479736328125,
-0.037445068359375,
0.021636962890625,
-0.0218353271484375,
-0.004547119140625,
-0.0151824951171875,
-0.0051727294921875,
-0.025360107421875,
-0.00848388671875,
-0.013336181640625,
0.0243682861328125,
-0.007083892822265625,
0.01053619384765625,
0.0088043212890625,
-0.0195159912109375,
-0.006420135498046875,
-0.0016355514526367188,
0.00426483154296875,
0.01220703125,
-0.046234130859375,
-0.0117034912109375,
-0.007320404052734375,
0.0281219482421875,
-0.020416259765625,
-0.0059967041015625,
0.01393890380859375,
-0.019805908203125,
0.020843505859375,
0.041290283203125,
-0.007190704345703125,
-0.007659912109375,
0.0221405029296875,
-0.0178985595703125,
0.00836944580078125,
0.00687408447265625,
-0.0262908935546875,
-0.01349639892578125,
-0.0186309814453125,
0.042083740234375,
-0.0033740997314453125,
0.012481689453125,
-0.0190277099609375,
0.0021762847900390625,
0.0012769699096679688,
0.01031494140625,
-0.01824951171875,
-0.0008087158203125,
0.0029621124267578125,
-0.007617950439453125,
0.0189971923828125,
-0.0167388916015625,
-0.007030487060546875,
-0.01129150390625,
0.00620269775390625,
0.04791259765625,
-0.00982666015625,
0.0142669677734375,
-0.0181121826171875,
0.0235595703125,
-0.01139068603515625,
-0.002666473388671875,
-0.009033203125,
-0.0032215118408203125,
-0.023406982421875,
0.035125732421875,
0.03106689453125,
0.016754150390625,
0.0251312255859375,
0.0193328857421875,
-0.005184173583984375,
-0.0265045166015625,
-0.006290435791015625,
0.0194244384765625,
0.0279998779296875,
0.0277252197265625,
0.01535797119140625,
0.017852783203125,
0.007320404052734375,
0.0024433135986328125,
0.0280914306640625,
0.0015659332275390625,
0.0306396484375,
-0.0222015380859375,
-0.0029773712158203125,
-0.00667572021484375,
0.028350830078125,
-0.01151275634765625,
0.0106964111328125,
-0.0278472900390625,
-0.01611328125,
-0.0239105224609375,
0.00836181640625,
-0.0208892822265625,
-0.0100555419921875,
0.01459503173828125,
0.0030975341796875,
-0.00826263427734375,
-0.035369873046875,
0.006206512451171875,
-0.00948333740234375,
0.004444122314453125,
0.0279693603515625,
0.01389312744140625,
-0.040771484375,
0.011566162109375,
-0.02362060546875,
0.0226898193359375,
-0.00848388671875,
-0.01505279541015625,
-0.0018606185913085938,
-0.015716552734375,
0.035919189453125,
-0.0157012939453125,
0.0037384033203125,
-0.0171966552734375,
-0.01483917236328125,
0.00803375244140625,
-0.03424072265625,
-0.007701873779296875,
-0.01166534423828125,
0.031005859375,
-0.0034847259521484375,
0.0167388916015625,
-0.010101318359375,
-0.01432037353515625,
0.031951904296875,
0.0056915283203125,
-0.02996826171875,
0.0002142190933227539,
0.0264739990234375,
-0.0022792816162109375,
-0.005657196044921875,
-0.0235443115234375,
-0.01287841796875,
0.017364501953125,
0.0204925537109375,
-0.045928955078125,
-0.0290374755859375,
-0.0206756591796875,
-0.000812530517578125,
-0.034942626953125,
0.0008921623229980469,
-0.008544921875,
-0.00933837890625,
-0.014739990234375,
-0.01070404052734375,
-0.0070037841796875,
0.0025959014892578125,
-0.0030574798583984375,
-0.0258941650390625,
-0.0143280029296875,
-0.0235443115234375,
0.00409698486328125,
0.0204925537109375,
0.0017900466918945312,
-0.035247802734375,
0.010162353515625,
0.0237274169921875,
0.0038280487060546875,
0.036468505859375,
0.029266357421875,
-0.00702667236328125,
-0.002552032470703125,
-0.0253448486328125,
-0.005672454833984375,
0.004093170166015625,
0.0172576904296875,
0.034454345703125,
-0.00888824462890625,
-0.002246856689453125,
0.0221099853515625,
0.00044655799865722656,
0.0005049705505371094,
-0.0195465087890625,
0.0171966552734375,
0.034027099609375,
-0.01202392578125,
0.0087127685546875,
-0.005893707275390625,
-0.0347900390625,
0.017303466796875,
-0.0005979537963867188,
0.025115966796875,
0.0092315673828125,
0.00341033935546875,
-0.0076904296875,
0.0469970703125,
-0.030731201171875,
-0.0031223297119140625,
0.002166748046875,
0.002960205078125,
0.0207061767578125,
0.0303192138671875,
-0.005237579345703125,
0.03106689453125,
-0.006053924560546875,
-0.010040283203125,
0.04632568359375,
-0.002349853515625,
-0.0278778076171875,
-0.027435302734375,
0.0118560791015625,
0.00444793701171875,
0.001522064208984375,
0.00308990478515625,
-0.0103759765625,
-0.0130767822265625,
-0.01849365234375,
-0.027740478515625,
-0.0036296844482421875,
0.0006709098815917969,
-0.026947021484375,
-0.01529693603515625,
0.017974853515625,
0.0341796875,
0.00699615478515625,
0.024261474609375,
-0.0104522705078125,
-0.005001068115234375,
-0.00998687744140625,
-0.0164031982421875,
-0.0172271728515625,
-0.020416259765625,
-0.0216064453125,
-0.034027099609375,
-0.020355224609375,
0.0211944580078125,
-0.0086669921875,
-0.01300048828125,
-0.005428314208984375,
0.01044464111328125,
-0.00958251953125,
-0.011871337890625,
-0.01528167724609375,
0.004650115966796875,
0.0164642333984375,
-0.01027679443359375,
0.002437591552734375,
0.0036029815673828125,
0.0009226799011230469,
0.02093505859375,
0.00453948974609375,
-0.0259246826171875,
-0.00455474853515625,
-0.03167724609375,
-0.0172271728515625,
0.0008444786071777344,
-0.01186370849609375,
0.00879669189453125,
0.0020771026611328125,
-0.0133514404296875,
0.0223388671875,
-0.0225067138671875,
-0.00035071372985839844,
-0.01226043701171875,
-0.0278167724609375,
0.032440185546875,
-0.0253753662109375,
0.002704620361328125,
0.00913238525390625,
-0.00629425048828125,
-0.0010976791381835938,
-0.028900146484375,
-0.0048675537109375,
0.021942138671875,
0.04620361328125,
-0.03289794921875,
0.032257080078125,
-0.005603790283203125,
0.023773193359375,
0.0027408599853515625,
-0.046478271484375,
0.005802154541015625,
0.01129150390625,
0.0196990966796875,
-0.012969970703125,
0.011444091796875,
0.02545166015625,
-0.02294921875,
-0.01055908203125,
-0.006805419921875,
0.01010894775390625,
0.0190277099609375,
-0.00638580322265625,
0.0260162353515625,
-0.03271484375,
0.0023059844970703125,
-0.01812744140625,
0.006038665771484375,
0.007015228271484375,
0.023040771484375,
0.01025390625,
-0.007801055908203125,
-0.0031375885009765625,
0.0291748046875,
-0.0015611648559570312,
0.023712158203125,
0.01541900634765625,
0.0245513916015625,
-0.039215087890625,
-0.005157470703125,
0.04351806640625,
-0.00994873046875,
0.05914306640625,
0.01971435546875,
-0.01293182373046875,
0.021148681640625,
-0.03253173828125,
-0.05438232421875,
0.0189056396484375,
0.0223846435546875,
-0.00862884521484375,
0.01180267333984375,
0.04803466796875,
-0.0037384033203125,
-0.01216888427734375,
-0.017822265625,
0.04022216796875,
0.051422119140625,
0.0151824951171875,
0.00701141357421875,
-0.00019884109497070312,
-0.0007014274597167969,
0.006702423095703125,
-0.00574493408203125,
-0.0131378173828125,
-0.0104522705078125,
0.006252288818359375,
-0.04595947265625,
-0.0011310577392578125,
-0.00928497314453125,
0.0008592605590820312,
0.0281524658203125,
0.00733184814453125,
-0.03533935546875,
0.0031108856201171875,
-0.01544952392578125,
0.0005049705505371094,
-0.0038051605224609375,
-0.00847625732421875,
0.005908966064453125,
-0.006526947021484375,
-0.016082763671875,
0.0213165283203125,
0.0126190185546875,
-0.00659942626953125,
0.016357421875,
-0.017303466796875,
-0.036346435546875,
-0.020111083984375,
0.00016367435455322266,
-0.00966644287109375,
-0.0083770751953125,
0.0242919921875,
-0.01800537109375,
0.03985595703125,
-0.0007486343383789062,
0.0084075927734375,
0.004665374755859375,
-0.0008368492126464844,
0.043487548828125,
0.02508544921875,
-0.0023441314697265625,
0.0194549560546875,
0.024658203125,
-0.0182952880859375,
-0.01169586181640625,
0.0156402587890625,
-0.033050537109375,
0.00997161865234375,
0.019195556640625,
-0.0080413818359375,
-0.019927978515625,
0.006458282470703125,
-0.011199951171875,
-0.0230712890625,
0.01641845703125,
-0.004322052001953125,
0.0281219482421875,
-0.0263214111328125,
0.01522064208984375,
-0.005413055419921875,
0.00942230224609375,
-0.020660400390625,
-0.054412841796875,
-0.034454345703125,
-0.017364501953125,
-0.0295867919921875,
0.00722503662109375,
0.00821685791015625,
0.0150604248046875,
0.03985595703125,
0.03271484375,
-0.0191650390625,
-0.0031585693359375,
0.00089263916015625,
0.004222869873046875,
-0.0105133056640625,
-0.01116180419921875,
-0.007450103759765625,
-0.0214691162109375,
-0.01248931884765625,
0.019775390625,
-0.048431396484375,
-0.015289306640625,
-0.019927978515625,
0.00844573974609375,
0.0279388427734375,
0.0112457275390625,
-0.0178375244140625,
0.0267333984375,
0.0024471282958984375,
0.0181121826171875,
-0.051025390625,
0.01708984375,
0.0022983551025390625,
0.01166534423828125,
0.02703857421875,
-0.0137176513671875,
-0.0252685546875,
0.03314208984375,
-0.00946807861328125,
-0.016876220703125,
0.02276611328125,
-0.01904296875,
0.0096282958984375,
0.002117156982421875,
-0.02691650390625,
0.0007424354553222656,
0.040557861328125,
-0.02911376953125,
-0.01531982421875,
-0.00289154052734375,
0.0035953521728515625,
0.007282257080078125,
0.028106689453125,
-0.004848480224609375,
-0.005893707275390625,
-0.0207977294921875,
0.010406494140625,
0.0024433135986328125,
-0.024688720703125,
-0.00833892822265625,
0.01123809814453125,
-0.01812744140625,
0.008331298828125,
-0.02618408203125,
0.0164031982421875,
0.0265960693359375,
-0.001918792724609375,
-0.004978179931640625,
-0.01358795166015625,
-0.0178070068359375,
0.010009765625,
-0.0144805908203125,
-0.005523681640625,
0.0090179443359375,
0.033935546875,
-0.00325775146484375,
-0.0067596435546875,
0.0014400482177734375,
-0.0184478759765625,
-0.01580810546875,
0.01435089111328125,
0.0017862319946289062,
0.0010747909545898438,
0.006145477294921875,
-0.005184173583984375,
-0.01666259765625,
0.01335906982421875,
-0.008636474609375,
-0.0120849609375,
0.003391265869140625,
-0.003143310546875,
0.0184326171875,
0.00637054443359375,
0.0090179443359375,
0.0171051025390625,
-0.017333984375,
0.01448822021484375,
0.0292510986328125,
0.00484466552734375,
0.0008177757263183594,
0.0213623046875,
0.005672454833984375,
0.01354217529296875,
-0.0038051605224609375,
0.025787353515625,
-0.0115814208984375,
-0.003452301025390625,
0.0214385986328125,
-0.010284423828125,
-0.01995849609375,
0.0034809112548828125,
0.032318115234375,
-0.0092926025390625,
0.0018091201782226562,
0.002834320068359375,
0.01806640625,
0.0013713836669921875,
0.00614166259765625,
-0.0073089599609375,
-0.00992584228515625,
-0.0256805419921875,
-0.0006012916564941406,
0.0423583984375,
-0.0192413330078125,
-0.00891876220703125,
-0.015838623046875,
0.0062255859375,
0.0382080078125,
0.018310546875,
0.016082763671875,
0.00522613525390625,
0.005710601806640625,
0.0091705322265625,
0.0207061767578125,
0.02294921875,
-0.005245208740234375,
-0.03961181640625,
0.0182952880859375,
0.0176239013671875,
-0.0167999267578125,
0.0188140869140625,
0.0186309814453125,
-0.003307342529296875,
-0.01143646240234375,
-0.016265869140625,
-0.022003173828125,
0.01035308837890625,
0.00968170166015625,
0.017791748046875,
-0.005718231201171875,
-0.024810791015625,
-0.015106201171875,
0.00290679931640625,
0.0261383056640625,
-0.01971435546875,
-0.0085906982421875,
0.0141143798828125,
0.01263427734375,
-0.00786590576171875,
0.0017633438110351562,
0.005329132080078125,
0.0254669189453125,
0.0236663818359375,
0.01184844970703125,
-0.01494598388671875,
-0.021087646484375,
-0.0024585723876953125,
-0.01142120361328125,
-0.00225830078125,
0.00490570068359375,
-0.0198516845703125,
0.030487060546875,
0.01450347900390625,
-0.02545166015625,
-0.01068115234375,
-0.0221099853515625,
-0.01531219482421875,
-0.009002685546875,
0.01274871826171875,
-0.01152801513671875,
0.00247955322265625,
0.0176239013671875,
0.02862548828125,
-0.001049041748046875,
0.0131988525390625,
-0.043914794921875,
0.0091705322265625,
0.060546875,
0.020965576171875,
0.035797119140625,
0.005184173583984375,
-0.00980377197265625,
0.019927978515625,
-0.0139007568359375,
0.01177978515625,
0.004604339599609375,
-0.0306243896484375,
0.00850677490234375,
0.0251312255859375,
-0.007656097412109375,
0.003910064697265625,
-0.0181121826171875,
-0.0311279296875,
0.01544952392578125,
0.0240936279296875,
-0.0167083740234375,
0.0276336669921875,
0.05255126953125,
0.01079559326171875,
-0.00919342041015625,
-0.01483154296875,
0.00452423095703125,
-0.01163482666015625,
-0.004550933837890625,
-0.022186279296875,
-0.007659912109375,
-0.00586700439453125,
0.0183868408203125,
0.0035419464111328125,
-0.01904296875,
-0.0025386810302734375,
0.0068206787109375,
0.003173828125,
0.007648468017578125,
0.001590728759765625,
-0.002384185791015625,
-0.005527496337890625,
0.01297760009765625,
-0.0064849853515625,
-0.035919189453125,
-0.02069091796875,
0.0274200439453125,
0.01532745361328125,
0.01552581787109375,
-0.0156707763671875,
0.005268096923828125,
-0.040008544921875,
0.024505615234375,
0.0193939208984375,
0.006977081298828125,
-0.0260162353515625,
-0.036468505859375,
-0.01041412353515625,
-0.0131378173828125,
0.0230865478515625,
0.00009506940841674805,
-0.00624847412109375,
0.0171051025390625,
0.0245208740234375,
-0.0154571533203125,
0.006282806396484375,
0.006496429443359375,
0.00006687641143798828,
0.0216064453125,
-0.02520751953125,
-0.046051025390625,
-0.01073455810546875,
-0.037445068359375,
0.01081085205078125,
-0.024993896484375,
0.0152587890625,
-0.00928497314453125,
0.022491455078125,
0.00492095947265625,
-0.00807952880859375,
0.010772705078125,
-0.01397705078125,
0.00647735595703125,
-0.0250244140625,
0.03741455078125,
0.00275421142578125,
0.053009033203125,
0.005702972412109375,
0.018585205078125,
-0.0197296142578125,
0.0033779144287109375,
-0.020233154296875,
-0.0181884765625,
0.006435394287109375,
0.001953125,
0.01416015625,
-0.046051025390625,
-0.01390838623046875,
0.032806396484375,
0.0029697418212890625,
-0.0036411285400390625,
0.01715087890625,
-0.00685882568359375,
0.006134033203125,
-0.054901123046875,
0.0003292560577392578,
0.02008056640625,
0.027496337890625,
-0.0289764404296875,
-0.014007568359375,
-0.016143798828125,
-0.002094268798828125,
0.0041351318359375,
0.01409149169921875,
0.0256500244140625,
-0.0012798309326171875,
0.0213470458984375,
-0.006565093994140625,
-0.0384521484375,
-0.007617950439453125,
-0.002490997314453125,
0.009307861328125,
0.00974273681640625,
-0.0166015625,
-0.01215362548828125,
-0.0005879402160644531,
-0.00428009033203125,
-0.015045166015625,
0.01169586181640625,
-0.0323486328125,
0.003269195556640625,
0.003246307373046875,
0.004276275634765625,
0.033935546875,
0.03021240234375,
0.00591278076171875,
-0.0223846435546875,
0.041656494140625,
0.00046324729919433594,
-0.00978851318359375,
0.0130462646484375,
-0.0146026611328125,
-0.0126953125,
0.0007114410400390625,
0.0166168212890625,
-0.00006896257400512695,
-0.0252532958984375,
-0.01904296875,
-0.0160980224609375,
0.00014495849609375,
0.0181121826171875,
0.003978729248046875,
0.005252838134765625,
-0.0242767333984375,
0.00823211669921875,
0.00978851318359375,
0.01151275634765625,
0.0024509429931640625,
0.0243072509765625,
0.01151275634765625,
-0.01239013671875,
0.006885528564453125,
0.01078033447265625,
-0.005023956298828125,
0.025146484375,
0.016143798828125,
0.0024814605712890625,
0.0026111602783203125,
-0.0013294219970703125,
0.0000883936882019043,
0.0162506103515625,
-0.004913330078125,
0.01084136962890625,
-0.01406097412109375,
-0.025390625,
-0.0150909423828125,
-0.0225982666015625,
-0.015655517578125,
-0.004741668701171875,
0.0005445480346679688,
-0.039764404296875,
0.0087738037109375,
-0.0270843505859375,
0.007747650146484375,
-0.0025539398193359375,
-0.0243072509765625,
0.051300048828125,
-0.028289794921875,
-0.007049560546875,
-0.005001068115234375,
0.0092926025390625,
-0.0118865966796875,
-0.020904541015625,
0.035308837890625,
-0.033843994140625,
0.002315521240234375,
0.0178985595703125,
-0.00809478759765625,
-0.015716552734375,
-0.016815185546875,
-0.04010009765625,
0.0211944580078125,
-0.0177001953125,
-0.047607421875,
-0.0310516357421875,
-0.00112152099609375,
-0.0052642822265625,
0.01335906982421875,
-0.0034694671630859375,
0.0014734268188476562,
-0.00058746337890625,
-0.024505615234375,
-0.0214691162109375,
-0.0186004638671875,
0.027862548828125,
-0.0003726482391357422,
-0.002307891845703125,
-0.0088043212890625,
-0.01025390625,
-0.007457733154296875,
-0.01483154296875,
-0.0257720947265625,
-0.0012922286987304688,
-0.027618408203125,
-0.02545166015625,
0.007747650146484375,
-0.002349853515625,
-0.005977630615234375,
0.0137786865234375,
0.009674072265625,
0.01123809814453125,
0.025543212890625,
-0.0171661376953125,
-0.011138916015625,
0.00017583370208740234,
-0.021820068359375,
-0.0181884765625,
0.01413726806640625,
0.0126495361328125,
-0.0237579345703125,
-0.00937652587890625,
0.0146484375,
0.040130615234375,
0.0090179443359375,
0.0060577392578125,
0.0057525634765625,
-0.00943756103515625,
-0.006160736083984375,
-0.0076751708984375,
-0.0012884140014648438,
-0.0020771026611328125,
0.022491455078125,
-0.021240234375,
0.03558349609375,
-0.008453369140625,
0.01541900634765625,
-0.005336761474609375,
-0.03936767578125,
-0.0225372314453125,
-0.03204345703125,
0.0207672119140625,
-0.0132598876953125,
-0.0228424072265625,
0.036895751953125,
-0.01506805419921875,
-0.004512786865234375,
0.0167083740234375,
0.03155517578125,
-0.0240478515625,
-0.03997802734375,
0.01482391357421875,
-0.00463104248046875,
0.0322265625,
0.018035888671875,
0.031219482421875,
-0.01432037353515625,
0.0069732666015625,
0.0173187255859375,
-0.006053924560546875,
0.01324462890625,
-0.0003101825714111328,
-0.0030975341796875,
0.0273284912109375,
-0.0008687973022460938,
-0.0290374755859375,
-0.00665283203125,
0.012420654296875,
-0.0279541015625,
-0.01113128662109375,
-0.002960205078125,
0.0281829833984375,
0.0169677734375,
-0.0262451171875,
-0.031463623046875,
-0.004322052001953125,
0.06298828125,
-0.0084228515625,
-0.032867431640625,
-0.005115509033203125,
-0.027923583984375,
0.039703369140625,
0.00232696533203125,
0.050323486328125,
0.0143280029296875,
0.00775909423828125,
-0.02044677734375,
-0.049407958984375,
-0.0010852813720703125,
0.016326904296875,
0.0009293556213378906,
0.0223236083984375,
-0.0093841552734375,
0.01038360595703125,
-0.0221710205078125,
-0.023193359375,
-0.0071563720703125,
-0.01678466796875,
-0.00928497314453125,
-0.020172119140625,
0.0059814453125,
-0.0079193115234375,
0.01389312744140625,
0.0084686279296875,
0.0217132568359375,
0.0037097930908203125,
-0.017822265625,
-0.01800537109375,
-0.03253173828125,
0.0165252685546875,
-0.0155029296875,
0.0192718505859375,
0.01306915283203125,
0.014984130859375,
0.00930023193359375,
-0.0012760162353515625,
-0.0181732177734375,
-0.0240020751953125,
-0.0157623291015625,
-0.044891357421875,
0.00670623779296875,
-0.0128173828125,
0.00020742416381835938,
-0.0254669189453125,
-0.0016956329345703125,
0.00931549072265625,
0.016632080078125,
-0.036712646484375,
-0.01390838623046875,
-0.0237884521484375,
-0.00753021240234375,
-0.012969970703125,
0.0166473388671875,
-0.0328369140625,
-0.0024509429931640625,
-0.0119476318359375,
0.01236724853515625,
-0.0257720947265625,
0.00933074951171875,
0.01428985595703125,
0.023406982421875,
-0.015167236328125,
-0.04345703125,
0.025909423828125,
0.00875091552734375,
-0.0084228515625,
0.00428009033203125,
-0.0169677734375,
-0.00826263427734375,
-0.002437591552734375,
0.035858154296875,
-0.0224761962890625,
0.007305145263671875,
-0.01287841796875,
-0.040618896484375,
-0.01190948486328125,
-0.0189971923828125,
-0.0206756591796875,
0.019287109375,
-0.00003802776336669922,
0.01534271240234375,
-0.0082550048828125,
0.004886627197265625,
-0.0013723373413085938,
-0.007656097412109375,
-0.0204010009765625,
0.0023517608642578125,
0.019805908203125,
0.0179290771484375,
0.008758544921875,
0.0027141571044921875,
-0.0106201171875,
0.00909423828125,
0.0282135009765625,
-0.0094146728515625,
0.010406494140625,
-0.0232696533203125,
-0.037933349609375,
0.003330230712890625,
-0.022979736328125,
-0.016326904296875,
0.0103302001953125,
0.01605224609375,
0.003688812255859375,
-0.00753021240234375,
0.0035953521728515625,
0.0016851425170898438,
-0.0051422119140625,
0.00016832351684570312,
-0.01284027099609375,
0.0034046173095703125,
0.040802001953125,
-0.00481414794921875,
-0.0221099853515625,
0.0287322998046875,
0.004711151123046875,
-0.005786895751953125,
0.0306854248046875,
0.027008056640625,
0.027099609375,
0.0025615692138671875,
-0.0048675537109375,
0.0150604248046875,
0.00991058349609375,
0.00397491455078125,
0.01352691650390625,
0.03607177734375,
-0.00855255126953125,
-0.036895751953125,
-0.0027408599853515625,
-0.0076141357421875,
0.0026569366455078125,
0.00952911376953125,
0.0238037109375,
-0.0235137939453125,
0.018829345703125,
0.01593017578125,
-0.03900146484375,
0.00339508056640625,
-0.0005145072937011719,
-0.0007343292236328125,
-0.0182647705078125,
0.00809478759765625,
0.018280029296875,
0.0194091796875,
-0.03546142578125,
0.004146575927734375,
0.002849578857421875,
0.00786590576171875,
0.005390167236328125,
0.0155487060546875,
-0.002349853515625,
-0.01522064208984375,
0.0254058837890625,
-0.002613067626953125,
-0.0019893646240234375,
0.00794219970703125,
0.0290985107421875,
-0.00948333740234375,
0.0032329559326171875,
0.00983428955078125,
-0.004680633544921875,
-0.021484375,
0.05126953125,
-0.004154205322265625,
-0.0105133056640625,
-0.0160064697265625,
0.0021533966064453125,
0.02154541015625,
0.0194854736328125,
0.0031414031982421875,
-0.0343017578125,
-0.013702392578125,
-0.0304412841796875,
0.01910400390625,
0.0128326416015625,
-0.04547119140625,
-0.0182342529296875,
-0.0173187255859375,
0.026214599609375,
0.019256591796875,
0.025299072265625,
0.01255035400390625,
-0.0132598876953125,
0.0011720657348632812,
-0.0290069580078125,
0.0035953521728515625,
0.0203857421875,
0.01251983642578125,
0.01064300537109375,
0.004772186279296875,
0.005222320556640625,
-0.0213165283203125,
-0.01364898681640625,
-0.0135650634765625,
0.00174713134765625,
0.01129150390625,
0.0120697021484375,
0.013641357421875,
0.011627197265625,
0.0030307769775390625,
0.00731658935546875,
0.00812530517578125,
0.0178680419921875,
0.0183258056640625,
-0.00020492076873779297,
0.031707763671875,
-0.007526397705078125,
-0.01386260986328125,
-0.0013103485107421875,
0.00417327880859375,
-0.00738525390625,
0.0173797607421875,
0.011138916015625,
-0.04486083984375,
0.02880859375,
-0.031494140625,
0.0136566162109375,
0.0128326416015625,
-0.036346435546875,
0.015106201171875,
-0.0101318359375,
0.0205841064453125,
0.021820068359375,
-0.007598876953125,
0.01418304443359375,
0.0244140625,
0.0014982223510742188,
-0.02880859375,
0.005695343017578125,
0.01552581787109375,
0.003658294677734375,
0.00125885009765625,
0.00902557373046875,
-0.0113677978515625,
-0.0250091552734375,
-0.0292816162109375,
0.002368927001953125,
-0.0167236328125,
-0.02374267578125,
0.01468658447265625,
0.01531219482421875,
0.022552490234375,
0.019561767578125,
0.010833740234375,
0.020355224609375,
0.036346435546875,
-0.06689453125,
-0.01305389404296875,
0.010650634765625,
0.0121002197265625,
0.0189971923828125,
-0.0073394775390625,
-0.00887298583984375,
-0.005496978759765625,
-0.01239013671875,
-0.02923583984375,
0.0005555152893066406,
0.0279083251953125,
-0.018798828125,
0.01241302490234375,
0.04241943359375,
-0.032073974609375,
0.0303192138671875,
0.027435302734375,
-0.02203369140625,
-0.0262603759765625,
0.0528564453125,
-0.01291656494140625,
0.004558563232421875,
0.00025963783264160156,
-0.00928497314453125,
0.0235595703125,
0.01477813720703125,
0.015106201171875,
-0.0161285400390625,
0.0258026123046875,
0.006847381591796875,
0.023651123046875,
0.017852783203125,
-0.023773193359375,
0.0255126953125,
0.0037326812744140625,
0.00569915771484375,
0.006603240966796875,
-0.01222991943359375,
0.0301513671875,
-0.0179901123046875,
-0.00579833984375,
0.0171966552734375,
-0.01678466796875,
0.0105438232421875,
-0.007686614990234375,
-0.023040771484375,
0.00440216064453125,
-0.0229644775390625,
-0.012451171875,
0.0168304443359375,
-0.01200103759765625,
0.00843048095703125,
-0.01617431640625,
0.00666046142578125,
0.010772705078125,
0.000021457672119140625,
0.0028285980224609375,
0.01280975341796875,
-0.002277374267578125,
-0.041961669921875,
0.02105712890625,
0.0021457672119140625,
0.01041412353515625,
-0.0242156982421875,
-0.0238800048828125,
-0.002490997314453125,
0.001255035400390625,
0.0029125213623046875,
0.019805908203125,
0.00324249267578125,
0.0310821533203125,
-0.0008044242858886719,
-0.042633056640625,
-0.005401611328125,
0.0092620849609375,
0.033111572265625,
0.001514434814453125,
-0.01751708984375,
-0.0166015625,
0.0279541015625,
-0.026336669921875,
0.0165863037109375,
0.00380706787109375,
-0.004444122314453125,
0.0171661376953125,
-0.0007276535034179688,
0.035797119140625,
-0.0003581047058105469,
-0.00832366943359375,
0.02362060546875,
-0.02801513671875,
-0.0037403106689453125,
-0.0232086181640625,
0.01126861572265625,
-0.0030345916748046875,
0.00004470348358154297,
-0.01087188720703125,
0.0151519775390625,
0.022216796875,
0.00023102760314941406,
0.05224609375,
0.021820068359375,
-0.023284912109375,
0.0297393798828125,
0.018768310546875,
0.003826141357421875,
0.0000845193862915039,
0.02490234375,
-0.007442474365234375,
-0.0131683349609375,
0.01543426513671875,
-0.01934814453125,
0.019134521484375,
0.02520751953125,
0.005199432373046875,
-0.0157928466796875,
-0.0195159912109375,
-0.009307861328125,
0.0034885406494140625,
-0.01033782958984375,
-0.0294036865234375,
-0.0262908935546875,
0.01201629638671875,
-0.0267791748046875,
-0.018341064453125,
0.005931854248046875,
0.009796142578125,
-0.056549072265625,
-0.00958251953125,
0.00930023193359375,
-0.00974273681640625,
-0.0010538101196289062,
-0.0204315185546875,
0.0216827392578125,
0.049285888671875,
0.007572174072265625,
-0.00484466552734375,
0.031280517578125,
0.06982421875,
-0.016204833984375,
0.0038509368896484375,
0.0200958251953125,
-0.03302001953125,
-0.0189971923828125,
-0.051727294921875,
-0.0136260986328125,
0.00001621246337890625,
0.01531982421875,
0.0382080078125,
-0.00662994384765625,
0.0284271240234375,
-0.025115966796875,
0.004467010498046875,
0.0091094970703125,
-0.023468017578125,
0.01360321044921875,
-0.05584716796875,
-0.0263519287109375,
0.00373077392578125,
-0.003997802734375,
0.0105743408203125,
0.006542205810546875,
-0.0137176513671875,
0.030029296875,
0.006526947021484375,
0.01023101806640625,
0.01023101806640625,
-0.00011295080184936523,
0.0094146728515625,
-0.01873779296875,
0.003284454345703125,
0.00946044921875,
-0.0228271484375,
0.002597808837890625,
0.004177093505859375,
-0.005397796630859375,
0.01416778564453125,
0.00670623779296875,
-0.01044464111328125,
-0.00563812255859375,
-0.029266357421875,
-0.01274871826171875,
-0.0121307373046875,
0.018798828125,
-0.00908660888671875,
-0.005710601806640625,
-0.0010099411010742188,
-0.0277862548828125,
-0.064453125,
-0.0280303955078125,
0.001628875732421875,
0.01641845703125,
0.0029659271240234375,
-0.000995635986328125,
-0.006565093994140625,
-0.013458251953125,
-0.01367950439453125,
-0.03204345703125,
-0.0098876953125,
0.0160980224609375,
0.032745361328125,
-0.0173797607421875,
-0.01251220703125,
-0.014495849609375,
0.0157012939453125,
-0.0142059326171875,
-0.00911712646484375,
-0.0169830322265625,
0.042572021484375,
0.02972412109375,
-0.025054931640625,
0.0169830322265625,
0.0240325927734375,
0.03302001953125,
0.04559326171875,
-0.0253448486328125,
0.041473388671875,
0.0115966796875,
0.0158843994140625,
0.0035800933837890625,
-0.0175933837890625,
-0.00897979736328125,
-0.023681640625,
0.0102996826171875,
-0.003826141357421875,
0.0205078125,
0.01354217529296875,
0.0026607513427734375,
-0.0136566162109375,
-0.0107574462890625,
0.00476837158203125,
-0.005767822265625,
0.01352691650390625,
0.0277252197265625,
0.00391387939453125,
0.0138092041015625,
-0.0194091796875,
0.01525115966796875,
0.003963470458984375,
-0.01419830322265625,
-0.014190673828125,
-0.0279388427734375,
-0.00316619873046875,
0.0295257568359375,
0.01439666748046875,
0.0058135986328125,
0.01122283935546875,
-0.01220703125,
-0.005466461181640625,
0.008514404296875,
-0.0242156982421875,
0.0237884521484375,
0.00571441650390625,
0.004245758056640625,
-0.015655517578125,
0.0082855224609375,
-0.0161895751953125,
0.0044097900390625,
0.02984619140625,
-0.006256103515625,
-0.00920867919921875,
-0.0308837890625,
0.053436279296875,
-0.027252197265625,
0.00701904296875,
-0.016571044921875,
0.0169525146484375,
-0.0266571044921875,
0.0163726806640625,
-0.00514984130859375,
0.02996826171875,
-0.0221099853515625,
-0.029754638671875,
-0.0220794677734375,
0.044281005859375,
0.0104522705078125,
-0.034271240234375,
0.014007568359375,
0.00714874267578125,
-0.0465087890625,
0.00664520263671875,
0.005580902099609375,
-0.020416259765625,
0.0259552001953125,
-0.00890350341796875,
-0.0229034423828125,
-0.0035877227783203125,
0.01441192626953125,
0.0007066726684570312,
-0.013153076171875,
-0.0247802734375,
0.01415252685546875,
0.024993896484375,
-0.029083251953125,
0.024383544921875,
0.0244293212890625,
-0.03338623046875,
0.022186279296875,
-0.025115966796875,
0.00988006591796875,
0.041748046875,
0.005504608154296875,
-0.0224609375,
0.00318145751953125,
-0.046905517578125,
0.0311126708984375,
-0.0004138946533203125,
0.009490966796875,
-0.0029201507568359375,
0.012237548828125,
0.038177490234375,
-0.043914794921875,
-0.033203125,
-0.01230621337890625,
0.025726318359375,
-0.0015897750854492188,
-0.002307891845703125,
0.0041351318359375,
-0.01342010498046875,
0.0064849853515625,
-0.025909423828125,
0.034515380859375,
-0.024810791015625,
-0.006946563720703125,
-0.01448822021484375,
0.00878143310546875,
0.0167388916015625,
-0.0091552734375,
-0.031585693359375,
-0.031768798828125,
-0.0014247894287109375,
-0.0195770263671875,
0.0171356201171875,
0.00901031494140625,
-0.0025463104248046875,
0.021026611328125,
0.00467681884765625,
0.00102996826171875,
-0.03302001953125,
-0.01241302490234375,
0.0131683349609375,
0.0167999267578125,
0.01971435546875,
-0.01666259765625,
0.004665374755859375,
-0.02825927734375,
0.034759521484375,
-0.01519775390625,
-0.005962371826171875,
0.0164337158203125,
-0.0240478515625,
0.0009527206420898438,
-0.00020456314086914062,
-0.008056640625,
-0.0021877288818359375,
0.01132965087890625,
0.012786865234375,
0.036468505859375,
-0.0173797607421875,
0.0137786865234375,
-0.0200653076171875,
-0.027618408203125,
-0.02374267578125,
-0.041229248046875,
0.0121002197265625,
0.0191802978515625,
0.0419921875,
-0.0027103424072265625,
-0.01177978515625,
0.0170135498046875,
-0.0280303955078125,
0.007568359375,
0.0037994384765625,
-0.0166473388671875,
-0.007656097412109375,
-0.014739990234375,
-0.0038738250732421875,
-0.0128631591796875,
0.0008864402770996094,
0.0035724639892578125,
0.0018053054809570312,
-0.005245208740234375,
-0.0158233642578125,
-0.0034656524658203125,
0.046539306640625,
0.0216827392578125,
0.04351806640625,
-0.005664825439453125,
0.00650787353515625,
0.001659393310546875,
-0.000431060791015625,
0.02020263671875,
0.0105133056640625,
-0.006000518798828125,
0.0165863037109375,
0.0264129638671875,
-0.00922393798828125,
0.00397491455078125
] |
ours_468
|
The sequence \(\{(p_{n}, c_{n})\}\) starts with:
\[
(2, 4), (3, 6), (5, 8), (7, 9), (11, 10), (13, 12), (17, 14), \ldots
\]
For these pairs, \(n = 1, 4, 5, 6\) satisfy \(\left|p_{n} - c_{n}\right| < 3\), while \(p_{7} = c_{7} + 3\). For \(n \geq 7\), note that \(p_{n+1} \geq p_{n} + 2\) by parity, while \(c_{n+1} \leq c_{n} + 2\) (since one of \(c_{n} + 1, c_{n} + 2\) is even and thus composite). Thus, \(f(n) = p_{n} - c_{n}\) is nondecreasing, so no other \(n\) works. Therefore, the sum is \(1 + 4 + 5 + 6 = 16\).
\(\boxed{16}\)
|
16
|
{
"competition": "us_comps",
"dataset": "Ours",
"posts": null,
"source": "OMOFall18Solns.md"
}
|
Let \((p_{1}, p_{2}, \ldots) = (2, 3, \ldots)\) be the list of all prime numbers, and \((c_{1}, c_{2}, \ldots) = (4, 6, \ldots)\) be the list of all composite numbers, both in increasing order. Compute the sum of all positive integers \(n\) such that \(\left|p_{n} - c_{n}\right| < 3\).
|
[
"/Mathematics/DiscreteMathematics/GeneralDiscreteMathematics/DiscreteMath",
"/Mathematics/DiscreteMathematics/GeneralDiscreteMathematics/DiscreteMathematics",
"/Mathematics/NumberTheory/GeneralNumberTheory/ElementaryNumberTheory",
"/Mathematics/NumberTheory/GeneralNumberTheory/NumberTheory",
"/Mathematics/NumberTheory/Integers/N",
"/Mathematics/NumberTheory/Integers/NonnegativeInteger",
"/Mathematics/NumberTheory/Integers/PositiveInteger",
"/Mathematics/NumberTheory/Integers/WholeNumber",
"/Mathematics/NumberTheory/Integers/Z-Plus",
"/Mathematics/NumberTheory/PrimeNumbers/PrimeNumberSequences",
"/Mathematics/NumberTheory/Sequences/IncreasingSequence",
"/Mathematics/NumberTheory/Sequences/IntegerSequence",
"/Mathematics/NumberTheory/Sequences/Sequence"
] |
Show that the difference p_n − c_n is nondecreasing by comparing prime gaps (≥2) with composite gaps (≤2), limiting solutions to early terms.
|
[
0.00021076202392578125,
0.0007262229919433594,
0.0110626220703125,
0.030914306640625,
0.0008311271667480469,
-0.0112457275390625,
-0.00302886962890625,
0.00962066650390625,
0.0108642578125,
-0.0279083251953125,
-0.0175018310546875,
-0.0067901611328125,
0.0022068023681640625,
-0.001911163330078125,
-0.00732421875,
0.0011806488037109375,
0.022064208984375,
0.01056671142578125,
-0.002002716064453125,
-0.0093841552734375,
-0.0011320114135742188,
-0.0039520263671875,
-0.038970947265625,
0.008941650390625,
-0.035369873046875,
-0.005916595458984375,
-0.020416259765625,
0.00015842914581298828,
0.02349853515625,
0.0135955810546875,
-0.01427459716796875,
-0.033599853515625,
-0.01465606689453125,
-0.037109375,
-0.0001895427703857422,
0.010284423828125,
-0.000514984130859375,
0.003261566162109375,
-0.00937652587890625,
-0.055572509765625,
-0.0084381103515625,
0.023040771484375,
0.0157318115234375,
0.00443267822265625,
0.0031642913818359375,
0.0130767822265625,
0.01152801513671875,
0.007450103759765625,
-0.019134521484375,
0.01100921630859375,
0.007701873779296875,
0.0262603759765625,
-0.00949859619140625,
-0.00708770751953125,
-0.0037593841552734375,
-0.05926513671875,
0.0200347900390625,
0.004055023193359375,
-0.013397216796875,
-0.006526947021484375,
0.0013217926025390625,
0.00833892822265625,
0.0266876220703125,
-0.00673675537109375,
0.00559234619140625,
-0.0090789794921875,
0.044036865234375,
-0.00885772705078125,
0.0054168701171875,
-0.0210418701171875,
0.009857177734375,
0.008514404296875,
0.01282501220703125,
0.03912353515625,
0.035125732421875,
0.006877899169921875,
-0.0075225830078125,
0.0181732177734375,
-0.0160980224609375,
0.0020694732666015625,
0.00269317626953125,
0.0049896240234375,
0.00421142578125,
0.015045166015625,
-0.00799560546875,
0.04437255859375,
0.00921630859375,
0.00608062744140625,
-0.0007224082946777344,
-0.0131988525390625,
0.0014028549194335938,
0.0126190185546875,
0.00977325439453125,
-0.01371002197265625,
-0.006649017333984375,
-0.027069091796875,
0.0124664306640625,
-0.004261016845703125,
-0.01006317138671875,
0.0114898681640625,
-0.0019321441650390625,
-0.01332855224609375,
0.020263671875,
-0.0293426513671875,
-0.056304931640625,
-0.0230255126953125,
-0.01369476318359375,
0.0216217041015625,
-0.0057830810546875,
0.004772186279296875,
0.0153045654296875,
-0.007785797119140625,
0.037841796875,
0.006839752197265625,
-0.01030731201171875,
0.0187225341796875,
0.035675048828125,
0.0288238525390625,
-0.015655517578125,
-0.01471710205078125,
-0.001346588134765625,
0.01380157470703125,
-0.0106658935546875,
0.01445770263671875,
0.006420135498046875,
-0.028717041015625,
-0.01593017578125,
-0.01070404052734375,
0.005924224853515625,
0.01062774658203125,
0.035797119140625,
-0.00887298583984375,
-0.01255035400390625,
-0.00955963134765625,
-0.042510986328125,
-0.00640869140625,
0.014434814453125,
-0.01284027099609375,
0.006134033203125,
-0.004245758056640625,
-0.00876617431640625,
-0.00194549560546875,
-0.00714874267578125,
0.0137939453125,
0.01442718505859375,
0.0202484130859375,
0.00007009506225585938,
-0.035430908203125,
-0.00769805908203125,
-0.0007295608520507812,
-0.0012254714965820312,
0.0022640228271484375,
0.007579803466796875,
-0.006191253662109375,
-0.017486572265625,
0.014373779296875,
0.00562286376953125,
0.040435791015625,
-0.006351470947265625,
0.00838470458984375,
0.0035305023193359375,
0.006011962890625,
-0.01422119140625,
-0.006366729736328125,
0.009918212890625,
-0.0163726806640625,
0.0205535888671875,
-0.004322052001953125,
0.01155853271484375,
0.014923095703125,
0.0029201507568359375,
-0.01317596435546875,
-0.004451751708984375,
-0.006641387939453125,
-0.02691650390625,
-0.0019388198852539062,
-0.021270751953125,
0.0013971328735351562,
0.004734039306640625,
0.029296875,
0.00899505615234375,
-0.0325927734375,
0.03515625,
-0.01226806640625,
-0.01244354248046875,
-0.0196685791015625,
0.00026106834411621094,
-0.00701141357421875,
0.006145477294921875,
0.019866943359375,
0.0003266334533691406,
0.0248870849609375,
-0.0185546875,
0.0015125274658203125,
-0.01030731201171875,
0.00012290477752685547,
-0.00914764404296875,
0.0286407470703125,
0.0010547637939453125,
0.00829315185546875,
0.0021152496337890625,
-0.009796142578125,
-0.00942230224609375,
0.005229949951171875,
0.009613037109375,
-0.005405426025390625,
0.0002129077911376953,
0.00653839111328125,
0.0014095306396484375,
0.00920867919921875,
0.0191802978515625,
0.004123687744140625,
0.0095672607421875,
-0.031036376953125,
-0.00537109375,
0.0084686279296875,
-0.01218414306640625,
-0.006160736083984375,
-0.005916595458984375,
-0.07275390625,
0.0172271728515625,
0.007320404052734375,
0.00893402099609375,
-0.00013446807861328125,
-0.0152587890625,
0.004283905029296875,
0.0138092041015625,
0.00926971435546875,
0.0040283203125,
0.00848388671875,
0.037353515625,
0.00494384765625,
0.01386260986328125,
-0.006473541259765625,
0.001888275146484375,
-0.007663726806640625,
-0.020538330078125,
-0.0044708251953125,
0.0164947509765625,
0.0004029273986816406,
0.05712890625,
0.005893707275390625,
0.0152435302734375,
0.006481170654296875,
-0.0058135986328125,
0.0028820037841796875,
0.00890350341796875,
-0.00771331787109375,
-0.00769805908203125,
-0.0002694129943847656,
-0.0109710693359375,
-0.00710296630859375,
-0.0019330978393554688,
0.00855255126953125,
-0.002895355224609375,
-0.005977630615234375,
0.01253509521484375,
-0.0015926361083984375,
0.0026187896728515625,
0.01140594482421875,
-0.008453369140625,
-0.0192718505859375,
-0.016845703125,
-0.01163482666015625,
0.0167083740234375,
-0.00128173828125,
0.02667236328125,
-0.00888824462890625,
-0.0030689239501953125,
-0.00835418701171875,
0.01214599609375,
-0.009307861328125,
-0.02020263671875,
0.0037746429443359375,
0.039154052734375,
0.005290985107421875,
0.00548553466796875,
0.0291595458984375,
0.00899505615234375,
0.005313873291015625,
-0.00971221923828125,
-0.035308837890625,
-0.00850677490234375,
0.03057861328125,
-0.0004489421844482422,
-0.019500732421875,
0.00811004638671875,
-0.0333251953125,
0.00844573974609375,
0.0009636878967285156,
-0.006298065185546875,
0.0023212432861328125,
-0.004505157470703125,
-0.00592041015625,
0.042388916015625,
0.00942230224609375,
-0.0011472702026367188,
0.002422332763671875,
-0.004962921142578125,
-0.017547607421875,
0.004192352294921875,
-0.0012636184692382812,
0.005950927734375,
-0.0166168212890625,
0.01251220703125,
0.0236968994140625,
0.007259368896484375,
0.0283966064453125,
-0.0021381378173828125,
-0.0142974853515625,
-0.0111236572265625,
0.0059661865234375,
0.00946807861328125,
-0.0022182464599609375,
-0.01250457763671875,
-0.040283203125,
-0.0011138916015625,
0.0214996337890625,
-0.00743865966796875,
-0.0038318634033203125,
0.01305389404296875,
-0.016265869140625,
0.002758026123046875,
0.00701141357421875,
0.0192413330078125,
-0.01335906982421875,
0.01522064208984375,
0.033233642578125,
-0.022674560546875,
0.0146484375,
-0.032623291015625,
-0.002422332763671875,
0.011932373046875,
-0.0279083251953125,
-0.010650634765625,
0.0077056884765625,
-0.005519866943359375,
0.00997161865234375,
-0.0014257431030273438,
0.0211944580078125,
0.016693115234375,
-0.0160369873046875,
-0.0022869110107421875,
0.0258636474609375,
-0.00904083251953125,
0.008026123046875,
-0.034637451171875,
-0.0163116455078125,
-0.0238189697265625,
-0.0171966552734375,
-0.028076171875,
0.0108184814453125,
0.0180206298828125,
-0.01568603515625,
-0.0136871337890625,
-0.00278472900390625,
-0.0142059326171875,
0.02288818359375,
-0.0098114013671875,
0.022491455078125,
-0.017364501953125,
-0.004852294921875,
-0.002460479736328125,
-0.0174102783203125,
0.0185699462890625,
-0.03265380859375,
-0.00997161865234375,
0.00202178955078125,
-0.04461669921875,
-0.00801849365234375,
-0.022918701171875,
0.0219573974609375,
0.0030727386474609375,
-0.0018987655639648438,
-0.0394287109375,
-0.023651123046875,
0.0185546875,
-0.014801025390625,
-0.01053619384765625,
0.020233154296875,
0.01251220703125,
0.0172271728515625,
-0.02642822265625,
0.0228424072265625,
-0.014129638671875,
0.0127716064453125,
-0.0011854171752929688,
-0.00423431396484375,
-0.03363037109375,
0.011138916015625,
-0.007205963134765625,
0.0139312744140625,
0.01131439208984375,
0.0168609619140625,
-0.0007839202880859375,
-0.0264739990234375,
0.0120391845703125,
0.029937744140625,
0.0484619140625,
-0.0189971923828125,
-0.016357421875,
-0.01294708251953125,
-0.03094482421875,
0.021881103515625,
-0.011566162109375,
-0.0150146484375,
0.004383087158203125,
0.01192474365234375,
0.0252227783203125,
0.0010623931884765625,
0.01263427734375,
0.0251922607421875,
-0.00701141357421875,
-0.03155517578125,
-0.005809783935546875,
0.0006823539733886719,
-0.0065155029296875,
0.025054931640625,
-0.0195465087890625,
-0.01727294921875,
-0.00278472900390625,
-0.0418701171875,
-0.048675537109375,
-0.004730224609375,
0.0308380126953125,
0.0285797119140625,
-0.00914764404296875,
0.027435302734375,
-0.0171966552734375,
-0.0022735595703125,
0.0169525146484375,
-0.02227783203125,
0.019287109375,
0.0295562744140625,
-0.00701141357421875,
0.03729248046875,
-0.00696563720703125,
0.0129241943359375,
-0.022216796875,
0.0161895751953125,
-0.00042247772216796875,
-0.0235137939453125,
0.0071563720703125,
0.01485443115234375,
0.007396697998046875,
0.00262451171875,
-0.0067138671875,
0.02178955078125,
-0.0200042724609375,
0.0009765625,
-0.0089874267578125,
-0.004673004150390625,
-0.004779815673828125,
0.0224609375,
-0.0155487060546875,
0.019744873046875,
-0.00946807861328125,
-0.029296875,
-0.04034423828125,
-0.034881591796875,
-0.0052337646484375,
0.0085906982421875,
-0.0283660888671875,
0.010009765625,
0.02935791015625,
0.035552978515625,
-0.00524139404296875,
0.0196533203125,
-0.010498046875,
0.0279998779296875,
-0.0176544189453125,
-0.00531768798828125,
-0.01233673095703125,
-0.0096282958984375,
-0.031829833984375,
0.032684326171875,
-0.0165557861328125,
0.014312744140625,
0.00971221923828125,
0.00801849365234375,
0.0005025863647460938,
0.00445556640625,
-0.0380859375,
0.0031280517578125,
0.0031490325927734375,
-0.002712249755859375,
0.01424407958984375,
-0.00852203369140625,
0.0254974365234375,
-0.014495849609375,
-0.006877899169921875,
0.0215606689453125,
-0.043182373046875,
-0.0264892578125,
0.0008068084716796875,
-0.0285186767578125,
-0.01056671142578125,
-0.002925872802734375,
0.00453948974609375,
0.0021762847900390625,
0.031707763671875,
-0.003078460693359375,
-0.006992340087890625,
0.0194091796875,
0.01442718505859375,
-0.0238037109375,
0.037750244140625,
0.01279449462890625,
0.04522705078125,
-0.01206207275390625,
-0.01274871826171875,
0.0006566047668457031,
0.032867431640625,
-0.044342041015625,
0.0177154541015625,
-0.0260772705078125,
0.003513336181640625,
0.0108795166015625,
-0.0146026611328125,
-0.0209503173828125,
-0.033416748046875,
0.0137939453125,
0.03839111328125,
0.007190704345703125,
0.0181427001953125,
0.006343841552734375,
-0.01837158203125,
-0.03668212890625,
0.0302886962890625,
0.0014200210571289062,
-0.0012922286987304688,
0.00031566619873046875,
0.0199432373046875,
-0.0224761962890625,
-0.0219573974609375,
0.023345947265625,
0.032928466796875,
-0.006694793701171875,
0.041748046875,
0.007904052734375,
0.028900146484375,
-0.023681640625,
0.0108184814453125,
0.0088958740234375,
-0.0237884521484375,
-0.02197265625,
-0.00732421875,
0.01004791259765625,
0.00917816162109375,
0.0134735107421875,
-0.01544952392578125,
-0.00518035888671875,
-0.019287109375,
0.022796630859375,
-0.0176544189453125,
-0.01378631591796875,
0.0263824462890625,
0.0321044921875,
-0.0333251953125,
-0.006778717041015625,
0.014251708984375,
0.00243377685546875,
-0.005512237548828125,
0.0003650188446044922,
0.0042572021484375,
-0.01090240478515625,
-0.002582550048828125,
0.0183258056640625,
-0.01373291015625,
-0.044525146484375,
0.0242462158203125,
0.0400390625,
0.0027866363525390625,
-0.0260772705078125,
-0.03131103515625,
-0.0060272216796875,
-0.04669189453125,
-0.01560211181640625,
0.01374053955078125,
-0.049285888671875,
0.0202789306640625,
0.0119476318359375,
0.0308837890625,
0.0167083740234375,
-0.0059051513671875,
0.00804901123046875,
0.0294952392578125,
0.03692626953125,
0.032073974609375,
-0.0275115966796875,
-0.0240020751953125,
0.0143585205078125,
0.013763427734375,
-0.01153564453125,
-0.0194091796875,
0.0117034912109375,
0.03533935546875,
-0.00278472900390625,
0.0192718505859375,
-0.002841949462890625,
-0.0008420944213867188,
0.0121002197265625,
-0.010498046875,
0.032623291015625,
-0.0119781494140625,
-0.0021800994873046875,
0.00279998779296875,
0.03936767578125,
0.0207061767578125,
0.0016345977783203125,
-0.005542755126953125,
-0.0218658447265625,
0.016082763671875,
-0.012359619140625,
0.022369384765625,
-0.0034923553466796875,
-0.026580810546875,
-0.000789642333984375,
-0.0104827880859375,
0.021026611328125,
0.023834228515625,
0.0245361328125,
-0.0145111083984375,
0.0158538818359375,
-0.01519775390625,
0.0001609325408935547,
0.055328369140625,
-0.0124359130859375,
-0.01425933837890625,
0.00289154052734375,
-0.04290771484375,
-0.0128326416015625,
0.0143585205078125,
-0.036651611328125,
-0.01468658447265625,
-0.022918701171875,
-0.0216064453125,
0.02459716796875,
-0.00978851318359375,
-0.04443359375,
0.007427215576171875,
-0.0033359527587890625,
0.0011644363403320312,
-0.02874755859375,
-0.022247314453125,
0.00917816162109375,
0.0023860931396484375,
0.01094818115234375,
0.0205841064453125,
0.0283660888671875,
-0.00496673583984375,
-0.007747650146484375,
0.0013685226440429688,
0.0159759521484375,
0.034423828125,
0.033050537109375,
0.03546142578125,
-0.0159759521484375,
0.030487060546875,
-0.0003261566162109375,
0.0027942657470703125,
0.0093994140625,
0.004337310791015625,
-0.005084991455078125,
-0.022308349609375,
-0.0118408203125,
0.0640869140625,
-0.030609130859375,
0.0002627372741699219,
-0.01959228515625,
0.0225830078125,
0.0202178955078125,
0.0209503173828125,
0.01149749755859375,
0.0138397216796875,
-0.006988525390625,
-0.01192474365234375,
0.0033721923828125,
-0.00165557861328125,
0.0274200439453125,
0.0217132568359375,
0.004795074462890625,
0.0220794677734375,
-0.0033359527587890625,
0.0176239013671875,
0.01451873779296875,
-0.031829833984375,
0.0067596435546875,
-0.01113128662109375,
0.01197052001953125,
0.01236724853515625,
0.016204833984375,
0.00847625732421875,
0.01174163818359375,
0.00618743896484375,
-0.0247650146484375,
0.0009756088256835938,
-0.00286102294921875,
-0.0203399658203125,
-0.0071563720703125,
-0.003208160400390625,
-0.0209503173828125,
0.02374267578125,
0.01399993896484375,
0.024444580078125,
-0.02117919921875,
0.01995849609375,
0.0157318115234375,
-0.0175018310546875,
0.0254364013671875,
0.004001617431640625,
-0.0211639404296875,
-0.031463623046875,
0.0037021636962890625,
-0.0200042724609375,
0.0089569091796875,
-0.004497528076171875,
-0.01451873779296875,
0.007293701171875,
-0.02484130859375,
-0.05804443359375,
0.01263427734375,
-0.0020580291748046875,
-0.01107025146484375,
-0.0035400390625,
0.01971435546875,
-0.011138916015625,
-0.029388427734375,
0.0037021636962890625,
0.01213836669921875,
-0.03515625,
-0.006500244140625,
-0.016204833984375,
-0.0086669921875,
0.0108642578125,
0.01280975341796875,
0.0266571044921875,
-0.003368377685546875,
0.01207733154296875,
0.032623291015625,
0.011688232421875,
0.01507568359375,
0.0235595703125,
-0.02789306640625,
0.01526641845703125,
0.00894927978515625,
-0.023040771484375,
-0.0013589859008789062,
-0.008148193359375,
0.00838470458984375,
0.0197601318359375,
-0.02569580078125,
-0.02008056640625,
-0.032928466796875,
-0.0028285980224609375,
0.00212860107421875,
0.02783203125,
-0.038665771484375,
0.0213470458984375,
-0.0088348388671875,
-0.002040863037109375,
-0.01334381103515625,
-0.01055145263671875,
-0.02178955078125,
0.00867462158203125,
-0.031585693359375,
-0.03045654296875,
-0.0168609619140625,
-0.0621337890625,
0.062744140625,
-0.034881591796875,
0.027069091796875,
0.0047760009765625,
0.0025463104248046875,
0.0217742919921875,
-0.005641937255859375,
-0.01739501953125,
0.004878997802734375,
-0.0004987716674804688,
-0.0308380126953125,
0.0217437744140625,
0.021240234375,
0.01213836669921875,
0.01163482666015625,
0.0181427001953125,
0.0328369140625,
0.0153045654296875,
-0.021240234375,
0.004772186279296875,
-0.0072479248046875,
0.04339599609375,
-0.01092529296875,
-0.0176239013671875,
-0.021026611328125,
-0.003948211669921875,
0.025421142578125,
-0.0110626220703125,
-0.00829315185546875,
0.008026123046875,
-0.002712249755859375,
0.00039458274841308594,
0.00016510486602783203,
-0.0160369873046875,
0.02056884765625,
0.0284271240234375,
0.004302978515625,
0.006839752197265625,
-0.003711700439453125,
0.0263671875,
0.01751708984375,
0.01788330078125,
0.007965087890625,
-0.041015625,
-0.03070068359375,
0.0282440185546875,
-0.0014476776123046875,
-0.0266265869140625,
0.0288848876953125,
-0.006195068359375,
-0.023193359375,
-0.01380157470703125,
0.030670166015625,
-0.0135345458984375,
-0.01248931884765625,
-0.01812744140625,
0.0169219970703125,
-0.012298583984375,
-0.029754638671875,
0.02880859375,
0.0113677978515625,
-0.0106658935546875,
0.01763916015625,
-0.0290374755859375,
-0.001041412353515625,
-0.01381683349609375,
-0.0235595703125,
0.006877899169921875,
0.0081024169921875,
-0.00902557373046875,
0.024383544921875,
0.00872039794921875,
0.00344085693359375,
0.007694244384765625,
-0.0325927734375,
0.007274627685546875,
-0.01496124267578125,
-0.0231475830078125,
0.035675048828125,
-0.0015230178833007812,
-0.03192138671875,
0.032745361328125,
0.0197601318359375,
0.0189056396484375,
0.00139617919921875,
0.001674652099609375,
0.021514892578125,
0.04119873046875,
0.01262664794921875,
-0.004486083984375,
-0.00970458984375,
0.0241851806640625,
-0.066162109375,
0.01065826416015625,
-0.0159149169921875,
-0.01036834716796875,
0.033599853515625,
-0.018157958984375,
-0.0196533203125,
0.0197906494140625,
0.0042572021484375,
0.0300445556640625,
-0.03253173828125,
-0.03570556640625,
-0.02020263671875,
0.023223876953125,
0.00891876220703125,
0.0267791748046875,
0.0347900390625,
-0.01308441162109375,
0.0213775634765625,
0.01447296142578125,
-0.032257080078125,
-0.0187530517578125,
-0.0031452178955078125,
-0.02886962890625,
-0.0027618408203125,
0.04254150390625,
0.00664520263671875,
-0.028045654296875,
-0.0166778564453125,
-0.01141357421875,
-0.01120758056640625,
-0.014556884765625,
-0.01910400390625,
-0.00836181640625,
0.005992889404296875,
-0.025787353515625,
-0.01519775390625,
-0.0192718505859375,
-0.003818511962890625,
0.001346588134765625,
-0.0107421875,
0.0228118896484375,
0.022796630859375,
-0.032470703125,
-0.03857421875,
-0.01546478271484375,
0.02374267578125,
0.0011262893676757812,
0.0121612548828125,
-0.0115814208984375,
-0.01123046875,
0.029327392578125,
0.01214599609375,
-0.059906005859375,
-0.0020885467529296875,
-0.0130615234375,
0.0017871856689453125,
-0.01096343994140625,
-0.0235748291015625,
0.0133209228515625,
-0.032196044921875,
-0.006229400634765625,
-0.03961181640625,
0.012481689453125,
-0.0006771087646484375,
0.00772857666015625,
-0.01296234130859375,
-0.0197906494140625,
0.0245361328125,
0.03973388671875,
0.04083251953125,
-0.015869140625,
0.004711151123046875,
-0.008575439453125,
-0.001750946044921875,
0.0035343170166015625,
0.01447296142578125,
-0.005157470703125,
0.0259552001953125,
-0.045440673828125,
-0.035888671875,
-0.01357269287109375,
0.07122802734375,
0.0253143310546875,
-0.0258331298828125,
-0.016357421875,
0.006450653076171875,
-0.0167083740234375,
0.005870819091796875,
0.0222015380859375,
0.0206451416015625,
-0.004390716552734375,
-0.0013141632080078125,
0.027435302734375,
-0.00812530517578125,
0.06170654296875,
-0.016693115234375,
0.00222015380859375,
-0.0212249755859375,
0.016448974609375,
-0.0173187255859375,
-0.0587158203125,
-0.0511474609375,
-0.00872802734375,
0.004974365234375,
0.00984954833984375,
0.026763916015625,
0.0208282470703125,
-0.0025539398193359375,
-0.0087432861328125,
-0.003742218017578125,
0.017730712890625,
-0.05853271484375,
0.0026149749755859375,
0.023162841796875,
-0.0164947509765625,
0.00449371337890625,
-0.0074310302734375,
-0.00441741943359375,
-0.017669677734375,
0.036163330078125,
-0.004688262939453125,
-0.0222015380859375,
-0.005100250244140625,
0.0089874267578125,
0.0220489501953125,
-0.0340576171875,
0.021514892578125,
-0.01407623291015625,
-0.0220184326171875,
0.040374755859375,
0.00634765625,
0.0019588470458984375,
-0.02587890625,
-0.01055908203125,
0.01032257080078125,
-0.0035228729248046875,
0.022003173828125,
-0.01031494140625,
-0.01270294189453125,
0.0207672119140625,
-0.00201416015625,
0.00777435302734375,
0.0283660888671875,
0.016693115234375,
0.02691650390625,
0.0159454345703125,
0.016326904296875,
0.01910400390625,
-0.022979736328125,
0.007904052734375,
0.0122833251953125,
0.024749755859375,
-0.019866943359375,
0.044647216796875,
-0.0038776397705078125,
0.01319122314453125,
-0.0386962890625,
0.049957275390625,
-0.0287017822265625,
-0.0157470703125,
-0.0318603515625,
-0.0064849853515625,
0.034820556640625,
-0.0251617431640625,
-0.033599853515625,
0.01165008544921875,
0.036346435546875,
0.0108184814453125,
0.0234375,
0.0031566619873046875,
0.01910400390625,
0.0113983154296875,
0.0047454833984375,
-0.01268768310546875,
0.0112457275390625,
-0.02471923828125,
-0.0003261566162109375,
0.032440185546875,
-0.007572174072265625,
-0.00799560546875,
0.027618408203125,
-0.01245880126953125,
0.00255584716796875,
-0.0020599365234375,
0.01171875,
0.00969696044921875,
-0.026641845703125,
0.0012960433959960938,
-0.01959228515625,
0.01317596435546875,
-0.01044464111328125,
0.0268096923828125,
-0.0105438232421875,
0.0263214111328125,
-0.0153045654296875,
0.0106658935546875,
0.0443115234375,
0.010284423828125,
0.004276275634765625,
-0.04278564453125,
-0.01308441162109375,
0.006198883056640625,
0.0012760162353515625,
-0.006988525390625,
-0.048095703125,
-0.0098114013671875,
0.00916290283203125,
0.0141448974609375,
-0.021453857421875,
0.0135955810546875,
-0.0008335113525390625,
-0.025665283203125,
-0.0145416259765625,
0.0019063949584960938,
0.00856781005859375,
-0.0208740234375,
0.00258636474609375,
-0.00949859619140625,
0.011199951171875,
0.01001739501953125,
-0.021728515625,
0.0096435546875,
-0.01593017578125,
0.0556640625,
0.0084381103515625,
-0.01021575927734375,
0.0166168212890625,
0.0199127197265625,
-0.01422119140625,
-0.0120697021484375,
-0.015838623046875,
-0.0189056396484375,
-0.00936126708984375,
0.00563812255859375,
0.00727081298828125,
0.0291900634765625,
0.047149658203125,
0.01174163818359375,
-0.01849365234375,
0.01428985595703125,
-0.007965087890625,
-0.01434326171875,
-0.00074005126953125,
-0.0032329559326171875,
0.024383544921875,
0.0096435546875,
0.001926422119140625,
0.01534271240234375,
-0.005306243896484375,
0.0285797119140625,
0.020721435546875,
0.01654052734375,
-0.006591796875,
-0.01041412353515625,
-0.031585693359375,
-0.0236663818359375,
-0.0272369384765625,
0.0283203125,
-0.00493621826171875,
-0.005168914794921875,
0.021240234375,
-0.0043182373046875,
0.0268096923828125,
0.0211181640625,
0.01800537109375,
0.0007328987121582031,
0.01140594482421875,
0.0262908935546875,
0.0210723876953125,
0.0199432373046875,
0.032684326171875,
-0.02703857421875,
-0.0146484375,
-0.0177764892578125,
0.02587890625,
-0.0159454345703125,
0.0069580078125,
-0.017974853515625,
-0.0121002197265625,
0.00951385498046875,
0.0213775634765625,
-0.0278778076171875,
-0.0300750732421875,
0.0171966552734375,
-0.037322998046875,
0.0160980224609375,
0.01702880859375,
0.0008101463317871094,
-0.00914764404296875,
0.0208740234375,
0.006687164306640625,
-0.0302886962890625,
0.00396728515625,
-0.02093505859375,
0.002399444580078125,
-0.0264739990234375,
0.048065185546875,
0.0012521743774414062,
0.00908660888671875,
-0.01300811767578125,
0.033966064453125,
0.012786865234375,
-0.018341064453125,
0.00510406494140625,
-0.0013227462768554688,
0.008514404296875,
-0.006160736083984375,
0.0110931396484375,
-0.0217742919921875,
-0.033416748046875,
0.0121002197265625,
0.00737762451171875,
-0.0188140869140625,
-0.00033473968505859375,
0.0230712890625,
0.024566650390625,
-0.00980377197265625,
-0.0038013458251953125,
-0.0201263427734375,
0.0005497932434082031,
0.00899505615234375,
-0.024810791015625,
-0.00876617431640625,
-0.00905609130859375,
0.017486572265625,
0.005535125732421875,
-0.006275177001953125,
0.0001468658447265625,
0.01430511474609375,
0.01617431640625,
-0.014312744140625,
0.024627685546875,
-0.0050506591796875,
-0.00801849365234375,
-0.0162353515625,
-0.0026912689208984375,
-0.048187255859375,
-0.01291656494140625,
0.006622314453125,
-0.0178985595703125,
-0.01611328125,
-0.0039215087890625,
0.008148193359375,
0.013641357421875,
0.01251220703125,
0.0216217041015625,
-0.01381683349609375,
0.014251708984375,
-0.02996826171875,
0.0249786376953125,
-0.0250396728515625,
0.00910186767578125,
0.0467529296875,
-0.0183258056640625,
0.0297393798828125,
-0.01049041748046875,
0.0019407272338867188,
-0.01171112060546875,
-0.045745849609375,
0.0035686492919921875,
0.01255035400390625,
0.01015472412109375,
-0.007457733154296875,
-0.01123809814453125,
-0.0114593505859375,
0.016326904296875,
-0.02215576171875,
-0.01195526123046875,
0.0229949951171875,
-0.00039386749267578125,
-0.0267333984375,
0.01629638671875,
0.01271820068359375,
-0.0263671875,
-0.0029506683349609375,
0.0132293701171875,
-0.00472259521484375,
0.040863037109375,
-0.01171875,
-0.02239990234375,
-0.00836944580078125,
0.00016319751739501953,
0.029327392578125,
0.034759521484375,
-0.01398468017578125,
-0.0303192138671875,
0.01520538330078125,
0.005950927734375,
-0.0206146240234375,
0.019561767578125,
-0.0026607513427734375,
-0.01392364501953125,
-0.0242156982421875,
-0.01534271240234375,
0.0234832763671875,
-0.0175933837890625,
-0.0194091796875,
-0.00507354736328125,
0.030181884765625,
0.01512908935546875,
-0.012481689453125,
0.01309967041015625,
-0.0186614990234375,
-0.023040771484375,
-0.005970001220703125,
0.01513671875,
-0.0191497802734375,
0.01033782958984375,
0.0175018310546875,
-0.0109100341796875,
0.00112152099609375,
0.013275146484375,
-0.006992340087890625,
-0.0206756591796875,
0.011962890625,
-0.013885498046875,
0.01641845703125,
-0.01097869873046875,
0.0017423629760742188,
0.0208587646484375,
-0.0005865097045898438,
-0.006000518798828125,
-0.00742340087890625,
-0.0350341796875,
-0.031341552734375,
0.029571533203125,
0.0360107421875,
-0.015777587890625,
-0.0005507469177246094,
-0.0015897750854492188,
-0.0163421630859375,
0.0213470458984375,
-0.0258331298828125,
-0.030792236328125,
-0.0102081298828125,
-0.027130126953125,
0.01302337646484375,
-0.0132904052734375,
-0.0031147003173828125,
-0.032196044921875,
-0.025665283203125,
-0.014617919921875,
0.006336212158203125,
0.00811767578125,
-0.00867462158203125,
-0.01120758056640625,
0.0193939208984375,
-0.027801513671875,
0.01306915283203125,
0.05914306640625,
0.00855255126953125,
-0.00923919677734375,
0.0269012451171875,
0.0318603515625,
-0.003936767578125,
-0.0164947509765625,
-0.0633544921875,
0.0097198486328125,
-0.01410675048828125,
0.0023593902587890625,
0.01033782958984375,
0.004077911376953125,
0.0107879638671875,
-0.008056640625,
-0.0006265640258789062,
-0.014801025390625,
0.0251007080078125,
0.04498291015625,
0.017364501953125,
0.03997802734375,
-0.040985107421875,
0.005451202392578125,
-0.002681732177734375,
0.0279998779296875,
-0.01334381103515625,
0.037872314453125,
0.00992584228515625,
-0.0209197998046875,
0.0022716522216796875,
0.034942626953125,
-0.00838470458984375,
0.020233154296875,
-0.00870513916015625,
0.00222015380859375,
-0.042205810546875,
0.00926971435546875,
0.0272369384765625,
-0.0171051025390625,
0.0305023193359375,
0.015533447265625,
0.0257720947265625,
0.01090240478515625,
-0.0091705322265625,
-0.01325225830078125,
-0.0191497802734375,
0.0133056640625,
0.0243377685546875,
0.018768310546875,
0.0212554931640625,
-0.014434814453125,
0.0096893310546875,
0.007717132568359375,
0.01016998291015625,
0.01200103759765625,
0.00101470947265625,
-0.0106658935546875,
0.00986480712890625,
0.0169525146484375,
-0.02374267578125,
-0.0126495361328125,
0.0157928466796875,
0.0206146240234375,
-0.0213623046875,
-0.0177154541015625,
0.010589599609375,
0.0256195068359375,
0.031524658203125,
-0.016326904296875,
0.041473388671875,
-0.043426513671875,
-0.0067901611328125,
-0.03448486328125,
0.005313873291015625,
-0.0233154296875,
0.008392333984375,
0.0168609619140625,
0.0232086181640625,
-0.00679779052734375,
0.0307769775390625,
0.0306549072265625,
-0.003406524658203125,
-0.010162353515625,
-0.015228271484375,
-0.04058837890625,
-0.00762176513671875,
-0.029052734375,
-0.00472259521484375,
-0.01262664794921875,
-0.00010925531387329102,
-0.0016832351684570312,
0.02191162109375,
0.0008063316345214844,
0.0150299072265625,
-0.00881195068359375,
-0.0175628662109375,
0.03094482421875,
0.0264739990234375,
-0.005313873291015625,
-0.0311431884765625,
0.00992584228515625,
-0.0028438568115234375,
-0.01654052734375,
0.032745361328125,
-0.01064300537109375,
0.011566162109375,
0.0198822021484375,
-0.005077362060546875,
0.00913238525390625,
-0.0055694580078125,
0.0005602836608886719,
0.003505706787109375,
0.0179443359375,
0.005054473876953125,
-0.0160369873046875,
0.01285552978515625,
-0.009521484375,
-0.03173828125,
-0.003002166748046875,
0.0164337158203125,
-0.004917144775390625,
-0.00357818603515625,
-0.00701141357421875,
0.0047760009765625,
-0.004489898681640625,
0.0016908645629882812,
-0.007503509521484375,
0.042877197265625,
0.039306640625,
-0.0289306640625,
-0.016326904296875,
-0.006183624267578125,
0.018890380859375,
-0.00707244873046875,
-0.019012451171875,
-0.0023059844970703125,
-0.011566162109375,
0.01340484619140625,
-0.007266998291015625,
-0.025177001953125,
-0.036651611328125,
0.00711822509765625,
0.0404052734375,
0.0197601318359375,
0.023162841796875,
-0.006877899169921875,
0.017669677734375,
-0.0164031982421875,
-0.004489898681640625,
-0.031402587890625,
0.040252685546875,
0.024139404296875,
0.00826263427734375,
0.0018444061279296875,
-0.033966064453125,
-0.030487060546875,
0.03125,
-0.006317138671875,
-0.00284576416015625,
0.0039520263671875,
-0.0171356201171875,
-0.0284271240234375,
0.011474609375,
-0.03131103515625,
-0.0030803680419921875,
0.0093536376953125,
-0.0294342041015625,
-0.004161834716796875,
-0.0113983154296875,
0.017608642578125,
0.0284423828125,
0.0200958251953125,
0.042724609375,
-0.01328277587890625,
-0.02520751953125,
-0.002048492431640625,
-0.002414703369140625,
-0.0012989044189453125,
0.019073486328125,
-0.00934600830078125,
0.003925323486328125,
0.01641845703125,
-0.0083465576171875,
-0.0003304481506347656,
0.03485107421875,
-0.00946044921875,
-0.026611328125,
-0.01922607421875,
-0.006000518798828125,
-0.00841522216796875,
-0.0167388916015625,
0.0147857666015625,
-0.00922393798828125,
-0.0011472702026367188,
-0.023223876953125,
0.0022563934326171875,
0.0183258056640625,
0.01788330078125,
-0.007686614990234375,
0.02471923828125,
-0.037017822265625,
0.0083160400390625,
0.007450103759765625,
-0.05255126953125,
-0.00528717041015625,
0.0214996337890625,
0.006618499755859375,
0.0166168212890625,
0.01425933837890625,
0.0338134765625,
-0.016845703125,
0.01044464111328125,
-0.001987457275390625,
0.003459930419921875,
-0.04229736328125,
-0.007503509521484375,
-0.005096435546875,
-0.01007080078125,
0.008270263671875,
0.027191162109375,
-0.027557373046875,
-0.0012073516845703125,
0.00775909423828125,
0.01456451416015625,
0.0176544189453125,
-0.017364501953125,
-0.002197265625,
-0.003448486328125,
-0.006763458251953125,
0.001373291015625,
0.0294647216796875,
0.016357421875,
0.0206146240234375,
0.035491943359375,
0.0233917236328125,
0.0132904052734375,
-0.0022525787353515625,
-0.019134521484375,
0.00830078125,
-0.007465362548828125,
-0.03936767578125,
0.02825927734375,
-0.01273345947265625,
-0.0263824462890625,
-0.028076171875,
-0.0158233642578125,
0.020477294921875,
-0.004489898681640625,
0.002086639404296875,
-0.006275177001953125,
0.00603485107421875,
0.00905609130859375,
0.007465362548828125,
0.0119781494140625,
0.0166473388671875,
-0.02239990234375,
0.01094818115234375,
0.0126953125,
-0.01348876953125,
0.0015811920166015625,
0.0205078125,
-0.038055419921875,
-0.00550079345703125,
-0.0040740966796875,
0.004100799560546875,
0.0179901123046875,
-0.0006031990051269531,
0.007904052734375,
-0.001979827880859375,
0.01067352294921875,
0.0006246566772460938,
0.01108551025390625,
-0.00914764404296875,
-0.01120758056640625,
-0.0242462158203125,
-0.00537109375,
0.0248565673828125,
0.0044097900390625,
-0.01418304443359375,
0.014862060546875,
0.0092926025390625,
0.041168212890625,
-0.00879669189453125,
-0.007709503173828125,
-0.0496826171875,
-0.006191253662109375,
-0.0160980224609375,
0.02099609375,
0.00463104248046875,
-0.0006322860717773438,
0.0345458984375,
0.0015163421630859375,
0.0134429931640625,
-0.02459716796875,
-0.01213836669921875,
0.0020923614501953125,
0.003429412841796875,
0.0038661956787109375,
0.026611328125,
-0.0168914794921875,
-0.001651763916015625,
0.028411865234375,
-0.048095703125,
-0.0204010009765625,
-0.00849151611328125,
-0.0007638931274414062,
0.003692626953125,
0.011322021484375,
0.0282745361328125,
-0.003719329833984375,
-0.021728515625,
0.006786346435546875,
0.0028667449951171875,
0.0291900634765625,
0.035003662109375,
-0.00920867919921875,
0.0038623809814453125,
0.0023746490478515625,
0.0094757080078125,
0.0238494873046875,
-0.00617218017578125,
-0.005084991455078125,
-0.01436614990234375,
0.0267181396484375,
0.0088043212890625,
0.0020904541015625,
0.0206756591796875,
-0.01032257080078125,
-0.0183258056640625,
-0.032135009765625,
-0.00977325439453125,
0.0038471221923828125,
-0.04925537109375,
-0.0087432861328125,
-0.0022716522216796875,
-0.006320953369140625,
0.013153076171875,
-0.016632080078125,
-0.022308349609375,
-0.021942138671875,
0.0423583984375,
0.0169830322265625,
-0.00994873046875,
0.01131439208984375,
-0.0017499923706054688,
0.01270294189453125,
-0.0164794921875,
0.006603240966796875,
-0.021636962890625,
-0.01204681396484375,
0.0252532958984375,
-0.008880615234375,
-0.0206298828125,
-0.0201873779296875,
0.00033664703369140625,
0.00696563720703125,
-0.0202789306640625,
0.0283203125,
-0.006011962890625,
0.01108551025390625,
-0.017669677734375,
-0.002529144287109375,
0.02587890625,
0.0081634521484375,
-0.00565338134765625,
0.004909515380859375,
0.0165863037109375,
0.0237579345703125,
-0.0222015380859375,
-0.01029205322265625,
-0.0192718505859375,
0.0033397674560546875,
0.01029205322265625,
-0.018890380859375,
-0.0179443359375,
0.007709503173828125,
0.02069091796875,
0.016937255859375,
0.02398681640625,
0.04229736328125,
0.0242156982421875,
0.00836181640625,
0.0154571533203125,
0.01515960693359375,
0.0164794921875,
0.0166168212890625,
0.00007814168930053711,
-0.00014507770538330078,
0.035919189453125,
-0.005031585693359375,
0.0301971435546875,
0.0208740234375,
0.00792694091796875,
0.03228759765625,
-0.009063720703125,
-0.0178985595703125,
-0.0303802490234375,
-0.0228271484375,
-0.00396728515625,
0.0190277099609375,
-0.0295257568359375,
-0.002338409423828125,
0.0027618408203125,
-0.00817108154296875,
-0.00005441904067993164,
0.0162353515625,
-0.01398468017578125,
0.033233642578125,
-0.0133209228515625,
-0.0039520263671875,
-0.024627685546875,
-0.0020542144775390625,
-0.01617431640625,
0.0078277587890625,
-0.009002685546875,
-0.005886077880859375,
-0.01611328125,
-0.016876220703125,
0.0207366943359375,
-0.0079193115234375,
0.0452880859375,
0.00901031494140625,
-0.0023097991943359375,
-0.00965118408203125,
-0.00621795654296875,
0.0002951622009277344,
0.006237030029296875,
-0.0208892822265625,
0.014862060546875,
-0.0168304443359375,
-0.00608062744140625,
0.0245819091796875,
-0.0168304443359375,
0.002201080322265625,
0.0009813308715820312,
0.0031108856201171875,
0.005390167236328125,
0.0282135009765625,
0.0208282470703125,
-0.0249786376953125,
-0.0243682861328125,
0.0095062255859375,
0.008026123046875,
0.0011034011840820312,
0.0017652511596679688,
-0.00919342041015625,
0.0019397735595703125,
-0.000591278076171875,
-0.0021514892578125,
0.0288848876953125,
-0.02008056640625,
-0.01448822021484375,
-0.0233612060546875,
-0.02410888671875,
0.0243682861328125,
-0.005985260009765625,
0.0078582763671875,
-0.0212554931640625,
-0.023681640625,
0.020843505859375,
0.051666259765625,
0.00505828857421875,
0.0195159912109375,
-0.01499176025390625,
-0.0160675048828125,
0.01812744140625,
0.01207733154296875,
-0.0256195068359375,
0.045867919921875,
0.00421905517578125,
0.0271148681640625,
-0.0194854736328125,
-0.04302978515625,
0.008636474609375,
0.0159149169921875,
0.0028018951416015625,
-0.037506103515625,
0.0212249755859375,
0.00762939453125,
-0.01110076904296875,
0.0262451171875,
-0.00022864341735839844,
0.0035190582275390625,
0.01229095458984375,
-0.056060791015625,
-0.0004372596740722656,
-0.00968170166015625,
0.017120361328125,
0.0095062255859375,
-0.010955810546875,
0.052886962890625,
-0.0164031982421875,
-0.0081024169921875,
0.0236053466796875,
-0.01192474365234375,
-0.0035190582275390625,
0.0018472671508789062,
-0.004062652587890625,
-0.0213775634765625,
-0.03375244140625,
-0.003200531005859375,
0.0283660888671875,
-0.0628662109375,
-0.0235595703125,
-0.049102783203125,
0.0092926025390625,
-0.0166778564453125,
-0.02191162109375,
-0.041015625,
-0.035919189453125,
-0.00927734375,
-0.047393798828125,
-0.0408935546875,
-0.01119232177734375,
-0.0223236083984375,
0.0151519775390625,
-0.016357421875,
0.0007190704345703125,
-0.00804901123046875,
-0.012542724609375,
0.010162353515625,
-0.0183563232421875,
-0.032958984375,
0.0072174072265625,
-0.01470947265625,
-0.0268096923828125,
-0.0285491943359375,
-0.02801513671875,
-0.0318603515625,
0.0196990966796875,
0.0135650634765625,
0.00885772705078125,
0.0014867782592773438,
0.0135650634765625,
0.0249176025390625,
-0.0021190643310546875,
0.03338623046875,
-0.00974273681640625,
-0.00807952880859375,
-0.037384033203125,
-0.004230499267578125,
-0.0059356689453125,
0.00533294677734375,
-0.00859832763671875,
0.01145172119140625,
0.0178680419921875,
-0.0008134841918945312,
0.0249786376953125,
0.00640869140625,
0.00914764404296875,
-0.007251739501953125,
-0.0003139972686767578,
0.0159912109375,
0.0357666015625,
-0.0127105712890625,
0.0088348388671875,
-0.0007662773132324219,
0.0204620361328125,
0.00823211669921875,
-0.0002028942108154297,
-0.0350341796875,
-0.0193328857421875,
-0.02288818359375,
-0.01551055908203125,
-0.01479339599609375,
-0.00397491455078125,
0.00881195068359375,
0.047943115234375,
-0.0007748603820800781,
-0.00835418701171875,
0.0085906982421875,
0.0024566650390625,
-0.02069091796875,
-0.0216827392578125,
0.0328369140625,
0.0192718505859375,
0.0273895263671875,
-0.0024623870849609375,
0.00885009765625,
-0.0021343231201171875,
0.0191650390625,
0.03900146484375,
0.001953125,
0.004913330078125,
0.033203125,
0.006198883056640625,
0.0160675048828125,
-0.0231170654296875,
-0.02313232421875,
-0.0172882080078125,
0.006893157958984375,
-0.0171051025390625,
-0.015625,
0.00308990478515625,
0.0019216537475585938,
-0.0188446044921875,
-0.00897979736328125,
-0.0267181396484375,
0.0173797607421875,
0.0169219970703125,
0.0018014907836914062,
-0.0168914794921875,
0.00971221923828125,
-0.0279693603515625,
0.04864501953125,
-0.0028839111328125,
0.040771484375,
-0.0161285400390625,
-0.0024356842041015625,
0.00586700439453125,
-0.028472900390625,
-0.00942230224609375,
0.01082611083984375,
0.00659942626953125,
0.041900634765625,
0.0007147789001464844,
-0.0258941650390625,
-0.003795623779296875,
-0.009735107421875,
-0.006679534912109375,
-0.003143310546875,
0.01009368896484375,
-0.00860595703125,
-0.0102691650390625,
-0.0156402587890625,
0.0009307861328125,
-0.0116729736328125,
0.01364898681640625,
0.018707275390625,
-0.030914306640625,
-0.047088623046875,
-0.0132293701171875,
-0.0083770751953125,
-0.00627899169921875,
0.016082763671875,
-0.0013246536254882812,
0.0171661376953125,
-0.0182342529296875,
-0.004840850830078125,
-0.0036640167236328125,
-0.0408935546875,
-0.0093994140625,
-0.022796630859375,
0.038787841796875,
-0.0203094482421875,
-0.0012712478637695312,
-0.017364501953125,
0.02227783203125,
0.0136566162109375,
-0.0010585784912109375,
-0.0268096923828125,
-0.0159759521484375,
-0.00592803955078125,
0.022125244140625,
0.004993438720703125,
0.033721923828125,
-0.0128326416015625,
0.0025997161865234375,
-0.0227203369140625,
-0.0184326171875,
-0.03521728515625,
-0.01342010498046875,
0.00066375732421875,
0.031829833984375,
0.01509857177734375,
-0.0276336669921875,
0.007152557373046875,
-0.0112457275390625,
0.0007586479187011719,
0.0009427070617675781,
-0.05413818359375,
-0.0399169921875,
0.01395416259765625,
0.037811279296875,
-0.01369476318359375,
0.039825439453125,
-0.03314208984375,
0.01297760009765625,
0.004344940185546875,
0.002552032470703125,
0.0196990966796875,
0.00560760498046875,
0.007228851318359375,
0.0006313323974609375,
0.006916046142578125,
-0.002410888671875,
0.0160064697265625,
-0.00310516357421875,
-0.005401611328125,
-0.01702880859375,
0.0136871337890625,
-0.0109405517578125,
0.01031494140625,
-0.00908660888671875,
0.00460052490234375,
-0.0218048095703125,
0.037261962890625,
-0.01386260986328125,
0.0013341903686523438,
0.0009484291076660156,
-0.0178070068359375,
0.00405120849609375,
0.01027679443359375,
-0.036773681640625,
0.0146331787109375,
0.01032257080078125,
0.0018482208251953125,
0.015960693359375,
0.0067291259765625,
0.006397247314453125,
-0.0263214111328125,
-0.02294921875,
-0.0166015625,
-0.0210723876953125,
0.00827789306640625,
-0.00879669189453125,
0.0018138885498046875,
-0.01238250732421875,
0.02294921875,
0.01410675048828125,
0.038543701171875,
0.0177154541015625,
0.0200347900390625,
-0.0280303955078125,
-0.02313232421875,
-0.0190887451171875,
-0.0048828125,
0.005702972412109375,
-0.00952911376953125,
0.0206146240234375,
0.00557708740234375,
-0.00913238525390625,
-0.013092041015625,
-0.0091705322265625,
-0.01349639892578125,
-0.0007791519165039062,
0.02349853515625,
-0.0022792816162109375,
0.0092315673828125,
-0.0009379386901855469,
0.002719879150390625,
0.032379150390625,
0.0018815994262695312,
0.014923095703125,
-0.0194244384765625,
0.01763916015625,
-0.0217437744140625,
-0.0064697265625,
-0.0226898193359375,
-0.0198822021484375,
0.0193939208984375,
0.007205963134765625,
-0.0163726806640625,
0.008392333984375,
-0.01329803466796875,
-0.0295562744140625,
-0.008941650390625,
-0.00447845458984375,
-0.006900787353515625,
0.0011959075927734375,
0.0223846435546875,
-0.01177978515625,
-0.0157928466796875,
0.0119171142578125,
-0.0218963623046875,
-0.0259552001953125,
0.00695037841796875,
-0.0006480216979980469,
-0.03863525390625,
-0.040496826171875,
0.001922607421875,
0.00865936279296875,
0.010162353515625,
-0.0008902549743652344,
-0.02471923828125,
-0.0001633167266845703,
-0.01244354248046875,
0.0273284912109375,
0.0163421630859375,
-0.0019216537475585938,
0.01104736328125,
0.0115814208984375,
-0.026641845703125,
0.037994384765625,
0.0027675628662109375,
-0.0017042160034179688,
-0.0108184814453125,
0.037689208984375,
-0.0020275115966796875,
0.0093994140625,
0.01247406005859375,
0.0218505859375,
0.0105133056640625,
0.00864410400390625,
0.02276611328125,
-0.01226806640625,
-0.01544952392578125,
0.00562286376953125,
-0.01338958740234375,
-0.0259857177734375,
-0.0012464523315429688,
-0.003070831298828125,
-0.0350341796875,
-0.006927490234375,
0.00799560546875,
0.0017938613891601562,
-0.006946563720703125,
0.0298004150390625,
-0.00634002685546875,
0.0183258056640625,
0.0177764892578125,
0.01302337646484375,
-0.01248931884765625,
0.035614013671875,
0.01561737060546875,
-0.0032863616943359375,
0.0176239013671875,
-0.008392333984375,
0.03155517578125,
-0.01128387451171875,
-0.0139007568359375,
-0.0036487579345703125,
-0.0246124267578125,
0.00563812255859375,
-0.0010747909545898438,
0.0220184326171875,
-0.00965118408203125,
0.016510009765625,
0.0006108283996582031,
0.006420135498046875,
-0.0016880035400390625,
-0.034149169921875,
-0.01270294189453125,
0.0272369384765625,
0.0017461776733398438,
-0.01042938232421875,
-0.002796173095703125,
0.003021240234375,
-0.0191650390625,
0.000457763671875,
-0.0236053466796875,
-0.037078857421875,
-0.01039886474609375,
-0.01485443115234375,
0.0172882080078125,
0.025726318359375,
-0.032745361328125,
0.006771087646484375,
0.020782470703125,
-0.013763427734375,
0.00817108154296875,
0.00496673583984375,
-0.00579071044921875,
0.0156402587890625,
0.032989501953125,
0.0187225341796875,
-0.007282257080078125,
0.0084228515625,
-0.01806640625,
-0.02459716796875,
-0.00994873046875,
-0.01409149169921875,
0.024993896484375,
-0.009490966796875,
0.042327880859375,
-0.0109710693359375,
-0.0038299560546875,
-0.005615234375,
-0.0004935264587402344,
-0.0127105712890625,
0.012451171875,
-0.0025310516357421875,
0.0015630722045898438,
-0.01534271240234375,
0.00937652587890625,
0.01287841796875,
0.01390838623046875,
0.00882720947265625,
-0.008941650390625,
0.0064544677734375,
0.0171356201171875,
0.0263519287109375,
-0.016326904296875,
0.01031494140625,
-0.006481170654296875,
0.0007486343383789062,
-0.01910400390625,
0.019927978515625,
-0.0090484619140625,
0.024383544921875,
-0.00865936279296875,
-0.0009207725524902344,
0.0226898193359375,
0.021575927734375,
-0.01995849609375,
0.00850677490234375,
-0.03033447265625,
0.0135650634765625,
-0.00579833984375,
-0.016326904296875,
0.042022705078125,
-0.004909515380859375,
-0.0206146240234375,
-0.03228759765625,
0.01189422607421875,
-0.0027561187744140625,
-0.020965576171875,
0.0014772415161132812,
-0.00914764404296875,
0.00952911376953125,
0.00484466552734375,
0.0017499923706054688,
0.01959228515625,
0.01788330078125,
-0.0137786865234375,
-0.01629638671875,
-0.0034656524658203125,
0.0035839080810546875,
0.035125732421875,
0.0099029541015625,
0.005401611328125,
0.01361083984375,
-0.0191192626953125,
-0.0277252197265625,
0.00699615478515625,
0.0086212158203125,
0.0285797119140625,
-0.020965576171875,
-0.016937255859375,
0.0033321380615234375,
0.007045745849609375,
-0.00688934326171875,
-0.004718780517578125,
0.0198974609375,
0.0019130706787109375,
0.02825927734375,
0.0218963623046875,
0.01409149169921875,
0.00244903564453125,
-0.032073974609375,
-0.0028667449951171875,
-0.035247802734375,
0.01383209228515625,
0.0338134765625,
-0.0013475418090820312,
0.016143798828125,
0.0257720947265625,
-0.020416259765625,
-0.03668212890625,
-0.0121307373046875,
0.00775146484375,
0.03533935546875,
-0.0122528076171875,
-0.0012969970703125,
0.028167724609375,
0.007808685302734375,
0.001354217529296875,
-0.0006990432739257812,
-0.0141143798828125,
-0.022705078125,
-0.0222320556640625,
0.0165557861328125,
-0.01025390625,
0.029205322265625,
-0.0133056640625,
-0.0037059783935546875,
-0.0150909423828125,
-0.023345947265625,
0.00579071044921875,
-0.00933074951171875,
-0.02587890625,
0.009063720703125,
-0.0264739990234375,
0.004001617431640625,
-0.0069427490234375,
-0.01959228515625,
-0.02728271484375,
0.004421234130859375,
-0.041717529296875,
-0.0266265869140625,
-0.00504302978515625,
-0.0019817352294921875,
0.0204010009765625,
0.004848480224609375,
0.01065826416015625,
0.02410888671875,
0.0267181396484375,
0.01009368896484375,
0.0084686279296875,
0.0435791015625,
-0.007228851318359375,
-0.00804901123046875,
-0.0157012939453125,
-0.031036376953125,
-0.01389312744140625,
-0.025177001953125,
-0.021881103515625,
-0.0006256103515625,
-0.0040283203125,
0.0518798828125,
-0.016998291015625,
0.004547119140625,
-0.037200927734375,
-0.017333984375,
0.002033233642578125,
-0.002002716064453125,
0.0238494873046875,
-0.043853759765625,
-0.00397491455078125,
-0.0239105224609375,
-0.005611419677734375,
0.0201416015625,
0.01111602783203125,
0.00884246826171875,
-0.030303955078125,
0.00821685791015625,
-0.03204345703125,
0.00852203369140625,
-0.01064300537109375,
-0.0113677978515625,
0.0021381378173828125,
0.0059356689453125,
-0.0135498046875,
-0.02691650390625,
0.0078582763671875,
-0.007617950439453125,
-0.0087127685546875,
0.00705718994140625,
-0.0032596588134765625,
-0.0201568603515625,
-0.01141357421875,
-0.01232147216796875,
0.0142059326171875,
0.001026153564453125,
0.0187225341796875,
0.035247802734375,
-0.01049041748046875,
-0.0152435302734375,
-0.0333251953125,
-0.035980224609375,
0.006008148193359375,
-0.00983428955078125,
-0.0146026611328125,
-0.011962890625,
-0.03167724609375,
-0.029022216796875,
-0.0305633544921875,
-0.0068206787109375,
-0.006328582763671875,
-0.01509857177734375,
0.0124053955078125,
0.015869140625,
-0.0013799667358398438,
0.004840850830078125,
0.0023174285888671875,
-0.002513885498046875,
-0.003082275390625,
0.0025196075439453125,
0.00768280029296875,
0.017059326171875,
-0.01554107666015625,
-0.045166015625,
0.0037021636962890625,
-0.0028228759765625,
0.052337646484375,
0.03741455078125,
-0.01255035400390625,
0.0213470458984375,
0.0006470680236816406,
0.016632080078125,
0.0228729248046875,
-0.0257110595703125,
0.017364501953125,
-0.01141357421875,
-0.00018608570098876953,
0.001995086669921875,
-0.0002522468566894531,
0.019622802734375,
-0.00511932373046875,
-0.03643798828125,
-0.0007777214050292969,
-0.04150390625,
0.0011091232299804688,
0.0169677734375,
0.0557861328125,
-0.0030059814453125,
0.02178955078125,
-0.0114288330078125,
0.0014600753784179688,
0.0173187255859375,
-0.042022705078125,
0.0016508102416992188,
-0.0016193389892578125,
0.0012559890747070312,
-0.0002696514129638672,
0.0035305023193359375,
0.007232666015625,
0.0110321044921875,
-0.01043701171875,
0.00232696533203125,
0.01560211181640625,
-0.01031494140625,
0.03265380859375,
0.0134735107421875,
-0.0232696533203125,
0.00975799560546875,
0.03143310546875,
-0.039215087890625,
0.0180206298828125,
0.03192138671875,
0.0153656005859375,
0.01280975341796875,
-0.01000213623046875,
0.03411865234375,
-0.03387451171875,
-0.021759033203125,
0.0226287841796875,
0.006473541259765625,
-0.0247344970703125,
0.003749847412109375,
-0.01273345947265625,
0.004863739013671875,
-0.03228759765625,
0.0001823902130126953,
-0.032562255859375,
0.041534423828125,
0.01171875,
-0.025543212890625,
-0.01012420654296875,
0.032379150390625,
0.017242431640625,
-0.01320648193359375,
0.032562255859375,
0.00881195068359375,
-0.00823211669921875,
-0.0275421142578125,
0.01323699951171875,
0.0211029052734375,
-0.00798797607421875,
0.013458251953125,
-0.00542449951171875,
-0.046356201171875,
0.01250457763671875,
-0.0141754150390625,
-0.01146697998046875,
0.016204833984375,
0.007030487060546875,
-0.01088714599609375,
-0.0323486328125,
-0.01959228515625,
-0.0037250518798828125,
0.045440673828125,
-0.003326416015625,
-0.034332275390625,
-0.02142333984375,
-0.038360595703125,
0.00688934326171875,
-0.02783203125,
0.00389862060546875,
0.02545166015625,
0.016571044921875,
0.0246734619140625,
-0.033050537109375,
-0.047576904296875,
-0.018646240234375,
0.01230621337890625,
0.0115509033203125,
0.003330230712890625,
-0.0157928466796875,
-0.003940582275390625,
0.0108795166015625,
-0.0199737548828125,
-0.0035915374755859375,
-0.01386260986328125,
0.01041412353515625,
-0.005680084228515625,
-0.0008730888366699219,
-0.02655029296875,
-0.032379150390625,
-0.07366943359375,
-0.027191162109375,
-0.03643798828125,
0.00576019287109375,
0.03350830078125,
-0.03656005859375,
-0.00566864013671875,
0.0005803108215332031,
0.03204345703125,
0.03167724609375,
-0.0083160400390625,
0.0131683349609375,
-0.0224761962890625,
-0.008056640625,
0.01218414306640625,
0.0170135498046875,
-0.0201263427734375,
-0.0001875162124633789,
-0.0200653076171875,
0.007122039794921875,
-0.0182952880859375,
0.0008006095886230469,
-0.003376007080078125,
0.01081085205078125,
0.00490570068359375,
-0.0138397216796875,
0.0092010498046875,
-0.0175628662109375,
0.0133056640625,
0.00894927978515625,
-0.0132904052734375,
-0.01013946533203125,
-0.013702392578125,
-0.01654052734375,
-0.03173828125,
-0.02825927734375,
0.0156402587890625,
-0.01389312744140625,
0.018524169921875,
-0.033782958984375,
0.00873565673828125,
0.01171112060546875,
-0.037872314453125,
-0.0008754730224609375,
0.002475738525390625,
0.0200042724609375,
-0.00018322467803955078,
-0.0020999908447265625,
0.0069732666015625,
-0.020172119140625,
0.0222930908203125,
0.021728515625,
-0.0006761550903320312,
0.0005421638488769531,
0.01197052001953125,
-0.0260772705078125,
0.0161285400390625,
0.033294677734375,
0.0308990478515625,
-0.0184173583984375,
0.0004208087921142578,
0.0010347366333007812,
-0.01071929931640625,
0.0018930435180664062,
-0.0028362274169921875,
-0.01971435546875,
-0.00920867919921875,
0.0205535888671875,
-0.01092529296875,
0.019195556640625
] |
ours_469
|
Let the numbers be \(a_{1}, a_{2}, \ldots, a_{n}\). By the Trivial Inequality,
\[
\left(a_{1}-1\right)^{2}+\left(a_{2}-1\right)^{2}+\ldots+\left(a_{n}-1\right)^{2} \geq 0
\]
so
\[
\begin{aligned}
0 & \leq \left(a_{1}^{2}+a_{2}^{2}+\ldots+a_{n}^{2}\right) - 2\left(a_{1}+a_{2}+\ldots+a_{n}\right) + n \\
& = -\left(a_{1}+a_{2}+\ldots+a_{n}\right) + n
\end{aligned}
\]
and hence
\[
\frac{a_{1}+a_{2}+\ldots+a_{n}}{n} \leq 1
\]
Equality holds whenever \(a_{1}=a_{2}=\ldots=a_{n}=1\).
Thus, the largest possible value of the arithmetic mean is \(\boxed{1}\).
|
1
|
{
"competition": "us_comps",
"dataset": "Ours",
"posts": null,
"source": "OMOFall18Solns.md"
}
|
Katie has a list of real numbers such that the sum of the numbers on her list is equal to the sum of the squares of the numbers on her list. Compute the largest possible value of the arithmetic mean of her numbers.
|
[
"/Mathematics/Algebra/AlgebraicEquations/AlgebraicEquation",
"/Mathematics/Algebra/AlgebraicIdentities/CompletingtheSquare",
"/Mathematics/Algebra/Sums/PowerSum",
"/Mathematics/Algebra/Sums/Sum"
] |
Rewrite the condition using (a_i − 1)² ≥ 0 to bound the average by 1.
|
[
-0.000003814697265625,
0.0021114349365234375,
0.0244598388671875,
0.05657958984375,
0.0001583099365234375,
-0.0091552734375,
-0.01380157470703125,
0.027984619140625,
0.007053375244140625,
0.0252227783203125,
0.0211334228515625,
-0.03179931640625,
0.0016088485717773438,
0.00231170654296875,
-0.017730712890625,
0.01171875,
0.0281219482421875,
0.0268707275390625,
0.046722412109375,
-0.00601959228515625,
-0.00516510009765625,
-0.019256591796875,
-0.04156494140625,
0.003902435302734375,
-0.055419921875,
-0.0386962890625,
-0.01739501953125,
-0.0216827392578125,
-0.001232147216796875,
0.031280517578125,
-0.026214599609375,
-0.0312347412109375,
0.00237274169921875,
-0.006622314453125,
0.0027179718017578125,
0.01274871826171875,
-0.006420135498046875,
-0.004856109619140625,
-0.029693603515625,
-0.024261474609375,
-0.01136016845703125,
0.02130126953125,
-0.0013484954833984375,
0.00046324729919433594,
-0.01110076904296875,
-0.025634765625,
0.00009769201278686523,
-0.01451873779296875,
-0.00997161865234375,
0.006580352783203125,
0.0006661415100097656,
-0.0003616809844970703,
0.0269012451171875,
-0.00815582275390625,
0.020477294921875,
-0.006683349609375,
-0.01690673828125,
0.0017995834350585938,
-0.0172271728515625,
0.00687408447265625,
-0.0035419464111328125,
0.0321044921875,
-0.01739501953125,
-0.0007767677307128906,
-0.00093841552734375,
-0.0125732421875,
-0.01934814453125,
-0.00879669189453125,
-0.0089111328125,
-0.0158538818359375,
0.01491546630859375,
0.0008578300476074219,
-0.01348114013671875,
-0.005069732666015625,
0.0215301513671875,
-0.011444091796875,
-0.01203155517578125,
0.01739501953125,
-0.0210723876953125,
0.011444091796875,
0.01059722900390625,
0.01309967041015625,
0.0223236083984375,
-0.0013713836669921875,
-0.00846099853515625,
-0.001514434814453125,
-0.00818634033203125,
0.006771087646484375,
-0.01335906982421875,
-0.0308990478515625,
-0.0021820068359375,
0.037017822265625,
-0.004619598388671875,
0.014739990234375,
-0.001194000244140625,
-0.003223419189453125,
-0.0247039794921875,
0.002254486083984375,
-0.0142364501953125,
0.0018110275268554688,
0.001544952392578125,
-0.0021877288818359375,
0.0126953125,
-0.00252532958984375,
-0.021575927734375,
0.005786895751953125,
-0.00026607513427734375,
-0.015411376953125,
-0.0067138671875,
0.007259368896484375,
0.0198211669921875,
0.00669097900390625,
0.007633209228515625,
0.02288818359375,
-0.0074005126953125,
-0.00615692138671875,
0.011627197265625,
0.0224456787109375,
0.007007598876953125,
0.052764892578125,
-0.0090789794921875,
0.007354736328125,
-0.003940582275390625,
-0.0038852691650390625,
0.0007748603820800781,
0.026214599609375,
0.0139617919921875,
-0.0254974365234375,
-0.01399993896484375,
0.006305694580078125,
-0.0228271484375,
-0.005168914794921875,
-0.026214599609375,
0.0039520263671875,
-0.03778076171875,
0.0022258758544921875,
0.00995635986328125,
-0.0171356201171875,
-0.01065826416015625,
-0.011260986328125,
0.0088958740234375,
-0.003459930419921875,
0.004634857177734375,
0.00833892822265625,
-0.014312744140625,
0.003467559814453125,
0.0014791488647460938,
-0.01526641845703125,
-0.0015821456909179688,
-0.00508880615234375,
0.0035800933837890625,
-0.0153350830078125,
-0.0038089752197265625,
0.0009493827819824219,
-0.005481719970703125,
-0.007122039794921875,
0.01482391357421875,
0.006755828857421875,
0.0126495361328125,
-0.0095062255859375,
0.0023937225341796875,
-0.024322509765625,
-0.035430908203125,
0.053955078125,
-0.01263427734375,
-0.005199432373046875,
-0.01299285888671875,
0.006103515625,
-0.004428863525390625,
-0.01427459716796875,
-0.0013246536254882812,
0.0177764892578125,
-0.01560211181640625,
-0.0107574462890625,
-0.021697998046875,
-0.01187896728515625,
-0.01113128662109375,
-0.0234375,
-0.0006632804870605469,
-0.0177764892578125,
-0.0185394287109375,
-0.0221405029296875,
0.0008821487426757812,
0.0015125274658203125,
-0.0037841796875,
-0.0006327629089355469,
0.006252288818359375,
-0.00933074951171875,
0.035125732421875,
0.010162353515625,
0.0189208984375,
0.02020263671875,
-0.01495361328125,
-0.01482391357421875,
0.007549285888671875,
-0.00771331787109375,
-0.020172119140625,
-0.01100921630859375,
0.0088348388671875,
0.0011529922485351562,
0.0009031295776367188,
0.01546478271484375,
-0.0121307373046875,
-0.0016155242919921875,
0.01242828369140625,
-0.006877899169921875,
-0.00804901123046875,
-0.003002166748046875,
0.00865936279296875,
0.006381988525390625,
0.0131378173828125,
0.0065155029296875,
0.01361083984375,
-0.01727294921875,
-0.00823211669921875,
0.0267333984375,
-0.00753021240234375,
-0.00856781005859375,
0.00250244140625,
0.0012569427490234375,
-0.0034389495849609375,
0.01056671142578125,
0.0027313232421875,
-0.00682830810546875,
-0.01326751708984375,
0.0039825439453125,
-0.0078277587890625,
-0.005268096923828125,
0.00426483154296875,
0.0028057098388671875,
0.0115966796875,
-0.004489898681640625,
0.002712249755859375,
-0.01149749755859375,
-0.021697998046875,
0.02685546875,
-0.050445556640625,
-0.004268646240234375,
0.0272979736328125,
-0.018585205078125,
0.019805908203125,
-0.0181732177734375,
0.0028400421142578125,
0.002002716064453125,
-0.004730224609375,
-0.0081787109375,
0.005458831787109375,
-0.019378662109375,
0.0088653564453125,
-0.0077972412109375,
-0.008056640625,
0.00023663043975830078,
-0.0262298583984375,
-0.0130462646484375,
-0.0036869049072265625,
0.0006842613220214844,
-0.008453369140625,
-0.03546142578125,
-0.01922607421875,
-0.0017538070678710938,
-0.0095062255859375,
-0.0257110595703125,
-0.004993438720703125,
0.01251983642578125,
-0.0274505615234375,
0.025909423828125,
0.0232391357421875,
-0.0251922607421875,
0.022979736328125,
-0.019805908203125,
0.0202789306640625,
-0.0167694091796875,
-0.00913238525390625,
0.0199737548828125,
-0.0031833648681640625,
-0.0004723072052001953,
0.0021419525146484375,
-0.007171630859375,
0.0102081298828125,
0.01456451416015625,
0.0016393661499023438,
0.01348876953125,
-0.00780487060546875,
0.0029773712158203125,
0.0068206787109375,
0.00970458984375,
0.033782958984375,
-0.01593017578125,
0.008819580078125,
0.0259857177734375,
-0.01505279541015625,
-0.00897979736328125,
-0.01189422607421875,
-0.0081329345703125,
0.04058837890625,
-0.01261138916015625,
-0.005069732666015625,
0.00540924072265625,
0.01056671142578125,
0.015899658203125,
0.0247039794921875,
-0.030181884765625,
-0.022857666015625,
-0.0224151611328125,
0.022247314453125,
0.00921630859375,
0.01177978515625,
-0.002655029296875,
-0.01261138916015625,
-0.0030155181884765625,
-0.00197601318359375,
0.003330230712890625,
-0.0021514892578125,
-0.01654052734375,
-0.0125885009765625,
-0.0443115234375,
0.024017333984375,
-0.028961181640625,
-0.00754547119140625,
0.00103759765625,
-0.0151519775390625,
0.0034732818603515625,
0.020843505859375,
0.0119476318359375,
0.004001617431640625,
-0.00997161865234375,
0.015350341796875,
-0.0009622573852539062,
0.0082550048828125,
0.039947509765625,
-0.031097412109375,
0.02447509765625,
-0.01180267333984375,
-0.00008618831634521484,
0.00353240966796875,
0.0059814453125,
-0.0197601318359375,
0.007587432861328125,
0.0003895759582519531,
0.00844573974609375,
0.0162811279296875,
-0.01702880859375,
-0.006763458251953125,
-0.007633209228515625,
-0.052093505859375,
0.0041351318359375,
-0.004253387451171875,
0.00876617431640625,
0.0237274169921875,
-0.0106048583984375,
0.00042057037353515625,
-0.00469207763671875,
0.01171875,
0.01053619384765625,
-0.03167724609375,
0.00632476806640625,
-0.002689361572265625,
0.00604248046875,
0.01242828369140625,
0.021148681640625,
0.0030803680419921875,
-0.0197601318359375,
0.007442474365234375,
-0.006500244140625,
0.00109100341796875,
-0.0168304443359375,
-0.01800537109375,
0.0201873779296875,
-0.00907135009765625,
0.020538330078125,
0.00687408447265625,
-0.0045013427734375,
0.01483917236328125,
-0.038482666015625,
-0.0089874267578125,
0.018707275390625,
-0.0228424072265625,
-0.0287628173828125,
0.00960540771484375,
-0.002040863037109375,
-0.0024509429931640625,
-0.005367279052734375,
-0.01180267333984375,
-0.0009694099426269531,
-0.0015707015991210938,
0.0170745849609375,
-0.02960205078125,
-0.0252532958984375,
-0.026611328125,
0.0203857421875,
-0.0170440673828125,
-0.0186920166015625,
-0.005401611328125,
0.00579833984375,
0.020477294921875,
-0.039398193359375,
0.003173828125,
-0.00595855712890625,
0.034576416015625,
-0.0008072853088378906,
-0.0457763671875,
-0.001468658447265625,
-0.042755126953125,
0.00208282470703125,
-0.01499176025390625,
-0.00363922119140625,
-0.0007457733154296875,
0.00628662109375,
0.008270263671875,
0.0015840530395507812,
0.0222320556640625,
-0.0061798095703125,
0.0036106109619140625,
-0.02288818359375,
-0.020782470703125,
0.0030765533447265625,
0.02349853515625,
0.004779815673828125,
-0.01678466796875,
0.005748748779296875,
-0.01255035400390625,
-0.0013179779052734375,
-0.00968170166015625,
-0.0009675025939941406,
0.0310821533203125,
0.0081329345703125,
-0.01480865478515625,
0.06732177734375,
0.0292205810546875,
0.004741668701171875,
0.025909423828125,
0.0189666748046875,
0.003582000732421875,
0.0207977294921875,
-0.0091705322265625,
0.010986328125,
0.0193939208984375,
-0.020416259765625,
0.00258636474609375,
0.008392333984375,
-0.011199951171875,
0.017791748046875,
-0.018463134765625,
-0.00356292724609375,
0.0172882080078125,
0.01123809814453125,
0.0110015869140625,
0.0241546630859375,
0.0186767578125,
0.0231170654296875,
-0.008880615234375,
0.0122528076171875,
-0.0018558502197265625,
-0.001682281494140625,
-0.05126953125,
0.0447998046875,
0.012420654296875,
-0.021331787109375,
-0.019561767578125,
0.01678466796875,
0.022674560546875,
-0.01374053955078125,
-0.00855255126953125,
0.008544921875,
-0.019256591796875,
-0.015869140625,
-0.005680084228515625,
0.0252227783203125,
0.0007166862487792969,
0.028900146484375,
0.018585205078125,
-0.0221405029296875,
0.000027954578399658203,
-0.0263671875,
0.0031414031982421875,
0.061767578125,
-0.006404876708984375,
0.0196533203125,
-0.0172271728515625,
-0.0003514289855957031,
-0.004848480224609375,
-0.0016307830810546875,
0.01641845703125,
0.0295257568359375,
-0.00695037841796875,
0.017303466796875,
0.0063934326171875,
0.01666259765625,
-0.0156402587890625,
-0.01076507568359375,
-0.0017299652099609375,
0.0133056640625,
0.008148193359375,
-0.046478271484375,
0.0177001953125,
-0.02667236328125,
0.026275634765625,
0.00653839111328125,
0.00617218017578125,
0.0013275146484375,
0.0104217529296875,
-0.052001953125,
-0.0088348388671875,
-0.019622802734375,
0.037841796875,
-0.005214691162109375,
0.00562286376953125,
0.005649566650390625,
-0.01189422607421875,
0.0251617431640625,
0.017669677734375,
0.0079193115234375,
-0.00788116455078125,
-0.0394287109375,
-0.017974853515625,
0.0013370513916015625,
-0.007358551025390625,
-0.02484130859375,
0.01459503173828125,
-0.002017974853515625,
0.00662994384765625,
-0.00446319580078125,
0.02685546875,
0.007221221923828125,
-0.0032806396484375,
0.020416259765625,
-0.026031494140625,
0.0186767578125,
0.0015954971313476562,
0.01094818115234375,
-0.0008497238159179688,
-0.0450439453125,
-0.0125274658203125,
0.02789306640625,
-0.031585693359375,
-0.00519561767578125,
0.030029296875,
0.0022106170654296875,
0.016204833984375,
0.0294189453125,
-0.00811004638671875,
0.006671905517578125,
0.01517486572265625,
0.01617431640625,
0.0009937286376953125,
-0.00696563720703125,
-0.02642822265625,
0.027496337890625,
-0.000995635986328125,
0.01459503173828125,
0.0557861328125,
0.02716064453125,
0.0007143020629882812,
-0.01030731201171875,
-0.003589630126953125,
0.002155303955078125,
-0.014862060546875,
0.016448974609375,
-0.016937255859375,
-0.0023632049560546875,
-0.006015777587890625,
0.021728515625,
-0.0018167495727539062,
-0.0207366943359375,
0.019775390625,
-0.028167724609375,
-0.005298614501953125,
-0.0067596435546875,
-0.018157958984375,
-0.00005143880844116211,
-0.0025539398193359375,
-0.0287628173828125,
-0.01186370849609375,
0.00689697265625,
-0.005039215087890625,
-0.0259857177734375,
0.018951416015625,
-0.037567138671875,
0.0103912353515625,
-0.0128173828125,
0.0294952392578125,
0.021575927734375,
-0.004924774169921875,
-0.02679443359375,
-0.0153045654296875,
-0.0264434814453125,
-0.0251312255859375,
0.014801025390625,
0.0226898193359375,
0.007297515869140625,
-0.00728607177734375,
0.03631591796875,
0.00803375244140625,
0.00678253173828125,
0.0137786865234375,
-0.0199737548828125,
-0.022552490234375,
-0.04302978515625,
0.025115966796875,
-0.0269775390625,
0.0257720947265625,
-0.0008087158203125,
-0.0261383056640625,
0.0124664306640625,
-0.0011434555053710938,
-0.0124969482421875,
-0.0244140625,
0.00313568115234375,
-0.01690673828125,
0.001399993896484375,
0.00498199462890625,
0.01385498046875,
-0.034942626953125,
0.02886962890625,
0.0201873779296875,
-0.006404876708984375,
-0.03558349609375,
0.0017786026000976562,
0.040771484375,
-0.00434112548828125,
-0.016693115234375,
-0.01025390625,
-0.0084381103515625,
-0.0021610260009765625,
-0.039581298828125,
0.010833740234375,
0.0126953125,
-0.0276641845703125,
0.01155853271484375,
0.0167236328125,
-0.00507354736328125,
0.0025634765625,
0.0191650390625,
0.00702667236328125,
0.010833740234375,
-0.017608642578125,
-0.0201416015625,
0.0250396728515625,
0.01056671142578125,
0.0147705078125,
0.0247039794921875,
0.016082763671875,
-0.003387451171875,
-0.06597900390625,
0.01812744140625,
0.028564453125,
-0.0010824203491210938,
0.0249786376953125,
-0.0482177734375,
0.0088653564453125,
-0.0011539459228515625,
0.01471710205078125,
0.026092529296875,
0.0234222412109375,
0.0208587646484375,
0.008941650390625,
0.013824462890625,
-0.04071044921875,
0.0168914794921875,
0.0118255615234375,
-0.002727508544921875,
-0.0016927719116210938,
0.010833740234375,
-0.019287109375,
-0.032073974609375,
-0.00830841064453125,
0.006931304931640625,
-0.005809783935546875,
0.01512908935546875,
0.00994110107421875,
-0.03582763671875,
-0.0113677978515625,
0.007122039794921875,
-0.0002338886260986328,
0.00868988037109375,
0.0087432861328125,
0.01143646240234375,
-0.04547119140625,
0.04296875,
-0.00534820556640625,
0.0142822265625,
0.01381683349609375,
0.011474609375,
0.00545501708984375,
0.0197296142578125,
-0.01546478271484375,
0.00835418701171875,
-0.0014333724975585938,
0.01407623291015625,
0.00030231475830078125,
-0.0162506103515625,
-0.0020122528076171875,
-0.020904541015625,
-0.009490966796875,
-0.0020122528076171875,
-0.01641845703125,
0.03662109375,
-0.017242431640625,
0.01110076904296875,
0.01074981689453125,
-0.01036834716796875,
0.0028076171875,
-0.00501251220703125,
-0.00786590576171875,
-0.00524139404296875,
-0.045623779296875,
-0.0232391357421875,
0.0156707763671875,
-0.0275726318359375,
0.02886962890625,
0.00464630126953125,
-0.0121307373046875,
0.0062103271484375,
-0.01788330078125,
-0.0119171142578125,
-0.016204833984375,
-0.0007815361022949219,
0.01290130615234375,
-0.01502227783203125,
0.0152587890625,
-0.0005350112915039062,
-0.0247955322265625,
-0.01519775390625,
-0.01104736328125,
0.0364990234375,
0.0247802734375,
0.0126953125,
-0.0268402099609375,
0.0015411376953125,
-0.0089874267578125,
-0.0182037353515625,
-0.0213775634765625,
-0.0027008056640625,
0.02642822265625,
-0.0295257568359375,
-0.00927734375,
0.0231475830078125,
-0.0367431640625,
-0.0009212493896484375,
0.032623291015625,
0.033355712890625,
-0.005153656005859375,
-0.0241546630859375,
-0.002918243408203125,
0.0170745849609375,
-0.00339508056640625,
0.01065826416015625,
0.0013885498046875,
-0.00743865966796875,
-0.052337646484375,
0.033721923828125,
0.0056610107421875,
0.0060882568359375,
-0.0253448486328125,
-0.007205963134765625,
0.0082244873046875,
0.034423828125,
-0.00286865234375,
-0.00334930419921875,
0.0094757080078125,
-0.023468017578125,
0.0202484130859375,
-0.02410888671875,
0.021331787109375,
-0.0213470458984375,
-0.03240966796875,
-0.0112762451171875,
-0.0246734619140625,
-0.014801025390625,
0.0382080078125,
0.00577545166015625,
0.0033779144287109375,
0.0097808837890625,
0.0310516357421875,
-0.0177459716796875,
0.03204345703125,
-0.0274810791015625,
0.0235137939453125,
0.00811004638671875,
-0.0142974853515625,
0.002391815185546875,
0.006481170654296875,
-0.0156707763671875,
0.0193939208984375,
-0.036376953125,
0.01120758056640625,
-0.0253448486328125,
-0.0181427001953125,
-0.0039005279541015625,
-0.01263427734375,
0.02685546875,
-0.0169219970703125,
-0.0008921623229980469,
0.0014009475708007812,
-0.0011816024780273438,
-0.007312774658203125,
-0.0180511474609375,
0.0012712478637695312,
-0.005603790283203125,
-0.00959014892578125,
-0.025299072265625,
-0.035858154296875,
-0.0120086669921875,
-0.0198974609375,
-0.0002428293228149414,
-0.006435394287109375,
0.00962066650390625,
-0.03704833984375,
-0.007740020751953125,
0.003780364990234375,
0.03936767578125,
0.0008749961853027344,
-0.0012960433959960938,
-0.0310516357421875,
0.023895263671875,
-0.025909423828125,
-0.0192108154296875,
0.00965118408203125,
0.0103607177734375,
-0.005245208740234375,
0.0118560791015625,
0.0238037109375,
-0.0012073516845703125,
0.016387939453125,
-0.011077880859375,
0.00649261474609375,
-0.0234832763671875,
-0.017578125,
-0.00792694091796875,
-0.0186920166015625,
0.00453948974609375,
-0.006191253662109375,
-0.0309906005859375,
0.015380859375,
0.00543975830078125,
0.0127716064453125,
0.0232696533203125,
0.00681304931640625,
-0.06707763671875,
-0.001068115234375,
0.0189208984375,
0.00043892860412597656,
-0.01617431640625,
0.00004464387893676758,
-0.01325225830078125,
-0.01331329345703125,
-0.00263214111328125,
0.00469207763671875,
0.01016998291015625,
0.00884246826171875,
0.02056884765625,
0.03387451171875,
-0.04779052734375,
0.0240020751953125,
-0.01383209228515625,
0.0158843994140625,
0.053802490234375,
-0.0073089599609375,
-0.00496673583984375,
0.00750732421875,
0.016754150390625,
-0.027923583984375,
0.0010843276977539062,
-0.00601959228515625,
0.0138702392578125,
-0.0281829833984375,
0.00750732421875,
-0.0147247314453125,
0.01495361328125,
0.0168914794921875,
-0.009307861328125,
0.0167999267578125,
0.0169677734375,
0.0155029296875,
0.01641845703125,
0.0282745361328125,
0.0199127197265625,
0.02069091796875,
0.020843505859375,
-0.014923095703125,
0.029266357421875,
-0.03424072265625,
0.004791259765625,
0.00505828857421875,
0.007175445556640625,
-0.02178955078125,
0.05511474609375,
0.0015201568603515625,
0.0019626617431640625,
-0.003520965576171875,
-0.0202178955078125,
-0.006954193115234375,
0.0133056640625,
0.0046844482421875,
0.0181427001953125,
0.006862640380859375,
-0.020355224609375,
-0.01151275634765625,
-0.008392333984375,
-0.0261993408203125,
-0.0205535888671875,
0.000583648681640625,
0.0297393798828125,
0.027618408203125,
-0.02166748046875,
0.00421142578125,
-0.0531005859375,
0.021697998046875,
-0.0075531005859375,
0.03076171875,
-0.0204010009765625,
-0.0094451904296875,
0.0247650146484375,
0.0159759521484375,
-0.00304412841796875,
-0.0017452239990234375,
-0.01226043701171875,
-0.0592041015625,
-0.01401519775390625,
0.0144500732421875,
0.0015230178833007812,
-0.031402587890625,
0.005908966064453125,
-0.0193023681640625,
0.0281524658203125,
-0.024139404296875,
-0.03143310546875,
-0.0008301734924316406,
-0.01708984375,
0.0179443359375,
-0.016937255859375,
0.0248565673828125,
-0.01177978515625,
0.004734039306640625,
-0.0018768310546875,
-0.0025634765625,
-0.005523681640625,
-0.024383544921875,
0.0091705322265625,
-0.039764404296875,
0.0272674560546875,
-0.01267242431640625,
0.021392822265625,
0.0167388916015625,
-0.0228424072265625,
0.01303863525390625,
0.002872467041015625,
0.01377105712890625,
-0.0251922607421875,
0.0187225341796875,
0.010467529296875,
-0.0081939697265625,
-0.00843048095703125,
0.002216339111328125,
-0.0220184326171875,
0.00994873046875,
0.02801513671875,
-0.01171112060546875,
-0.000031054019927978516,
-0.010345458984375,
0.008270263671875,
0.005779266357421875,
-0.046722412109375,
0.00701904296875,
0.0105438232421875,
0.01041412353515625,
-0.0085601806640625,
-0.017486572265625,
0.015411376953125,
0.01335906982421875,
-0.0183563232421875,
-0.0031299591064453125,
-0.0069732666015625,
-0.04925537109375,
-0.01062774658203125,
-0.0012159347534179688,
-0.0187530517578125,
-0.00797271728515625,
0.029937744140625,
0.005321502685546875,
-0.0235443115234375,
-0.026611328125,
-0.0153045654296875,
-0.0235748291015625,
0.0019092559814453125,
0.00017368793487548828,
0.0240936279296875,
-0.016265869140625,
0.052734375,
-0.01082611083984375,
-0.016204833984375,
0.0264434814453125,
0.01474761962890625,
-0.01073455810546875,
-0.0140533447265625,
0.0008897781372070312,
-0.034027099609375,
0.006038665771484375,
0.00801849365234375,
-0.005462646484375,
-0.041259765625,
0.0130615234375,
-0.004970550537109375,
-0.01122283935546875,
0.043609619140625,
0.0122833251953125,
0.0118560791015625,
0.0268707275390625,
0.02264404296875,
0.00994873046875,
0.002826690673828125,
-0.0261383056640625,
-0.0118408203125,
0.0188140869140625,
-0.00039839744567871094,
0.0195770263671875,
0.002063751220703125,
-0.005313873291015625,
-0.054718017578125,
-0.041534423828125,
0.0017194747924804688,
-0.0240478515625,
-0.0254669189453125,
-0.008819580078125,
-0.0024051666259765625,
0.0135040283203125,
-0.0211944580078125,
0.036407470703125,
0.03155517578125,
0.01561737060546875,
0.0092010498046875,
-0.01515960693359375,
-0.01641845703125,
-0.0012531280517578125,
0.033782958984375,
-0.007305145263671875,
-0.01233673095703125,
-0.01067352294921875,
0.00798797607421875,
-0.006313323974609375,
-0.031768798828125,
-0.0089874267578125,
0.026702880859375,
-0.005237579345703125,
-0.034637451171875,
-0.0582275390625,
0.016204833984375,
0.051788330078125,
-0.0220489501953125,
-0.01552581787109375,
-0.003200531005859375,
-0.0103302001953125,
-0.004901885986328125,
0.004138946533203125,
0.01128387451171875,
0.0090789794921875,
-0.013763427734375,
0.0041351318359375,
0.00586700439453125,
0.058319091796875,
-0.02978515625,
-0.0083770751953125,
0.01480865478515625,
0.0089874267578125,
-0.03533935546875,
-0.011505126953125,
-0.023223876953125,
0.038726806640625,
0.01110076904296875,
0.004604339599609375,
-0.0146484375,
0.0035419464111328125,
0.004138946533203125,
-0.0286102294921875,
0.0182342529296875,
-0.02313232421875,
0.015350341796875,
-0.0081787109375,
0.036834716796875,
0.01108551025390625,
0.0238189697265625,
-0.00571441650390625,
-0.0169219970703125,
0.018402099609375,
0.01751708984375,
0.0170440673828125,
-0.0078277587890625,
-0.0003933906555175781,
-0.0016994476318359375,
-0.00675201416015625,
0.01207733154296875,
-0.0040435791015625,
0.00030875205993652344,
-0.0248870849609375,
-0.0027332305908203125,
-0.0043182373046875,
0.00014460086822509766,
0.0158843994140625,
0.0283660888671875,
-0.016571044921875,
0.0288848876953125,
0.0291748046875,
0.01006317138671875,
0.010833740234375,
-0.0231170654296875,
-0.022186279296875,
-0.0322265625,
0.01751708984375,
0.004276275634765625,
-0.00441741943359375,
-0.0435791015625,
0.0194549560546875,
-0.004547119140625,
-0.0041351318359375,
0.0164031982421875,
0.024749755859375,
-0.00939178466796875,
-0.02044677734375,
-0.018524169921875,
-0.0140228271484375,
0.01039886474609375,
0.04425048828125,
-0.005405426025390625,
0.00415802001953125,
0.008514404296875,
-0.0445556640625,
-0.0005445480346679688,
-0.021575927734375,
-0.0211181640625,
0.0271453857421875,
-0.020843505859375,
-0.0009760856628417969,
-0.0155029296875,
0.0023174285888671875,
0.040740966796875,
-0.0089263916015625,
0.018829345703125,
-0.00823211669921875,
0.030731201171875,
0.0083160400390625,
-0.01319122314453125,
0.021514892578125,
-0.00594329833984375,
-0.0013837814331054688,
0.01129150390625,
0.012542724609375,
-0.035369873046875,
-0.019317626953125,
0.0413818359375,
-0.007488250732421875,
-0.017669677734375,
0.0210723876953125,
-0.003292083740234375,
-0.0125274658203125,
0.01090240478515625,
-0.0100860595703125,
0.0002682209014892578,
0.0189666748046875,
0.01155853271484375,
0.0015897750854492188,
0.01617431640625,
-0.0187530517578125,
0.00457763671875,
0.03167724609375,
-0.03826904296875,
-0.00513458251953125,
-0.026214599609375,
0.0305938720703125,
-0.0178070068359375,
-0.0290069580078125,
0.0081024169921875,
-0.041046142578125,
-0.021331787109375,
0.01800537109375,
0.022064208984375,
0.0396728515625,
0.028656005859375,
-0.0129241943359375,
-0.0157012939453125,
0.01126861572265625,
-0.01806640625,
0.0187530517578125,
0.016845703125,
0.004932403564453125,
-0.00925445556640625,
-0.02044677734375,
-0.006084442138671875,
-0.0228271484375,
-0.01611328125,
0.01541900634765625,
-0.0195159912109375,
-0.005035400390625,
-0.0210723876953125,
-0.007129669189453125,
0.002071380615234375,
-0.0193328857421875,
-0.0185089111328125,
0.023834228515625,
0.01001739501953125,
0.00974273681640625,
-0.026824951171875,
0.01178741455078125,
-0.0239410400390625,
-0.019805908203125,
0.026611328125,
-0.0000152587890625,
0.0018243789672851562,
0.033355712890625,
0.00811767578125,
-0.0223846435546875,
0.0037250518798828125,
0.017242431640625,
0.004756927490234375,
0.0225372314453125,
0.0036220550537109375,
0.0227508544921875,
0.015350341796875,
-0.0078887939453125,
-0.0025768280029296875,
-0.004131317138671875,
0.0016012191772460938,
-0.00940704345703125,
0.0190582275390625,
-0.014801025390625,
-0.0078582763671875,
0.011993408203125,
-0.01262664794921875,
0.036651611328125,
-0.0013523101806640625,
0.0189971923828125,
0.005767822265625,
0.01513671875,
0.035552978515625,
0.03131103515625,
-0.027587890625,
0.00665283203125,
-0.01409912109375,
0.01470184326171875,
-0.0084075927734375,
0.0089111328125,
-0.059967041015625,
0.004314422607421875,
-0.00946807861328125,
-0.003582000732421875,
0.017974853515625,
-0.004302978515625,
-0.0362548828125,
0.019439697265625,
-0.06365966796875,
0.01284027099609375,
0.01513671875,
0.050384521484375,
0.0005998611450195312,
0.01129150390625,
0.001087188720703125,
0.0017414093017578125,
-0.01104736328125,
-0.01453399658203125,
0.008392333984375,
-0.0011653900146484375,
-0.0158538818359375,
-0.015960693359375,
-0.0007991790771484375,
-0.006198883056640625,
0.007488250732421875,
-0.037811279296875,
0.01230621337890625,
0.033050537109375,
0.0079498291015625,
-0.01529693603515625,
0.00286102294921875,
0.01029205322265625,
-0.0207366943359375,
0.0206451416015625,
0.0213165283203125,
0.01161956787109375,
0.003875732421875,
-0.00727081298828125,
-0.009185791015625,
-0.0173187255859375,
-0.019989013671875,
0.0016956329345703125,
0.01537322998046875,
-0.00279998779296875,
0.0023250579833984375,
0.00444793701171875,
-0.0015010833740234375,
0.0167236328125,
0.01332855224609375,
-0.0037517547607421875,
0.006961822509765625,
-0.00989532470703125,
-0.0163116455078125,
0.004230499267578125,
-0.033905029296875,
0.015960693359375,
0.0156097412109375,
-0.0184326171875,
0.0209197998046875,
-0.0201263427734375,
-0.0123748779296875,
-0.0204010009765625,
-0.003040313720703125,
0.0152740478515625,
0.00603485107421875,
-0.05072021484375,
0.0014438629150390625,
0.0181884765625,
0.021087646484375,
0.03790283203125,
-0.01537322998046875,
0.00391387939453125,
0.037567138671875,
0.014404296875,
0.0229949951171875,
0.01261138916015625,
0.0238189697265625,
-0.0146484375,
-0.00397491455078125,
-0.0238800048828125,
-0.0062255859375,
-0.007411956787109375,
0.0015668869018554688,
0.000995635986328125,
0.01180267333984375,
-0.01345062255859375,
0.00241851806640625,
0.0037441253662109375,
0.00466156005859375,
-0.006801605224609375,
0.0034809112548828125,
0.01042938232421875,
-0.006011962890625,
0.0010499954223632812,
0.0027256011962890625,
0.0458984375,
-0.00302886962890625,
0.00125885009765625,
-0.005741119384765625,
0.0040283203125,
-0.01226043701171875,
0.0156097412109375,
-0.035430908203125,
-0.0079498291015625,
-0.0040435791015625,
0.0014181137084960938,
-0.019073486328125,
-0.0009236335754394531,
0.0140533447265625,
-0.04534912109375,
-0.0025005340576171875,
-0.003551483154296875,
-0.01421356201171875,
0.0025768280029296875,
-0.0372314453125,
-0.0058135986328125,
0.0032176971435546875,
0.01233673095703125,
0.0230712890625,
-0.004978179931640625,
0.0004930496215820312,
-0.0270843505859375,
0.02008056640625,
0.035064697265625,
0.01470947265625,
0.0270538330078125,
-0.000988006591796875,
0.0246429443359375,
-0.007213592529296875,
-0.0369873046875,
0.0011043548583984375,
0.00543975830078125,
0.0088653564453125,
-0.00875091552734375,
0.01062774658203125,
-0.007648468017578125,
-0.0250091552734375,
0.003314971923828125,
-0.0029201507568359375,
0.012115478515625,
-0.0179901123046875,
-0.01468658447265625,
0.0078887939453125,
-0.006031036376953125,
-0.0263671875,
0.007843017578125,
-0.0082855224609375,
0.0225830078125,
-0.0021820068359375,
0.0186309814453125,
0.00873565673828125,
0.0007929801940917969,
-0.019683837890625,
0.0036830902099609375,
-0.0028514862060546875,
-0.006622314453125,
0.0294647216796875,
0.0006403923034667969,
-0.0267333984375,
0.01153564453125,
0.0301055908203125,
0.0198974609375,
-0.0007810592651367188,
0.01971435546875,
0.058380126953125,
-0.0029277801513671875,
0.028289794921875,
-0.01160430908203125,
-0.0011081695556640625,
-0.019866943359375,
-0.00936126708984375,
0.0292510986328125,
0.019927978515625,
-0.037567138671875,
0.0281219482421875,
-0.0022430419921875,
0.033172607421875,
0.035858154296875,
-0.00429534912109375,
0.0284423828125,
0.0192108154296875,
0.0032806396484375,
-0.00293731689453125,
0.00635528564453125,
-0.0302581787109375,
0.003692626953125,
0.01070404052734375,
-0.0254058837890625,
-0.04620361328125,
0.003582000732421875,
0.0198211669921875,
-0.0160675048828125,
0.00634765625,
-0.0236968994140625,
-0.01311492919921875,
0.01311492919921875,
-0.0010366439819335938,
0.0147247314453125,
0.027587890625,
0.016082763671875,
-0.0131072998046875,
0.007648468017578125,
-0.0193328857421875,
0.0047149658203125,
-0.0195159912109375,
0.019439697265625,
0.01224517822265625,
0.0121612548828125,
0.00899505615234375,
0.0164031982421875,
-0.017303466796875,
-0.003955841064453125,
-0.01024627685546875,
0.011962890625,
0.02642822265625,
-0.0035648345947265625,
-0.0377197265625,
0.004833221435546875,
0.0108795166015625,
-0.00023353099822998047,
-0.0243377685546875,
0.01004791259765625,
-0.000019252300262451172,
0.024658203125,
0.036285400390625,
-0.013092041015625,
0.0318603515625,
0.005191802978515625,
0.0289459228515625,
-0.0026569366455078125,
-0.00991058349609375,
-0.01467132568359375,
-0.0196533203125,
-0.02569580078125,
-0.02838134765625,
0.004276275634765625,
0.03326416015625,
-0.0166015625,
-0.018310546875,
-0.036376953125,
-0.0303802490234375,
0.0197906494140625,
-0.0019683837890625,
-0.0008883476257324219,
-0.00701904296875,
-0.0288848876953125,
-0.0057525634765625,
0.004947662353515625,
0.0075225830078125,
0.03375244140625,
-0.025665283203125,
-0.02197265625,
-0.00818634033203125,
-0.0073699951171875,
0.016571044921875,
0.01074981689453125,
0.024627685546875,
-0.00788116455078125,
-0.00902557373046875,
-0.020721435546875,
0.0312042236328125,
0.01474761962890625,
0.034149169921875,
-0.00890350341796875,
0.009613037109375,
-0.006999969482421875,
-0.0399169921875,
0.031524658203125,
-0.004058837890625,
-0.01213836669921875,
0.005893707275390625,
-0.0523681640625,
-0.01953125,
0.0177764892578125,
-0.04449462890625,
-0.023956298828125,
0.0016298294067382812,
0.00787353515625,
-0.01332855224609375,
0.01042938232421875,
0.034149169921875,
-0.0355224609375,
-0.061431884765625,
0.036834716796875,
0.007656097412109375,
-0.0136566162109375,
-0.01560211181640625,
0.005908966064453125,
0.027435302734375,
-0.0038318634033203125,
0.00820159912109375,
-0.0200958251953125,
-0.01593017578125,
0.015655517578125,
-0.0166168212890625,
-0.057647705078125,
-0.02685546875,
0.025238037109375,
0.01470184326171875,
-0.0027408599853515625,
0.048614501953125,
-0.006336212158203125,
0.0202178955078125,
-0.01297760009765625,
-0.014801025390625,
-0.0185546875,
0.006313323974609375,
0.036651611328125,
0.023895263671875,
-0.0284423828125,
0.032989501953125,
-0.034393310546875,
-0.00606536865234375,
-0.0018930435180664062,
-0.0088043212890625,
-0.01285552978515625,
-0.00208282470703125,
0.0272979736328125,
0.015960693359375,
0.02398681640625,
0.0149078369140625,
-0.0150604248046875,
0.0028781890869140625,
0.0256195068359375,
0.0034637451171875,
0.0031108856201171875,
-0.037017822265625,
0.04229736328125,
0.004375457763671875,
-0.003387451171875,
0.007709503173828125,
0.0234375,
-0.022247314453125,
-0.006252288818359375,
0.0032596588134765625,
-0.0128326416015625,
0.0284881591796875,
0.0093994140625,
0.02362060546875,
0.01468658447265625,
0.010009765625,
-0.0167236328125,
0.0031681060791015625,
0.01386260986328125,
0.05560302734375,
0.020721435546875,
-0.00583648681640625,
0.0293731689453125,
-0.025177001953125,
-0.0287933349609375,
-0.00009363889694213867,
-0.0218048095703125,
-0.019073486328125,
0.0019254684448242188,
-0.017669677734375,
-0.0285491943359375,
0.0325927734375,
-0.02081298828125,
0.03302001953125,
0.00457000732421875,
-0.017822265625,
0.004364013671875,
-0.00707244873046875,
0.026519775390625,
0.009063720703125,
0.0033893585205078125,
0.0078277587890625,
0.0118865966796875,
-0.009796142578125,
-0.01297760009765625,
0.016387939453125,
0.0074615478515625,
-0.00855255126953125,
0.0135040283203125,
0.0290679931640625,
-0.007152557373046875,
0.01556396484375,
0.028411865234375,
0.0230560302734375,
-0.0028171539306640625,
0.0164337158203125,
-0.0202789306640625,
0.0039005279541015625,
-0.004398345947265625,
0.01727294921875,
0.0219573974609375,
-0.01079559326171875,
0.0279388427734375,
-0.00406646728515625,
-0.0274658203125,
0.00662994384765625,
0.009124755859375,
-0.0208892822265625,
-0.00746917724609375,
-0.015350341796875,
-0.0252838134765625,
-0.0264892578125,
-0.0260009765625,
-0.0236358642578125,
0.0158538818359375,
-0.028289794921875,
-0.0192108154296875,
0.02655029296875,
-0.029205322265625,
-0.00600433349609375,
0.00823974609375,
-0.036590576171875,
-0.016815185546875,
0.0034198760986328125,
-0.00919342041015625,
0.0259552001953125,
-0.01262664794921875,
-0.005344390869140625,
-0.0003616809844970703,
-0.0131988525390625,
-0.0110015869140625,
-0.01227569580078125,
-0.01898193359375,
-0.0046234130859375,
-0.0467529296875,
-0.00817108154296875,
-0.0026531219482421875,
0.034820556640625,
0.031341552734375,
0.0013675689697265625,
0.0011272430419921875,
-0.031951904296875,
0.0090179443359375,
0.0065460205078125,
-0.0014801025390625,
-0.0268096923828125,
-0.0276031494140625,
0.00885009765625,
-0.02197265625,
-0.0232086181640625,
0.0018749237060546875,
-0.028350830078125,
0.0062713623046875,
-0.0164642333984375,
-0.017364501953125,
-0.0226898193359375,
-0.0218048095703125,
0.01363372802734375,
0.002288818359375,
-0.0245819091796875,
-0.0152130126953125,
0.0294036865234375,
0.0225067138671875,
-0.01708984375,
0.0020923614501953125,
0.0628662109375,
0.0097808837890625,
-0.0015172958374023438,
0.006267547607421875,
0.0198516845703125,
0.0184173583984375,
0.0012750625610351562,
-0.0106048583984375,
-0.023162841796875,
0.0058746337890625,
-0.0143585205078125,
0.02777099609375,
-0.040863037109375,
-0.042999267578125,
0.03985595703125,
-0.019012451171875,
-0.0195465087890625,
0.00469207763671875,
-0.0176849365234375,
0.01715087890625,
-0.0212860107421875,
-0.008209228515625,
-0.0277252197265625,
0.033538818359375,
0.00676727294921875,
0.045928955078125,
-0.01114654541015625,
0.033355712890625,
0.0153045654296875,
-0.035125732421875,
-0.0006799697875976562,
0.02056884765625,
0.0013875961303710938,
-0.0330810546875,
0.01511383056640625,
-0.000598907470703125,
-0.01129913330078125,
0.009765625,
-0.03289794921875,
0.0203094482421875,
0.01552581787109375,
-0.019775390625,
-0.0290069580078125,
-0.000759124755859375,
0.0008301734924316406,
-0.01345062255859375,
0.01226043701171875,
-0.03289794921875,
-0.0167999267578125,
0.0133514404296875,
-0.007457733154296875,
0.004486083984375,
-0.01013946533203125,
-0.0028076171875,
-0.0167236328125,
0.01812744140625,
-0.019256591796875,
0.01422882080078125,
0.03472900390625,
0.00206756591796875,
0.036865234375,
-0.0162811279296875,
0.0291290283203125,
0.024169921875,
-0.04010009765625,
0.006931304931640625,
-0.005764007568359375,
0.00848388671875,
0.0036258697509765625,
0.02935791015625,
-0.00989532470703125,
-0.00800323486328125,
-0.0181427001953125,
-0.0033435821533203125,
-0.005146026611328125,
-0.0255126953125,
0.0081787109375,
-0.0121612548828125,
-0.005702972412109375,
-0.03570556640625,
-0.0016050338745117188,
0.0027256011962890625,
0.00505828857421875,
0.004276275634765625,
0.0038928985595703125,
-0.027801513671875,
0.048370361328125,
0.012115478515625,
-0.05157470703125,
0.00672149658203125,
-0.001079559326171875,
0.0121002197265625,
0.007389068603515625,
-0.01436614990234375,
-0.0013685226440429688,
0.0090484619140625,
-0.030670166015625,
0.00031256675720214844,
-0.022735595703125,
-0.0038509368896484375,
-0.00502777099609375,
-0.000008404254913330078,
0.008575439453125,
-0.0121612548828125,
-0.0107879638671875,
-0.00024819374084472656,
-0.030670166015625,
0.006317138671875,
0.0000718235969543457,
0.04254150390625,
-0.0288543701171875,
0.01044464111328125,
0.0191497802734375,
-0.007640838623046875,
0.029632568359375,
-0.01378631591796875,
0.01666259765625,
-0.00981903076171875,
0.01462554931640625,
-0.01385498046875,
0.031768798828125,
0.0396728515625,
-0.0014390945434570312,
-0.01080322265625,
-0.01580810546875,
-0.0193634033203125,
-0.0021839141845703125,
-0.0193939208984375,
-0.00780487060546875,
0.01256561279296875,
-0.0118560791015625,
0.03179931640625,
-0.00475311279296875,
-0.04644775390625,
-0.01629638671875,
-0.006717681884765625,
0.04119873046875,
-0.009735107421875,
-0.03387451171875,
0.034942626953125,
0.01204681396484375,
-0.018035888671875,
-0.025146484375,
0.006816864013671875,
0.008544921875,
0.00592803955078125,
-0.0110626220703125,
-0.0287933349609375,
-0.02178955078125,
0.027099609375,
0.032257080078125,
0.0004963874816894531,
-0.02789306640625,
0.00920867919921875,
0.0170135498046875,
-0.016998291015625,
-0.01544952392578125,
0.004238128662109375,
0.01453399658203125,
0.0008478164672851562,
-0.04107666015625,
-0.037200927734375,
-0.00919342041015625,
-0.01348114013671875,
-0.0211334228515625,
0.0017642974853515625,
-0.002288818359375,
0.0127716064453125,
-0.0142059326171875,
0.01522064208984375,
0.004344940185546875,
-0.055877685546875,
-0.018646240234375,
0.0227203369140625,
0.00074005126953125,
-0.0028285980224609375,
0.029083251953125,
-0.037261962890625,
0.0211639404296875,
0.02056884765625,
0.0190277099609375,
-0.00466156005859375,
0.01532745361328125,
0.0062255859375,
-0.004413604736328125,
0.00154876708984375,
-0.04150390625,
0.0155792236328125,
0.037078857421875,
-0.007110595703125,
0.011505126953125,
-0.00525665283203125,
0.051544189453125,
-0.00759124755859375,
-0.0019931793212890625,
-0.0160064697265625,
0.01019287109375,
0.0010156631469726562,
-0.03515625,
0.0246429443359375,
-0.0338134765625,
-0.01462554931640625,
0.025909423828125,
-0.0048370361328125,
0.00862884521484375,
-0.00798797607421875,
-0.020111083984375,
0.0030422210693359375,
-0.023651123046875,
0.002147674560546875,
-0.021331787109375,
-0.006877899169921875,
-0.01505279541015625,
-0.0014619827270507812,
-0.00406646728515625,
0.01031494140625,
-0.004222869873046875,
-0.031829833984375,
-0.004764556884765625,
0.007274627685546875,
-0.032379150390625,
-0.01485443115234375,
-0.004688262939453125,
-0.0404052734375,
-0.00882720947265625,
0.0296478271484375,
-0.01026153564453125,
0.0188140869140625,
0.00013589859008789062,
0.0044708251953125,
0.0229949951171875,
0.01375579833984375,
0.0031414031982421875,
-0.006793975830078125,
-0.0004112720489501953,
0.017608642578125,
-0.0172576904296875,
0.017547607421875,
-0.0176239013671875,
-0.00875091552734375,
0.0159149169921875,
-0.00939178466796875,
-0.02227783203125,
-0.031158447265625,
0.006420135498046875,
0.0189056396484375,
-0.021392822265625,
0.005245208740234375,
0.01422882080078125,
-0.00882720947265625,
-0.005352020263671875,
-0.01788330078125,
-0.0055389404296875,
0.004680633544921875,
-0.01128387451171875,
-0.003437042236328125,
-0.0157012939453125,
-0.0239715576171875,
0.00751495361328125,
-0.01177978515625,
0.01371002197265625,
-0.034271240234375,
-0.009490966796875,
-0.01491546630859375,
-0.003696441650390625,
-0.007648468017578125,
0.0229949951171875,
-0.005588531494140625,
0.022125244140625,
0.009521484375,
0.00981903076171875,
0.03173828125,
-0.0030670166015625,
-0.050323486328125,
0.00478363037109375,
0.01141357421875,
0.034393310546875,
-0.0305938720703125,
-0.00547027587890625,
-0.0281829833984375,
0.031646728515625,
0.04241943359375,
0.00930023193359375,
0.006000518798828125,
0.034698486328125,
-0.0267791748046875,
-0.0214996337890625,
0.039459228515625,
0.004108428955078125,
-0.017059326171875,
0.01235198974609375,
0.00447845458984375,
-0.043121337890625,
-0.0179595947265625,
0.019989013671875,
0.000018417835235595703,
0.01092529296875,
-0.00946044921875,
-0.01079559326171875,
-0.01071929931640625,
-0.004749298095703125,
0.0165557861328125,
-0.028167724609375,
0.00872802734375,
0.044830322265625,
-0.0281829833984375,
0.0008320808410644531,
0.0265655517578125,
-0.0131683349609375,
-0.01377105712890625,
-0.0139923095703125,
0.042938232421875,
0.0244598388671875,
0.00954437255859375,
-0.00936126708984375,
-0.01371002197265625,
0.00437164306640625,
-0.0146026611328125,
0.01018524169921875,
-0.0145263671875,
0.004291534423828125,
-0.0263214111328125,
0.01285552978515625,
-0.0228424072265625,
-0.006961822509765625,
0.025909423828125,
-0.0242462158203125,
-0.028350830078125,
-0.01068115234375,
0.01270294189453125,
-0.0267333984375,
-0.00444793701171875,
0.0177459716796875,
-0.038299560546875,
-0.02886962890625,
0.0130462646484375,
-0.0215606689453125,
0.00959014892578125,
0.01447296142578125,
0.0100860595703125,
0.01093292236328125,
-0.008758544921875,
0.026458740234375,
-0.00273895263671875,
0.0014066696166992188,
0.0079345703125,
-0.026519775390625,
0.0024566650390625,
-0.0308380126953125,
-0.01534271240234375,
-0.0146026611328125,
-0.00445556640625,
-0.00472259521484375,
0.00238037109375,
-0.02374267578125,
0.013153076171875,
0.02618408203125,
0.00897979736328125,
-0.025360107421875,
0.002414703369140625,
-0.0239410400390625,
-0.0192413330078125,
0.004222869873046875,
0.023223876953125,
-0.01068878173828125,
-0.0173492431640625,
0.007434844970703125,
-0.0056304931640625,
-0.020751953125,
-0.004550933837890625,
-0.0382080078125,
0.03564453125,
0.0014820098876953125,
-0.0240325927734375,
0.0150299072265625,
0.0249786376953125,
-0.00960540771484375,
0.01058197021484375,
0.029754638671875,
-0.02032470703125,
-0.0017900466918945312,
0.0019092559814453125,
-0.0225830078125,
0.00977325439453125,
0.025726318359375,
0.0166473388671875,
0.00140380859375,
0.005859375,
0.01065826416015625,
-0.00562286376953125,
-0.0186309814453125,
-0.03955078125,
0.04559326171875,
0.0007276535034179688,
0.012664794921875,
-0.0024566650390625,
-0.03045654296875,
-0.01494598388671875,
0.00861358642578125,
-0.016571044921875,
-0.04541015625,
-0.0054779052734375,
0.0191497802734375,
0.01214599609375,
0.052459716796875,
0.01464080810546875,
0.000042319297790527344,
0.0004887580871582031,
0.039031982421875,
-0.01617431640625,
0.005634307861328125,
0.01232147216796875,
0.00809478759765625,
-0.00029158592224121094,
0.0044097900390625,
0.01071929931640625,
-0.0022678375244140625,
-0.0264434814453125,
-0.0175628662109375,
-0.00440216064453125,
-0.01097869873046875,
0.00399017333984375,
0.00296783447265625,
0.0202484130859375,
0.044342041015625,
0.003925323486328125,
0.0234222412109375,
-0.05450439453125,
0.03363037109375,
0.001811981201171875,
0.022735595703125,
-0.0296783447265625,
-0.0215911865234375,
-0.0149688720703125,
-0.00943756103515625,
0.01025390625,
0.005390167236328125,
0.0198211669921875,
-0.035858154296875,
0.005611419677734375,
0.0208587646484375,
0.00585174560546875,
-0.01221466064453125,
-0.0176544189453125,
0.0012874603271484375,
-0.00907135009765625,
0.020111083984375,
0.015960693359375,
-0.0253448486328125,
0.014190673828125,
-0.005596160888671875,
0.018768310546875,
0.004383087158203125,
0.035247802734375,
0.0196380615234375,
-0.00066375732421875,
0.0117950439453125,
-0.01611328125,
-0.0004787445068359375,
0.00115966796875,
-0.0006723403930664062,
-0.0009212493896484375,
-0.02374267578125,
-0.0078125,
0.0223541259765625,
0.00954437255859375,
0.028533935546875,
0.0029850006103515625,
-0.012603759765625,
0.037261962890625,
-0.020294189453125,
-0.0101470947265625,
-0.0084991455078125,
-0.0033817291259765625,
-0.01480865478515625,
-0.01375579833984375,
0.0307769775390625,
-0.04864501953125,
-0.00848388671875,
-0.0032253265380859375,
0.019866943359375,
-0.0316162109375,
0.022247314453125,
0.015045166015625,
0.01885986328125,
0.032958984375,
-0.009796142578125,
-0.00699615478515625,
-0.0008883476257324219,
-0.02313232421875,
-0.03338623046875,
0.0039215087890625,
-0.00849151611328125,
0.013153076171875,
0.006671905517578125,
-0.017608642578125,
-0.03082275390625,
0.004962921142578125,
-0.0002932548522949219,
-0.036041259765625,
0.006526947021484375,
0.0086669921875,
0.0271759033203125,
0.0239715576171875,
0.0193328857421875,
0.012908935546875,
0.00763702392578125,
0.0273284912109375,
0.0028247833251953125,
-0.0193634033203125,
-0.021087646484375,
-0.0132904052734375,
-0.03289794921875,
-0.01302337646484375,
-0.0169525146484375,
-0.0267181396484375,
-0.038299560546875,
-0.0187835693359375,
-0.006946563720703125,
-0.011962890625,
0.0007624626159667969,
-0.01751708984375,
-0.0217742919921875,
-0.00754547119140625,
-0.0189666748046875,
0.01120758056640625,
0.0275726318359375,
-0.002925872802734375,
-0.00916290283203125,
0.0156402587890625,
0.0008382797241210938,
-0.002948760986328125,
0.01152801513671875,
0.014068603515625,
0.01097869873046875,
0.0108184814453125,
0.0018558502197265625,
0.004344940185546875,
0.01134490966796875,
-0.001209259033203125,
-0.0236053466796875,
0.01178741455078125,
0.033172607421875,
-0.029083251953125,
0.0019512176513671875,
0.007450103759765625,
0.0101470947265625,
-0.00952911376953125,
-0.0099334716796875,
0.001056671142578125,
0.0108795166015625,
0.008453369140625,
0.002094268798828125,
-0.0215301513671875,
0.00567626953125,
-0.030914306640625,
0.033599853515625,
-0.02850341796875,
-0.01000213623046875,
-0.010345458984375,
-0.03485107421875,
-0.0309600830078125,
-0.00919342041015625,
0.02618408203125,
0.0250091552734375,
-0.0108795166015625,
0.02734375,
-0.0264892578125,
-0.044952392578125,
-0.00211334228515625,
0.029205322265625,
0.0075531005859375,
-0.0087127685546875,
-0.01018524169921875,
0.006977081298828125,
0.0181732177734375,
-0.0217437744140625,
-0.005764007568359375,
-0.0003044605255126953,
-0.0117950439453125,
-0.00203704833984375,
0.00838470458984375,
-0.032379150390625,
0.01898193359375,
0.01303863525390625,
-0.003284454345703125,
0.00904083251953125,
0.00408935546875,
0.01141357421875,
0.00527191162109375,
-0.00001811981201171875,
-0.0277099609375,
-0.042266845703125,
-0.030242919921875,
0.034515380859375,
-0.0001728534698486328,
-0.0213775634765625,
-0.0191192626953125,
-0.01496124267578125,
-0.007740020751953125,
-0.0155181884765625,
0.026153564453125,
0.0157928466796875,
-0.00977325439453125,
-0.010040283203125,
0.05548095703125,
0.050933837890625,
0.04254150390625,
0.0074005126953125,
0.027374267578125,
0.005222320556640625,
0.009063720703125,
0.0092010498046875,
0.02117919921875,
0.021209716796875,
0.0025787353515625,
0.012664794921875,
0.000728607177734375,
0.01491546630859375,
-0.0011682510375976562,
-0.009490966796875,
-0.004730224609375,
-0.0100860595703125,
0.00899505615234375,
-0.0208587646484375,
-0.036285400390625,
0.044464111328125,
0.017578125,
-0.012359619140625,
0.020538330078125,
-0.01421356201171875,
-0.0199432373046875,
0.026519775390625,
0.0295562744140625,
-0.0168914794921875,
0.0022716522216796875,
0.006893157958984375,
-0.000001430511474609375,
0.0191802978515625,
-0.042694091796875,
-0.029510498046875,
-0.0010938644409179688,
-0.00313568115234375,
0.0184326171875,
-0.03936767578125,
0.0122833251953125,
0.0233306884765625,
0.007404327392578125,
0.026092529296875,
0.007843017578125,
-0.0008029937744140625,
0.0205230712890625,
-0.030517578125,
-0.0164337158203125,
-0.0201416015625,
0.0054168701171875,
-0.00785064697265625,
0.008575439453125,
0.01387786865234375,
-0.0238800048828125,
-0.005268096923828125,
-0.010101318359375,
0.0018625259399414062,
0.01293182373046875,
-0.0286712646484375,
-0.0187530517578125,
-0.01100921630859375,
-0.0194244384765625,
0.035888671875,
-0.0389404296875,
0.01032257080078125,
0.019439697265625,
-0.004871368408203125,
0.032012939453125,
0.0218505859375,
-0.02777099609375,
0.00791168212890625,
-0.0036144256591796875,
0.0283966064453125,
-0.0030517578125,
0.0242462158203125,
0.0302734375,
-0.0002079010009765625,
0.0252532958984375,
-0.01331329345703125,
0.0233917236328125,
0.0275421142578125,
-0.043670654296875,
0.0302886962890625,
0.0179595947265625,
-0.01287841796875,
0.0518798828125,
-0.0018148422241210938,
0.0222320556640625,
0.0038509368896484375,
0.007068634033203125,
0.0018835067749023438,
0.0014753341674804688,
-0.01264190673828125,
-0.0153045654296875,
-0.004547119140625,
0.04766845703125,
0.00007355213165283203,
-0.01052093505859375,
-0.0031585693359375,
-0.01531219482421875,
-0.01312255859375,
0.025177001953125,
-0.016448974609375,
0.0247650146484375,
0.038116455078125,
-0.034271240234375,
-0.02056884765625,
-0.0243377685546875,
-0.018096923828125,
0.0237579345703125,
-0.020538330078125,
0.0299835205078125,
-0.0003323554992675781,
0.048736572265625,
-0.005802154541015625,
0.0150299072265625,
-0.00798797607421875,
-0.01512908935546875,
0.018798828125,
-0.0019550323486328125,
0.01053619384765625,
-0.04046630859375,
-0.0265350341796875,
-0.01033782958984375,
0.044219970703125,
-0.0269317626953125,
-0.0102081298828125,
-0.0281982421875,
0.0006580352783203125,
-0.032470703125,
0.00739288330078125,
0.00833892822265625,
-0.01552581787109375,
-0.0084228515625,
-0.0014286041259765625,
-0.00583648681640625,
0.03216552734375,
-0.00281524658203125,
-0.01116943359375,
0.0027923583984375,
0.01387786865234375,
0.0161590576171875,
-0.0186767578125,
0.00888824462890625,
0.0228424072265625,
-0.039398193359375,
-0.007511138916015625,
-0.0037555694580078125,
-0.00058746337890625,
0.01290130615234375,
0.008880615234375,
-0.0031452178955078125,
-0.00728607177734375,
0.007030487060546875,
-0.01340484619140625,
0.0160369873046875,
-0.034454345703125,
-0.0013532638549804688,
-0.01149749755859375,
0.0117034912109375,
0.002685546875,
0.0250701904296875,
-0.035552978515625,
0.01105499267578125,
-0.0161285400390625,
0.0015306472778320312,
0.034637451171875,
0.0406494140625,
-0.038482666015625,
-0.0124359130859375,
-0.01430511474609375,
-0.0009760856628417969,
-0.0136260986328125,
0.0078277587890625,
0.00469207763671875,
0.01311492919921875,
-0.004840850830078125,
0.006160736083984375,
-0.0022373199462890625,
-0.028350830078125,
0.02069091796875,
-0.0296173095703125,
-0.0079193115234375,
0.005130767822265625,
-0.006946563720703125,
0.06329345703125,
0.00392913818359375,
0.02978515625,
-0.00896453857421875,
-0.0146026611328125,
-0.05303955078125,
0.015838623046875,
0.0297393798828125,
-0.0028076171875,
0.016754150390625,
-0.006061553955078125,
-0.0036258697509765625,
-0.0236663818359375,
0.01503753662109375,
0.004566192626953125,
-0.059967041015625,
-0.01442718505859375,
0.0164642333984375,
0.045379638671875,
-0.01561737060546875,
0.0006351470947265625,
-0.0083160400390625,
-0.01233673095703125,
-0.05059814453125,
-0.00860595703125,
0.0030498504638671875,
-0.01309967041015625,
-0.030029296875,
0.0293731689453125,
0.021453857421875,
0.01165008544921875,
-0.01003265380859375,
0.0080718994140625,
-0.0179443359375,
0.006404876708984375,
0.00958251953125,
0.0352783203125,
0.00899505615234375,
0.02667236328125,
-0.035369873046875,
0.03790283203125,
-0.004337310791015625,
0.0009565353393554688,
-0.020782470703125,
-0.0224151611328125,
-0.004169464111328125,
0.0139923095703125,
-0.003570556640625,
0.0131683349609375,
-0.006866455078125,
0.0167236328125,
-0.01080322265625,
-0.002056121826171875,
0.01293182373046875,
-0.0218963623046875,
0.021881103515625,
0.0181884765625,
0.00502777099609375,
-0.01251220703125,
-0.0096588134765625,
-0.01271820068359375,
0.0038394927978515625,
0.00171661376953125,
-0.033355712890625,
-0.0219573974609375,
-0.0010557174682617188,
-0.01422882080078125,
0.039703369140625,
0.01548004150390625,
-0.0021915435791015625,
-0.0193939208984375,
-0.042205810546875,
-0.0200042724609375,
0.01299285888671875,
0.006755828857421875,
-0.01507568359375,
0.006557464599609375,
-0.02044677734375,
-0.005603790283203125
] |
ours_470
|
The quadratic \(x(3-x)\) takes on all values in the range \(\left(-\infty, \frac{9}{4}\right)\). This means \(3^{x(3-x)}\) can take on all values in the range \(\left(0,3^{\frac{9}{4}}\right)\). Since \(11^{4}<3^{9}<12^{4}\), the largest integer that can be expressed in this form is \(11\).
\(\boxed{11}\)
|
11
|
{
"competition": "us_comps",
"dataset": "Ours",
"posts": null,
"source": "OMOFall18Solns.md"
}
|
Compute the largest integer that can be expressed in the form \(3^{x(3-x)}\) for some real number \(x\).
|
[
"/Mathematics/Algebra/AlgebraicEquations/QuadraticEquation",
"/Mathematics/Algebra/AlgebraicEquations/QuadraticFormula"
] |
Identify the maximum of the quadratic exponent x(3‑x) as 9/4, yielding the largest possible value 3^{9/4}.
|
[
-0.000049054622650146484,
-0.0107574462890625,
0.03485107421875,
0.01181793212890625,
-0.0006008148193359375,
0.0230712890625,
0.032928466796875,
0.00662994384765625,
0.00815582275390625,
-0.0197601318359375,
0.019866943359375,
-0.06414794921875,
-0.00027823448181152344,
0.032562255859375,
0.00701904296875,
-0.036102294921875,
0.006633758544921875,
0.011749267578125,
0.0206756591796875,
-0.002422332763671875,
-0.00994873046875,
-0.03692626953125,
-0.045074462890625,
0.00920867919921875,
-0.0484619140625,
-0.009521484375,
-0.020172119140625,
-0.0030231475830078125,
0.023468017578125,
-0.01776123046875,
-0.00875091552734375,
-0.034393310546875,
-0.0114288330078125,
-0.0294189453125,
0.000499725341796875,
0.0020961761474609375,
-0.00330352783203125,
0.00013148784637451172,
-0.019317626953125,
-0.055450439453125,
0.007404327392578125,
0.0194854736328125,
0.0127716064453125,
0.0214691162109375,
-0.011016845703125,
0.0168609619140625,
0.0010957717895507812,
-0.017242431640625,
0.00653076171875,
0.01038360595703125,
-0.0052337646484375,
0.00018787384033203125,
0.0178375244140625,
-0.015533447265625,
-0.0172271728515625,
-0.038330078125,
0.0012140274047851562,
-0.0014133453369140625,
-0.015594482421875,
0.0258331298828125,
-0.002216339111328125,
-0.02001953125,
-0.000005543231964111328,
0.0027523040771484375,
-0.002979278564453125,
-0.0176239013671875,
-0.0020618438720703125,
-0.03131103515625,
0.0113983154296875,
-0.002605438232421875,
-0.006885528564453125,
-0.017608642578125,
-0.0243072509765625,
0.01064300537109375,
0.02093505859375,
-0.00865936279296875,
-0.012603759765625,
0.003345489501953125,
0.0188751220703125,
0.005008697509765625,
-0.002655029296875,
0.0163421630859375,
0.0094146728515625,
-0.00628662109375,
0.0237274169921875,
0.01419830322265625,
-0.005039215087890625,
0.00112152099609375,
-0.034088134765625,
-0.0210723876953125,
0.0081024169921875,
0.06939697265625,
0.01432037353515625,
-0.05645751953125,
0.0038604736328125,
0.0299224853515625,
-0.0157318115234375,
-0.007488250732421875,
-0.0106658935546875,
0.0156707763671875,
-0.0140228271484375,
0.007904052734375,
0.005565643310546875,
-0.02374267578125,
-0.06378173828125,
-0.0123138427734375,
-0.0017614364624023438,
0.00246429443359375,
0.0131683349609375,
0.01070404052734375,
-0.0029850006103515625,
-0.01277923583984375,
0.0262298583984375,
0.0225677490234375,
-0.0116119384765625,
0.0179901123046875,
-0.0025959014892578125,
0.0251922607421875,
-0.006534576416015625,
0.003326416015625,
-0.0019626617431640625,
0.0184173583984375,
0.0022373199462890625,
0.014251708984375,
0.005229949951171875,
0.0285797119140625,
0.0030670166015625,
-0.01385498046875,
-0.00873565673828125,
0.0012187957763671875,
-0.007579803466796875,
-0.00505828857421875,
-0.038238525390625,
-0.006595611572265625,
-0.05224609375,
-0.01480865478515625,
0.00861358642578125,
-0.010772705078125,
-0.0325927734375,
-0.0128936767578125,
0.012237548828125,
0.001087188720703125,
0.0011053085327148438,
-0.0259246826171875,
-0.023162841796875,
-0.013671875,
0.00482940673828125,
-0.021453857421875,
0.004425048828125,
0.0010614395141601562,
0.011962890625,
0.0012655258178710938,
-0.0133056640625,
0.014678955078125,
0.005096435546875,
0.0024394989013671875,
0.0025959014892578125,
-0.003749847412109375,
-0.005889892578125,
0.01202392578125,
-0.0104217529296875,
-0.00377655029296875,
0.024627685546875,
-0.0038909912109375,
0.0017242431640625,
-0.01233673095703125,
-0.00262451171875,
0.0009560585021972656,
-0.00002664327621459961,
-0.00702667236328125,
0.02099609375,
-0.00533294677734375,
0.0089263916015625,
-0.0177001953125,
-0.0170135498046875,
-0.00540924072265625,
-0.019775390625,
-0.006145477294921875,
-0.0025634765625,
-0.015106201171875,
-0.002330780029296875,
-0.00785064697265625,
0.0277252197265625,
0.0016880035400390625,
0.01611328125,
-0.016632080078125,
-0.0005130767822265625,
-0.0070343017578125,
0.020416259765625,
0.0015277862548828125,
-0.03448486328125,
0.01165008544921875,
0.001438140869140625,
-0.01873779296875,
-0.00811767578125,
-0.003261566162109375,
-0.019256591796875,
-0.02923583984375,
0.034637451171875,
0.012054443359375,
0.0200653076171875,
0.0055999755859375,
0.0073699951171875,
0.006916046142578125,
0.00714111328125,
-0.00006210803985595703,
0.0069580078125,
0.007472991943359375,
-0.0125274658203125,
0.010498046875,
0.009552001953125,
0.0136566162109375,
0.00644683837890625,
-0.0489501953125,
-0.02215576171875,
0.0067901611328125,
-0.00638580322265625,
-0.002681732177734375,
0.00856781005859375,
-0.01251220703125,
-0.00457000732421875,
0.0048370361328125,
0.007755279541015625,
-0.007732391357421875,
-0.00823211669921875,
0.00356292724609375,
-0.013275146484375,
0.005382537841796875,
0.0161895751953125,
-0.0021686553955078125,
0.00995635986328125,
-0.0009374618530273438,
-0.0013360977172851562,
-0.003208160400390625,
-0.01153564453125,
0.0008234977722167969,
-0.0188140869140625,
-0.019561767578125,
0.0104217529296875,
-0.0245513916015625,
-0.0003058910369873047,
-0.00899505615234375,
-0.006011962890625,
-0.004230499267578125,
0.0209197998046875,
-0.01241302490234375,
0.01044464111328125,
-0.01090240478515625,
0.007411956787109375,
-0.020538330078125,
0.003143310546875,
0.02349853515625,
-0.007720947265625,
-0.01474761962890625,
-0.019866943359375,
-0.01470184326171875,
0.01035308837890625,
-0.03240966796875,
-0.01275634765625,
0.0248870849609375,
0.0012731552124023438,
0.0013799667358398438,
-0.023590087890625,
-0.0040740966796875,
-0.01419830322265625,
-0.00504302978515625,
-0.0035648345947265625,
-0.011474609375,
0.01537322998046875,
-0.0054931640625,
0.02508544921875,
-0.004215240478515625,
-0.0017147064208984375,
0.005741119384765625,
-0.0047760009765625,
-0.00492095947265625,
-0.0041046142578125,
0.006191253662109375,
0.0216064453125,
0.01432037353515625,
0.02435302734375,
0.00312042236328125,
0.01154327392578125,
0.0038700103759765625,
0.0233154296875,
-0.0203399658203125,
0.01538848876953125,
-0.019378662109375,
-0.022705078125,
0.0196075439453125,
0.0012273788452148438,
0.01342010498046875,
-0.01534271240234375,
0.00011777877807617188,
0.038482666015625,
0.01300811767578125,
-0.006793975830078125,
0.013214111328125,
0.01309967041015625,
0.00989532470703125,
-0.002716064453125,
-0.0092620849609375,
-0.004669189453125,
-0.031341552734375,
-0.007587432861328125,
-0.011474609375,
-0.00640869140625,
0.007049560546875,
-0.0154266357421875,
-0.017486572265625,
0.00957489013671875,
0.01910400390625,
-0.004550933837890625,
0.007659912109375,
-0.036590576171875,
-0.023681640625,
0.027008056640625,
0.030120849609375,
0.002655029296875,
-0.0036640167236328125,
-0.01363372802734375,
-0.01351165771484375,
-0.0165252685546875,
0.0177764892578125,
-0.020416259765625,
-0.01470947265625,
-0.0026035308837890625,
0.01007843017578125,
-0.0014057159423828125,
0.042938232421875,
-0.029876708984375,
0.0301666259765625,
0.0089874267578125,
-0.019073486328125,
-0.01122283935546875,
0.0282440185546875,
-0.01220703125,
0.034820556640625,
-0.01204681396484375,
-0.0235137939453125,
0.0168609619140625,
-0.0030517578125,
0.026885986328125,
-0.036834716796875,
-0.005825042724609375,
0.0072784423828125,
0.0147552490234375,
0.01297760009765625,
0.0207366943359375,
-0.01230621337890625,
-0.0290985107421875,
-0.01410675048828125,
-0.0143890380859375,
0.004241943359375,
-0.0286102294921875,
0.0219879150390625,
-0.006557464599609375,
0.015228271484375,
0.021209716796875,
0.002628326416015625,
-0.0022258758544921875,
-0.019805908203125,
-0.00839996337890625,
-0.01230621337890625,
-0.01476287841796875,
-0.005779266357421875,
-0.0100250244140625,
0.01290130615234375,
-0.045196533203125,
-0.00595855712890625,
-0.0143585205078125,
-0.037322998046875,
0.006572723388671875,
-0.0059051513671875,
-0.00568389892578125,
0.00736236572265625,
0.0054779052734375,
-0.021240234375,
0.01348876953125,
0.03228759765625,
0.004863739013671875,
0.0174560546875,
-0.0173797607421875,
0.01824951171875,
0.005733489990234375,
-0.0182952880859375,
0.0123138427734375,
-0.0067596435546875,
-0.0112457275390625,
0.0001766681671142578,
-0.0103912353515625,
0.007282257080078125,
0.0079498291015625,
0.0267486572265625,
-0.00412750244140625,
-0.041961669921875,
-0.0009508132934570312,
-0.0107574462890625,
0.017333984375,
-0.0153961181640625,
-0.0137786865234375,
-0.00968170166015625,
-0.01241302490234375,
-0.01183319091796875,
0.002838134765625,
-0.024017333984375,
-0.00896453857421875,
-0.0020618438720703125,
0.0008025169372558594,
0.00942230224609375,
-0.0224761962890625,
-0.036102294921875,
0.003482818603515625,
0.0066986083984375,
-0.0019474029541015625,
0.00986480712890625,
0.028228759765625,
0.0021514892578125,
-0.01495361328125,
0.0097503662109375,
0.00041294097900390625,
0.01534271240234375,
-0.01103973388671875,
-0.0254364013671875,
0.03131103515625,
0.023590087890625,
-0.048583984375,
0.020355224609375,
-0.003116607666015625,
-0.01454925537109375,
0.004138946533203125,
-0.016357421875,
-0.0011167526245117188,
0.041229248046875,
-0.005962371826171875,
0.0185546875,
-0.006046295166015625,
0.025482177734375,
-0.0304412841796875,
-0.005023956298828125,
-0.02984619140625,
0.007274627685546875,
0.007678985595703125,
-0.033477783203125,
-0.0028362274169921875,
0.019927978515625,
0.0333251953125,
0.00569915771484375,
0.0626220703125,
-0.01837158203125,
-0.00786590576171875,
-0.0157318115234375,
-0.017486572265625,
-0.0284576416015625,
-0.0241241455078125,
0.0128326416015625,
0.0306854248046875,
-0.02325439453125,
-0.00258636474609375,
-0.04876708984375,
-0.02777099609375,
-0.00737762451171875,
-0.0238494873046875,
-0.01328277587890625,
0.00696563720703125,
0.0063934326171875,
-0.0300445556640625,
0.036834716796875,
-0.01003265380859375,
0.032501220703125,
0.018310546875,
-0.034210205078125,
0.0089263916015625,
-0.0197296142578125,
-0.04254150390625,
0.003963470458984375,
-0.025360107421875,
0.030029296875,
-0.01080322265625,
0.002323150634765625,
0.0296783447265625,
0.0146636962890625,
-0.01611328125,
0.0501708984375,
0.00574493408203125,
0.0036106109619140625,
0.0124969482421875,
0.00928497314453125,
-0.035797119140625,
0.028900146484375,
0.0025081634521484375,
0.058074951171875,
-0.011505126953125,
-0.04425048828125,
-0.0029621124267578125,
0.01049041748046875,
0.01435089111328125,
0.02655029296875,
-0.023193359375,
-0.0011882781982421875,
0.027587890625,
-0.002849578857421875,
-0.0031642913818359375,
0.0029659271240234375,
0.020660400390625,
0.00997161865234375,
0.0012187957763671875,
0.0225067138671875,
0.019683837890625,
0.022064208984375,
0.033172607421875,
0.0232086181640625,
0.0112152099609375,
-0.03900146484375,
0.0182037353515625,
-0.018402099609375,
-0.000263214111328125,
-0.003444671630859375,
0.01207733154296875,
-0.056488037109375,
-0.04608154296875,
0.021148681640625,
0.0531005859375,
0.0093841552734375,
-0.0056610107421875,
0.0246734619140625,
0.0014944076538085938,
0.01055908203125,
0.01099395751953125,
-0.0091094970703125,
-0.0128936767578125,
0.002838134765625,
0.0006618499755859375,
-0.0053558349609375,
-0.021331787109375,
0.005558013916015625,
-0.0061187744140625,
0.005443572998046875,
0.025787353515625,
0.033782958984375,
0.017059326171875,
0.004108428955078125,
0.023590087890625,
-0.04327392578125,
0.0052947998046875,
0.01340484619140625,
-0.017608642578125,
-0.01206207275390625,
0.0117645263671875,
0.0146331787109375,
0.0151519775390625,
0.0169830322265625,
0.0216827392578125,
0.0139923095703125,
-0.00464630126953125,
0.02294921875,
0.047149658203125,
0.028350830078125,
-0.0270843505859375,
0.04022216796875,
-0.01393890380859375,
-0.00043654441833496094,
0.022369384765625,
0.018585205078125,
0.01512908935546875,
-0.0009002685546875,
0.02789306640625,
0.0097198486328125,
0.002964019775390625,
-0.039154052734375,
-0.012725830078125,
0.0097503662109375,
0.0030727386474609375,
0.0223541259765625,
-0.0013675689697265625,
-0.01361083984375,
-0.017547607421875,
-0.0011129379272460938,
-0.03466796875,
-0.04034423828125,
0.0095062255859375,
0.0118560791015625,
0.004085540771484375,
-0.040191650390625,
-0.0176239013671875,
-0.0189208984375,
0.0423583984375,
0.037445068359375,
0.0276641845703125,
-0.00432586669921875,
0.00946044921875,
0.013092041015625,
0.0040283203125,
-0.00970458984375,
0.0208740234375,
-0.05059814453125,
0.0246124267578125,
-0.01052093505859375,
-0.0153045654296875,
-0.02203369140625,
0.04443359375,
0.022979736328125,
-0.006092071533203125,
0.01264190673828125,
0.01335906982421875,
0.00439453125,
0.018280029296875,
0.007312774658203125,
-0.01512908935546875,
-0.0009131431579589844,
-0.01383209228515625,
0.0179443359375,
-0.0276336669921875,
0.026702880859375,
0.00591278076171875,
0.01398468017578125,
-0.0253448486328125,
-0.0176849365234375,
0.031524658203125,
-0.0292205810546875,
-0.03717041015625,
0.019134521484375,
-0.0215301513671875,
-0.0209503173828125,
0.01183319091796875,
-0.01033782958984375,
0.01910400390625,
0.0166473388671875,
-0.00030541419982910156,
-0.0042877197265625,
0.004688262939453125,
-0.0179443359375,
0.0377197265625,
-0.0002932548522949219,
-0.0199127197265625,
-0.0134735107421875,
-0.01482391357421875,
0.0169219970703125,
-0.047393798828125,
-0.032012939453125,
0.01629638671875,
-0.021209716796875,
0.027191162109375,
-0.07415771484375,
-0.028350830078125,
-0.0157318115234375,
0.022125244140625,
-0.0068206787109375,
0.0013132095336914062,
-0.0139312744140625,
-0.0299530029296875,
0.0206146240234375,
-0.020416259765625,
0.02178955078125,
-0.01337432861328125,
0.012939453125,
-0.01910400390625,
-0.03155517578125,
0.03656005859375,
0.037261962890625,
-0.0289154052734375,
0.006816864013671875,
0.02825927734375,
0.006500244140625,
0.0188751220703125,
0.00760650634765625,
0.0244903564453125,
-0.01277923583984375,
0.0229034423828125,
0.0026416778564453125,
0.01397705078125,
-0.0165863037109375,
0.0164947509765625,
-0.02618408203125,
0.005435943603515625,
-0.035919189453125,
-0.0024509429931640625,
0.005825042724609375,
0.016845703125,
-0.005157470703125,
0.012359619140625,
0.0110321044921875,
0.0206146240234375,
-0.0142669677734375,
0.00511932373046875,
0.03277587890625,
0.0028934478759765625,
-0.024444580078125,
-0.006591796875,
-0.005649566650390625,
0.020477294921875,
0.00728607177734375,
0.00992584228515625,
0.0308990478515625,
0.02166748046875,
-0.0048980712890625,
-0.0232086181640625,
0.005474090576171875,
-0.0136871337890625,
-0.0138702392578125,
0.0247344970703125,
0.02410888671875,
0.01678466796875,
0.00007414817810058594,
-0.0281219482421875,
-0.0318603515625,
0.0010423660278320312,
0.01175689697265625,
-0.0188446044921875,
0.037506103515625,
0.004917144775390625,
-0.0113067626953125,
-0.0214996337890625,
0.002338409423828125,
-0.01483154296875,
-0.01477813720703125,
0.0222320556640625,
-0.01520538330078125,
0.027740478515625,
0.00905609130859375,
0.0022525787353515625,
-0.0010232925415039062,
-0.01495361328125,
0.0171356201171875,
0.0161285400390625,
0.024017333984375,
-0.0020160675048828125,
-0.039459228515625,
-0.00867462158203125,
0.03680419921875,
-0.00992584228515625,
-0.032867431640625,
-0.018218994140625,
0.00653839111328125,
-0.0251312255859375,
-0.0221405029296875,
-0.01849365234375,
-0.04180908203125,
-0.0142059326171875,
-0.0022907257080078125,
0.058563232421875,
-0.005435943603515625,
0.006557464599609375,
0.003936767578125,
0.0010404586791992188,
0.02667236328125,
-0.0386962890625,
-0.0016021728515625,
0.0152435302734375,
0.011199951171875,
0.04315185546875,
0.0285797119140625,
0.0141143798828125,
-0.01241302490234375,
0.0007543563842773438,
-0.035064697265625,
-0.0162811279296875,
0.0166778564453125,
0.030059814453125,
0.043212890625,
-0.0128936767578125,
-0.00001537799835205078,
-0.0170745849609375,
-0.0142822265625,
-0.0079193115234375,
0.00041961669921875,
-0.000774383544921875,
-0.01082611083984375,
-0.0280609130859375,
0.00975799560546875,
-0.01078033447265625,
-0.01300811767578125,
-0.017486572265625,
0.0010433197021484375,
0.04266357421875,
0.0038242340087890625,
-0.0118865966796875,
-0.0167236328125,
0.0306549072265625,
-0.006481170654296875,
0.03179931640625,
-0.005069732666015625,
0.0430908203125,
0.0124053955078125,
0.00438690185546875,
0.0109405517578125,
-0.04278564453125,
-0.012298583984375,
0.0008869171142578125,
-0.01220703125,
0.004314422607421875,
0.007110595703125,
-0.018585205078125,
-0.01032257080078125,
-0.01131439208984375,
-0.0377197265625,
0.0009112358093261719,
-0.01593017578125,
-0.0244903564453125,
0.01123809814453125,
0.00485992431640625,
-0.03399658203125,
-0.02471923828125,
0.0144500732421875,
0.00470733642578125,
-0.00267791748046875,
0.0015878677368164062,
0.033111572265625,
-0.01947021484375,
0.0193328857421875,
0.0254364013671875,
-0.044036865234375,
0.0187530517578125,
-0.01226043701171875,
0.01568603515625,
-0.002216339111328125,
0.018463134765625,
-0.0146331787109375,
0.006778717041015625,
-0.0016775131225585938,
-0.0072174072265625,
0.026123046875,
-0.01202392578125,
-0.0218658447265625,
-0.01177978515625,
0.007244110107421875,
-0.01224517822265625,
-0.01605224609375,
0.03765869140625,
0.027496337890625,
0.0157318115234375,
-0.01476287841796875,
-0.0128173828125,
0.0184783935546875,
0.009735107421875,
0.016754150390625,
-0.021209716796875,
-0.0007147789001464844,
-0.0037288665771484375,
-0.0084381103515625,
-0.020904541015625,
0.0181732177734375,
0.0146331787109375,
-0.0146484375,
0.00867462158203125,
-0.0248260498046875,
0.00717926025390625,
-0.00208282470703125,
-0.024810791015625,
0.004329681396484375,
0.0017175674438476562,
0.0389404296875,
-0.007801055908203125,
0.02008056640625,
0.019927978515625,
0.0024967193603515625,
-0.006519317626953125,
0.0390625,
0.0024871826171875,
-0.01094818115234375,
-0.0006732940673828125,
-0.005702972412109375,
-0.0221099853515625,
-0.00579833984375,
0.0160675048828125,
-0.00632476806640625,
0.01163482666015625,
-0.0196990966796875,
0.00872039794921875,
-0.01247406005859375,
0.0145416259765625,
-0.01442718505859375,
0.005706787109375,
-0.0019931793212890625,
0.018341064453125,
0.0166168212890625,
0.0146636962890625,
0.0275421142578125,
0.014404296875,
-0.0380859375,
0.0162200927734375,
0.001819610595703125,
0.01580810546875,
-0.0069122314453125,
-0.0115966796875,
0.0148468017578125,
0.0499267578125,
-0.02520751953125,
-0.002239227294921875,
0.00501251220703125,
-0.0013904571533203125,
0.0136260986328125,
-0.03717041015625,
0.00445556640625,
0.0159912109375,
-0.01483154296875,
-0.003200531005859375,
-0.0021343231201171875,
0.010345458984375,
-0.0088043212890625,
0.01187896728515625,
-0.01293182373046875,
0.0115509033203125,
0.01421356201171875,
0.0007967948913574219,
0.006755828857421875,
-0.04754638671875,
0.0002187490463256836,
-0.00255584716796875,
0.0310821533203125,
0.01374053955078125,
-0.044769287109375,
0.0215911865234375,
-0.00372314453125,
-0.0169677734375,
-0.00502777099609375,
-0.00800323486328125,
-0.001491546630859375,
-0.0200653076171875,
0.0389404296875,
0.00567626953125,
-0.032073974609375,
-0.007328033447265625,
0.0018482208251953125,
0.00707244873046875,
-0.0079193115234375,
0.00020205974578857422,
-0.00836181640625,
-0.039398193359375,
0.058013916015625,
-0.02178955078125,
0.02044677734375,
0.00688934326171875,
-0.0015764236450195312,
0.002460479736328125,
-0.019744873046875,
-0.0158233642578125,
0.0030727386474609375,
-0.005947113037109375,
-0.004154205322265625,
-0.0164794921875,
0.016021728515625,
0.00493621826171875,
0.04010009765625,
-0.0299835205078125,
-0.0016498565673828125,
0.0033397674560546875,
0.007259368896484375,
-0.0380859375,
0.01629638671875,
-0.002185821533203125,
0.00737762451171875,
-0.0164794921875,
-0.0032291412353515625,
-0.005878448486328125,
-0.024749755859375,
-0.024749755859375,
0.0182342529296875,
-0.0008268356323242188,
-0.0246429443359375,
-0.0158538818359375,
0.0036640167236328125,
-0.0087432861328125,
0.005680084228515625,
0.029144287109375,
-0.0181121826171875,
0.006683349609375,
-0.00684356689453125,
0.0274200439453125,
-0.0281982421875,
-0.0244140625,
-0.006908416748046875,
-0.02764892578125,
-0.0296478271484375,
-0.00846099853515625,
0.00498199462890625,
-0.021087646484375,
0.051727294921875,
0.01898193359375,
0.016021728515625,
-0.0145111083984375,
0.0006189346313476562,
0.0231781005859375,
-0.02032470703125,
-0.005092620849609375,
-0.03778076171875,
-0.006412506103515625,
-0.003856658935546875,
0.0133514404296875,
-0.004150390625,
-0.005886077880859375,
0.0229339599609375,
-0.0012950897216796875,
-0.001628875732421875,
-0.0242919921875,
0.01091766357421875,
-0.002593994140625,
0.0034961700439453125,
0.036529541015625,
-0.01194000244140625,
-0.00855255126953125,
0.01502227783203125,
0.031829833984375,
-0.0206756591796875,
0.006755828857421875,
-0.01800537109375,
-0.0045166015625,
-0.01250457763671875,
0.031585693359375,
-0.0135498046875,
-0.006160736083984375,
-0.00920867919921875,
0.00818634033203125,
0.03338623046875,
0.0080413818359375,
0.005886077880859375,
0.0255126953125,
0.01174163818359375,
-0.0357666015625,
0.0233917236328125,
0.0029449462890625,
0.024749755859375,
-0.011138916015625,
0.0298309326171875,
-0.027435302734375,
0.0003573894500732422,
0.028472900390625,
0.01788330078125,
-0.0113677978515625,
0.0052947998046875,
0.00862884521484375,
-0.01377105712890625,
-0.0009765625,
0.002979278564453125,
0.012481689453125,
-0.022216796875,
-0.0011005401611328125,
-0.0028133392333984375,
-0.002651214599609375,
0.00882720947265625,
-0.02276611328125,
-0.0105438232421875,
0.035369873046875,
-0.0267333984375,
-0.01715087890625,
-0.0210113525390625,
-0.005596160888671875,
-0.004199981689453125,
-0.02960205078125,
0.0012617111206054688,
0.03179931640625,
0.028564453125,
-0.004657745361328125,
0.00431060791015625,
0.01355743408203125,
-0.0020427703857421875,
-0.0013332366943359375,
-0.0055694580078125,
0.004055023193359375,
0.03326416015625,
-0.0151519775390625,
0.016082763671875,
-0.033966064453125,
-0.0018301010131835938,
0.0204925537109375,
-0.0029125213623046875,
0.0002655982971191406,
-0.02349853515625,
-0.0018682479858398438,
0.04718017578125,
-0.032196044921875,
0.009124755859375,
-0.0306396484375,
-0.0280609130859375,
0.003192901611328125,
-0.01502227783203125,
0.0160980224609375,
0.004657745361328125,
0.01947021484375,
0.006038665771484375,
-0.004184722900390625,
-0.0003993511199951172,
-0.031829833984375,
0.0133056640625,
0.0241851806640625,
0.020721435546875,
-0.01403045654296875,
-0.0247650146484375,
-0.030609130859375,
0.0176544189453125,
0.0283966064453125,
0.025604248046875,
-0.0013818740844726562,
-0.0302734375,
0.004657745361328125,
-0.01221466064453125,
0.01178741455078125,
-0.0013914108276367188,
0.012969970703125,
-0.017791748046875,
0.00490570068359375,
0.03265380859375,
0.0166473388671875,
0.006439208984375,
-0.018768310546875,
-0.02935791015625,
0.0093994140625,
0.015899658203125,
0.02056884765625,
0.0233917236328125,
-0.0111541748046875,
0.01406097412109375,
0.0221405029296875,
0.0104522705078125,
-0.032867431640625,
-0.006412506103515625,
-0.0272216796875,
0.01126861572265625,
0.0284271240234375,
0.007701873779296875,
-0.013427734375,
0.01371002197265625,
-0.0004544258117675781,
0.023406982421875,
-0.0021038055419921875,
-0.024444580078125,
0.031219482421875,
0.01096343994140625,
-0.0217437744140625,
0.0292510986328125,
0.0032520294189453125,
0.002960205078125,
0.0127105712890625,
-0.005603790283203125,
-0.010650634765625,
0.0152435302734375,
-0.0020160675048828125,
0.0199737548828125,
0.011566162109375,
0.01500701904296875,
0.007659912109375,
0.0129241943359375,
-0.0081024169921875,
-0.0220489501953125,
0.011138916015625,
0.0498046875,
-0.03363037109375,
0.02728271484375,
-0.007045745849609375,
0.0022029876708984375,
-0.0254974365234375,
0.0267181396484375,
-0.018585205078125,
-0.01507568359375,
-0.00579833984375,
0.038360595703125,
-0.0189056396484375,
-0.0216827392578125,
0.0058746337890625,
0.00661468505859375,
0.00485992431640625,
-0.0304107666015625,
-0.006072998046875,
0.0136871337890625,
-0.004940032958984375,
0.022430419921875,
-0.0018186569213867188,
0.0124359130859375,
-0.0367431640625,
0.0266265869140625,
-0.0075836181640625,
-0.031646728515625,
0.0013780593872070312,
-0.0082550048828125,
-0.002971649169921875,
0.038299560546875,
-0.0083160400390625,
-0.0090789794921875,
0.0266571044921875,
-0.012237548828125,
-0.01104736328125,
0.0229644775390625,
0.039031982421875,
0.006862640380859375,
0.0032253265380859375,
-0.0131378173828125,
0.02423095703125,
-0.0102691650390625,
0.0147552490234375,
-0.0020008087158203125,
0.01242828369140625,
0.0152130126953125,
-0.04302978515625,
-0.0271148681640625,
0.037261962890625,
-0.0108184814453125,
-0.0225372314453125,
-0.01428985595703125,
-0.0023860931396484375,
-0.00595855712890625,
0.005527496337890625,
-0.01464080810546875,
-0.019561767578125,
-0.0119171142578125,
0.0224456787109375,
0.0239410400390625,
0.009613037109375,
0.038116455078125,
-0.01444244384765625,
0.0060272216796875,
0.0019292831420898438,
-0.017333984375,
0.020751953125,
0.018829345703125,
0.01160430908203125,
-0.01206207275390625,
0.049041748046875,
-0.023101806640625,
-0.0217742919921875,
0.0035266876220703125,
-0.03271484375,
-0.00965118408203125,
-0.0100555419921875,
-0.0093536376953125,
-0.00579071044921875,
-0.0235443115234375,
0.01068115234375,
0.0245361328125,
0.005229949951171875,
-0.0046844482421875,
0.00835418701171875,
0.03558349609375,
0.02081298828125,
0.0012454986572265625,
-0.01275634765625,
-0.035980224609375,
-0.0157928466796875,
0.045257568359375,
0.0197906494140625,
0.0311126708984375,
-0.000988006591796875,
0.0169219970703125,
-0.0233154296875,
-0.01334381103515625,
0.049957275390625,
-0.048370361328125,
-0.01788330078125,
0.01314544677734375,
-0.01861572265625,
0.0030498504638671875,
0.0164794921875,
0.031982421875,
-0.035552978515625,
0.00545501708984375,
-0.01219940185546875,
-0.004482269287109375,
-0.025299072265625,
0.012054443359375,
0.006793975830078125,
-0.011077880859375,
-0.0002880096435546875,
0.00884246826171875,
-0.0174407958984375,
-0.000995635986328125,
0.0303192138671875,
-0.0225677490234375,
0.0167388916015625,
0.0225982666015625,
0.0302886962890625,
0.0147552490234375,
0.0157470703125,
0.0195159912109375,
-0.02557373046875,
0.0282440185546875,
0.02276611328125,
0.01224517822265625,
-0.0013742446899414062,
-0.0300140380859375,
-0.0031032562255859375,
-0.0155029296875,
-0.0072784423828125,
0.022186279296875,
0.01509857177734375,
-0.042327880859375,
-0.0059356689453125,
-0.016204833984375,
-0.0029506683349609375,
0.0238800048828125,
-0.019500732421875,
-0.007564544677734375,
0.0241241455078125,
0.0134124755859375,
-0.001430511474609375,
0.016876220703125,
-0.033843994140625,
0.01091766357421875,
-0.01189422607421875,
-0.0010728836059570312,
-0.0121917724609375,
0.037017822265625,
0.004817962646484375,
0.001068115234375,
-0.0129547119140625,
-0.0243072509765625,
0.01171875,
-0.0032749176025390625,
0.00341033935546875,
0.0018167495727539062,
-0.007297515869140625,
0.0170440673828125,
0.0032634735107421875,
0.0036163330078125,
0.011688232421875,
0.0160675048828125,
0.0240325927734375,
0.00933837890625,
-0.01111602783203125,
0.006103515625,
0.0206451416015625,
-0.0005779266357421875,
-0.0048065185546875,
0.0204925537109375,
0.0299072265625,
-0.01287841796875,
-0.0080108642578125,
0.00508880615234375,
-0.032196044921875,
0.02410888671875,
-0.041351318359375,
0.007221221923828125,
-0.0086517333984375,
0.0167388916015625,
-0.01036834716796875,
0.0173492431640625,
-0.00984954833984375,
0.035064697265625,
-0.0092620849609375,
0.0109100341796875,
0.0032596588134765625,
-0.0120849609375,
-0.015655517578125,
0.03460693359375,
-0.03302001953125,
-0.0130157470703125,
0.01386260986328125,
0.0219573974609375,
-0.05596923828125,
0.027130126953125,
0.04193115234375,
-0.041961669921875,
-0.0020599365234375,
0.0124053955078125,
-0.00971221923828125,
-0.0189666748046875,
0.0010204315185546875,
0.01056671142578125,
0.0242462158203125,
0.00909423828125,
0.036834716796875,
-0.0117340087890625,
0.043212890625,
-0.0050811767578125,
-0.006328582763671875,
0.0262603759765625,
0.01131439208984375,
-0.0155487060546875,
-0.00646209716796875,
0.0052490234375,
-0.0008978843688964844,
0.0066070556640625,
-0.0038738250732421875,
0.045196533203125,
0.00019419193267822266,
0.005649566650390625,
-0.0038166046142578125,
0.0174407958984375,
0.0192413330078125,
-0.0171356201171875,
-0.019256591796875,
0.041717529296875,
-0.016265869140625,
-0.00936126708984375,
-0.0059051513671875,
-0.0264434814453125,
0.0159454345703125,
-0.01416778564453125,
-0.01491546630859375,
0.04412841796875,
0.01010894775390625,
0.007110595703125,
-0.033599853515625,
-0.0136260986328125,
-0.05035400390625,
0.0006213188171386719,
-0.00977325439453125,
0.0033721923828125,
0.031829833984375,
0.01201629638671875,
-0.0128021240234375,
0.043548583984375,
0.0022525787353515625,
-0.00470733642578125,
-0.007373809814453125,
-0.00006788969039916992,
0.006076812744140625,
-0.016387939453125,
0.01458740234375,
-0.02398681640625,
0.006946563720703125,
-0.016845703125,
-0.0229034423828125,
0.033843994140625,
-0.01904296875,
-0.043701171875,
0.0292205810546875,
-0.00592803955078125,
-0.0137786865234375,
0.0105438232421875,
-0.02117919921875,
0.032257080078125,
0.032012939453125,
0.03521728515625,
-0.035064697265625,
0.005146026611328125,
0.0013074874877929688,
-0.0056915283203125,
0.0201263427734375,
0.0028667449951171875,
-0.0176849365234375,
-0.005512237548828125,
0.0216064453125,
-0.01351165771484375,
-0.016021728515625,
-0.0238037109375,
0.0286712646484375,
0.016204833984375,
0.027191162109375,
-0.00439453125,
0.042999267578125,
0.0338134765625,
-0.006313323974609375,
0.01611328125,
0.01093292236328125,
0.0074310302734375,
-0.0377197265625,
-0.005359649658203125,
-0.01232147216796875,
0.021484375,
-0.00865936279296875,
-0.01137542724609375,
0.01519775390625,
0.0011911392211914062,
0.04656982421875,
0.00490570068359375,
-0.00044226646423339844,
0.0114898681640625,
-0.0112152099609375,
-0.0237884521484375,
0.00565338134765625,
-0.01338958740234375,
-0.0126190185546875,
0.0343017578125,
0.004909515380859375,
0.04168701171875,
0.0208282470703125,
-0.0162353515625,
-0.024322509765625,
0.0062713623046875,
-0.0050506591796875,
0.0302734375,
-0.02001953125,
-0.0184478759765625,
-0.007076263427734375,
-0.0194854736328125,
-0.00494384765625,
-0.01268768310546875,
0.007770538330078125,
-0.022735595703125,
0.028167724609375,
-0.0287933349609375,
0.00215911865234375,
0.012451171875,
0.043365478515625,
0.01050567626953125,
-0.0141448974609375,
-0.0225830078125,
-0.0283203125,
-0.0236968994140625,
0.0224761962890625,
-0.0174713134765625,
-0.0208282470703125,
-0.00876617431640625,
0.005664825439453125,
-0.0009613037109375,
0.0357666015625,
0.0047149658203125,
-0.0172882080078125,
-0.0177459716796875,
-0.004657745361328125,
0.002246856689453125,
0.037384033203125,
-0.003910064697265625,
0.0041961669921875,
-0.009857177734375,
-0.0048675537109375,
-0.0186920166015625,
0.0254058837890625,
-0.002780914306640625,
0.023284912109375,
-0.00614166259765625,
-0.00865936279296875,
-0.01428985595703125,
0.0158233642578125,
0.017120361328125,
-0.0264434814453125,
-0.0037841796875,
-0.019805908203125,
-0.004787445068359375,
0.01511383056640625,
-0.007781982421875,
-0.0130462646484375,
-0.0177154541015625,
0.00731658935546875,
0.005584716796875,
0.0104827880859375,
0.00994110107421875,
-0.0229339599609375,
0.005611419677734375,
0.00959014892578125,
-0.0010290145874023438,
-0.032501220703125,
0.0060577392578125,
-0.0313720703125,
0.01715087890625,
-0.01189422607421875,
-0.0009064674377441406,
0.0438232421875,
0.00559234619140625,
-0.010040283203125,
0.0013647079467773438,
0.0211334228515625,
-0.00661468505859375,
0.0011434555053710938,
0.00899505615234375,
-0.0190277099609375,
0.00943756103515625,
-0.013824462890625,
0.005584716796875,
0.01763916015625,
0.0105438232421875,
-0.0004303455352783203,
-0.0261993408203125,
0.00423431396484375,
0.0165252685546875,
-0.01499176025390625,
0.0079803466796875,
0.0160064697265625,
0.0290374755859375,
-0.028900146484375,
-0.016510009765625,
0.0149688720703125,
0.007602691650390625,
0.0019464492797851562,
0.0007796287536621094,
0.02886962890625,
-0.00649261474609375,
0.0033092498779296875,
0.04150390625,
0.006961822509765625,
-0.00878143310546875,
-0.024566650390625,
-0.0093536376953125,
-0.03265380859375,
-0.032989501953125,
0.0416259765625,
0.01253509521484375,
0.034210205078125,
0.0182037353515625,
-0.0024738311767578125,
0.007160186767578125,
0.0241546630859375,
0.01226043701171875,
0.0047760009765625,
0.004238128662109375,
0.006633758544921875,
0.0115203857421875,
-0.033416748046875,
0.022430419921875,
-0.02081298828125,
-0.029998779296875,
-0.03118896484375,
0.0027637481689453125,
0.0003407001495361328,
0.006504058837890625,
-0.004016876220703125,
-0.0222320556640625,
0.0283355712890625,
0.005817413330078125,
0.01174163818359375,
-0.0190277099609375,
0.0197296142578125,
0.012847900390625,
0.0035400390625,
0.0134124755859375,
-0.017730712890625,
0.01068115234375,
0.01506805419921875,
-0.005107879638671875,
0.0035343170166015625,
0.0011301040649414062,
0.0280609130859375,
0.037322998046875,
-0.0059356689453125,
-0.00537109375,
-0.0165863037109375,
0.0209808349609375,
0.052154541015625,
0.0099639892578125,
0.0023345947265625,
0.03460693359375,
0.036224365234375,
0.0180206298828125,
0.0193939208984375,
-0.048431396484375,
0.00940704345703125,
0.03851318359375,
-0.038543701171875,
-0.0177764892578125,
-0.01366424560546875,
-0.0081024169921875,
0.0305633544921875,
-0.029052734375,
0.004253387451171875,
-0.01523590087890625,
-0.01119232177734375,
-0.0197296142578125,
0.01242828369140625,
0.00917816162109375,
-0.031524658203125,
0.0216827392578125,
-0.01187896728515625,
-0.01454925537109375,
0.00832366943359375,
-0.01446533203125,
-0.028533935546875,
-0.0009255409240722656,
-0.0182342529296875,
-0.0026035308837890625,
-0.0243377685546875,
-0.0028228759765625,
0.0161285400390625,
0.0193939208984375,
0.01078033447265625,
-0.00542449951171875,
0.005229949951171875,
-0.0142669677734375,
-0.0140380859375,
-0.0135650634765625,
0.027984619140625,
-0.00762176513671875,
0.0097808837890625,
0.02001953125,
0.0025882720947265625,
0.01531982421875,
-0.007259368896484375,
0.0240631103515625,
0.0039215087890625,
-0.0009593963623046875,
-0.0201416015625,
0.024139404296875,
0.01361083984375,
0.0084381103515625,
-0.0236053466796875,
0.04156494140625,
-0.002696990966796875,
-0.0100860595703125,
-0.07135009765625,
0.0169830322265625,
-0.01690673828125,
0.010162353515625,
-0.0031566619873046875,
-0.02191162109375,
-0.01555633544921875,
-0.018341064453125,
-0.02838134765625,
0.03326416015625,
0.03900146484375,
0.005584716796875,
-0.00403594970703125,
0.017913818359375,
0.0226898193359375,
0.039520263671875,
-0.01042938232421875,
0.023956298828125,
0.006435394287109375,
-0.00470733642578125,
-0.00406646728515625,
-0.0194854736328125,
0.00014793872833251953,
0.01190948486328125,
-0.00881195068359375,
0.0052337646484375,
-0.0103607177734375,
-0.0189361572265625,
0.0145111083984375,
-0.00449371337890625,
0.01044464111328125,
0.0029010772705078125,
0.004913330078125,
0.0192718505859375,
0.0272216796875,
0.00719451904296875,
-0.0270233154296875,
-0.0022754669189453125,
-0.001094818115234375,
0.0199737548828125,
-0.0152435302734375,
0.0068817138671875,
0.00753021240234375,
-0.0230560302734375,
0.01065826416015625,
-0.05010986328125,
-0.0104522705078125,
-0.004695892333984375,
0.03570556640625,
-0.0131378173828125,
0.039306640625,
0.0031147003173828125,
-0.01275634765625,
-0.00807952880859375,
-0.0023441314697265625,
0.0088958740234375,
-0.0027332305908203125,
0.026947021484375,
0.006053924560546875,
0.00904083251953125,
-0.0015344619750976562,
-0.0013360977172851562,
-0.0275115966796875,
0.01309967041015625,
0.0225372314453125,
0.0066070556640625,
-0.0077362060546875,
0.01163482666015625,
0.02069091796875,
-0.01284027099609375,
0.00014007091522216797,
0.0164947509765625,
0.01519775390625,
0.0200042724609375,
-0.0088043212890625,
-0.01399993896484375,
0.00543975830078125,
0.0242156982421875,
-0.016510009765625,
0.0264129638671875,
-0.0244903564453125,
0.0181884765625,
0.0130767822265625,
0.0256500244140625,
0.0186004638671875,
-0.0230255126953125,
0.00600433349609375,
-0.050384521484375,
-0.0221710205078125,
-0.00258636474609375,
0.0177154541015625,
-0.045623779296875,
-0.022979736328125,
-0.0177001953125,
-0.01172637939453125,
0.00637054443359375,
0.0330810546875,
0.0025730133056640625,
-0.0017175674438476562,
-0.0236358642578125,
0.03192138671875,
0.003780364990234375,
-0.05621337890625,
-0.03131103515625,
-0.034698486328125,
-0.001308441162109375,
0.02557373046875,
0.0218353271484375,
0.03192138671875,
0.00766754150390625,
-0.0011281967163085938,
-0.0113525390625,
0.008697509765625,
0.021942138671875,
-0.01235198974609375,
-0.043426513671875,
0.0168914794921875,
-0.0207672119140625,
0.0022907257080078125,
-0.0386962890625,
-0.035888671875,
0.0181427001953125,
0.0238189697265625,
0.04290771484375,
-0.029998779296875,
0.006465911865234375,
0.02313232421875,
-0.01242828369140625,
0.02593994140625,
-0.00885772705078125,
-0.008056640625,
0.0148468017578125,
0.033782958984375,
0.00595855712890625,
0.0032253265380859375,
0.01042938232421875,
0.003688812255859375,
-0.005519866943359375,
-0.01212310791015625,
-0.0151519775390625,
0.037628173828125,
0.052337646484375,
-0.0280914306640625,
0.034881591796875,
0.0226287841796875,
0.0054931640625,
-0.01519775390625,
-0.0132598876953125,
0.006679534912109375,
-0.0099334716796875,
0.01715087890625,
0.011444091796875,
-0.0191192626953125,
0.043243408203125,
0.006381988525390625,
0.04608154296875,
0.01302337646484375,
-0.032440185546875,
0.035125732421875,
0.0010709762573242188,
-0.01087188720703125,
-0.0187835693359375,
-0.0209808349609375,
-0.0226593017578125,
0.0259857177734375,
0.016571044921875,
0.0013227462768554688,
0.032867431640625,
0.0114593505859375,
-0.008331298828125,
-0.00922393798828125,
0.0288848876953125,
0.0195465087890625,
0.00974273681640625,
-0.003292083740234375,
-0.033233642578125,
-0.026824951171875,
0.0161895751953125,
-0.0036468505859375,
0.006134033203125,
-0.04132080078125,
-0.024658203125,
0.01409912109375,
0.036163330078125,
0.00818634033203125,
-0.0219879150390625,
0.014617919921875,
-0.0238037109375,
0.00595855712890625,
0.01580810546875,
0.0207366943359375,
0.00634765625,
0.021331787109375,
0.0335693359375,
0.01715087890625,
-0.00983428955078125,
-0.0259552001953125,
-0.0202178955078125,
0.007537841796875,
0.0191192626953125,
-0.03265380859375,
0.020477294921875,
0.045654296875,
-0.0302276611328125,
0.00946044921875,
-0.01580810546875,
0.044647216796875,
-0.0012760162353515625,
-0.0014057159423828125,
-0.0225372314453125,
0.0300445556640625,
0.05487060546875,
0.0283203125,
-0.035858154296875,
-0.00033020973205566406,
-0.0305023193359375,
0.0086517333984375,
0.0135650634765625,
0.03363037109375,
0.0111083984375,
-0.0246124267578125,
0.026580810546875,
0.009918212890625,
0.0265655517578125,
-0.0274200439453125,
0.00948333740234375,
-0.0058746337890625,
0.00897979736328125,
0.01413726806640625,
0.0242919921875,
-0.01517486572265625,
-0.016387939453125,
-0.0489501953125,
0.01076507568359375,
-0.0184173583984375,
-0.007442474365234375,
0.007694244384765625,
-0.0148468017578125,
0.0012998580932617188,
0.016693115234375,
0.026885986328125,
0.024322509765625,
-0.00533294677734375,
-0.0361328125,
0.005779266357421875,
-0.0215606689453125,
0.045318603515625,
-0.0020160675048828125,
-0.0264434814453125,
-0.008148193359375,
0.0033664703369140625,
-0.0178070068359375,
0.0019102096557617188,
-0.01214599609375,
0.0031490325927734375,
-0.0194854736328125,
0.0033969879150390625,
-0.029083251953125,
0.0089874267578125,
-0.002513885498046875,
-0.01654052734375,
0.00980377197265625,
0.01385498046875,
0.01090240478515625,
0.012359619140625,
-0.005199432373046875,
-0.0000845193862915039,
-0.022613525390625,
0.0095672607421875,
-0.0167694091796875,
0.0026302337646484375,
-0.004058837890625,
0.01036834716796875,
-0.0100860595703125,
-0.01253509521484375,
-0.0206146240234375,
-0.05645751953125,
-0.00794219970703125,
-0.00046181678771972656,
0.0242462158203125,
-0.00859832763671875,
0.00884246826171875,
-0.03216552734375,
0.0225067138671875,
-0.00887298583984375,
0.01200103759765625,
-0.01107025146484375,
0.001186370849609375,
-0.04034423828125,
-0.0311126708984375,
0.025543212890625,
-0.0226593017578125,
-0.0032596588134765625,
-0.0165557861328125,
-0.01507568359375,
0.036041259765625,
-0.02850341796875,
0.00936126708984375,
0.004184722900390625,
0.01515960693359375,
0.032958984375,
0.025604248046875,
-0.0223541259765625,
0.00611114501953125,
0.0010061264038085938,
-0.0218963623046875,
0.0284576416015625,
0.006916046142578125,
0.00010633468627929688,
-0.01496124267578125,
0.01190185546875,
-0.0477294921875,
0.0273895263671875,
0.0238189697265625,
-0.0014200210571289062,
-0.0312347412109375,
0.0078277587890625,
-0.012603759765625,
0.01190948486328125,
-0.0009946823120117188,
0.0013856887817382812,
0.049407958984375,
-0.01158905029296875,
-0.0025272369384765625,
-0.01065826416015625,
0.0180816650390625,
0.0003349781036376953,
0.018951416015625,
0.023895263671875,
-0.008209228515625,
0.01024627685546875,
0.030120849609375,
-0.004085540771484375,
-0.004795074462890625,
0.027679443359375,
-0.00875091552734375,
0.005016326904296875,
-0.0013055801391601562,
-0.033355712890625,
0.016204833984375,
-0.03155517578125,
0.012603759765625,
-0.0201568603515625,
-0.006412506103515625,
-0.01107025146484375,
-0.03131103515625,
-0.0026874542236328125,
-0.01438140869140625,
-0.0185699462890625,
0.00873565673828125,
-0.0031585693359375,
0.005458831787109375,
0.03179931640625,
0.0004563331604003906,
0.01373291015625,
-0.0181732177734375,
0.0215301513671875,
0.0032558441162109375,
0.0157623291015625,
0.0048065185546875,
-0.0006809234619140625,
0.00194549560546875,
0.01849365234375,
0.0164794921875,
-0.00064849853515625,
-0.005107879638671875,
-0.0018510818481445312,
-0.0068817138671875,
-0.0045623779296875,
0.00154876708984375,
0.0404052734375,
0.0234222412109375,
-0.0161590576171875,
-0.020355224609375,
-0.04071044921875,
0.0198211669921875,
0.03192138671875,
0.0027942657470703125,
0.025604248046875,
-0.007755279541015625,
0.024688720703125,
-0.002742767333984375,
0.007511138916015625,
-0.01385498046875,
-0.004398345947265625,
0.0163726806640625,
0.0292205810546875,
-0.01477813720703125,
-0.0025730133056640625,
-0.01345062255859375,
-0.0301513671875,
-0.01513671875,
-0.00444793701171875,
-0.034942626953125,
-0.0059967041015625,
0.004772186279296875,
-0.0052642822265625,
-0.01338958740234375,
0.01268768310546875,
-0.0019931793212890625,
-0.0000584721565246582,
0.032318115234375,
-0.005062103271484375,
0.005802154541015625,
-0.025726318359375,
-0.007720947265625,
0.037322998046875,
-0.0190582275390625,
0.005825042724609375,
-0.024505615234375,
-0.02520751953125,
-0.0335693359375,
0.00916290283203125,
-0.01294708251953125,
-0.00786590576171875,
0.01641845703125,
-0.0130767822265625,
-0.0073394775390625,
0.0035114288330078125,
-0.024139404296875,
-0.01039886474609375,
-0.00911712646484375,
0.030975341796875,
-0.010528564453125,
-0.007049560546875,
0.03082275390625,
0.0152435302734375,
-0.0220184326171875,
0.0228118896484375,
0.0352783203125,
0.05230712890625,
-0.01329803466796875,
-0.0101470947265625,
0.018341064453125,
-0.01580810546875,
-0.02301025390625,
0.004199981689453125,
0.0092010498046875,
0.059661865234375,
-0.00711822509765625,
0.0303955078125,
-0.0016880035400390625,
0.0251312255859375,
0.0006504058837890625,
0.00015103816986083984,
0.0003287792205810547,
-0.012542724609375,
-0.007415771484375,
-0.0268096923828125,
0.0226593017578125,
-0.033416748046875,
-0.0048675537109375,
0.00400543212890625,
0.0010251998901367188,
-0.007625579833984375,
-0.041656494140625,
0.007465362548828125,
0.00008893013000488281,
0.01006317138671875,
-0.004436492919921875,
-0.01119232177734375,
-0.01959228515625,
0.00841522216796875,
0.0263519287109375,
0.01044464111328125,
0.0001347064971923828,
-0.0008945465087890625,
0.035247802734375,
0.0047607421875,
0.0061492919921875,
-0.01529693603515625,
-0.0254058837890625,
0.03369140625,
-0.012603759765625,
0.01013946533203125,
0.005802154541015625,
-0.03228759765625,
0.00322723388671875,
0.01448822021484375,
-0.006061553955078125,
0.0258331298828125,
-0.00629425048828125,
0.01319122314453125,
0.01727294921875,
-0.0189361572265625,
-0.01425933837890625,
-0.005313873291015625,
0.0235137939453125,
0.00879669189453125,
0.0084075927734375,
-0.0209503173828125,
-0.02337646484375,
0.006710052490234375,
0.0029754638671875,
-0.00218963623046875,
-0.046142578125,
-0.000965118408203125,
0.00015175342559814453,
-0.01873779296875,
0.018157958984375,
-0.0110931396484375,
0.0223236083984375,
-0.0055389404296875,
0.014984130859375,
-0.032623291015625,
0.0085296630859375,
-0.038818359375,
0.0164794921875,
0.0032825469970703125,
0.003925323486328125,
-0.0285797119140625,
0.01222991943359375,
-0.01082611083984375,
0.01169586181640625,
-0.00930023193359375,
-0.0124969482421875,
0.02508544921875,
0.0078277587890625,
-0.0276031494140625,
0.0269012451171875,
-0.0000661611557006836,
-0.01140594482421875,
0.00047707557678222656,
0.009674072265625,
0.028717041015625,
-0.0107574462890625,
-0.0217132568359375,
-0.033355712890625,
0.020751953125,
-0.03582763671875,
0.0009107589721679688,
-0.013336181640625,
0.0204925537109375,
-0.0191497802734375,
0.021270751953125,
0.0141448974609375,
-0.04388427734375,
0.01558685302734375,
-0.0183868408203125,
0.006725311279296875,
-0.01385498046875,
0.0035991668701171875,
0.0093841552734375,
0.0187225341796875,
-0.01467132568359375,
-0.006336212158203125,
0.0034351348876953125,
-0.0078582763671875,
0.01141357421875,
0.0202178955078125,
0.040191650390625,
-0.0012178421020507812,
0.005985260009765625,
-0.0022487640380859375,
0.0038356781005859375,
-0.0110931396484375,
0.0267181396484375,
-0.0016794204711914062,
-0.004245758056640625,
-0.030426025390625,
0.00426483154296875,
-0.019012451171875,
-0.0222930908203125,
0.00821685791015625,
-0.010345458984375,
0.0149688720703125,
-0.0155487060546875,
-0.018768310546875,
-0.002132415771484375,
-0.011322021484375,
-0.012664794921875,
0.0001989603042602539,
-0.00039649009704589844,
0.01154327392578125,
-0.0169219970703125,
0.01947021484375,
-0.003269195556640625,
0.00565338134765625,
-0.01003265380859375,
-0.00856781005859375,
0.0159912109375,
0.0055694580078125,
-0.04766845703125,
-0.0082550048828125,
-0.0122528076171875,
0.015960693359375,
-0.0265960693359375,
0.01538848876953125,
-0.00698089599609375,
0.032745361328125,
-0.004215240478515625,
0.005565643310546875,
0.0108795166015625,
-0.021514892578125,
0.006351470947265625,
-0.0216064453125,
-0.01024627685546875,
0.024932861328125,
0.011077880859375,
-0.01216888427734375,
0.0090484619140625,
0.0040435791015625,
-0.00807952880859375,
-0.00955963134765625,
0.03192138671875,
-0.00492095947265625,
-0.007083892822265625,
-0.00017726421356201172,
-0.02545166015625,
-0.0017528533935546875,
0.006984710693359375,
-0.031829833984375,
0.00450897216796875,
0.0090179443359375,
-0.0253143310546875,
0.0143280029296875,
0.00006967782974243164,
0.005435943603515625,
0.0180511474609375,
0.0240478515625,
0.032440185546875,
0.0084075927734375,
-0.0267486572265625,
0.00594329833984375,
-0.00433349609375,
-0.0173797607421875,
0.0113677978515625,
-0.017822265625,
0.0413818359375,
-0.0311737060546875,
-0.0134124755859375,
-0.00279998779296875,
-0.0089111328125,
0.0149078369140625,
0.0200653076171875,
-0.0066070556640625,
0.01369476318359375,
0.0131378173828125,
-0.0209197998046875,
0.0003638267517089844,
0.032501220703125,
0.04962158203125,
0.012176513671875,
-0.0128173828125,
-0.038330078125,
-0.0098724365234375,
-0.007556915283203125,
0.038665771484375,
-0.017181396484375,
-0.00351715087890625,
-0.0084075927734375,
0.00244140625,
0.0135650634765625,
-0.027008056640625,
-0.0257415771484375,
-0.00708770751953125,
-0.04461669921875,
0.0203704833984375,
-0.01386260986328125,
0.0028743743896484375,
0.01727294921875,
-0.0136566162109375,
-0.0161895751953125,
-0.00019431114196777344,
-0.0168304443359375,
0.0017023086547851562,
-0.006397247314453125,
-0.00984954833984375,
-0.003421783447265625,
-0.02691650390625,
0.0143890380859375,
-0.006389617919921875,
-0.0110015869140625,
-0.018890380859375,
-0.01861572265625,
-0.00868988037109375,
-0.0170135498046875,
0.004970550537109375,
-0.035308837890625,
-0.005756378173828125,
0.01934814453125,
0.0142364501953125,
-0.005702972412109375,
-0.0063323974609375,
-0.0206298828125,
0.01580810546875,
0.010101318359375,
0.01532745361328125,
-0.0186767578125,
0.00550079345703125,
-0.0160675048828125,
-0.01526641845703125,
-0.0097198486328125,
-0.0037097930908203125,
0.0145111083984375,
-0.004619598388671875,
0.01235198974609375,
-0.0235443115234375,
-0.00882720947265625,
0.022308349609375,
-0.01107025146484375,
-0.03765869140625,
0.0284423828125,
0.0132293701171875,
0.025604248046875,
0.039306640625,
-0.024261474609375,
0.00904083251953125,
-0.00550079345703125,
-0.02203369140625,
0.0228118896484375,
-0.028900146484375,
0.0233154296875,
0.001064300537109375,
-0.02362060546875,
0.0321044921875,
-0.0025787353515625,
-0.01617431640625,
0.01513671875,
0.0148468017578125,
0.0079498291015625,
0.0200042724609375,
0.003269195556640625,
-0.005664825439453125,
0.016204833984375,
-0.0297393798828125,
0.015228271484375,
-0.03973388671875,
-0.006633758544921875,
0.00010061264038085938,
0.03314208984375,
-0.0041351318359375,
0.01340484619140625,
0.005207061767578125,
-0.0160675048828125,
0.0017185211181640625,
-0.0229644775390625,
0.01220703125,
-0.02386474609375,
-0.00009363889694213867,
0.0088348388671875,
0.005344390869140625,
-0.0168304443359375,
-0.02490234375,
0.033172607421875,
-0.027984619140625,
0.0082855224609375,
0.005329132080078125,
-0.00873565673828125,
-0.0298614501953125,
-0.006366729736328125,
0.006992340087890625,
-0.005680084228515625,
-0.0194854736328125,
0.00836944580078125,
-0.017120361328125,
0.0290069580078125,
-0.03070068359375,
-0.0024585723876953125,
-0.0010499954223632812,
0.01094818115234375,
0.0171356201171875,
-0.01503753662109375,
0.01617431640625,
0.0204010009765625,
-0.006137847900390625,
0.0036258697509765625,
-0.005176544189453125,
-0.0057373046875,
0.029632568359375,
-0.01363372802734375,
0.00934600830078125,
0.01806640625,
0.0009984970092773438,
-0.01398468017578125,
0.01317596435546875,
-0.034942626953125,
0.0266571044921875,
0.0159759521484375,
0.0165863037109375,
0.0008578300476074219,
-0.006622314453125,
0.0157318115234375,
-0.0017852783203125,
0.0183563232421875,
0.032745361328125,
0.0246734619140625,
0.050689697265625,
-0.02252197265625,
-0.02691650390625,
0.0015430450439453125,
0.008270263671875,
-0.03546142578125,
-0.0012664794921875,
0.029876708984375,
0.00252532958984375,
-0.0061492919921875,
-0.003826141357421875,
-0.04022216796875,
-0.01421356201171875,
0.003662109375,
-0.0164031982421875,
0.004352569580078125,
0.01305389404296875,
0.0203094482421875,
0.023162841796875,
0.0224761962890625,
-0.045257568359375,
-0.0114593505859375,
-0.013336181640625,
0.006137847900390625,
-0.02728271484375,
-0.007617950439453125,
-0.034423828125,
-0.002964019775390625,
-0.0340576171875,
-0.0012254714965820312,
0.00994873046875,
0.00926971435546875,
-0.0217132568359375,
-0.0007243156433105469,
0.00443267822265625,
0.0288238525390625,
0.05242919921875,
-0.0164642333984375,
0.0156402587890625,
-0.0084686279296875,
-0.03179931640625,
-0.003261566162109375,
-0.0033969879150390625,
0.006633758544921875,
0.0087432861328125,
-0.0269622802734375,
0.00861358642578125,
-0.0232696533203125,
0.0258026123046875,
0.00821685791015625,
-0.011505126953125,
-0.0037021636962890625,
0.0129852294921875,
-0.0095367431640625,
-0.0176849365234375,
0.01409912109375,
0.01039886474609375,
-0.0140380859375,
0.01959228515625,
-0.021240234375,
0.0029125213623046875,
0.0140380859375,
0.043426513671875,
0.0210418701171875,
-0.0153045654296875,
-0.014068603515625,
-0.0244903564453125,
0.0208892822265625,
-0.00565338134765625,
-0.02239990234375,
-0.001270294189453125,
-0.004299163818359375,
0.01001739501953125,
0.026947021484375,
-0.0170440673828125,
0.0139617919921875,
-0.0309906005859375,
-0.0004489421844482422,
0.0291900634765625,
-0.007236480712890625,
-0.004482269287109375,
-0.013031005859375,
-0.0005688667297363281,
-0.006824493408203125,
-0.012725830078125,
-0.015472412109375,
-0.0160064697265625,
-0.0102691650390625,
-0.0014543533325195312,
0.00653839111328125,
-0.0155181884765625,
-0.01552581787109375,
-0.01306915283203125,
-0.0280303955078125,
-0.01146697998046875,
0.016021728515625,
-0.0057525634765625
] |
ours_471
|
Let \(R_1\) be the radius of \(\omega_1\), and let \(R_2\) be the radius of \(\omega_2\). Then \(\frac{A_1}{A_2} = \frac{\pi R_1^2}{\pi R_2^2} = \left(\frac{R_1}{R_2}\right)^2\), and \(\frac{R_1}{R_2} = \frac{2R_1 \sin \angle ABC}{2R_2 \sin \angle ABM} = \frac{AC}{AM}\), by the Extended Law of Sines. Thus \(\frac{A_1}{A_2} = \frac{AC^2}{AM^2}\). Now \(AM^2 = \frac{2AB^2 + 2AC^2 - BC^2}{4} = \frac{95}{2}\), so \(\frac{A_1}{A_2} = \frac{81}{\left(\frac{95}{2}\right)} = \frac{162}{95}\), so the answer is \(16295\).
\(\boxed{16295}\)
|
16295
|
{
"competition": "us_comps",
"dataset": "Ours",
"posts": null,
"source": "OMOFall18Solns.md"
}
|
In triangle \(ABC\), \(AB = 8\), \(AC = 9\), and \(BC = 10\). Let \(M\) be the midpoint of \(BC\). Circle \(\omega_1\) with area \(A_1\) passes through \(A\), \(B\), and \(C\). Circle \(\omega_2\) with area \(A_2\) passes through \(A\), \(B\), and \(M\). Then \(\frac{A_1}{A_2} = \frac{m}{n}\) for relatively prime positive integers \(m\) and \(n\). Compute \(100m + n\).
|
[
"/Mathematics/Geometry/GeneralGeometry/EuclideanGeometry",
"/Mathematics/Geometry/GeneralGeometry/Geometry",
"/Mathematics/Geometry/PlaneGeometry/Circles",
"/Mathematics/Geometry/PlaneGeometry/CircularTriangles",
"/Mathematics/Geometry/PlaneGeometry/Triangles"
] |
Apply the extended law of sines to turn the ratio of circumradii into the ratio of side lengths AC and AM.
|
[
-0.00010854005813598633,
0.00202178955078125,
0.0458984375,
0.008056640625,
-0.000046312808990478516,
0.0361328125,
-0.00687408447265625,
0.015960693359375,
0.0011768341064453125,
-0.0240478515625,
-0.005084991455078125,
0.03326416015625,
-0.007251739501953125,
0.0228271484375,
-0.01528167724609375,
-0.0181427001953125,
-0.000568389892578125,
-0.03533935546875,
0.022857666015625,
0.001415252685546875,
-0.0150299072265625,
-0.023406982421875,
-0.05926513671875,
0.0091705322265625,
0.005970001220703125,
-0.0292510986328125,
-0.01373291015625,
-0.008453369140625,
-0.01380157470703125,
-0.0087432861328125,
-0.0187225341796875,
-0.006313323974609375,
0.00799560546875,
-0.01280975341796875,
0.0007395744323730469,
0.00373077392578125,
0.0190887451171875,
-0.0022487640380859375,
-0.0017271041870117188,
-0.026763916015625,
-0.0016946792602539062,
0.020263671875,
-0.0199432373046875,
0.00507354736328125,
0.0007781982421875,
-0.00514984130859375,
-0.0007944107055664062,
-0.00601959228515625,
0.0205230712890625,
-0.01264190673828125,
0.0035533905029296875,
0.00766754150390625,
-0.0140533447265625,
-0.017333984375,
-0.00029754638671875,
-0.038238525390625,
-0.023284912109375,
0.0010671615600585938,
0.005283355712890625,
-0.025054931640625,
0.0017557144165039062,
0.030426025390625,
-0.0007352828979492188,
-0.0292205810546875,
-0.00333404541015625,
-0.0106658935546875,
-0.0176849365234375,
-0.0182342529296875,
-0.00494384765625,
0.01548004150390625,
0.053497314453125,
-0.0237274169921875,
0.007503509521484375,
0.0162353515625,
0.0229644775390625,
-0.00630950927734375,
-0.015960693359375,
0.0018682479858398438,
-0.00481414794921875,
-0.00479888916015625,
-0.0116119384765625,
-0.0001049041748046875,
0.01219940185546875,
-0.01947021484375,
0.0257110595703125,
-0.016021728515625,
0.00942230224609375,
0.01177215576171875,
0.03472900390625,
-0.00945281982421875,
-0.006198883056640625,
-0.003314971923828125,
-0.0171966552734375,
0.01117706298828125,
0.0015583038330078125,
0.01519012451171875,
0.01319122314453125,
-0.0096893310546875,
-0.0172271728515625,
0.00397491455078125,
-0.01776123046875,
0.005218505859375,
0.00738525390625,
-0.0148773193359375,
0.028778076171875,
-0.01654052734375,
0.0003409385681152344,
0.0265350341796875,
-0.0009708404541015625,
-0.007843017578125,
0.018096923828125,
-0.00969696044921875,
0.0024623870849609375,
0.032867431640625,
0.0177459716796875,
-0.01508331298828125,
0.016815185546875,
-0.01059722900390625,
0.01202392578125,
-0.002094268798828125,
0.0037250518798828125,
0.01116180419921875,
0.0008044242858886719,
0.005084991455078125,
0.005657196044921875,
0.0266571044921875,
0.00498199462890625,
-0.01262664794921875,
-0.038055419921875,
0.006832122802734375,
0.027801513671875,
0.00536346435546875,
-0.05859375,
-0.01812744140625,
-0.04595947265625,
0.00823211669921875,
0.00969696044921875,
0.004688262939453125,
-0.0281829833984375,
-0.02069091796875,
0.0026760101318359375,
-0.010833740234375,
0.00559234619140625,
-0.061279296875,
0.01093292236328125,
-0.043975830078125,
-0.020263671875,
0.0084991455078125,
0.012359619140625,
0.010955810546875,
-0.026824951171875,
-0.002017974853515625,
0.0026912689208984375,
0.001861572265625,
-0.01189422607421875,
-0.0150146484375,
0.006938934326171875,
0.0272674560546875,
0.0115509033203125,
0.0046234130859375,
-0.0019426345825195312,
-0.0157928466796875,
-0.0052947998046875,
0.01551055908203125,
-0.002346038818359375,
-0.0065765380859375,
-0.027130126953125,
0.01276397705078125,
-0.0291900634765625,
-0.0018482208251953125,
-0.00366973876953125,
0.02191162109375,
-0.00476837158203125,
-0.0186767578125,
0.00002562999725341797,
0.006206512451171875,
-0.0222015380859375,
0.0118255615234375,
-0.020599365234375,
0.005950927734375,
-0.00916290283203125,
-0.0209197998046875,
0.0288238525390625,
0.00978851318359375,
-0.0239105224609375,
0.0114593505859375,
0.0101165771484375,
0.006938934326171875,
0.020843505859375,
0.007476806640625,
-0.018768310546875,
-0.0191650390625,
-0.0024127960205078125,
0.001697540283203125,
0.01751708984375,
-0.003131866455078125,
-0.049896240234375,
-0.005664825439453125,
0.032501220703125,
-0.010498046875,
-0.00603485107421875,
-0.0145416259765625,
0.0165557861328125,
0.01216888427734375,
-0.0123291015625,
0.02081298828125,
-0.00048422813415527344,
0.0000028014183044433594,
-0.019622802734375,
0.00237274169921875,
0.01380157470703125,
0.00876617431640625,
-0.006378173828125,
0.005771636962890625,
-0.0005159378051757812,
-0.01322174072265625,
-0.014373779296875,
0.01239776611328125,
0.00847625732421875,
0.01904296875,
0.0028171539306640625,
-0.0180206298828125,
0.01334381103515625,
-0.03265380859375,
-0.01499176025390625,
0.0141143798828125,
-0.0008864402770996094,
-0.0008835792541503906,
0.0140380859375,
-0.00853729248046875,
0.00460052490234375,
0.0024871826171875,
0.006145477294921875,
-0.005474090576171875,
-0.001522064208984375,
-0.005161285400390625,
-0.034210205078125,
-0.007526397705078125,
0.0101470947265625,
-0.007320404052734375,
0.03680419921875,
-0.0157470703125,
0.00907135009765625,
-0.0035953521728515625,
0.01035308837890625,
0.0128631591796875,
0.01183319091796875,
-0.01122283935546875,
0.0016326904296875,
0.0016422271728515625,
-0.0140380859375,
0.031280517578125,
0.004344940185546875,
-0.0202789306640625,
-0.0301361083984375,
0.01207733154296875,
0.0006780624389648438,
-0.005954742431640625,
-0.01122283935546875,
-0.0025005340576171875,
-0.003620147705078125,
-0.0226287841796875,
0.00830841064453125,
-0.00933837890625,
-0.009918212890625,
0.028167724609375,
-0.01190948486328125,
0.0189056396484375,
0.003719329833984375,
-0.00798797607421875,
0.058837890625,
-0.0218658447265625,
-0.005664825439453125,
-0.004352569580078125,
0.007564544677734375,
-0.04010009765625,
0.004955291748046875,
-0.0022716522216796875,
0.0023860931396484375,
0.01390838623046875,
0.024261474609375,
-0.01345062255859375,
-0.02496337890625,
0.004199981689453125,
0.0106964111328125,
0.0120849609375,
0.00278472900390625,
-0.040069580078125,
0.0007863044738769531,
0.019500732421875,
-0.0054779052734375,
0.02099609375,
-0.0208740234375,
-0.010772705078125,
0.037933349609375,
-0.00024175643920898438,
-0.007080078125,
0.0284271240234375,
0.0157470703125,
0.02252197265625,
0.0264892578125,
-0.0102996826171875,
-0.00905609130859375,
-0.030242919921875,
0.018218994140625,
0.02484130859375,
0.007354736328125,
-0.0011301040649414062,
-0.0087738037109375,
-0.0298004150390625,
0.00707244873046875,
0.0008730888366699219,
-0.0012636184692382812,
0.0018415451049804688,
-0.023651123046875,
-0.048492431640625,
-0.0154266357421875,
-0.0008497238159179688,
-0.0004642009735107422,
0.042938232421875,
-0.001773834228515625,
0.01010894775390625,
0.0035190582275390625,
0.004261016845703125,
0.022613525390625,
-0.02789306640625,
0.001934051513671875,
-0.0008378028869628906,
0.01546478271484375,
0.02386474609375,
-0.0261688232421875,
0.01506805419921875,
-0.00307464599609375,
-0.031829833984375,
-0.004138946533203125,
0.01739501953125,
-0.007244110107421875,
0.018402099609375,
0.00225830078125,
0.0015134811401367188,
0.0010938644409179688,
0.01305389404296875,
0.0048065185546875,
-0.07904052734375,
-0.02557373046875,
0.039031982421875,
0.01221466064453125,
-0.0013475418090820312,
-0.0311126708984375,
-0.00858306884765625,
0.0116119384765625,
0.00966644287109375,
0.01242828369140625,
-0.0014772415161132812,
-0.00650787353515625,
-0.0076141357421875,
0.0005970001220703125,
0.0125732421875,
-0.0025653839111328125,
0.0201873779296875,
0.01502227783203125,
-0.01654052734375,
-0.005962371826171875,
0.0135498046875,
-0.017333984375,
-0.00852203369140625,
-0.01097869873046875,
-0.0223846435546875,
-0.0616455078125,
0.00909423828125,
-0.0114898681640625,
-0.0272979736328125,
0.00812530517578125,
0.0069122314453125,
0.033966064453125,
0.0082550048828125,
-0.0285491943359375,
0.0172576904296875,
-0.0174102783203125,
0.00020432472229003906,
-0.0218963623046875,
-0.0129547119140625,
0.01727294921875,
0.0279998779296875,
-0.0250244140625,
0.0103759765625,
0.03082275390625,
-0.032470703125,
-0.0213165283203125,
-0.0030345916748046875,
-0.00955963134765625,
0.009918212890625,
-0.01690673828125,
-0.02703857421875,
-0.0253143310546875,
0.002590179443359375,
-0.00872802734375,
-0.00811004638671875,
0.03546142578125,
-0.006366729736328125,
-0.0543212890625,
0.001407623291015625,
0.00009042024612426758,
-0.0205078125,
0.0003256797790527344,
0.003173828125,
-0.0201263427734375,
0.0266876220703125,
-0.0029277801513671875,
0.0191650390625,
-0.0036449432373046875,
-0.00525665283203125,
0.0080108642578125,
-0.0218963623046875,
-0.0113525390625,
0.0207977294921875,
-0.00991058349609375,
0.00885009765625,
-0.017547607421875,
-0.0010089874267578125,
0.0259552001953125,
0.01035308837890625,
0.026580810546875,
-0.0152435302734375,
0.00991058349609375,
0.0179290771484375,
-0.007965087890625,
0.03863525390625,
0.013885498046875,
0.005771636962890625,
0.03558349609375,
-0.0034332275390625,
-0.018798828125,
0.0247039794921875,
-0.0091705322265625,
0.0013856887817382812,
-0.002178192138671875,
-0.01788330078125,
0.003940582275390625,
0.0221710205078125,
-0.0008425712585449219,
0.01099395751953125,
0.007389068603515625,
0.0091705322265625,
-0.01224517822265625,
0.0006098747253417969,
0.0112152099609375,
0.00823211669921875,
0.0010786056518554688,
0.01192474365234375,
-0.0282745361328125,
-0.04339599609375,
0.0357666015625,
-0.029541015625,
0.01995849609375,
0.01409912109375,
0.061920166015625,
-0.0308380126953125,
-0.040283203125,
0.0178375244140625,
0.004276275634765625,
0.01313018798828125,
0.003566741943359375,
0.03497314453125,
-0.0007429122924804688,
0.0173797607421875,
-0.014495849609375,
0.0287322998046875,
0.0092620849609375,
0.00957489013671875,
-0.00925445556640625,
-0.024444580078125,
0.0172576904296875,
-0.024627685546875,
-0.01995849609375,
0.022491455078125,
0.0119171142578125,
-0.01102447509765625,
-0.01186370849609375,
-0.010406494140625,
-0.0243988037109375,
-0.0003647804260253906,
0.00861358642578125,
-0.0022792816162109375,
-0.006710052490234375,
0.006816864013671875,
0.0167388916015625,
0.0029010772705078125,
-0.011383056640625,
-0.0302581787109375,
-0.0306549072265625,
-0.0006213188171386719,
-0.001049041748046875,
-0.039520263671875,
-0.03155517578125,
-0.033294677734375,
0.04364013671875,
-0.0064544677734375,
0.013427734375,
0.00682830810546875,
0.0109405517578125,
-0.0214996337890625,
-0.018218994140625,
0.0246429443359375,
-0.0034618377685546875,
-0.0521240234375,
0.035064697265625,
0.0024662017822265625,
0.0023365020751953125,
-0.0248565673828125,
-0.011138916015625,
0.024078369140625,
0.01226043701171875,
-0.031341552734375,
-0.0039043426513671875,
0.01751708984375,
-0.016693115234375,
-0.02264404296875,
0.0049896240234375,
0.046051025390625,
-0.040130615234375,
0.0248565673828125,
0.0269775390625,
-0.0127716064453125,
0.02362060546875,
0.025115966796875,
-0.002719879150390625,
-0.016357421875,
-0.0008225440979003906,
0.0014925003051757812,
-0.0022983551025390625,
0.015380859375,
-0.06549072265625,
0.007152557373046875,
-0.0043792724609375,
0.015899658203125,
-0.0014247894287109375,
-0.03289794921875,
0.00907135009765625,
-0.007488250732421875,
-0.0193328857421875,
-0.012298583984375,
0.01267242431640625,
-0.0277862548828125,
0.019378662109375,
-0.012939453125,
-0.0269927978515625,
0.025238037109375,
0.0008831024169921875,
0.02081298828125,
0.003265380859375,
0.02203369140625,
-0.036285400390625,
0.0216064453125,
-0.049957275390625,
-0.00269317626953125,
-0.037750244140625,
-0.0003895759582519531,
-0.0017795562744140625,
0.040283203125,
0.0024433135986328125,
0.00417327880859375,
0.00876617431640625,
-0.01519775390625,
-0.03277587890625,
0.006183624267578125,
0.01090240478515625,
0.0033283233642578125,
-0.00611114501953125,
-0.040740966796875,
0.0124969482421875,
0.003101348876953125,
-0.004695892333984375,
0.02191162109375,
0.0201873779296875,
-0.0265960693359375,
-0.0009131431579589844,
-0.0009226799011230469,
0.031890869140625,
-0.02630615234375,
0.015777587890625,
0.050506591796875,
-0.0038928985595703125,
-0.014373779296875,
-0.007778167724609375,
-0.005329132080078125,
-0.00312042236328125,
-0.008392333984375,
0.0328369140625,
0.01276397705078125,
-0.01873779296875,
0.01180267333984375,
0.01140594482421875,
-0.022918701171875,
-0.005344390869140625,
-0.016448974609375,
0.005588531494140625,
-0.00958251953125,
0.0230865478515625,
0.00811767578125,
-0.0006732940673828125,
-0.0145263671875,
-0.0517578125,
0.01983642578125,
-0.00814056396484375,
-0.004486083984375,
-0.024749755859375,
-0.0025157928466796875,
0.0179443359375,
0.0374755859375,
-0.01605224609375,
0.001575469970703125,
-0.0169525146484375,
0.0134735107421875,
0.00516510009765625,
-0.002567291259765625,
-0.0279388427734375,
0.0230560302734375,
0.004119873046875,
-0.03118896484375,
0.0048828125,
0.01186370849609375,
-0.0034198760986328125,
-0.0009241104125976562,
0.0015478134155273438,
-0.00992584228515625,
-0.006114959716796875,
-0.0389404296875,
-0.0020542144775390625,
-0.043914794921875,
-0.0135650634765625,
0.01447296142578125,
-0.024169921875,
-0.0191497802734375,
-0.021240234375,
-0.0267181396484375,
0.01953125,
0.01364898681640625,
-0.0136566162109375,
-0.0260467529296875,
0.0057830810546875,
0.00846099853515625,
0.0221099853515625,
-0.046295166015625,
-0.0257568359375,
-0.01678466796875,
-0.033050537109375,
-0.01065826416015625,
-0.005535125732421875,
0.01413726806640625,
0.0020542144775390625,
-0.0005178451538085938,
0.0323486328125,
0.0261688232421875,
-0.002716064453125,
-0.00258636474609375,
-0.03643798828125,
-0.0267486572265625,
0.037261962890625,
0.015777587890625,
-0.00850677490234375,
-0.01078033447265625,
-0.00730133056640625,
0.006359100341796875,
-0.003124237060546875,
-0.005641937255859375,
-0.04547119140625,
-0.0300445556640625,
0.01042938232421875,
0.034942626953125,
-0.01885986328125,
-0.018646240234375,
0.006622314453125,
-0.0042572021484375,
-0.006000518798828125,
0.028533935546875,
-0.014434814453125,
0.002216339111328125,
0.0194549560546875,
0.0277862548828125,
-0.0215606689453125,
0.0198516845703125,
0.040313720703125,
-0.0192718505859375,
-0.01348876953125,
0.04315185546875,
-0.01175689697265625,
0.004116058349609375,
-0.01004791259765625,
0.003002166748046875,
-0.00838470458984375,
0.021026611328125,
-0.0096282958984375,
0.00905609130859375,
-0.0016803741455078125,
-0.0010995864868164062,
0.0357666015625,
-0.0054473876953125,
0.0098876953125,
-0.0204620361328125,
0.00506591796875,
-0.04693603515625,
0.00884246826171875,
-0.026763916015625,
-0.03448486328125,
-0.0239105224609375,
-0.01233673095703125,
0.0223388671875,
-0.03350830078125,
0.01329803466796875,
-0.039337158203125,
-0.01403045654296875,
-0.0202789306640625,
0.006313323974609375,
-0.045135498046875,
-0.0079498291015625,
-0.019927978515625,
0.0190887451171875,
-0.027740478515625,
0.005207061767578125,
-0.04364013671875,
-0.006717681884765625,
0.00862884521484375,
-0.01556396484375,
-0.002376556396484375,
0.021270751953125,
0.0014705657958984375,
-0.00699615478515625,
-0.020660400390625,
0.0174407958984375,
0.0022716522216796875,
-0.0234527587890625,
0.0195770263671875,
0.007091522216796875,
-0.005359649658203125,
0.01218414306640625,
-0.0189056396484375,
-0.04852294921875,
-0.0030002593994140625,
0.034576416015625,
0.0308074951171875,
-0.027435302734375,
0.004207611083984375,
-0.00798797607421875,
-0.0076141357421875,
-0.0282440185546875,
-0.0122528076171875,
-0.031707763671875,
-0.011810302734375,
-0.01654052734375,
0.036865234375,
0.03155517578125,
-0.04248046875,
-0.0310516357421875,
-0.0121612548828125,
-0.006252288818359375,
-0.0058135986328125,
-0.0190887451171875,
0.0201873779296875,
0.00914764404296875,
-0.01500701904296875,
-0.0157470703125,
0.0110321044921875,
-0.028778076171875,
-0.0013818740844726562,
-0.01348114013671875,
0.006145477294921875,
-0.0207061767578125,
-0.007663726806640625,
0.0169677734375,
0.00951385498046875,
-0.006847381591796875,
0.0171966552734375,
0.01081085205078125,
0.0142974853515625,
-0.02117919921875,
-0.037750244140625,
-0.0013647079467773438,
0.038665771484375,
-0.00955963134765625,
-0.0035419464111328125,
0.021484375,
-0.020599365234375,
0.01666259765625,
-0.03973388671875,
-0.00969696044921875,
-0.0181884765625,
-0.00832366943359375,
0.02239990234375,
0.0015058517456054688,
0.020843505859375,
0.01113128662109375,
-0.0028247833251953125,
0.0019283294677734375,
-0.01605224609375,
-0.02008056640625,
-0.0148773193359375,
0.005222320556640625,
-0.0019330978393554688,
-0.003360748291015625,
-0.00437164306640625,
-0.02276611328125,
-0.0304412841796875,
0.00592803955078125,
0.0244903564453125,
0.00023937225341796875,
0.01788330078125,
0.0080108642578125,
-0.0201416015625,
0.016693115234375,
0.0160980224609375,
-0.01116943359375,
0.01445770263671875,
-0.012786865234375,
0.004302978515625,
-0.0282135009765625,
0.01702880859375,
0.02215576171875,
0.0175323486328125,
0.0099334716796875,
-0.034149169921875,
0.0214080810546875,
-0.0231170654296875,
0.00202178955078125,
-0.042724609375,
-0.009979248046875,
0.0204010009765625,
0.0103607177734375,
0.0244903564453125,
0.0030651092529296875,
0.0299072265625,
-0.024322509765625,
-0.0176849365234375,
0.005199432373046875,
-0.021270751953125,
-0.00016260147094726562,
0.0020732879638671875,
0.00807952880859375,
0.004734039306640625,
-0.0230865478515625,
0.0203399658203125,
-0.0017681121826171875,
0.0042572021484375,
0.041656494140625,
0.0261077880859375,
-0.022552490234375,
0.01473236083984375,
0.01354217529296875,
0.025390625,
0.005306243896484375,
-0.0311126708984375,
-0.004154205322265625,
-0.04608154296875,
0.020538330078125,
0.0200653076171875,
0.0025310516357421875,
0.01197052001953125,
-0.005096435546875,
0.0040130615234375,
-0.01261138916015625,
0.00821685791015625,
-0.0149078369140625,
0.0041046142578125,
0.0011386871337890625,
0.00815582275390625,
0.00209808349609375,
-0.007717132568359375,
0.01117706298828125,
0.030029296875,
0.01352691650390625,
0.031829833984375,
-0.031494140625,
0.0225982666015625,
0.00502777099609375,
0.00505828857421875,
0.028839111328125,
0.0178375244140625,
0.015960693359375,
0.05645751953125,
0.006683349609375,
-0.004619598388671875,
0.006256103515625,
-0.0263214111328125,
-0.0005555152893066406,
-0.019775390625,
-0.007904052734375,
0.010498046875,
-0.01056671142578125,
0.01473236083984375,
0.023468017578125,
0.00014221668243408203,
-0.00373077392578125,
-0.006175994873046875,
-0.04144287109375,
0.040679931640625,
-0.00799560546875,
-0.002597808837890625,
-0.0133056640625,
0.01099395751953125,
-0.0280609130859375,
-0.012420654296875,
0.0220947265625,
0.01922607421875,
-0.02239990234375,
0.0018625259399414062,
-0.0181732177734375,
-0.0256195068359375,
-0.0086822509765625,
0.01812744140625,
0.005222320556640625,
-0.007293701171875,
0.02490234375,
0.0207061767578125,
0.00714111328125,
0.0027713775634765625,
0.0021800994873046875,
-0.01007843017578125,
0.00832366943359375,
-0.007171630859375,
0.01064300537109375,
0.020172119140625,
0.0284423828125,
0.0021457672119140625,
-0.0232696533203125,
-0.0027217864990234375,
-0.0357666015625,
0.0004143714904785156,
0.01517486572265625,
-0.04693603515625,
0.0171661376953125,
-0.006092071533203125,
0.021240234375,
-0.01207733154296875,
-0.025177001953125,
0.0114288330078125,
0.0249786376953125,
-0.017547607421875,
-0.04327392578125,
-0.0002982616424560547,
-0.046722412109375,
0.0271453857421875,
0.004718780517578125,
0.01355743408203125,
0.01605224609375,
-0.015411376953125,
0.002849578857421875,
-0.00580596923828125,
0.02642822265625,
0.0257415771484375,
0.01019287109375,
0.007465362548828125,
-0.0189056396484375,
0.031524658203125,
-0.007442474365234375,
-0.00925445556640625,
0.01245880126953125,
-0.010894775390625,
0.036651611328125,
-0.01155853271484375,
0.00724029541015625,
0.0275115966796875,
0.0316162109375,
-0.004665374755859375,
0.023712158203125,
-0.0258636474609375,
0.0095367431640625,
0.01399993896484375,
0.0114593505859375,
-0.004825592041015625,
-0.0024852752685546875,
0.01277923583984375,
0.021148681640625,
-0.0024585723876953125,
-0.045501708984375,
-0.01290130615234375,
0.007110595703125,
0.00311279296875,
0.0161285400390625,
0.05682373046875,
0.0034694671630859375,
-0.0293121337890625,
0.019012451171875,
-0.005107879638671875,
0.006206512451171875,
0.028106689453125,
0.002506256103515625,
0.01690673828125,
-0.00858306884765625,
0.0440673828125,
-0.0052490234375,
-0.005062103271484375,
0.0487060546875,
-0.038543701171875,
0.0297088623046875,
-0.025543212890625,
-0.01045989990234375,
0.0006976127624511719,
-0.018035888671875,
0.01276397705078125,
0.01099395751953125,
-0.024017333984375,
0.024658203125,
0.0211029052734375,
0.00286865234375,
0.01052093505859375,
-0.0196533203125,
-0.01532745361328125,
0.0276031494140625,
0.00940704345703125,
0.01541900634765625,
-0.00551605224609375,
0.0178680419921875,
-0.00624847412109375,
0.00325775146484375,
-0.01629638671875,
0.01210784912109375,
0.00258636474609375,
0.0364990234375,
-0.0292510986328125,
0.0122222900390625,
-0.0025844573974609375,
-0.040985107421875,
-0.03179931640625,
-0.029144287109375,
0.023101806640625,
0.01512908935546875,
-0.01427459716796875,
-0.0246429443359375,
0.0197296142578125,
0.0093536376953125,
-0.0007653236389160156,
0.00341796875,
-0.0015430450439453125,
-0.0215606689453125,
-0.01119232177734375,
-0.02703857421875,
0.00896453857421875,
-0.00698089599609375,
0.02044677734375,
0.009857177734375,
-0.0292510986328125,
0.01285552978515625,
-0.012176513671875,
-0.0169525146484375,
-0.02703857421875,
0.006702423095703125,
-0.014556884765625,
0.0077056884765625,
0.021209716796875,
-0.002040863037109375,
0.034210205078125,
0.0179901123046875,
0.00388336181640625,
-0.01323699951171875,
0.0157928466796875,
0.0290069580078125,
0.004344940185546875,
-0.004283905029296875,
0.01117706298828125,
0.0174102783203125,
0.025390625,
-0.028961181640625,
-0.0154571533203125,
-0.0248565673828125,
0.03411865234375,
0.00624847412109375,
-0.016876220703125,
0.01488494873046875,
-0.01136016845703125,
0.03607177734375,
-0.056365966796875,
0.02130126953125,
-0.01922607421875,
-0.00853729248046875,
-0.0032634735107421875,
-0.0443115234375,
0.0157928466796875,
-0.031982421875,
0.0006079673767089844,
-0.003810882568359375,
-0.011322021484375,
0.01500701904296875,
-0.038848876953125,
-0.007293701171875,
0.0267333984375,
0.01715087890625,
-0.0158843994140625,
-0.032623291015625,
0.016693115234375,
-0.0234375,
0.0030078887939453125,
-0.04205322265625,
-0.0115814208984375,
0.0014066696166992188,
0.006011962890625,
-0.0214996337890625,
0.018341064453125,
0.01215362548828125,
0.039764404296875,
0.0009870529174804688,
-0.01605224609375,
0.038238525390625,
-0.007781982421875,
0.021881103515625,
-0.003498077392578125,
-0.0287017822265625,
-0.0240936279296875,
0.0119781494140625,
-0.011871337890625,
0.01470184326171875,
-0.005733489990234375,
0.0281829833984375,
0.0175323486328125,
0.0197601318359375,
-0.020965576171875,
-0.009429931640625,
-0.004901885986328125,
-0.0228729248046875,
0.019500732421875,
-0.03009033203125,
0.0231781005859375,
0.0135040283203125,
0.00012993812561035156,
0.0216064453125,
-0.00830078125,
-0.02484130859375,
0.02978515625,
-0.018402099609375,
-0.038238525390625,
-0.0139007568359375,
-0.0021209716796875,
0.0201416015625,
-0.0113983154296875,
-0.0206146240234375,
0.0096435546875,
0.01739501953125,
0.002079010009765625,
-0.006526947021484375,
0.0018863677978515625,
-0.005035400390625,
-0.0272979736328125,
0.01267242431640625,
0.00939178466796875,
-0.0199127197265625,
-0.00856781005859375,
-0.0159759521484375,
-0.015625,
0.000850677490234375,
-0.006565093994140625,
0.01788330078125,
-0.004962921142578125,
-0.012725830078125,
0.006832122802734375,
0.0022125244140625,
0.0004897117614746094,
-0.01000213623046875,
-0.031097412109375,
0.0008831024169921875,
-0.0100555419921875,
0.0170135498046875,
-0.004192352294921875,
0.030029296875,
0.01776123046875,
0.037384033203125,
-0.0187225341796875,
0.0155487060546875,
-0.0007948875427246094,
0.005954742431640625,
-0.019927978515625,
0.02984619140625,
0.001300811767578125,
0.0132293701171875,
0.029052734375,
0.0132904052734375,
-0.004611968994140625,
0.0204010009765625,
-0.0201568603515625,
-0.0214996337890625,
-0.006610870361328125,
0.01015472412109375,
-0.0094146728515625,
-0.0034503936767578125,
0.04107666015625,
-0.0022430419921875,
-0.00908660888671875,
-0.006481170654296875,
-0.0189666748046875,
-0.00630950927734375,
-0.022613525390625,
-0.007556915283203125,
0.00510406494140625,
-0.005672454833984375,
-0.0007257461547851562,
0.018035888671875,
0.01224517822265625,
0.030303955078125,
-0.01250457763671875,
-0.0274658203125,
-0.039459228515625,
-0.0263214111328125,
-0.041168212890625,
0.0061187744140625,
-0.0307769775390625,
-0.028961181640625,
0.01247406005859375,
0.007289886474609375,
-0.021759033203125,
0.0245361328125,
-0.053741455078125,
0.00791168212890625,
0.01480865478515625,
-0.003864288330078125,
0.0026378631591796875,
-0.0005478858947753906,
0.0106048583984375,
0.0035190582275390625,
-0.044281005859375,
-0.0177764892578125,
-0.006282806396484375,
-0.01142120361328125,
0.00412750244140625,
0.01568603515625,
0.0253143310546875,
0.0030345916748046875,
-0.0232696533203125,
0.0047607421875,
-0.0267791748046875,
0.0005879402160644531,
0.0115509033203125,
0.0121917724609375,
0.0028667449951171875,
0.024627685546875,
-0.003391265869140625,
0.0253448486328125,
-0.018157958984375,
-0.043365478515625,
0.0017681121826171875,
0.0364990234375,
-0.04937744140625,
-0.0006346702575683594,
-0.0177154541015625,
-0.00859832763671875,
0.00939178466796875,
-0.0021648406982421875,
0.0081024169921875,
-0.019012451171875,
-0.036041259765625,
-0.0030994415283203125,
-0.05255126953125,
0.060821533203125,
-0.01947021484375,
-0.0157623291015625,
-0.0107421875,
-0.01279449462890625,
0.0089874267578125,
0.01617431640625,
0.0301513671875,
0.022003173828125,
0.006122589111328125,
-0.01363372802734375,
-0.01322174072265625,
0.0109405517578125,
-0.0158233642578125,
-0.029083251953125,
0.0071258544921875,
0.00519561767578125,
0.01136016845703125,
0.03863525390625,
0.0181121826171875,
0.0013179779052734375,
0.0201873779296875,
0.00606536865234375,
-0.0105743408203125,
0.04248046875,
0.0146942138671875,
-0.0004930496215820312,
-0.0007491111755371094,
-0.02606201171875,
0.003696441650390625,
0.014862060546875,
-0.0177459716796875,
0.002716064453125,
0.020355224609375,
-0.00646209716796875,
-0.0158538818359375,
-0.0196990966796875,
-0.01117706298828125,
0.037841796875,
-0.0005717277526855469,
0.0249481201171875,
0.0240936279296875,
0.04437255859375,
0.002445220947265625,
0.0225830078125,
-0.007595062255859375,
-0.0307159423828125,
-0.0032901763916015625,
0.0372314453125,
0.0290679931640625,
-0.0157623291015625,
-0.005420684814453125,
-0.021148681640625,
0.001251220703125,
-0.006282806396484375,
-0.006679534912109375,
-0.015594482421875,
0.00484466552734375,
0.0226898193359375,
-0.0014133453369140625,
-0.0157012939453125,
0.00751495361328125,
-0.0014982223510742188,
0.0198974609375,
0.011322021484375,
0.0230712890625,
-0.0104217529296875,
0.0013017654418945312,
-0.0176239013671875,
0.0083770751953125,
-0.004840850830078125,
-0.016754150390625,
-0.0015363693237304688,
-0.0285797119140625,
-0.002033233642578125,
-0.02069091796875,
-0.0187835693359375,
-0.0213470458984375,
-0.007724761962890625,
-0.01409149169921875,
-0.01422882080078125,
-0.007099151611328125,
-0.00707244873046875,
0.01097869873046875,
0.00582122802734375,
0.0248260498046875,
0.00923919677734375,
0.01727294921875,
0.00926971435546875,
-0.021575927734375,
-0.004329681396484375,
-0.0132598876953125,
0.013671875,
-0.004985809326171875,
-0.006847381591796875,
0.0487060546875,
0.00942230224609375,
-0.0233001708984375,
0.0026073455810546875,
0.0007653236389160156,
-0.0269317626953125,
0.022705078125,
0.0023193359375,
-0.0031070709228515625,
0.03228759765625,
-0.044891357421875,
-0.0305328369140625,
0.00888824462890625,
0.038482666015625,
0.0177764892578125,
0.020843505859375,
0.014678955078125,
0.0012187957763671875,
0.022674560546875,
-0.01349639892578125,
0.040069580078125,
0.0152435302734375,
0.01502227783203125,
-0.0426025390625,
-0.0224609375,
0.0038394927978515625,
-0.021514892578125,
-0.01385498046875,
0.000732421875,
-0.00757598876953125,
0.0271759033203125,
-0.00360870361328125,
-0.00830841064453125,
-0.01526641845703125,
-0.0009708404541015625,
0.003803253173828125,
0.0167999267578125,
-0.01251220703125,
-0.003658294677734375,
-0.00844573974609375,
0.0182647705078125,
0.032257080078125,
-0.01294708251953125,
0.005191802978515625,
-0.036834716796875,
0.0016765594482421875,
0.004791259765625,
-0.0015268325805664062,
-0.02252197265625,
0.0110321044921875,
0.0282745361328125,
-0.01129913330078125,
-0.0118255615234375,
-0.01371002197265625,
-0.0249176025390625,
0.006221771240234375,
-0.0037479400634765625,
-0.0030460357666015625,
0.01288604736328125,
0.027984619140625,
0.0221405029296875,
0.005481719970703125,
0.020599365234375,
-0.0030879974365234375,
0.02349853515625,
-0.0010251998901367188,
-0.017486572265625,
-0.0167694091796875,
0.00453948974609375,
-0.0236053466796875,
0.021881103515625,
-0.04156494140625,
-0.00043773651123046875,
-0.0234832763671875,
-0.030303955078125,
-0.0003383159637451172,
-0.025238037109375,
0.00826263427734375,
-0.02777099609375,
-0.0105743408203125,
-0.00438690185546875,
0.00506591796875,
0.0121002197265625,
0.0293731689453125,
-0.00852203369140625,
0.00089263916015625,
-0.0011186599731445312,
0.004039764404296875,
-0.031768798828125,
0.01529693603515625,
0.028045654296875,
-0.01100921630859375,
0.035308837890625,
0.0023441314697265625,
0.026092529296875,
-0.025146484375,
0.0242156982421875,
0.01343536376953125,
0.01751708984375,
-0.01555633544921875,
-0.0177459716796875,
-0.00690460205078125,
-0.007778167724609375,
-0.00894927978515625,
-0.016510009765625,
-0.0174407958984375,
0.0142822265625,
-0.0189208984375,
-0.0234527587890625,
-0.001903533935546875,
0.033294677734375,
0.00395965576171875,
-0.001857757568359375,
-0.00665283203125,
-0.0008826255798339844,
-0.005702972412109375,
-0.03314208984375,
0.005336761474609375,
0.0057830810546875,
0.01702880859375,
0.00681304931640625,
0.00109100341796875,
-0.019439697265625,
0.0273284912109375,
-0.025970458984375,
-0.0141754150390625,
-0.04107666015625,
-0.00684356689453125,
0.0007381439208984375,
0.0242156982421875,
-0.0033283233642578125,
-0.004520416259765625,
0.00920867919921875,
-0.0075836181640625,
-0.01538848876953125,
-0.0035381317138671875,
-0.0146484375,
0.00485992431640625,
0.00843048095703125,
0.033355712890625,
0.015655517578125,
0.004962921142578125,
0.0027751922607421875,
0.0141143798828125,
-0.0009412765502929688,
-0.0242156982421875,
0.00942230224609375,
0.006534576416015625,
0.007843017578125,
0.025726318359375,
0.02142333984375,
0.0262603759765625,
-0.00821685791015625,
-0.0212249755859375,
-0.00011730194091796875,
-0.0416259765625,
0.0146026611328125,
0.0185394287109375,
0.004215240478515625,
-0.00620269775390625,
0.0255126953125,
-0.047637939453125,
-0.011871337890625,
-0.0377197265625,
0.00957489013671875,
-0.00966644287109375,
0.0352783203125,
-0.0013647079467773438,
-0.0001932382583618164,
0.019073486328125,
-0.0157318115234375,
0.0195159912109375,
-0.01549530029296875,
-0.0013589859008789062,
-0.0185699462890625,
0.0081634521484375,
0.0323486328125,
0.0225372314453125,
0.0006074905395507812,
0.03558349609375,
0.035186767578125,
-0.01329803466796875,
0.030517578125,
0.003055572509765625,
-0.0185699462890625,
0.00917816162109375,
-0.0179901123046875,
-0.02008056640625,
0.0202789306640625,
-0.01248931884765625,
-0.0166015625,
-0.006092071533203125,
-0.01050567626953125,
-0.0241851806640625,
0.01271820068359375,
0.0034198760986328125,
0.0212860107421875,
-0.0093231201171875,
-0.0238189697265625,
0.035491943359375,
0.01125335693359375,
-0.0006442070007324219,
0.00640106201171875,
0.018798828125,
0.00927734375,
-0.041717529296875,
0.04217529296875,
-0.00788116455078125,
0.019317626953125,
-0.0017175674438476562,
0.011322021484375,
0.0284881591796875,
-0.0025234222412109375,
0.0245819091796875,
-0.0128173828125,
-0.0229034423828125,
-0.00014221668243408203,
0.036865234375,
-0.01873779296875,
-0.0023479461669921875,
-0.0228118896484375,
-0.0262603759765625,
-0.006496429443359375,
0.009674072265625,
-0.036163330078125,
-0.0374755859375,
-0.01727294921875,
0.0040130615234375,
-0.032196044921875,
-0.028106689453125,
0.0211334228515625,
-0.00179290771484375,
0.0003228187561035156,
-0.006103515625,
0.00971221923828125,
-0.006793975830078125,
0.01007080078125,
-0.046234130859375,
-0.0009732246398925781,
0.02105712890625,
0.03668212890625,
0.0206451416015625,
-0.0228118896484375,
0.0182037353515625,
-0.03240966796875,
-0.0301971435546875,
0.0074462890625,
0.0227203369140625,
0.032562255859375,
-0.0012369155883789062,
-0.012420654296875,
-0.006435394287109375,
0.009368896484375,
-0.0101318359375,
0.062164306640625,
0.005672454833984375,
-0.0096435546875,
0.021942138671875,
-0.0258026123046875,
0.017333984375,
-0.026824951171875,
-0.0005574226379394531,
0.016326904296875,
0.0009675025939941406,
-0.0421142578125,
0.00643157958984375,
-0.01116943359375,
0.0052337646484375,
-0.00815582275390625,
0.01299285888671875,
-0.01001739501953125,
0.0156097412109375,
0.012359619140625,
0.0294036865234375,
-0.01306915283203125,
0.0158538818359375,
0.0206146240234375,
-0.0215606689453125,
0.0008182525634765625,
0.00003701448440551758,
-0.0238800048828125,
0.005809783935546875,
-0.0100250244140625,
0.00290679931640625,
-0.0016546249389648438,
-0.01265716552734375,
-0.0195159912109375,
0.01151275634765625,
0.0266876220703125,
-0.01016998291015625,
-0.032745361328125,
-0.017242431640625,
0.005970001220703125,
0.0013408660888671875,
0.01059722900390625,
-0.00010514259338378906,
0.020751953125,
-0.005290985107421875,
0.04266357421875,
-0.0036869049072265625,
-0.0186767578125,
-0.0169677734375,
0.004367828369140625,
0.00836181640625,
-0.00756072998046875,
-0.0243072509765625,
0.03125,
-0.0042877197265625,
-0.0262451171875,
0.0097503662109375,
0.033782958984375,
-0.0155487060546875,
0.0060882568359375,
-0.01093292236328125,
-0.0090484619140625,
-0.00615692138671875,
0.00699615478515625,
0.01416778564453125,
-0.0250091552734375,
0.04437255859375,
-0.0289154052734375,
-0.00392913818359375,
-0.0014867782592773438,
0.001422882080078125,
-0.018157958984375,
0.0108642578125,
0.0185394287109375,
0.0029201507568359375,
0.00640869140625,
0.0090789794921875,
-0.0020999908447265625,
-0.00795745849609375,
-0.002925872802734375,
-0.0115509033203125,
-0.0008921623229980469,
-0.00658416748046875,
-0.005161285400390625,
-0.041748046875,
0.0179290771484375,
-0.01284027099609375,
-0.0225067138671875,
-0.028350830078125,
-0.0141754150390625,
-0.005218505859375,
0.032623291015625,
0.011322021484375,
0.0225830078125,
-0.00904083251953125,
-0.0487060546875,
0.022308349609375,
0.0218658447265625,
0.01175689697265625,
0.018707275390625,
-0.0202789306640625,
-0.01055145263671875,
0.0236663818359375,
-0.0177154541015625,
-0.02325439453125,
-0.027557373046875,
-0.0028228759765625,
0.0141754150390625,
0.00989532470703125,
-0.015777587890625,
-0.00167083740234375,
-0.044403076171875,
-0.005290985107421875,
0.0189361572265625,
-0.03643798828125,
-0.01287078857421875,
-0.0245361328125,
-0.004497528076171875,
0.016082763671875,
0.01073455810546875,
0.033721923828125,
-0.0130615234375,
-0.01517486572265625,
-0.003204345703125,
-0.00957489013671875,
0.004634857177734375,
0.01171875,
0.0201568603515625,
-0.038116455078125,
0.0269927978515625,
-0.033447265625,
-0.01384735107421875,
0.0029010772705078125,
0.02923583984375,
-0.0085601806640625,
-0.006320953369140625,
0.009796142578125,
-0.0235748291015625,
-0.034515380859375,
0.01442718505859375,
-0.02862548828125,
0.0046539306640625,
0.01137542724609375,
-0.0026187896728515625,
0.023468017578125,
-0.005306243896484375,
0.0036869049072265625,
-0.0052642822265625,
0.0019207000732421875,
0.0022754669189453125,
0.044189453125,
0.0042877197265625,
0.024261474609375,
-0.0218658447265625,
0.004428863525390625,
0.0114288330078125,
-0.00539398193359375,
-0.0139312744140625,
0.009033203125,
0.0015230178833007812,
0.0037097930908203125,
-0.002849578857421875,
-0.035980224609375,
0.00530242919921875,
-0.0120086669921875,
0.0303955078125,
-0.0179901123046875,
-0.01453399658203125,
0.0015954971313476562,
-0.005054473876953125,
0.0276641845703125,
0.004642486572265625,
0.01006317138671875,
0.004505157470703125,
-0.00787353515625,
0.043792724609375,
-0.0029544830322265625,
0.0130157470703125,
0.006649017333984375,
0.007022857666015625,
0.003940582275390625,
-0.018341064453125,
0.0010318756103515625,
0.0007867813110351562,
0.01358795166015625,
-0.0055694580078125,
0.0017328262329101562,
-0.005985260009765625,
0.019805908203125,
0.0128326416015625,
-0.0367431640625,
-0.016510009765625,
-0.031646728515625,
-0.01187896728515625,
0.006732940673828125,
-0.0069580078125,
-0.0144195556640625,
0.006988525390625,
0.0020961761474609375,
0.020416259765625,
0.0022449493408203125,
-0.0276947021484375,
0.01450347900390625,
-0.031005859375,
0.037628173828125,
-0.0159149169921875,
-0.0285797119140625,
0.038818359375,
0.00632476806640625,
-0.007778167724609375,
0.0128021240234375,
0.02923583984375,
-0.005100250244140625,
0.0010805130004882812,
0.02093505859375,
-0.00567626953125,
0.0156097412109375,
-0.039093017578125,
0.009033203125,
0.01568603515625,
-0.01306915283203125,
0.00553131103515625,
0.0103759765625,
-0.0015659332275390625,
-0.00310516357421875,
-0.00891876220703125,
-0.0269317626953125,
-0.018798828125,
-0.01324462890625,
0.0243072509765625,
-0.016265869140625,
-0.0198974609375,
0.042572021484375,
0.0340576171875,
0.01788330078125,
-0.033477783203125,
-0.0148773193359375,
0.020477294921875,
0.01605224609375,
0.0009984970092773438,
0.005558013916015625,
0.0124664306640625,
-0.00205230712890625,
0.02191162109375,
0.04083251953125,
-0.03424072265625,
0.02203369140625,
0.037384033203125,
-0.01271820068359375,
0.0032196044921875,
0.019439697265625,
0.014434814453125,
-0.00818634033203125,
-0.0239105224609375,
-0.01177978515625,
-0.0078125,
0.008087158203125,
-0.0242156982421875,
0.004367828369140625,
-0.006984710693359375,
0.0086669921875,
-0.0196990966796875,
0.019317626953125,
0.0297088623046875,
-0.03497314453125,
0.010528564453125,
0.0226898193359375,
0.00597381591796875,
0.005558013916015625,
-0.005268096923828125,
0.0178375244140625,
-0.031463623046875,
-0.0112152099609375,
-0.01727294921875,
-0.009185791015625,
0.012054443359375,
0.01168060302734375,
-0.01438140869140625,
-0.01250457763671875,
-0.0208587646484375,
0.027679443359375,
0.0287933349609375,
0.0224609375,
-0.0261383056640625,
0.0163116455078125,
-0.009613037109375,
-0.0014734268188476562,
0.020751953125,
-0.0036067962646484375,
0.005443572998046875,
0.0181884765625,
0.0091552734375,
-0.012542724609375,
0.005199432373046875,
0.00867462158203125,
-0.0072479248046875,
0.03912353515625,
0.0167236328125,
0.00005227327346801758,
-0.0002968311309814453,
-0.0025806427001953125,
0.0010099411010742188,
0.016387939453125,
0.00603485107421875,
0.009918212890625,
-0.0173187255859375,
0.0276336669921875,
-0.01320648193359375,
0.026031494140625,
-0.016937255859375,
-0.003856658935546875,
-0.017974853515625,
0.0150299072265625,
0.006744384765625,
0.003726959228515625,
-0.00890350341796875,
-0.0165252685546875,
-0.0167999267578125,
0.02655029296875,
-0.010528564453125,
0.015777587890625,
-0.02459716796875,
0.0158233642578125,
-0.034942626953125,
0.02069091796875,
0.0257415771484375,
0.017181396484375,
0.014190673828125,
-0.00788116455078125,
-0.0017042160034179688,
0.00313568115234375,
0.0035305023193359375,
0.003810882568359375,
0.031494140625,
-0.0303802490234375,
0.02911376953125,
-0.019073486328125,
-0.00699615478515625,
0.002635955810546875,
-0.0243377685546875,
0.011474609375,
0.00286865234375,
-0.024017333984375,
-0.005008697509765625,
0.0021419525146484375,
-0.033233642578125,
-0.044281005859375,
0.0119476318359375,
-0.031890869140625,
0.0226593017578125,
-0.0189056396484375,
-0.028961181640625,
-0.0027294158935546875,
0.006862640380859375,
-0.020263671875,
-0.03082275390625,
0.003170013427734375,
-0.0104217529296875,
-0.00438690185546875,
0.019744873046875,
-0.0030059814453125,
0.007480621337890625,
0.01546478271484375,
0.007282257080078125,
0.01441192626953125,
-0.06829833984375,
0.001007080078125,
0.00835418701171875,
0.0231170654296875,
0.004581451416015625,
0.001087188720703125,
-0.0018215179443359375,
-0.0180816650390625,
0.004573822021484375,
-0.0080413818359375,
-0.002223968505859375,
0.026397705078125,
0.01690673828125,
-0.00870513916015625,
0.00762939453125,
0.018310546875,
0.0283966064453125,
-0.045989990234375,
-0.01580810546875,
0.005298614501953125,
-0.036102294921875,
-0.008544921875,
0.01477813720703125,
-0.00270843505859375,
0.020843505859375,
0.0167083740234375,
-0.007049560546875,
-0.01045989990234375,
0.03131103515625,
-0.0020923614501953125,
-0.04412841796875,
0.03924560546875,
0.01085662841796875,
-0.01031494140625,
0.00830841064453125,
0.028167724609375,
-0.032135009765625,
-0.0005350112915039062,
0.00042891502380371094,
0.02215576171875,
0.0183563232421875,
0.019561767578125,
0.00862884521484375,
0.026275634765625,
-0.0267333984375,
-0.0086212158203125,
0.028778076171875,
-0.0005707740783691406,
0.0443115234375,
-0.016326904296875,
0.0302581787109375,
0.020294189453125,
-0.018585205078125,
0.0195159912109375,
-0.017822265625,
-0.0139312744140625,
-0.0020885467529296875,
0.0286712646484375,
-0.01079559326171875,
-0.040374755859375,
-0.033966064453125,
-0.0258026123046875,
0.01806640625,
-0.0222625732421875,
-0.01490020751953125,
0.006496429443359375,
0.0357666015625,
0.005695343017578125,
-0.0056915283203125,
-0.047393798828125,
0.04461669921875,
-0.00905609130859375,
0.0057220458984375,
-0.00789642333984375,
-0.0057373046875,
0.016326904296875,
0.0133209228515625,
-0.0252532958984375,
0.01513671875,
0.00736236572265625,
-0.014434814453125,
-0.005245208740234375,
-0.0017986297607421875,
-0.0256805419921875,
0.007251739501953125,
0.021728515625,
-0.0084381103515625,
0.00439453125,
-0.0023784637451171875,
0.006122589111328125,
-0.019073486328125,
-0.0210113525390625,
-0.0207977294921875,
0.03729248046875,
-0.0163421630859375,
-0.032012939453125,
0.020843505859375,
-0.00856781005859375,
-0.00803375244140625,
0.00678253173828125,
-0.0136871337890625,
0.018157958984375,
-0.00748443603515625,
0.036895751953125,
0.0012722015380859375,
0.0078125,
-0.005889892578125,
-0.009002685546875,
-0.020751953125,
-0.0086517333984375,
-0.033477783203125,
-0.047760009765625,
0.006267547607421875,
0.0205841064453125,
-0.031982421875,
-0.006595611572265625,
0.00980377197265625,
0.01186370849609375,
-0.018402099609375,
-0.00212860107421875,
0.00838470458984375,
-0.00373077392578125,
0.021270751953125,
-0.051300048828125,
-0.0188140869140625,
0.01247406005859375,
-0.03143310546875,
-0.023040771484375,
-0.01435089111328125,
0.006092071533203125,
0.0238494873046875,
-0.01611328125,
0.0016126632690429688,
-0.0196380615234375,
0.010833740234375,
0.0167694091796875,
0.0089111328125,
-0.025604248046875,
0.01513671875,
0.01195526123046875,
0.01274871826171875,
-0.020263671875,
-0.0247650146484375,
0.010498046875,
0.01898193359375,
-0.0196685791015625,
-0.02276611328125,
0.0290679931640625,
-0.00838470458984375,
-0.004241943359375,
-0.0031185150146484375,
-0.03778076171875,
0.018218994140625,
-0.01244354248046875,
0.022247314453125,
-0.0166168212890625,
0.0168304443359375,
-0.007511138916015625,
-0.002498626708984375,
0.0215606689453125,
0.0406494140625,
0.02813720703125,
-0.01303863525390625,
0.04425048828125,
0.011810302734375,
0.0158843994140625,
0.006900787353515625,
-0.001979827880859375,
0.005542755126953125,
-0.017669677734375,
0.0141143798828125,
-0.02117919921875,
0.0120697021484375,
0.0095367431640625,
0.028564453125,
-0.0256805419921875,
-0.046234130859375,
-0.001918792724609375,
0.0010080337524414062,
-0.01361846923828125,
-0.00968170166015625,
0.01270294189453125,
0.042572021484375,
0.00655364990234375,
0.035858154296875,
0.01177978515625,
0.01267242431640625,
-0.033294677734375,
-0.00742340087890625,
0.033538818359375,
-0.0147705078125,
0.02374267578125,
0.0279541015625,
-0.03656005859375,
0.0032520294189453125,
-0.0457763671875,
0.0167083740234375,
0.0138092041015625,
0.0262451171875,
0.0103759765625,
-0.0032958984375,
-0.0167388916015625,
-0.0012149810791015625,
0.01204681396484375,
-0.035186767578125,
0.0092926025390625,
0.0177459716796875,
-0.003215789794921875,
0.00373077392578125,
0.0115966796875,
0.0009407997131347656,
-0.00860595703125,
-0.010650634765625,
0.00023102760314941406,
0.0214080810546875,
0.0016946792602539062,
0.0004029273986816406,
-0.01399993896484375,
0.006011962890625,
0.00682830810546875,
0.00583648681640625,
0.0073394775390625,
-0.0325927734375,
0.01715087890625,
-0.00757598876953125,
0.0135650634765625,
0.04620361328125,
-0.00746917724609375,
-0.0108489990234375,
-0.030792236328125,
0.0171356201171875,
0.03350830078125,
-0.017822265625,
0.029815673828125,
0.033966064453125,
0.01019287109375,
0.007198333740234375,
-0.01995849609375,
-0.01503753662109375,
0.036102294921875,
0.001247406005859375,
-0.01361083984375,
-0.0099639892578125,
-0.016815185546875,
-0.01084136962890625,
0.0007643699645996094,
-0.003021240234375,
-0.0207977294921875,
-0.017181396484375,
0.0160064697265625,
-0.01371002197265625,
0.009674072265625,
0.023773193359375,
-0.0261077880859375,
0.0150604248046875,
0.00550079345703125,
0.0019006729125976562,
0.00673675537109375,
-0.020965576171875,
-0.0171966552734375,
0.0207672119140625,
-0.02484130859375,
0.011962890625,
0.0026874542236328125,
-0.005077362060546875,
0.01345062255859375,
-0.005031585693359375,
0.0157623291015625,
-0.01203155517578125,
0.0224609375,
0.0272979736328125,
-0.003643035888671875,
0.01509857177734375,
0.01702880859375,
-0.0156097412109375,
0.0306549072265625,
-0.0300140380859375,
0.01308441162109375,
-0.0274658203125,
0.018798828125,
-0.00826263427734375,
0.0123748779296875,
0.0115814208984375,
-0.02252197265625,
-0.004489898681640625,
-0.037017822265625,
0.0009717941284179688,
-0.01007843017578125,
-0.038818359375,
0.004703521728515625,
0.0256500244140625,
-0.0009603500366210938,
0.006458282470703125,
-0.01517486572265625,
-0.0321044921875,
-0.004634857177734375,
-0.019744873046875,
-0.00862884521484375,
-0.006259918212890625,
0.033538818359375,
0.003940582275390625,
-0.0177154541015625,
-0.0162200927734375,
-0.014678955078125,
0.025482177734375,
-0.007518768310546875,
-0.040374755859375,
-0.00452423095703125,
0.00888824462890625,
0.04736328125,
-0.0091094970703125,
-0.004657745361328125,
0.008819580078125,
0.0038394927978515625,
-0.01059722900390625,
0.01258087158203125,
-0.004634857177734375,
-0.0316162109375,
0.005523681640625,
0.0015382766723632812,
-0.00201416015625,
0.0005688667297363281,
0.04180908203125,
0.01268768310546875,
0.0008645057678222656,
0.0183258056640625,
0.008880615234375,
-0.01111602783203125,
-0.01148223876953125,
-0.0079193115234375,
0.016632080078125,
-0.0016460418701171875,
-0.004840850830078125,
0.030792236328125,
0.01538848876953125,
0.0396728515625,
-0.0015001296997070312,
0.0176544189453125,
-0.0036182403564453125,
0.0098114013671875,
0.00394439697265625,
0.01068115234375,
-0.00484466552734375,
-0.006683349609375,
0.0053863525390625,
-0.0633544921875,
-0.0213470458984375,
0.0299835205078125,
0.00983428955078125,
-0.035980224609375,
0.007328033447265625,
0.0283050537109375,
-0.01690673828125,
-0.01500701904296875,
-0.01776123046875,
0.00789642333984375,
-0.00028634071350097656,
-0.0028076171875,
-0.0152435302734375,
-0.0164947509765625,
-0.004634857177734375,
0.00232696533203125,
-0.01157379150390625,
-0.01392364501953125,
-0.0164947509765625,
0.00580596923828125,
0.0265960693359375,
-0.0147247314453125,
-0.01354217529296875,
-0.020660400390625,
-0.041046142578125,
0.0482177734375,
-0.01435089111328125,
0.00687408447265625,
-0.0166015625,
0.0185699462890625,
-0.02813720703125,
0.01531219482421875,
-0.0134429931640625,
0.01605224609375,
0.01174163818359375,
0.02923583984375,
0.01030731201171875,
-0.0143585205078125,
0.0005578994750976562,
0.005352020263671875,
0.006534576416015625,
-0.0002608299255371094,
-0.0050048828125,
0.03741455078125,
-0.010467529296875,
-0.01195526123046875,
-0.00305938720703125,
-0.0024089813232421875,
-0.00763702392578125,
-0.0006628036499023438,
-0.0274505615234375,
-0.0006160736083984375,
0.00524139404296875,
0.00749969482421875,
-0.0265960693359375,
-0.0066070556640625,
-0.0244903564453125,
0.0019664764404296875,
-0.006805419921875,
-0.00766754150390625,
0.0242919921875,
0.0024356842041015625,
0.04608154296875,
0.01059722900390625,
-0.020538330078125,
0.016387939453125,
0.006256103515625,
0.0248260498046875,
0.03448486328125,
-0.00884246826171875,
0.0015573501586914062,
0.01284027099609375,
0.01666259765625,
0.0298004150390625,
-0.041717529296875,
-0.0023555755615234375,
0.0142822265625,
-0.01216888427734375,
-0.00550079345703125,
-0.045562744140625,
0.00043129920959472656,
0.0145721435546875,
0.0150604248046875,
0.0302581787109375,
-0.0030689239501953125,
0.0159149169921875,
0.03668212890625,
-0.0295562744140625,
0.0006504058837890625,
0.0101470947265625,
0.0184478759765625,
0.0174102783203125,
0.044281005859375,
0.01012420654296875,
0.0035800933837890625,
-0.0010938644409179688,
-0.030670166015625,
0.023345947265625,
-0.038909912109375,
0.004276275634765625,
0.00897979736328125,
-0.0121612548828125,
0.02569580078125,
-0.0164794921875,
-0.00368499755859375,
0.007808685302734375,
-0.0316162109375,
-0.01043701171875,
0.006313323974609375,
0.00691986083984375,
-0.036285400390625,
-0.01183319091796875,
0.0123138427734375,
0.0019130706787109375,
0.051513671875,
-0.004886627197265625,
-0.01244354248046875,
-0.0023632049560546875,
-0.010955810546875,
0.01495361328125,
-0.000035643577575683594,
-0.00634765625,
0.0216827392578125,
0.0020656585693359375,
0.0285491943359375,
0.0194549560546875,
-0.0167236328125,
0.0195770263671875,
0.025970458984375,
0.001377105712890625,
-0.01406097412109375,
0.017486572265625,
-0.00891876220703125,
0.033843994140625,
-0.0032958984375,
0.029052734375,
0.027435302734375,
0.0577392578125,
-0.03216552734375,
0.024261474609375,
-0.0206451416015625,
0.015045166015625,
-0.031951904296875,
-0.0079345703125,
-0.017974853515625,
0.057769775390625,
0.0225372314453125,
-0.00656890869140625,
0.0235748291015625,
0.025177001953125,
-0.028106689453125,
0.005817413330078125,
0.01068878173828125,
-0.005359649658203125,
0.051177978515625,
0.0151519775390625,
-0.020599365234375,
-0.01117706298828125,
-0.0179290771484375,
-0.008209228515625,
0.016510009765625,
-0.01364898681640625,
0.01012420654296875,
-0.0247344970703125,
-0.0184783935546875,
-0.0201568603515625,
-0.00893402099609375,
-0.0218048095703125,
-0.00009113550186157227,
-0.005901336669921875,
-0.00616455078125,
0.0131378173828125,
-0.01264190673828125,
-0.00514984130859375,
0.016082763671875,
-0.0160064697265625,
-0.02276611328125,
-0.01192474365234375,
-0.00963592529296875,
0.01226043701171875,
-0.005107879638671875,
-0.043426513671875,
-0.0225677490234375,
-0.024078369140625,
0.029632568359375,
-0.0123748779296875,
0.004833221435546875,
0.0164337158203125,
-0.03424072265625,
-0.01226043701171875,
0.002674102783203125,
0.027099609375,
0.00661468505859375,
-0.0199737548828125,
-0.006420135498046875,
-0.04425048828125,
0.005023956298828125,
-0.00397491455078125,
-0.017364501953125,
-0.031982421875,
-0.00527191162109375,
0.0074462890625,
0.0124969482421875,
0.0123291015625,
-0.023223876953125,
-0.021514892578125,
-0.0307159423828125,
0.01641845703125,
0.00949859619140625,
-0.0285186767578125,
-0.02880859375,
-0.013702392578125,
-0.03692626953125,
-0.0007319450378417969,
0.00476837158203125,
0.0234832763671875,
-0.0139312744140625,
-0.00684356689453125,
-0.01271820068359375,
-0.01030731201171875,
-0.0032787322998046875,
-0.020843505859375,
0.0102081298828125,
0.0034637451171875,
-0.007205963134765625,
-0.0106048583984375,
0.0256500244140625,
-0.020416259765625,
0.0281829833984375,
-0.006175994873046875,
-0.0143280029296875,
0.0160675048828125,
0.0021190643310546875,
0.023468017578125,
-0.0064239501953125,
-0.0096588134765625,
-0.0123443603515625,
0.00969696044921875,
-0.0249176025390625,
-0.005970001220703125,
0.0188751220703125,
0.01369476318359375,
0.0178375244140625,
0.0208740234375,
0.01453399658203125,
0.035369873046875,
-0.0288848876953125,
-0.0262451171875,
0.0085296630859375,
0.0006432533264160156,
0.039886474609375,
-0.0018434524536132812
] |
ours_472
|
For each \(i\), the probability that Patchouli gets exactly one question right in Part \(i\) is \(i \cdot\left(\frac{1}{i+1}\right) \cdot\left(\frac{i}{i+1}\right)^{i-1}=\left(\frac{i}{i+1}\right)^{i}\), which is exactly the same as her getting all questions wrong in that part. Therefore, the probability that Patchouli gets exactly one question right overall is \(k\) times the probability that she gets no questions right. Hence \(k=2018\) and the number of questions is \(\frac{k(k+1)}{2} = 2037171\).
\(\boxed{2037171}\)
|
2037171
|
{
"competition": "us_comps",
"dataset": "Ours",
"posts": null,
"source": "OMOFall18Solns.md"
}
|
Patchouli is taking an exam with \(k > 1\) parts, numbered Part \(1, 2, \ldots, k\). It is known that for \(i = 1, 2, \ldots, k\), Part \(i\) contains \(i\) multiple choice questions, each of which has \((i+1)\) answer choices. It is known that if she guesses randomly on every single question, the probability that she gets exactly one question correct is equal to \(2018\) times the probability that she gets no questions correct. Compute the number of questions that are on the exam.
|
[
"/Mathematics/ProbabilityandStatistics/Probability/MultiplicationPrinciple",
"/Mathematics/ProbabilityandStatistics/Probability/ProbabilityMeasure",
"/Mathematics/ProbabilityandStatistics/Probability/ProbabilitySpace",
"/Mathematics/ProbabilityandStatistics/Probability/SampleSpace"
] |
Notice that in each part the chance of exactly one correct answer equals the chance of none, so the overall ratio reduces to the number of parts.
|
[
-0.00012433528900146484,
0.020294189453125,
0.0117645263671875,
0.01259613037109375,
-0.00043964385986328125,
-0.007572174072265625,
0.060272216796875,
-0.00658416748046875,
-0.007793426513671875,
0.01187896728515625,
0.01149749755859375,
-0.02935791015625,
-0.0022563934326171875,
-0.052490234375,
0.0038967132568359375,
-0.052825927734375,
0.030181884765625,
0.033111572265625,
0.0162353515625,
-0.0074005126953125,
-0.005001068115234375,
-0.037017822265625,
-0.0282440185546875,
0.00797271728515625,
-0.01537322998046875,
-0.0072021484375,
-0.025390625,
0.013763427734375,
-0.0188446044921875,
0.01302337646484375,
-0.027740478515625,
-0.0220184326171875,
-0.01032257080078125,
-0.03253173828125,
-0.001873016357421875,
0.0186614990234375,
0.005840301513671875,
-0.0052032470703125,
-0.0101165771484375,
-0.0166168212890625,
0.01309967041015625,
0.0036983489990234375,
0.007904052734375,
0.022552490234375,
0.015625,
0.0218963623046875,
0.0015048980712890625,
-0.01464080810546875,
-0.01171875,
-0.007411956787109375,
-0.005298614501953125,
0.0159912109375,
0.017303466796875,
-0.00505828857421875,
0.02362060546875,
-0.08477783203125,
-0.02459716796875,
-0.00858306884765625,
-0.022705078125,
-0.01023101806640625,
0.005443572998046875,
0.017303466796875,
0.0151519775390625,
-0.0173492431640625,
-0.0012083053588867188,
-0.01407623291015625,
0.0209808349609375,
-0.04205322265625,
-0.0006284713745117188,
-0.0157012939453125,
0.023193359375,
-0.0096588134765625,
-0.0212554931640625,
0.0027523040771484375,
0.058807373046875,
-0.0091705322265625,
-0.0173797607421875,
0.01248931884765625,
0.011627197265625,
0.016387939453125,
0.01447296142578125,
0.00270843505859375,
0.0020618438720703125,
-0.0066986083984375,
0.00875091552734375,
0.0030460357666015625,
-0.0005202293395996094,
-0.00176239013671875,
0.0113067626953125,
-0.0169830322265625,
0.0187530517578125,
0.045379638671875,
0.0022945404052734375,
-0.00830841064453125,
0.01155853271484375,
-0.0243377685546875,
0.0007982254028320312,
-0.01343536376953125,
-0.0032100677490234375,
0.011444091796875,
-0.017913818359375,
0.0017251968383789062,
0.0198974609375,
0.0122222900390625,
-0.047210693359375,
-0.0012187957763671875,
-0.0164794921875,
-0.0002372264862060547,
-0.01560211181640625,
-0.0036373138427734375,
0.008636474609375,
-0.0115814208984375,
-0.0076904296875,
0.0127105712890625,
0.00043010711669921875,
0.0230865478515625,
0.020263671875,
0.0204925537109375,
-0.00980377197265625,
0.0219573974609375,
0.01378631591796875,
0.00971221923828125,
-0.00864410400390625,
-0.01160430908203125,
0.017486572265625,
0.0227813720703125,
-0.0119781494140625,
-0.0004055500030517578,
0.0224456787109375,
0.024383544921875,
0.011016845703125,
0.01000213623046875,
-0.0201263427734375,
-0.030517578125,
-0.06689453125,
0.00543212890625,
0.008209228515625,
-0.01235198974609375,
-0.0213470458984375,
-0.01151275634765625,
0.013275146484375,
-0.00508880615234375,
0.00829315185546875,
-0.006561279296875,
0.00957489013671875,
0.0018720626831054688,
-0.0017681121826171875,
-0.022003173828125,
-0.0031490325927734375,
-0.004791259765625,
0.005336761474609375,
-0.007843017578125,
0.0143280029296875,
0.0035495758056640625,
-0.01120758056640625,
0.0255279541015625,
-0.0008482933044433594,
0.00482177734375,
0.0102386474609375,
0.004558563232421875,
-0.0016393661499023438,
-0.024658203125,
-0.026214599609375,
0.0380859375,
-0.00018775463104248047,
0.00536346435546875,
0.0035343170166015625,
0.007106781005859375,
-0.0096893310546875,
0.01367950439453125,
-0.0008821487426757812,
0.0007476806640625,
0.00829315185546875,
-0.0068359375,
-0.007419586181640625,
0.006500244140625,
-0.01104736328125,
0.00421142578125,
0.0035839080810546875,
0.04669189453125,
0.01300811767578125,
-0.018890380859375,
0.018829345703125,
0.014862060546875,
-0.0060882568359375,
0.009796142578125,
0.0001531839370727539,
0.005443572998046875,
0.021270751953125,
0.00608062744140625,
-0.0191497802734375,
-0.0122528076171875,
0.0017614364624023438,
0.00807952880859375,
-0.00038361549377441406,
-0.01354217529296875,
-0.0280609130859375,
0.00315093994140625,
0.042449951171875,
0.0167388916015625,
0.00833892822265625,
-0.00035953521728515625,
0.026397705078125,
0.00496673583984375,
0.00623321533203125,
0.0019216537475585938,
-0.0020961761474609375,
-0.005802154541015625,
0.0020503997802734375,
-0.0090179443359375,
0.01239776611328125,
0.00908660888671875,
-0.0164642333984375,
-0.035858154296875,
0.009857177734375,
0.00598907470703125,
-0.02435302734375,
-0.0012264251708984375,
0.0009407997131347656,
-0.00988006591796875,
0.0098419189453125,
0.002666473388671875,
0.00020933151245117188,
-0.01654052734375,
-0.020660400390625,
0.0091705322265625,
-0.005096435546875,
0.005321502685546875,
0.0013370513916015625,
0.01148223876953125,
0.01445770263671875,
0.01490020751953125,
-0.0238189697265625,
-0.0102691650390625,
-0.0021209716796875,
0.0131378173828125,
0.004138946533203125,
-0.03125,
-0.0004799365997314453,
-0.01342010498046875,
0.03985595703125,
0.0014791488647460938,
-0.0018453598022460938,
0.004177093505859375,
-0.00611114501953125,
-0.0055084228515625,
-0.007411956787109375,
-0.01175689697265625,
0.0112762451171875,
-0.01065826416015625,
-0.032012939453125,
0.007587432861328125,
0.01042938232421875,
-0.0133514404296875,
0.011962890625,
-0.0218353271484375,
0.007389068603515625,
-0.01116943359375,
-0.00661468505859375,
-0.0576171875,
-0.007080078125,
-0.01288604736328125,
0.00135040283203125,
-0.01154327392578125,
0.0107269287109375,
0.014251708984375,
-0.0187530517578125,
-0.003772735595703125,
0.01375579833984375,
0.0015106201171875,
0.0039825439453125,
-0.0196533203125,
-0.01300048828125,
0.01470184326171875,
-0.0289306640625,
-0.003971099853515625,
0.004901885986328125,
-0.0013427734375,
-0.0054779052734375,
-0.006092071533203125,
0.002407073974609375,
0.0116424560546875,
-0.033660888671875,
0.0169525146484375,
-0.0102081298828125,
0.00881195068359375,
0.0038280487060546875,
0.00017344951629638672,
-0.01239776611328125,
0.0059967041015625,
0.0020294189453125,
0.0277099609375,
0.001850128173828125,
-0.0220947265625,
-0.007152557373046875,
-0.0521240234375,
0.00574493408203125,
0.0132293701171875,
0.02130126953125,
-0.0026111602783203125,
0.02679443359375,
-0.029327392578125,
-0.007678985595703125,
-0.0015497207641601562,
-0.01324462890625,
0.01116180419921875,
-0.0011615753173828125,
0.0182037353515625,
-0.015106201171875,
0.00307464599609375,
-0.0012454986572265625,
0.0156402587890625,
0.0084228515625,
-0.0243072509765625,
-0.0177154541015625,
-0.0286865234375,
-0.0218963623046875,
0.00870513916015625,
-0.0257110595703125,
0.01430511474609375,
0.0157318115234375,
0.00287628173828125,
-0.01251983642578125,
-0.00901031494140625,
0.0070648193359375,
-0.018463134765625,
0.0194244384765625,
0.011993408203125,
-0.00786590576171875,
0.02215576171875,
-0.018829345703125,
0.0112762451171875,
-0.0111236572265625,
-0.00885009765625,
0.0026111602783203125,
0.0237274169921875,
0.0133514404296875,
0.04638671875,
-0.01474761962890625,
0.01525115966796875,
-0.0001189112663269043,
-0.007904052734375,
0.004558563232421875,
0.00151824951171875,
0.007320404052734375,
0.01788330078125,
0.0158538818359375,
-0.01038360595703125,
0.01092529296875,
0.01074981689453125,
-0.0106658935546875,
0.00782012939453125,
-0.0085601806640625,
0.02276611328125,
-0.031494140625,
0.034027099609375,
-0.004619598388671875,
0.011932373046875,
-0.00954437255859375,
0.04132080078125,
-0.0022411346435546875,
-0.00658416748046875,
0.0118255615234375,
-0.03253173828125,
0.01119232177734375,
-0.0169219970703125,
-0.02093505859375,
0.0248870849609375,
-0.0149688720703125,
-0.00998687744140625,
-0.0220794677734375,
-0.00519561767578125,
-0.004535675048828125,
0.01019287109375,
-0.0202178955078125,
0.0074462890625,
0.0110321044921875,
-0.01873779296875,
0.00902557373046875,
-0.015380859375,
0.011627197265625,
0.041412353515625,
-0.0015668869018554688,
0.0306396484375,
-0.03131103515625,
-0.0037021636962890625,
-0.0007538795471191406,
0.0230560302734375,
-0.01593017578125,
-0.0001703500747680664,
-0.01093292236328125,
0.0203704833984375,
0.0020923614501953125,
-0.004337310791015625,
0.00731658935546875,
-0.0556640625,
0.0003619194030761719,
0.01316070556640625,
0.0283660888671875,
-0.0322265625,
-0.0171356201171875,
-0.00827789306640625,
-0.0279388427734375,
-0.01136016845703125,
-0.00316619873046875,
0.014984130859375,
-0.01200103759765625,
-0.01419830322265625,
-0.01207733154296875,
-0.005168914794921875,
0.00641632080078125,
0.01910400390625,
0.007171630859375,
0.022003173828125,
-0.00806427001953125,
-0.0004801750183105469,
0.022125244140625,
-0.022796630859375,
-0.0156097412109375,
-0.0141143798828125,
-0.020843505859375,
-0.0199127197265625,
-0.00455474853515625,
0.00862884521484375,
-0.00562286376953125,
-0.009857177734375,
-0.0154876708984375,
0.03460693359375,
-0.00975799560546875,
0.0201416015625,
-0.0007295608520507812,
-0.013885498046875,
-0.016357421875,
0.01360321044921875,
-0.00019872188568115234,
0.0634765625,
0.0102996826171875,
-0.00118255615234375,
0.0029449462890625,
0.026214599609375,
-0.034759521484375,
0.007293701171875,
0.012298583984375,
0.0256500244140625,
-0.05035400390625,
0.000652313232421875,
-0.014251708984375,
0.0308380126953125,
-0.08624267578125,
0.035308837890625,
-0.0223388671875,
0.00850677490234375,
0.015350341796875,
-0.0280303955078125,
-0.01467132568359375,
0.0121307373046875,
0.033050537109375,
-0.03900146484375,
0.01326751708984375,
-0.00247955322265625,
-0.0222320556640625,
-0.0213470458984375,
0.0023670196533203125,
-0.0126953125,
-0.028289794921875,
-0.000217437744140625,
0.004852294921875,
0.01355743408203125,
-0.028472900390625,
0.0226898193359375,
-0.018035888671875,
-0.014495849609375,
-0.002185821533203125,
-0.01119232177734375,
-0.026824951171875,
0.05548095703125,
0.02435302734375,
0.01551055908203125,
-0.01403045654296875,
-0.01349639892578125,
0.029632568359375,
0.032257080078125,
0.00008153915405273438,
0.0550537109375,
0.022369384765625,
-0.00597381591796875,
0.0270538330078125,
0.01026153564453125,
-0.044158935546875,
-0.041107177734375,
-0.0014925003051757812,
0.05230712890625,
-0.01474761962890625,
0.005054473876953125,
0.011810302734375,
-0.0159454345703125,
0.006359100341796875,
-0.027740478515625,
0.01373291015625,
0.00601959228515625,
0.0028228759765625,
0.009185791015625,
-0.021484375,
0.03778076171875,
-0.006351470947265625,
0.0225067138671875,
0.0501708984375,
0.005626678466796875,
0.01528167724609375,
-0.0257110595703125,
0.01248931884765625,
0.0003533363342285156,
0.0120391845703125,
-0.0096282958984375,
0.01383209228515625,
-0.01374053955078125,
0.043701171875,
-0.039215087890625,
0.0228424072265625,
0.044097900390625,
-0.0183563232421875,
0.01374053955078125,
0.034332275390625,
-0.014892578125,
0.0024261474609375,
0.00608062744140625,
-0.011383056640625,
-0.0153045654296875,
-0.0198822021484375,
-0.0115203857421875,
0.026641845703125,
-0.01114654541015625,
0.01407623291015625,
-0.007709503173828125,
-0.05633544921875,
-0.015960693359375,
0.015350341796875,
0.005313873291015625,
-0.021026611328125,
-0.0008869171142578125,
-0.0170440673828125,
-0.01556396484375,
-0.008087158203125,
-0.0212554931640625,
-0.0083465576171875,
-0.01026153564453125,
-0.01215362548828125,
0.01438140869140625,
-0.03704833984375,
0.0239105224609375,
0.0162811279296875,
0.0159454345703125,
0.0246734619140625,
-0.011749267578125,
-0.057342529296875,
0.041168212890625,
0.016754150390625,
0.0016946792602539062,
-0.0212249755859375,
-0.01090240478515625,
0.005146026611328125,
0.0090789794921875,
0.003925323486328125,
0.007099151611328125,
0.028289794921875,
-0.013946533203125,
0.0246124267578125,
-0.0203704833984375,
-0.00836181640625,
-0.0626220703125,
-0.0104827880859375,
-0.0009522438049316406,
0.01248931884765625,
0.01309967041015625,
0.01363372802734375,
0.0093994140625,
-0.0079345703125,
0.0136260986328125,
-0.00585174560546875,
-0.042877197265625,
0.0193023681640625,
0.005504608154296875,
-0.01593017578125,
0.0019330978393554688,
0.005214691162109375,
0.0017719268798828125,
0.03167724609375,
-0.0152435302734375,
0.03662109375,
-0.00225067138671875,
0.0220489501953125,
0.00606536865234375,
0.0033111572265625,
0.0218048095703125,
0.0130767822265625,
-0.01197052001953125,
-0.005435943603515625,
-0.0184326171875,
-0.034515380859375,
0.0037670135498046875,
0.01384735107421875,
-0.01340484619140625,
0.005924224853515625,
0.0178070068359375,
-0.032379150390625,
0.005153656005859375,
-0.006526947021484375,
0.0292510986328125,
-0.0231170654296875,
0.00992584228515625,
0.037567138671875,
0.0116119384765625,
-0.0027675628662109375,
0.016998291015625,
0.027008056640625,
-0.00318145751953125,
-0.041839599609375,
-0.036163330078125,
0.015838623046875,
-0.040130615234375,
-0.00815582275390625,
-0.0149993896484375,
0.00287628173828125,
0.01154327392578125,
-0.01381683349609375,
-0.0106048583984375,
0.0021686553955078125,
-0.0160675048828125,
0.004398345947265625,
-0.009735107421875,
-0.01519012451171875,
-0.0243072509765625,
0.00986480712890625,
0.016204833984375,
0.019683837890625,
-0.0176849365234375,
0.0036640167236328125,
-0.0035839080810546875,
-0.004207611083984375,
-0.0138397216796875,
-0.0029125213623046875,
0.0198516845703125,
0.0299530029296875,
-0.0236358642578125,
0.0030307769775390625,
0.004657745361328125,
0.0262603759765625,
0.0189208984375,
-0.0208892822265625,
0.022796630859375,
-0.025848388671875,
-0.0094451904296875,
-0.016387939453125,
0.006916046142578125,
0.004638671875,
0.0194854736328125,
-0.00011259317398071289,
-0.0391845703125,
0.01392364501953125,
0.002140045166015625,
-0.004573822021484375,
0.0009136199951171875,
0.031005859375,
0.019287109375,
-0.04229736328125,
-0.006008148193359375,
-0.0181884765625,
-0.024658203125,
0.015594482421875,
-0.0038509368896484375,
-0.01494598388671875,
-0.0126953125,
0.0185699462890625,
-0.0009508132934570312,
0.049896240234375,
-0.02001953125,
-0.0098114013671875,
-0.0087432861328125,
0.0181732177734375,
-0.00008946657180786133,
-0.005275726318359375,
0.0007681846618652344,
0.0170135498046875,
0.00524139404296875,
0.015838623046875,
0.00010955333709716797,
0.01399993896484375,
-0.006618499755859375,
0.0462646484375,
0.00797271728515625,
0.006137847900390625,
0.010986328125,
0.009307861328125,
0.0321044921875,
0.0035381317138671875,
-0.0147552490234375,
-0.0012369155883789062,
0.0116424560546875,
-0.0157623291015625,
-0.006206512451171875,
0.0256195068359375,
0.002979278564453125,
0.014923095703125,
-0.019744873046875,
0.0008111000061035156,
-0.0111083984375,
-0.02032470703125,
0.0257110595703125,
-0.0197906494140625,
0.006134033203125,
-0.0341796875,
0.0299835205078125,
-0.0137939453125,
0.0022106170654296875,
-0.0280609130859375,
-0.05157470703125,
-0.0028171539306640625,
-0.008636474609375,
0.0197296142578125,
-0.01026153564453125,
-0.03387451171875,
0.026763916015625,
-0.007427215576171875,
0.0016422271728515625,
0.01105499267578125,
0.00876617431640625,
-0.003910064697265625,
-0.032928466796875,
-0.019378662109375,
-0.018157958984375,
-0.0028629302978515625,
-0.011993408203125,
-0.01751708984375,
-0.0054473876953125,
-0.021514892578125,
0.01366424560546875,
-0.004970550537109375,
-0.015655517578125,
0.01303863525390625,
-0.0235748291015625,
0.021270751953125,
0.03009033203125,
0.0145263671875,
-0.0037078857421875,
0.039794921875,
0.0032825469970703125,
0.0102996826171875,
-0.01178741455078125,
-0.0002665519714355469,
-0.004276275634765625,
0.005466461181640625,
0.0014600753784179688,
-0.0251617431640625,
-0.023834228515625,
-0.0015268325805664062,
-0.0012788772583007812,
0.02105712890625,
0.004253387451171875,
-0.0303955078125,
0.01690673828125,
-0.01116180419921875,
-0.0136566162109375,
-0.0302581787109375,
0.0124664306640625,
-0.0237274169921875,
0.00888824462890625,
-0.0254669189453125,
-0.0318603515625,
0.0294647216796875,
0.01000213623046875,
-0.0130767822265625,
-0.0162200927734375,
0.01558685302734375,
0.00579071044921875,
0.00904083251953125,
0.0093841552734375,
-0.051025390625,
-0.0063629150390625,
0.0197601318359375,
-0.0099334716796875,
-0.00313568115234375,
0.0080108642578125,
-0.007579803466796875,
-0.0198211669921875,
-0.032135009765625,
-0.0069580078125,
0.017242431640625,
-0.0293121337890625,
0.01428985595703125,
-0.0228424072265625,
0.016876220703125,
0.030975341796875,
-0.010772705078125,
0.006969451904296875,
-0.0214385986328125,
-0.035308837890625,
0.01206207275390625,
-0.040191650390625,
-0.01041412353515625,
0.01800537109375,
0.0215301513671875,
-0.031280517578125,
-0.01812744140625,
0.029510498046875,
0.027099609375,
0.0136871337890625,
0.002292633056640625,
0.0239410400390625,
0.0128936767578125,
0.0180816650390625,
-0.005939483642578125,
-0.0300750732421875,
0.0054931640625,
-0.0386962890625,
0.008941650390625,
-0.02398681640625,
-0.0209197998046875,
-0.00312042236328125,
-0.006931304931640625,
0.0258026123046875,
-0.016265869140625,
0.0275726318359375,
-0.0203704833984375,
-0.01953125,
-0.0179443359375,
-0.00799560546875,
0.017425537109375,
-0.0042877197265625,
0.0023059844970703125,
0.0097808837890625,
0.00685882568359375,
-0.038665771484375,
-0.036590576171875,
-0.01203155517578125,
0.0011425018310546875,
-0.0021343231201171875,
-0.004917144775390625,
-0.006744384765625,
-0.00852203369140625,
-0.0117340087890625,
-0.01113128662109375,
0.01345062255859375,
0.002826690673828125,
-0.0310211181640625,
0.0241546630859375,
-0.0017604827880859375,
0.006046295166015625,
-0.013031005859375,
0.028778076171875,
0.0183868408203125,
-0.00334930419921875,
0.032745361328125,
-0.0028629302978515625,
0.00824737548828125,
0.0010614395141601562,
0.010284423828125,
0.016998291015625,
0.00759124755859375,
-0.006160736083984375,
-0.01558685302734375,
0.0173187255859375,
-0.03948974609375,
0.03131103515625,
-0.026153564453125,
0.031890869140625,
-0.008026123046875,
0.0021762847900390625,
-0.007965087890625,
-0.0017137527465820312,
-0.0589599609375,
0.0107879638671875,
-0.028564453125,
0.03924560546875,
0.0168914794921875,
0.00653076171875,
0.02288818359375,
-0.01389312744140625,
0.0135040283203125,
0.034912109375,
0.00417327880859375,
0.0240020751953125,
-0.000029265880584716797,
-0.0012350082397460938,
-0.0206146240234375,
-0.00925445556640625,
-0.01329803466796875,
0.010284423828125,
0.00008350610733032227,
0.0161895751953125,
0.004329681396484375,
-0.0087127685546875,
-0.0142669677734375,
0.008026123046875,
0.01222991943359375,
-0.0095367431640625,
0.024078369140625,
-0.01055145263671875,
-0.00151824951171875,
0.004177093505859375,
-0.08551025390625,
-0.0000024437904357910156,
0.00875091552734375,
0.0374755859375,
0.0119171142578125,
0.00461578369140625,
-0.02740478515625,
-0.0379638671875,
0.0098419189453125,
0.00022733211517333984,
0.02581787109375,
-0.0301513671875,
0.0146026611328125,
0.0112152099609375,
0.00054168701171875,
-0.0167083740234375,
0.015960693359375,
-0.0028553009033203125,
-0.00838470458984375,
0.0131988525390625,
0.03826904296875,
0.0111846923828125,
-0.00240325927734375,
-0.059112548828125,
-0.003574371337890625,
0.046783447265625,
-0.016143798828125,
-0.0151824951171875,
0.016876220703125,
-0.00585174560546875,
-0.0144500732421875,
-0.01047515869140625,
0.0198211669921875,
-0.017578125,
0.006221771240234375,
0.0035762786865234375,
0.00197601318359375,
-0.0305633544921875,
-0.00530242919921875,
0.016326904296875,
0.0009860992431640625,
-0.012054443359375,
0.026824951171875,
-0.0160675048828125,
0.014862060546875,
0.00872802734375,
-0.02117919921875,
0.001834869384765625,
0.010772705078125,
-0.0150146484375,
-0.007171630859375,
-0.0196685791015625,
-0.00154876708984375,
0.032745361328125,
0.0015974044799804688,
0.0164794921875,
-0.0130157470703125,
-0.0206451416015625,
-0.01554107666015625,
-0.0226287841796875,
-0.026153564453125,
-0.0240478515625,
0.009307861328125,
-0.048095703125,
-0.010406494140625,
-0.0267486572265625,
0.04302978515625,
0.0080413818359375,
0.01468658447265625,
0.0075531005859375,
0.008819580078125,
0.0141143798828125,
0.0101165771484375,
-0.0311431884765625,
-0.039794921875,
-0.004756927490234375,
-0.01009368896484375,
0.01351165771484375,
0.007678985595703125,
0.0308685302734375,
-0.0021800994873046875,
-0.051513671875,
0.0115814208984375,
-0.016143798828125,
-0.0304412841796875,
-0.003910064697265625,
-0.030487060546875,
0.0282440185546875,
-0.042633056640625,
0.0013933181762695312,
-0.01873779296875,
0.01220703125,
0.0195159912109375,
0.0235137939453125,
0.01438140869140625,
-0.0200042724609375,
0.0244903564453125,
0.0172576904296875,
-0.00525665283203125,
0.0186004638671875,
0.034210205078125,
-0.039886474609375,
0.006397247314453125,
0.0303955078125,
0.01611328125,
0.03143310546875,
-0.00363922119140625,
0.0323486328125,
0.021820068359375,
0.0025634765625,
-0.00792694091796875,
0.003871917724609375,
-0.009857177734375,
0.01666259765625,
-0.0034923553466796875,
-0.0271759033203125,
0.00736236572265625,
0.0036449432373046875,
0.0279541015625,
-0.04791259765625,
-0.0296173095703125,
-0.009490966796875,
0.0134735107421875,
-0.01148223876953125,
-0.015533447265625,
-0.0079345703125,
-0.0126953125,
-0.006923675537109375,
0.019805908203125,
0.01242828369140625,
0.01224517822265625,
0.0301361083984375,
-0.039825439453125,
0.003589630126953125,
0.025604248046875,
0.0024051666259765625,
0.0052642822265625,
-0.01444244384765625,
-0.007358551025390625,
0.019378662109375,
-0.00843048095703125,
-0.01230621337890625,
0.0071563720703125,
0.02825927734375,
-0.02386474609375,
0.0016040802001953125,
-0.0202178955078125,
-0.01375579833984375,
0.047454833984375,
-0.0274810791015625,
0.0108489990234375,
-0.0031585693359375,
0.028839111328125,
-0.033843994140625,
-0.0293426513671875,
0.0035305023193359375,
-0.006656646728515625,
-0.00971221923828125,
0.0045166015625,
0.01451873779296875,
0.00969696044921875,
-0.00372314453125,
-0.0107421875,
0.00287628173828125,
-0.0253143310546875,
0.00460052490234375,
-0.03533935546875,
-0.0095062255859375,
-0.017547607421875,
-0.0087127685546875,
0.02606201171875,
-0.028839111328125,
0.035552978515625,
0.0025882720947265625,
-0.01358795166015625,
0.0141143798828125,
-0.0105743408203125,
-0.0010242462158203125,
-0.019287109375,
0.004665374755859375,
0.01763916015625,
0.0216217041015625,
0.0027751922607421875,
-0.03802490234375,
0.00830841064453125,
0.0108642578125,
0.022125244140625,
-0.018768310546875,
-0.01168060302734375,
0.01324462890625,
-0.01428985595703125,
-0.016876220703125,
-0.0235595703125,
-0.008514404296875,
-0.01491546630859375,
0.0156097412109375,
0.0269317626953125,
0.004772186279296875,
0.0048980712890625,
0.00597381591796875,
0.01007843017578125,
0.00377655029296875,
0.030731201171875,
-0.0273284912109375,
-0.014862060546875,
-0.01898193359375,
-0.00260162353515625,
-0.0242767333984375,
0.0008220672607421875,
0.01019287109375,
-0.0113983154296875,
-0.0084991455078125,
-0.003582000732421875,
-0.003936767578125,
-0.00405120849609375,
-0.0122222900390625,
0.01361083984375,
-0.039306640625,
-0.0223541259765625,
-0.00992584228515625,
-0.0242767333984375,
-0.0008893013000488281,
0.041595458984375,
0.0272216796875,
-0.004596710205078125,
0.00014710426330566406,
-0.01416015625,
-0.01226806640625,
0.0111541748046875,
-0.0328369140625,
0.0190887451171875,
-0.0313720703125,
0.0292510986328125,
-0.002140045166015625,
-0.00804901123046875,
0.01056671142578125,
0.00676727294921875,
0.0166778564453125,
-0.01006317138671875,
0.02728271484375,
0.00963592529296875,
-0.0278778076171875,
0.0022296905517578125,
-0.01922607421875,
-0.0088043212890625,
0.0236358642578125,
0.0173492431640625,
0.0027618408203125,
0.009857177734375,
0.0296783447265625,
0.0063018798828125,
-0.002239227294921875,
0.021514892578125,
-0.00803375244140625,
0.01078033447265625,
-0.017547607421875,
-0.003299713134765625,
-0.01215362548828125,
0.0149383544921875,
0.01439666748046875,
0.025604248046875,
0.00292205810546875,
-0.002758026123046875,
0.026031494140625,
0.0133819580078125,
-0.006084442138671875,
0.0020904541015625,
0.0004279613494873047,
0.025787353515625,
-0.009918212890625,
0.0306243896484375,
-0.040985107421875,
-0.0176849365234375,
0.01186370849609375,
-0.023651123046875,
0.00501251220703125,
-0.01010894775390625,
0.0129547119140625,
-0.036590576171875,
-0.023345947265625,
-0.005084991455078125,
0.0177001953125,
0.0269012451171875,
0.0198211669921875,
0.0173797607421875,
-0.01421356201171875,
-0.0108795166015625,
-0.0185546875,
0.019989013671875,
-0.0129852294921875,
-0.01023101806640625,
0.01311492919921875,
-0.0066375732421875,
-0.0267181396484375,
-0.03228759765625,
-0.01092529296875,
-0.01068115234375,
-0.0285491943359375,
-0.021484375,
0.02618408203125,
0.0176544189453125,
-0.032867431640625,
0.0318603515625,
-0.0204620361328125,
-0.0256500244140625,
0.007617950439453125,
0.01013946533203125,
0.0058135986328125,
0.006603240966796875,
-0.019073486328125,
0.0229644775390625,
-0.00637054443359375,
-0.01678466796875,
-0.0021343231201171875,
-0.0042572021484375,
0.0263671875,
-0.004543304443359375,
0.023040771484375,
-0.0294342041015625,
-0.02239990234375,
-0.0085906982421875,
0.01104736328125,
-0.014373779296875,
0.006145477294921875,
0.0195770263671875,
-0.002105712890625,
-0.01491546630859375,
-0.023956298828125,
0.032745361328125,
0.0011138916015625,
0.015777587890625,
0.042022705078125,
-0.005191802978515625,
0.014495849609375,
-0.008209228515625,
-0.013458251953125,
-0.01348876953125,
-0.00250244140625,
0.013275146484375,
0.0015411376953125,
0.01291656494140625,
0.0007104873657226562,
-0.00807952880859375,
0.01824951171875,
-0.0012121200561523438,
0.01508331298828125,
0.003818511962890625,
-0.042144775390625,
0.0212860107421875,
-0.031280517578125,
0.019805908203125,
0.0008678436279296875,
-0.003955841064453125,
-0.0022068023681640625,
-0.01392364501953125,
-0.0135650634765625,
-0.0219879150390625,
0.00820159912109375,
-0.021484375,
0.009918212890625,
0.0111236572265625,
-0.040130615234375,
-0.01776123046875,
-0.01543426513671875,
-0.0187835693359375,
-0.0009136199951171875,
0.0082550048828125,
0.004852294921875,
0.004749298095703125,
-0.0041961669921875,
-0.000896453857421875,
0.0312347412109375,
0.01983642578125,
0.005092620849609375,
0.031463623046875,
-0.00018334388732910156,
-0.02362060546875,
-0.016143798828125,
-0.016143798828125,
0.0092926025390625,
-0.0006737709045410156,
-0.036407470703125,
0.0117645263671875,
0.0501708984375,
-0.003143310546875,
-0.033477783203125,
-0.0224456787109375,
0.006053924560546875,
0.036712646484375,
-0.00923919677734375,
0.002838134765625,
0.0163726806640625,
-0.0156402587890625,
-0.006378173828125,
0.006771087646484375,
0.0072174072265625,
-0.013885498046875,
0.031341552734375,
0.0021514892578125,
0.0101165771484375,
0.00974273681640625,
-0.00887298583984375,
-0.0302734375,
0.003261566162109375,
0.01090240478515625,
-0.02099609375,
-0.01227569580078125,
0.055755615234375,
0.00485992431640625,
0.016326904296875,
-0.032867431640625,
0.028778076171875,
0.0243988037109375,
0.046875,
0.0092620849609375,
0.0165863037109375,
0.007015228271484375,
-0.007419586181640625,
0.01149749755859375,
0.0099029541015625,
0.0119476318359375,
-0.00881195068359375,
0.0184326171875,
-0.007511138916015625,
0.05169677734375,
-0.0005526542663574219,
0.01141357421875,
-0.0132904052734375,
0.0289154052734375,
-0.00966644287109375,
-0.010040283203125,
-0.00478363037109375,
-0.00896453857421875,
0.0022830963134765625,
-0.020233154296875,
0.003936767578125,
0.03656005859375,
0.0266571044921875,
-0.01546478271484375,
0.0251922607421875,
-0.033355712890625,
0.005535125732421875,
0.01328277587890625,
0.005489349365234375,
0.00453948974609375,
0.0112152099609375,
0.0140838623046875,
-0.0343017578125,
0.01285552978515625,
0.0165863037109375,
-0.0104522705078125,
0.006114959716796875,
0.026458740234375,
-0.01329803466796875,
0.005489349365234375,
-0.036712646484375,
-0.00972747802734375,
-0.018829345703125,
0.004108428955078125,
-0.01708984375,
0.0177764892578125,
0.039276123046875,
-0.0192413330078125,
-0.025146484375,
-0.044036865234375,
0.03253173828125,
0.023193359375,
0.01511383056640625,
0.0211334228515625,
-0.027191162109375,
-0.02984619140625,
-0.0233612060546875,
-0.007083892822265625,
-0.0163421630859375,
-0.0200347900390625,
-0.0012903213500976562,
-0.01395416259765625,
-0.0087432861328125,
-0.007213592529296875,
-0.0369873046875,
0.016754150390625,
-0.0452880859375,
-0.0081024169921875,
-0.006168365478515625,
-0.0093536376953125,
-0.00250244140625,
0.048797607421875,
0.01385498046875,
0.03094482421875,
-0.0167388916015625,
0.004833221435546875,
0.039306640625,
0.0123748779296875,
0.01111602783203125,
0.030181884765625,
0.0008902549743652344,
-0.021087646484375,
0.01265716552734375,
-0.020233154296875,
-0.007717132568359375,
0.019134521484375,
0.02020263671875,
0.0210723876953125,
-0.00246429443359375,
0.00974273681640625,
-0.0223236083984375,
-0.0193328857421875,
0.01934814453125,
-0.0168914794921875,
-0.016357421875,
-0.00807952880859375,
-0.0211334228515625,
0.02734375,
-0.0226593017578125,
-0.0164642333984375,
-0.0120086669921875,
-0.0143280029296875,
0.004146575927734375,
0.002750396728515625,
0.006038665771484375,
0.023162841796875,
0.015960693359375,
0.019775390625,
-0.0216522216796875,
0.0184478759765625,
0.05352783203125,
-0.034088134765625,
0.015289306640625,
-0.0170135498046875,
-0.00333404541015625,
0.00176239013671875,
-0.00492095947265625,
-0.02178955078125,
0.004100799560546875,
-0.007049560546875,
0.0115509033203125,
-0.03515625,
0.0474853515625,
0.0031452178955078125,
0.0275115966796875,
0.026763916015625,
-0.0171356201171875,
-0.00484466552734375,
0.0058441162109375,
0.00299835205078125,
-0.009735107421875,
-0.017852783203125,
0.01102447509765625,
-0.0073394775390625,
0.0012121200561523438,
0.005741119384765625,
-0.0220794677734375,
-0.0214080810546875,
-0.0302886962890625,
0.02520751953125,
0.048797607421875,
0.004425048828125,
-0.01044464111328125,
-0.00937652587890625,
0.01499176025390625,
-0.045379638671875,
-0.050506591796875,
0.0068511962890625,
-0.0166778564453125,
0.0238494873046875,
0.01068878173828125,
-0.0034732818603515625,
-0.03387451171875,
-0.0011224746704101562,
-0.01171875,
0.015533447265625,
-0.045257568359375,
-0.0023975372314453125,
-0.0254364013671875,
0.00412750244140625,
0.006755828857421875,
-0.014678955078125,
0.022003173828125,
-0.017120361328125,
0.043853759765625,
-0.0145263671875,
0.024688720703125,
0.00885009765625,
0.01512908935546875,
-0.017822265625,
-0.00792694091796875,
-0.021148681640625,
0.0146026611328125,
0.0198974609375,
-0.0045013427734375,
0.0037059783935546875,
-0.004100799560546875,
-0.0135650634765625,
-0.0261383056640625,
-0.01052093505859375,
0.0199127197265625,
-0.0007152557373046875,
-0.01457977294921875,
-0.033355712890625,
-0.023956298828125,
0.006256103515625,
0.01380157470703125,
-0.009429931640625,
0.0254669189453125,
-0.006565093994140625,
0.01290130615234375,
-0.0116424560546875,
0.00778961181640625,
0.01502227783203125,
0.0003211498260498047,
-0.003108978271484375,
-0.0103912353515625,
-0.006435394287109375,
-0.005664825439453125,
0.0240020751953125,
-0.03057861328125,
0.0137939453125,
-0.03839111328125,
-0.037628173828125,
-0.00371551513671875,
0.0157470703125,
-0.00799560546875,
-0.01016998291015625,
-0.02032470703125,
0.0164947509765625,
-0.0014286041259765625,
-0.0256805419921875,
-0.0126953125,
0.0069122314453125,
-0.0159454345703125,
-0.018402099609375,
0.01116943359375,
-0.0296783447265625,
0.02508544921875,
0.0142822265625,
-0.0020771026611328125,
-0.00476837158203125,
0.007152557373046875,
0.01885986328125,
0.00643157958984375,
-0.016998291015625,
0.021209716796875,
0.0048065185546875,
-0.006801605224609375,
0.0247802734375,
-0.01219940185546875,
-0.006988525390625,
0.0014352798461914062,
0.0166168212890625,
0.00940704345703125,
-0.0211029052734375,
0.006195068359375,
-0.0116424560546875,
-0.007617950439453125,
0.017486572265625,
-0.042755126953125,
0.0211639404296875,
-0.02374267578125,
-0.0071258544921875,
0.00836181640625,
-0.0205078125,
0.0025043487548828125,
0.0244293212890625,
-0.0141754150390625,
0.0204010009765625,
-0.0130767822265625,
-0.003520965576171875,
0.002567291259765625,
0.02606201171875,
0.01316070556640625,
-0.0164794921875,
0.01412200927734375,
0.0213470458984375,
-0.01418304443359375,
0.0035305023193359375,
0.005462646484375,
-0.0030670166015625,
0.0037899017333984375,
0.01099395751953125,
0.033782958984375,
0.005130767822265625,
0.007114410400390625,
-0.0323486328125,
0.005367279052734375,
0.00872039794921875,
0.002185821533203125,
-0.004154205322265625,
-0.00839996337890625,
0.00995635986328125,
-0.0213623046875,
0.0002617835998535156,
-0.0303802490234375,
0.0216522216796875,
0.002902984619140625,
0.00836944580078125,
-0.01558685302734375,
0.0008635520935058594,
0.011138916015625,
-0.0063934326171875,
0.02581787109375,
-0.0011644363403320312,
-0.03662109375,
-0.019561767578125,
0.0001405477523803711,
0.018951416015625,
0.0088043212890625,
-0.0006108283996582031,
0.01255035400390625,
-0.030914306640625,
0.017822265625,
0.003078460693359375,
0.04302978515625,
-0.0052490234375,
0.0019702911376953125,
0.0010519027709960938,
0.0186309814453125,
0.00592803955078125,
0.007465362548828125,
0.0284881591796875,
0.015106201171875,
0.010833740234375,
-0.0109405517578125,
0.0016345977783203125,
0.01174163818359375,
-0.011383056640625,
0.0301513671875,
0.05035400390625,
-0.022705078125,
-0.002285003662109375,
-0.000056624412536621094,
0.011077880859375,
0.0223541259765625,
-0.005191802978515625,
0.009674072265625,
0.00977325439453125,
-0.01248931884765625,
-0.015777587890625,
-0.030426025390625,
0.01263427734375,
-0.014556884765625,
0.0413818359375,
-0.0025482177734375,
-0.00894927978515625,
0.0080108642578125,
-0.0499267578125,
-0.01021575927734375,
0.023284912109375,
-0.01157379150390625,
-0.001434326171875,
0.032745361328125,
-0.04205322265625,
0.004909515380859375,
-0.0156707763671875,
0.00775909423828125,
-0.0026721954345703125,
0.0142974853515625,
-0.01195526123046875,
-0.023040771484375,
0.01096343994140625,
-0.046844482421875,
-0.034759521484375,
0.037841796875,
-0.01194000244140625,
0.0283660888671875,
-0.01247406005859375,
0.01904296875,
-0.0014934539794921875,
0.0057220458984375,
-0.0021419525146484375,
-0.04290771484375,
-0.002147674560546875,
-0.016937255859375,
-0.002445220947265625,
-0.0035037994384765625,
-0.0142364501953125,
-0.0382080078125,
-0.00020825862884521484,
-0.005710601806640625,
0.020477294921875,
-0.004795074462890625,
0.004302978515625,
-0.01282501220703125,
-0.004116058349609375,
0.01371002197265625,
0.021484375,
-0.0318603515625,
-0.042938232421875,
0.0308074951171875,
-0.01177215576171875,
0.0043487548828125,
-0.00942230224609375,
0.04547119140625,
0.04217529296875,
-0.0301055908203125,
-0.012451171875,
0.039093017578125,
0.03411865234375,
0.005176544189453125,
-0.004276275634765625,
0.000011146068572998047,
-0.0163421630859375,
-0.0010280609130859375,
-0.0159912109375,
-0.01250457763671875,
-0.0140228271484375,
0.01526641845703125,
0.00421905517578125,
-0.03985595703125,
-0.005443572998046875,
-0.031982421875,
-0.033843994140625,
0.020477294921875,
-0.015167236328125,
-0.0494384765625,
0.0258331298828125,
0.003391265869140625,
-0.00106048583984375,
0.045166015625,
0.00510406494140625,
0.0012273788452148438,
-0.0279083251953125,
0.0129241943359375,
0.0164337158203125,
0.0091552734375,
-0.01055145263671875,
0.00014257431030273438,
-0.0263214111328125,
0.0182647705078125,
0.0311737060546875,
0.0153045654296875,
0.038330078125,
-0.0152435302734375,
0.03753662109375,
0.007495880126953125,
-0.01488494873046875,
0.00823974609375,
-0.006809234619140625,
0.04046630859375,
-0.0170135498046875,
-0.037384033203125,
-0.0014104843139648438,
0.04132080078125,
0.00965118408203125,
-0.045135498046875,
-0.0010576248168945312,
0.020416259765625,
-0.006256103515625,
0.006793975830078125,
0.016448974609375,
-0.0183563232421875,
0.01264190673828125,
-0.0118408203125,
-0.049346923828125,
0.00811004638671875,
-0.0297088623046875,
-0.0259552001953125,
0.0023212432861328125,
-0.0034027099609375,
0.0197906494140625,
-0.001712799072265625,
0.0250701904296875,
0.042755126953125,
-0.0328369140625,
0.004215240478515625,
-0.0016565322875976562,
-0.032623291015625,
-0.0124664306640625,
-0.042755126953125,
0.0028629302978515625,
-0.0030059814453125,
-0.01229095458984375,
0.0194091796875,
-0.0226593017578125,
0.0007815361022949219,
0.01271820068359375,
0.006954193115234375,
-0.0305633544921875,
0.03924560546875,
0.0192413330078125,
-0.0254974365234375,
0.042449951171875,
-0.00162506103515625,
-0.0197296142578125,
0.01910400390625,
0.006061553955078125,
0.0090484619140625,
-0.006298065185546875,
-0.04022216796875,
-0.003597259521484375,
-0.022918701171875,
-0.020660400390625,
0.0013551712036132812,
0.0280609130859375,
0.0240936279296875,
-0.024566650390625,
-0.007720947265625,
0.01207733154296875,
-0.026824951171875,
-0.0193328857421875,
0.0203704833984375,
0.0159149169921875,
-0.012603759765625,
0.0004699230194091797,
0.00514984130859375,
-0.04681396484375,
0.043212890625,
0.00850677490234375,
0.006412506103515625,
-0.0264434814453125,
0.01556396484375,
0.0169525146484375,
0.0174560546875,
-0.0035610198974609375,
-0.005603790283203125,
-0.00719451904296875,
0.007762908935546875,
-0.01314544677734375,
0.0254364013671875,
-0.00957489013671875,
-0.029388427734375,
0.0287933349609375,
-0.0099945068359375,
0.0149078369140625,
-0.01519012451171875,
-0.0203857421875,
0.021697998046875,
-0.017578125,
0.0114288330078125,
0.0168304443359375,
-0.01308441162109375,
0.0248565673828125,
0.032073974609375,
0.026275634765625,
-0.04296875,
-0.0299224853515625,
0.024810791015625,
-0.003986358642578125,
-0.0172882080078125,
-0.0166015625,
-0.00316619873046875,
-0.0190582275390625,
0.005039215087890625,
0.01611328125,
-0.017364501953125,
0.0006113052368164062,
0.002689361572265625,
-0.01143646240234375,
0.010467529296875,
-0.034942626953125,
0.00946807861328125,
-0.00630950927734375,
0.0176544189453125,
-0.0216827392578125,
0.01580810546875,
0.01134490966796875,
-0.0229339599609375,
0.0372314453125,
0.01279449462890625,
0.02581787109375,
0.0214080810546875,
0.0111083984375,
0.01226043701171875,
-0.03228759765625,
0.015167236328125,
0.01088714599609375,
0.00354766845703125,
-0.007633209228515625,
0.040130615234375,
0.01434326171875,
0.0199737548828125,
0.0157470703125,
0.0190887451171875,
0.004894256591796875,
-0.025360107421875,
0.0033588409423828125,
0.01036834716796875,
0.01708984375,
-0.00807952880859375,
0.0077972412109375,
0.01557159423828125,
-0.007740020751953125,
0.0203399658203125,
-0.00860595703125,
0.0406494140625,
-0.02154541015625,
0.0105743408203125,
0.011993408203125,
0.0016355514526367188,
0.035675048828125,
-0.0036525726318359375,
-0.010833740234375,
0.00428009033203125,
-0.0125732421875,
-0.003875732421875,
-0.01021575927734375,
-0.0021228790283203125,
0.00020170211791992188,
-0.00064849853515625,
0.00421142578125,
-0.0222015380859375,
0.00861358642578125,
-0.00780487060546875,
0.0123138427734375,
-0.0106048583984375,
0.008087158203125,
-0.0087127685546875,
-0.011505126953125,
-0.00414276123046875,
0.006305694580078125,
-0.0135955810546875,
0.00010091066360473633,
-0.026153564453125,
-0.006610870361328125,
-0.0382080078125,
-0.00775146484375,
0.01197052001953125,
0.041046142578125,
-0.019989013671875,
0.00769805908203125,
-0.0185699462890625,
0.0113983154296875,
0.00872802734375,
-0.0004944801330566406,
0.036895751953125,
-0.0004792213439941406,
0.0095977783203125,
0.01372528076171875,
-0.042694091796875,
-0.004238128662109375,
0.0038242340087890625,
-0.0107574462890625,
-0.0069427490234375,
0.0046844482421875,
-0.018768310546875,
0.0231170654296875,
-0.007457733154296875,
0.00841522216796875,
-0.0248565673828125,
0.0102691650390625,
-0.0129852294921875,
-0.00445556640625,
0.0263671875,
-0.0165863037109375,
-0.00041604042053222656,
-0.015777587890625,
-0.026580810546875,
-0.005191802978515625,
0.017852783203125,
0.0083465576171875,
-0.001911163330078125,
-0.0029125213623046875,
0.0036830902099609375,
-0.0239105224609375,
-0.0294189453125,
-0.00699615478515625,
0.005100250244140625,
-0.00473785400390625,
0.01538848876953125,
0.00926971435546875,
0.037506103515625,
0.00896453857421875,
-0.0107421875,
-0.0166473388671875,
-0.007122039794921875,
-0.0146026611328125,
0.01434326171875,
0.004558563232421875,
0.00724029541015625,
-0.00030922889709472656,
-0.0203094482421875,
0.0032024383544921875,
0.0172576904296875,
0.01275634765625,
0.00909423828125,
0.05010986328125,
0.042327880859375,
-0.01213836669921875,
0.028533935546875,
-0.00830841064453125,
-0.0157318115234375,
-0.039031982421875,
-0.0243072509765625,
-0.0143585205078125,
-0.014373779296875,
-0.007965087890625,
-0.0006256103515625,
-0.00647735595703125,
-0.00299072265625,
0.025726318359375,
0.002788543701171875,
0.033203125,
-0.003360748291015625,
-0.0036182403564453125,
-0.00762176513671875,
0.00527191162109375,
0.004730224609375,
0.00980377197265625,
0.021331787109375,
-0.01070404052734375,
-0.01922607421875,
-0.0016489028930664062,
0.0186767578125,
0.01145172119140625,
0.043060302734375,
0.0152130126953125,
-0.0107574462890625,
0.00970458984375,
0.0207672119140625,
0.0004723072052001953,
-0.0001531839370727539,
-0.005126953125,
-0.0207061767578125,
-0.04388427734375,
0.0182647705078125,
-0.002124786376953125,
0.0194854736328125,
0.049652099609375,
-0.0059051513671875,
-0.007259368896484375,
-0.0028972625732421875,
0.039520263671875,
0.003101348876953125,
-0.00074005126953125,
0.02001953125,
-0.0026340484619140625,
-0.0281829833984375,
-0.0220489501953125,
0.0196533203125,
0.0047760009765625,
-0.0113983154296875,
-0.00099945068359375,
0.02044677734375,
0.01372528076171875,
0.031158447265625,
-0.00971221923828125,
0.020477294921875,
-0.0160675048828125,
0.01800537109375,
-0.008819580078125,
0.006404876708984375,
-0.0221099853515625,
-0.01442718505859375,
0.0024051666259765625,
-0.02362060546875,
0.0161590576171875,
0.00534820556640625,
-0.028778076171875,
0.030975341796875,
-0.01071929931640625,
0.019866943359375,
0.0119476318359375,
0.006107330322265625,
0.00048828125,
0.0002295970916748047,
0.026824951171875,
-0.012237548828125,
-0.0106964111328125,
-0.00209808349609375,
-0.00939178466796875,
-0.006603240966796875,
0.0272369384765625,
-0.01361846923828125,
0.0247802734375,
-0.0289306640625,
-0.007282257080078125,
0.01285552978515625,
0.059539794921875,
-0.03131103515625,
0.0050048828125,
-0.02423095703125,
0.00649261474609375,
0.0018854141235351562,
-0.0011720657348632812,
0.02508544921875,
-0.010406494140625,
0.0225830078125,
-0.01220703125,
-0.028045654296875,
0.05029296875,
0.0248565673828125,
-0.008087158203125,
-0.050689697265625,
-0.0066070556640625,
0.038055419921875,
0.0196990966796875,
0.0116729736328125,
-0.020721435546875,
-0.0335693359375,
0.003414154052734375,
-0.003482818603515625,
-0.01061248779296875,
-0.0556640625,
0.0123291015625,
0.01407623291015625,
0.0012502670288085938,
0.037445068359375,
0.0274810791015625,
-0.0250244140625,
0.0023860931396484375,
0.019866943359375,
-0.003345489501953125,
-0.026824951171875,
0.008331298828125,
0.0083770751953125,
-0.005615234375,
-0.023193359375,
0.0160369873046875,
0.01324462890625,
-0.047943115234375,
0.0077667236328125,
0.0012903213500976562,
0.00991058349609375,
-0.03985595703125,
0.00949859619140625,
0.00872802734375,
0.009613037109375,
0.01222991943359375,
0.01194000244140625,
-0.0537109375,
-0.0010366439819335938,
0.0162200927734375,
0.0318603515625,
-0.0027904510498046875,
-0.00128173828125,
0.0055694580078125,
-0.006214141845703125,
-0.0224761962890625,
0.0170745849609375,
0.0021762847900390625,
-0.020965576171875,
0.003017425537109375,
-0.0303955078125,
-0.0019855499267578125,
-0.004695892333984375,
0.006320953369140625,
-0.00119781494140625,
-0.0200347900390625,
0.033966064453125,
0.0014352798461914062,
-0.0227813720703125,
0.01197052001953125,
0.0091705322265625,
0.0306243896484375,
0.00646209716796875,
-0.021026611328125,
0.0205230712890625,
0.00782012939453125,
0.01386260986328125,
0.01149749755859375,
-0.0109710693359375,
-0.0048065185546875,
0.002819061279296875,
0.0157012939453125,
-0.017059326171875,
0.0118255615234375,
0.003337860107421875,
0.033050537109375,
0.0208587646484375,
-0.00334930419921875,
-0.034576416015625,
0.0224609375,
-0.01374053955078125,
-0.0005426406860351562,
-0.0279541015625,
-0.01403045654296875,
0.0152130126953125,
-0.024871826171875,
0.004638671875,
-0.0321044921875,
-0.012176513671875,
0.0083465576171875,
-0.01061248779296875,
-0.02984619140625,
-0.00534820556640625,
0.0462646484375,
0.00919342041015625,
-0.018890380859375,
-0.0017375946044921875,
0.00933074951171875,
-0.017242431640625,
0.0008540153503417969,
0.01331329345703125,
-0.0025787353515625,
-0.00499725341796875,
0.01071929931640625,
0.00817108154296875,
0.01006317138671875,
-0.0007596015930175781,
0.04522705078125,
0.0209503173828125,
0.005886077880859375,
0.023223876953125,
-0.028717041015625,
0.0295562744140625,
-0.00734710693359375,
-0.021942138671875,
0.0084228515625,
0.028045654296875,
0.00760650634765625,
-0.02203369140625,
-0.01250457763671875,
0.0235137939453125,
0.0031585693359375,
-0.01538848876953125,
0.006954193115234375,
-0.0063018798828125,
-0.00811767578125,
-0.0002460479736328125,
-0.0225372314453125,
0.00865936279296875,
-0.016357421875,
-0.036590576171875,
0.020538330078125,
-0.0234375,
0.0282440185546875,
0.0081787109375,
-0.005825042724609375,
0.01641845703125,
-0.0068359375,
0.011993408203125,
0.0131988525390625,
-0.014862060546875,
0.0291595458984375,
0.0202484130859375,
-0.023590087890625,
0.028228759765625,
0.0028228759765625,
0.006328582763671875,
0.024810791015625,
-0.007427215576171875,
-0.0208587646484375,
-0.03656005859375,
-0.006427764892578125,
0.039794921875,
0.025634765625,
0.061187744140625,
0.016998291015625,
-0.0137176513671875,
0.0290374755859375,
-0.021881103515625,
-0.0101470947265625,
-0.0186004638671875,
-0.01480865478515625,
-0.0193634033203125,
-0.0019855499267578125,
-0.01555633544921875,
-0.0173187255859375,
0.0057525634765625,
0.039794921875,
0.004241943359375,
0.00537872314453125,
-0.037750244140625,
-0.00116729736328125,
0.00028204917907714844,
0.0157928466796875,
0.01262664794921875,
-0.004192352294921875,
0.0016851425170898438,
0.0188446044921875,
-0.0167083740234375,
-0.036163330078125,
0.0269927978515625,
0.0028781890869140625,
0.00621795654296875,
0.0216217041015625,
-0.006740570068359375,
-0.014251708984375,
0.002803802490234375,
-0.026153564453125,
-0.0298919677734375,
0.003875732421875,
0.01045989990234375,
0.000001430511474609375,
-0.009918212890625,
0.0036716461181640625,
0.0226287841796875,
0.0037689208984375,
-0.00884246826171875,
0.001056671142578125,
-0.0498046875,
0.01424407958984375,
-0.0025348663330078125,
-0.01375579833984375,
-0.052032470703125,
-0.01090240478515625,
0.0262603759765625,
0.002655029296875,
-0.013916015625,
0.0018463134765625,
0.0091094970703125,
0.0164947509765625,
-0.00229644775390625,
-0.018707275390625,
0.0033168792724609375,
0.01285552978515625,
-0.0030193328857421875,
0.04364013671875,
-0.0050201416015625,
0.009979248046875,
0.0275421142578125,
-0.01654052734375,
0.00621795654296875,
-0.0005125999450683594,
0.0419921875,
-0.01103973388671875,
0.019073486328125,
-0.03448486328125,
0.00006324052810668945,
0.0023193359375,
0.0102996826171875,
0.021331787109375,
-0.031768798828125,
-0.004688262939453125,
0.0160369873046875,
-0.01235198974609375,
-0.035247802734375,
0.0058746337890625,
0.01177978515625,
0.036590576171875,
0.013885498046875,
0.0161895751953125,
-0.025390625,
0.01276397705078125,
-0.0028839111328125,
0.018585205078125,
-0.00975799560546875,
0.006107330322265625,
0.0015020370483398438,
-0.047454833984375,
-0.004009246826171875,
0.0021800994873046875,
0.0266876220703125,
-0.0253753662109375,
0.00406646728515625,
0.01375579833984375,
-0.0283203125,
0.01383209228515625,
-0.0005240440368652344,
-0.00193023681640625,
0.0143280029296875,
0.0038394927978515625,
-0.024322509765625,
0.01319122314453125,
-0.0294036865234375,
0.012603759765625,
-0.033905029296875,
-0.0007643699645996094,
0.007049560546875,
-0.01390838623046875,
-0.020294189453125,
-0.004467010498046875,
-0.01314544677734375,
-0.0186004638671875,
-0.01506805419921875,
0.0017938613891601562,
-0.036041259765625,
-0.0014781951904296875,
-0.016510009765625,
-0.025299072265625,
-0.0190887451171875,
0.01152801513671875,
-0.00726318359375,
0.0133056640625,
0.0230560302734375,
-0.0168304443359375,
0.01070404052734375,
-0.0210723876953125,
-0.0024127960205078125,
-0.015777587890625,
0.041168212890625,
-0.03564453125,
0.004367828369140625,
-0.00783538818359375,
0.0027751922607421875,
-0.0008721351623535156,
-0.00013911724090576172,
0.01065826416015625,
0.025115966796875,
-0.0253753662109375,
0.0222625732421875,
0.039276123046875,
0.033935546875,
0.0469970703125,
-0.023529052734375,
0.03118896484375,
-0.0223541259765625,
0.029144287109375,
0.01061248779296875,
-0.00446319580078125,
0.0263824462890625,
0.01143646240234375,
-0.00623321533203125,
0.0115203857421875,
-0.0008320808410644531,
-0.020111083984375,
0.0160675048828125,
0.0207672119140625,
-0.0080718994140625,
-0.00147247314453125,
-0.0034847259521484375,
-0.015777587890625,
0.005001068115234375,
-0.042449951171875,
0.019287109375,
-0.0177154541015625,
-0.009918212890625,
0.0216217041015625,
-0.0102386474609375,
-0.01195526123046875,
0.0038299560546875,
-0.0030689239501953125,
-0.006038665771484375,
0.03009033203125,
-0.0280303955078125,
-0.007297515869140625,
0.0107421875,
0.004634857177734375,
-0.0156097412109375,
-0.019195556640625,
-0.0143280029296875,
-0.0294952392578125,
0.0166473388671875,
-0.01018524169921875,
0.01108551025390625,
0.00029206275939941406,
0.0042877197265625,
-0.015380859375,
0.0028171539306640625,
0.01224517822265625,
-0.00933074951171875,
0.0052947998046875,
0.047210693359375,
0.005878448486328125,
0.034881591796875,
-0.0284576416015625,
-0.040252685546875,
-0.0032138824462890625,
0.00861358642578125,
-0.01448822021484375,
-0.00878143310546875,
-0.0008130073547363281,
-0.0089263916015625,
-0.019683837890625,
-0.01235198974609375,
-0.013031005859375,
0.01355743408203125,
0.006015777587890625,
-0.0009207725524902344,
0.00033593177795410156,
-0.0164337158203125,
-0.000591278076171875,
-0.013397216796875,
-0.018402099609375,
0.0172271728515625,
0.00350189208984375,
-0.01100921630859375,
-0.01027679443359375,
-0.01372528076171875,
0.01079559326171875,
0.00594329833984375,
0.0110931396484375,
0.0287628173828125,
0.0004000663757324219,
0.014190673828125,
0.01678466796875,
-0.0173492431640625,
-0.02447509765625,
-0.009796142578125,
-0.007648468017578125,
-0.02117919921875,
-0.00426483154296875,
0.0020351409912109375,
0.0069580078125,
-0.037994384765625,
-0.0190582275390625,
-0.04559326171875,
-0.015625,
0.00423431396484375,
0.002658843994140625,
0.00685882568359375,
0.008209228515625,
0.022308349609375,
-0.0012407302856445312,
0.01322174072265625,
-0.0025539398193359375,
0.0144195556640625,
-0.041046142578125,
-0.01202392578125,
0.0194091796875,
0.023773193359375,
-0.0268402099609375,
-0.00217437744140625,
-0.004550933837890625,
-0.01629638671875,
-0.0074310302734375,
0.020538330078125,
-0.01131439208984375,
-0.077880859375,
-0.0055389404296875,
0.0148468017578125,
0.016754150390625,
-0.0157470703125,
-0.0161895751953125,
-0.004512786865234375,
0.00795745849609375,
0.0217132568359375,
-0.01488494873046875,
-0.0105743408203125,
-0.0018634796142578125,
-0.026611328125,
-0.00872039794921875,
0.0101776123046875,
-0.0015993118286132812,
-0.017730712890625,
0.007293701171875,
-0.01061248779296875,
-0.002033233642578125,
-0.0155487060546875,
-0.006153106689453125,
0.0015048980712890625,
0.024993896484375,
-0.0225677490234375,
-0.0014438629150390625,
0.007610321044921875,
-0.012603759765625,
-0.010467529296875,
-0.014984130859375,
0.02130126953125,
-0.01320648193359375,
0.01220703125,
0.008697509765625,
-0.01342010498046875,
0.0284423828125,
-0.0469970703125,
-0.008758544921875,
0.0215606689453125,
-0.00835418701171875,
-0.0159149169921875,
-0.00571441650390625,
0.0008053779602050781,
-0.00930023193359375,
0.0151214599609375,
0.031463623046875,
0.03570556640625,
0.00878143310546875,
0.0160675048828125,
-0.006923675537109375,
0.0232391357421875,
0.0010786056518554688,
0.00832366943359375,
-0.0362548828125,
-0.033599853515625,
-0.0151519775390625,
-0.01403045654296875,
0.0286712646484375,
0.019287109375,
0.0306854248046875,
-0.00942230224609375,
0.002582550048828125,
0.01329803466796875,
0.0298614501953125
] |
ours_473
|
Solution. By considering the position of the remaining M, we find that the number of ways is equal to \(1 \cdot 13 + 2 \cdot 12 + \cdots + 13 \cdot 1 = \binom{15}{3} = 455\).
\(\boxed{455}\)
|
455
|
{
"competition": "us_comps",
"dataset": "Ours",
"posts": null,
"source": "OMOFall18Solns.md"
}
|
Compute the number of ways to erase 24 letters from the string "OMOMO . . OMO" (with length 27), such that the three remaining letters are O, M, and O in that order. Note that the order in which they are erased does not matter.
|
[
"/Mathematics/DiscreteMathematics/Combinatorics/BinomialCoefficients",
"/Mathematics/DiscreteMathematics/Combinatorics/CombinatorialIdentities",
"/Mathematics/DiscreteMathematics/Combinatorics/Enumeration",
"/Mathematics/DiscreteMathematics/Combinatorics/GeneralCombinatorics",
"/Mathematics/DiscreteMathematics/GeneralDiscreteMathematics/DiscreteMath",
"/Mathematics/DiscreteMathematics/GeneralDiscreteMathematics/DiscreteMathematics",
"/Mathematics/DiscreteMathematics/GeneralDiscreteMathematics/FiniteMathematics",
"/Mathematics/RecreationalMathematics/Puzzles/Puzzle"
] |
Fix the position of the middle letter and count choices for the left and right O's, reducing to a simple combination count.
|
[
-0.00007605552673339844,
-0.008514404296875,
0.0195465087890625,
-0.0027313232421875,
-0.0005173683166503906,
0.0352783203125,
0.017333984375,
-0.0316162109375,
0.0093536376953125,
0.0012683868408203125,
0.038726806640625,
0.011688232421875,
-0.0026721954345703125,
-0.00316619873046875,
-0.040191650390625,
-0.023162841796875,
0.01503753662109375,
0.0360107421875,
-0.01421356201171875,
0.0002956390380859375,
-0.01529693603515625,
-0.044219970703125,
-0.002899169921875,
-0.0076141357421875,
0.004238128662109375,
-0.007144927978515625,
-0.0237884521484375,
0.0280609130859375,
0.0257720947265625,
-0.017425537109375,
-0.0005192756652832031,
-0.0243072509765625,
0.0217132568359375,
-0.00818634033203125,
-0.0014982223510742188,
-0.003704071044921875,
0.0203399658203125,
-0.0055084228515625,
0.0224151611328125,
-0.04705810546875,
0.0080718994140625,
-0.004734039306640625,
-0.00881195068359375,
0.019195556640625,
0.00019240379333496094,
0.035247802734375,
-0.004688262939453125,
0.01480865478515625,
-0.0021305084228515625,
-0.0111236572265625,
-0.01157379150390625,
0.006256103515625,
-0.005527496337890625,
-0.024658203125,
-0.0177001953125,
-0.086669921875,
-0.0085296630859375,
0.004314422607421875,
-0.018341064453125,
0.0166015625,
-0.00022470951080322266,
-0.01181793212890625,
0.00530242919921875,
-0.018798828125,
-0.005306243896484375,
-0.01300811767578125,
0.035675048828125,
-0.003570556640625,
0.00717926025390625,
-0.0099639892578125,
-0.01953125,
-0.042510986328125,
-0.0256500244140625,
0.03240966796875,
-0.004764556884765625,
-0.023040771484375,
-0.00399017333984375,
0.008087158203125,
0.0037822723388671875,
-0.00318145751953125,
0.0038928985595703125,
0.02410888671875,
0.00013637542724609375,
0.005207061767578125,
0.028045654296875,
-0.011627197265625,
0.01143646240234375,
-0.005245208740234375,
-0.0028839111328125,
-0.026611328125,
-0.01221466064453125,
0.0132904052734375,
-0.00217437744140625,
0.0184173583984375,
0.00455474853515625,
0.01348114013671875,
0.0077972412109375,
-0.0145416259765625,
-0.032012939453125,
0.007659912109375,
-0.00531768798828125,
0.008453369140625,
0.0269775390625,
0.00945281982421875,
-0.01517486572265625,
-0.0213470458984375,
0.006473541259765625,
0.004978179931640625,
-0.00920867919921875,
0.0018033981323242188,
-0.0001773834228515625,
0.00165557861328125,
0.04583740234375,
0.0129852294921875,
-0.00730133056640625,
-0.0142822265625,
0.0178375244140625,
-0.019439697265625,
-0.00653076171875,
0.0213775634765625,
0.00835418701171875,
0.00154876708984375,
-0.002716064453125,
0.01128387451171875,
0.0030765533447265625,
0.017242431640625,
-0.005306243896484375,
-0.002216339111328125,
0.02947998046875,
0.007244110107421875,
0.0206451416015625,
-0.00475311279296875,
-0.018402099609375,
-0.030487060546875,
-0.051116943359375,
-0.00041031837463378906,
0.0025005340576171875,
-0.0184173583984375,
0.00714874267578125,
0.00005239248275756836,
-0.005664825439453125,
-0.00720977783203125,
-0.006595611572265625,
-0.0028247833251953125,
-0.00868988037109375,
-0.016326904296875,
-0.011566162109375,
-0.041473388671875,
0.005504608154296875,
0.00484466552734375,
-0.0093841552734375,
0.0148468017578125,
0.016876220703125,
0.004398345947265625,
-0.020263671875,
-0.0018053054809570312,
0.0088348388671875,
0.006198883056640625,
-0.00848388671875,
0.0121917724609375,
-0.002490997314453125,
-0.001155853271484375,
-0.000004947185516357422,
0.037017822265625,
0.0030364990234375,
0.005443572998046875,
0.0096588134765625,
0.0142974853515625,
-0.00942230224609375,
0.0264129638671875,
0.006496429443359375,
0.00371551513671875,
-0.00261688232421875,
-0.013824462890625,
0.0027637481689453125,
0.00957489013671875,
0.0128936767578125,
0.023529052734375,
-0.01006317138671875,
0.033111572265625,
-0.0287933349609375,
-0.05169677734375,
-0.0036258697509765625,
0.006435394287109375,
0.005828857421875,
0.002838134765625,
-0.0165252685546875,
0.006404876708984375,
0.0066986083984375,
-0.0018701553344726562,
-0.01519775390625,
-0.039031982421875,
-0.003314971923828125,
0.0038127899169921875,
-0.00991058349609375,
-0.0092010498046875,
-0.01279449462890625,
-0.026123046875,
0.0147247314453125,
0.016845703125,
0.01425933837890625,
-0.00824737548828125,
-0.0050506591796875,
0.01227569580078125,
0.004791259765625,
-0.005168914794921875,
0.0017061233520507812,
0.0017385482788085938,
0.0031452178955078125,
0.0094757080078125,
-0.00460052490234375,
-0.0330810546875,
-0.0277252197265625,
-0.003787994384765625,
-0.0156402587890625,
0.0011892318725585938,
-0.0263824462890625,
-0.007030487060546875,
-0.000885009765625,
0.0015659332275390625,
-0.0113372802734375,
0.00119781494140625,
-0.0173797607421875,
-0.0292816162109375,
-0.0293731689453125,
0.0181121826171875,
-0.0078125,
0.010162353515625,
-0.004547119140625,
0.00012874603271484375,
-0.00334930419921875,
0.003780364990234375,
-0.0025959014892578125,
0.0026340484619140625,
-0.00908660888671875,
0.0012369155883789062,
0.0135650634765625,
-0.0230865478515625,
0.02239990234375,
-0.0282135009765625,
0.0596923828125,
-0.0142822265625,
-0.0029354095458984375,
-0.00562286376953125,
-0.0015316009521484375,
-0.004150390625,
0.0032825469970703125,
-0.0086822509765625,
-0.0033054351806640625,
-0.0089111328125,
-0.0260162353515625,
0.0154876708984375,
0.00928497314453125,
-0.008087158203125,
-0.014678955078125,
-0.010040283203125,
-0.0012998580932617188,
0.020965576171875,
-0.00606536865234375,
-0.0126190185546875,
-0.0108795166015625,
-0.01580810546875,
0.00424957275390625,
-0.028564453125,
0.017669677734375,
-0.042083740234375,
0.006259918212890625,
-0.0020599365234375,
0.0104217529296875,
-0.0008449554443359375,
0.03448486328125,
-0.00310516357421875,
-0.00339508056640625,
0.020721435546875,
0.00910186767578125,
-0.0160675048828125,
-0.01332855224609375,
0.0012874603271484375,
-0.0113983154296875,
0.01313018798828125,
0.003818511962890625,
0.00795745849609375,
-0.01019287109375,
0.00495147705078125,
0.016876220703125,
0.01418304443359375,
0.00421142578125,
-0.0107574462890625,
-0.0178375244140625,
-0.006671905517578125,
0.01206207275390625,
0.011962890625,
0.0029735565185546875,
-0.01470184326171875,
0.0054931640625,
-0.08160400390625,
0.01006317138671875,
0.0092926025390625,
0.013031005859375,
-0.0148468017578125,
0.0272674560546875,
-0.01508331298828125,
-0.0012493133544921875,
0.0245361328125,
0.005401611328125,
0.01554107666015625,
-0.0007381439208984375,
0.0116729736328125,
0.013336181640625,
-0.004726409912109375,
-0.0260009765625,
0.004917144775390625,
0.005725860595703125,
0.011260986328125,
0.006374359130859375,
-0.0411376953125,
-0.0219268798828125,
0.021209716796875,
-0.0186614990234375,
0.047637939453125,
0.00983428955078125,
-0.01297760009765625,
-0.0304107666015625,
-0.01216888427734375,
0.03607177734375,
-0.0003581047058105469,
0.016021728515625,
0.0213470458984375,
-0.0236053466796875,
0.026336669921875,
-0.03399658203125,
0.019622802734375,
-0.0168914794921875,
-0.017730712890625,
-0.00589752197265625,
0.0233154296875,
0.003253936767578125,
0.03106689453125,
-0.00994110107421875,
0.012176513671875,
0.0178985595703125,
0.02227783203125,
0.00937652587890625,
0.007442474365234375,
0.0154571533203125,
0.0021495819091796875,
0.0364990234375,
-0.003337860107421875,
-0.0187835693359375,
-0.0205078125,
-0.00862884521484375,
0.0209503173828125,
0.01666259765625,
0.01416778564453125,
-0.0175933837890625,
0.0159912109375,
0.01349639892578125,
0.01983642578125,
0.00511932373046875,
0.0036792755126953125,
0.03558349609375,
0.00708770751953125,
-0.002147674560546875,
0.0147705078125,
-0.01422882080078125,
-0.024566650390625,
0.006622314453125,
0.00921630859375,
0.000732421875,
-0.0140838623046875,
-0.01088714599609375,
0.0016727447509765625,
0.0204315185546875,
-0.003662109375,
-0.01180267333984375,
0.0003676414489746094,
-0.0179595947265625,
0.0121307373046875,
-0.003490447998046875,
-0.005596160888671875,
-0.0041351318359375,
0.05535888671875,
-0.020660400390625,
0.039459228515625,
-0.038482666015625,
-0.02874755859375,
0.004680633544921875,
-0.01953125,
-0.01263427734375,
-0.0036468505859375,
-0.007080078125,
0.00829315185546875,
-0.01491546630859375,
-0.0227203369140625,
0.0160980224609375,
-0.01445770263671875,
0.007236480712890625,
0.01216888427734375,
0.016082763671875,
-0.003002166748046875,
-0.00962066650390625,
-0.0026264190673828125,
-0.007110595703125,
-0.0340576171875,
0.01044464111328125,
-0.008544921875,
-0.0285186767578125,
-0.00815582275390625,
-0.00677490234375,
-0.0019817352294921875,
-0.0243682861328125,
0.0202178955078125,
0.01328277587890625,
0.001773834228515625,
0.0003197193145751953,
0.0295257568359375,
0.0134124755859375,
-0.0258941650390625,
-0.029327392578125,
-0.01184844970703125,
-0.01222991943359375,
-0.0022068023681640625,
-0.0034351348876953125,
-0.006702423095703125,
0.0270843505859375,
0.00749969482421875,
0.0013713836669921875,
0.0214691162109375,
-0.0132598876953125,
0.0058135986328125,
0.0004291534423828125,
-0.01800537109375,
0.01392364501953125,
0.02325439453125,
0.0013751983642578125,
0.00658416748046875,
0.0201416015625,
0.004581451416015625,
-0.0244293212890625,
-0.0017938613891601562,
0.01096343994140625,
-0.024169921875,
0.0250244140625,
0.007389068603515625,
-0.0310211181640625,
0.01372528076171875,
-0.0004239082336425781,
0.02044677734375,
-0.021484375,
0.0005121231079101562,
-0.0474853515625,
-0.0020160675048828125,
0.0193328857421875,
-0.017578125,
-0.021575927734375,
0.040252685546875,
-0.009521484375,
-0.00720977783203125,
-0.00946044921875,
-0.0257568359375,
0.01085662841796875,
-0.007358551025390625,
0.04534912109375,
-0.01183319091796875,
-0.00260162353515625,
0.019378662109375,
-0.0162506103515625,
0.0252685546875,
-0.005451202392578125,
-0.000705718994140625,
-0.00048661231994628906,
0.0020008087158203125,
-0.0386962890625,
0.002780914306640625,
-0.0305023193359375,
0.0298309326171875,
0.0099945068359375,
0.00412750244140625,
0.006412506103515625,
-0.01297760009765625,
-0.0170440673828125,
0.032745361328125,
-0.0084228515625,
0.057952880859375,
0.011016845703125,
0.016693115234375,
0.0188140869140625,
0.0089263916015625,
-0.019927978515625,
0.0029621124267578125,
-0.002307891845703125,
0.00994873046875,
-0.037872314453125,
-0.0021514892578125,
-0.004695892333984375,
0.0240325927734375,
0.0015077590942382812,
-0.0312042236328125,
-0.038421630859375,
0.016265869140625,
0.035369873046875,
-0.01189422607421875,
-0.014739990234375,
0.04205322265625,
0.00617218017578125,
-0.0070648193359375,
0.039825439453125,
0.0201263427734375,
0.00304412841796875,
-0.0038967132568359375,
-0.0020618438720703125,
0.009765625,
0.019805908203125,
-0.0278167724609375,
0.006397247314453125,
0.0211639404296875,
0.0241241455078125,
-0.036590576171875,
0.004802703857421875,
0.022552490234375,
-0.054046630859375,
0.04364013671875,
0.015960693359375,
0.0014276504516601562,
0.008544921875,
0.01348114013671875,
0.02020263671875,
-0.004116058349609375,
-0.053070068359375,
0.01100921630859375,
-0.01464080810546875,
-0.00939178466796875,
0.04449462890625,
-0.036590576171875,
-0.001476287841796875,
0.003368377685546875,
-0.01702880859375,
-0.019134521484375,
0.0011873245239257812,
0.0244140625,
0.003437042236328125,
-0.012847900390625,
0.0180816650390625,
-0.0007205009460449219,
-0.032379150390625,
-0.0012836456298828125,
-0.0171051025390625,
-0.030120849609375,
-0.05426025390625,
0.0012149810791015625,
-0.0045166015625,
0.0019702911376953125,
-0.0115509033203125,
-0.013763427734375,
-0.0218963623046875,
-0.000713348388671875,
0.0291595458984375,
-0.00196075439453125,
-0.00998687744140625,
-0.00390625,
0.02783203125,
0.003925323486328125,
0.019805908203125,
0.0198211669921875,
0.0275115966796875,
-0.0157928466796875,
-0.017913818359375,
0.00945281982421875,
0.0036602020263671875,
-0.02496337890625,
0.0161285400390625,
0.007843017578125,
0.0032825469970703125,
0.0015363693237304688,
0.016937255859375,
0.0034351348876953125,
-0.033905029296875,
0.0228271484375,
0.005367279052734375,
0.01125335693359375,
0.001735687255859375,
0.04620361328125,
-0.02386474609375,
0.038482666015625,
0.016845703125,
0.005252838134765625,
0.035736083984375,
0.00893402099609375,
-0.00403594970703125,
0.0091094970703125,
-0.02862548828125,
0.005840301513671875,
0.01047515869140625,
0.01149749755859375,
0.022064208984375,
-0.0165557861328125,
0.006832122802734375,
-0.02630615234375,
-0.03173828125,
-0.00980377197265625,
-0.0244903564453125,
-0.0111541748046875,
-0.0289459228515625,
0.0171966552734375,
-0.0278167724609375,
0.0160064697265625,
-0.0031871795654296875,
-0.01535797119140625,
-0.03253173828125,
0.01267242431640625,
-0.0018854141235351562,
0.0228118896484375,
-0.00563812255859375,
0.03094482421875,
0.0280609130859375,
0.00554656982421875,
-0.0020046234130859375,
-0.0172576904296875,
-0.0280609130859375,
-0.0325927734375,
0.007762908935546875,
-0.0031414031982421875,
0.02520751953125,
-0.010345458984375,
0.01403045654296875,
-0.02557373046875,
-0.02471923828125,
-0.0230560302734375,
0.0154571533203125,
-0.009490966796875,
-0.01232147216796875,
-0.0301361083984375,
0.0202789306640625,
0.0179901123046875,
-0.0002722740173339844,
-0.01042938232421875,
0.0013856887817382812,
0.0099639892578125,
0.0301361083984375,
-0.006191253662109375,
-0.0215911865234375,
0.0199432373046875,
0.01041412353515625,
-0.03863525390625,
-0.041015625,
0.027099609375,
-0.0283203125,
-0.03326416015625,
-0.01384735107421875,
0.01471710205078125,
0.0009813308715820312,
0.0032501220703125,
-0.00481414794921875,
-0.000732421875,
-0.041778564453125,
-0.000644683837890625,
0.004062652587890625,
-0.01117706298828125,
0.01476287841796875,
-0.01251983642578125,
0.03369140625,
-0.006069183349609375,
0.0218963623046875,
0.0155029296875,
-0.0029048919677734375,
-0.01561737060546875,
-0.01479339599609375,
-0.006992340087890625,
0.03936767578125,
-0.021453857421875,
0.00150299072265625,
-0.006542205810546875,
-0.00849151611328125,
-0.005519866943359375,
0.024169921875,
-0.032958984375,
0.0168304443359375,
-0.00795745849609375,
0.014007568359375,
0.0258331298828125,
-0.007236480712890625,
0.01025390625,
0.0188140869140625,
0.0138397216796875,
0.016510009765625,
0.020721435546875,
0.00018036365509033203,
-0.01837158203125,
0.0223236083984375,
-0.00031113624572753906,
0.00980377197265625,
-0.0292205810546875,
-0.0004897117614746094,
0.055419921875,
0.0014142990112304688,
-0.0036563873291015625,
0.0162811279296875,
-0.0222320556640625,
-0.0133514404296875,
-0.033843994140625,
0.02392578125,
-0.0048065185546875,
0.002674102783203125,
-0.0142974853515625,
-0.0029621124267578125,
0.011566162109375,
-0.00525665283203125,
0.0157012939453125,
-0.04022216796875,
0.0002727508544921875,
-0.034149169921875,
-0.031829833984375,
-0.01435089111328125,
-0.0017032623291015625,
-0.033599853515625,
-0.032501220703125,
0.01091766357421875,
0.00806427001953125,
0.03741455078125,
0.0033397674560546875,
-0.048797607421875,
-0.016357421875,
-0.002452850341796875,
-0.0098114013671875,
0.0189208984375,
-0.03814697265625,
-0.01531219482421875,
-0.05364990234375,
-0.03857421875,
-0.0010004043579101562,
0.007266998291015625,
0.0084075927734375,
-0.0200958251953125,
0.023956298828125,
-0.005367279052734375,
-0.01383209228515625,
0.0017614364624023438,
-0.039276123046875,
-0.00395965576171875,
-0.01035308837890625,
0.00836944580078125,
0.0428466796875,
0.01641845703125,
-0.0092926025390625,
-0.0018815994262695312,
-0.0098114013671875,
0.0081787109375,
-0.0223846435546875,
0.033599853515625,
0.016265869140625,
0.035919189453125,
0.0206756591796875,
0.0232391357421875,
-0.0022411346435546875,
-0.01039886474609375,
0.00801849365234375,
0.0194244384765625,
0.00424957275390625,
-0.0228118896484375,
0.01456451416015625,
-0.007659912109375,
-0.0172576904296875,
-0.00537109375,
-0.035064697265625,
0.0245361328125,
0.0106048583984375,
-0.0034275054931640625,
0.00751495361328125,
-0.02777099609375,
0.006011962890625,
-0.03143310546875,
0.0005288124084472656,
-0.0017223358154296875,
0.01558685302734375,
-0.006259918212890625,
-0.0242156982421875,
-0.0305328369140625,
0.006683349609375,
0.01079559326171875,
-0.011993408203125,
-0.0004220008850097656,
0.0203857421875,
-0.00873565673828125,
0.03289794921875,
-0.0240936279296875,
-0.007465362548828125,
0.00856781005859375,
-0.0345458984375,
0.022247314453125,
-0.003093719482421875,
0.028778076171875,
-0.008270263671875,
-0.006748199462890625,
0.004817962646484375,
0.0011043548583984375,
-0.0050201416015625,
0.023773193359375,
-0.0509033203125,
-0.029510498046875,
0.01474761962890625,
0.013763427734375,
-0.00970458984375,
0.0084381103515625,
0.027862548828125,
0.03143310546875,
0.0162200927734375,
-0.0032024383544921875,
-0.01194000244140625,
-0.01800537109375,
0.017547607421875,
0.056365966796875,
-0.01102447509765625,
-0.0007739067077636719,
-0.0143585205078125,
-0.005916595458984375,
-0.0258941650390625,
0.0172271728515625,
0.0146026611328125,
0.005954742431640625,
0.042633056640625,
-0.0023517608642578125,
0.024383544921875,
0.0027065277099609375,
0.0060272216796875,
-0.003986358642578125,
0.0313720703125,
0.0164337158203125,
0.0280303955078125,
0.00786590576171875,
-0.0015134811401367188,
-0.0027103424072265625,
-0.042938232421875,
-0.04052734375,
-0.006908416748046875,
-0.01544952392578125,
0.002681732177734375,
-0.022430419921875,
0.00440216064453125,
-0.0197296142578125,
-0.018524169921875,
-0.01910400390625,
0.01010894775390625,
0.00917816162109375,
-0.002826690673828125,
0.000392913818359375,
-0.0280914306640625,
-0.007434844970703125,
-0.011474609375,
-0.0169219970703125,
0.0023250579833984375,
-0.00331878662109375,
0.027618408203125,
0.01305389404296875,
0.005802154541015625,
-0.000621795654296875,
0.01837158203125,
0.0030364990234375,
0.0155487060546875,
0.01136016845703125,
-0.00812530517578125,
0.04473876953125,
-0.008697509765625,
0.005916595458984375,
-0.0234375,
0.054901123046875,
0.00681304931640625,
0.005207061767578125,
-0.0313720703125,
0.05499267578125,
-0.01187896728515625,
-0.0216217041015625,
0.00021946430206298828,
0.018829345703125,
-0.0031986236572265625,
0.029754638671875,
0.02423095703125,
0.005985260009765625,
0.00841522216796875,
0.0229949951171875,
-0.0193634033203125,
0.02789306640625,
-0.0215606689453125,
-0.01013946533203125,
0.01335906982421875,
-0.0033550262451171875,
-0.0075531005859375,
0.009307861328125,
-0.0096435546875,
0.0028133392333984375,
0.0126953125,
0.0301971435546875,
0.036407470703125,
0.0009775161743164062,
0.042633056640625,
-0.0027675628662109375,
-0.03125,
-0.01183319091796875,
-0.0153656005859375,
-0.0038967132568359375,
-0.0318603515625,
0.023223876953125,
0.040313720703125,
-0.0228271484375,
0.01934814453125,
0.0028324127197265625,
0.01123046875,
-0.018341064453125,
-0.0087890625,
-0.01445770263671875,
0.018310546875,
-0.00960540771484375,
-0.0198516845703125,
-0.0288238525390625,
0.021728515625,
-0.0273590087890625,
0.0002911090850830078,
0.01018524169921875,
0.0367431640625,
0.0295867919921875,
0.0294952392578125,
0.031463623046875,
-0.0252227783203125,
-0.042236328125,
-0.01372528076171875,
-0.01334381103515625,
0.0251617431640625,
0.028717041015625,
0.0088653564453125,
-0.0174102783203125,
-0.005340576171875,
0.00595855712890625,
0.0168609619140625,
0.00408172607421875,
-0.000005125999450683594,
-0.004558563232421875,
0.005962371826171875,
0.0028324127197265625,
-0.039459228515625,
0.01456451416015625,
-0.004405975341796875,
-0.007678985595703125,
0.031890869140625,
-0.034271240234375,
-0.0294036865234375,
0.02520751953125,
-0.01175689697265625,
0.0335693359375,
0.03472900390625,
-0.029388427734375,
-0.0102081298828125,
-0.0034961700439453125,
-0.0029144287109375,
-0.005252838134765625,
0.009307861328125,
0.03179931640625,
-0.0280303955078125,
-0.01806640625,
-0.011077880859375,
0.0015964508056640625,
-0.0305023193359375,
0.0008416175842285156,
-0.005825042724609375,
0.00156402587890625,
0.0164337158203125,
0.016876220703125,
0.00530242919921875,
-0.01139068603515625,
0.0333251953125,
-0.011871337890625,
-0.013092041015625,
-0.0224761962890625,
0.0015354156494140625,
0.01169586181640625,
-0.0220947265625,
-0.0005555152893066406,
0.036956787109375,
0.01111602783203125,
0.0281219482421875,
0.02056884765625,
0.018768310546875,
-0.042572021484375,
-0.0038585662841796875,
0.01078033447265625,
-0.014404296875,
0.00616455078125,
0.02001953125,
0.0241546630859375,
-0.0209197998046875,
-0.0012569427490234375,
-0.0280609130859375,
-0.0003070831298828125,
0.0205535888671875,
0.0019626617431640625,
0.0047454833984375,
-0.004650115966796875,
0.0120849609375,
0.0218505859375,
-0.0015001296997070312,
-0.000835418701171875,
-0.0017414093017578125,
0.0055084228515625,
-0.003215789794921875,
0.034149169921875,
-0.015838623046875,
0.0276947021484375,
-0.038543701171875,
0.0294952392578125,
-0.019195556640625,
0.01071929931640625,
-0.0180206298828125,
-0.006473541259765625,
0.0105743408203125,
-0.00806427001953125,
-0.01070404052734375,
-0.01430511474609375,
-0.0019016265869140625,
0.005908966064453125,
0.0236053466796875,
-0.035797119140625,
0.022186279296875,
0.0305633544921875,
0.0257568359375,
-0.0160064697265625,
-0.0295867919921875,
0.0220794677734375,
-0.035369873046875,
-0.003635406494140625,
0.01114654541015625,
0.035888671875,
0.01507568359375,
-0.01108551025390625,
-0.0335693359375,
-0.01401519775390625,
-0.02044677734375,
-0.0155792236328125,
-0.0212249755859375,
-0.0098419189453125,
-0.0024089813232421875,
-0.0182037353515625,
-0.0102691650390625,
-0.003082275390625,
-0.00762176513671875,
0.0094451904296875,
-0.0162353515625,
-0.032989501953125,
-0.0015287399291992188,
0.00232696533203125,
0.00992584228515625,
0.005916595458984375,
-0.024261474609375,
-0.026397705078125,
0.0275421142578125,
-0.0077972412109375,
-0.0194091796875,
-0.041748046875,
0.02105712890625,
0.0193328857421875,
0.000919342041015625,
0.0019054412841796875,
0.011688232421875,
0.01340484619140625,
-0.0020694732666015625,
-0.01314544677734375,
-0.01409912109375,
0.01261138916015625,
0.0154876708984375,
0.0097503662109375,
-0.01128387451171875,
-0.0076141357421875,
0.040802001953125,
-0.014190673828125,
0.009735107421875,
-0.0113983154296875,
0.01535797119140625,
0.0011806488037109375,
0.0010156631469726562,
0.003978729248046875,
0.00852203369140625,
0.006313323974609375,
0.01806640625,
-0.026611328125,
0.0163116455078125,
-0.04473876953125,
0.0105133056640625,
0.00841522216796875,
0.01085662841796875,
0.0034198760986328125,
-0.01165008544921875,
0.0006656646728515625,
-0.0029926300048828125,
0.02178955078125,
0.001499176025390625,
0.019683837890625,
-0.0011415481567382812,
0.015228271484375,
-0.02410888671875,
0.016632080078125,
-0.0089874267578125,
-0.00009256601333618164,
-0.033935546875,
-0.0112762451171875,
0.0152740478515625,
0.01445770263671875,
-0.00040268898010253906,
-0.0099639892578125,
-0.01641845703125,
-0.040374755859375,
0.05657958984375,
-0.00827789306640625,
-0.007648468017578125,
-0.0255889892578125,
0.00727081298828125,
-0.0019397735595703125,
0.00437164306640625,
0.017730712890625,
-0.0235137939453125,
-0.005962371826171875,
-0.011932373046875,
-0.019378662109375,
0.018310546875,
0.0050506591796875,
0.0255584716796875,
-0.014190673828125,
0.042327880859375,
0.01371002197265625,
0.000018775463104248047,
-0.01788330078125,
0.01178741455078125,
-0.01467132568359375,
0.01024627685546875,
-0.0086669921875,
0.01232147216796875,
0.0033779144287109375,
-0.01503753662109375,
-0.00856781005859375,
0.014312744140625,
-0.004230499267578125,
0.0125274658203125,
0.0294036865234375,
-0.02764892578125,
0.00251007080078125,
0.0297393798828125,
-0.006183624267578125,
-0.054443359375,
0.0101318359375,
-0.0035266876220703125,
-0.00292205810546875,
0.0157623291015625,
0.0273590087890625,
-0.01318359375,
-0.01456451416015625,
0.0221710205078125,
-0.0178070068359375,
0.0200347900390625,
-0.01280975341796875,
-0.042144775390625,
-0.00015997886657714844,
0.003932952880859375,
0.01141357421875,
0.01385498046875,
0.00875091552734375,
-0.0112152099609375,
0.0145111083984375,
-0.00537109375,
-0.026947021484375,
0.01800537109375,
-0.0283660888671875,
-0.013031005859375,
0.0107269287109375,
0.039093017578125,
-0.0404052734375,
-0.01446533203125,
-0.0194549560546875,
0.01806640625,
0.0151824951171875,
0.00649261474609375,
0.00890350341796875,
-0.0302581787109375,
-0.01386260986328125,
-0.0126190185546875,
-0.00519561767578125,
0.029571533203125,
0.0094757080078125,
0.00865936279296875,
-0.0025348663330078125,
-0.0029544830322265625,
-0.01071929931640625,
-0.0113677978515625,
-0.03216552734375,
-0.03753662109375,
-0.00791168212890625,
0.00864410400390625,
0.0013494491577148438,
0.01006317138671875,
-0.0068206787109375,
-0.0160980224609375,
-0.062286376953125,
0.006053924560546875,
-0.005950927734375,
-0.0260772705078125,
-0.01483154296875,
0.0117034912109375,
0.00678253173828125,
-0.0137786865234375,
-0.01776123046875,
-0.00353240966796875,
0.012603759765625,
0.03759765625,
-0.0008859634399414062,
0.0139007568359375,
0.02911376953125,
-0.0340576171875,
0.0019350051879882812,
-0.0268402099609375,
0.0260162353515625,
0.0219573974609375,
-0.01084136962890625,
-0.0308380126953125,
-0.0007734298706054688,
-0.00852203369140625,
-0.01299285888671875,
0.01340484619140625,
-0.00737762451171875,
-0.01062774658203125,
-0.01302337646484375,
0.002292633056640625,
-0.0154266357421875,
0.01904296875,
0.0031757354736328125,
-0.0004086494445800781,
0.038177490234375,
-0.0036144256591796875,
-0.0185089111328125,
-0.020355224609375,
0.011505126953125,
0.006412506103515625,
0.021087646484375,
0.05096435546875,
0.020111083984375,
-0.007755279541015625,
0.017913818359375,
-0.0019683837890625,
0.02813720703125,
0.005985260009765625,
0.005329132080078125,
-0.0256805419921875,
-0.050018310546875,
0.01336669921875,
0.001491546630859375,
0.023651123046875,
-0.0210723876953125,
0.0272216796875,
0.01410675048828125,
-0.0187835693359375,
-0.025482177734375,
-0.0141448974609375,
0.0008902549743652344,
-0.0037364959716796875,
0.004367828369140625,
0.0005993843078613281,
-0.0160675048828125,
-0.01016998291015625,
-0.02276611328125,
-0.006916046142578125,
-0.01434326171875,
-0.02239990234375,
0.00878143310546875,
0.0107421875,
0.00254058837890625,
-0.0076904296875,
0.028594970703125,
0.01531982421875,
0.0117645263671875,
0.0306549072265625,
-0.00496673583984375,
-0.01433563232421875,
-0.00926971435546875,
-0.0186004638671875,
-0.0275115966796875,
-0.0165557861328125,
-0.0041656494140625,
0.01305389404296875,
0.0163116455078125,
-0.0258331298828125,
-0.044677734375,
-0.057037353515625,
-0.042877197265625,
0.01296234130859375,
-0.00897979736328125,
-0.000014722347259521484,
0.0157928466796875,
0.0101470947265625,
-0.0156097412109375,
0.013763427734375,
0.00506591796875,
-0.005237579345703125,
0.00940704345703125,
-0.017822265625,
0.00904083251953125,
-0.0018787384033203125,
-0.0123748779296875,
-0.01314544677734375,
-0.0033435821533203125,
-0.009063720703125,
0.00560760498046875,
-0.0428466796875,
0.01483917236328125,
0.005550384521484375,
0.0003933906555175781,
-0.0015659332275390625,
0.051910400390625,
-0.031158447265625,
-0.0014123916625976562,
0.005542755126953125,
0.03497314453125,
-0.0106201171875,
0.01033782958984375,
-0.0258331298828125,
0.017730712890625,
0.00328826904296875,
-0.04205322265625,
0.0462646484375,
-0.0171051025390625,
0.034637451171875,
0.00528717041015625,
0.0170745849609375,
0.01508331298828125,
-0.00846099853515625,
0.00893402099609375,
-0.03558349609375,
-0.0022449493408203125,
-0.015350341796875,
-0.019622802734375,
-0.01169586181640625,
-0.01380157470703125,
0.013397216796875,
0.01390838623046875,
0.0312042236328125,
-0.005847930908203125,
-0.0285491943359375,
-0.0234832763671875,
0.034149169921875,
-0.031036376953125,
-0.01140594482421875,
0.016204833984375,
0.016693115234375,
-0.0244598388671875,
0.01325225830078125,
0.019134521484375,
-0.0294952392578125,
0.0198974609375,
0.0287933349609375,
0.03857421875,
-0.00798797607421875,
0.01065826416015625,
-0.004810333251953125,
0.00013446807861328125,
-0.01605224609375,
0.03173828125,
0.0099945068359375,
0.0255584716796875,
-0.03076171875,
0.00565338134765625,
0.00919342041015625,
-0.0223236083984375,
-0.01058197021484375,
-0.017608642578125,
-0.0011196136474609375,
0.017791748046875,
0.01052093505859375,
-0.022613525390625,
0.0107421875,
-0.039642333984375,
0.0004601478576660156,
0.0111846923828125,
-0.01023101806640625,
0.0100250244140625,
-0.022613525390625,
-0.003536224365234375,
-0.040313720703125,
-0.04901123046875,
0.002582550048828125,
-0.01345062255859375,
0.00989532470703125,
0.0230255126953125,
0.0233917236328125,
0.00899505615234375,
0.0263671875,
0.0199432373046875,
0.01409912109375,
-0.0158538818359375,
-0.01189422607421875,
-0.0240020751953125,
0.00429534912109375,
0.01666259765625,
0.0023593902587890625,
0.0006232261657714844,
-0.029052734375,
-0.017730712890625,
-0.0103759765625,
-0.00296783447265625,
0.03662109375,
-0.0235595703125,
0.006526947021484375,
0.005512237548828125,
-0.008514404296875,
-0.0037994384765625,
-0.034088134765625,
0.01201629638671875,
0.011138916015625,
-0.00946044921875,
0.0064544677734375,
-0.0173187255859375,
-0.0238494873046875,
-0.0005497932434082031,
-0.008880615234375,
0.01186370849609375,
-0.0328369140625,
0.01397705078125,
0.00922393798828125,
0.02166748046875,
0.01189422607421875,
-0.01467132568359375,
0.037200927734375,
0.0132293701171875,
-0.0248260498046875,
0.0396728515625,
0.00829315185546875,
-0.0205535888671875,
0.012786865234375,
0.006084442138671875,
-0.038116455078125,
-0.0191497802734375,
-0.004100799560546875,
-0.006984710693359375,
0.006015777587890625,
0.0225830078125,
0.004398345947265625,
0.0540771484375,
0.0011920928955078125,
-0.0181121826171875,
-0.0362548828125,
-0.00823974609375,
-0.004375457763671875,
0.01438140869140625,
0.0088043212890625,
0.028564453125,
0.0016031265258789062,
-0.0259552001953125,
-0.0139617919921875,
-0.0121307373046875,
-0.011566162109375,
-0.01312255859375,
0.012298583984375,
0.0279083251953125,
-0.00974273681640625,
0.0162200927734375,
-0.00015473365783691406,
-0.01502227783203125,
-0.022857666015625,
-0.046875,
-0.006572723388671875,
-0.0017290115356445312,
0.01849365234375,
0.01007080078125,
-0.0153961181640625,
-0.0194854736328125,
0.0298309326171875,
-0.00505828857421875,
-0.007007598876953125,
-0.0111541748046875,
-0.00795745849609375,
0.011810302734375,
0.06353759765625,
-0.00423431396484375,
-0.01132965087890625,
-0.003803253173828125,
-0.03955078125,
0.033233642578125,
-0.03631591796875,
-0.00196075439453125,
0.00726318359375,
0.006183624267578125,
0.01348876953125,
-0.0287017822265625,
0.01297760009765625,
-0.01496124267578125,
0.018829345703125,
0.032073974609375,
-0.0196685791015625,
-0.0221405029296875,
-0.0029296875,
-0.0062408447265625,
0.016937255859375,
0.0306549072265625,
-0.0091400146484375,
-0.01190185546875,
-0.0287322998046875,
0.0032634735107421875,
-0.0136260986328125,
0.002582550048828125,
0.0011701583862304688,
0.0312347412109375,
0.00469207763671875,
0.0224609375,
-0.014739990234375,
0.00824737548828125,
0.00620269775390625,
0.01061248779296875,
-0.030426025390625,
-0.0022869110107421875,
0.00885009765625,
0.0179443359375,
0.0007076263427734375,
-0.01837158203125,
0.0145416259765625,
0.01528167724609375,
-0.00861358642578125,
-0.004344940185546875,
-0.030242919921875,
0.0028553009033203125,
0.005397796630859375,
-0.0037136077880859375,
0.0110015869140625,
-0.0111541748046875,
-0.0048828125,
0.015045166015625,
0.0020389556884765625,
-0.0240020751953125,
-0.0008463859558105469,
0.033355712890625,
0.018646240234375,
-0.007598876953125,
0.0157623291015625,
0.01385498046875,
-0.00525665283203125,
0.0303497314453125,
-0.0006847381591796875,
0.0391845703125,
0.00457000732421875,
-0.01497650146484375,
-0.011322021484375,
0.00457763671875,
0.010528564453125,
-0.0063018798828125,
-0.0145416259765625,
-0.005458831787109375,
0.0153656005859375,
0.01396942138671875,
-0.0013713836669921875,
0.01812744140625,
0.0175018310546875,
0.0117340087890625,
0.017730712890625,
-0.03521728515625,
0.004734039306640625,
0.0024871826171875,
0.017425537109375,
0.01265716552734375,
-0.0254974365234375,
0.0099029541015625,
0.01210784912109375,
-0.0364990234375,
0.0229339599609375,
-0.004344940185546875,
-0.0226593017578125,
0.01605224609375,
-0.006023406982421875,
-0.01373291015625,
-0.0156097412109375,
0.002655029296875,
0.01715087890625,
0.007724761962890625,
0.01552581787109375,
-0.0233154296875,
0.0020961761474609375,
-0.00994110107421875,
0.00907135009765625,
0.02239990234375,
-0.00859832763671875,
-0.0028781890869140625,
-0.021087646484375,
0.030975341796875,
-0.0031070709228515625,
0.01071929931640625,
-0.0207672119140625,
-0.0021190643310546875,
0.004611968994140625,
-0.01500701904296875,
-0.0107421875,
-0.021942138671875,
0.02508544921875,
-0.01202392578125,
-0.01044464111328125,
0.017486572265625,
-0.001811981201171875,
0.01151275634765625,
0.02288818359375,
0.0203094482421875,
-0.00714874267578125,
0.003246307373046875,
0.00916290283203125,
0.0096588134765625,
0.0269012451171875,
0.018829345703125,
-0.01422119140625,
0.0121307373046875,
-0.023162841796875,
0.0012378692626953125,
-0.029510498046875,
-0.00807952880859375,
-0.0167694091796875,
0.0440673828125,
-0.015350341796875,
-0.048736572265625,
-0.01189422607421875,
0.004352569580078125,
0.007415771484375,
0.01320648193359375,
0.035980224609375,
0.04638671875,
-0.0018892288208007812,
-0.01419830322265625,
-0.03985595703125,
0.00015628337860107422,
0.0019931793212890625,
0.0201568603515625,
-0.0151214599609375,
-0.027252197265625,
-0.005157470703125,
0.01103973388671875,
0.004024505615234375,
-0.02398681640625,
0.0186920166015625,
-0.023162841796875,
0.00252532958984375,
-0.0040283203125,
0.0223236083984375,
0.033294677734375,
0.0008287429809570312,
-0.0059356689453125,
-0.0290679931640625,
-0.005985260009765625,
-0.0731201171875,
0.0024242401123046875,
0.005809783935546875,
0.005260467529296875,
0.043701171875,
-0.0177001953125,
-0.0312042236328125,
0.015380859375,
-0.00775909423828125,
0.005222320556640625,
-0.00904083251953125,
-0.004364013671875,
-0.0207977294921875,
-0.00455474853515625,
-0.0013170242309570312,
-0.00010830163955688477,
0.01192474365234375,
-0.01010894775390625,
0.016815185546875,
0.036895751953125,
-0.01611328125,
0.0037479400634765625,
0.006809234619140625,
0.02862548828125,
-0.0041656494140625,
-0.0211029052734375,
0.00726318359375,
-0.054718017578125,
0.0169219970703125,
-0.01084136962890625,
0.0292205810546875,
-0.01282501220703125,
-0.022125244140625,
-0.0343017578125,
0.01204681396484375,
0.0166473388671875,
-0.0153656005859375,
0.007358551025390625,
-0.0299072265625,
-0.0184478759765625,
0.00785064697265625,
-0.0011911392211914062,
0.005420684814453125,
0.01110076904296875,
-0.0440673828125,
0.03741455078125,
-0.01131439208984375,
0.016937255859375,
0.002803802490234375,
0.0049896240234375,
0.008941650390625,
0.0183563232421875,
-0.003002166748046875,
0.03411865234375,
-0.006732940673828125,
-0.020904541015625,
0.031585693359375,
-0.006237030029296875,
-0.02899169921875,
-0.0301971435546875,
0.00014960765838623047,
0.0033206939697265625,
0.0031890869140625,
-0.0166015625,
0.010040283203125,
-0.042327880859375,
-0.0024471282958984375,
0.059967041015625,
-0.007476806640625,
-0.00323486328125,
-0.00609588623046875,
-0.017547607421875,
-0.0096893310546875,
0.00501251220703125,
0.0291595458984375,
-0.019012451171875,
-0.038665771484375,
0.01065826416015625,
0.0243988037109375,
0.0265960693359375,
-0.0135498046875,
0.028472900390625,
-0.0298004150390625,
0.0018930435180664062,
-0.0037860870361328125,
0.004123687744140625,
0.00958251953125,
-0.0186004638671875,
0.017120361328125,
0.0039215087890625,
-0.024810791015625,
0.00728607177734375,
0.00817108154296875,
0.007495880126953125,
-0.02239990234375,
-0.0232391357421875,
-0.00032138824462890625,
0.02606201171875,
0.0037384033203125,
-0.029693603515625,
0.026885986328125,
-0.016845703125,
0.00460052490234375,
-0.0294647216796875,
0.022613525390625,
-0.005035400390625,
0.0006074905395507812,
-0.0291290283203125,
-0.01271820068359375,
0.037017822265625,
-0.001186370849609375,
-0.0249176025390625,
0.0193939208984375,
-0.01465606689453125,
0.02392578125,
-0.00466156005859375,
0.0384521484375,
0.0491943359375,
-0.03070068359375,
-0.0091705322265625,
0.01202392578125,
-0.02392578125,
-0.0270843505859375,
-0.0293426513671875,
-0.0101470947265625,
-0.03338623046875,
-0.0157318115234375,
-0.01081085205078125,
0.021697998046875,
0.00434112548828125,
0.0015630722045898438,
-0.01428985595703125,
0.02056884765625,
0.019866943359375,
0.057037353515625,
-0.00435638427734375,
0.01486968994140625,
-0.030303955078125,
0.01198577880859375,
-0.00042438507080078125,
-0.0224151611328125,
-0.002689361572265625,
0.0281219482421875,
-0.0232696533203125,
-0.034515380859375,
0.002475738525390625,
-0.028350830078125,
-0.0140838623046875,
-0.0113525390625,
-0.01092529296875,
0.00901031494140625,
-0.0028171539306640625,
-0.0010328292846679688,
0.0170440673828125,
-0.0357666015625,
-0.01554107666015625,
0.0177459716796875,
-0.0192108154296875,
-0.02093505859375,
-0.00963592529296875,
-0.0253448486328125,
0.018768310546875,
-0.0036029815673828125,
0.0031890869140625,
-0.0190277099609375,
-0.021240234375,
-0.01004791259765625,
0.0016889572143554688,
0.050537109375,
-0.01338958740234375,
-0.042755126953125,
-0.01348876953125,
0.005176544189453125,
0.01157379150390625,
0.0222930908203125,
0.031982421875,
-0.00661468505859375,
0.0240936279296875,
0.006336212158203125,
0.0022125244140625,
-0.0105438232421875,
0.018951416015625,
0.0278167724609375,
0.03302001953125,
0.0115203857421875,
-0.00409698486328125,
0.035125732421875,
0.01910400390625,
-0.0124664306640625,
-0.0036983489990234375,
-0.0164031982421875,
0.027374267578125,
0.009307861328125,
0.005428314208984375,
-0.0247039794921875,
0.02679443359375,
-0.01055145263671875,
0.00933837890625,
0.05572509765625,
-0.0027141571044921875,
0.03509521484375,
0.00936126708984375,
0.003879547119140625,
0.005466461181640625,
0.0218353271484375,
0.0107421875,
0.028564453125,
0.00531005859375,
-0.00716400146484375,
0.0261688232421875,
0.028228759765625,
-0.0006866455078125,
0.025390625,
-0.020050048828125,
0.0005745887756347656,
-0.004978179931640625,
0.0022602081298828125,
-0.01189422607421875,
-0.03411865234375,
0.00560760498046875,
0.00208282470703125,
0.01561737060546875,
-0.00829315185546875,
0.027984619140625,
-0.0081634521484375,
0.01776123046875,
0.0167388916015625,
0.010955810546875,
-0.021026611328125,
0.00446319580078125,
-0.023590087890625,
-0.027557373046875,
0.0188140869140625,
0.01904296875,
-0.004985809326171875,
0.0081329345703125,
0.002033233642578125,
-0.004302978515625,
0.01180267333984375,
-0.0083770751953125,
0.04705810546875,
0.01044464111328125,
0.019012451171875,
-0.008331298828125,
0.053741455078125,
0.05950927734375,
-0.01067352294921875,
0.0180816650390625,
-0.001430511474609375,
-0.005084991455078125,
0.0269317626953125,
-0.000009715557098388672,
-0.019500732421875,
0.0058746337890625,
-0.005329132080078125,
-0.0219268798828125,
0.03173828125,
0.00913238525390625,
-0.01514434814453125,
0.0003809928894042969,
0.024810791015625,
0.01593017578125,
0.010223388671875,
-0.040924072265625,
-0.02789306640625,
0.0008287429809570312,
0.02130126953125,
-0.0207672119140625,
0.00505828857421875,
-0.0119171142578125,
-0.01336669921875,
-0.01132965087890625,
0.0244903564453125,
0.004230499267578125,
0.05584716796875,
-0.016448974609375,
0.00885009765625,
-0.00838470458984375,
-0.004543304443359375,
-0.00281524658203125,
-0.00021839141845703125,
-0.00803375244140625,
0.004322052001953125,
-0.00042366981506347656,
-0.035736083984375,
-0.0167388916015625,
-0.0154571533203125,
0.0078887939453125,
0.007678985595703125,
0.040496826171875,
-0.0262908935546875,
-0.036834716796875,
0.02264404296875,
-0.0184173583984375,
-0.0029125213623046875,
0.005702972412109375,
0.0197601318359375,
-0.018585205078125,
-0.0202789306640625,
-0.0171661376953125,
-0.01763916015625,
-0.014984130859375,
-0.0183868408203125,
-0.012054443359375,
-0.0196685791015625,
-0.00937652587890625,
-0.01275634765625,
0.01776123046875,
-0.005706787109375,
-0.024627685546875,
-0.012237548828125,
-0.017669677734375,
0.01251983642578125,
-0.0193328857421875,
-0.0027103424072265625,
0.01125335693359375,
0.01070404052734375,
0.01349639892578125,
-0.0165863037109375,
-0.030914306640625,
-0.007625579833984375,
-0.033172607421875,
-0.0286865234375,
0.0234375,
-0.01233673095703125,
-0.0000035762786865234375,
0.0081634521484375,
-0.040283203125,
-0.00919342041015625,
0.005825042724609375,
0.0299072265625,
0.01544189453125,
-0.0029582977294921875,
-0.008148193359375,
0.0021457672119140625,
0.004894256591796875,
-0.0160369873046875,
-0.0163726806640625,
-0.0277862548828125,
-0.0196685791015625,
0.040130615234375,
0.01678466796875,
-0.042083740234375,
0.007411956787109375,
0.007137298583984375,
-0.0250244140625,
0.022369384765625,
0.00917816162109375,
-0.0192718505859375,
-0.010986328125,
0.00977325439453125,
0.0030345916748046875,
0.0226593017578125,
0.02880859375,
-0.0103759765625,
-0.0023345947265625,
-0.0311279296875,
-0.0215606689453125,
0.01910400390625,
0.04052734375,
0.0010251998901367188,
0.004390716552734375,
0.0230255126953125,
-0.031280517578125,
0.0306396484375,
-0.00787353515625,
-0.0270538330078125,
0.0166473388671875,
-0.0252532958984375,
0.0043182373046875,
0.004795074462890625,
0.0250091552734375,
-0.004093170166015625,
-0.0217437744140625,
0.0020046234130859375,
0.0134429931640625,
0.03167724609375,
0.0020580291748046875,
-0.017974853515625,
0.0169677734375,
-0.0202178955078125,
-0.02325439453125,
-0.00006181001663208008,
-0.00443267822265625,
0.022003173828125,
0.0063018798828125,
0.021728515625,
0.0310821533203125,
-0.006305694580078125,
0.0123138427734375,
0.03973388671875,
0.01134490966796875,
-0.00860595703125,
-0.0144195556640625,
-0.005718231201171875,
0.018646240234375,
0.006977081298828125,
0.0008373260498046875,
0.004940032958984375,
0.017303466796875,
0.0294647216796875,
0.01349639892578125,
-0.0041961669921875,
0.0504150390625,
-0.0093994140625,
-0.005344390869140625,
-0.0009450912475585938,
-0.0139617919921875,
0.0450439453125,
-0.01324462890625,
0.031463623046875,
-0.0029125213623046875,
0.001399993896484375,
0.01708984375,
0.00240325927734375,
-0.006465911865234375,
0.005481719970703125,
-0.00528717041015625,
0.0236053466796875,
-0.0003218650817871094,
-0.0200958251953125,
-0.00675201416015625,
0.026641845703125,
-0.060943603515625,
-0.005702972412109375,
-0.014892578125,
0.009765625,
-0.0128631591796875,
0.0099945068359375,
-0.0135040283203125,
-0.0029468536376953125,
0.00144195556640625,
-0.007457733154296875,
0.01398468017578125,
0.0182037353515625,
-0.01143646240234375,
-0.00014340877532958984,
-0.031219482421875,
0.01140594482421875,
0.0218658447265625,
0.0174560546875,
-0.009002685546875,
-0.016754150390625,
0.01190185546875,
0.0236053466796875,
-0.00972747802734375,
0.0009098052978515625,
-0.03924560546875,
-0.003582000732421875,
0.02142333984375,
-0.01064300537109375,
0.0212554931640625,
-0.0028076171875,
-0.0226593017578125,
0.032073974609375,
0.0118560791015625,
0.0083160400390625,
-0.020477294921875,
0.003681182861328125,
0.00978851318359375,
0.00042557716369628906,
-0.022552490234375,
0.00909423828125,
0.026519775390625,
-0.053863525390625,
-0.0006318092346191406,
-0.023834228515625,
0.004589080810546875,
-0.021331787109375,
0.0199737548828125,
-0.0182647705078125,
0.0080718994140625,
0.007633209228515625,
0.041839599609375,
-0.0186920166015625,
0.0056915283203125,
0.0026912689208984375,
0.034698486328125,
0.030059814453125,
0.0186614990234375,
-0.0015382766723632812,
0.00383758544921875,
-0.0017986297607421875,
0.0135498046875,
0.018768310546875,
0.0227203369140625,
-0.0058746337890625,
-0.0192413330078125,
-0.02020263671875,
-0.02996826171875,
-0.04205322265625,
0.0006008148193359375,
0.003673553466796875,
0.041168212890625,
-0.0016622543334960938,
-0.0325927734375,
0.01212310791015625,
-0.017913818359375,
0.0214080810546875,
0.0101470947265625,
-0.0178985595703125,
-0.006084442138671875,
0.00799560546875,
0.06671142578125,
0.01442718505859375,
0.01549530029296875,
0.001064300537109375,
0.01397705078125,
-0.01520538330078125,
-0.02288818359375,
0.000036835670471191406,
0.0164947509765625,
-0.01029205322265625,
-0.0072174072265625,
-0.00965118408203125,
0.0097808837890625,
0.00749969482421875,
-0.002384185791015625,
-0.02813720703125,
-0.014801025390625,
-0.006969451904296875,
0.032012939453125,
-0.012969970703125,
-0.0201873779296875,
-0.0231475830078125,
0.0193328857421875,
-0.0036468505859375,
0.00812530517578125,
-0.01262664794921875,
-0.020111083984375,
-0.01146697998046875,
-0.0223541259765625,
-0.0182647705078125,
-0.003662109375,
0.008514404296875,
-0.0274200439453125,
-0.02227783203125,
-0.0248870849609375,
-0.005023956298828125,
-0.0167694091796875,
0.0291900634765625,
-0.00397491455078125,
0.01021575927734375,
-0.00440216064453125,
0.01271820068359375,
0.0254364013671875,
0.0216064453125,
-0.0083465576171875,
-0.0297698974609375,
-0.00030159950256347656,
-0.0259857177734375,
0.0043182373046875,
0.05859375,
-0.0271148681640625,
-0.02886962890625,
-0.01800537109375,
-0.01605224609375,
-0.00963592529296875,
-0.01151275634765625,
-0.0303955078125,
0.0269317626953125,
0.01006317138671875,
-0.0279388427734375,
-0.0016317367553710938,
0.019744873046875,
0.0120391845703125,
-0.0008988380432128906,
-0.030914306640625,
0.0098876953125,
-0.0082550048828125,
0.020477294921875,
-0.035003662109375,
-0.00598907470703125,
0.0158538818359375,
-0.018798828125,
0.040496826171875,
0.0175628662109375,
-0.0160980224609375,
-0.00966644287109375,
0.029998779296875,
0.0221099853515625,
-0.0218505859375,
0.009552001953125,
0.00647735595703125,
-0.004425048828125,
-0.0203857421875,
0.03143310546875,
-0.0017747879028320312,
-0.0028400421142578125,
0.0141754150390625,
0.01629638671875,
-0.0018329620361328125,
0.0229339599609375,
-0.006587982177734375,
0.0215911865234375,
-0.0240936279296875,
-0.027130126953125,
-0.0296478271484375,
0.01221466064453125,
-0.03521728515625,
0.0017681121826171875,
-0.006267547607421875,
-0.02008056640625,
0.01322174072265625,
0.00977325439453125,
-0.0019207000732421875,
0.007808685302734375,
0.00577545166015625,
-0.006900787353515625,
-0.0219268798828125,
0.01392364501953125,
0.0013675689697265625,
-0.0093231201171875,
0.007251739501953125,
-0.00007855892181396484,
-0.037994384765625,
0.00650787353515625,
0.006198883056640625,
-0.0111541748046875,
0.0011911392211914062,
-0.0015306472778320312,
-0.00946044921875,
0.036529541015625,
-0.01338958740234375,
-0.057647705078125,
-0.0126495361328125,
-0.0108489990234375,
-0.038421630859375,
-0.0164337158203125,
-0.0024509429931640625,
-0.00788116455078125,
0.017974853515625,
0.01873779296875,
0.01126861572265625,
-0.0146026611328125,
-0.01134490966796875,
0.0005822181701660156,
0.01076507568359375,
0.002750396728515625,
-0.01505279541015625,
0.019805908203125,
0.032012939453125,
0.024383544921875,
0.017425537109375,
0.0116729736328125,
0.00859832763671875,
0.0037250518798828125,
-0.0297393798828125,
-0.0154876708984375,
-0.001453399658203125,
0.0182647705078125,
-0.033203125,
0.01172637939453125,
-0.0200042724609375,
0.0206298828125,
0.007610321044921875,
0.020294189453125,
0.028106689453125,
0.0182647705078125,
0.04119873046875,
0.02960205078125,
-0.0098724365234375,
-0.0008721351623535156,
-0.0164031982421875,
-0.026123046875,
0.0155181884765625,
0.0165252685546875,
0.00319671630859375,
-0.01541900634765625,
0.002368927001953125,
-0.0206756591796875,
-0.03704833984375,
-0.0247039794921875,
-0.0211334228515625,
0.0274505615234375,
-0.0006380081176757812,
-0.0092620849609375,
-0.03009033203125,
0.0126190185546875,
0.0057373046875,
0.0203399658203125,
-0.00653076171875,
0.013641357421875,
0.01154327392578125,
-0.03363037109375,
0.0019407272338867188,
-0.0002428293228149414,
0.01490020751953125,
-0.01557159423828125,
0.01502227783203125,
-0.0160369873046875,
-0.0091094970703125,
-0.023468017578125,
0.02532958984375,
0.00038170814514160156,
-0.015655517578125,
-0.006084442138671875,
-0.0134735107421875,
-0.022186279296875,
0.0236358642578125,
-0.0164031982421875,
0.0239105224609375,
0.00162506103515625,
-0.0182037353515625,
-0.0113525390625,
0.01045989990234375,
0.0171051025390625,
0.01812744140625,
0.0092620849609375,
-0.038360595703125,
-0.005329132080078125,
0.00762939453125,
-0.00876617431640625,
-0.0191497802734375,
-0.011322021484375,
-0.0006933212280273438,
0.0276031494140625,
0.0240325927734375,
0.005706787109375,
0.00109100341796875,
0.01953125,
-0.0246734619140625,
-0.0023517608642578125,
0.040283203125,
0.00801849365234375,
0.015106201171875,
0.0015344619750976562,
0.0004799365997314453,
-0.00867462158203125,
-0.0087738037109375,
0.0174713134765625,
-0.00820159912109375,
0.00567626953125,
0.01058197021484375,
0.01151275634765625,
0.046600341796875,
0.0205841064453125,
0.0256195068359375,
0.022491455078125,
-0.0093994140625,
0.019256591796875,
-0.0027942657470703125,
-0.0101165771484375,
0.0209808349609375,
-0.0318603515625,
0.0034198760986328125,
0.01141357421875,
-0.00923919677734375,
0.04058837890625,
-0.00897216796875,
-0.00357818603515625,
0.03515625,
-0.010833740234375,
-0.01329803466796875,
0.0129547119140625,
-0.007335662841796875,
0.0021209716796875,
0.0323486328125,
0.01081085205078125,
-0.00623321533203125,
0.011993408203125,
-0.0127105712890625,
0.032562255859375,
0.007083892822265625,
0.0119476318359375,
0.032806396484375,
-0.029815673828125,
-0.0210418701171875,
0.02850341796875,
-0.028289794921875,
0.012176513671875,
0.01287078857421875,
0.0066070556640625,
-0.0164642333984375,
0.0091552734375,
-0.01099395751953125,
-0.010833740234375,
0.017608642578125,
0.0092010498046875,
0.0254058837890625,
-0.003753662109375,
0.005401611328125,
-0.032928466796875,
0.0274810791015625,
0.0174560546875,
-0.022491455078125,
-0.012176513671875,
0.0055999755859375,
0.0221710205078125,
0.0367431640625,
-0.001796722412109375,
-0.01001739501953125,
-0.02978515625,
0.0165252685546875,
-0.031463623046875,
-0.0223846435546875,
-0.0028839111328125,
-0.0089874267578125,
-0.0193634033203125,
-0.0049591064453125,
0.030181884765625,
0.006977081298828125,
0.018280029296875,
-0.0044708251953125,
0.0001741647720336914,
0.022491455078125,
0.01265716552734375,
-0.033203125,
-0.00763702392578125,
-0.0280914306640625,
-0.0026378631591796875,
0.01812744140625,
0.015106201171875,
-0.0188751220703125,
-0.00003325939178466797,
-0.024078369140625,
-0.036163330078125,
0.019744873046875,
0.01071929931640625,
-0.0004222393035888672,
-0.01100921630859375,
-0.03582763671875,
-0.03240966796875,
-0.0128326416015625,
0.0341796875,
-0.0014324188232421875,
-0.0364990234375,
0.01195526123046875,
-0.0003707408905029297,
-0.0022430419921875,
-0.001888275146484375,
-0.037750244140625,
0.004871368408203125,
0.01052093505859375,
0.0323486328125,
0.016937255859375,
0.0112457275390625,
0.0013284683227539062,
0.030029296875,
0.004730224609375,
-0.007232666015625,
-0.01593017578125,
-0.00711822509765625,
-0.01384735107421875,
-0.01396942138671875,
-0.00405120849609375,
-0.037994384765625,
0.009033203125,
-0.004398345947265625,
0.008544921875,
-0.02789306640625,
0.019439697265625,
0.00418853759765625,
-0.0249176025390625,
-0.0097198486328125,
-0.019317626953125,
0.0477294921875,
0.0169677734375,
0.004486083984375,
0.0160980224609375,
-0.0073699951171875,
0.0020999908447265625,
-0.0041656494140625,
0.0136566162109375,
0.0018186569213867188,
-0.0174560546875,
-0.01050567626953125,
0.0245208740234375,
-0.017181396484375,
-0.007419586181640625,
0.00012624263763427734,
-0.010986328125,
-0.0033054351806640625,
-0.012908935546875,
-0.0307464599609375,
0.0009379386901855469,
0.006031036376953125,
-0.0289764404296875,
-0.01122283935546875,
-0.0201263427734375,
-0.040374755859375,
-0.035247802734375,
-0.00701141357421875,
0.0243377685546875,
-0.0177001953125,
0.01088714599609375,
-0.02581787109375,
0.0311126708984375,
0.0187835693359375,
-0.052642822265625,
-0.030364990234375,
0.000881195068359375,
0.008544921875,
0.0138702392578125,
-0.02740478515625,
0.0246124267578125,
-0.009002685546875,
0.04052734375,
0.02105712890625,
0.0115966796875,
0.0244598388671875,
0.0263519287109375,
-0.01287841796875,
-0.0009012222290039062,
-0.0061187744140625,
-0.01192474365234375,
-0.0001804828643798828,
-0.0220947265625,
0.0023651123046875,
0.0063323974609375,
0.02001953125,
0.02069091796875,
-0.0032558441162109375,
0.0082855224609375,
-0.01372528076171875,
0.004741668701171875,
0.0274810791015625
] |
ours_474
|
Let \( M = N + 1 = 2p \), where \( p \) is prime. We note that by Ceva's theorem or barycentric coordinates, it is equivalent to finding the number of solutions \((a, b, c) \in [N]^3\) to \( abc = (M-a)(M-b)(M-c) \). We claim that for any such solution, we require \( p \in \{a, b, c\} \). Indeed, since \( abc \equiv -abc \pmod{p} \) (from \( p \mid M \)), we obtain \( p \mid abc \), and so \( p \) divides one of \( a, b, c \). Since \( a, b, c \in [1, 2p-1] \), one of \( a, b, c \) is \( p \).
If \( a = p \), then we get that \( b + c = M \), so there are \( N \) solutions for this case. Thus, there are \( 3N - 2 = 6049 \) total solutions since \((p, p, p)\) is counted thrice.
\(\boxed{6049}\)
|
6049
|
{
"competition": "us_comps",
"dataset": "Ours",
"posts": null,
"source": "OMOFall18Solns.md"
}
|
Let \( ABC \) be the triangle with vertices located at the center of masses of three distinct points. Assume the three are not collinear. Let \( N=2017 \), and define the \( A \)-ntipodes to be the points \( A_{1}, \ldots, A_{N} \) on segment \( BC \) such that \( BA_{1}=A_{1}A_{2}=\cdots=A_{N-1}A_{N}=A_{N}C \), and similarly define the \( B, C \)-ntipodes. A line \(\ell_{A}\) through \( A \) is called a qevian if it passes through an \( A \)-ntipode, and similarly we define qevians through \( B \) and \( C \). Compute the number of ordered triples \((\ell_{A}, \ell_{B}, \ell_{C})\) of concurrent qevians through \( A, B, C \), respectively.
|
[
"/Mathematics/Geometry/CoordinateGeometry/BarycentricCoordinates",
"/Mathematics/Geometry/DivisionProblems/NumberPartitioningProblem",
"/Mathematics/Geometry/GeneralGeometry/EuclideanGeometry",
"/Mathematics/Geometry/GeneralGeometry/Geometry",
"/Mathematics/Geometry/PlaneGeometry/Triangles",
"/Mathematics/NumberTheory/Congruences/Congruence",
"/Mathematics/NumberTheory/Congruences/CongruenceEquation",
"/Mathematics/NumberTheory/Congruences/Mod",
"/Mathematics/NumberTheory/Congruences/ModularArithmetic",
"/Mathematics/NumberTheory/Congruences/Modulus",
"/Mathematics/NumberTheory/DiophantineEquations/Diophantine",
"/Mathematics/NumberTheory/DiophantineEquations/DiophantineEquation",
"/Mathematics/NumberTheory/PrimeNumbers/PrimeFactorization",
"/Mathematics/NumberTheory/PrimeNumbers/PrimeNumberProperties"
] |
Use Ceva to translate concurrency into abc=(M−a)(M−b)(M−c) and apply modulo‑p (with M=2p) to force one of a,b,c to equal p.
|
[
-0.00014030933380126953,
-0.0166015625,
0.0013637542724609375,
0.0194854736328125,
-0.00028705596923828125,
0.061187744140625,
0.0229034423828125,
-0.0088348388671875,
0.00203704833984375,
0.0163726806640625,
0.0374755859375,
-0.0174713134765625,
0.0006704330444335938,
-0.0014467239379882812,
-0.02166748046875,
-0.0086822509765625,
-0.00276947021484375,
0.0013036727905273438,
0.006313323974609375,
-0.0030384063720703125,
-0.0005497932434082031,
0.0066986083984375,
-0.04058837890625,
0.031219482421875,
-0.005863189697265625,
0.0097503662109375,
-0.01568603515625,
0.026123046875,
-0.0157470703125,
0.01268768310546875,
0.0008225440979003906,
-0.035400390625,
0.003253936767578125,
0.005157470703125,
-0.00104522705078125,
0.0125732421875,
-0.040191650390625,
0.005619049072265625,
-0.008331298828125,
-0.019561767578125,
-0.02166748046875,
0.03363037109375,
0.019744873046875,
0.0182342529296875,
-0.00604248046875,
0.00876617431640625,
0.007328033447265625,
-0.00031185150146484375,
-0.0035076141357421875,
0.01317596435546875,
0.006031036376953125,
0.0116424560546875,
-0.0167694091796875,
-0.0088043212890625,
-0.017608642578125,
-0.07965087890625,
-0.0247802734375,
0.0027141571044921875,
-0.0024700164794921875,
0.00792694091796875,
0.004863739013671875,
-0.01043701171875,
0.0005078315734863281,
-0.0175018310546875,
-0.004486083984375,
-0.008331298828125,
-0.0304412841796875,
-0.01568603515625,
0.003498077392578125,
-0.02099609375,
0.0185394287109375,
-0.0037097930908203125,
0.005382537841796875,
0.02166748046875,
0.033111572265625,
-0.01041412353515625,
-0.005001068115234375,
0.0212860107421875,
0.0019969940185546875,
-0.00464630126953125,
0.011383056640625,
0.009246826171875,
-0.01000213623046875,
-0.04254150390625,
0.0171051025390625,
0.0254974365234375,
0.00011867284774780273,
0.005977630615234375,
0.043182373046875,
-0.0034351348876953125,
0.00789642333984375,
0.01015472412109375,
0.01239776611328125,
0.0079498291015625,
0.0021381378173828125,
-0.005504608154296875,
0.00860595703125,
-0.00431060791015625,
-0.020538330078125,
0.0092620849609375,
-0.0248870849609375,
-0.007152557373046875,
0.016754150390625,
-0.01120758056640625,
-0.0211639404296875,
-0.01385498046875,
-0.00894927978515625,
-0.004825592041015625,
-0.0231475830078125,
0.016845703125,
0.00904083251953125,
0.0005617141723632812,
-0.00014340877532958984,
0.0006923675537109375,
0.01203155517578125,
-0.004634857177734375,
0.0049591064453125,
-0.01416778564453125,
0.0106201171875,
-0.0229644775390625,
-0.006893157958984375,
0.005489349365234375,
-0.01654052734375,
0.00588226318359375,
0.01250457763671875,
-0.035369873046875,
-0.012237548828125,
-0.00799560546875,
-0.001262664794921875,
0.01898193359375,
0.034942626953125,
0.0006260871887207031,
-0.0304412841796875,
-0.03985595703125,
-0.03546142578125,
0.00897979736328125,
0.00698089599609375,
-0.0107269287109375,
-0.0036907196044921875,
0.0110931396484375,
-0.00047707557678222656,
-0.01102447509765625,
0.00965118408203125,
-0.0260009765625,
0.0038852691650390625,
-0.044921875,
0.006195068359375,
-0.0175323486328125,
-0.0017766952514648438,
-0.00286865234375,
0.004688262939453125,
-0.0235748291015625,
0.0154266357421875,
0.00472259521484375,
-0.01248931884765625,
-0.01171112060546875,
0.0035247802734375,
0.0181732177734375,
0.0207061767578125,
0.026336669921875,
-0.0025920867919921875,
-0.004085540771484375,
0.02001953125,
0.0009794235229492188,
0.0025768280029296875,
0.0118255615234375,
-0.01116943359375,
0.0069122314453125,
-0.0207977294921875,
0.00577545166015625,
-0.0115203857421875,
-0.0078887939453125,
0.01517486572265625,
-0.001201629638671875,
0.001842498779296875,
-0.007488250732421875,
-0.01541900634765625,
0.012481689453125,
-0.0248565673828125,
0.0017910003662109375,
0.0059661865234375,
-0.0183868408203125,
0.0286407470703125,
0.019744873046875,
0.0002161264419555664,
0.0096435546875,
0.0004661083221435547,
0.018524169921875,
0.005764007568359375,
0.004779815673828125,
-0.039215087890625,
-0.0077972412109375,
-0.00815582275390625,
0.0193634033203125,
0.016448974609375,
-0.0007014274597167969,
-0.048004150390625,
0.016387939453125,
-0.01259613037109375,
0.0181884765625,
0.004444122314453125,
-0.010894775390625,
-0.00982666015625,
-0.0024566650390625,
0.0010318756103515625,
-0.002307891845703125,
0.0173797607421875,
-0.0171966552734375,
0.00021946430206298828,
-0.0014743804931640625,
0.0107574462890625,
0.01495361328125,
-0.0030307769775390625,
-0.0009131431579589844,
-0.00461578369140625,
-0.01910400390625,
-0.023101806640625,
-0.0006914138793945312,
0.0009474754333496094,
-0.038299560546875,
0.00867462158203125,
-0.0035800933837890625,
-0.0125732421875,
-0.00785064697265625,
-0.00603485107421875,
0.016510009765625,
-0.01187896728515625,
-0.0072174072265625,
0.016387939453125,
0.00972747802734375,
0.0019550323486328125,
-0.0037403106689453125,
0.0011444091796875,
-0.00421142578125,
-0.0178680419921875,
-0.01451873779296875,
-0.012847900390625,
0.0030422210693359375,
0.00794219970703125,
0.0015134811401367188,
0.05792236328125,
-0.0182952880859375,
0.0058441162109375,
0.0055999755859375,
-0.006671905517578125,
0.00511932373046875,
0.004848480224609375,
-0.0014820098876953125,
0.0017566680908203125,
-0.009368896484375,
-0.048797607421875,
0.0226898193359375,
-0.004505157470703125,
-0.01404571533203125,
-0.00467681884765625,
0.01148223876953125,
-0.0038433074951171875,
-0.0207366943359375,
-0.0173187255859375,
0.0018262863159179688,
0.0020160675048828125,
-0.0032291412353515625,
-0.0009474754333496094,
-0.0110626220703125,
0.00003504753112792969,
0.036285400390625,
-0.00609588623046875,
-0.0129547119140625,
0.03173828125,
0.0048980712890625,
0.025634765625,
-0.0254364013671875,
-0.0249481201171875,
-0.0018987655639648438,
0.032135009765625,
-0.0023365020751953125,
-0.004589080810546875,
0.0096435546875,
0.01461029052734375,
0.0132293701171875,
0.0206451416015625,
-0.00505828857421875,
0.0173797607421875,
-0.0010805130004882812,
0.0126495361328125,
-0.01187896728515625,
-0.0158538818359375,
-0.027435302734375,
-0.0188751220703125,
0.01113128662109375,
0.0145263671875,
-0.01873779296875,
-0.01007080078125,
-0.0030956268310546875,
0.0438232421875,
-0.0292205810546875,
-0.0212554931640625,
0.01537322998046875,
0.0011625289916992188,
0.0080718994140625,
0.0228729248046875,
-0.0230865478515625,
0.004791259765625,
0.043670654296875,
-0.0198516845703125,
0.01788330078125,
0.00846099853515625,
-0.0018148422241210938,
-0.02001953125,
-0.0157470703125,
0.004901885986328125,
0.0057220458984375,
-0.00962066650390625,
0.0115509033203125,
0.0014400482177734375,
-0.037200927734375,
0.0085296630859375,
0.0229034423828125,
0.00826263427734375,
0.006221771240234375,
0.01067352294921875,
0.0078277587890625,
-0.01287841796875,
-0.0126800537109375,
0.05267333984375,
-0.01215362548828125,
0.006805419921875,
0.045989990234375,
-0.03070068359375,
-0.01259613037109375,
-0.011627197265625,
0.004913330078125,
-0.0208740234375,
-0.00414276123046875,
-0.03204345703125,
0.01512908935546875,
-0.01039886474609375,
0.01099395751953125,
0.010101318359375,
0.002197265625,
0.0112457275390625,
0.003757476806640625,
0.017181396484375,
-0.0251617431640625,
0.0030689239501953125,
0.031768798828125,
-0.035797119140625,
-0.008392333984375,
-0.0477294921875,
-0.032867431640625,
0.00884246826171875,
0.0216522216796875,
0.0323486328125,
0.0174102783203125,
-0.030609130859375,
0.00231170654296875,
0.00022649765014648438,
-0.009246826171875,
-0.0018358230590820312,
0.03594970703125,
0.00853729248046875,
-0.0010576248168945312,
-0.01230621337890625,
-0.0106048583984375,
0.0104217529296875,
-0.03216552734375,
0.0034847259521484375,
0.02081298828125,
-0.042633056640625,
-0.0082244873046875,
0.006816864013671875,
-0.004146575927734375,
0.01308441162109375,
-0.0007915496826171875,
-0.009552001953125,
0.012664794921875,
0.01312255859375,
0.0223388671875,
-0.023834228515625,
-0.0125579833984375,
-0.0117340087890625,
0.0160064697265625,
0.0020618438720703125,
0.029022216796875,
-0.033447265625,
0.0066680908203125,
0.00791168212890625,
-0.035919189453125,
-0.0179443359375,
0.01708984375,
-0.0240936279296875,
0.0160980224609375,
-0.01277923583984375,
-0.02923583984375,
0.0127105712890625,
-0.01959228515625,
-0.0030117034912109375,
0.0009832382202148438,
-0.0018367767333984375,
-0.03253173828125,
-0.0078887939453125,
-0.00885772705078125,
-0.00852203369140625,
0.0220794677734375,
-0.0020580291748046875,
0.00128936767578125,
0.0147857666015625,
0.0179443359375,
-0.0022716522216796875,
0.022613525390625,
0.0117340087890625,
0.0026798248291015625,
0.0074920654296875,
-0.006351470947265625,
-0.0267791748046875,
0.009552001953125,
0.019866943359375,
0.0242919921875,
-0.024383544921875,
0.004245758056640625,
0.009063720703125,
-0.021209716796875,
0.022308349609375,
-0.012115478515625,
0.007335662841796875,
0.00662994384765625,
0.002105712890625,
0.036224365234375,
-0.00516510009765625,
0.0022678375244140625,
-0.0019989013671875,
0.0130767822265625,
-0.00748443603515625,
0.0276947021484375,
0.0238800048828125,
-0.0177154541015625,
0.05267333984375,
-0.007617950439453125,
-0.015655517578125,
0.00551605224609375,
0.0011510848999023438,
-0.037506103515625,
0.0135498046875,
0.0089111328125,
0.00594329833984375,
0.0008540153503417969,
0.0232696533203125,
0.02923583984375,
-0.01617431640625,
0.01049041748046875,
-0.01934814453125,
-0.0411376953125,
0.0008816719055175781,
-0.011505126953125,
0.0295562744140625,
0.0184173583984375,
0.003627777099609375,
-0.059661865234375,
-0.0242462158203125,
-0.013397216796875,
0.018951416015625,
0.0220947265625,
-0.0287628173828125,
-0.0140533447265625,
-0.0198974609375,
0.0189666748046875,
-0.0295562744140625,
0.0180511474609375,
0.027191162109375,
-0.01290130615234375,
-0.03912353515625,
-0.04534912109375,
-0.0232696533203125,
0.004848480224609375,
-0.046051025390625,
0.028350830078125,
0.04058837890625,
0.03375244140625,
-0.033203125,
0.01264190673828125,
-0.0115814208984375,
0.002490997314453125,
-0.0026836395263671875,
0.005645751953125,
0.0017414093017578125,
0.0182952880859375,
0.01345062255859375,
0.00415802001953125,
0.01371002197265625,
-0.037689208984375,
0.02276611328125,
0.00899505615234375,
-0.03277587890625,
-0.0013303756713867188,
-0.033599853515625,
-0.025909423828125,
0.00910186767578125,
0.0091552734375,
0.0290374755859375,
0.01497650146484375,
0.00746917724609375,
-0.001953125,
0.03253173828125,
0.00415802001953125,
-0.0283203125,
-0.01326751708984375,
0.0122222900390625,
0.0020694732666015625,
-0.00445556640625,
0.0005245208740234375,
-0.0025997161865234375,
-0.00902557373046875,
-0.029693603515625,
-0.01473236083984375,
0.0118408203125,
0.00521087646484375,
0.00487518310546875,
0.0005841255187988281,
0.0149688720703125,
0.01971435546875,
-0.01515960693359375,
0.03179931640625,
0.007717132568359375,
0.0140838623046875,
-0.0062255859375,
0.041839599609375,
0.00042700767517089844,
-0.005641937255859375,
-0.0023059844970703125,
0.0068206787109375,
0.01148223876953125,
0.00565338134765625,
-0.00611114501953125,
0.0015716552734375,
-0.01812744140625,
0.030181884765625,
0.00823974609375,
-0.0015211105346679688,
0.0255889892578125,
-0.00995635986328125,
-0.0154571533203125,
-0.0233917236328125,
-0.0196990966796875,
-0.03729248046875,
-0.025482177734375,
-0.0037174224853515625,
-0.0239105224609375,
0.0005483627319335938,
-0.0235748291015625,
0.020050048828125,
0.01519012451171875,
0.00344085693359375,
-0.00439453125,
0.013641357421875,
-0.0035953521728515625,
0.03662109375,
-0.006092071533203125,
0.0313720703125,
-0.01154327392578125,
0.005260467529296875,
0.032989501953125,
0.002094268798828125,
0.02325439453125,
-0.0005335807800292969,
0.00389862060546875,
-0.007965087890625,
0.021881103515625,
-0.017852783203125,
-0.0198974609375,
-0.04132080078125,
0.0153045654296875,
0.005619049072265625,
-0.004558563232421875,
-0.00449371337890625,
0.0142822265625,
-0.0006117820739746094,
-0.0174713134765625,
0.018829345703125,
0.0265655517578125,
-0.012969970703125,
0.0232086181640625,
0.019561767578125,
0.016082763671875,
-0.0189666748046875,
0.031494140625,
0.018035888671875,
0.0082244873046875,
0.01105499267578125,
0.008209228515625,
-0.01009368896484375,
-0.008575439453125,
0.0142059326171875,
-0.00681304931640625,
0.01453399658203125,
-0.01953125,
-0.0247955322265625,
0.024383544921875,
-0.01349639892578125,
-0.0121002197265625,
0.00827789306640625,
-0.0170135498046875,
-0.0255889892578125,
-0.008026123046875,
0.0213623046875,
-0.016845703125,
-0.017669677734375,
-0.007190704345703125,
0.019622802734375,
0.0055389404296875,
0.012908935546875,
-0.01284027099609375,
-0.01202392578125,
0.0216522216796875,
-0.01352691650390625,
0.01142120361328125,
-0.042633056640625,
0.01177978515625,
0.0230865478515625,
-0.0247650146484375,
-0.0006375312805175781,
-0.0220184326171875,
0.04327392578125,
0.001117706298828125,
0.027313232421875,
-0.00913238525390625,
0.0158538818359375,
-0.0024471282958984375,
-0.0447998046875,
0.007293701171875,
-0.020233154296875,
0.007137298583984375,
-0.047637939453125,
-0.006366729736328125,
0.0020885467529296875,
0.008575439453125,
-0.051971435546875,
-0.0170440673828125,
0.01303863525390625,
0.006134033203125,
-0.0040283203125,
0.01910400390625,
0.033538818359375,
0.007289886474609375,
-0.035430908203125,
-0.00026869773864746094,
0.036407470703125,
-0.00804901123046875,
0.034881591796875,
0.0092620849609375,
0.022674560546875,
-0.025146484375,
-0.001392364501953125,
-0.0010089874267578125,
0.01097869873046875,
0.0300140380859375,
-0.0218505859375,
-0.036895751953125,
-0.0095367431640625,
0.040252685546875,
-0.035614013671875,
0.016143798828125,
-0.032806396484375,
0.0048065185546875,
-0.0027618408203125,
-0.0084991455078125,
-0.024444580078125,
0.002170562744140625,
0.0084228515625,
-0.0108489990234375,
0.006114959716796875,
0.008209228515625,
-0.01284027099609375,
-0.0123443603515625,
-0.0007939338684082031,
0.0029468536376953125,
-0.024200439453125,
-0.015838623046875,
0.0174713134765625,
0.0224609375,
0.0104522705078125,
0.01282501220703125,
-0.0002677440643310547,
0.0160675048828125,
-0.01904296875,
-0.0009636878967285156,
0.03680419921875,
0.03253173828125,
0.01068115234375,
0.0215911865234375,
0.006771087646484375,
0.01154327392578125,
-0.005176544189453125,
-0.045745849609375,
-0.026336669921875,
-0.0009379386901855469,
0.004291534423828125,
0.00603485107421875,
-0.0233306884765625,
-0.0478515625,
-0.0005412101745605469,
0.02838134765625,
0.0022735595703125,
0.00439453125,
-0.00428009033203125,
-0.0079803466796875,
-0.04425048828125,
0.0000024437904357910156,
0.0209808349609375,
-0.032745361328125,
-0.025970458984375,
-0.03240966796875,
-0.039459228515625,
-0.01372528076171875,
0.005657196044921875,
-0.01477813720703125,
-0.04595947265625,
0.002162933349609375,
0.0059967041015625,
-0.00922393798828125,
0.01334381103515625,
-0.04266357421875,
0.029296875,
-0.00969696044921875,
-0.021881103515625,
0.01111602783203125,
0.0096435546875,
-0.00485992431640625,
-0.030120849609375,
-0.042633056640625,
-0.021942138671875,
-0.0057830810546875,
-0.023590087890625,
-0.00023555755615234375,
0.020843505859375,
-0.0089874267578125,
-0.0289764404296875,
0.004116058349609375,
-0.0300445556640625,
0.00763702392578125,
-0.0034999847412109375,
0.06036376953125,
-0.0194244384765625,
0.0026607513427734375,
-0.03143310546875,
0.01045989990234375,
-0.0014705657958984375,
0.00988006591796875,
-0.042388916015625,
0.004238128662109375,
0.034942626953125,
0.035980224609375,
-0.00891876220703125,
0.00884246826171875,
-0.0110321044921875,
-0.039154052734375,
0.002155303955078125,
0.01274871826171875,
-0.00919342041015625,
-0.018585205078125,
0.02984619140625,
-0.0030345916748046875,
0.0004425048828125,
0.027923583984375,
-0.002227783203125,
0.01233673095703125,
-0.0060882568359375,
-0.00799560546875,
0.0037517547607421875,
-0.02850341796875,
0.016082763671875,
-0.004840850830078125,
-0.0019931793212890625,
-0.00939178466796875,
0.0010881423950195312,
0.025543212890625,
-0.00589752197265625,
-0.053466796875,
-0.002460479736328125,
0.0245513916015625,
-0.01032257080078125,
-0.0085601806640625,
-0.023681640625,
-0.0037689208984375,
0.03594970703125,
-0.007785797119140625,
0.0045623779296875,
0.0026702880859375,
-0.001537322998046875,
0.0013179779052734375,
-0.0044097900390625,
-0.00946807861328125,
0.039215087890625,
0.005115509033203125,
0.006351470947265625,
0.016876220703125,
-0.03839111328125,
-0.0219879150390625,
-0.0044403076171875,
-0.0028591156005859375,
-0.041046142578125,
0.0022754669189453125,
-0.033294677734375,
-0.0054168701171875,
0.0180816650390625,
0.040252685546875,
0.0272979736328125,
0.002964019775390625,
0.0022754669189453125,
-0.032958984375,
0.046905517578125,
0.00428009033203125,
0.0126800537109375,
0.01873779296875,
-0.00244140625,
0.0106964111328125,
-0.003223419189453125,
0.0169677734375,
0.005977630615234375,
-0.005039215087890625,
0.01384735107421875,
-0.023406982421875,
0.033966064453125,
-0.0232086181640625,
-0.0035247802734375,
-0.026519775390625,
0.01081085205078125,
0.03936767578125,
-0.00981903076171875,
0.01557159423828125,
0.00417327880859375,
0.006206512451171875,
-0.0323486328125,
-0.053985595703125,
-0.0124969482421875,
-0.0023021697998046875,
0.0173797607421875,
0.014495849609375,
0.0197906494140625,
-0.031463623046875,
-0.06219482421875,
-0.01007843017578125,
0.0013875961303710938,
0.01265716552734375,
0.018798828125,
0.03570556640625,
-0.0246124267578125,
-0.00804901123046875,
0.0175628662109375,
0.0266876220703125,
0.00457763671875,
0.0501708984375,
0.0330810546875,
0.0015230178833007812,
0.01320648193359375,
0.017547607421875,
0.001377105712890625,
-0.00234222412109375,
0.006267547607421875,
-0.0240936279296875,
-0.0189666748046875,
0.01201629638671875,
-0.038604736328125,
0.0294036865234375,
-0.0085601806640625,
0.0230560302734375,
-0.037384033203125,
-0.018890380859375,
-0.0298919677734375,
0.0191650390625,
-0.019500732421875,
0.005153656005859375,
-0.0036163330078125,
-0.005138397216796875,
0.027130126953125,
0.02435302734375,
0.059051513671875,
-0.005035400390625,
0.00783538818359375,
0.020355224609375,
0.006885528564453125,
0.0229949951171875,
-0.030059814453125,
-0.015869140625,
0.01032257080078125,
0.00949859619140625,
-0.0178985595703125,
0.0061492919921875,
0.03125,
-0.02130126953125,
-0.01454925537109375,
-0.00867462158203125,
-0.00829315185546875,
-0.0209808349609375,
-0.015869140625,
0.037567138671875,
0.003757476806640625,
-0.0089111328125,
0.00864410400390625,
0.003978729248046875,
-0.0205841064453125,
0.0343017578125,
-0.003360748291015625,
-0.00909423828125,
0.007701873779296875,
0.00506591796875,
-0.0372314453125,
-0.035186767578125,
-0.020294189453125,
0.0010166168212890625,
0.034454345703125,
-0.007476806640625,
0.01241302490234375,
-0.004581451416015625,
0.031951904296875,
-0.02593994140625,
0.0225372314453125,
0.005939483642578125,
0.00936126708984375,
0.0244598388671875,
0.007503509521484375,
0.01080322265625,
0.021453857421875,
0.004852294921875,
-0.0209503173828125,
-0.01251220703125,
0.0026721954345703125,
0.008819580078125,
0.01206207275390625,
-0.01497650146484375,
0.033111572265625,
-0.01055145263671875,
0.025482177734375,
-0.0169525146484375,
-0.0025157928466796875,
-0.04998779296875,
-0.015777587890625,
-0.03533935546875,
-0.01641845703125,
0.0153656005859375,
-0.00621795654296875,
-0.040313720703125,
0.00417327880859375,
-0.0113525390625,
0.0289459228515625,
0.00968170166015625,
-0.01015472412109375,
0.02001953125,
0.01318359375,
0.0125274658203125,
-0.0175018310546875,
-0.0445556640625,
0.0027065277099609375,
-0.021575927734375,
0.00185394287109375,
0.006855010986328125,
-0.0027790069580078125,
-0.0234375,
-0.01276397705078125,
-0.03521728515625,
-0.00543975830078125,
0.006916046142578125,
0.00482177734375,
-0.0250244140625,
0.0030765533447265625,
0.00836944580078125,
0.00640869140625,
-0.0013208389282226562,
0.0014085769653320312,
0.02978515625,
-0.01209259033203125,
-0.0113677978515625,
-0.050323486328125,
0.00858306884765625,
-0.013427734375,
-0.0137176513671875,
-0.0009455680847167969,
0.0170135498046875,
-0.0024738311767578125,
0.03936767578125,
0.0106658935546875,
-0.0560302734375,
-0.00433349609375,
0.0034313201904296875,
-0.0077667236328125,
-0.0180206298828125,
-0.0013933181762695312,
0.0201416015625,
-0.0296783447265625,
0.02301025390625,
-0.0250091552734375,
-0.004245758056640625,
0.01102447509765625,
0.0126953125,
0.021514892578125,
-0.006008148193359375,
-0.01178741455078125,
0.00632476806640625,
-0.00630950927734375,
0.0101470947265625,
-0.026031494140625,
-0.0292816162109375,
0.018646240234375,
-0.011199951171875,
0.01403045654296875,
-0.010955810546875,
0.00611114501953125,
0.0166168212890625,
-0.01119232177734375,
0.0023555755615234375,
-0.00103759765625,
-0.051544189453125,
0.01477813720703125,
-0.0029315948486328125,
0.01340484619140625,
-0.00006902217864990234,
0.0027980804443359375,
-0.0078125,
0.037933349609375,
-0.042938232421875,
0.002460479736328125,
0.011871337890625,
-0.005886077880859375,
-0.0008373260498046875,
-0.052886962890625,
0.01084136962890625,
-0.018402099609375,
-0.0280303955078125,
-0.025604248046875,
0.013580322265625,
0.022674560546875,
-0.023468017578125,
-0.028472900390625,
0.00022077560424804688,
0.01177978515625,
0.0013761520385742188,
-0.0084686279296875,
-0.006023406982421875,
0.0023822784423828125,
0.0012073516845703125,
-0.0133514404296875,
0.0025157928466796875,
-0.0119476318359375,
0.016632080078125,
-0.01035308837890625,
-0.022979736328125,
0.0148162841796875,
0.01497650146484375,
0.0033416748046875,
-0.0301361083984375,
-0.0132598876953125,
0.0110321044921875,
0.029266357421875,
-0.032470703125,
-0.0033626556396484375,
0.0032711029052734375,
0.0176239013671875,
-0.0196990966796875,
-0.014617919921875,
-0.000843048095703125,
0.007843017578125,
0.007354736328125,
-0.044830322265625,
0.0009732246398925781,
-0.0105438232421875,
0.0134124755859375,
-0.0285491943359375,
-0.01806640625,
-0.009368896484375,
0.0162200927734375,
0.026885986328125,
-0.050201416015625,
-0.0012254714965820312,
-0.004573822021484375,
-0.014801025390625,
0.01727294921875,
-0.016998291015625,
-0.0245819091796875,
-0.00408935546875,
0.0026035308837890625,
0.011322021484375,
-0.0010709762573242188,
-0.00643157958984375,
-0.04119873046875,
-0.0214080810546875,
0.0299835205078125,
0.0086517333984375,
-0.00803375244140625,
-0.030120849609375,
0.023712158203125,
0.01055145263671875,
0.0182037353515625,
0.012542724609375,
-0.0037250518798828125,
-0.0302734375,
0.0191192626953125,
0.0131683349609375,
0.0032405853271484375,
-0.01548004150390625,
0.03826904296875,
-0.012237548828125,
0.00968170166015625,
-0.003040313720703125,
0.01110076904296875,
0.0181121826171875,
-0.0002340078353881836,
-0.03717041015625,
-0.021240234375,
0.04833984375,
0.00316619873046875,
0.02020263671875,
-0.0278778076171875,
0.033782958984375,
0.01561737060546875,
0.00731658935546875,
-0.006633758544921875,
-0.030120849609375,
-0.0175628662109375,
-0.004291534423828125,
0.002044677734375,
-0.009490966796875,
-0.01093292236328125,
0.0167694091796875,
-0.0015325546264648438,
0.0225677490234375,
0.004726409912109375,
-0.01263427734375,
-0.00005179643630981445,
0.020660400390625,
-0.0164642333984375,
0.01465606689453125,
-0.0169677734375,
0.01042938232421875,
-0.022918701171875,
-0.01434326171875,
0.0130157470703125,
0.0290069580078125,
-0.0142669677734375,
0.0301361083984375,
0.03375244140625,
-0.021697998046875,
-0.01207733154296875,
-0.02166748046875,
0.010955810546875,
-0.01465606689453125,
-0.01432037353515625,
-0.01332855224609375,
-0.030242919921875,
-0.010406494140625,
0.0185546875,
0.00574493408203125,
-0.0069580078125,
0.005382537841796875,
0.01468658447265625,
0.0390625,
-0.0165252685546875,
-0.0175933837890625,
-0.01488494873046875,
-0.02459716796875,
0.00980377197265625,
-0.01392364501953125,
-0.00943756103515625,
-0.00481414794921875,
0.0350341796875,
0.01561737060546875,
-0.01029205322265625,
0.0110931396484375,
0.0038661956787109375,
0.004669189453125,
-0.0063018798828125,
0.049774169921875,
0.0035762786865234375,
-0.021453857421875,
0.004268646240234375,
0.03289794921875,
0.00786590576171875,
0.00841522216796875,
-0.0010175704956054688,
0.00492095947265625,
-0.006786346435546875,
0.0193634033203125,
-0.0219268798828125,
0.028289794921875,
0.01898193359375,
0.00980377197265625,
-0.0019254684448242188,
0.0169525146484375,
0.005283355712890625,
0.047943115234375,
-0.050140380859375,
-0.03179931640625,
0.01192474365234375,
0.01605224609375,
0.00905609130859375,
-0.00644683837890625,
-0.00447845458984375,
0.020660400390625,
-0.056976318359375,
0.01436614990234375,
-0.01232147216796875,
0.00469207763671875,
-0.0012044906616210938,
0.0167999267578125,
-0.02899169921875,
0.0214385986328125,
-0.00475311279296875,
0.012176513671875,
-0.0013761520385742188,
0.042633056640625,
-0.01149749755859375,
0.005046844482421875,
0.0012464523315429688,
-0.001377105712890625,
0.0014028549194335938,
-0.0006270408630371094,
0.01027679443359375,
0.0291595458984375,
0.0023670196533203125,
-0.042388916015625,
-0.0139923095703125,
-0.01078033447265625,
0.001117706298828125,
-0.0002880096435546875,
-0.0201568603515625,
0.0048370361328125,
-0.0275115966796875,
-0.0185089111328125,
-0.01096343994140625,
0.0301513671875,
0.03533935546875,
0.01308441162109375,
0.052001953125,
0.0187530517578125,
-0.0037593841552734375,
0.00806427001953125,
-0.0183563232421875,
-0.00844573974609375,
0.003086090087890625,
0.0218658447265625,
0.0180511474609375,
-0.005718231201171875,
-0.008087158203125,
0.00852203369140625,
-0.0074462890625,
0.01078033447265625,
0.041015625,
-0.0121612548828125,
-0.036376953125,
-0.01152801513671875,
-0.0117950439453125,
0.05224609375,
0.01776123046875,
0.0238189697265625,
0.0014181137084960938,
-0.0135498046875,
-0.00873565673828125,
-0.0054168701171875,
0.0171356201171875,
-0.01666259765625,
0.0091094970703125,
0.007007598876953125,
-0.0101776123046875,
-0.003101348876953125,
-0.0236053466796875,
0.0012607574462890625,
-0.0171661376953125,
-0.012542724609375,
-0.01555633544921875,
0.03253173828125,
0.01045989990234375,
0.0096435546875,
0.01239013671875,
0.0172119140625,
-0.008544921875,
-0.01461029052734375,
0.035369873046875,
-0.0023784637451171875,
-0.0088958740234375,
0.007686614990234375,
-0.007419586181640625,
-0.0102386474609375,
-0.006473541259765625,
0.0098419189453125,
0.0227813720703125,
0.00299072265625,
-0.043304443359375,
-0.02569580078125,
-0.01910400390625,
0.0073089599609375,
0.0103607177734375,
0.0214385986328125,
-0.01380157470703125,
0.0092315673828125,
-0.00617218017578125,
0.03265380859375,
-0.006877899169921875,
-0.0169219970703125,
-0.013214111328125,
0.018310546875,
0.0307464599609375,
-0.0025634765625,
-0.03350830078125,
-0.01134490966796875,
0.0236358642578125,
-0.007488250732421875,
0.015899658203125,
-0.03155517578125,
-0.02471923828125,
0.03167724609375,
-0.00691986083984375,
0.0006275177001953125,
0.01192474365234375,
-0.01457977294921875,
0.007366180419921875,
0.01197052001953125,
0.03472900390625,
-0.01442718505859375,
0.019561767578125,
-0.0172882080078125,
-0.0416259765625,
-0.005584716796875,
-0.004398345947265625,
0.0007047653198242188,
-0.003963470458984375,
0.017913818359375,
-0.02850341796875,
-0.002429962158203125,
0.0102386474609375,
-0.0133514404296875,
-0.01113128662109375,
-0.0191802978515625,
-0.00005310773849487305,
-0.00879669189453125,
-0.01126861572265625,
-0.01232147216796875,
-0.0006799697875976562,
0.0173187255859375,
0.0166473388671875,
0.0216522216796875,
0.0210418701171875,
-0.0174102783203125,
-0.003688812255859375,
0.01337432861328125,
-0.0279388427734375,
-0.005550384521484375,
-0.01168060302734375,
-0.00853729248046875,
-0.0657958984375,
0.03326416015625,
-0.004459381103515625,
-0.0338134765625,
0.0311431884765625,
0.01155853271484375,
-0.0120391845703125,
0.043426513671875,
-0.0274810791015625,
0.00901031494140625,
0.010467529296875,
0.023773193359375,
0.0044403076171875,
-0.0024585723876953125,
-0.0034084320068359375,
-0.0281829833984375,
-0.00281524658203125,
-0.034637451171875,
0.04754638671875,
-0.01947021484375,
-0.003795623779296875,
0.0022125244140625,
0.0200958251953125,
-0.039154052734375,
-0.0212554931640625,
-0.00010973215103149414,
-0.000007987022399902344,
0.0287628173828125,
0.015594482421875,
0.00910186767578125,
-0.01409912109375,
-0.0260467529296875,
-0.0010433197021484375,
0.015716552734375,
-0.0165557861328125,
0.01029205322265625,
-0.0213165283203125,
-0.01800537109375,
0.018524169921875,
0.01885986328125,
0.0011844635009765625,
0.029022216796875,
0.00750732421875,
0.0013380050659179688,
0.012420654296875,
0.0018720626831054688,
-0.0035495758056640625,
0.01323699951171875,
-0.00859832763671875,
-0.006862640380859375,
0.0002295970916748047,
0.0042266845703125,
-0.0076751708984375,
-0.007476806640625,
0.01258087158203125,
-0.0164337158203125,
0.00041604042053222656,
0.00762939453125,
0.033294677734375,
-0.007442474365234375,
0.0157928466796875,
-0.0114898681640625,
0.003139495849609375,
0.0007429122924804688,
-0.0198211669921875,
0.036773681640625,
-0.0021038055419921875,
-0.03564453125,
-0.0015802383422851562,
-0.029998779296875,
0.0172271728515625,
-0.01236724853515625,
-0.019378662109375,
0.0005154609680175781,
0.0212554931640625,
0.01227569580078125,
-0.00984954833984375,
0.01441192626953125,
0.005908966064453125,
-0.0229339599609375,
0.0236663818359375,
0.0211944580078125,
-0.017608642578125,
0.0188140869140625,
-0.031707763671875,
-0.025360107421875,
-0.0172271728515625,
0.0016813278198242188,
0.03924560546875,
0.00386810302734375,
0.0192108154296875,
0.0059814453125,
0.027618408203125,
0.0191497802734375,
-0.02386474609375,
0.018341064453125,
0.040679931640625,
0.01395416259765625,
-0.0027179718017578125,
-0.0170135498046875,
0.03619384765625,
-0.0067138671875,
-0.01165008544921875,
0.0013303756713867188,
-0.0057220458984375,
-0.0203399658203125,
-0.024505615234375,
-0.019775390625,
0.0389404296875,
0.0025081634521484375,
-0.0091400146484375,
-0.0040740966796875,
0.0212860107421875,
-0.04150390625,
-0.0023365020751953125,
0.0299835205078125,
0.0011606216430664062,
0.02056884765625,
0.01142120361328125,
0.0113525390625,
-0.01049041748046875,
0.04302978515625,
0.0224609375,
-0.044525146484375,
-0.0102081298828125,
0.01351165771484375,
-0.01904296875,
0.0153350830078125,
0.036285400390625,
-0.0125579833984375,
0.048309326171875,
-0.02691650390625,
0.00616455078125,
-0.0213165283203125,
-0.018829345703125,
0.00222015380859375,
0.01297760009765625,
0.00925445556640625,
-0.02825927734375,
-0.01605224609375,
0.012603759765625,
0.034912109375,
-0.0004248619079589844,
-0.00850677490234375,
-0.0093841552734375,
-0.0299224853515625,
0.0144805908203125,
0.00916290283203125,
0.040496826171875,
0.0226287841796875,
0.0045013427734375,
-0.0202789306640625,
-0.005130767822265625,
-0.0139312744140625,
0.0113372802734375,
0.00925445556640625,
0.0241546630859375,
0.02130126953125,
0.0111541748046875,
-0.031158447265625,
-0.0138702392578125,
0.0195770263671875,
-0.007160186767578125,
0.003513336181640625,
0.01094818115234375,
-0.01248931884765625,
0.024322509765625,
-0.0282745361328125,
-0.0347900390625,
0.0189056396484375,
-0.0123138427734375,
-0.0158538818359375,
-0.007080078125,
0.0283050537109375,
0.00893402099609375,
0.007007598876953125,
-0.0255889892578125,
0.028961181640625,
0.016693115234375,
-0.0193328857421875,
0.0167236328125,
-0.01389312744140625,
0.02435302734375,
0.011199951171875,
-0.00261688232421875,
-0.02508544921875,
0.041107177734375,
0.00698089599609375,
-0.0019893646240234375,
-0.002651214599609375,
-0.0027179718017578125,
0.0004527568817138672,
0.011566162109375,
-0.027801513671875,
0.005268096923828125,
-0.004467010498046875,
0.003047943115234375,
0.047515869140625,
-0.012298583984375,
-0.0259246826171875,
0.0271759033203125,
0.00539398193359375,
0.0186004638671875,
-0.00926971435546875,
0.0035915374755859375,
-0.0238494873046875,
-0.0213165283203125,
-0.0186614990234375,
0.01219940185546875,
-0.001094818115234375,
-0.00018489360809326172,
0.0253448486328125,
-0.00800323486328125,
-0.0228729248046875,
0.0014982223510742188,
-0.005893707275390625,
-0.0198974609375,
-0.00302886962890625,
0.0194549560546875,
-0.023101806640625,
0.002315521240234375,
0.00939178466796875,
0.00662994384765625,
-0.0032825469970703125,
0.0017747879028320312,
-0.00572967529296875,
-0.0092926025390625,
0.0012111663818359375,
0.00341033935546875,
0.0210723876953125,
-0.00559234619140625,
-0.0180816650390625,
0.01708984375,
0.00809478759765625,
-0.004802703857421875,
-0.0173797607421875,
0.00479888916015625,
0.0027408599853515625,
0.043121337890625,
-0.037017822265625,
-0.001453399658203125,
0.0195770263671875,
0.0010223388671875,
-0.0211029052734375,
0.00905609130859375,
0.01451873779296875,
0.0003159046173095703,
-0.015533447265625,
-0.002765655517578125,
-0.051177978515625,
0.010498046875,
0.00850677490234375,
0.026092529296875,
-0.0012912750244140625,
-0.00732421875,
0.0235137939453125,
0.02587890625,
-0.0029888153076171875,
0.0028362274169921875,
-0.0079193115234375,
-0.006473541259765625,
-0.01479339599609375,
-0.0248260498046875,
0.0137481689453125,
0.0284576416015625,
0.0160675048828125,
0.0225982666015625,
-0.001708984375,
0.011871337890625,
0.0048065185546875,
0.00754547119140625,
0.03875732421875,
-0.025115966796875,
-0.0235137939453125,
0.0045928955078125,
-0.0267181396484375,
0.0106048583984375,
-0.0032520294189453125,
0.00695037841796875,
-0.005870819091796875,
0.007671356201171875,
-0.0204925537109375,
-0.02313232421875,
-0.0263824462890625,
0.0006346702575683594,
0.00481414794921875,
-0.01441192626953125,
0.0225067138671875,
-0.0307159423828125,
-0.0106048583984375,
-0.00914764404296875,
-0.033447265625,
0.000003933906555175781,
0.0174407958984375,
-0.001468658447265625,
-0.01141357421875,
0.05047607421875,
-0.0211181640625,
-0.0185699462890625,
0.005283355712890625,
0.003948211669921875,
-0.0138092041015625,
-0.01995849609375,
-0.032562255859375,
-0.0058135986328125,
-0.01375579833984375,
-0.00318145751953125,
-0.0233917236328125,
0.003604888916015625,
0.0077972412109375,
-0.0177001953125,
0.015655517578125,
-0.001094818115234375,
-0.0076141357421875,
0.0027141571044921875,
0.01763916015625,
0.01113128662109375,
0.00446319580078125,
-0.001953125,
0.02069091796875,
0.0055084228515625,
-0.021728515625,
-0.0175628662109375,
-0.0186309814453125,
0.0034770965576171875,
0.01342010498046875,
0.0177459716796875,
0.01134490966796875,
-0.027008056640625,
-0.01282501220703125,
-0.0197906494140625,
-0.0240020751953125,
0.0272979736328125,
0.0166778564453125,
-0.0146942138671875,
-0.00426483154296875,
0.01580810546875,
0.005794525146484375,
-0.022491455078125,
-0.01169586181640625,
0.01068115234375,
0.007213592529296875,
-0.004077911376953125,
0.0254669189453125,
0.038116455078125,
0.0109405517578125,
-0.021087646484375,
0.0159912109375,
0.02056884765625,
0.0185089111328125,
0.01873779296875,
-0.01422882080078125,
0.0020999908447265625,
0.023651123046875,
-0.024993896484375,
0.017913818359375,
0.00643157958984375,
-0.0433349609375,
0.021728515625,
-0.00860595703125,
-0.01088714599609375,
-0.00799560546875,
-0.006649017333984375,
-0.04547119140625,
0.037750244140625,
-0.004787445068359375,
-0.016265869140625,
0.0260772705078125,
-0.0010671615600585938,
0.0018568038940429688,
0.0008053779602050781,
-0.00969696044921875,
-0.0016202926635742188,
-0.0208740234375,
-0.0023021697998046875,
-0.0224609375,
0.01416015625,
0.0152587890625,
0.025482177734375,
-0.0221405029296875,
0.0148773193359375,
-0.0235748291015625,
-0.011016845703125,
0.040008544921875,
-0.025177001953125,
0.0205841064453125,
0.003971099853515625,
-0.0002980232238769531,
-0.00818634033203125,
-0.0391845703125,
0.040252685546875,
-0.02972412109375,
-0.018341064453125,
0.01500701904296875,
-0.0035533905029296875,
-0.014007568359375,
-0.0199432373046875,
0.03179931640625,
0.018646240234375,
0.0015268325805664062,
0.0176544189453125,
0.040496826171875,
0.00962066650390625,
0.02838134765625,
-0.01378631591796875,
0.01448822021484375,
0.0200958251953125,
-0.0160675048828125,
-0.0179595947265625,
0.0192413330078125,
-0.012908935546875,
0.00018465518951416016,
-0.0235595703125,
-0.0026397705078125,
0.033111572265625,
-0.0289764404296875,
-0.00023758411407470703,
-0.00804901123046875,
-0.0207977294921875,
-0.01169586181640625,
-0.027679443359375,
-0.0055999755859375,
-0.031036376953125,
-0.0296478271484375,
0.01549530029296875,
0.033294677734375,
0.03656005859375,
0.0267181396484375,
0.01580810546875,
0.00807952880859375,
-0.0118560791015625,
0.015655517578125,
-0.0426025390625,
0.01230621337890625,
0.0184173583984375,
0.0241851806640625,
-0.0255279541015625,
-0.0094451904296875,
0.006683349609375,
-0.0186309814453125,
-0.01241302490234375,
0.01331329345703125,
0.006622314453125,
-0.013580322265625,
0.01197052001953125,
0.02691650390625,
0.007080078125,
-0.01039886474609375,
0.0157012939453125,
0.0189361572265625,
-0.0100860595703125,
-0.025390625,
0.01568603515625,
0.00017499923706054688,
-0.017425537109375,
0.01399993896484375,
-0.01528167724609375,
-0.0284881591796875,
0.0338134765625,
0.0037078857421875,
-0.034515380859375,
-0.00800323486328125,
0.006622314453125,
-0.0147552490234375,
0.0007634162902832031,
-0.00812530517578125,
0.031585693359375,
-0.00321197509765625,
-0.022491455078125,
-0.0117340087890625,
0.00270843505859375,
0.0098419189453125,
0.0036468505859375,
-0.009765625,
-0.010345458984375,
0.0177459716796875,
-0.0053253173828125,
-0.0232696533203125,
-0.004360198974609375,
-0.031524658203125,
0.0232391357421875,
-0.0142822265625,
-0.0110015869140625,
0.0291900634765625,
0.002506256103515625,
0.03094482421875,
-0.037078857421875,
-0.021240234375,
0.0237579345703125,
0.003170013427734375,
-0.0174407958984375,
-0.02166748046875,
0.0028057098388671875,
0.01386260986328125,
0.0009241104125976562,
0.0163116455078125,
-0.01910400390625,
0.032379150390625,
0.0230255126953125,
0.00809478759765625,
-0.01428985595703125,
0.006069183349609375,
0.01534271240234375,
0.01055908203125,
0.052276611328125,
-0.0204010009765625,
0.004486083984375,
0.02294921875,
-0.038818359375,
0.01442718505859375,
0.0219573974609375,
-0.031951904296875,
-0.02532958984375,
0.006816864013671875,
0.0158843994140625,
-0.042022705078125,
0.017730712890625,
0.022308349609375,
0.0007815361022949219,
-0.021514892578125,
-0.0372314453125,
-0.00910186767578125,
0.00841522216796875,
0.0035400390625,
0.00026726722717285156,
-0.029632568359375,
-0.011077880859375,
-0.026092529296875,
0.00846099853515625,
0.0196990966796875,
-0.01445770263671875,
0.0162811279296875,
0.04840087890625,
0.0255126953125,
0.0111083984375,
0.0257415771484375,
0.00431060791015625,
0.034332275390625,
-0.002223968505859375,
0.0032291412353515625,
0.017425537109375,
0.062225341796875,
0.002941131591796875,
-0.02276611328125,
-0.0309600830078125,
-0.003032684326171875,
-0.019317626953125,
0.0096588134765625,
0.00885772705078125,
-0.03546142578125,
-0.0118255615234375,
0.027008056640625,
0.0205078125,
0.01021575927734375,
-0.0225067138671875,
0.005504608154296875,
-0.0010976791381835938,
0.005367279052734375,
-0.0117950439453125,
-0.00435638427734375,
-0.038421630859375,
-0.007904052734375,
0.009429931640625,
-0.0157012939453125,
0.002666473388671875,
-0.0231170654296875,
-0.00757598876953125,
0.01418304443359375,
-0.023345947265625,
0.01120758056640625,
0.017242431640625,
0.060516357421875,
-0.025970458984375,
0.0081634521484375,
-0.028106689453125,
-0.0121002197265625,
0.01509857177734375,
-0.007312774658203125,
0.00499725341796875,
-0.01715087890625,
-0.0142822265625,
0.00045013427734375,
0.0074462890625,
-0.005474090576171875,
0.0197601318359375,
-0.020172119140625,
0.00835418701171875,
-0.03082275390625,
0.0054168701171875,
0.002727508544921875,
-0.0185394287109375,
-0.0033817291259765625,
0.01312255859375,
-0.0207977294921875,
0.01108551025390625,
0.030303955078125,
-0.01197052001953125,
-0.03277587890625,
0.0158233642578125,
-0.007335662841796875,
0.0036182403564453125,
-0.0032176971435546875,
-0.024810791015625,
-0.0220489501953125,
0.01446533203125,
-0.03704833984375,
-0.0101776123046875,
0.00032138824462890625,
-0.0069732666015625,
-0.00022804737091064453,
-0.007305145263671875,
-0.0196075439453125,
0.0181732177734375,
0.04986572265625,
0.01323699951171875,
-0.0080108642578125,
-0.03125,
-0.03887939453125,
-0.0269012451171875,
-0.0253448486328125,
0.005939483642578125,
-0.034912109375,
-0.01161956787109375,
-0.0037078857421875,
-0.01384735107421875,
-0.0265655517578125,
0.0174407958984375,
-0.00104522705078125,
0.023834228515625,
0.0087127685546875,
0.01329803466796875,
0.01071929931640625,
0.039398193359375,
-0.015411376953125,
0.01279449462890625,
-0.007610321044921875,
-0.0044708251953125,
-0.0012273788452148438,
0.017608642578125,
-0.020538330078125,
0.039031982421875,
-0.007099151611328125,
-0.0110015869140625,
0.00124359130859375,
0.0030117034912109375,
-0.034454345703125,
0.00196075439453125,
0.004550933837890625,
-0.0110015869140625,
0.003566741943359375,
0.0128936767578125,
0.012481689453125,
-0.0004725456237792969,
-0.003509521484375,
-0.005069732666015625,
-0.026763916015625,
0.035400390625,
0.02947998046875,
0.037841796875,
0.00824737548828125,
-0.039398193359375,
0.03076171875,
0.01904296875,
0.0024261474609375,
0.027069091796875,
-0.038330078125,
0.00839996337890625,
0.03607177734375,
0.01084136962890625,
0.0122833251953125,
0.00439453125,
-0.018310546875,
-0.0166168212890625,
0.012176513671875,
0.01190185546875,
-0.0001342296600341797,
-0.0187225341796875,
0.0037593841552734375,
-0.00012230873107910156,
0.0004360675811767578,
0.0027408599853515625,
0.0196533203125,
0.00014078617095947266,
-0.004962921142578125,
0.0271148681640625,
-0.0220184326171875,
0.022705078125,
0.0184326171875,
0.00988006591796875,
-0.00848388671875,
-0.004016876220703125,
0.0159759521484375,
-0.0086669921875,
0.0029144287109375,
0.0010423660278320312,
-0.0273895263671875,
-0.0004107952117919922,
0.037017822265625,
-0.02508544921875,
0.00803375244140625,
0.002071380615234375,
-0.006439208984375,
-0.0249481201171875,
0.005832672119140625,
0.0142669677734375,
0.04388427734375,
0.03192138671875,
-0.0172882080078125,
-0.01837158203125,
0.027374267578125,
0.00579071044921875,
-0.0017147064208984375,
-0.02862548828125,
0.0210723876953125,
-0.01186370849609375,
0.037750244140625,
-0.02459716796875,
-0.004726409912109375,
-0.004638671875,
0.026123046875,
-0.0082244873046875,
0.0016412734985351562,
0.00928497314453125,
-0.0235443115234375,
0.0210113525390625,
-0.027496337890625,
-0.0111236572265625,
0.00028824806213378906,
0.0007233619689941406,
-0.0303497314453125,
-0.005435943603515625,
0.035003662109375,
-0.0015745162963867188,
-0.0079345703125,
-0.0231781005859375,
0.01180267333984375,
0.02093505859375,
0.029266357421875,
0.0035419464111328125,
-0.0177764892578125,
0.01336669921875,
-0.007183074951171875,
0.0015316009521484375,
-0.037841796875,
-0.0210418701171875,
0.0208282470703125,
-0.021453857421875,
0.022430419921875,
0.01050567626953125,
-0.0240478515625,
-0.01551055908203125,
-0.003604888916015625,
0.0283203125,
-0.00014531612396240234,
-0.0037078857421875,
0.0124969482421875,
0.00601959228515625,
-0.0005488395690917969,
0.00820159912109375,
0.00689697265625,
-0.0283355712890625,
-0.033905029296875,
-0.00960540771484375,
-0.00438690185546875,
-0.0083160400390625,
-0.0212554931640625,
0.051422119140625,
-0.0171051025390625,
0.052734375,
0.0297698974609375,
0.0379638671875,
-0.013336181640625,
-0.007190704345703125,
0.0196533203125,
0.000415802001953125,
0.034454345703125,
-0.0042724609375,
-0.0303802490234375,
-0.021820068359375,
-0.0037059783935546875,
-0.000039577484130859375,
0.033050537109375,
-0.03076171875,
-0.0028705596923828125,
-0.0211944580078125,
0.0152130126953125,
-0.003131866455078125,
0.009613037109375,
-0.0104217529296875,
-0.01485443115234375,
-0.0051422119140625,
-0.0143585205078125,
-0.0165252685546875,
-0.00858306884765625,
-0.00885009765625,
0.0273895263671875,
0.01435089111328125,
0.0007081031799316406,
0.00891876220703125,
-0.009979248046875,
0.002452850341796875,
0.0180206298828125,
0.035400390625,
-0.01102447509765625,
0.00414276123046875,
-0.0026493072509765625,
-0.031494140625,
0.0014743804931640625,
0.03692626953125,
-0.0390625,
-0.015167236328125,
-0.0045013427734375,
-0.0118408203125,
-0.0023937225341796875,
0.037811279296875,
0.00791168212890625,
0.006023406982421875,
0.01045989990234375,
0.00324249267578125,
-0.026763916015625,
-0.040924072265625,
-0.0205230712890625,
0.00019252300262451172,
0.0181427001953125,
0.0029087066650390625,
-0.0159759521484375,
-0.0208587646484375,
-0.011566162109375,
-0.00720977783203125,
-0.01715087890625,
0.00939178466796875,
0.0178680419921875,
0.0064239501953125,
0.01084136962890625,
0.03265380859375,
0.007762908935546875,
-0.05194091796875,
0.032806396484375,
0.004367828369140625,
0.01273345947265625,
-0.0264129638671875,
0.027801513671875,
0.018035888671875,
0.00893402099609375,
0.0273590087890625,
0.00717926025390625,
0.03204345703125,
-0.0245361328125,
0.021697998046875,
0.0126495361328125,
0.016021728515625,
0.0095672607421875,
-0.005092620849609375,
-0.0044708251953125,
0.03857421875,
-0.005893707275390625,
-0.03131103515625,
0.01421356201171875,
-0.0035266876220703125,
-0.0232696533203125,
0.008697509765625,
-0.0213165283203125,
0.0019063949584960938,
-0.003597259521484375,
-0.0130462646484375,
0.0095062255859375,
-0.0361328125,
0.023040771484375,
-0.00955963134765625,
-0.02557373046875,
0.020172119140625,
0.00986480712890625,
0.020263671875,
0.0029239654541015625,
0.006053924560546875,
0.029052734375,
-0.0071563720703125,
-0.0026950836181640625,
-0.02008056640625,
-0.03424072265625,
-0.01947021484375,
-0.00699615478515625,
0.0162506103515625,
0.007740020751953125,
-0.0282440185546875,
-0.00644683837890625,
0.034423828125,
0.00009989738464355469,
-0.0133056640625,
0.033294677734375,
-0.01084136962890625,
0.0229339599609375,
-0.032440185546875,
0.028076171875,
0.002696990966796875,
-0.00568389892578125,
-0.0482177734375,
0.00112152099609375,
-0.003963470458984375,
-0.020782470703125,
0.0152740478515625,
0.016265869140625,
0.01032257080078125,
-0.0024700164794921875,
-0.0114288330078125,
-0.025146484375,
-0.0218963623046875,
0.008209228515625,
-0.0078277587890625,
0.01560211181640625,
-0.003208160400390625,
0.006191253662109375,
-0.0191497802734375,
0.005863189697265625,
0.0025234222412109375,
0.01436614990234375,
-0.0011968612670898438,
0.01561737060546875,
-0.02105712890625,
0.0237884521484375,
0.013458251953125,
-0.0185699462890625,
0.002391815185546875,
-0.021514892578125,
-0.0027027130126953125,
-0.00707244873046875,
-0.0005702972412109375,
-0.000431060791015625,
-0.0012073516845703125,
0.00412750244140625,
-0.0092315673828125,
0.0184326171875,
0.00897216796875,
0.00714874267578125,
-0.0019683837890625,
0.02142333984375,
-0.008026123046875,
-0.0203094482421875,
0.002613067626953125,
0.020050048828125,
-0.02520751953125,
0.0010347366333007812,
0.0044097900390625,
0.01308441162109375,
-0.005222320556640625,
0.00977325439453125,
0.0135345458984375,
0.00949859619140625,
-0.0112457275390625,
-0.004741668701171875,
0.010101318359375,
0.021820068359375,
0.002696990966796875,
0.013702392578125,
0.0183258056640625,
0.0203399658203125,
0.007808685302734375,
-0.02142333984375,
-0.00860595703125,
-0.01308441162109375,
-0.03424072265625,
-0.0250701904296875,
-0.011871337890625,
0.049468994140625,
-0.00506591796875,
-0.02496337890625,
0.021087646484375,
0.00934600830078125,
0.00588226318359375,
0.0001786947250366211,
-0.0006880760192871094,
0.0174407958984375,
0.0233612060546875,
-0.0223541259765625,
-0.0487060546875,
0.01556396484375,
0.0019588470458984375,
0.0036983489990234375,
0.00409698486328125,
0.0155792236328125,
-0.018768310546875,
-0.0164794921875,
0.040496826171875,
-0.03717041015625,
0.0201263427734375,
-0.047393798828125,
0.005046844482421875,
0.00632476806640625,
-0.01042938232421875,
0.01348114013671875,
0.00873565673828125,
0.01296234130859375,
0.002933502197265625,
0.0186920166015625,
-0.0350341796875,
-0.0035400390625,
0.0157012939453125,
0.00836181640625,
-0.016876220703125,
0.01386260986328125,
0.0289764404296875,
0.0021572113037109375,
-0.0038394927978515625,
-0.02972412109375,
0.01263427734375,
0.00603485107421875,
-0.029815673828125,
0.0271148681640625,
-0.0003113746643066406,
-0.027923583984375,
-0.00347137451171875,
0.00562286376953125,
0.025390625,
-0.003780364990234375,
-0.0372314453125,
0.00116729736328125,
0.005184173583984375,
-0.0024662017822265625,
-0.01294708251953125,
-0.01073455810546875,
0.033233642578125,
-0.002971649169921875,
0.01274871826171875,
0.04034423828125,
0.033660888671875,
-0.0146026611328125,
-0.0110931396484375,
0.0018463134765625,
0.0177459716796875,
0.01088714599609375,
0.04510498046875,
-0.00418853759765625,
0.01474761962890625,
0.01525115966796875,
0.033905029296875,
0.026214599609375,
-0.0085296630859375,
0.0161895751953125,
0.0123291015625,
0.02667236328125,
0.034637451171875,
-0.00568389892578125,
0.033416748046875,
0.0247802734375,
0.0105743408203125,
0.02801513671875,
-0.001895904541015625,
-0.00315093994140625,
-0.00824737548828125,
-0.01544952392578125,
-0.005802154541015625,
0.034210205078125,
-0.0321044921875,
-0.0000788569450378418,
0.0213775634765625,
-0.0132293701171875,
0.01413726806640625,
0.0088958740234375,
-0.0003199577331542969,
0.0014448165893554688,
0.0002541542053222656,
0.038330078125,
0.0135040283203125,
-0.03375244140625,
-0.005615234375,
0.018646240234375,
-0.0164947509765625,
0.0222015380859375,
0.0005478858947753906,
-0.0198974609375,
-0.03350830078125,
0.0029468536376953125,
-0.03741455078125,
0.0081787109375,
-0.00010544061660766602,
-0.0254364013671875,
0.0189971923828125,
-0.004550933837890625,
0.0118408203125,
0.005687713623046875,
-0.0008606910705566406,
0.0258941650390625,
-0.040985107421875,
0.00669097900390625,
0.04498291015625,
0.0125274658203125,
0.022247314453125,
-0.005634307861328125,
-0.02056884765625,
-0.021881103515625,
0.0203857421875,
-0.01544189453125,
-0.0238800048828125,
-0.0174407958984375,
0.0021820068359375,
0.002716064453125,
0.036712646484375,
0.0003566741943359375,
0.0019350051879882812,
0.0289459228515625,
-0.01027679443359375,
0.0008273124694824219,
0.00749969482421875,
0.038604736328125,
-0.060791015625,
-0.0011682510375976562,
0.0142364501953125,
0.01032257080078125,
0.011932373046875,
0.0076446533203125,
0.01486968994140625,
-0.00022161006927490234,
0.0223388671875,
-0.00862884521484375,
0.0183868408203125,
-0.019134521484375,
-0.0003364086151123047,
-0.005283355712890625,
-0.024261474609375,
-0.02978515625,
-0.028350830078125,
0.01084136962890625,
-0.021636962890625,
-0.01177978515625,
0.05487060546875,
-0.01143646240234375,
-0.01250457763671875,
-0.0025424957275390625,
-0.027099609375,
-0.038055419921875,
0.00943756103515625,
-0.0015716552734375,
-0.002651214599609375,
0.004581451416015625,
0.01268768310546875,
-0.017730712890625,
0.0041656494140625,
0.00798797607421875,
-0.0159149169921875,
-0.009674072265625,
-0.0009298324584960938,
-0.0235748291015625,
-0.00922393798828125,
-0.03631591796875,
-0.0111236572265625,
-0.056060791015625,
-0.0188140869140625,
-0.0005068778991699219,
-0.00868988037109375,
0.00856781005859375,
-0.060791015625,
0.002552032470703125,
-0.0264739990234375,
0.0251617431640625,
0.051177978515625,
-0.0283050537109375,
0.03729248046875,
-0.0166778564453125,
0.03741455078125,
-0.0156097412109375,
0.0015611648559570312,
-0.015106201171875,
-0.0213775634765625,
-0.0101165771484375,
-0.0023136138916015625,
-0.0274200439453125,
-0.00009548664093017578,
-0.0210723876953125,
-0.01080322265625,
0.0025768280029296875,
0.043426513671875,
-0.004779815673828125,
-0.01305389404296875,
0.0163726806640625,
-0.0345458984375,
-0.0204620361328125,
0.01186370849609375,
0.00981903076171875,
-0.0026340484619140625,
-0.023834228515625,
0.0247802734375,
-0.00937652587890625,
0.03546142578125,
-0.016632080078125,
0.019805908203125,
0.012847900390625,
-0.0224761962890625,
-0.0085906982421875,
-0.0017023086547851562,
0.0146484375,
0.0186767578125,
0.0217742919921875,
0.023223876953125,
0.02703857421875,
0.0222320556640625,
0.0068359375,
0.0048980712890625,
-0.0165557861328125,
0.023468017578125,
0.0037364959716796875,
0.0132904052734375,
0.006595611572265625,
-0.006168365478515625,
-0.01349639892578125,
0.011688232421875,
-0.0212554931640625,
0.0010585784912109375,
-0.01271820068359375,
0.008575439453125,
0.00487518310546875,
0.0200958251953125,
-0.0018396377563476562,
0.0118408203125,
0.017913818359375
] |
ours_475
|
We claim that in general the game is fair if \( N = M + 1 \). This implies that the answer is \( 5 \) by Fermat's Little Theorem. Indeed, consider the following game: Ann and Drew flip a coin repeatedly, and Ann wants to get to \( N \) heads, while Drew wants to get to \( M \) tails. By replacing "runs" (i.e., maximal strings of only heads or tails) with a spin of a slot machine, we see that the two games are the same, so long as the first flip is heads, since the first run is heads. So, we need \( N = M + 1 \).
Thus, \( N = 2^{2018} + 1 \). We need to find the remainder of \( N \) when divided by \( 2018 \).
Since \( 2018 = 2 \times 1009 \), we use Fermat's Little Theorem, which states that if \( p \) is a prime, then for any integer \( a \) not divisible by \( p \), \( a^{p-1} \equiv 1 \pmod{p} \).
Applying this to \( 1009 \), we have \( 2^{1008} \equiv 1 \pmod{1009} \). Therefore, \( 2^{2018} = (2^{1008})^2 \times 2^2 \equiv 1^2 \times 4 \equiv 4 \pmod{1009} \).
Since \( 2^{2018} \equiv 0 \pmod{2} \), we have \( 2^{2018} + 1 \equiv 1 \pmod{2} \).
Using the Chinese Remainder Theorem, we solve the system:
\[
\begin{align*}
N &\equiv 4 + 1 \equiv 5 \pmod{1009}, \\
N &\equiv 1 \pmod{2}.
\end{align*}
\]
Thus, the remainder when \( N \) is divided by \( 2018 \) is \(\boxed{5}\).
|
5
|
{
"competition": "us_comps",
"dataset": "Ours",
"posts": null,
"source": "OMOFall18Solns.md"
}
|
Ann and Drew have purchased a mysterious slot machine; each time it is spun, it chooses a random positive integer such that \( k \) is chosen with probability \( 2^{-k} \) for every positive integer \( k \), and then it outputs \( k \) tokens. Let \( N \) be a fixed integer. Ann and Drew alternate turns spinning the machine, with Ann going first. Ann wins if she receives at least \( N \) total tokens from the slot machine before Drew receives at least \( M=2^{2018} \) total tokens, and Drew wins if he receives \( M \) tokens before Ann receives \( N \) tokens. If each person has the same probability of winning, compute the remainder when \( N \) is divided by \( 2018 \).
|
[
"/Mathematics/NumberTheory/Arithmetic",
"/Mathematics/NumberTheory/Congruences/ChineseRemainderTheorem",
"/Mathematics/NumberTheory/Congruences/Congruence",
"/Mathematics/NumberTheory/Congruences/FermatsLittleTheorem",
"/Mathematics/NumberTheory/Congruences/ModularArithmetic",
"/Mathematics/NumberTheory/GeneralNumberTheory/ElementaryMethods",
"/Mathematics/NumberTheory/GeneralNumberTheory/ElementaryNumberTheory",
"/Mathematics/NumberTheory/GeneralNumberTheory/NumberTheory",
"/Mathematics/NumberTheory/Integers/Integer",
"/Mathematics/NumberTheory/Integers/N",
"/Mathematics/NumberTheory/Integers/PositiveInteger",
"/Mathematics/ProbabilityandStatistics/Probability/CoinFlipping",
"/Mathematics/ProbabilityandStatistics/Probability/ProbabilitySpace",
"/Mathematics/ProbabilityandStatistics/Probability/SampleSpace"
] |
Model each spin as a maximal run of identical coin flips and see that the game is fair only when Ann’s target exceeds Drew’s by one token.
|
[
-0.0003027915954589844,
0.040313720703125,
0.0301666259765625,
-0.0158538818359375,
-0.0013761520385742188,
0.05853271484375,
0.0269012451171875,
-0.05517578125,
-0.0124969482421875,
0.02313232421875,
0.05224609375,
-0.045867919921875,
-0.002227783203125,
-0.035247802734375,
-0.01325225830078125,
-0.01117706298828125,
0.048187255859375,
0.0249481201171875,
0.01270294189453125,
0.0021762847900390625,
-0.0123291015625,
-0.031768798828125,
-0.020904541015625,
0.0112457275390625,
0.006103515625,
-0.0394287109375,
-0.018341064453125,
0.01104736328125,
0.009246826171875,
0.02099609375,
-0.025299072265625,
0.033447265625,
0.045440673828125,
-0.01360321044921875,
-0.0019474029541015625,
0.0026798248291015625,
0.01357269287109375,
0.0034770965576171875,
0.0167388916015625,
-0.0247344970703125,
0.0129852294921875,
0.034149169921875,
-0.0135650634765625,
0.00505828857421875,
-0.0034618377685546875,
0.003856658935546875,
-0.011505126953125,
-0.0164337158203125,
0.009185791015625,
-0.0171661376953125,
-0.01073455810546875,
0.00998687744140625,
0.029541015625,
-0.01727294921875,
-0.0252532958984375,
-0.076904296875,
0.01395416259765625,
-0.0019330978393554688,
0.04791259765625,
-0.03936767578125,
-0.001644134521484375,
0.0035076141357421875,
0.005321502685546875,
-0.0234832763671875,
-0.000004291534423828125,
-0.01378631591796875,
-0.0033473968505859375,
0.001758575439453125,
-0.0140838623046875,
-0.004390716552734375,
0.03607177734375,
-0.007843017578125,
-0.035430908203125,
0.0148773193359375,
0.049407958984375,
-0.0161590576171875,
-0.007843017578125,
-0.00905609130859375,
0.020355224609375,
-0.0124053955078125,
-0.012847900390625,
0.0233917236328125,
0.007572174072265625,
0.0120086669921875,
0.01678466796875,
0.017547607421875,
-0.0273284912109375,
0.005481719970703125,
0.01666259765625,
-0.0202484130859375,
-0.01123046875,
0.01120758056640625,
0.00885772705078125,
-0.04266357421875,
0.003917694091796875,
0.0009012222290039062,
0.00792694091796875,
-0.020416259765625,
-0.0187835693359375,
-0.004016876220703125,
-0.0186309814453125,
-0.004985809326171875,
-0.00537109375,
0.001605987548828125,
-0.0247039794921875,
-0.005825042724609375,
-0.018524169921875,
0.00872802734375,
-0.0243377685546875,
-0.0021419525146484375,
0.0005536079406738281,
0.00033020973205566406,
0.0303192138671875,
-0.003376007080078125,
-0.0249176025390625,
0.007579803466796875,
-0.01160430908203125,
-0.0007734298706054688,
-0.00945281982421875,
0.032958984375,
0.004207611083984375,
0.0127105712890625,
-0.01078033447265625,
-0.01049041748046875,
-0.0003769397735595703,
0.00676727294921875,
-0.003017425537109375,
-0.0125732421875,
0.05419921875,
0.026123046875,
0.0234375,
0.00357818603515625,
-0.03900146484375,
-0.00281524658203125,
-0.031463623046875,
0.004261016845703125,
-0.01544189453125,
-0.00963592529296875,
-0.018524169921875,
-0.0111083984375,
0.017242431640625,
-0.0098724365234375,
0.00400543212890625,
0.01377105712890625,
-0.003841400146484375,
0.00003737211227416992,
-0.0184173583984375,
-0.0408935546875,
0.01125335693359375,
-0.001796722412109375,
-0.0219573974609375,
-0.00548553466796875,
0.010833740234375,
0.0008397102355957031,
-0.014007568359375,
0.00861358642578125,
0.00634765625,
0.0179901123046875,
-0.0177764892578125,
0.0085601806640625,
0.011383056640625,
-0.0208892822265625,
-0.006679534912109375,
0.062744140625,
-0.0284576416015625,
0.001323699951171875,
-0.018218994140625,
-0.0174407958984375,
-0.006671905517578125,
-0.00418853759765625,
-0.0074920654296875,
-0.0054931640625,
0.004119873046875,
-0.00484466552734375,
-0.0003733634948730469,
-0.00818634033203125,
0.0036296844482421875,
-0.03436279296875,
-0.00403594970703125,
0.038604736328125,
0.00981903076171875,
-0.04864501953125,
0.01181793212890625,
0.00800323486328125,
-0.00395965576171875,
0.013519287109375,
-0.0009565353393554688,
0.00576019287109375,
0.0159454345703125,
0.00225830078125,
0.0179901123046875,
-0.016754150390625,
0.000751495361328125,
0.0010385513305664062,
-0.0205841064453125,
-0.00141143798828125,
-0.0029754638671875,
-0.022369384765625,
0.047760009765625,
-0.00528717041015625,
0.03424072265625,
0.00926971435546875,
-0.0207366943359375,
0.01168060302734375,
-0.002223968505859375,
-0.01371002197265625,
0.0075531005859375,
0.0016632080078125,
0.01367950439453125,
-0.003185272216796875,
0.0007967948913574219,
-0.041046142578125,
0.00487518310546875,
0.002590179443359375,
-0.004100799560546875,
0.0154571533203125,
-0.0003924369812011719,
0.007415771484375,
0.0191192626953125,
-0.04461669921875,
0.01947021484375,
0.004123687744140625,
-0.0104827880859375,
-0.0005474090576171875,
-0.018646240234375,
-0.007068634033203125,
-0.013885498046875,
-0.01132965087890625,
-0.01515960693359375,
0.0212860107421875,
0.029754638671875,
0.0102386474609375,
-0.00662994384765625,
0.0034618377685546875,
0.01003265380859375,
0.01561737060546875,
0.01654052734375,
-0.025238037109375,
0.03228759765625,
-0.03021240234375,
0.01262664794921875,
-0.003742218017578125,
-0.0037097930908203125,
0.00447845458984375,
-0.0158538818359375,
-0.00024378299713134766,
-0.0104217529296875,
0.0141143798828125,
0.00756072998046875,
-0.0035610198974609375,
-0.006183624267578125,
-0.0030879974365234375,
-0.00920867919921875,
-0.0053253173828125,
-0.0136871337890625,
0.0058746337890625,
-0.0036144256591796875,
0.0011949539184570312,
-0.0203704833984375,
-0.01739501953125,
-0.005062103271484375,
-0.0263671875,
-0.00029969215393066406,
-0.01389312744140625,
0.00508880615234375,
0.042022705078125,
0.0192718505859375,
-0.01910400390625,
0.0174102783203125,
-0.004871368408203125,
0.029449462890625,
0.00135040283203125,
-0.0178680419921875,
0.0297393798828125,
-0.0022945404052734375,
-0.041015625,
-0.0020160675048828125,
-0.003368377685546875,
-0.0028133392333984375,
-0.00298309326171875,
0.00203704833984375,
-0.020263671875,
-0.02825927734375,
-0.0029125213623046875,
-0.006183624267578125,
-0.00605010986328125,
-0.01010894775390625,
-0.0092620849609375,
-0.04412841796875,
0.0003101825714111328,
-0.0029811859130859375,
0.02703857421875,
-0.00920867919921875,
0.0022602081298828125,
0.024322509765625,
-0.030548095703125,
0.003726959228515625,
0.003368377685546875,
-0.002643585205078125,
-0.0265960693359375,
0.0214080810546875,
-0.006198883056640625,
-0.005504608154296875,
-0.0099639892578125,
-0.01415252685546875,
0.042205810546875,
-0.0121307373046875,
0.0077362060546875,
-0.007793426513671875,
-0.05474853515625,
0.0002911090850830078,
0.0137939453125,
0.020538330078125,
-0.01318359375,
-0.02886962890625,
-0.0307769775390625,
0.0006132125854492188,
0.0233612060546875,
0.00388336181640625,
-0.0018320083618164062,
0.00374603271484375,
0.0164337158203125,
-0.03424072265625,
-0.01153564453125,
-0.002655029296875,
0.0088958740234375,
0.002197265625,
0.0238800048828125,
-0.023284912109375,
-0.01690673828125,
0.0035762786865234375,
0.007781982421875,
0.007701873779296875,
-0.00879669189453125,
-0.0008835792541503906,
0.00540924072265625,
0.014739990234375,
0.00017321109771728516,
0.0263519287109375,
-0.01045989990234375,
-0.029083251953125,
-0.014312744140625,
-0.022674560546875,
-0.0372314453125,
-0.0278778076171875,
0.007434844970703125,
0.019439697265625,
-0.023101806640625,
0.0016040802001953125,
0.01549530029296875,
0.01568603515625,
0.004852294921875,
-0.00403594970703125,
0.0013227462768554688,
-0.01041412353515625,
0.0216827392578125,
0.01392364501953125,
0.026824951171875,
-0.020050048828125,
0.01470947265625,
0.01702880859375,
0.005245208740234375,
-0.0082550048828125,
0.00788116455078125,
-0.00878143310546875,
-0.0300140380859375,
-0.02825927734375,
0.0065765380859375,
-0.04095458984375,
-0.003692626953125,
0.00238037109375,
-0.0201416015625,
0.0136871337890625,
0.03662109375,
-0.056488037109375,
0.00792694091796875,
0.01038360595703125,
0.006107330322265625,
-0.0266571044921875,
-0.0142364501953125,
0.0089263916015625,
0.0196685791015625,
-0.0006489753723144531,
0.0195159912109375,
-0.036468505859375,
-0.00908660888671875,
0.02899169921875,
-0.0076904296875,
-0.0221099853515625,
0.01104736328125,
-0.011138916015625,
0.002899169921875,
-0.0175933837890625,
0.0041351318359375,
0.0159454345703125,
0.01200103759765625,
-0.01036834716796875,
-0.003559112548828125,
0.0162506103515625,
-0.0142974853515625,
0.006145477294921875,
-0.041229248046875,
-0.0301361083984375,
0.036163330078125,
-0.0054473876953125,
-0.01059722900390625,
-0.007083892822265625,
-0.024200439453125,
-0.0095062255859375,
0.021240234375,
-0.00437164306640625,
0.0007395744323730469,
0.00501251220703125,
0.00008153915405273438,
0.0245819091796875,
-0.010162353515625,
-0.003154754638671875,
-0.039337158203125,
-0.0120391845703125,
0.0005083084106445312,
-0.00823211669921875,
-0.027557373046875,
0.0133056640625,
0.0166778564453125,
-0.005687713623046875,
0.0147705078125,
-0.021820068359375,
0.0150146484375,
-0.018218994140625,
0.00820159912109375,
-0.006683349609375,
-0.015899658203125,
0.01348876953125,
0.019317626953125,
0.02984619140625,
0.0274810791015625,
0.0279388427734375,
0.0015697479248046875,
-0.01371002197265625,
0.0321044921875,
0.0272216796875,
-0.01103973388671875,
-0.0042724609375,
-0.0140838623046875,
-0.039947509765625,
0.01372528076171875,
0.0168304443359375,
0.0216217041015625,
-0.074462890625,
-0.01174163818359375,
-0.0132598876953125,
0.01430511474609375,
-0.0001691579818725586,
-0.0297698974609375,
0.018707275390625,
0.02984619140625,
0.00502777099609375,
-0.01763916015625,
0.0210418701171875,
-0.0200653076171875,
-0.00788116455078125,
-0.00921630859375,
-0.00795745849609375,
-0.0003802776336669922,
-0.0308685302734375,
-0.00968170166015625,
-0.031768798828125,
0.0010986328125,
0.00811004638671875,
0.021453857421875,
-0.00957489013671875,
-0.0018186569213867188,
0.021759033203125,
0.01206207275390625,
-0.00560760498046875,
0.038848876953125,
-0.02606201171875,
0.0110931396484375,
-0.0184173583984375,
-0.041168212890625,
0.01544952392578125,
0.0300140380859375,
-0.01273345947265625,
0.0760498046875,
0.0029621124267578125,
0.005435943603515625,
0.035797119140625,
0.0035991668701171875,
-0.0194854736328125,
-0.0269317626953125,
-0.005199432373046875,
-0.0155792236328125,
-0.019439697265625,
-0.0108642578125,
-0.0162353515625,
0.0131378173828125,
0.004146575927734375,
-0.0045166015625,
-0.01312255859375,
-0.0074615478515625,
-0.015777587890625,
0.003551483154296875,
-0.0147705078125,
0.016693115234375,
-0.019195556640625,
0.0005617141723632812,
0.02740478515625,
-0.003833770751953125,
-0.0048065185546875,
-0.01003265380859375,
-0.005748748779296875,
0.005035400390625,
0.026885986328125,
-0.007350921630859375,
0.0009465217590332031,
-0.00443267822265625,
0.038116455078125,
0.0199737548828125,
0.03228759765625,
0.01153564453125,
-0.02178955078125,
0.0310211181640625,
0.031341552734375,
0.00118255615234375,
-0.0235595703125,
0.015838623046875,
0.00688934326171875,
-0.0011320114135742188,
-0.0115966796875,
0.024139404296875,
-0.0014829635620117188,
-0.03875732421875,
0.01239013671875,
0.006099700927734375,
0.0288848876953125,
0.018768310546875,
0.01277923583984375,
-0.017486572265625,
-0.006511688232421875,
-0.01458740234375,
0.006809234619140625,
-0.0074310302734375,
-0.007785797119140625,
-0.0241546630859375,
-0.0044708251953125,
-0.020355224609375,
0.005985260009765625,
0.010223388671875,
-0.019287109375,
0.035675048828125,
0.006092071533203125,
-0.0131072998046875,
-0.0022125244140625,
-0.00820159912109375,
-0.02581787109375,
0.0321044921875,
-0.02728271484375,
0.014892578125,
0.020660400390625,
0.0102691650390625,
-0.0018367767333984375,
0.01507568359375,
-0.0018110275268554688,
0.004428863525390625,
0.040374755859375,
-0.0019397735595703125,
-0.0142669677734375,
0.022552490234375,
-0.0223388671875,
-0.056182861328125,
0.00946044921875,
-0.027923583984375,
0.0026226043701171875,
0.0014295578002929688,
-0.02197265625,
-0.00678253173828125,
-0.0094757080078125,
-0.00916290283203125,
-0.00795745849609375,
-0.01479339599609375,
0.0119476318359375,
0.0176239013671875,
-0.0088348388671875,
0.0283660888671875,
0.04583740234375,
0.021575927734375,
0.0279541015625,
0.031951904296875,
0.00927734375,
-0.01031494140625,
0.002712249755859375,
0.0188140869140625,
0.00431060791015625,
0.00841522216796875,
-0.0086822509765625,
-0.01084136962890625,
-0.0062103271484375,
-0.01432037353515625,
-0.0181732177734375,
-0.038787841796875,
-0.00830078125,
0.0226593017578125,
-0.00783538818359375,
0.0066986083984375,
-0.0199737548828125,
-0.005756378173828125,
0.00890350341796875,
-0.005184173583984375,
0.01250457763671875,
0.0253753662109375,
0.0313720703125,
-0.0048370361328125,
-0.0028705596923828125,
0.026458740234375,
0.042572021484375,
0.0027523040771484375,
-0.027618408203125,
0.006450653076171875,
0.01241302490234375,
-0.045318603515625,
0.0004029273986816406,
-0.01000213623046875,
0.0018711090087890625,
-0.0030651092529296875,
-0.005252838134765625,
0.004688262939453125,
0.024810791015625,
-0.027496337890625,
0.0137786865234375,
-0.0024433135986328125,
0.0014314651489257812,
-0.00879669189453125,
0.033935546875,
0.0030517578125,
0.0228271484375,
0.0122222900390625,
0.00589752197265625,
0.011505126953125,
0.004810333251953125,
0.0013170242309570312,
-0.0020904541015625,
0.019073486328125,
-0.0049896240234375,
-0.05267333984375,
-0.0249481201171875,
-0.016387939453125,
0.00295257568359375,
-0.0013370513916015625,
-0.060394287109375,
0.0276336669921875,
-0.029083251953125,
0.0189361572265625,
-0.0008978843688964844,
-0.0020294189453125,
-0.01030731201171875,
0.013031005859375,
0.0021190643310546875,
-0.0237274169921875,
0.0281982421875,
-0.01076507568359375,
0.024261474609375,
0.005886077880859375,
-0.009429931640625,
0.0012683868408203125,
-0.05816650390625,
-0.0318603515625,
0.004467010498046875,
0.011138916015625,
0.03167724609375,
0.0261383056640625,
-0.00830078125,
-0.0020160675048828125,
0.040863037109375,
0.00926971435546875,
0.005466461181640625,
-0.000020384788513183594,
-0.01114654541015625,
-0.0570068359375,
0.0288848876953125,
0.0098724365234375,
-0.0013494491577148438,
0.03240966796875,
0.015716552734375,
0.00769805908203125,
0.012939453125,
0.0274658203125,
0.005352020263671875,
0.038543701171875,
0.02862548828125,
-0.00701904296875,
0.01471710205078125,
0.04034423828125,
0.014190673828125,
0.0498046875,
0.042999267578125,
-0.01526641845703125,
0.016815185546875,
0.007598876953125,
-0.027252197265625,
-0.00670623779296875,
-0.0036754608154296875,
0.02838134765625,
0.0199127197265625,
-0.003204345703125,
-0.012451171875,
-0.006481170654296875,
-0.007221221923828125,
0.00983428955078125,
-0.02972412109375,
-0.01275634765625,
-0.01491546630859375,
0.0069732666015625,
-0.0079193115234375,
0.002964019775390625,
-0.026611328125,
-0.03375244140625,
0.00870513916015625,
0.0029888153076171875,
0.0181884765625,
-0.01087188720703125,
-0.045257568359375,
0.01293182373046875,
0.0035686492919921875,
-0.00968170166015625,
0.0128173828125,
0.0009503364562988281,
-0.00446319580078125,
-0.03759765625,
-0.030914306640625,
0.00013267993927001953,
0.0014667510986328125,
0.03680419921875,
0.004241943359375,
-0.0058441162109375,
0.010040283203125,
-0.030670166015625,
0.00916290283203125,
-0.0430908203125,
-0.003734588623046875,
0.01073455810546875,
0.051422119140625,
-0.00298309326171875,
0.01267242431640625,
-0.0087890625,
0.00711822509765625,
0.0183563232421875,
0.015472412109375,
-0.001377105712890625,
0.0211181640625,
-0.0212554931640625,
0.006366729736328125,
0.00031304359436035156,
-0.0161590576171875,
0.010986328125,
-0.011627197265625,
-0.0165252685546875,
0.01204681396484375,
-0.035369873046875,
0.004608154296875,
0.02374267578125,
-0.0253448486328125,
-0.022247314453125,
-0.030487060546875,
0.01837158203125,
-0.023529052734375,
-0.0110931396484375,
-0.0220794677734375,
0.01206207275390625,
-0.01568603515625,
0.0243988037109375,
-0.049560546875,
-0.033843994140625,
-0.0015459060668945312,
-0.00829315185546875,
0.0143890380859375,
-0.003498077392578125,
-0.043304443359375,
0.01898193359375,
0.006549835205078125,
-0.00878143310546875,
-0.0083465576171875,
0.0064697265625,
-0.0143890380859375,
-0.00722503662109375,
0.002819061279296875,
-0.0017566680908203125,
0.01392364501953125,
-0.053466796875,
0.0274200439453125,
-0.0013427734375,
0.00787353515625,
0.025238037109375,
-0.00420379638671875,
-0.0281982421875,
-0.00022840499877929688,
-0.00501251220703125,
-0.00820159912109375,
-0.0166015625,
-0.024688720703125,
0.00856781005859375,
-0.0008063316345214844,
-0.044464111328125,
-0.01371002197265625,
0.0175323486328125,
-0.0007901191711425781,
0.0159454345703125,
0.0245208740234375,
0.006267547607421875,
0.0005617141723632812,
0.04156494140625,
-0.005451202392578125,
-0.01690673828125,
-0.00033164024353027344,
-0.01190948486328125,
-0.0171966552734375,
-0.017333984375,
0.014251708984375,
-0.003849029541015625,
-0.00673675537109375,
0.0207061767578125,
-0.01338958740234375,
0.046295166015625,
-0.00841522216796875,
-0.0002751350402832031,
-0.01093292236328125,
-0.035400390625,
0.006435394287109375,
0.045135498046875,
0.0135955810546875,
0.0200042724609375,
0.0106048583984375,
-0.00998687744140625,
-0.038848876953125,
-0.0033016204833984375,
-0.0037136077880859375,
-0.012054443359375,
0.02044677734375,
-0.0005350112915039062,
-0.039947509765625,
0.0010595321655273438,
-0.015228271484375,
-0.003692626953125,
-0.00656890869140625,
0.0166778564453125,
0.0224761962890625,
-0.0254058837890625,
0.027435302734375,
-0.0185394287109375,
0.00792694091796875,
-0.0017251968383789062,
-0.00927734375,
0.025390625,
-0.0070037841796875,
0.028228759765625,
0.0305023193359375,
0.03594970703125,
0.0274810791015625,
0.01087188720703125,
-0.0068206787109375,
-0.01477813720703125,
-0.00475311279296875,
-0.016510009765625,
0.0196990966796875,
-0.033050537109375,
0.020782470703125,
-0.00609588623046875,
-0.01230621337890625,
0.0036678314208984375,
0.0113983154296875,
0.0189361572265625,
0.0065460205078125,
0.0148162841796875,
0.0287322998046875,
0.039703369140625,
-0.004180908203125,
0.00585174560546875,
-0.00563812255859375,
0.0050506591796875,
0.0282440185546875,
0.024932861328125,
-0.0097198486328125,
-0.02337646484375,
0.0225982666015625,
0.002960205078125,
-0.0030422210693359375,
0.005306243896484375,
-0.00026869773864746094,
-0.005657196044921875,
-0.009796142578125,
-0.0158843994140625,
0.0025196075439453125,
0.01525115966796875,
0.0251922607421875,
0.01372528076171875,
0.0260467529296875,
0.0238037109375,
-0.000213623046875,
0.0119476318359375,
-0.0205230712890625,
-0.034912109375,
0.00399017333984375,
-0.002094268798828125,
0.015716552734375,
0.0131683349609375,
0.0087738037109375,
-0.032440185546875,
-0.00569915771484375,
-0.02392578125,
-0.0028228759765625,
-0.005279541015625,
0.0025005340576171875,
0.005840301513671875,
0.01343536376953125,
0.006130218505859375,
0.0005640983581542969,
-0.028656005859375,
0.02606201171875,
0.0157623291015625,
0.0191497802734375,
0.033355712890625,
0.0297698974609375,
0.012359619140625,
-0.0050201416015625,
-0.03338623046875,
0.0064697265625,
-0.00969696044921875,
-0.0164947509765625,
-0.01270294189453125,
-0.0184478759765625,
-0.0204620361328125,
-0.0341796875,
0.019256591796875,
-0.0012979507446289062,
0.0175323486328125,
0.0293731689453125,
-0.020782470703125,
-0.00153350830078125,
0.0103302001953125,
-0.01021575927734375,
0.01218414306640625,
-0.0240325927734375,
0.043243408203125,
-0.02734375,
0.0231170654296875,
0.01849365234375,
0.0185394287109375,
-0.0037937164306640625,
0.0241241455078125,
-0.01666259765625,
0.0015668869018554688,
-0.00069427490234375,
-0.0030422210693359375,
-0.00823211669921875,
0.01129913330078125,
-0.00701904296875,
-0.01287078857421875,
0.009368896484375,
-0.006195068359375,
-0.02703857421875,
-0.00786590576171875,
0.032073974609375,
0.00907135009765625,
-0.0262451171875,
-0.037872314453125,
-0.0277557373046875,
0.01751708984375,
0.007293701171875,
-0.00041866302490234375,
0.0216522216796875,
-0.0167236328125,
-0.03057861328125,
-0.0096588134765625,
-0.0143890380859375,
-0.01514434814453125,
0.01476287841796875,
-0.0142669677734375,
-0.0264434814453125,
0.0190582275390625,
0.0494384765625,
0.0035610198974609375,
-0.020416259765625,
-0.0055084228515625,
-0.010345458984375,
0.0023975372314453125,
-0.0097503662109375,
0.04254150390625,
0.03814697265625,
-0.0340576171875,
0.026519775390625,
-0.00554656982421875,
0.0096282958984375,
0.01511383056640625,
0.005615234375,
0.0377197265625,
-0.0240478515625,
0.0029544830322265625,
0.00244140625,
0.0024509429931640625,
0.01500701904296875,
0.0029201507568359375,
-0.01320648193359375,
0.004367828369140625,
0.0026454925537109375,
-0.00832366943359375,
-0.006710052490234375,
-0.007495880126953125,
0.0206146240234375,
-0.0153656005859375,
-0.0167236328125,
-0.01006317138671875,
-0.015716552734375,
0.0164642333984375,
-0.00737762451171875,
0.0030765533447265625,
-0.03131103515625,
-0.01525115966796875,
0.01416778564453125,
-0.00030159950256347656,
-0.049407958984375,
-0.01263427734375,
-0.005466461181640625,
0.0014514923095703125,
-0.028167724609375,
-0.0018482208251953125,
0.0242156982421875,
-0.004428863525390625,
-0.0171051025390625,
0.0170135498046875,
0.010223388671875,
0.0015306472778320312,
0.0244293212890625,
-0.0071868896484375,
-0.006740570068359375,
-0.003459930419921875,
-0.031707763671875,
0.002960205078125,
-0.0023212432861328125,
0.008087158203125,
0.0169830322265625,
0.0130157470703125,
0.0141754150390625,
0.00347900390625,
0.00946807861328125,
-0.0149688720703125,
-0.0259552001953125,
0.0026836395263671875,
-0.0200347900390625,
0.0217132568359375,
-0.01294708251953125,
0.0094757080078125,
0.0302886962890625,
0.0362548828125,
-0.0095977783203125,
-0.03057861328125,
0.03125,
0.01137542724609375,
-0.0030155181884765625,
-0.023101806640625,
0.0015096664428710938,
0.0177154541015625,
0.038177490234375,
-0.0167694091796875,
-0.034881591796875,
-0.041412353515625,
-0.01253509521484375,
-0.052032470703125,
0.0132598876953125,
-0.01137542724609375,
0.0035076141357421875,
0.038116455078125,
-0.03302001953125,
0.0360107421875,
-0.00818634033203125,
-0.01374053955078125,
-0.005809783935546875,
-0.00415802001953125,
0.012481689453125,
0.01119232177734375,
-0.0222625732421875,
0.0274658203125,
-0.0018863677978515625,
-0.0026111602783203125,
-0.03924560546875,
0.0014009475708007812,
0.0156707763671875,
0.03253173828125,
-0.0016717910766601562,
-0.00977325439453125,
0.003856658935546875,
-0.021820068359375,
-0.01483154296875,
-0.01194000244140625,
0.00794219970703125,
-0.003467559814453125,
-0.017547607421875,
-0.013641357421875,
-0.00640869140625,
0.00229644775390625,
0.0075531005859375,
0.00811004638671875,
-0.005886077880859375,
0.01035308837890625,
-0.038421630859375,
0.0074005126953125,
0.002227783203125,
-0.009613037109375,
0.00037980079650878906,
0.04217529296875,
-0.004062652587890625,
-0.0179290771484375,
-0.0011758804321289062,
0.01311492919921875,
-0.0005593299865722656,
0.015899658203125,
-0.016357421875,
0.001766204833984375,
-0.0120849609375,
-0.018035888671875,
-0.034271240234375,
0.01454925537109375,
-0.0024127960205078125,
0.044891357421875,
-0.013763427734375,
-0.010650634765625,
-0.0011949539184570312,
0.00457000732421875,
-0.00600433349609375,
0.0273590087890625,
-0.007442474365234375,
0.0223541259765625,
-0.051788330078125,
0.0465087890625,
-0.00782012939453125,
-0.016082763671875,
0.0020885467529296875,
-0.007442474365234375,
-0.015106201171875,
0.0016012191772460938,
0.01465606689453125,
-0.007335662841796875,
-0.00739288330078125,
-0.021209716796875,
-0.01366424560546875,
-0.033050537109375,
0.005443572998046875,
-0.000011920928955078125,
0.0086212158203125,
0.00879669189453125,
0.0037631988525390625,
0.00206756591796875,
0.0167999267578125,
0.0015583038330078125,
0.01116943359375,
0.01377105712890625,
-0.006099700927734375,
0.02099609375,
-0.01102447509765625,
0.000614166259765625,
0.009765625,
0.0010824203491210938,
0.0188446044921875,
-0.0279693603515625,
0.036773681640625,
0.006175994873046875,
-0.017822265625,
-0.007617950439453125,
0.0005445480346679688,
-0.02166748046875,
-0.0166473388671875,
0.0097808837890625,
-0.0248260498046875,
-0.01430511474609375,
-0.0024566650390625,
-0.0008769035339355469,
-0.034698486328125,
0.0005993843078613281,
0.019378662109375,
0.002506256103515625,
-0.0347900390625,
-0.0030536651611328125,
-0.0097808837890625,
0.0323486328125,
0.0197296142578125,
-0.006336212158203125,
0.00757598876953125,
-0.006473541259765625,
-0.020263671875,
-0.0007452964782714844,
-0.002178192138671875,
0.0268096923828125,
0.0104827880859375,
-0.0218658447265625,
0.0015668869018554688,
-0.003452301025390625,
0.00722503662109375,
0.01280975341796875,
-0.02978515625,
-0.005847930908203125,
0.008331298828125,
-0.0199737548828125,
0.0234222412109375,
0.007450103759765625,
-0.01010894775390625,
-0.0266571044921875,
0.0008025169372558594,
0.049102783203125,
-0.0099639892578125,
0.04205322265625,
-0.01386260986328125,
0.01461029052734375,
-0.0035037994384765625,
-0.0215606689453125,
-0.0037517547607421875,
-0.015899658203125,
0.03338623046875,
-0.01922607421875,
0.02947998046875,
-0.0411376953125,
-0.032684326171875,
-0.003818511962890625,
0.0306549072265625,
0.0184173583984375,
-0.0185394287109375,
-0.01517486572265625,
-0.0114288330078125,
0.0009298324584960938,
-0.0011873245239257812,
0.034881591796875,
-0.003108978271484375,
-0.0078887939453125,
0.01125335693359375,
0.0318603515625,
0.007457733154296875,
0.0133819580078125,
-0.0062713623046875,
0.0012598037719726562,
-0.01282501220703125,
0.0009984970092773438,
-0.037445068359375,
-0.014434814453125,
0.016998291015625,
0.021270751953125,
0.000530242919921875,
0.01338958740234375,
0.0228729248046875,
-0.0008516311645507812,
-0.030426025390625,
0.023529052734375,
-0.027069091796875,
0.00365447998046875,
0.006580352783203125,
-0.00786590576171875,
-0.01084136962890625,
-0.022430419921875,
0.01332855224609375,
-0.025146484375,
0.0253753662109375,
0.00545501708984375,
-0.015899658203125,
0.00400543212890625,
-0.0160064697265625,
0.00841522216796875,
-0.0229339599609375,
-0.028656005859375,
-0.0222625732421875,
0.003055572509765625,
0.0207366943359375,
-0.0079498291015625,
-0.0189361572265625,
0.020416259765625,
0.036834716796875,
-0.00838470458984375,
0.0374755859375,
0.048797607421875,
-0.005886077880859375,
0.006999969482421875,
-0.033905029296875,
-0.0174560546875,
-0.042572021484375,
-0.019683837890625,
-0.042510986328125,
0.01531982421875,
0.0173492431640625,
0.029052734375,
-0.0236053466796875,
-0.027801513671875,
-0.032623291015625,
0.011474609375,
-0.0214385986328125,
0.017547607421875,
0.01064300537109375,
0.0081787109375,
-0.003490447998046875,
0.011566162109375,
0.006046295166015625,
-0.0252532958984375,
0.00917816162109375,
0.003787994384765625,
-0.006744384765625,
0.0112762451171875,
-0.03594970703125,
-0.0238800048828125,
0.01401519775390625,
-0.0240478515625,
-0.0482177734375,
-0.036895751953125,
-0.00740814208984375,
-0.00022459030151367188,
0.027374267578125,
-0.01580810546875,
0.027862548828125,
-0.0004546642303466797,
0.032928466796875,
0.01123809814453125,
0.029144287109375,
0.0089569091796875,
0.023406982421875,
0.0111846923828125,
0.01128387451171875,
-0.003383636474609375,
-0.029388427734375,
0.031890869140625,
-0.01026153564453125,
0.01496124267578125,
0.03326416015625,
0.007335662841796875,
-0.020782470703125,
0.016754150390625,
-0.0188751220703125,
-0.03399658203125,
-0.0138702392578125,
-0.005626678466796875,
-0.006519317626953125,
0.02349853515625,
-0.00943756103515625,
0.036376953125,
-0.017730712890625,
0.010040283203125,
0.0119476318359375,
-0.037841796875,
-0.002689361572265625,
0.0182037353515625,
0.0036182403564453125,
0.0164031982421875,
-0.0107269287109375,
0.0240020751953125,
-0.006343841552734375,
0.0237579345703125,
-0.0161285400390625,
-0.01494598388671875,
-0.0304107666015625,
0.004222869873046875,
0.0023651123046875,
0.05511474609375,
-0.0190582275390625,
-0.0288848876953125,
0.0217437744140625,
-0.00960540771484375,
0.0013093948364257812,
0.004886627197265625,
0.00647735595703125,
-0.0078277587890625,
0.0293426513671875,
-0.0335693359375,
0.03662109375,
-0.007171630859375,
0.0024700164794921875,
-0.00384521484375,
-0.03900146484375,
-0.01071929931640625,
-0.005222320556640625,
0.002986907958984375,
-0.0159759521484375,
0.00713348388671875,
0.017242431640625,
0.0224761962890625,
-0.01483917236328125,
-0.003326416015625,
-0.01812744140625,
0.0237884521484375,
-0.01447296142578125,
-0.0301666259765625,
-0.0199432373046875,
-0.003765106201171875,
-0.00206756591796875,
0.05926513671875,
-0.006076812744140625,
0.007633209228515625,
-0.01690673828125,
-0.04229736328125,
0.0216522216796875,
0.0244293212890625,
-0.00396728515625,
0.00209808349609375,
0.012908935546875,
-0.030975341796875,
0.01229095458984375,
-0.0238037109375,
-0.009735107421875,
0.019744873046875,
0.020721435546875,
-0.02362060546875,
-0.019012451171875,
0.0282745361328125,
-0.0218048095703125,
-0.0288848876953125,
0.01471710205078125,
-0.0029449462890625,
-0.006885528564453125,
-0.00182342529296875,
-0.07122802734375,
-0.030731201171875,
0.020477294921875,
-0.01288604736328125,
-0.002696990966796875,
-0.0017414093017578125,
-0.0154266357421875,
-0.01800537109375,
0.02813720703125,
-0.00006079673767089844,
0.0121002197265625,
-0.01320648193359375,
-0.00009238719940185547,
-0.0069732666015625,
-0.002635955810546875,
-0.007843017578125,
0.006801605224609375,
0.00010764598846435547,
-0.0289764404296875,
0.01068115234375,
-0.0178375244140625,
0.0196380615234375,
-0.004459381103515625,
-0.01096343994140625,
-0.01424407958984375,
-0.0025157928466796875,
0.016326904296875,
0.020355224609375,
0.0161590576171875,
0.0107574462890625,
-0.0186614990234375,
0.005413055419921875,
-0.0180206298828125,
0.0276336669921875,
-0.0095672607421875,
-0.005138397216796875,
-0.0159149169921875,
0.02130126953125,
0.017120361328125,
0.012176513671875,
-0.0201568603515625,
-0.0228729248046875,
-0.01483154296875,
-0.00677490234375,
0.031280517578125,
0.00609588623046875,
0.0293121337890625,
-0.00022113323211669922,
0.003116607666015625,
-0.00655364990234375,
-0.03839111328125,
-0.01279449462890625,
0.01041412353515625,
0.0025997161865234375,
0.01194000244140625,
0.005130767822265625,
-0.042694091796875,
0.030242919921875,
-0.027008056640625,
-0.0191497802734375,
-0.0126800537109375,
0.00975799560546875,
-0.009857177734375,
0.026214599609375,
-0.01148223876953125,
-0.005657196044921875,
0.003376007080078125,
0.00815582275390625,
0.01568603515625,
0.0181427001953125,
0.019561767578125,
0.0020923614501953125,
0.029388427734375,
-0.007564544677734375,
-0.00732421875,
-0.016265869140625,
0.031402587890625,
-0.03057861328125,
-0.006252288818359375,
-0.032073974609375,
-0.0138397216796875,
0.00266265869140625,
0.005191802978515625,
0.0008058547973632812,
0.0074462890625,
0.0200653076171875,
-0.002086639404296875,
-0.01983642578125,
-0.027496337890625,
-0.0093231201171875,
-0.0188140869140625,
0.014007568359375,
0.0172119140625,
-0.009796142578125,
0.021270751953125,
-0.00528717041015625,
-0.004718780517578125,
0.007190704345703125,
0.02301025390625,
-0.0151214599609375,
-0.0253448486328125,
-0.02716064453125,
0.03167724609375,
0.0108184814453125,
-0.0234832763671875,
-0.002712249755859375,
-0.024688720703125,
-0.021209716796875,
-0.008819580078125,
0.01495361328125,
0.03143310546875,
0.032684326171875,
-0.005859375,
0.026580810546875,
0.0139312744140625,
-0.03814697265625,
0.01213836669921875,
0.0197906494140625,
-0.018157958984375,
-0.005207061767578125,
0.0250701904296875,
-0.00904083251953125,
-0.0101318359375,
0.0147857666015625,
-0.0166168212890625,
0.0254669189453125,
0.01181793212890625,
0.01531219482421875,
0.01519775390625,
0.0005335807800292969,
0.00864410400390625,
0.00731658935546875,
0.0008993148803710938,
0.01169586181640625,
-0.021392822265625,
-0.0201873779296875,
0.04107666015625,
0.009307861328125,
-0.00955963134765625,
-0.0106048583984375,
0.021697998046875,
-0.005229949951171875,
0.0008497238159179688,
0.012420654296875,
-0.02349853515625,
0.0179595947265625,
-0.0182037353515625,
0.020782470703125,
-0.0003533363342285156,
-0.0187530517578125,
0.00176239013671875,
0.028289794921875,
-0.01250457763671875,
-0.01004791259765625,
-0.0024776458740234375,
0.02435302734375,
0.00852203369140625,
0.0085296630859375,
0.02264404296875,
-0.0303802490234375,
0.0025787353515625,
-0.001628875732421875,
0.022491455078125,
0.0187225341796875,
0.0287017822265625,
-0.0193634033203125,
0.004146575927734375,
0.006595611572265625,
-0.0239105224609375,
0.007274627685546875,
0.0042266845703125,
-0.015625,
0.0016956329345703125,
0.00612640380859375,
0.0165252685546875,
0.0279998779296875,
-0.0027790069580078125,
-0.014862060546875,
0.0295562744140625,
-0.0149688720703125,
0.0311431884765625,
-0.00806427001953125,
0.02618408203125,
0.01442718505859375,
-0.0178070068359375,
0.0014657974243164062,
0.0260467529296875,
-0.015838623046875,
0.02734375,
-0.0107574462890625,
-0.016754150390625,
0.015350341796875,
-0.038787841796875,
-0.00518035888671875,
0.002407073974609375,
-0.00433349609375,
-0.001346588134765625,
-0.0026950836181640625,
-0.0084228515625,
0.01081085205078125,
0.022369384765625,
-0.0100555419921875,
0.01171112060546875,
-0.0174713134765625,
0.00555419921875,
0.0201568603515625,
-0.006748199462890625,
0.01113128662109375,
-0.0305633544921875,
-0.0227508544921875,
0.0021114349365234375,
-0.0090789794921875,
0.01152801513671875,
0.0034923553466796875,
0.044342041015625,
0.005435943603515625,
-0.01006317138671875,
0.007144927978515625,
-0.00934600830078125,
0.0130615234375,
0.01544189453125,
0.007274627685546875,
-0.018280029296875,
0.0285797119140625,
-0.012420654296875,
-0.0189971923828125,
-0.00923919677734375,
0.00823974609375,
0.0175933837890625,
0.0180511474609375,
-0.01654052734375,
-0.0182952880859375,
-0.0084381103515625,
-0.0345458984375,
-0.005031585693359375,
0.018218994140625,
0.01396942138671875,
0.021514892578125,
0.007770538330078125,
-0.017974853515625,
0.0007419586181640625,
-0.009033203125,
0.0147705078125,
0.003170013427734375,
-0.0169677734375,
-0.01007080078125,
-0.01171875,
0.00550079345703125,
-0.05780029296875,
-0.0236968994140625,
0.01386260986328125,
-0.00818634033203125,
0.0005812644958496094,
-0.03619384765625,
0.0204010009765625,
-0.01303863525390625,
0.038818359375,
-0.0128173828125,
-0.04193115234375,
-0.01287841796875,
-0.034515380859375,
-0.0191192626953125,
0.01396942138671875,
0.014801025390625,
-0.0095062255859375,
0.0021877288818359375,
0.00042438507080078125,
0.0157623291015625,
-0.028656005859375,
0.0127716064453125,
-0.04522705078125,
-0.0172576904296875,
0.017608642578125,
-0.0178985595703125,
-0.00820159912109375,
-0.01171875,
0.0372314453125,
-0.0248260498046875,
0.0163726806640625,
0.01464080810546875,
0.0153350830078125,
-0.0186614990234375,
-0.0034580230712890625,
0.003173828125,
0.0297698974609375,
-0.0012922286987304688,
-0.005451202392578125,
0.0053863525390625,
0.00202178955078125,
0.005001068115234375,
-0.0007271766662597656,
0.0029735565185546875,
0.004787445068359375,
-0.016265869140625,
0.004383087158203125,
0.0129852294921875,
-0.0312347412109375,
0.0182952880859375,
-0.004611968994140625,
-0.0394287109375,
0.03887939453125,
-0.0178985595703125,
-0.00759124755859375,
0.01556396484375,
0.00348663330078125,
0.032379150390625,
0.0070343017578125,
0.004474639892578125,
-0.020294189453125,
-0.047515869140625,
0.0135955810546875,
-0.0044403076171875,
-0.0006608963012695312,
-0.00791168212890625,
0.030914306640625,
-0.00885772705078125,
-0.01412200927734375,
0.013885498046875,
0.048370361328125,
-0.0023822784423828125,
-0.024078369140625,
0.03857421875,
0.01195526123046875,
0.0177154541015625,
0.036590576171875,
-0.02667236328125,
0.033599853515625,
-0.032257080078125,
-0.0213775634765625,
-0.01904296875,
-0.0078125,
0.0029392242431640625,
-0.03662109375,
0.0175323486328125,
-0.0037937164306640625,
-0.027801513671875,
0.008148193359375,
0.0196380615234375,
0.00942230224609375,
-0.01090240478515625,
-0.003528594970703125,
-0.035400390625,
0.018829345703125,
0.01378631591796875,
-0.04193115234375,
-0.01434326171875,
-0.00745391845703125,
-0.0025730133056640625,
0.0000998377799987793,
0.007106781005859375,
0.055419921875,
-0.02923583984375,
0.003742218017578125,
0.001758575439453125,
-0.050933837890625,
-0.01837158203125,
-0.020782470703125,
0.00855255126953125,
-0.0017175674438476562,
-0.007297515869140625,
-0.00763702392578125,
-0.0017881393432617188,
0.03515625,
-0.003879547119140625,
-0.028472900390625,
-0.0230865478515625,
0.010406494140625,
0.0003657341003417969,
-0.040191650390625,
0.0183868408203125,
0.0013904571533203125,
-0.0160369873046875,
0.046661376953125,
-0.0301971435546875,
0.04534912109375,
-0.01232147216796875,
0.01117706298828125,
0.0037097930908203125,
-0.0006775856018066406,
-0.0223236083984375,
0.0052337646484375,
0.006084442138671875,
-0.0203857421875,
-0.0235748291015625,
0.002742767333984375,
0.01425933837890625,
-0.0165557861328125,
-0.0084991455078125,
-0.01522064208984375,
0.03179931640625,
-0.003177642822265625,
0.0034694671630859375,
0.0033359527587890625,
-0.048858642578125,
0.006591796875,
-0.018829345703125,
-0.029266357421875,
-0.00733184814453125,
0.0249176025390625,
-0.0289764404296875,
-0.0266876220703125,
0.001262664794921875,
0.005802154541015625,
0.00669097900390625,
0.03302001953125,
0.00927734375,
0.004848480224609375,
0.025604248046875,
-0.04168701171875,
-0.00824737548828125,
0.0011243820190429688,
0.01288604736328125,
-0.0292205810546875,
0.011383056640625,
0.0214996337890625,
0.00818634033203125,
0.0229034423828125,
0.019989013671875,
-0.02447509765625,
0.017913818359375,
0.01207733154296875,
0.0208282470703125,
-0.0308380126953125,
-0.0447998046875,
-0.006805419921875,
-0.0034236907958984375,
0.0178680419921875,
-0.0172119140625,
0.0122833251953125,
0.002864837646484375,
-0.0177459716796875,
0.036834716796875,
-0.008453369140625,
0.0162811279296875,
0.0125579833984375,
0.01245880126953125,
0.0077972412109375,
-0.0117950439453125,
0.0135040283203125,
-0.01131439208984375,
0.028472900390625,
-0.023773193359375,
0.0355224609375,
0.029541015625,
-0.005382537841796875,
0.0218963623046875,
-0.00307464599609375,
0.01274871826171875,
-0.023956298828125,
-0.00283050537109375,
0.0301971435546875,
-0.0185699462890625,
-0.017486572265625,
0.01154327392578125,
-0.0301666259765625,
-0.00246429443359375,
-0.005950927734375,
0.004802703857421875,
0.00482940673828125,
-0.00531768798828125,
0.01103973388671875,
0.02789306640625,
-0.01335906982421875,
0.01495361328125,
0.0227813720703125,
0.01934814453125,
-0.010986328125,
0.01363372802734375,
0.0202178955078125,
0.019927978515625,
0.030487060546875,
-0.0266571044921875,
0.0204010009765625,
0.00682830810546875,
0.0207061767578125,
0.0219268798828125,
0.00415802001953125,
0.0068359375,
0.0168609619140625,
-0.0164031982421875,
0.0220947265625,
-0.01629638671875,
0.01261138916015625,
0.00811004638671875,
-0.028167724609375,
-0.0286712646484375,
0.01934814453125,
0.0033111572265625,
0.003925323486328125,
0.036407470703125,
0.00833892822265625,
0.01230621337890625,
-0.0176239013671875,
0.00817108154296875,
-0.00910186767578125,
0.007694244384765625,
-0.0206146240234375,
-0.022552490234375,
-0.00868988037109375,
0.009765625,
-0.02655029296875,
-0.00012242794036865234,
-0.04632568359375,
-0.0029964447021484375,
0.010589599609375,
0.016937255859375,
0.00021851062774658203,
0.01593017578125,
-0.06304931640625,
0.041412353515625,
0.007038116455078125,
0.0101318359375,
0.006786346435546875,
0.019287109375,
-0.0239715576171875,
-0.0183868408203125,
-0.013946533203125,
0.01216888427734375,
-0.01342010498046875,
-0.025543212890625,
0.00652313232421875,
0.004459381103515625,
-0.003753662109375,
0.01053619384765625,
-0.00717926025390625,
0.0158233642578125,
0.005725860595703125,
0.004604339599609375,
0.0213470458984375,
-0.0106964111328125,
0.0216217041015625,
-0.0295562744140625,
-0.0109100341796875,
-0.0306243896484375,
-0.00016736984252929688,
-0.0084686279296875,
0.001430511474609375,
-0.032073974609375,
0.01247406005859375,
-0.00262451171875,
-0.0119781494140625,
-0.00919342041015625,
-0.0157318115234375,
-0.005695343017578125,
0.00843048095703125,
-0.002666473388671875,
0.018524169921875,
0.0085296630859375,
-0.00042939186096191406,
-0.00507354736328125,
-0.00962066650390625,
-0.0178680419921875,
-0.0250091552734375,
-0.057037353515625,
0.0183258056640625,
0.0056915283203125,
0.012969970703125,
-0.01776123046875,
-0.021453857421875,
-0.006191253662109375,
-0.00861358642578125,
-0.00543975830078125,
0.0037689208984375,
0.03302001953125,
0.03582763671875,
0.004238128662109375,
-0.00693511962890625,
-0.0074462890625,
0.0123748779296875,
-0.002010345458984375,
-0.01512908935546875,
-0.030120849609375,
-0.0134124755859375,
-0.01465606689453125,
0.004611968994140625,
-0.034912109375,
0.0104522705078125,
-0.005828857421875,
-0.01361846923828125,
0.0005941390991210938,
0.01995849609375,
0.0002663135528564453,
-0.01287078857421875,
0.014434814453125,
-0.0184173583984375,
0.00695037841796875,
-0.0014324188232421875,
-0.031890869140625,
-0.060211181640625,
-0.01806640625,
0.001277923583984375,
0.0092620849609375,
0.038726806640625,
0.02264404296875,
-0.0015325546264648438,
0.004497528076171875,
-0.005367279052734375,
0.003376007080078125,
0.021209716796875,
0.01224517822265625,
0.001617431640625,
-0.0400390625,
0.0191192626953125,
-0.03662109375,
-0.003452301025390625,
-0.007694244384765625,
-0.006305694580078125,
-0.00218963623046875,
0.0014772415161132812,
0.0159759521484375,
-0.01360321044921875,
-0.0029811859130859375,
0.0230712890625,
-0.0246734619140625,
-0.0166778564453125,
-0.0205841064453125,
0.0088653564453125,
-0.0035343170166015625,
-0.0074615478515625,
0.039825439453125,
-0.01197052001953125,
0.0104522705078125,
-0.0023708343505859375,
-0.0143585205078125,
0.041046142578125,
-0.0203857421875,
0.0167999267578125,
-0.012115478515625,
0.0018243789672851562,
-0.0234375,
0.00794219970703125,
0.0197906494140625,
-0.019805908203125,
0.006378173828125,
-0.01526641845703125,
-0.01153564453125,
0.00415802001953125,
-0.0132904052734375,
0.01151275634765625,
-0.0082550048828125,
0.0263671875,
0.02813720703125,
0.00643157958984375,
0.0265350341796875,
0.021820068359375,
0.00815582275390625,
0.012603759765625,
-0.0009593963623046875,
-0.00237274169921875,
0.0233001708984375,
0.01551055908203125,
0.01715087890625,
-0.023162841796875,
-0.029815673828125,
-0.0140228271484375,
0.05419921875,
-0.02691650390625,
0.024810791015625,
-0.026214599609375,
-0.003055572509765625,
-0.0107574462890625,
0.016845703125,
-0.02142333984375,
-0.0056915283203125,
0.0192413330078125,
0.0029735565185546875,
-0.01727294921875,
0.0152587890625,
0.019012451171875,
0.00960540771484375,
-0.006710052490234375,
-0.00395965576171875,
0.0010175704956054688,
0.0131072998046875,
0.0108795166015625,
-0.0242919921875,
-0.0256805419921875,
0.0175323486328125,
-0.001491546630859375,
-0.0535888671875,
-0.01739501953125,
0.007015228271484375,
0.0105743408203125,
-0.0001036524772644043,
0.02886962890625,
-0.0247039794921875,
0.0278778076171875,
-0.003658294677734375,
0.0250091552734375,
-0.0257110595703125,
-0.0223236083984375,
0.0261383056640625,
0.0124053955078125,
-0.0166015625,
-0.034515380859375,
0.018341064453125,
0.0189056396484375,
-0.0116729736328125,
-0.007770538330078125,
-0.00891876220703125,
0.0038013458251953125,
-0.03643798828125,
0.0229949951171875,
0.0008893013000488281,
0.0325927734375,
0.0072784423828125,
0.0231781005859375,
-0.0640869140625,
0.00872802734375,
-0.003635406494140625,
0.0214080810546875,
0.01114654541015625,
-0.01512908935546875,
0.01105499267578125,
-0.00366973876953125,
-0.00525665283203125,
0.0163421630859375,
0.00708770751953125,
-0.004405975341796875,
0.01495361328125,
-0.016876220703125,
0.01319122314453125,
0.002605438232421875,
0.01491546630859375,
0.0106201171875,
-0.0054931640625,
0.0196990966796875,
0.007587432861328125,
-0.032684326171875,
0.00278472900390625,
0.00432586669921875,
0.0401611328125,
0.008941650390625,
0.004413604736328125,
-0.03375244140625,
-0.003917694091796875,
0.021820068359375,
-0.01399993896484375,
-0.0012989044189453125,
-0.03497314453125,
0.0013170242309570312,
0.0239105224609375,
-0.0219268798828125,
0.020965576171875,
0.0113983154296875,
-0.006633758544921875,
-0.0199432373046875,
0.008636474609375,
-0.0180816650390625,
0.038604736328125,
0.023406982421875,
-0.0033664703369140625,
-0.038421630859375,
-0.0196990966796875,
0.0184478759765625,
-0.001972198486328125,
0.006275177001953125,
-0.01427459716796875,
-0.01331329345703125,
0.004253387451171875,
-0.0233917236328125,
-0.0101470947265625,
-0.0340576171875,
-0.00888824462890625,
-0.00433349609375,
-0.01727294921875,
-0.007106781005859375,
-0.00933837890625,
0.0028057098388671875,
0.0200958251953125,
0.01543426513671875,
0.00693511962890625,
-0.01207733154296875,
0.022491455078125,
0.01568603515625,
0.0033969879150390625,
0.0168304443359375,
0.0280609130859375,
0.0027980804443359375,
0.00951385498046875,
0.0219268798828125,
-0.003673553466796875,
0.044219970703125,
0.002773284912109375,
0.012237548828125,
0.008636474609375,
-0.0259552001953125,
-0.006679534912109375,
-0.0124053955078125,
-0.00424957275390625,
0.004222869873046875,
0.00217437744140625,
-0.0172882080078125,
0.00604248046875,
0.0201263427734375,
-0.0308380126953125,
-0.0066680908203125,
-0.0293426513671875,
-0.0030536651611328125,
-0.01383209228515625,
-0.03192138671875,
0.0212554931640625,
0.0008778572082519531,
0.006969451904296875,
-0.00362396240234375,
-0.0099945068359375,
0.005222320556640625,
-0.0399169921875,
0.0024890899658203125,
-0.007221221923828125,
-0.0023021697998046875,
0.004558563232421875,
0.0195770263671875,
0.01361083984375,
-0.00240325927734375,
0.00388336181640625,
0.012603759765625,
0.0036411285400390625,
-0.021270751953125,
0.0007085800170898438,
0.001522064208984375,
-0.056304931640625,
0.050201416015625,
0.01445770263671875,
0.0670166015625,
0.01155853271484375,
-0.027679443359375,
0.0160064697265625,
-0.018218994140625,
-0.01099395751953125,
-0.0516357421875,
-0.0009646415710449219,
-0.0186004638671875,
0.003143310546875,
0.00318145751953125,
-0.0089874267578125,
0.004150390625,
0.021331787109375,
0.00833892822265625,
0.0114898681640625,
-0.01458740234375,
0.01291656494140625,
0.00377655029296875,
0.01558685302734375,
0.01898193359375,
-0.02337646484375,
-0.0226593017578125,
0.006999969482421875,
-0.0212554931640625,
0.0031833648681640625,
-0.006130218505859375,
0.034149169921875,
0.0298004150390625,
-0.011383056640625,
-0.006633758544921875,
0.02349853515625,
0.01355743408203125,
-0.017974853515625,
-0.00994873046875,
0.002841949462890625,
-0.02056884765625,
-0.0159912109375,
0.003910064697265625,
0.017425537109375,
-0.0176239013671875,
0.00244140625,
0.0030574798583984375,
-0.0301513671875,
-0.01189422607421875,
0.01335906982421875,
0.0166015625,
-0.024627685546875,
-0.0216064453125,
-0.01055908203125,
-0.019775390625,
0.0120697021484375,
0.00482940673828125,
-0.018829345703125,
-0.006137847900390625,
0.0009860992431640625,
0.00685882568359375,
-0.045867919921875,
0.003570556640625,
-0.011016845703125,
0.031951904296875,
0.0228729248046875,
0.01181793212890625,
-0.00820159912109375,
0.0238800048828125,
0.032501220703125,
0.00201416015625,
-0.0034027099609375,
0.036865234375,
0.0005822181701660156,
0.001506805419921875,
-0.0102386474609375,
-0.0213165283203125,
-0.0224761962890625,
0.0323486328125,
-0.004947662353515625,
0.008056640625,
-0.0026454925537109375,
-0.036163330078125,
-0.01464080810546875,
-0.0291748046875,
-0.02191162109375,
-0.034698486328125,
0.01435089111328125,
0.01666259765625,
-0.0116119384765625,
-0.005157470703125,
0.01141357421875,
0.0039520263671875,
0.004909515380859375,
0.016937255859375,
-0.0023632049560546875,
-0.0030422210693359375,
-0.0023822784423828125,
0.0133819580078125,
-0.009796142578125,
-0.003490447998046875,
-0.016021728515625,
-0.0122222900390625,
0.0703125,
-0.020721435546875,
0.017059326171875,
-0.01861572265625,
-0.012298583984375,
0.01605224609375,
0.0039005279541015625,
-0.0043182373046875,
-0.0052490234375,
0.00839996337890625,
-0.0081787109375,
-0.0138397216796875,
0.015625,
-0.0161590576171875,
-0.02166748046875,
-0.0160675048828125,
0.00335693359375,
0.0035190582275390625,
-0.01055908203125,
-0.01153564453125,
-0.0089874267578125,
-0.006580352783203125,
-0.00545501708984375,
-0.033538818359375,
-0.01751708984375,
0.0036563873291015625,
-0.002788543701171875,
0.0139617919921875,
0.02142333984375,
0.0191802978515625,
-0.00783538818359375,
-0.025299072265625,
0.0016698837280273438,
-0.006099700927734375,
-0.016815185546875,
0.0234375,
0.0298614501953125,
-0.005481719970703125,
-0.0026187896728515625,
-0.0191650390625,
0.0172882080078125,
-0.0374755859375,
-0.007701873779296875,
0.0294647216796875,
-0.02587890625,
0.040618896484375,
-0.0033245086669921875,
0.033966064453125,
0.046295166015625,
-0.0299072265625,
0.033477783203125,
-0.0057525634765625,
0.015838623046875,
0.005401611328125,
-0.030670166015625,
0.0192718505859375,
0.0129241943359375,
0.002895355224609375,
0.032928466796875,
-0.021942138671875,
-0.0010538101196289062,
0.002216339111328125,
0.020538330078125,
-0.01401519775390625,
0.02154541015625,
0.006561279296875,
0.0171356201171875,
0.0227203369140625,
-0.0195159912109375,
0.0227813720703125,
-0.0177154541015625,
-0.01070404052734375,
0.001251220703125,
-0.000972747802734375,
0.004337310791015625,
0.01471710205078125,
-0.00848388671875,
-0.0006427764892578125,
0.00933837890625,
0.000713348388671875,
0.0033817291259765625,
-0.01177978515625,
-0.03485107421875,
-0.0189208984375,
-0.0198822021484375,
-0.0207061767578125,
0.005443572998046875,
0.01500701904296875,
-0.0261993408203125,
0.0022563934326171875,
0.01678466796875,
-0.01345062255859375,
-0.019317626953125,
0.0039005279541015625,
0.004459381103515625,
-0.036895751953125,
0.010345458984375,
-0.00010961294174194336,
0.01000213623046875,
0.03790283203125,
0.00899505615234375,
0.01187896728515625,
-0.01506805419921875,
0.041961669921875,
-0.0213775634765625,
-0.0163116455078125,
0.01235198974609375,
-0.0321044921875,
-0.0256500244140625,
0.0130157470703125,
0.016143798828125,
0.019378662109375,
-0.01351165771484375,
-0.018035888671875,
0.031494140625,
0.005031585693359375,
0.0301513671875,
0.0214385986328125,
-0.032745361328125,
0.0143585205078125,
0.01531219482421875,
-0.0010976791381835938,
-0.0219268798828125,
-0.0015954971313476562,
-0.004505157470703125,
0.0036869049072265625,
-0.0003376007080078125,
-0.0136566162109375,
0.01300048828125,
0.0134124755859375,
-0.01116180419921875,
-0.0135040283203125,
-0.038116455078125,
-0.0014410018920898438,
-0.00910186767578125,
-0.01346588134765625,
-0.0106658935546875,
0.01320648193359375,
0.0166778564453125,
-0.0291290283203125,
0.0130462646484375,
-0.04595947265625,
-0.02337646484375,
0.03314208984375,
-0.007740020751953125,
-0.0164031982421875,
-0.0010509490966796875,
-0.0098419189453125,
-0.00264739990234375,
0.02508544921875,
-0.01483154296875,
-0.01446533203125,
-0.020172119140625,
0.00605010986328125,
0.0208587646484375,
0.0201873779296875,
-0.0357666015625,
-0.01203155517578125,
-0.0012445449829101562,
-0.005832672119140625,
-0.01519012451171875,
-0.00589752197265625,
-0.00970458984375,
-0.05255126953125,
0.00466156005859375,
-0.0212860107421875,
-0.0077667236328125,
-0.0086669921875,
-0.0152130126953125,
-0.0027904510498046875,
-0.011932373046875,
0.02117919921875,
-0.0229034423828125,
0.0072174072265625,
-0.00885772705078125,
-0.036529541015625,
-0.0013418197631835938,
-0.011444091796875,
0.0196075439453125,
0.00882720947265625,
-0.0122833251953125,
0.0022487640380859375,
-0.0078277587890625,
0.0247344970703125,
-0.026031494140625,
-0.0250701904296875,
0.0302886962890625,
-0.061798095703125,
-0.0117340087890625,
-0.024261474609375,
-0.024932861328125,
0.017333984375,
-0.019500732421875,
-0.0029144287109375,
-0.007656097412109375,
-0.00995635986328125,
-0.007259368896484375,
0.01165008544921875,
0.027923583984375,
-0.027191162109375,
-0.0151214599609375,
0.00420379638671875,
0.00823211669921875,
0.007457733154296875,
0.0048828125,
-0.006198883056640625,
0.0014123916625976562,
0.007396697998046875,
-0.01271820068359375,
0.01111602783203125,
0.0107574462890625,
0.0281982421875,
-0.0178985595703125,
-0.005336761474609375,
0.01093292236328125,
0.0272064208984375,
-0.004146575927734375,
-0.00717926025390625,
-0.0264892578125,
-0.0367431640625,
0.003223419189453125,
0.002864837646484375,
0.018402099609375,
-0.009674072265625,
0.0025177001953125,
0.00576019287109375,
0.0308380126953125
] |
ours_476
|
Let \( N = 357! + 358! + 359! + 360! \). We can factor this expression as follows:
\[
N = 357! \cdot (1 + 358 + 358 \cdot 359 + 358 \cdot 359 \cdot 360)
\]
Simplifying inside the parentheses:
\[
1 + 358 + 358 \cdot 359 + 358 \cdot 359 \cdot 360 = 1 + 358(1 + 359(1 + 360))
\]
This simplifies to:
\[
1 + 358 + 358 \cdot 359 + 358 \cdot 359 \cdot 360 = 359 + 358 \cdot 360
\]
Further simplifying:
\[
359 + 358 \cdot 360 = 359^2 + 359 - 1 = 360^2 - 360 - 1 = 360^2 - 19^2
\]
Using the difference of squares:
\[
360^2 - 19^2 = (360 - 19)(360 + 19) = 341 \cdot 379
\]
Thus, we have:
\[
N = 357! \cdot 359 \cdot 341 \cdot 379
\]
Since 379 is a prime number, the largest prime factor of \( N \) is \( 379 \).
\(\boxed{379}\)
|
379
|
{
"competition": "us_comps",
"dataset": "Ours",
"posts": null,
"source": "OMOFall18Solns.md"
}
|
Compute the largest prime factor of \(357! + 358! + 359! + 360!\).
|
[
"/Mathematics/NumberTheory/Arithmetic/MultiplicationandDivision",
"/Mathematics/NumberTheory/GeneralNumberTheory/ElementaryMethods",
"/Mathematics/NumberTheory/GeneralNumberTheory/ElementaryNumberTheory",
"/Mathematics/NumberTheory/GeneralNumberTheory/HigherArithmetic",
"/Mathematics/NumberTheory/GeneralNumberTheory/NumberTheory",
"/Mathematics/NumberTheory/Integers/Integer",
"/Mathematics/NumberTheory/Integers/N",
"/Mathematics/NumberTheory/Integers/PositiveInteger",
"/Mathematics/NumberTheory/Integers/WholeNumber",
"/Mathematics/NumberTheory/Integers/Z",
"/Mathematics/NumberTheory/Integers/Z-Plus",
"/Mathematics/NumberTheory/PrimeNumbers/PrimeFactorization"
] |
Factor out the smallest factorial and simplify the remaining sum to a difference of squares that yields a large prime.
|
[
0.000059604644775390625,
-0.023590087890625,
0.03253173828125,
0.0228118896484375,
0.0005235671997070312,
0.006336212158203125,
0.02410888671875,
0.0219268798828125,
0.018341064453125,
0.0168914794921875,
0.0028247833251953125,
-0.022552490234375,
-0.000934600830078125,
0.0170440673828125,
-0.0276336669921875,
-0.0401611328125,
0.01195526123046875,
0.0106201171875,
0.0133819580078125,
-0.0055694580078125,
-0.00782012939453125,
0.005947113037109375,
0.0002837181091308594,
0.0218048095703125,
-0.0135498046875,
0.00583648681640625,
-0.0299224853515625,
-0.0174102783203125,
-0.04559326171875,
-0.0025997161865234375,
-0.0207977294921875,
-0.002685546875,
0.0199432373046875,
-0.0108795166015625,
-0.00032210350036621094,
-0.00597381591796875,
0.0221099853515625,
-0.005130767822265625,
0.0230255126953125,
-0.01192474365234375,
0.005489349365234375,
0.0135498046875,
0.01157379150390625,
-0.0029735565185546875,
-0.005462646484375,
0.03448486328125,
0.004711151123046875,
-0.038238525390625,
-0.01145172119140625,
0.0103302001953125,
-0.0067901611328125,
0.00812530517578125,
0.014373779296875,
-0.009796142578125,
-0.0494384765625,
-0.064453125,
0.045074462890625,
0.00824737548828125,
-0.00519561767578125,
0.0017147064208984375,
0.0032215118408203125,
0.01300048828125,
-0.0036678314208984375,
-0.005565643310546875,
0.0015916824340820312,
-0.0180206298828125,
0.000021159648895263672,
-0.0458984375,
0.0056610107421875,
-0.00555419921875,
0.00533294677734375,
-0.02276611328125,
-0.0020503997802734375,
0.01189422607421875,
0.04052734375,
-0.0096435546875,
-0.0011987686157226562,
-0.00667572021484375,
-0.00868988037109375,
0.0196685791015625,
0.0035419464111328125,
0.01276397705078125,
0.017822265625,
0.038421630859375,
0.0218505859375,
0.022247314453125,
0.03985595703125,
-0.0150909423828125,
-0.0242156982421875,
0.007595062255859375,
0.00768280029296875,
0.00479888916015625,
0.00141143798828125,
-0.038482666015625,
0.0013103485107421875,
0.00830841064453125,
0.0074462890625,
-0.00730133056640625,
-0.0154876708984375,
0.01129150390625,
0.0016155242919921875,
-0.017425537109375,
-0.0277557373046875,
-0.0198822021484375,
-0.065185546875,
-0.00797271728515625,
-0.00962066650390625,
0.01535797119140625,
0.004161834716796875,
0.00897979736328125,
0.0073394775390625,
-0.0166015625,
0.00890350341796875,
0.0186309814453125,
0.0040740966796875,
0.0162200927734375,
0.037261962890625,
0.00007891654968261719,
0.0234375,
-0.0341796875,
-0.00809478759765625,
0.0028076171875,
-0.0062103271484375,
0.02362060546875,
-0.00041294097900390625,
-0.03717041015625,
-0.003482818603515625,
-0.013336181640625,
-0.002666473388671875,
0.01324462890625,
0.02447509765625,
0.0031299591064453125,
-0.0267181396484375,
-0.0173797607421875,
-0.050872802734375,
0.0031223297119140625,
0.0126953125,
0.01177978515625,
-0.006443023681640625,
0.0048065185546875,
0.0013856887817382812,
-0.008575439453125,
-0.0106964111328125,
0.03326416015625,
-0.03399658203125,
0.0240325927734375,
0.00440216064453125,
-0.0128021240234375,
0.01519775390625,
-0.0016050338745117188,
0.0079193115234375,
0.00809478759765625,
0.0212554931640625,
0.0267333984375,
0.0019464492797851562,
0.02093505859375,
0.01360321044921875,
0.02984619140625,
0.006229400634765625,
0.0185546875,
0.004909515380859375,
0.0013675689697265625,
-0.00537109375,
0.0017042160034179688,
0.004852294921875,
-0.0124969482421875,
-0.019927978515625,
0.006679534912109375,
-0.014129638671875,
0.042327880859375,
0.0309295654296875,
0.0016002655029296875,
0.0110015869140625,
-0.0207061767578125,
-0.01812744140625,
-0.005512237548828125,
-0.01513671875,
0.045074462890625,
0.00485992431640625,
-0.0158843994140625,
0.0205535888671875,
-0.0018758773803710938,
0.03143310546875,
0.0049285888671875,
0.00884246826171875,
-0.0224609375,
-0.01222991943359375,
-0.01200103759765625,
0.02606201171875,
0.0230255126953125,
-0.02569580078125,
0.003795623779296875,
0.009552001953125,
0.01274871826171875,
-0.0029087066650390625,
0.006587982177734375,
-0.01523590087890625,
0.03363037109375,
0.02349853515625,
0.017730712890625,
-0.0310821533203125,
0.020721435546875,
0.042236328125,
0.01483917236328125,
0.002307891845703125,
-0.004913330078125,
0.01271820068359375,
0.008209228515625,
-0.0013828277587890625,
0.004184722900390625,
0.01690673828125,
0.00371551513671875,
0.007045745849609375,
-0.03790283203125,
-0.0190277099609375,
-0.0102691650390625,
-0.02532958984375,
-0.0008769035339355469,
0.016143798828125,
-0.024871826171875,
-0.0016803741455078125,
0.0009975433349609375,
0.0083160400390625,
0.00305938720703125,
-0.0005974769592285156,
-0.023345947265625,
0.0070953369140625,
0.004085540771484375,
-0.0015430450439453125,
-0.00508880615234375,
-0.01300811767578125,
0.0268402099609375,
-0.0275115966796875,
0.0009593963623046875,
-0.004459381103515625,
-0.0005035400390625,
-0.007419586181640625,
-0.0189361572265625,
0.021087646484375,
-0.031646728515625,
0.07708740234375,
-0.032684326171875,
-0.01035308837890625,
0.0035114288330078125,
0.0027790069580078125,
0.006622314453125,
0.02923583984375,
-0.0023517608642578125,
0.004467010498046875,
-0.0282745361328125,
-0.011627197265625,
0.003437042236328125,
0.0166778564453125,
-0.00989532470703125,
0.0201873779296875,
-0.0036144256591796875,
0.013671875,
-0.01290130615234375,
-0.0185699462890625,
0.0176239013671875,
0.005336761474609375,
0.00213623046875,
-0.031341552734375,
0.007232666015625,
0.0156097412109375,
-0.01800537109375,
-0.00017178058624267578,
-0.0205535888671875,
0.01496124267578125,
0.00909423828125,
0.00707244873046875,
-0.00778961181640625,
-0.0037593841552734375,
-0.0003323554992675781,
0.00928497314453125,
-0.004405975341796875,
0.0077972412109375,
-0.006565093994140625,
0.00798797607421875,
0.0094146728515625,
0.01291656494140625,
0.0029163360595703125,
0.007427215576171875,
-0.0016679763793945312,
-0.01522064208984375,
-0.0063323974609375,
0.0277862548828125,
-0.035064697265625,
-0.00876617431640625,
0.021392822265625,
-0.004482269287109375,
0.0007338523864746094,
0.00829315185546875,
-0.000019311904907226562,
0.050140380859375,
0.010711669921875,
0.0084075927734375,
0.0177154541015625,
0.0185546875,
-0.010406494140625,
-0.0042266845703125,
0.0232391357421875,
0.006053924560546875,
-0.022125244140625,
-0.0305633544921875,
-0.0005412101745605469,
-0.0010089874267578125,
-0.01377105712890625,
-0.007781982421875,
0.00701904296875,
-0.007343292236328125,
0.0033168792724609375,
0.01363372802734375,
0.0247650146484375,
-0.0176849365234375,
0.00275421142578125,
0.003238677978515625,
0.0009336471557617188,
-0.0384521484375,
0.004852294921875,
0.0037670135498046875,
-0.011962890625,
-0.01898193359375,
0.00637054443359375,
-0.0259552001953125,
-0.0244598388671875,
0.00511932373046875,
0.00359344482421875,
-0.005092620849609375,
0.03515625,
-0.032867431640625,
0.0083465576171875,
-0.01049041748046875,
-0.00792694091796875,
-0.00826263427734375,
-0.0012722015380859375,
-0.023956298828125,
0.012176513671875,
-0.01065826416015625,
0.01503753662109375,
-0.0025177001953125,
-0.0008935928344726562,
0.01493072509765625,
0.00801849365234375,
0.0233001708984375,
0.0228424072265625,
-0.030364990234375,
0.0157928466796875,
0.016998291015625,
-0.0242919921875,
-0.038116455078125,
-0.0189361572265625,
-0.024017333984375,
-0.0161895751953125,
-0.000194549560546875,
-0.0201416015625,
-0.0033130645751953125,
0.01120758056640625,
0.004581451416015625,
0.005222320556640625,
-0.0196990966796875,
-0.01617431640625,
-0.0161590576171875,
-0.0231475830078125,
0.00322723388671875,
-0.00385284423828125,
-0.0208282470703125,
0.0067901611328125,
-0.05218505859375,
0.0066375732421875,
-0.014739990234375,
0.0084991455078125,
0.010101318359375,
0.0005331039428710938,
-0.02850341796875,
-0.004825592041015625,
0.0041656494140625,
-0.0032291412353515625,
0.00429534912109375,
-0.008697509765625,
0.00238800048828125,
0.0311737060546875,
-0.0166473388671875,
0.0167999267578125,
-0.01123046875,
0.003246307373046875,
0.0113525390625,
0.011199951171875,
-0.0330810546875,
0.01462554931640625,
-0.0275115966796875,
0.039306640625,
0.00885009765625,
0.0182647705078125,
0.027313232421875,
-0.046875,
0.0009722709655761719,
0.00832366943359375,
0.043243408203125,
-0.0281829833984375,
-0.0007662773132324219,
-0.0143585205078125,
0.009918212890625,
-0.0188751220703125,
0.002750396728515625,
-0.0010223388671875,
-0.00754547119140625,
0.022064208984375,
-0.000036776065826416016,
0.0032787322998046875,
0.0038776397705078125,
-0.0147705078125,
0.007293701171875,
0.01062774658203125,
-0.0196533203125,
-0.00017142295837402344,
0.01739501953125,
-0.0064544677734375,
-0.0273284912109375,
-0.002574920654296875,
-0.035980224609375,
-0.00392913818359375,
-0.002696990966796875,
-0.0145416259765625,
0.029998779296875,
0.019195556640625,
-0.03411865234375,
0.0269622802734375,
0.01407623291015625,
-0.0247802734375,
0.0045623779296875,
-0.01556396484375,
0.007904052734375,
0.0210723876953125,
-0.0013895034790039062,
0.0307464599609375,
-0.0017118453979492188,
-0.015533447265625,
-0.01171112060546875,
-0.0062255859375,
-0.0031452178955078125,
0.0034122467041015625,
0.015167236328125,
-0.0033740997314453125,
-0.00760650634765625,
0.0179901123046875,
0.0272674560546875,
0.010955810546875,
0.04632568359375,
0.00011175870895385742,
-0.0207672119140625,
-0.01026153564453125,
0.01117706298828125,
-0.0232391357421875,
-0.038360595703125,
0.0182952880859375,
0.019256591796875,
-0.0186614990234375,
-0.032196044921875,
-0.0491943359375,
-0.0259552001953125,
-0.016082763671875,
-0.04083251953125,
0.0076904296875,
-0.0101318359375,
0.0221710205078125,
0.00806427001953125,
0.0084686279296875,
0.01708984375,
0.0290374755859375,
-0.0276641845703125,
0.00115966796875,
0.0240631103515625,
-0.007427215576171875,
-0.0567626953125,
0.0122222900390625,
0.0171966552734375,
0.04412841796875,
-0.0032176971435546875,
0.0023975372314453125,
0.00786590576171875,
0.0178985595703125,
-0.032440185546875,
0.00542449951171875,
0.00768280029296875,
0.0207366943359375,
0.01007080078125,
-0.0001684427261352539,
-0.007305145263671875,
0.031768798828125,
-0.000052988529205322266,
0.034759521484375,
-0.032806396484375,
-0.0227508544921875,
-0.00664520263671875,
0.01544952392578125,
0.016357421875,
0.007427215576171875,
0.004364013671875,
0.013763427734375,
-0.00783538818359375,
-0.053375244140625,
-0.0181121826171875,
0.0259246826171875,
-0.0019359588623046875,
-0.0006451606750488281,
0.050872802734375,
-0.005939483642578125,
-0.004940032958984375,
-0.015960693359375,
0.03021240234375,
0.01294708251953125,
0.0200958251953125,
-0.0277557373046875,
-0.0020294189453125,
-0.00806427001953125,
-0.00933837890625,
0.002750396728515625,
0.00406646728515625,
-0.0158538818359375,
-0.04437255859375,
0.0033206939697265625,
0.0467529296875,
0.0025577545166015625,
0.004375457763671875,
0.03167724609375,
0.0111541748046875,
-0.005374908447265625,
0.02154541015625,
-0.01690673828125,
0.00397491455078125,
-0.00047206878662109375,
0.019866943359375,
-0.006378173828125,
-0.0496826171875,
-0.0123748779296875,
0.01282501220703125,
0.0239105224609375,
0.0119781494140625,
0.00693511962890625,
0.0281982421875,
0.0011272430419921875,
-0.0002384185791015625,
-0.0016565322875976562,
-0.01432037353515625,
0.01045989990234375,
-0.048187255859375,
-0.0119781494140625,
-0.0211334228515625,
0.01256561279296875,
-0.01450347900390625,
0.0164337158203125,
0.006458282470703125,
-0.006092071533203125,
-0.017303466796875,
0.036346435546875,
0.0699462890625,
0.020782470703125,
-0.043975830078125,
0.004734039306640625,
0.0064544677734375,
-0.0236358642578125,
-0.004474639892578125,
0.007843017578125,
0.00689697265625,
-0.02801513671875,
-0.003284454345703125,
-0.003509521484375,
-0.0069580078125,
-0.022247314453125,
-0.00211334228515625,
0.0230560302734375,
0.01763916015625,
0.01474761962890625,
0.0076904296875,
-0.02777099609375,
-0.02081298828125,
-0.00005131959915161133,
-0.01099395751953125,
-0.04132080078125,
0.0214385986328125,
0.004604339599609375,
-0.0014142990112304688,
-0.043792724609375,
-0.0069122314453125,
-0.0038623809814453125,
0.009521484375,
0.027008056640625,
0.00543975830078125,
0.00726318359375,
-0.01611328125,
0.017913818359375,
0.025726318359375,
0.016357421875,
0.016021728515625,
-0.0124664306640625,
0.00705718994140625,
-0.0015716552734375,
0.007289886474609375,
0.010223388671875,
0.038299560546875,
-0.00031685829162597656,
0.01549530029296875,
0.0213775634765625,
0.012542724609375,
0.02374267578125,
-0.0154571533203125,
0.0170745849609375,
-0.0006313323974609375,
0.00002759695053100586,
0.0035343170166015625,
-0.0008797645568847656,
-0.0167999267578125,
0.0080413818359375,
0.0450439453125,
-0.004978179931640625,
-0.018707275390625,
-0.0249786376953125,
-0.0011548995971679688,
0.00846099853515625,
-0.004108428955078125,
0.00904083251953125,
0.001956939697265625,
0.0017633438110351562,
-0.0222625732421875,
-0.0239410400390625,
0.018829345703125,
-0.01285552978515625,
-0.0160064697265625,
-0.013763427734375,
-0.0206298828125,
-0.01593017578125,
0.01033782958984375,
0.0085296630859375,
0.006256103515625,
-0.0254669189453125,
-0.0025920867919921875,
0.035552978515625,
-0.03753662109375,
-0.00804901123046875,
0.01361846923828125,
-0.0210418701171875,
0.01554107666015625,
-0.036468505859375,
-0.01531982421875,
-0.015472412109375,
-0.0190277099609375,
-0.0033664703369140625,
0.0408935546875,
0.00749969482421875,
0.0166168212890625,
-0.01317596435546875,
-0.0133209228515625,
0.0458984375,
-0.0250244140625,
0.0182647705078125,
-0.0083465576171875,
-0.0291290283203125,
0.025909423828125,
0.0165557861328125,
-0.022125244140625,
0.0119171142578125,
0.035491943359375,
-0.00957489013671875,
-0.04315185546875,
0.00533294677734375,
-0.017791748046875,
-0.023345947265625,
0.0069732666015625,
-0.0257720947265625,
-0.0005702972412109375,
-0.015472412109375,
0.030914306640625,
-0.01039886474609375,
-0.00009465217590332031,
-0.0218353271484375,
-0.00388336181640625,
0.00922393798828125,
0.0286865234375,
0.002197265625,
0.006778717041015625,
-0.01430511474609375,
0.041046142578125,
0.002887725830078125,
-0.01123046875,
0.040496826171875,
-0.0244598388671875,
-0.0216827392578125,
-0.0052032470703125,
0.0377197265625,
0.009490966796875,
-0.01161956787109375,
0.0021343231201171875,
-0.0073394775390625,
0.0175628662109375,
-0.03021240234375,
0.0021877288818359375,
-0.010101318359375,
-0.031829833984375,
-0.020111083984375,
0.0311279296875,
-0.001850128173828125,
0.00977325439453125,
-0.0360107421875,
-0.0005846023559570312,
-0.01335906982421875,
0.01873779296875,
0.032135009765625,
-0.018768310546875,
0.01258087158203125,
-0.006633758544921875,
-0.0111846923828125,
-0.0318603515625,
-0.0261688232421875,
-0.0144500732421875,
0.00434112548828125,
-0.0251922607421875,
0.01152801513671875,
0.003658294677734375,
-0.00229644775390625,
-0.027740478515625,
0.0213775634765625,
-0.0401611328125,
0.01342010498046875,
0.0225677490234375,
0.031494140625,
-0.0187225341796875,
-0.0092620849609375,
0.004375457763671875,
0.007137298583984375,
-0.0032062530517578125,
0.0226593017578125,
-0.0302276611328125,
-0.002384185791015625,
-0.064453125,
0.005245208740234375,
0.01117706298828125,
-0.00897979736328125,
0.0179443359375,
0.00447845458984375,
0.035308837890625,
-0.00888824462890625,
0.012451171875,
0.024017333984375,
-0.005535125732421875,
0.022369384765625,
-0.0171966552734375,
-0.03643798828125,
-0.014739990234375,
-0.0005326271057128906,
0.01629638671875,
0.01294708251953125,
-0.0165557861328125,
-0.047760009765625,
0.007244110107421875,
-0.00679779052734375,
0.03497314453125,
0.0141448974609375,
0.0211334228515625,
0.00908660888671875,
-0.03179931640625,
-0.0216064453125,
-0.00193023681640625,
-0.00623321533203125,
-0.0011453628540039062,
-0.006412506103515625,
-0.0036983489990234375,
-0.01363372802734375,
-0.003948211669921875,
0.0044403076171875,
0.0110321044921875,
0.034698486328125,
0.01399993896484375,
-0.01019287109375,
0.026885986328125,
0.0035343170166015625,
-0.029296875,
0.01407623291015625,
0.040191650390625,
-0.0135650634765625,
0.04339599609375,
-0.01514434814453125,
-0.007381439208984375,
0.006587982177734375,
-0.0168609619140625,
-0.0153656005859375,
-0.0260467529296875,
-0.0206451416015625,
0.00916290283203125,
-0.032318115234375,
0.02850341796875,
0.00963592529296875,
-0.001087188720703125,
0.011932373046875,
-0.01171112060546875,
-0.0168304443359375,
-0.003948211669921875,
-0.01611328125,
-0.007472991943359375,
0.0171356201171875,
-0.005016326904296875,
-0.0019817352294921875,
-0.01525115966796875,
0.0025539398193359375,
0.01904296875,
0.006168365478515625,
0.0146942138671875,
0.0098419189453125,
-0.0176849365234375,
0.030426025390625,
0.018402099609375,
-0.0270233154296875,
0.00830841064453125,
-0.009674072265625,
0.0220184326171875,
0.0036563873291015625,
0.0145416259765625,
-0.0113525390625,
-0.00460052490234375,
0.01171112060546875,
0.040496826171875,
0.047576904296875,
-0.01457977294921875,
-0.0166778564453125,
-0.01505279541015625,
0.00444793701171875,
0.024261474609375,
-0.01580810546875,
0.0287933349609375,
-0.037384033203125,
-0.005306243896484375,
0.0210418701171875,
-0.00754547119140625,
0.025634765625,
-0.018402099609375,
0.0100555419921875,
-0.00426483154296875,
-0.0036487579345703125,
-0.0018053054809570312,
0.0445556640625,
-0.0010519027709960938,
0.005901336669921875,
0.03076171875,
-0.048980712890625,
0.006732940673828125,
0.01262664794921875,
0.006473541259765625,
-0.0146026611328125,
-0.00585174560546875,
-0.02984619140625,
0.03009033203125,
0.047454833984375,
-0.0264892578125,
0.00768280029296875,
-0.02496337890625,
0.0216064453125,
0.00962066650390625,
0.00971221923828125,
0.0034732818603515625,
-0.04876708984375,
0.0142669677734375,
-0.07427978515625,
0.0158538818359375,
-0.01507568359375,
-0.0012989044189453125,
-0.0303802490234375,
0.006557464599609375,
-0.0165252685546875,
0.01430511474609375,
-0.01995849609375,
0.004451751708984375,
0.005786895751953125,
-0.002048492431640625,
-0.0022430419921875,
-0.00876617431640625,
-0.0026493072509765625,
0.01056671142578125,
0.0283050537109375,
-0.01326751708984375,
0.0037479400634765625,
0.026031494140625,
-0.0015001296997070312,
0.00473785400390625,
0.0027942657470703125,
-0.024627685546875,
0.0279083251953125,
0.01499176025390625,
-0.0123748779296875,
0.01239013671875,
0.0121612548828125,
-0.036895751953125,
0.00389862060546875,
-0.0289306640625,
-0.005859375,
-0.0037288665771484375,
-0.003467559814453125,
-0.0305328369140625,
0.00406646728515625,
-0.0013380050659179688,
-0.0040435791015625,
-0.00563812255859375,
0.008544921875,
0.022003173828125,
0.0391845703125,
0.023406982421875,
-0.0206146240234375,
-0.025421142578125,
0.003204345703125,
-0.00804901123046875,
0.006557464599609375,
-0.02392578125,
-0.0181427001953125,
-0.007503509521484375,
-0.00681304931640625,
-0.0107879638671875,
-0.00542449951171875,
0.003997802734375,
-0.006984710693359375,
0.0024089813232421875,
0.0268096923828125,
0.03961181640625,
-0.037200927734375,
0.01035308837890625,
-0.0182647705078125,
0.022125244140625,
0.0038166046142578125,
-0.01326751708984375,
0.0030193328857421875,
-0.0267181396484375,
0.006744384765625,
0.0023059844970703125,
0.016082763671875,
-0.0210113525390625,
-0.001300811767578125,
-0.004268646240234375,
0.002166748046875,
0.004032135009765625,
-0.00807952880859375,
0.004886627197265625,
0.0006279945373535156,
-0.0229644775390625,
-0.01216888427734375,
0.019775390625,
0.0233306884765625,
0.018280029296875,
0.01666259765625,
-0.030029296875,
0.0148162841796875,
-0.00510406494140625,
0.01078033447265625,
-0.0139312744140625,
0.01641845703125,
-0.0227813720703125,
-0.01273345947265625,
-0.0247039794921875,
-0.0218353271484375,
0.01192474365234375,
-0.017608642578125,
-0.0015230178833007812,
0.00925445556640625,
-0.042633056640625,
-0.023590087890625,
-0.06805419921875,
0.01934814453125,
0.00850677490234375,
0.01456451416015625,
0.00467681884765625,
0.0036067962646484375,
0.00020873546600341797,
0.01092529296875,
-0.00701141357421875,
0.042144775390625,
-0.036102294921875,
-0.0316162109375,
-0.001434326171875,
0.012176513671875,
-0.0169219970703125,
0.00348663330078125,
0.0142059326171875,
-0.0021839141845703125,
-0.0210418701171875,
0.0303497314453125,
-0.002361297607421875,
-0.0140838623046875,
0.0038242340087890625,
-0.0192108154296875,
0.023101806640625,
-0.029327392578125,
0.01348114013671875,
-0.0355224609375,
-0.0247955322265625,
0.021148681640625,
-0.0057220458984375,
-0.0010004043579101562,
-0.0177459716796875,
0.0225372314453125,
0.018035888671875,
0.037841796875,
0.0277099609375,
-0.024017333984375,
-0.0118865966796875,
0.01413726806640625,
0.022552490234375,
-0.005367279052734375,
0.01995849609375,
-0.02813720703125,
0.0132293701171875,
0.007373809814453125,
0.0035076141357421875,
0.034210205078125,
0.004047393798828125,
-0.0258331298828125,
-0.004974365234375,
-0.0174102783203125,
0.0018367767333984375,
0.025054931640625,
0.01206207275390625,
-0.0019273757934570312,
-0.034088134765625,
0.0199737548828125,
-0.022796630859375,
-0.0022907257080078125,
-0.008331298828125,
0.0160675048828125,
0.0010251998901367188,
-0.052490234375,
0.0102996826171875,
0.0208587646484375,
0.0191650390625,
-0.005512237548828125,
-0.0196990966796875,
-0.0293121337890625,
0.0032863616943359375,
-0.01438140869140625,
0.0164794921875,
-0.004077911376953125,
0.0003211498260498047,
-0.0128326416015625,
-0.01012420654296875,
-0.003383636474609375,
-0.020965576171875,
0.0245819091796875,
0.040924072265625,
-0.0186309814453125,
0.01702880859375,
-0.0029449462890625,
-0.011383056640625,
-0.01511383056640625,
-0.0070953369140625,
0.022003173828125,
0.005596160888671875,
0.051025390625,
-0.0274200439453125,
-0.029998779296875,
-0.02099609375,
-0.0014238357543945312,
0.0290985107421875,
0.00656890869140625,
-0.0212249755859375,
0.0243682861328125,
0.0195465087890625,
0.02117919921875,
-0.008392333984375,
0.0094757080078125,
0.0219268798828125,
-0.00838470458984375,
-0.007495880126953125,
-0.01491546630859375,
-0.016143798828125,
-0.00013709068298339844,
-0.0157470703125,
0.01715087890625,
-0.0003323554992675781,
0.0009312629699707031,
0.003917694091796875,
0.002796173095703125,
0.01062774658203125,
-0.0126190185546875,
0.021484375,
-0.01442718505859375,
-0.010345458984375,
0.0035572052001953125,
-0.06658935546875,
0.032562255859375,
0.020233154296875,
0.03875732421875,
0.005764007568359375,
-0.005401611328125,
-0.01136016845703125,
0.01337432861328125,
-0.0148162841796875,
-0.000171661376953125,
-0.025482177734375,
-0.01715087890625,
0.0019741058349609375,
-0.00267791748046875,
-0.0293121337890625,
0.021636962890625,
-0.003902435302734375,
-0.0016164779663085938,
-0.009765625,
0.0230560302734375,
-0.0027332305908203125,
0.00977325439453125,
0.0018758773803710938,
0.006786346435546875,
0.0008530616760253906,
0.004688262939453125,
-0.01123809814453125,
0.028167724609375,
0.00759124755859375,
0.022125244140625,
0.029022216796875,
0.01303863525390625,
0.0075836181640625,
-0.020751953125,
-0.042572021484375,
-0.0177764892578125,
0.0253753662109375,
0.00904083251953125,
0.0177459716796875,
0.00653839111328125,
0.0157928466796875,
-0.00463104248046875,
-0.014404296875,
0.0008783340454101562,
0.0240478515625,
-0.010589599609375,
0.000476837158203125,
0.003467559814453125,
0.00881195068359375,
-0.0026149749755859375,
0.036956787109375,
-0.0509033203125,
0.03387451171875,
0.0026683807373046875,
-0.01264190673828125,
0.0008883476257324219,
0.0174102783203125,
-0.00014328956604003906,
-0.0229949951171875,
0.03363037109375,
-0.0187530517578125,
-0.033966064453125,
-0.01371002197265625,
0.013336181640625,
-0.0025386810302734375,
0.0202484130859375,
0.0382080078125,
-0.0043182373046875,
-0.0007958412170410156,
0.0140380859375,
-0.02239990234375,
-0.0012140274047851562,
0.007843017578125,
0.01166534423828125,
0.0121307373046875,
-0.0213165283203125,
0.00548553466796875,
0.00769805908203125,
0.0036487579345703125,
-0.0078887939453125,
-0.018798828125,
0.0130615234375,
-0.01296234130859375,
0.009124755859375,
0.01511383056640625,
0.03369140625,
-0.0193634033203125,
0.047027587890625,
-0.0247344970703125,
-0.0226287841796875,
0.0137481689453125,
0.0059356689453125,
-0.00655364990234375,
0.0239715576171875,
-0.02520751953125,
0.00713348388671875,
-0.0032863616943359375,
-0.00392913818359375,
-0.01125335693359375,
-0.01334381103515625,
0.0292510986328125,
-0.007671356201171875,
0.012451171875,
-0.0190582275390625,
0.032684326171875,
-0.01556396484375,
-0.0224151611328125,
0.003490447998046875,
-0.0130767822265625,
-0.001697540283203125,
-0.0166473388671875,
0.006061553955078125,
-0.010498046875,
0.01654052734375,
-0.01361083984375,
-0.004642486572265625,
-0.024322509765625,
-0.018524169921875,
0.0290985107421875,
-0.01007843017578125,
-0.03558349609375,
0.0035228729248046875,
0.007266998291015625,
0.00201416015625,
0.0004134178161621094,
0.045196533203125,
-0.01325225830078125,
0.0322265625,
-0.0004508495330810547,
0.010650634765625,
0.019256591796875,
-0.004993438720703125,
0.021514892578125,
-0.0298004150390625,
0.0308380126953125,
-0.003993988037109375,
-0.01297760009765625,
-0.0288238525390625,
-0.02301025390625,
0.0036182403564453125,
0.0114898681640625,
-0.010498046875,
-0.02386474609375,
-0.0220184326171875,
-0.004974365234375,
0.0306396484375,
-0.0024776458740234375,
-0.01033782958984375,
0.0166778564453125,
-0.01146697998046875,
0.040802001953125,
0.032867431640625,
-0.00876617431640625,
-0.021759033203125,
-0.0014219284057617188,
0.026336669921875,
0.026824951171875,
0.014984130859375,
-0.03656005859375,
0.0117340087890625,
-0.0218048095703125,
-0.0166473388671875,
0.0491943359375,
-0.02655029296875,
-0.0307159423828125,
-0.01313018798828125,
-0.00768280029296875,
-0.0258331298828125,
-0.0224151611328125,
0.01535797119140625,
-0.0394287109375,
-0.0062408447265625,
-0.009185791015625,
-0.037689208984375,
-0.0070648193359375,
0.01491546630859375,
-0.00107574462890625,
-0.0016889572143554688,
0.016998291015625,
0.00432586669921875,
-0.04754638671875,
0.00415802001953125,
0.016357421875,
0.0096893310546875,
-0.011383056640625,
0.022796630859375,
0.0011320114135742188,
0.04278564453125,
0.0045166015625,
0.0229644775390625,
0.01372528076171875,
0.00868988037109375,
-0.018341064453125,
-0.0252227783203125,
0.0162353515625,
-0.0165863037109375,
0.00441741943359375,
-0.01007080078125,
-0.01751708984375,
0.002460479736328125,
0.00925445556640625,
-0.024383544921875,
0.014068603515625,
-0.006214141845703125,
-0.00893402099609375,
0.010345458984375,
0.0100555419921875,
0.0061492919921875,
0.01326751708984375,
0.004180908203125,
-0.030181884765625,
-0.01332855224609375,
-0.0423583984375,
0.02435302734375,
-0.0175018310546875,
-0.007205963134765625,
-0.0020198822021484375,
-0.002811431884765625,
-0.033111572265625,
-0.01080322265625,
-0.0023193359375,
0.009368896484375,
0.0023136138916015625,
0.00868988037109375,
0.036163330078125,
0.000995635986328125,
-0.021453857421875,
-0.006683349609375,
0.0023784637451171875,
0.0240020751953125,
0.0017347335815429688,
0.006885528564453125,
0.0146484375,
0.0082855224609375,
-0.038970947265625,
-0.006404876708984375,
-0.033050537109375,
0.0267333984375,
0.01264190673828125,
0.0155181884765625,
-0.0224151611328125,
-0.00345611572265625,
-0.01029205322265625,
-0.005130767822265625,
-0.02764892578125,
-0.00275421142578125,
0.0009393692016601562,
0.0185089111328125,
-0.01262664794921875,
0.0129547119140625,
-0.02960205078125,
0.006069183349609375,
-0.0160064697265625,
0.031646728515625,
0.0108642578125,
0.040496826171875,
-0.00972747802734375,
-0.0064544677734375,
-0.031402587890625,
0.02972412109375,
-0.0269012451171875,
-0.0260009765625,
0.0102386474609375,
0.0247955322265625,
-0.053375244140625,
0.016387939453125,
0.0238800048828125,
-0.038055419921875,
0.0362548828125,
-0.018035888671875,
0.0128936767578125,
0.0323486328125,
-0.00789642333984375,
-0.0034770965576171875,
0.0093231201171875,
0.0112762451171875,
-0.0087127685546875,
-0.01036834716796875,
0.035308837890625,
-0.0006594657897949219,
-0.00635528564453125,
0.005680084228515625,
-0.028289794921875,
0.025482177734375,
0.030914306640625,
0.018585205078125,
-0.0005397796630859375,
-0.007381439208984375,
0.0257720947265625,
0.029754638671875,
-0.0269927978515625,
0.0128021240234375,
0.0252532958984375,
-0.01264190673828125,
0.0219268798828125,
-0.00470733642578125,
-0.01039886474609375,
-0.0090789794921875,
-0.01013946533203125,
-0.0198822021484375,
0.0016117095947265625,
-0.040985107421875,
0.01605224609375,
-0.0079498291015625,
-0.01611328125,
0.0215301513671875,
0.017913818359375,
0.005146026611328125,
-0.02459716796875,
0.0166778564453125,
-0.026275634765625,
0.0200347900390625,
-0.00455474853515625,
-0.0204010009765625,
0.0074615478515625,
-0.0138702392578125,
-0.0263671875,
0.05029296875,
0.0063323974609375,
-0.0028514862060546875,
0.0007376670837402344,
0.0130767822265625,
0.00921630859375,
-0.0225372314453125,
0.0271453857421875,
0.0296173095703125,
0.0199127197265625,
-0.007640838623046875,
-0.02294921875,
0.0186004638671875,
0.01319122314453125,
-0.043670654296875,
0.005184173583984375,
-0.0034027099609375,
0.01131439208984375,
0.045501708984375,
-0.003147125244140625,
0.0251617431640625,
0.008026123046875,
0.004566192626953125,
-0.03497314453125,
0.000732421875,
-0.0161895751953125,
-0.005199432373046875,
-0.0130462646484375,
-0.023834228515625,
0.01128387451171875,
-0.006946563720703125,
0.0080718994140625,
-0.01221466064453125,
0.00038170814514160156,
-0.031402587890625,
0.00965118408203125,
0.00505828857421875,
0.0177459716796875,
-0.0036182403564453125,
0.03143310546875,
0.0298309326171875,
0.004405975341796875,
-0.0014524459838867188,
0.01546478271484375,
0.0242462158203125,
-0.0231475830078125,
0.01157379150390625,
-0.029541015625,
-0.021209716796875,
0.01934814453125,
-0.00518798828125,
-0.001819610595703125,
-0.0447998046875,
0.01009368896484375,
0.002429962158203125,
-0.0023651123046875,
0.0135498046875,
0.0328369140625,
0.01416778564453125,
0.01131439208984375,
-0.004451751708984375,
-0.0132293701171875,
0.002483367919921875,
-0.01178741455078125,
0.03619384765625,
0.0206146240234375,
-0.0037326812744140625,
-0.027374267578125,
-0.01389312744140625,
-0.00519561767578125,
-0.0088958740234375,
0.0257720947265625,
-0.034271240234375,
-0.01273345947265625,
-0.026123046875,
-0.036041259765625,
-0.0018301010131835938,
-0.00007706880569458008,
-0.0198974609375,
0.01406097412109375,
-0.0164642333984375,
-0.015899658203125,
-0.0006647109985351562,
0.012237548828125,
0.0052032470703125,
0.0009589195251464844,
-0.0265045166015625,
-0.01348876953125,
0.00035762786865234375,
-0.00344085693359375,
-0.01082611083984375,
-0.014190673828125,
0.0036411285400390625,
0.0265350341796875,
-0.0220947265625,
0.01751708984375,
0.0176849365234375,
-0.036468505859375,
-0.02978515625,
0.006420135498046875,
-0.01727294921875,
0.042755126953125,
-0.002574920654296875,
0.0217437744140625,
-0.01439666748046875,
-0.01367950439453125,
-0.017364501953125,
0.01169586181640625,
-0.0142822265625,
-0.002960205078125,
0.0098419189453125,
-0.0240020751953125,
-0.0003726482391357422,
-0.00200653076171875,
0.006244659423828125,
-0.030364990234375,
-0.005817413330078125,
-0.01474761962890625,
-0.01763916015625,
0.01239013671875,
-0.0010442733764648438,
-0.0287017822265625,
-0.0300750732421875,
0.018951416015625,
0.01154327392578125,
0.004642486572265625,
-0.01042938232421875,
-0.019439697265625,
-0.00939178466796875,
-0.005802154541015625,
0.00720977783203125,
-0.003833770751953125,
-0.00732421875,
-0.00922393798828125,
0.01434326171875,
0.0250396728515625,
0.00841522216796875,
0.0140380859375,
0.006748199462890625,
0.0010242462158203125,
0.004222869873046875,
0.0236663818359375,
0.0137786865234375,
0.023223876953125,
0.0206146240234375,
0.0037841796875,
0.0083160400390625,
0.01407623291015625,
-0.0304412841796875,
-0.004634857177734375,
0.04150390625,
-0.00704193115234375,
-0.04052734375,
0.031463623046875,
0.01207733154296875,
-0.03240966796875,
-0.0026607513427734375,
0.0179901123046875,
0.047027587890625,
0.00713348388671875,
-0.0065765380859375,
-0.0146026611328125,
0.0606689453125,
-0.0209808349609375,
0.0248870849609375,
0.046600341796875,
-0.0015468597412109375,
-0.0010251998901367188,
-0.00566864013671875,
-0.01214599609375,
0.0209503173828125,
-0.006603240966796875,
0.034515380859375,
-0.027618408203125,
-0.014251708984375,
-0.023284912109375,
0.01483154296875,
0.0213470458984375,
0.0181427001953125,
-0.0093994140625,
0.02142333984375,
-0.021942138671875,
-0.00971221923828125,
0.005828857421875,
0.0127105712890625,
0.0160980224609375,
-0.00832366943359375,
-0.0207672119140625,
0.0214691162109375,
-0.01174163818359375,
-0.0155487060546875,
-0.006122589111328125,
0.0036945343017578125,
-0.004055023193359375,
0.004428863525390625,
-0.0189056396484375,
-0.023193359375,
0.0035152435302734375,
0.0204925537109375,
0.0106658935546875,
0.0263824462890625,
-0.0006079673767089844,
0.0177154541015625,
0.01070404052734375,
0.0090179443359375,
-0.033416748046875,
-0.006092071533203125,
0.0181884765625,
-0.0088958740234375,
0.0103302001953125,
0.006366729736328125,
0.0215606689453125,
0.0219879150390625,
0.0340576171875,
0.008209228515625,
-0.016571044921875,
0.01446533203125,
0.031829833984375,
0.033538818359375,
-0.00553131103515625,
0.03857421875,
-0.0189361572265625,
0.01200103759765625,
0.0186767578125,
-0.050079345703125,
-0.0032787322998046875,
0.0137176513671875,
-0.0083465576171875,
-0.01605224609375,
-0.002315521240234375,
-0.0126800537109375,
0.01409149169921875,
-0.01971435546875,
-0.0239410400390625,
-0.01068878173828125,
-0.0166168212890625,
-0.0241546630859375,
0.013763427734375,
0.037353515625,
0.00254058837890625,
0.006114959716796875,
-0.0235137939453125,
-0.01422119140625,
0.01451873779296875,
-0.0228729248046875,
-0.020263671875,
0.016815185546875,
-0.005474090576171875,
0.019012451171875,
0.027679443359375,
-0.00551605224609375,
0.0236663818359375,
0.04217529296875,
-0.003925323486328125,
0.0216827392578125,
0.015472412109375,
-0.01311492919921875,
-0.00946807861328125,
-0.01177215576171875,
0.0025844573974609375,
-0.031402587890625,
-0.0123748779296875,
-0.0042877197265625,
0.007762908935546875,
0.00841522216796875,
0.01345062255859375,
0.007228851318359375,
-0.01275634765625,
0.0032501220703125,
-0.0176849365234375,
0.00397491455078125,
-0.00424957275390625,
-0.00969696044921875,
-0.005527496337890625,
0.007068634033203125,
-0.005809783935546875,
0.01082611083984375,
-0.038787841796875,
0.035736083984375,
-0.00975799560546875,
0.0083160400390625,
0.004360198974609375,
-0.024993896484375,
-0.010711669921875,
0.01229095458984375,
-0.01953125,
0.02923583984375,
-0.0038471221923828125,
-0.006259918212890625,
0.016021728515625,
0.037750244140625,
0.044891357421875,
0.007965087890625,
-0.00341796875,
0.0289154052734375,
0.00356292724609375,
0.0042877197265625,
0.0077362060546875,
-0.008056640625,
0.02197265625,
0.052459716796875,
0.00787353515625,
0.0002651214599609375,
0.0121002197265625,
-0.0219879150390625,
0.003719329833984375,
0.0009388923645019531,
-0.0006318092346191406,
-0.0186767578125,
-0.022552490234375,
-0.00035953521728515625,
0.0038890838623046875,
-0.035980224609375,
0.0143890380859375,
0.01580810546875,
-0.00035452842712402344,
-0.02484130859375,
0.005741119384765625,
0.0115814208984375,
0.0154571533203125,
-0.03509521484375,
-0.0024871826171875,
0.0075225830078125,
-0.0128173828125,
-0.0185089111328125,
0.0018358230590820312,
0.00968170166015625,
0.055450439453125,
0.007526397705078125,
-0.004421234130859375,
-0.005298614501953125,
-0.01279449462890625,
0.0164642333984375,
-0.01312255859375,
0.0005240440368652344,
0.02313232421875,
-0.0118560791015625,
0.0180816650390625,
0.0222320556640625,
-0.0037822723388671875,
0.02471923828125,
-0.0103302001953125,
-0.005504608154296875,
0.004261016845703125,
-0.012054443359375,
-0.0010385513305664062,
-0.0008683204650878906,
-0.016204833984375,
0.03302001953125,
0.004581451416015625,
0.0267333984375,
-0.00449371337890625,
0.0007638931274414062,
0.031402587890625,
-0.01406097412109375,
-0.01727294921875,
0.0295257568359375,
0.022857666015625,
0.0211944580078125,
-0.0033397674560546875,
0.0148773193359375,
0.0019989013671875,
-0.038604736328125,
-0.0308837890625,
-0.055908203125,
-0.00400543212890625,
0.036651611328125,
0.002716064453125,
-0.0196380615234375,
0.00970458984375,
-0.0167694091796875,
-0.00565338134765625,
0.0413818359375,
0.00499725341796875,
0.02044677734375,
0.01085662841796875,
-0.021453857421875,
0.04925537109375,
-0.0202789306640625,
-0.0333251953125,
-0.0234527587890625,
0.013946533203125,
0.00734710693359375,
0.0034732818603515625,
-0.010284423828125,
0.009613037109375,
0.0017271041870117188,
0.0012845993041992188,
-0.0180511474609375,
0.01020050048828125,
0.0012569427490234375,
-0.038970947265625,
-0.00623321533203125,
-0.0019311904907226562,
-0.047210693359375,
-0.02130126953125,
-0.0038471221923828125,
-0.007389068603515625,
-0.0012006759643554688,
0.0154266357421875,
0.041046142578125,
-0.0026111602783203125,
0.03369140625,
-0.0029201507568359375,
-0.01544189453125,
0.00447845458984375,
-0.0133819580078125,
-0.006580352783203125,
-0.006649017333984375,
-0.0018491744995117188,
0.00004202127456665039,
-0.00811004638671875,
0.01428985595703125,
0.00643157958984375,
-0.02459716796875,
-0.0243072509765625,
-0.00714111328125,
0.007373809814453125,
0.0080108642578125,
0.017608642578125,
-0.001697540283203125,
-0.00020766258239746094,
0.0249786376953125,
0.003787994384765625,
-0.006877899169921875,
-0.006134033203125,
-0.0219573974609375,
0.007175445556640625,
-0.0052337646484375,
-0.0131072998046875,
0.054931640625,
-0.006946563720703125,
0.0281982421875,
-0.01198577880859375,
-0.0526123046875,
0.020599365234375,
-0.0124359130859375,
-0.013885498046875,
-0.007061004638671875,
-0.039093017578125,
-0.0121002197265625,
0.027252197265625,
0.0134124755859375,
-0.00018525123596191406,
0.010162353515625,
-0.01062774658203125,
0.01702880859375,
-0.003566741943359375,
0.004070281982421875,
-0.0012979507446289062,
0.01318359375,
-0.02264404296875,
0.0034580230712890625,
-0.035400390625,
0.01084136962890625,
-0.01311492919921875,
0.034271240234375,
-0.0301971435546875,
-0.001071929931640625,
0.01206207275390625,
0.004459381103515625,
-0.0177764892578125,
-0.054656982421875,
-0.005786895751953125,
-0.003448486328125,
-0.0032978057861328125,
0.0157012939453125,
0.0238189697265625,
0.02777099609375,
-0.0038661956787109375,
0.00946044921875,
0.0120697021484375,
-0.02020263671875,
-0.05889892578125,
-0.01401519775390625,
-0.02532958984375,
-0.00885772705078125,
-0.0036468505859375,
-0.00295257568359375,
0.0183868408203125,
-0.026519775390625,
0.0270843505859375,
-0.014862060546875,
0.0299835205078125,
0.0263214111328125,
0.0023899078369140625,
-0.0208587646484375,
0.012939453125,
0.046600341796875,
0.01497650146484375,
-0.0150146484375,
0.014068603515625,
-0.011138916015625,
0.055694580078125,
0.02593994140625,
0.01464080810546875,
0.014556884765625,
-0.027618408203125,
-0.007122039794921875,
-0.017852783203125,
0.005527496337890625,
-0.007312774658203125,
0.01103973388671875,
-0.0273284912109375,
0.030914306640625,
-0.01479339599609375,
0.01629638671875,
0.00853729248046875,
0.0014057159423828125,
-0.03680419921875,
0.00928497314453125,
0.0203399658203125,
-0.042633056640625,
-0.008026123046875,
-0.0197601318359375,
-0.03253173828125,
0.061492919921875,
0.01139068603515625,
0.031280517578125,
0.02740478515625,
0.0026187896728515625,
-0.004177093505859375,
-0.0212554931640625,
0.034637451171875,
-0.009552001953125,
0.0070648193359375,
0.005710601806640625,
0.0019855499267578125,
0.0037975311279296875,
-0.0180816650390625,
-0.0011386871337890625,
-0.01374053955078125,
0.00136566162109375,
-0.0223236083984375,
-0.0156402587890625,
-0.027862548828125,
0.032470703125,
-0.0245361328125,
-0.006465911865234375,
0.03839111328125,
-0.027618408203125,
-0.004573822021484375,
-0.016937255859375,
0.0213623046875,
-0.0156097412109375,
0.00972747802734375,
0.0171356201171875,
0.0126800537109375,
0.0158538818359375,
0.021209716796875,
-0.0123291015625,
0.0034122467041015625,
-0.010406494140625,
-0.0249481201171875,
-0.00560760498046875,
-0.003009796142578125,
0.0164947509765625,
-0.00782012939453125,
-0.00392913818359375,
-0.0285186767578125,
0.0022640228271484375,
0.007251739501953125,
0.015228271484375,
-0.04986572265625,
-0.028472900390625,
-0.0045928955078125,
-0.040679931640625,
0.01552581787109375,
-0.01739501953125,
0.00688934326171875,
-0.029876708984375,
-0.01123046875,
-0.027801513671875,
-0.041107177734375,
0.032684326171875,
0.01450347900390625,
0.00919342041015625,
-0.004974365234375,
0.01459503173828125,
0.0164947509765625,
-0.004261016845703125,
0.0237274169921875,
-0.022064208984375,
0.0085601806640625,
0.024444580078125,
0.0238037109375,
-0.0125274658203125,
0.007083892822265625,
-0.06396484375,
0.00525665283203125,
0.017608642578125,
-0.016845703125,
-0.007282257080078125,
0.048004150390625,
0.01369476318359375,
0.0289459228515625,
0.01152801513671875,
0.006786346435546875,
0.01200103759765625,
0.0036106109619140625,
0.01953125,
0.0261688232421875,
0.015625,
0.021881103515625,
-0.003925323486328125,
0.0252685546875,
0.00209808349609375,
0.00847625732421875,
0.0204925537109375,
-0.01186370849609375,
-0.00455474853515625,
-0.0212249755859375,
-0.0181121826171875,
-0.01611328125,
-0.0167694091796875,
-0.0223236083984375,
0.01515960693359375,
0.0007572174072265625,
0.00457000732421875,
0.01788330078125,
0.009918212890625,
0.0170440673828125,
-0.015625,
-0.00982666015625,
-0.017486572265625,
-0.007579803466796875,
0.0247955322265625,
0.00635528564453125,
0.006847381591796875,
-0.00534820556640625,
0.02142333984375,
0.0035991668701171875,
-0.0146331787109375,
0.00647735595703125,
0.03411865234375,
0.020843505859375,
-0.0173492431640625,
-0.000823974609375,
0.0181427001953125,
0.017608642578125,
-0.0130462646484375,
-0.006969451904296875,
0.0087738037109375,
0.021209716796875,
-0.0162811279296875,
0.0020961761474609375,
-0.01045989990234375,
0.0178070068359375,
0.01239776611328125,
-0.005184173583984375,
0.00559234619140625,
-0.010406494140625,
0.00405120849609375,
0.04302978515625,
-0.016754150390625,
0.00760650634765625,
0.00812530517578125,
0.0279083251953125,
-0.0007767677307128906,
0.00754547119140625,
-0.054962158203125,
-0.0103759765625,
0.00676727294921875,
0.03033447265625,
-0.00803375244140625,
0.00838470458984375,
-0.0148773193359375,
-0.051177978515625,
0.0126495361328125,
0.00995635986328125,
-0.0017366409301757812,
-0.01338958740234375,
-0.0125885009765625,
-0.004955291748046875,
0.00493621826171875,
0.023101806640625,
-0.0018777847290039062,
0.01047515869140625,
0.05029296875,
-0.022216796875,
-0.0247802734375,
-0.0224151611328125,
0.006351470947265625,
0.042572021484375,
-0.0211181640625,
-0.0160980224609375,
-0.036834716796875,
-0.0010290145874023438,
-0.00919342041015625,
-0.00017142295837402344,
0.00434112548828125,
-0.00165557861328125,
0.0218658447265625,
0.0150146484375,
-0.00756072998046875,
0.0195770263671875,
0.0020599365234375,
-0.0303955078125,
-0.02032470703125,
0.033477783203125,
-0.032958984375,
-0.0024051666259765625,
0.0122833251953125,
0.001255035400390625,
-0.007038116455078125,
0.01219940185546875,
-0.00899505615234375,
0.01300048828125,
-0.01526641845703125,
-0.0188446044921875,
-0.015106201171875,
-0.007488250732421875,
-0.00846099853515625,
-0.01189422607421875,
-0.0120697021484375,
0.03045654296875,
0.0300750732421875,
0.0194091796875,
0.00859832763671875,
-0.007049560546875,
-0.020599365234375,
0.0201416015625,
-0.00760650634765625,
-0.0005917549133300781,
-0.00997161865234375,
0.01611328125,
-0.00881195068359375,
-0.0089111328125,
0.0076446533203125,
-0.0019445419311523438,
-0.0034198760986328125,
-0.0111083984375,
-0.0145263671875,
-0.025634765625,
0.00014829635620117188,
-0.00030875205993652344,
-0.01666259765625,
-0.00510406494140625,
-0.0227813720703125,
0.0036067962646484375,
0.0204315185546875,
0.0183563232421875,
-0.00218963623046875,
-0.01904296875,
0.004302978515625,
0.0187835693359375,
0.01110076904296875,
0.0181884765625,
0.004241943359375,
0.029052734375,
-0.018524169921875,
-0.00394439697265625,
0.00975799560546875,
-0.0211639404296875,
-0.01187896728515625,
0.017913818359375,
-0.0010328292846679688,
0.035308837890625,
-0.011749267578125,
0.00850677490234375,
-0.0135955810546875,
0.00885772705078125,
0.007068634033203125,
-0.00516510009765625,
-0.003997802734375,
0.004791259765625,
0.0025348663330078125,
0.00970458984375,
-0.04315185546875,
0.00791168212890625,
-0.0036411285400390625,
-0.01898193359375,
-0.01386260986328125,
0.0230712890625,
0.0196380615234375,
-0.004611968994140625,
0.00545501708984375,
-0.007343292236328125,
0.0160369873046875,
-0.0028133392333984375,
-0.0253448486328125,
-0.013824462890625,
0.041229248046875,
-0.0198822021484375,
0.0027103424072265625,
-0.0004534721374511719,
-0.01715087890625,
0.01070404052734375,
0.0214996337890625,
0.0107574462890625,
-0.0137176513671875,
0.00018608570098876953,
-0.023406982421875,
0.0131683349609375,
0.0061187744140625,
-0.00879669189453125,
0.033538818359375,
-0.007297515869140625,
0.005855560302734375,
0.0004191398620605469,
-0.00531768798828125,
-0.003200531005859375,
-0.0291290283203125,
-0.02716064453125,
-0.0159149169921875,
-0.017242431640625,
-0.0396728515625,
0.01454925537109375,
-0.014007568359375,
0.0233612060546875,
-0.023590087890625,
-0.030517578125,
0.04632568359375,
-0.0283966064453125,
0.00731658935546875,
-0.013092041015625,
0.004413604736328125,
0.0013132095336914062,
-0.0202484130859375,
-0.016357421875,
0.01473236083984375,
0.0003654956817626953,
-0.0021419525146484375,
0.0235595703125,
-0.01389312744140625,
-0.0026531219482421875,
0.0261993408203125,
0.024139404296875,
0.00585174560546875,
0.01221466064453125,
0.005615234375,
0.0156402587890625,
0.00577545166015625,
0.0171661376953125,
0.00091552734375,
-0.0033435821533203125,
-0.017120361328125,
-0.0104522705078125,
0.025787353515625,
-0.00656890869140625,
0.0075836181640625,
-0.01104736328125,
0.01824951171875,
-0.0102996826171875,
-0.021484375,
0.00405120849609375,
-0.007373809814453125,
0.016387939453125,
-0.018798828125,
-0.0083160400390625,
0.036529541015625,
-0.020050048828125,
0.033172607421875,
-0.0019779205322265625,
0.01229095458984375,
-0.0279388427734375,
0.0019893646240234375,
-0.0210723876953125,
0.006317138671875,
-0.03045654296875,
0.01959228515625,
-0.00682830810546875,
-0.0159454345703125,
0.023773193359375,
-0.0005774497985839844,
0.00012290477752685547,
0.000050127506256103516,
0.0012454986572265625,
-0.0282440185546875,
-0.0024242401123046875,
-0.03607177734375,
-0.0128326416015625,
-0.03887939453125,
0.0209503173828125,
-0.011688232421875,
0.0263671875,
-0.0280609130859375,
-0.039794921875,
-0.0167694091796875,
-0.00400543212890625,
-0.006061553955078125,
0.015777587890625,
-0.01261138916015625,
-0.01873779296875,
-0.03448486328125,
0.002567291259765625,
-0.011383056640625,
-0.0286865234375,
-0.0135955810546875,
0.0382080078125,
0.0002663135528564453,
-0.0138702392578125,
-0.007587432861328125,
-0.0220184326171875,
0.01235198974609375,
-0.0146484375,
-0.00460052490234375,
0.053619384765625,
-0.00003141164779663086,
-0.007373809814453125,
0.0025348663330078125,
0.0243988037109375,
0.00537109375,
0.04461669921875,
0.007781982421875,
0.0007905960083007812,
-0.0261993408203125,
-0.0305633544921875,
0.0065765380859375,
0.015625,
0.012664794921875,
0.0124359130859375,
-0.010711669921875,
-0.0276031494140625,
-0.004917144775390625,
-0.022918701171875,
-0.0007371902465820312,
0.03302001953125,
0.048675537109375,
-0.0160675048828125,
0.009033203125,
0.008331298828125,
-0.00438690185546875,
-0.032012939453125,
0.01413726806640625,
-0.0278472900390625,
0.004180908203125,
0.00135040283203125,
0.002716064453125,
0.0352783203125,
0.001613616943359375,
0.00142669677734375,
-0.02191162109375,
-0.040435791015625,
0.00457763671875,
-0.028656005859375,
0.0299224853515625,
0.04058837890625,
-0.012359619140625,
-0.012115478515625,
-0.002262115478515625,
0.0029430389404296875,
-0.0231475830078125,
0.0220794677734375,
-0.01165008544921875,
-0.0323486328125,
0.01496124267578125,
-0.00466156005859375,
-0.012847900390625,
0.0007843971252441406,
-0.0118255615234375,
-0.015960693359375,
-0.015869140625,
0.0080718994140625,
0.004604339599609375,
-0.0112762451171875,
0.0106353759765625,
0.00772857666015625,
0.009124755859375,
-0.0122528076171875,
-0.01531982421875,
-0.00690460205078125,
0.0082550048828125,
0.03253173828125,
0.031646728515625,
-0.0169525146484375,
-0.010528564453125,
-0.0172882080078125,
0.00001239776611328125,
0.01427459716796875,
-0.0116119384765625,
0.016357421875,
-0.0224761962890625,
-0.0175018310546875,
0.004665374755859375,
0.0016984939575195312,
0.0247344970703125,
0.006439208984375,
-0.01523590087890625,
0.051666259765625,
0.0268707275390625,
0.03607177734375,
0.003360748291015625,
-0.03692626953125,
0.00013685226440429688,
-0.004352569580078125,
0.0004558563232421875,
-0.00867462158203125,
-0.0221405029296875,
0.01142120361328125,
-0.0002675056457519531,
-0.0155792236328125,
0.004207611083984375,
-0.003192901611328125,
0.0299072265625,
0.01502227783203125,
0.0033721923828125,
-0.00693511962890625,
0.0194549560546875,
-0.0596923828125,
0.001312255859375,
0.0126800537109375,
-0.0255584716796875,
0.021759033203125,
-0.0065765380859375,
-0.0423583984375,
0.002803802490234375,
0.0162200927734375,
0.006591796875,
0.017120361328125,
-0.006378173828125,
0.0130615234375,
0.036712646484375,
-0.038299560546875,
0.0189056396484375,
-0.0159759521484375,
0.004650115966796875,
0.0020809173583984375,
0.0228118896484375,
-0.012420654296875,
-0.0233001708984375,
0.0096435546875,
-0.0017566680908203125,
-0.0088958740234375,
-0.0134124755859375,
0.025726318359375,
-0.03460693359375,
0.0269622802734375,
0.00698089599609375,
0.00978851318359375,
-0.03533935546875,
0.0150604248046875,
-0.0106201171875,
0.034271240234375,
-0.0291900634765625,
-0.024749755859375,
-0.0095977783203125,
0.033905029296875,
-0.009033203125,
-0.003940582275390625,
0.04180908203125,
-0.01250457763671875,
-0.010223388671875,
0.0050506591796875,
-0.00794219970703125,
-0.005840301513671875,
0.0149993896484375,
-0.0008225440979003906,
-0.0186309814453125,
0.0004527568817138672,
-0.01245880126953125,
0.01245880126953125,
0.01329803466796875,
-0.046539306640625,
0.00650787353515625,
0.0048065185546875,
0.0171051025390625,
0.0330810546875,
-0.017608642578125,
-0.0275726318359375,
-0.04168701171875,
0.00243377685546875,
0.005649566650390625,
0.038421630859375,
0.01560211181640625,
0.007251739501953125,
0.0003399848937988281,
-0.023193359375,
0.04132080078125,
-0.0269927978515625,
-0.0131683349609375,
0.0283660888671875,
0.006671905517578125,
0.0037593841552734375,
-0.005908966064453125,
-0.05487060546875,
-0.004947662353515625,
0.035400390625,
0.01544189453125,
0.0011472702026367188,
-0.0275421142578125,
0.003936767578125,
0.0006899833679199219,
0.006694793701171875,
-0.0155181884765625,
-0.0013723373413085938,
-0.0181732177734375,
0.003650665283203125,
0.007598876953125,
-0.0221099853515625,
0.00295257568359375,
-0.03729248046875,
-0.051422119140625,
0.0102691650390625,
0.0192718505859375,
0.0126800537109375,
0.0010852813720703125,
0.02166748046875,
0.00534820556640625,
0.0252532958984375,
0.020599365234375,
-0.0036487579345703125,
0.00984954833984375,
0.01654052734375,
0.0264434814453125,
0.01284027099609375,
-0.0066375732421875,
0.00299835205078125,
0.01058197021484375,
-0.03509521484375,
-0.007320404052734375,
-0.03375244140625,
0.013580322265625,
-0.0005245208740234375,
-0.0133819580078125,
-0.002254486083984375,
0.0114898681640625,
0.004955291748046875,
-0.0211334228515625,
0.004940032958984375,
0.01320648193359375,
-0.0474853515625,
0.0100555419921875,
-0.019287109375,
-0.0140533447265625,
0.0144805908203125,
-0.0184173583984375,
-0.00850677490234375,
-0.0145111083984375,
0.0205078125,
-0.029296875,
0.01364898681640625,
0.0158233642578125,
-0.0308685302734375,
0.0273284912109375,
-0.014923095703125,
0.01206207275390625,
-0.0047454833984375,
0.004901885986328125,
0.031341552734375,
-0.0115814208984375,
0.00998687744140625,
0.0243988037109375,
0.0015058517456054688,
0.002986907958984375,
-0.0217742919921875,
0.0233306884765625,
0.009307861328125,
-0.01910400390625,
0.0309600830078125,
-0.005451202392578125,
0.0032634735107421875,
-0.0017175674438476562,
-0.007663726806640625,
-0.0006899833679199219,
0.008697509765625,
-0.01532745361328125,
-0.0022640228271484375,
0.01214599609375,
0.0017986297607421875,
0.00775909423828125
] |
ours_478
|
The cross product of the two vectors \( AB \) and \( AC \) is a vector perpendicular to the plane, with its magnitude equal to twice the area of the triangle. This cross product is a multiple of \([3,5,7]\), which means that it must have a magnitude of at least \(\sqrt{3^{2}+5^{2}+7^{2}}=\sqrt{83}\). Since we know that \([1,-2,1] \times [2,3,-3]=[3,5,7]\), the minimum actually possible (the two component vectors are clearly parallel to the plane). So the minimal area is \(\frac{\sqrt{83}}{2}\) and the answer is \(8302\).
\(\boxed{8302}\)
|
8302
|
{
"competition": "us_comps",
"dataset": "Ours",
"posts": null,
"source": "OMOFall18Solns.md"
}
|
Three non-collinear lattice points \( A, B, C \) lie on the plane \( 1+3x+5y+7z=0 \). The minimal possible area of triangle \( ABC \) can be expressed as \(\frac{\sqrt{m}}{n}\) where \( m, n \) are positive integers such that there does not exist a prime \( p \) dividing \( n \) with \( p^{2} \) dividing \( m \). Compute \( 100m+n \).
|
[
"/Mathematics/Geometry/CoordinateGeometry/AnalyticGeometry",
"/Mathematics/Geometry/CoordinateGeometry/Cartesian",
"/Mathematics/Geometry/CoordinateGeometry/CartesianCoordinateSystem",
"/Mathematics/Geometry/CoordinateGeometry/CartesianCoordinates",
"/Mathematics/Geometry/GeneralGeometry/EuclideanGeometry",
"/Mathematics/Geometry/GeneralGeometry/Geometry",
"/Mathematics/Geometry/GeneralGeometry/MensurationFormula",
"/Mathematics/Geometry/MultidimensionalGeometry",
"/Mathematics/Geometry/PlaneGeometry/Triangles",
"/Mathematics/Geometry/Points/LatticePoint",
"/Mathematics/NumberTheory/Integers/Integer",
"/Mathematics/NumberTheory/Integers/PositiveInteger",
"/Mathematics/NumberTheory/Integers/Z",
"/Mathematics/NumberTheory/Integers/Z-Plus"
] |
Bound the triangle’s area by the length of the plane’s normal vector, since the cross product of two side vectors equals a multiple of the normal.
|
[
0.0001894235610961914,
-0.033294677734375,
0.038421630859375,
0.020751953125,
0.0012531280517578125,
0.02093505859375,
-0.0016469955444335938,
-0.00432586669921875,
0.0229644775390625,
0.0118560791015625,
0.00970458984375,
0.0013227462768554688,
-0.0018243789672851562,
0.051544189453125,
-0.0038242340087890625,
-0.0021495819091796875,
-0.0032405853271484375,
0.006439208984375,
0.02227783203125,
-0.0016641616821289062,
-0.0138092041015625,
0.0032787322998046875,
-0.058135986328125,
0.031494140625,
-0.013763427734375,
0.002239227294921875,
-0.02337646484375,
-0.007472991943359375,
0.017242431640625,
-0.0209197998046875,
-0.033721923828125,
0.0031948089599609375,
0.010223388671875,
-0.019287109375,
0.0014705657958984375,
-0.0164031982421875,
0.0223388671875,
0.00525665283203125,
-0.01494598388671875,
-0.09210205078125,
-0.007476806640625,
0.01483154296875,
0.0109405517578125,
0.02093505859375,
0.034027099609375,
-0.023773193359375,
-0.0078582763671875,
0.0092620849609375,
-0.0089111328125,
-0.006191253662109375,
0.006679534912109375,
0.01551055908203125,
-0.009765625,
-0.01434326171875,
-0.0108642578125,
-0.0357666015625,
0.0013952255249023438,
0.006008148193359375,
-0.003566741943359375,
0.016510009765625,
-0.0095062255859375,
-0.01433563232421875,
-0.01751708984375,
0.005420684814453125,
0.0012903213500976562,
-0.011322021484375,
0.024505615234375,
-0.069580078125,
0.0131683349609375,
-0.031585693359375,
0.044677734375,
-0.0132598876953125,
-0.01030731201171875,
0.01332855224609375,
-0.008697509765625,
-0.00670623779296875,
0.000034868717193603516,
0.017974853515625,
-0.038482666015625,
0.01430511474609375,
0.0030059814453125,
0.0024700164794921875,
0.000743865966796875,
-0.0386962890625,
0.01197052001953125,
-0.030426025390625,
0.006069183349609375,
0.00041937828063964844,
0.05303955078125,
-0.0036602020263671875,
-0.0007147789001464844,
0.03643798828125,
-0.006244659423828125,
-0.0028438568115234375,
0.0013704299926757812,
0.01134490966796875,
0.014495849609375,
-0.0099029541015625,
-0.01343536376953125,
-0.001796722412109375,
0.00030350685119628906,
-0.011322021484375,
0.016448974609375,
-0.03228759765625,
-0.03607177734375,
-0.00623321533203125,
-0.0171356201171875,
0.036468505859375,
-0.0049591064453125,
0.0102691650390625,
0.005908966064453125,
-0.0038967132568359375,
0.00397491455078125,
-0.005279541015625,
0.0224151611328125,
-0.004276275634765625,
0.00978851318359375,
-0.00557708740234375,
-0.0029392242431640625,
-0.01212310791015625,
0.0057525634765625,
0.00928497314453125,
0.004070281982421875,
0.0129241943359375,
0.005611419677734375,
-0.035247802734375,
-0.004058837890625,
-0.0191802978515625,
-0.03948974609375,
0.001277923583984375,
-0.01000213623046875,
0.0003895759582519531,
-0.024322509765625,
-0.02789306640625,
-0.0232696533203125,
0.029998779296875,
-0.007434844970703125,
-0.01171112060546875,
-0.0037517547607421875,
-0.0302581787109375,
0.00839996337890625,
-0.0025348663330078125,
-0.0003647804260253906,
-0.03167724609375,
-0.00804901123046875,
-0.041595458984375,
-0.006618499755859375,
-0.031494140625,
0.0015430450439453125,
-0.005340576171875,
0.005367279052734375,
-0.0264129638671875,
0.025299072265625,
0.005374908447265625,
-0.00646209716796875,
-0.01432037353515625,
0.01247406005859375,
0.0165863037109375,
0.00531768798828125,
0.0209197998046875,
-0.01654052734375,
-0.007305145263671875,
0.002643585205078125,
0.055694580078125,
0.010162353515625,
-0.0111846923828125,
0.002349853515625,
0.02008056640625,
-0.02099609375,
0.0019044876098632812,
0.011199951171875,
0.0027904510498046875,
-0.00110626220703125,
-0.0201263427734375,
0.00299072265625,
-0.0169677734375,
-0.004123687744140625,
0.0156097412109375,
-0.005859375,
0.01580810546875,
-0.00003737211227416992,
0.0088043212890625,
0.0443115234375,
-0.0022945404052734375,
0.00589752197265625,
0.000820159912109375,
0.00629425048828125,
0.0035572052001953125,
0.015655517578125,
0.0214996337890625,
-0.0241851806640625,
-0.01244354248046875,
-0.008209228515625,
0.00818634033203125,
-0.002384185791015625,
-0.017364501953125,
-0.0233001708984375,
-0.0298614501953125,
0.00240325927734375,
0.0190277099609375,
0.004032135009765625,
0.0013704299926757812,
0.0220184326171875,
-0.0030460357666015625,
-0.00992584228515625,
0.0008854866027832031,
0.00817108154296875,
-0.001407623291015625,
0.00258636474609375,
0.00667572021484375,
-0.00749969482421875,
-0.0162200927734375,
-0.0002486705780029297,
-0.0048828125,
-0.0238494873046875,
0.0023479461669921875,
-0.01503753662109375,
-0.00021469593048095703,
-0.0005431175231933594,
-0.038909912109375,
0.0133056640625,
0.0003952980041503906,
-0.0019178390502929688,
-0.0020542144775390625,
-0.00855255126953125,
0.004016876220703125,
-0.0006623268127441406,
0.00250244140625,
-0.00015473365783691406,
-0.00919342041015625,
0.00556182861328125,
0.0039215087890625,
-0.01033782958984375,
0.007595062255859375,
-0.01373291015625,
-0.007396697998046875,
-0.0333251953125,
-0.01558685302734375,
0.0201263427734375,
0.0011768341064453125,
0.021575927734375,
-0.005878448486328125,
0.01177215576171875,
-0.02105712890625,
-0.0245208740234375,
-0.00281524658203125,
0.01446533203125,
-0.01166534423828125,
0.0201873779296875,
-0.0191650390625,
-0.0274200439453125,
0.0078582763671875,
-0.0010280609130859375,
-0.029388427734375,
-0.020050048828125,
-0.0014085769653320312,
0.00412750244140625,
0.000728607177734375,
-0.02349853515625,
-0.00965118408203125,
-0.00971221923828125,
-0.01904296875,
-0.00959014892578125,
-0.007244110107421875,
0.0009832382202148438,
0.01244354248046875,
0.004444122314453125,
-0.026702880859375,
0.008880615234375,
-0.009429931640625,
0.0187225341796875,
-0.0237884521484375,
-0.041778564453125,
-0.00012493133544921875,
0.049041748046875,
0.0000743865966796875,
-0.019561767578125,
0.00809478759765625,
0.0246124267578125,
0.0054473876953125,
-0.0026988983154296875,
0.0051116943359375,
0.007305145263671875,
0.008941650390625,
-0.0033130645751953125,
-0.032989501953125,
0.04071044921875,
-0.03546142578125,
-0.00283050537109375,
0.02105712890625,
0.006198883056640625,
-0.01751708984375,
0.0120086669921875,
-0.009918212890625,
-0.002841949462890625,
0.0181121826171875,
0.004604339599609375,
0.0259246826171875,
0.017486572265625,
-0.00421142578125,
0.01557159423828125,
-0.00023663043975830078,
-0.009765625,
0.01480865478515625,
0.007190704345703125,
0.017303466796875,
-0.0004413127899169922,
-0.001911163330078125,
0.00934600830078125,
0.01377105712890625,
0.01265716552734375,
0.00508880615234375,
0.0108642578125,
-0.01543426513671875,
-0.050445556640625,
-0.03900146484375,
-0.0168304443359375,
0.0070648193359375,
-0.009857177734375,
0.0213623046875,
0.0011472702026367188,
0.0239105224609375,
0.001445770263671875,
0.0191650390625,
0.0010433197021484375,
-0.0236663818359375,
-0.0010957717895507812,
-0.0033512115478515625,
-0.0283966064453125,
-0.00284576416015625,
0.007354736328125,
0.005489349365234375,
0.0034160614013671875,
-0.037322998046875,
-0.0013217926025390625,
0.0157012939453125,
-0.0019512176513671875,
0.0469970703125,
0.00551605224609375,
-0.0023326873779296875,
0.02557373046875,
-0.0068359375,
0.028350830078125,
-0.01611328125,
0.0030384063720703125,
0.044830322265625,
-0.01422119140625,
-0.004611968994140625,
0.00736236572265625,
-0.044219970703125,
0.010711669921875,
0.01708984375,
0.0184478759765625,
0.0093231201171875,
-0.00618743896484375,
-0.0019817352294921875,
0.035675048828125,
-0.002460479736328125,
0.01141357421875,
0.033966064453125,
0.00554656982421875,
-0.00727081298828125,
-0.0228118896484375,
-0.0030536651611328125,
-0.0166015625,
-0.018798828125,
0.0022449493408203125,
-0.00994110107421875,
-0.00579833984375,
-0.00970458984375,
-0.0171356201171875,
-0.0206756591796875,
0.0022144317626953125,
0.002208709716796875,
0.020721435546875,
-0.0022563934326171875,
-0.0224761962890625,
0.015838623046875,
0.005649566650390625,
-0.0101165771484375,
-0.001148223876953125,
0.002796173095703125,
0.00909423828125,
0.02294921875,
-0.020843505859375,
0.006465911865234375,
0.005878448486328125,
-0.03759765625,
-0.0178985595703125,
0.018890380859375,
-0.0233612060546875,
0.0285797119140625,
-0.004184722900390625,
-0.0177764892578125,
0.006557464599609375,
-0.053558349609375,
-0.01212310791015625,
0.017669677734375,
0.0204010009765625,
-0.0298309326171875,
-0.0221710205078125,
0.0015325546264648438,
0.01885986328125,
-0.040252685546875,
0.01556396484375,
-0.0146331787109375,
0.0008058547973632812,
0.01045989990234375,
-0.00991058349609375,
-0.007762908935546875,
0.0157928466796875,
0.0179901123046875,
0.00457000732421875,
0.00943756103515625,
-0.0157928466796875,
0.00604248046875,
0.00856781005859375,
-0.01210784912109375,
-0.0179290771484375,
0.0164642333984375,
0.0006246566772460938,
-0.0347900390625,
0.017486572265625,
-0.025970458984375,
0.007732391357421875,
0.036834716796875,
-0.0157928466796875,
0.0216827392578125,
-0.0164642333984375,
0.00782012939453125,
0.01050567626953125,
0.01155853271484375,
0.005603790283203125,
0.035430908203125,
-0.003875732421875,
0.0111236572265625,
0.045379638671875,
-0.005218505859375,
-0.01424407958984375,
0.0047149658203125,
-0.004695892333984375,
-0.0004935264587402344,
-0.0079345703125,
0.005558013916015625,
0.0294036865234375,
-0.005680084228515625,
0.0215301513671875,
0.01074981689453125,
0.036163330078125,
-0.01947021484375,
-0.00963592529296875,
-0.03680419921875,
-0.008331298828125,
-0.018707275390625,
-0.033172607421875,
0.012908935546875,
0.02923583984375,
0.019012451171875,
-0.0155487060546875,
-0.0293121337890625,
0.031005859375,
-0.0031375885009765625,
-0.033538818359375,
-0.00043487548828125,
0.016571044921875,
-0.004138946533203125,
-0.0189666748046875,
0.02130126953125,
-0.007694244384765625,
-0.01052093505859375,
-0.0172882080078125,
-0.016082763671875,
-0.01229095458984375,
-0.00040793418884277344,
-0.01386260986328125,
0.037567138671875,
0.0142974853515625,
0.01114654541015625,
-0.0265960693359375,
0.0124053955078125,
-0.006595611572265625,
0.021148681640625,
0.005535125732421875,
0.0298614501953125,
-0.01538848876953125,
0.0249786376953125,
0.01267242431640625,
-0.0029125213623046875,
0.034576416015625,
-0.0256500244140625,
-0.0035495758056640625,
0.018524169921875,
-0.0297698974609375,
-0.011810302734375,
-0.0066680908203125,
0.0095367431640625,
0.0160064697265625,
0.039459228515625,
-0.01390838623046875,
-0.01190185546875,
-0.006656646728515625,
-0.0185394287109375,
0.0024127960205078125,
-0.020416259765625,
-0.016326904296875,
0.00434112548828125,
0.0038547515869140625,
-0.003814697265625,
0.0099334716796875,
-0.001377105712890625,
0.007534027099609375,
0.02056884765625,
-0.0216827392578125,
-0.0302734375,
0.0083160400390625,
0.0190887451171875,
-0.005767822265625,
-0.003849029541015625,
0.017486572265625,
0.034454345703125,
-0.01505279541015625,
0.0270538330078125,
0.018951416015625,
0.0142822265625,
0.011260986328125,
0.036346435546875,
0.013519287109375,
0.00789642333984375,
-0.01050567626953125,
0.0025768280029296875,
0.01200103759765625,
-0.01074981689453125,
-0.0120086669921875,
0.004856109619140625,
-0.041290283203125,
0.028564453125,
-0.0145721435546875,
-0.0012111663818359375,
0.0272369384765625,
0.0161895751953125,
-0.01312255859375,
-0.01540374755859375,
0.0265045166015625,
-0.06671142578125,
0.00679779052734375,
-0.025115966796875,
0.0010852813720703125,
0.027618408203125,
0.0142669677734375,
0.02166748046875,
0.01284027099609375,
0.01224517822265625,
-0.024658203125,
0.0008387565612792969,
-0.05865478515625,
-0.00009608268737792969,
0.0113067626953125,
0.0108489990234375,
0.01433563232421875,
0.007564544677734375,
0.0237884521484375,
0.00373077392578125,
-0.00879669189453125,
-0.0037384033203125,
0.0185546875,
-0.0299072265625,
0.0027923583984375,
-0.044219970703125,
0.01091766357421875,
-0.0203399658203125,
0.0031108856201171875,
0.017333984375,
0.0006799697875976562,
-0.0050201416015625,
0.0197296142578125,
-0.03643798828125,
-0.06451416015625,
-0.0234375,
0.006359100341796875,
-0.036224365234375,
0.030364990234375,
0.0236968994140625,
-0.005146026611328125,
0.0196380615234375,
-0.0321044921875,
0.002536773681640625,
-0.0179595947265625,
0.005794525146484375,
0.01383209228515625,
0.0008592605590820312,
-0.0228729248046875,
0.0167999267578125,
0.01020050048828125,
0.038787841796875,
-0.00920867919921875,
0.0012674331665039062,
0.0027618408203125,
-0.0103607177734375,
0.02288818359375,
0.0009908676147460938,
0.01087188720703125,
0.0213470458984375,
-0.001682281494140625,
0.0494384765625,
-0.00665283203125,
0.005146026611328125,
-0.019775390625,
0.04156494140625,
0.01392364501953125,
0.01049041748046875,
-0.0149688720703125,
-0.01198577880859375,
-0.01442718505859375,
0.0227508544921875,
0.01441192626953125,
0.0235443115234375,
0.0011034011840820312,
0.02984619140625,
-0.003620147705078125,
0.01203155517578125,
-0.0296478271484375,
0.0069732666015625,
0.0013360977172851562,
0.0008549690246582031,
0.012481689453125,
-0.01038360595703125,
0.020843505859375,
-0.03509521484375,
-0.01090240478515625,
-0.0299530029296875,
-0.00968170166015625,
-0.00244903564453125,
0.0164642333984375,
-0.0002918243408203125,
-0.0176849365234375,
-0.033660888671875,
-0.0032825469970703125,
-0.01557159423828125,
-0.039886474609375,
-0.005756378173828125,
-0.012359619140625,
0.0118408203125,
0.0010461807250976562,
-0.038177490234375,
-0.0254364013671875,
-0.040008544921875,
-0.00795745849609375,
0.0263671875,
0.0251922607421875,
0.0214385986328125,
-0.04132080078125,
0.004100799560546875,
0.004146575927734375,
0.032928466796875,
-0.015472412109375,
-0.022705078125,
-0.043792724609375,
0.0227203369140625,
0.0195159912109375,
0.0005726814270019531,
-0.0082550048828125,
-0.01450347900390625,
-0.005962371826171875,
0.003360748291015625,
-0.003025054931640625,
0.0019931793212890625,
-0.007472991943359375,
-0.0096588134765625,
-0.003265380859375,
-0.0081329345703125,
-0.00885772705078125,
-0.0237579345703125,
-0.0164031982421875,
-0.006145477294921875,
0.0022869110107421875,
-0.023223876953125,
-0.0080718994140625,
0.0159454345703125,
0.0253448486328125,
-0.0091552734375,
0.00914764404296875,
0.0047149658203125,
0.01415252685546875,
0.00954437255859375,
-0.00959014892578125,
0.040008544921875,
0.0035610198974609375,
0.00397491455078125,
0.0005660057067871094,
0.01934814453125,
0.00732421875,
-0.006656646728515625,
-0.0513916015625,
0.032958984375,
-0.001129150390625,
-0.032135009765625,
-0.0006437301635742188,
-0.00667572021484375,
-0.003265380859375,
-0.0257720947265625,
0.017578125,
-0.0032062530517578125,
0.00325775146484375,
0.0080108642578125,
-0.0232696533203125,
-0.0069580078125,
-0.02227783203125,
-0.001049041748046875,
-0.0276641845703125,
0.002010345458984375,
-0.0231781005859375,
0.00270843505859375,
-0.04937744140625,
-0.0291595458984375,
-0.023223876953125,
-0.01401519775390625,
-0.0027675628662109375,
0.010345458984375,
0.0181121826171875,
-0.00411224365234375,
0.007244110107421875,
-0.01050567626953125,
-0.019073486328125,
-0.01233673095703125,
0.0110931396484375,
0.011016845703125,
0.0009431838989257812,
-0.034820556640625,
-0.0145416259765625,
-0.00803375244140625,
-0.01360321044921875,
-0.029083251953125,
0.0190277099609375,
0.0222015380859375,
-0.0172119140625,
-0.0244293212890625,
-0.00609588623046875,
-0.041107177734375,
-0.002719879150390625,
0.00911712646484375,
0.041656494140625,
-0.01314544677734375,
0.00952911376953125,
-0.0026493072509765625,
-0.01395416259765625,
0.0193328857421875,
0.01861572265625,
-0.01227569580078125,
-0.00960540771484375,
0.033233642578125,
0.0249481201171875,
-0.01045989990234375,
-0.00765228271484375,
-0.0211944580078125,
-0.034210205078125,
0.0148162841796875,
-0.006805419921875,
-0.00757598876953125,
0.00234222412109375,
-0.005268096923828125,
0.005603790283203125,
0.010467529296875,
0.020111083984375,
-0.006908416748046875,
-0.01145172119140625,
-0.005207061767578125,
-0.01580810546875,
0.0003113746643066406,
-0.0238037109375,
0.051055908203125,
0.00152587890625,
-0.014495849609375,
0.0141448974609375,
0.00353240966796875,
0.0279388427734375,
-0.0010929107666015625,
-0.0178680419921875,
-0.0121917724609375,
0.05499267578125,
-0.0016794204711914062,
0.01345062255859375,
-0.0086822509765625,
0.029205322265625,
0.0166168212890625,
-0.0299835205078125,
0.01059722900390625,
-0.01029205322265625,
-0.0159454345703125,
0.007442474365234375,
-0.00901031494140625,
0.024566650390625,
0.007801055908203125,
-0.0021648406982421875,
0.0288238525390625,
-0.00487518310546875,
-0.0312042236328125,
-0.01242828369140625,
0.0205230712890625,
0.01129150390625,
-0.004489898681640625,
-0.019744873046875,
-0.005435943603515625,
-0.004596710205078125,
0.03369140625,
0.01264190673828125,
-0.0035858154296875,
-0.0006480216979980469,
0.005016326904296875,
-0.012451171875,
0.0177459716796875,
0.0219573974609375,
-0.0110015869140625,
-0.01300048828125,
-0.01142120361328125,
0.0091094970703125,
-0.00244140625,
0.0118865966796875,
-0.01447296142578125,
0.0164947509765625,
0.019195556640625,
-0.0078887939453125,
0.04058837890625,
-0.0211334228515625,
-0.01467132568359375,
-0.02996826171875,
0.037200927734375,
0.01412200927734375,
-0.015869140625,
0.016876220703125,
-0.00705718994140625,
-0.0109405517578125,
-0.019195556640625,
-0.0171051025390625,
0.003482818603515625,
-0.0135650634765625,
-0.0011281967163085938,
-0.00600433349609375,
0.017364501953125,
0.019683837890625,
-0.008056640625,
-0.0012359619140625,
-0.00017964839935302734,
0.0225372314453125,
0.032867431640625,
0.048736572265625,
-0.00615692138671875,
0.010467529296875,
0.0156402587890625,
-0.0014066696166992188,
-0.0150299072265625,
-0.00250244140625,
0.0070953369140625,
-0.00211334228515625,
0.001941680908203125,
0.008270263671875,
0.002044677734375,
-0.00856781005859375,
0.0235137939453125,
0.01447296142578125,
-0.01348876953125,
0.0200042724609375,
-0.01375579833984375,
-0.019317626953125,
-0.0163421630859375,
-0.0010881423950195312,
-0.0166168212890625,
0.002788543701171875,
0.01078033447265625,
-0.01666259765625,
-0.01238250732421875,
0.0292510986328125,
-0.0161895751953125,
-0.006610870361328125,
0.00971221923828125,
0.033355712890625,
0.0244903564453125,
-0.0095367431640625,
0.00848388671875,
0.03546142578125,
-0.0139617919921875,
0.014007568359375,
-0.0030498504638671875,
-0.031707763671875,
0.028594970703125,
-0.01380157470703125,
-0.01373291015625,
0.01105499267578125,
0.015533447265625,
0.020660400390625,
-0.02655029296875,
0.00189208984375,
-0.0170135498046875,
-0.0013294219970703125,
-0.04058837890625,
0.040679931640625,
0.0013208389282226562,
-0.0186309814453125,
-0.041107177734375,
-0.005218505859375,
-0.0251617431640625,
0.000988006591796875,
-0.0224609375,
-0.005741119384765625,
0.03125,
0.006801605224609375,
0.005794525146484375,
-0.03277587890625,
-0.0009145736694335938,
0.0009946823120117188,
0.0357666015625,
-0.027099609375,
0.009521484375,
-0.0003542900085449219,
0.039398193359375,
-0.033782958984375,
-0.007106781005859375,
0.0185546875,
0.0037689208984375,
0.0072021484375,
-0.0335693359375,
-0.003284454345703125,
0.0097198486328125,
0.0015888214111328125,
-0.0164947509765625,
0.002033233642578125,
-0.029052734375,
-0.0032196044921875,
-0.0016345977783203125,
-0.032684326171875,
0.00981903076171875,
-0.011993408203125,
0.040008544921875,
-0.0056304931640625,
0.00641632080078125,
-0.02703857421875,
-0.004985809326171875,
-0.0390625,
-0.0380859375,
0.00685882568359375,
-0.025146484375,
-0.02801513671875,
0.00852203369140625,
0.031097412109375,
0.04058837890625,
0.01172637939453125,
-0.00957489013671875,
-0.030303955078125,
-0.00463104248046875,
-0.01369476318359375,
-0.00836944580078125,
-0.028106689453125,
-0.0187225341796875,
-0.01580810546875,
-0.01485443115234375,
0.022918701171875,
-0.01708984375,
0.03424072265625,
-0.00432586669921875,
-0.0167694091796875,
0.02874755859375,
0.0239105224609375,
0.039703369140625,
-0.00545501708984375,
0.002849578857421875,
0.0185394287109375,
-0.0094146728515625,
0.0213470458984375,
-0.00507354736328125,
0.037933349609375,
0.024017333984375,
0.009307861328125,
-0.042633056640625,
-0.02447509765625,
-0.046875,
-0.017730712890625,
0.01552581787109375,
-0.00844573974609375,
0.025787353515625,
0.03558349609375,
-0.002597808837890625,
-0.061492919921875,
-0.00527191162109375,
0.0126800537109375,
-0.01806640625,
-0.01214599609375,
-0.002559661865234375,
0.006683349609375,
-0.02325439453125,
0.003635406494140625,
-0.028533935546875,
0.019378662109375,
0.0198974609375,
-0.0013885498046875,
0.005519866943359375,
0.0059661865234375,
-0.00799560546875,
-0.024139404296875,
-0.04193115234375,
0.0028781890869140625,
-0.0241241455078125,
-0.03009033203125,
-0.0185089111328125,
0.01062774658203125,
-0.018463134765625,
0.04150390625,
-0.0374755859375,
0.0272369384765625,
0.025421142578125,
0.0161285400390625,
0.0091705322265625,
-0.004840850830078125,
0.01739501953125,
-0.0027599334716796875,
0.0141754150390625,
-0.048248291015625,
0.004749298095703125,
0.0128021240234375,
0.01390838623046875,
-0.03387451171875,
0.022705078125,
-0.0208892822265625,
-0.0240631103515625,
-0.044586181640625,
0.0068817138671875,
-0.0012636184692382812,
-0.037322998046875,
-0.01898193359375,
-0.0027561187744140625,
0.01541900634765625,
0.022705078125,
-0.005542755126953125,
-0.0212554931640625,
-0.005725860595703125,
-0.01715087890625,
0.00012242794036865234,
-0.039306640625,
-0.012237548828125,
0.00342559814453125,
0.01168060302734375,
-0.0003612041473388672,
-0.000988006591796875,
-0.00809478759765625,
0.0205841064453125,
-0.0116424560546875,
-0.02166748046875,
0.0005702972412109375,
0.010528564453125,
0.0159149169921875,
-0.03045654296875,
-0.02410888671875,
-0.01107025146484375,
0.009796142578125,
0.0015344619750976562,
0.0029582977294921875,
-0.0088348388671875,
0.0304718017578125,
-0.010345458984375,
-0.0343017578125,
0.0416259765625,
0.01020050048828125,
0.0031833648681640625,
-0.01554107666015625,
-0.027679443359375,
0.009521484375,
0.0215606689453125,
0.005893707275390625,
-0.04083251953125,
-0.0005397796630859375,
-0.0095062255859375,
0.057403564453125,
-0.0657958984375,
0.00722503662109375,
0.01096343994140625,
0.003650665283203125,
0.006885528564453125,
0.0155029296875,
-0.021636962890625,
-0.004611968994140625,
-0.0190277099609375,
0.01343536376953125,
-0.01422882080078125,
-0.00812530517578125,
-0.040069580078125,
-0.01495361328125,
0.0426025390625,
0.035400390625,
-0.011077880859375,
0.0084991455078125,
0.01134490966796875,
0.01168060302734375,
0.01361083984375,
0.0025386810302734375,
-0.0103759765625,
-0.005207061767578125,
0.037261962890625,
0.0020389556884765625,
0.02752685546875,
-0.01922607421875,
0.020660400390625,
-0.016204833984375,
0.0019445419311523438,
0.0301361083984375,
-0.0017824172973632812,
0.0214691162109375,
-0.00942230224609375,
-0.016510009765625,
0.01248931884765625,
-0.0029239654541015625,
0.01081085205078125,
-0.01209259033203125,
-0.001392364501953125,
0.038421630859375,
0.041229248046875,
0.0120849609375,
0.0035877227783203125,
-0.0245819091796875,
-0.01345062255859375,
-0.050811767578125,
0.0235137939453125,
-0.0217437744140625,
-0.017974853515625,
0.00516510009765625,
-0.01277923583984375,
0.0013685226440429688,
0.028045654296875,
-0.003009796142578125,
0.03253173828125,
-0.00934600830078125,
-0.0014476776123046875,
0.007045745849609375,
-0.00775146484375,
0.0019855499267578125,
0.0208282470703125,
-0.022979736328125,
0.007366180419921875,
0.0203857421875,
0.00006663799285888672,
-0.019927978515625,
0.048126220703125,
-0.0079803466796875,
-0.0011835098266601562,
0.00337982177734375,
-0.009368896484375,
-0.00714874267578125,
-0.0282745361328125,
-0.0208282470703125,
-0.042816162109375,
0.004299163818359375,
0.02545166015625,
-0.005706787109375,
-0.0372314453125,
0.037322998046875,
0.0082244873046875,
0.0146636962890625,
-0.0176849365234375,
0.00626373291015625,
-0.0163726806640625,
-0.0289459228515625,
0.006500244140625,
0.00785064697265625,
-0.0166015625,
-0.0250396728515625,
-0.0265655517578125,
0.00820159912109375,
-0.0152587890625,
-0.00627899169921875,
-0.00286102294921875,
0.0285186767578125,
-0.0458984375,
0.01247406005859375,
-0.01015472412109375,
-0.03558349609375,
0.017333984375,
0.00926971435546875,
-0.0027217864990234375,
0.018707275390625,
0.00867462158203125,
0.00714874267578125,
0.0218505859375,
-0.0110626220703125,
-0.0180816650390625,
-0.00185394287109375,
0.0167999267578125,
-0.02105712890625,
0.05804443359375,
0.0025386810302734375,
0.000003933906555175781,
-0.019256591796875,
-0.0282135009765625,
-0.014678955078125,
0.016326904296875,
-0.0062408447265625,
0.009979248046875,
-0.0013055801391601562,
0.01387786865234375,
0.02606201171875,
-0.02880859375,
0.01152801513671875,
-0.04150390625,
-0.02191162109375,
-0.0034389495849609375,
-0.0127716064453125,
-0.0296783447265625,
-0.0098114013671875,
0.00955963134765625,
0.0224761962890625,
-0.0012998580932617188,
0.0457763671875,
-0.0200347900390625,
-0.006496429443359375,
-0.0143280029296875,
-0.00445556640625,
-0.00591278076171875,
0.01739501953125,
0.009857177734375,
0.000919342041015625,
0.005985260009765625,
-0.0202789306640625,
-0.0103912353515625,
-0.031494140625,
-0.0079193115234375,
0.01922607421875,
0.02642822265625,
-0.0159149169921875,
0.006229400634765625,
-0.019287109375,
-0.02581787109375,
0.0203704833984375,
0.003742218017578125,
-0.00809478759765625,
0.01406097412109375,
0.03887939453125,
-0.004009246826171875,
0.059661865234375,
-0.01617431640625,
-0.01035308837890625,
-0.0194549560546875,
0.026458740234375,
0.0093536376953125,
-0.009735107421875,
-0.03228759765625,
0.024139404296875,
0.00960540771484375,
-0.01511383056640625,
0.048492431640625,
-0.03717041015625,
-0.0196685791015625,
-0.008941650390625,
0.0017414093017578125,
0.0093536376953125,
0.0082550048828125,
-0.00677490234375,
-0.01409149169921875,
-0.026641845703125,
-0.01763916015625,
-0.0033130645751953125,
0.039947509765625,
-0.004268646240234375,
-0.0021495819091796875,
-0.01364898681640625,
0.0020122528076171875,
0.053314208984375,
-0.047332763671875,
0.0128173828125,
-0.022430419921875,
0.01117706298828125,
0.0240478515625,
0.0287017822265625,
-0.023468017578125,
0.0018672943115234375,
0.00510406494140625,
-0.001926422119140625,
0.008270263671875,
0.0151519775390625,
0.0180816650390625,
-0.006458282470703125,
-0.0117950439453125,
-0.02166748046875,
-0.015106201171875,
-0.0303955078125,
-0.01493072509765625,
0.0196380615234375,
0.0282440185546875,
-0.0223541259765625,
-0.01107025146484375,
-0.006069183349609375,
-0.007404327392578125,
0.057708740234375,
-0.0005106925964355469,
0.0022068023681640625,
-0.01509857177734375,
0.005687713623046875,
-0.0030460357666015625,
0.050872802734375,
-0.0282745361328125,
-0.0184173583984375,
-0.01287841796875,
-0.004791259765625,
0.0145416259765625,
0.032684326171875,
-0.01209259033203125,
0.01163482666015625,
-0.00173187255859375,
0.0146026611328125,
-0.00588226318359375,
0.01261138916015625,
0.041778564453125,
-0.01611328125,
0.0022640228271484375,
0.01552581787109375,
0.01087188720703125,
-0.00101470947265625,
0.026519775390625,
-0.00281524658203125,
0.0394287109375,
-0.0245819091796875,
-0.0065460205078125,
-0.0007076263427734375,
-0.027252197265625,
-0.0139312744140625,
-0.0255584716796875,
0.009124755859375,
-0.000988006591796875,
-0.0004742145538330078,
0.0216522216796875,
-0.004138946533203125,
-0.038116455078125,
-0.023284912109375,
-0.0019550323486328125,
-0.0197906494140625,
-0.0116424560546875,
0.0291595458984375,
-0.0104522705078125,
-0.0033740997314453125,
-0.01849365234375,
0.00319671630859375,
0.0033130645751953125,
0.0216827392578125,
0.006103515625,
0.01025390625,
0.01206207275390625,
0.03314208984375,
-0.015899658203125,
0.01312255859375,
0.01525115966796875,
0.01558685302734375,
-0.01540374755859375,
0.01016998291015625,
0.0057830810546875,
-0.022369384765625,
0.0111541748046875,
0.005245208740234375,
-0.01096343994140625,
0.021575927734375,
-0.0204925537109375,
-0.0396728515625,
0.01544189453125,
0.0167694091796875,
0.0034580230712890625,
-0.0128021240234375,
0.0177764892578125,
-0.0537109375,
-0.0235748291015625,
0.004116058349609375,
0.0213165283203125,
0.0172576904296875,
-0.0177154541015625,
0.00455474853515625,
0.0026111602783203125,
-0.026580810546875,
-0.0030612945556640625,
0.00542449951171875,
0.0052032470703125,
-0.005443572998046875,
0.00374603271484375,
0.00025844573974609375,
-0.0159759521484375,
-0.0211944580078125,
0.007354736328125,
0.01108551025390625,
0.01959228515625,
-0.005443572998046875,
-0.01045989990234375,
-0.0208282470703125,
0.014556884765625,
0.00995635986328125,
-0.0030193328857421875,
-0.0054168701171875,
-0.0076141357421875,
-0.0155029296875,
0.0010538101196289062,
0.0209808349609375,
-0.0247039794921875,
0.0008530616760253906,
0.0106658935546875,
-0.016204833984375,
-0.0240478515625,
0.0245513916015625,
-0.01708984375,
0.0115966796875,
0.037322998046875,
-0.0033702850341796875,
0.0164794921875,
-0.01088714599609375,
0.02777099609375,
-0.0146331787109375,
-0.0063629150390625,
-0.00894927978515625,
0.02032470703125,
-0.0082244873046875,
-0.0219268798828125,
0.01200103759765625,
0.0156402587890625,
-0.047393798828125,
-0.004360198974609375,
-0.0163116455078125,
-0.016937255859375,
-0.004558563232421875,
-0.0191497802734375,
0.01328277587890625,
0.0077972412109375,
-0.00429534912109375,
-0.002674102783203125,
-0.01413726806640625,
0.006481170654296875,
0.018890380859375,
0.005100250244140625,
0.0025463104248046875,
-0.0242767333984375,
-0.036712646484375,
-0.00939178466796875,
-0.026397705078125,
-0.045379638671875,
-0.024993896484375,
0.0008368492126464844,
-0.000019073486328125,
0.029815673828125,
0.017852783203125,
0.02215576171875,
0.0244140625,
0.00995635986328125,
-0.00066375732421875,
-0.00608062744140625,
0.0161895751953125,
0.0008268356323242188,
-0.0230560302734375,
0.033538818359375,
0.005886077880859375,
-0.01983642578125,
-0.0010738372802734375,
0.00559234619140625,
-0.0343017578125,
-0.01200103759765625,
-0.021392822265625,
0.0053253173828125,
0.00893402099609375,
0.007537841796875,
-0.010986328125,
-0.00274658203125,
-0.027679443359375,
-0.025482177734375,
0.03045654296875,
0.011016845703125,
0.01751708984375,
0.03765869140625,
-0.02276611328125,
-0.0268707275390625,
-0.004459381103515625,
0.0276641845703125,
-0.040069580078125,
-0.0026302337646484375,
-0.0225830078125,
-0.030029296875,
0.0012311935424804688,
-0.01593017578125,
0.0036163330078125,
0.035980224609375,
-0.018951416015625,
-0.0061187744140625,
-0.031524658203125,
0.0287322998046875,
0.012725830078125,
0.0303192138671875,
0.03326416015625,
-0.039306640625,
-0.03558349609375,
-0.01555633544921875,
0.00992584228515625,
-0.00563812255859375,
-0.003337860107421875,
-0.00341033935546875,
-0.01288604736328125,
0.0145111083984375,
-0.0042877197265625,
0.02374267578125,
0.0214996337890625,
-0.008087158203125,
-0.019744873046875,
-0.0048828125,
0.002628326416015625,
0.04730224609375,
0.0012493133544921875,
-0.004802703857421875,
-0.03680419921875,
0.0029964447021484375,
-0.0179290771484375,
-0.0157928466796875,
-0.03289794921875,
0.00373077392578125,
0.005779266357421875,
0.0131378173828125,
-0.0169677734375,
0.019866943359375,
-0.0010862350463867188,
-0.05621337890625,
-0.007205963134765625,
-0.0008320808410644531,
0.004596710205078125,
-0.00994873046875,
0.025543212890625,
0.0299072265625,
-0.018524169921875,
-0.0274810791015625,
0.006103515625,
0.01506805419921875,
-0.0010547637939453125,
0.035003662109375,
0.0306854248046875,
0.01271820068359375,
0.0291290283203125,
0.00218963623046875,
-0.01216888427734375,
0.0244903564453125,
0.004962921142578125,
0.0247650146484375,
0.0255126953125,
0.030792236328125,
0.00934600830078125,
0.0295867919921875,
0.005886077880859375,
0.00704193115234375,
0.0003228187561035156,
-0.0225372314453125,
0.032501220703125,
0.002838134765625,
-0.01715087890625,
0.02587890625,
0.0203399658203125,
0.008514404296875,
-0.01021575927734375,
0.00553131103515625,
-0.0180816650390625,
0.044708251953125,
-0.003665924072265625,
-0.01715087890625,
0.019989013671875,
0.0085296630859375,
0.0218048095703125,
-0.00864410400390625,
0.0127105712890625,
0.01068115234375,
-0.005626678466796875,
-0.0297393798828125,
0.0011501312255859375,
0.023834228515625,
-0.0124053955078125,
0.000919342041015625,
0.0302886962890625,
0.0164031982421875,
0.0231170654296875,
-0.015869140625,
0.018585205078125,
0.006984710693359375,
-0.030059814453125,
0.01120758056640625,
0.004329681396484375,
0.0012426376342773438,
0.0096893310546875,
0.007663726806640625,
0.00021910667419433594,
0.0003371238708496094,
-0.049072265625,
-0.0078582763671875,
0.006649017333984375,
-0.0221710205078125,
-0.0004982948303222656,
0.0013256072998046875,
0.019805908203125,
-0.0022449493408203125,
-0.0015211105346679688,
0.01267242431640625,
0.0328369140625,
0.032012939453125,
0.00577545166015625,
-0.0100860595703125,
-0.0189971923828125,
0.035888671875,
0.0223388671875,
0.0160980224609375,
-0.00823211669921875,
0.00433349609375,
0.00316619873046875,
-0.0054473876953125,
0.0361328125,
-0.033203125,
-0.0258941650390625,
0.0240936279296875,
0.0002892017364501953,
-0.016845703125,
-0.00824737548828125,
0.0216827392578125,
0.022369384765625,
-0.01068878173828125,
-0.015228271484375,
0.004306793212890625,
-0.01183319091796875,
0.0260772705078125,
0.0655517578125,
0.03564453125,
0.01274871826171875,
0.0233917236328125,
-0.02459716796875,
0.005496978759765625,
-0.0220947265625,
-0.0289764404296875,
-0.00742340087890625,
-0.00714111328125,
-0.0224151611328125,
-0.007389068603515625,
-0.0186309814453125,
0.0077362060546875,
0.017059326171875,
0.01052093505859375,
0.0196380615234375,
-0.01190185546875,
-0.0084075927734375,
-0.02655029296875,
0.006511688232421875,
-0.02508544921875,
0.0224456787109375,
-0.0136566162109375,
-0.0168304443359375,
0.024993896484375,
-0.0168609619140625,
-0.01111602783203125,
-0.03582763671875,
-0.017364501953125,
0.02142333984375,
0.006877899169921875,
-0.0155792236328125,
0.02130126953125,
0.006214141845703125,
0.0022182464599609375,
0.000934600830078125,
0.0072784423828125,
-0.01702880859375,
0.0014925003051757812,
0.0005502700805664062,
0.0267486572265625,
0.0157623291015625,
0.01058197021484375,
0.030853271484375,
0.001834869384765625,
-0.0027618408203125,
-0.018890380859375,
0.048309326171875,
-0.0217437744140625,
-0.003448486328125,
-0.02008056640625,
-0.0025882720947265625,
-0.03619384765625,
0.00830078125,
0.01142120361328125,
0.02337646484375,
-0.0210418701171875,
-0.012542724609375,
-0.01445770263671875,
-0.0027141571044921875,
0.045745849609375,
0.0149383544921875,
-0.0174713134765625,
-0.03582763671875,
-0.0229339599609375,
-0.006015777587890625,
-0.0177001953125,
-0.0223846435546875,
0.0121612548828125,
-0.0083770751953125,
0.035491943359375,
0.0169677734375,
0.006298065185546875,
-0.023406982421875,
-0.004161834716796875,
0.038330078125,
0.0015897750854492188,
0.0054473876953125,
0.0167999267578125,
-0.012786865234375,
0.0079498291015625,
0.0231475830078125,
0.0018463134765625,
-0.005893707275390625,
0.01483917236328125,
0.0079498291015625,
0.0108184814453125,
0.0022068023681640625,
-0.0262451171875,
-0.0014667510986328125,
-0.005573272705078125,
0.0084381103515625,
0.0224456787109375,
-0.0281524658203125,
-0.02410888671875,
0.047576904296875,
0.0294952392578125,
-0.0192108154296875,
-0.0080718994140625,
0.0032901763916015625,
0.0004851818084716797,
-0.0228271484375,
-0.0078582763671875,
0.0094451904296875,
-0.0293731689453125,
0.00511932373046875,
0.01324462890625,
-0.0277099609375,
0.0213470458984375,
-0.0309600830078125,
0.032379150390625,
0.0225372314453125,
-0.005496978759765625,
-0.002071380615234375,
0.004425048828125,
-0.0011348724365234375,
-0.0275421142578125,
-0.050445556640625,
0.018524169921875,
-0.006023406982421875,
-0.0027904510498046875,
0.013916015625,
-0.00933837890625,
-0.00400543212890625,
-0.0066375732421875,
0.0248260498046875,
0.00390625,
-0.01503753662109375,
-0.023193359375,
0.0182647705078125,
0.0017337799072265625,
0.01041412353515625,
0.0255279541015625,
-0.00023627281188964844,
0.05877685546875,
0.00710296630859375,
-0.00563812255859375,
-0.003330230712890625,
-0.0213775634765625,
-0.0281982421875,
-0.02337646484375,
-0.0238800048828125,
0.028961181640625,
-0.04241943359375,
-0.0100555419921875,
-0.044952392578125,
0.002071380615234375,
0.00237274169921875,
-0.007236480712890625,
0.0141143798828125,
-0.020782470703125,
-0.0281524658203125,
0.0289154052734375,
0.036407470703125,
0.0160675048828125,
0.00962066650390625,
0.01390838623046875,
-0.02532958984375,
-0.0041656494140625,
-0.006275177001953125,
-0.032318115234375,
0.0135040283203125,
-0.00926971435546875,
-0.00921630859375,
-0.006622314453125,
0.038543701171875,
0.006256103515625,
0.0011892318725585938,
-0.002887725830078125,
0.0033245086669921875,
-0.006378173828125,
-0.012451171875,
-0.0217437744140625,
-0.031524658203125,
-0.0120849609375,
-0.01502227783203125,
0.0213165283203125,
0.02020263671875,
0.0081024169921875,
0.020477294921875,
0.01259613037109375,
0.0131988525390625,
-0.01580810546875,
0.00847625732421875,
-0.028228759765625,
-0.004734039306640625,
-0.0031147003173828125,
0.018890380859375,
-0.01218414306640625,
0.0078277587890625,
0.02215576171875,
-0.009979248046875,
0.00527191162109375,
0.0082550048828125,
0.00742340087890625,
-0.0167388916015625,
-0.0310821533203125,
-0.0184478759765625,
-0.00986480712890625,
-0.007099151611328125,
-0.017486572265625,
-0.0298614501953125,
-0.01025390625,
0.01076507568359375,
-0.036834716796875,
-0.04339599609375,
0.0157928466796875,
-0.027130126953125,
0.0199127197265625,
0.0138092041015625,
-0.022125244140625,
0.00830841064453125,
0.017303466796875,
0.02716064453125,
-0.0251617431640625,
-0.027099609375,
0.0278472900390625,
0.0126495361328125,
-0.017181396484375,
-0.04119873046875,
-0.0099334716796875,
-0.0126953125,
0.01049041748046875,
0.0188446044921875,
0.001888275146484375,
0.02740478515625,
0.017730712890625,
0.002689361572265625,
0.00759124755859375,
0.0200653076171875,
0.0187835693359375,
-0.017120361328125,
0.0026187896728515625,
0.001979827880859375,
-0.0080108642578125,
0.027069091796875,
-0.017181396484375,
0.005764007568359375,
0.0026035308837890625,
0.0010461807250976562,
0.00649261474609375,
-0.0184326171875,
-0.016387939453125,
-0.026763916015625,
-0.002025604248046875,
-0.0111083984375,
0.02325439453125,
0.004230499267578125,
0.0001118779182434082,
-0.01306915283203125,
-0.01690673828125,
-0.0343017578125,
0.0168609619140625,
0.00873565673828125,
-0.0308074951171875,
-0.020233154296875,
0.0017833709716796875,
-0.0084991455078125,
-0.0186309814453125,
-0.018829345703125,
0.025177001953125,
0.0082244873046875,
-0.0016202926635742188,
0.03533935546875,
0.01433563232421875,
0.0313720703125,
-0.00035643577575683594,
0.0007181167602539062,
-0.0025177001953125,
0.0570068359375,
-0.008331298828125,
-0.00006908178329467773,
0.020416259765625,
0.0318603515625,
0.01824951171875,
0.00621795654296875,
-0.0015821456909179688,
0.00331878662109375,
-0.00902557373046875,
-0.01270294189453125,
0.007755279541015625,
0.0203399658203125,
-0.0035648345947265625,
0.0094146728515625,
-0.003940582275390625,
0.0074615478515625,
-0.00504302978515625,
0.0180816650390625,
-0.0118865966796875,
-0.0228271484375,
-0.00994110107421875,
0.0068206787109375,
0.0027294158935546875,
0.0138092041015625,
-0.015411376953125,
0.005939483642578125,
-0.01358795166015625,
0.0084991455078125,
0.01605224609375,
0.043731689453125,
0.01343536376953125,
-0.0006589889526367188,
-0.01079559326171875,
-0.029388427734375,
0.0118865966796875,
0.006305694580078125,
0.0225982666015625,
0.00786590576171875,
-0.03448486328125,
0.0084991455078125,
-0.0277557373046875,
-0.005893707275390625,
0.041900634765625,
0.027862548828125,
0.01549530029296875,
-0.03466796875,
0.0074920654296875,
0.004119873046875,
-0.014923095703125,
0.0242767333984375,
0.0102081298828125,
0.01629638671875,
-0.018463134765625,
0.00485992431640625,
-0.0298309326171875,
-0.0225982666015625,
-0.0110931396484375,
0.00278472900390625,
0.022369384765625,
-0.0007171630859375,
0.017181396484375,
-0.003368377685546875,
0.00798797607421875,
-0.028289794921875,
0.0098724365234375,
-0.035430908203125,
0.005580902099609375,
-0.0036792755126953125,
0.01039886474609375,
-0.018798828125,
-0.005672454833984375,
0.055267333984375,
-0.0015392303466796875,
-0.03936767578125,
-0.0220184326171875,
-0.0267181396484375,
-0.02911376953125,
-0.0244903564453125,
0.01255035400390625,
-0.0433349609375,
-0.00621795654296875,
0.00676727294921875,
0.0024166107177734375,
0.00011360645294189453,
-0.01511383056640625,
0.02130126953125,
-0.00031185150146484375,
-0.00750732421875,
-0.00910186767578125,
0.01004791259765625,
0.0002880096435546875,
-0.022216796875,
-0.01861572265625,
-0.022064208984375,
-0.0321044921875,
0.011871337890625,
0.0106658935546875,
-0.028228759765625,
0.007106781005859375,
0.021759033203125,
0.005405426025390625,
-0.0006890296936035156,
0.034393310546875,
0.0011606216430664062,
0.0147552490234375,
0.00550079345703125,
-0.01419830322265625,
-0.007061004638671875,
-0.0105743408203125,
0.0145263671875,
-0.01035308837890625,
-0.002452850341796875,
0.034820556640625,
-0.007293701171875,
0.0185546875,
0.013946533203125,
0.025970458984375,
-0.00836944580078125,
-0.0292816162109375,
0.01387786865234375,
0.0014553070068359375,
-0.0298614501953125,
0.005126953125,
-0.00627899169921875,
0.01503753662109375,
0.0308685302734375,
-0.026641845703125,
0.0021953582763671875,
-0.01776123046875,
-0.0235443115234375,
0.0108489990234375,
-0.00003844499588012695,
0.0193328857421875,
-0.02313232421875,
-0.007781982421875,
0.005664825439453125,
-0.0011157989501953125,
0.00560760498046875,
0.00775909423828125,
0.035064697265625,
0.02203369140625,
-0.004550933837890625,
0.021240234375,
0.00421142578125,
0.037109375,
0.00437164306640625,
0.0002484321594238281,
-0.03936767578125,
0.004116058349609375,
0.01049041748046875,
0.01323699951171875,
-0.0037479400634765625,
0.00457763671875,
-0.02252197265625,
-0.0247039794921875,
0.0177001953125,
0.0125885009765625,
0.00726318359375,
0.004451751708984375,
0.01183319091796875,
-0.006977081298828125,
0.0321044921875,
-0.0207061767578125,
0.01473236083984375,
0.01444244384765625,
0.002727508544921875,
-0.007083892822265625,
0.002758026123046875,
-0.00922393798828125,
0.00859832763671875,
-0.01215362548828125,
-0.005706787109375,
-0.0065460205078125,
0.0159454345703125,
-0.0281524658203125,
-0.0006866455078125,
0.008331298828125,
-0.0188446044921875,
-0.048980712890625,
0.0039043426513671875,
-0.00926971435546875,
-0.01044464111328125,
-0.01800537109375,
-0.0131378173828125,
-0.0010967254638671875,
-0.014739990234375,
0.01515960693359375,
-0.0029449462890625,
-0.0276641845703125,
0.048065185546875,
-0.0172119140625,
-0.0183563232421875,
-0.011627197265625,
0.0139007568359375,
0.02313232421875,
-0.002475738525390625,
0.0018482208251953125,
-0.004852294921875,
-0.004802703857421875,
-0.0214691162109375,
-0.002849578857421875,
-0.006343841552734375,
-0.0245361328125,
-0.022979736328125,
0.00492095947265625,
0.01140594482421875,
-0.00786590576171875,
-0.0002262592315673828,
0.006801605224609375,
-0.00927734375,
0.01561737060546875,
-0.0000024437904357910156,
0.0284423828125,
0.02001953125,
0.005939483642578125,
-0.0124664306640625,
-0.0024566650390625,
0.0131072998046875,
0.0063018798828125,
0.001739501953125,
-0.0175323486328125,
0.0158843994140625,
-0.033050537109375,
0.01508331298828125,
0.041046142578125,
-0.0110015869140625,
0.0172882080078125,
-0.02069091796875,
0.050537109375,
-0.025634765625,
0.0241241455078125,
0.026885986328125,
0.0007143020629882812,
-0.0007872581481933594,
-0.004138946533203125,
-0.005489349365234375,
-0.0185089111328125,
0.0254974365234375,
0.0169219970703125,
0.0239105224609375,
-0.00542449951171875,
0.0192718505859375,
-0.00498199462890625,
-0.000934600830078125,
-0.0038166046142578125,
-0.038330078125,
0.00899505615234375,
-0.00571441650390625,
0.012054443359375,
0.005046844482421875,
-0.0233612060546875,
0.0194244384765625,
0.00658416748046875,
-0.0133819580078125,
0.002613067626953125,
-0.009796142578125,
0.0313720703125,
0.0008769035339355469,
0.03131103515625,
0.0156097412109375,
0.056396484375,
-0.01561737060546875,
0.01076507568359375,
0.00917816162109375,
-0.00452423095703125,
-0.0022945404052734375,
0.01393890380859375,
-0.0281829833984375,
0.01435089111328125,
-0.0158233642578125,
0.024993896484375,
-0.01309967041015625,
0.032135009765625,
-0.00010418891906738281,
-0.02313232421875,
0.0027828216552734375,
0.0256805419921875,
0.002948760986328125,
-0.042236328125,
-0.022979736328125,
0.016448974609375,
0.034332275390625,
-0.002536773681640625,
-0.021881103515625,
-0.0066986083984375,
-0.01148223876953125,
-0.0059814453125,
0.023712158203125,
0.0019969940185546875,
0.01373291015625,
0.01171112060546875,
-0.0228424072265625,
0.00998687744140625,
0.03070068359375,
-0.0289459228515625,
0.01824951171875,
-0.004364013671875,
-0.01461029052734375,
-0.009918212890625,
0.01329803466796875,
0.0279693603515625,
-0.0142364501953125,
0.005764007568359375,
0.00742340087890625,
0.009552001953125,
0.01418304443359375,
-0.015045166015625,
0.033538818359375,
0.0265960693359375,
-0.00496673583984375,
0.0218048095703125,
-0.044219970703125,
-0.0139007568359375,
0.02679443359375,
-0.0291595458984375,
-0.0028362274169921875,
0.00878143310546875,
-0.0256500244140625,
-0.00013005733489990234,
-0.043212890625,
0.0036449432373046875,
-0.0083770751953125,
-0.01178741455078125,
0.029510498046875,
-0.03472900390625,
0.0293121337890625,
-0.00440216064453125,
0.0239715576171875,
-0.0033359527587890625,
-0.0018529891967773438,
0.018829345703125,
0.004932403564453125,
-0.0182647705078125,
0.01238250732421875,
0.001255035400390625,
-0.019256591796875,
-0.02392578125,
-0.0226593017578125,
-0.03955078125,
-0.00951385498046875,
0.0189056396484375,
0.00732421875,
0.0148162841796875,
0.0245513916015625,
0.01331329345703125,
-0.00003224611282348633,
-0.020660400390625,
0.0164794921875,
-0.0169677734375,
0.0192718505859375,
-0.031402587890625,
-0.0003082752227783203,
-0.01275634765625,
0.01995849609375,
-0.0188140869140625,
0.03216552734375,
-0.01302337646484375,
-0.0201263427734375,
0.0244293212890625,
-0.0180511474609375,
0.010406494140625,
-0.0114288330078125,
-0.0023441314697265625,
0.00887298583984375,
-0.019775390625,
-0.00859832763671875,
0.00334930419921875,
-0.01145172119140625,
-0.0038242340087890625,
0.0134429931640625,
-0.017333984375,
0.0282745361328125,
-0.01241302490234375,
0.00882720947265625,
0.02081298828125,
0.01120758056640625,
-0.0011644363403320312,
0.037078857421875,
-0.0143890380859375,
-0.0189056396484375,
-0.0157012939453125,
-0.0254974365234375,
0.0077667236328125,
-0.0318603515625,
-0.0015420913696289062,
-0.003513336181640625,
-0.01177215576171875,
9.5367431640625e-7,
-0.0043487548828125,
-0.00064849853515625,
0.0152435302734375,
-0.01116180419921875,
-0.0163116455078125,
-0.002025604248046875,
0.002201080322265625,
-0.01197052001953125,
0.0335693359375,
-0.004955291748046875,
-0.003326416015625,
-0.01093292236328125,
0.033538818359375,
-0.037628173828125,
0.0161590576171875,
-0.017791748046875,
0.0056915283203125,
-0.00939178466796875,
-0.0045013427734375,
-0.004119873046875,
0.0227813720703125,
0.0186920166015625,
-0.00287628173828125,
0.0151519775390625,
0.0292816162109375,
-0.006275177001953125,
0.026947021484375,
-0.0035381317138671875,
-0.022613525390625,
0.005870819091796875,
-0.036895751953125,
-0.0137481689453125,
0.021270751953125,
0.0338134765625,
0.038116455078125,
-0.020050048828125,
0.00989532470703125,
-0.0006761550903320312,
-0.0039520263671875,
0.0382080078125,
0.0025653839111328125,
0.0254058837890625,
-0.0176849365234375,
-0.0026607513427734375,
-0.01035308837890625,
0.0127716064453125,
-0.006244659423828125,
0.02685546875,
-0.0144500732421875,
0.01189422607421875,
-0.0280914306640625,
0.003612518310546875,
0.0301666259765625,
-0.004016876220703125,
0.003765106201171875,
-0.037139892578125,
0.00576019287109375,
0.0149688720703125,
0.007465362548828125,
0.0211639404296875,
0.017425537109375,
-0.0090484619140625,
0.01354217529296875,
-0.006763458251953125,
-0.0291595458984375,
-0.00034880638122558594,
0.010223388671875,
-0.00872802734375,
0.0082855224609375,
-0.0097198486328125,
0.0178985595703125,
0.02191162109375,
-0.03302001953125,
-0.00757598876953125,
-0.00914764404296875,
-0.0033283233642578125,
0.004749298095703125,
0.01035308837890625,
-0.011016845703125,
-0.0259857177734375,
-0.0277557373046875,
-0.0301666259765625,
-0.00537109375,
-0.005321502685546875,
-0.0117645263671875,
-0.004146575927734375,
-0.02154541015625,
-0.01503753662109375,
-0.0301055908203125,
-0.004772186279296875,
0.00600433349609375,
0.0060272216796875,
0.0330810546875,
0.023529052734375,
0.0212249755859375,
0.0217437744140625,
-0.0097198486328125,
0.01430511474609375,
-0.002655029296875,
0.037750244140625,
0.0438232421875,
-0.0214691162109375,
0.035125732421875,
0.008575439453125,
0.0013284683227539062,
0.01276397705078125,
-0.0168914794921875,
0.0171661376953125,
0.0035800933837890625,
0.0025615692138671875,
0.01512908935546875,
-0.01116180419921875,
0.01068878173828125,
0.01496124267578125,
0.01201629638671875,
0.0276641845703125,
-0.0289306640625,
0.0032672882080078125,
0.0166778564453125,
-0.0091400146484375,
0.001743316650390625,
0.0225372314453125,
-0.01715087890625,
0.0251617431640625,
0.0213623046875,
-0.002544403076171875,
0.0029087066650390625,
0.0010786056518554688,
-0.005767822265625,
-0.0008254051208496094,
-0.0263214111328125,
0.00727081298828125,
0.023590087890625,
-0.02178955078125,
-0.00428009033203125,
0.0257720947265625,
-0.03619384765625,
0.0517578125,
-0.018798828125,
-0.0010471343994140625,
-0.00997161865234375,
0.0031604766845703125,
-0.0261383056640625,
0.00588226318359375,
0.01493072509765625,
-0.05792236328125,
0.0237884521484375,
0.00943756103515625,
0.02752685546875,
-0.008758544921875,
-0.02764892578125,
0.015838623046875,
-0.010162353515625,
-0.031402587890625,
0.029510498046875,
0.0030155181884765625,
0.0438232421875,
-0.032257080078125,
-0.039825439453125,
-0.023834228515625,
-0.023223876953125,
0.01274871826171875,
-0.0411376953125,
0.005859375,
0.01727294921875,
-0.0207672119140625,
0.013702392578125,
0.03277587890625,
0.00824737548828125,
0.001781463623046875,
-0.034912109375,
-0.0115509033203125,
0.0186614990234375,
0.032867431640625,
-0.012451171875,
0.00994110107421875,
-0.016143798828125,
0.038970947265625,
0.0161590576171875,
0.016204833984375,
0.0130767822265625,
0.01033782958984375,
-0.037994384765625,
-0.03363037109375,
0.028045654296875,
-0.00007522106170654297,
0.0133056640625,
0.016143798828125,
-0.0150909423828125,
-0.0232391357421875,
-0.045562744140625,
0.0255584716796875,
0.00946807861328125,
-0.0260162353515625,
0.03765869140625,
-0.0214080810546875,
0.0298309326171875,
-0.0096282958984375,
-0.01230621337890625,
-0.04443359375,
-0.01520538330078125,
-0.010498046875,
0.007625579833984375,
0.0058746337890625,
0.00817108154296875,
-0.0006999969482421875,
-0.01959228515625,
-0.02130126953125,
-0.0195465087890625,
-0.027679443359375,
0.00836181640625,
0.002712249755859375,
0.012420654296875,
-0.017120361328125,
-0.044219970703125,
-0.028045654296875,
0.006130218505859375,
0.00594329833984375,
-0.0040130615234375,
-0.022979736328125,
-0.001194000244140625,
0.0012989044189453125,
-0.005672454833984375,
0.0175323486328125,
0.01325225830078125,
-0.02325439453125,
-0.0122833251953125,
-0.0253143310546875,
0.0142822265625,
-0.01727294921875,
-0.01409149169921875,
-0.0216217041015625,
-0.0019855499267578125,
-0.0280914306640625,
-0.039215087890625,
0.0138702392578125,
-0.0208892822265625,
-0.01139068603515625,
-0.0177459716796875,
0.0154876708984375,
0.01453399658203125,
0.005489349365234375,
-0.0003592967987060547,
0.00824737548828125,
-0.055084228515625,
0.0162811279296875,
-0.01025390625,
-0.01143646240234375,
-0.0159149169921875,
0.0060882568359375,
0.003658294677734375,
0.01406097412109375,
0.0231781005859375,
-0.038177490234375,
0.0084075927734375,
0.00782012939453125,
-0.01113128662109375,
-0.0278472900390625,
0.01331329345703125,
0.0212554931640625,
0.00991058349609375,
-0.0167999267578125,
0.0142974853515625,
0.0139617919921875,
0.0035648345947265625,
0.0273895263671875,
0.007686614990234375,
-0.01666259765625,
-0.0003559589385986328,
-0.01262664794921875,
-0.01983642578125,
0.02435302734375,
0.0125579833984375,
-0.0091400146484375,
0.0284881591796875,
0.005603790283203125,
-0.007266998291015625,
0.0157318115234375,
0.0220947265625,
-0.0162353515625,
0.046051025390625,
0.0143890380859375,
0.007740020751953125,
0.01983642578125
] |
ours_479
|
Solution. Let \(P\) be the polynomial we are considering. Assume that \(P\) has only real roots. Then by Newton's Inequality,
\[
\frac{159^{2}}{\binom{6}{3}^{2}} \geq \frac{60 \times 240}{\binom{6}{2}\binom{6}{4}}
\]
which is not true, leading to a contradiction. Thus, \(P\) has at least one complex root. Because the coefficients of \(P\) are real, it must have another complex root, so there are at most \(4\) real roots. To show that this is the maximum, we construct such a \(P\). Consider
\[
P(x)=x^{6}-A x^{5}+60 x^{4}-159 x^{3}+240 x^{2}+x
\]
for \(A\) arbitrarily large. It has a real root of \(0\). Now, divide out \(x\) to get
\[
\frac{P(x)}{x}=Q(x)=x^{5}-A x^{4}+60 x^{3}-159 x^{2}+240 x+1.
\]
We aim to show that this can have \(3\) real roots. Note that \(Q(0)=1\), so there exists a negative root of \(Q\). Now, \(A\) can be constructed such that the inequality
\[
x^{5}+60 x^{3}-159 x^{2}+240 x+1<A x^{4}
\]
holds for some positive \(x\), say \(x=1\). But then \(Q(1)<0\), so there exists a root of \(Q\) in \((0,1)\) and some other root after \(1\), so there are at least \(3\) real roots of \(Q\). Then there are at least \(4\) real roots of \(P\), but there are at most \(4\) real roots of \(P\), so there are exactly \(4\) real roots of \(P\). Thus, the largest possible number of distinct real solutions to \(P(x)=0\) is \(4\).
\(\boxed{4}\)
|
4
|
{
"competition": "us_comps",
"dataset": "Ours",
"posts": null,
"source": "OMOFall18Solns.md"
}
|
Compute the largest possible number of distinct real solutions for \(x\) to the equation
\[
x^{6}+a x^{5}+60 x^{4}-159 x^{3}+240 x^{2}+b x+c=0,
\]
where \(a, b\), and \(c\) are real numbers.
|
[
"/Mathematics/Algebra/AlgebraicEquations/AlgebraicEquation",
"/Mathematics/Algebra/AlgebraicEquations/AlgebraicExpression",
"/Mathematics/Algebra/AlgebraicEquations/SexticEquation",
"/Mathematics/Algebra/Polynomials/Polynomial",
"/Mathematics/Algebra/Polynomials/PolynomialDegree",
"/Mathematics/Algebra/Polynomials/PolynomialEquation",
"/Mathematics/Algebra/Polynomials/PolynomialRoots",
"/Mathematics/Algebra/Polynomials/RealPolynomial",
"/Mathematics/Algebra/Polynomials/UnivariatePolynomial"
] |
Use Newton's inequality on the coefficients to prove the polynomial cannot have all real roots, limiting real roots to at most four.
|
[
0.00011074542999267578,
-0.004093170166015625,
0.0200042724609375,
0.058929443359375,
0.0004208087921142578,
0.00414276123046875,
-0.0004982948303222656,
0.0131072998046875,
0.000888824462890625,
-0.00595855712890625,
-0.0281524658203125,
-0.030120849609375,
-0.002460479736328125,
0.0172119140625,
-0.023223876953125,
0.004520416259765625,
0.0182647705078125,
0.0026874542236328125,
0.005413055419921875,
-0.005199432373046875,
-0.00170135498046875,
0.01026153564453125,
-0.050384521484375,
-0.00214385986328125,
-0.00958251953125,
0.0077972412109375,
-0.0244293212890625,
-0.019378662109375,
-0.0160980224609375,
-0.0112762451171875,
0.00750732421875,
-0.02606201171875,
-0.04742431640625,
-0.0287017822265625,
0.0045013427734375,
-0.003948211669921875,
0.017425537109375,
-0.00510406494140625,
-0.014312744140625,
-0.03814697265625,
-0.00738525390625,
-0.002079010009765625,
-0.006282806396484375,
0.005405426025390625,
-0.017333984375,
0.0064697265625,
-0.0027866363525390625,
-0.016693115234375,
-0.00925445556640625,
0.015106201171875,
0.003162384033203125,
0.00986480712890625,
0.00960540771484375,
0.00283050537109375,
-0.0214996337890625,
-0.0280303955078125,
-0.044036865234375,
-0.0014438629150390625,
-0.0275726318359375,
0.01849365234375,
-0.003246307373046875,
-0.0084686279296875,
0.0006337165832519531,
-0.0202178955078125,
0.004062652587890625,
0.005016326904296875,
0.0050048828125,
-0.003543853759765625,
0.007312774658203125,
-0.0162506103515625,
-0.011505126953125,
-0.02716064453125,
-0.00844573974609375,
0.05657958984375,
0.0299530029296875,
-0.00882720947265625,
-0.0029773712158203125,
0.00942230224609375,
0.004398345947265625,
0.0184478759765625,
0.0289459228515625,
0.0013513565063476562,
-0.004150390625,
-0.00634765625,
0.0093231201171875,
0.01303863525390625,
-0.02423095703125,
-0.002925872802734375,
-0.041259765625,
0.0086669921875,
0.007221221923828125,
0.05108642578125,
-0.01192474365234375,
-0.003894805908203125,
-0.0083160400390625,
0.007476806640625,
-0.023468017578125,
-0.0019741058349609375,
-0.02490234375,
0.0098419189453125,
-0.0011186599731445312,
-0.005016326904296875,
-0.006744384765625,
-0.01296234130859375,
-0.03253173828125,
-0.006977081298828125,
-0.01218414306640625,
0.0179595947265625,
0.01143646240234375,
0.001438140869140625,
-0.0167388916015625,
-0.0066070556640625,
0.0156402587890625,
-0.005405426025390625,
-0.00789642333984375,
0.0310821533203125,
0.0089874267578125,
0.0006775856018066406,
-0.0016622543334960938,
-0.01947021484375,
0.005035400390625,
-0.0013065338134765625,
-0.0174713134765625,
0.00612640380859375,
0.0156097412109375,
-0.02239990234375,
0.0009007453918457031,
-0.0310211181640625,
-0.0260772705078125,
-0.0113372802734375,
0.00011688470840454102,
-0.000043511390686035156,
-0.006061553955078125,
-0.023712158203125,
-0.0518798828125,
-0.01161956787109375,
0.0185394287109375,
-0.0005345344543457031,
-0.024383544921875,
-0.0015935897827148438,
0.006450653076171875,
-0.007476806640625,
0.001129150390625,
-0.01355743408203125,
0.0003833770751953125,
-0.003757476806640625,
-0.012481689453125,
-0.001491546630859375,
0.0018939971923828125,
0.001880645751953125,
0.0287628173828125,
-0.015716552734375,
0.0184173583984375,
0.0274505615234375,
-0.012786865234375,
0.020965576171875,
-0.0095672607421875,
-0.00812530517578125,
0.006500244140625,
0.01338958740234375,
0.0023097991943359375,
-0.0240478515625,
-0.0022335052490234375,
-0.0111846923828125,
0.016326904296875,
-0.0236663818359375,
0.01666259765625,
0.004894256591796875,
-0.012451171875,
0.0100860595703125,
0.0292816162109375,
0.008880615234375,
0.0222625732421875,
-0.03070068359375,
-0.020660400390625,
-0.008392333984375,
-0.01392364501953125,
0.00940704345703125,
0.0038814544677734375,
-0.005252838134765625,
-0.0007653236389160156,
-0.0238037109375,
0.035430908203125,
-0.007045745849609375,
0.00833892822265625,
-0.0011348724365234375,
0.012786865234375,
0.00412750244140625,
0.031768798828125,
0.00634002685546875,
-0.017578125,
0.00646209716796875,
-0.005191802978515625,
-0.0247039794921875,
-0.00962066650390625,
0.0178375244140625,
0.00772857666015625,
0.0091094970703125,
-0.002777099609375,
-0.01108551025390625,
0.006336212158203125,
-0.0018644332885742188,
0.038848876953125,
0.0145111083984375,
0.0111083984375,
-0.0182647705078125,
-0.0018091201782226562,
-0.0109100341796875,
-0.0086212158203125,
0.0010805130004882812,
-0.0043792724609375,
-0.01812744140625,
-0.0078277587890625,
-0.05743408203125,
-0.012298583984375,
-0.0115966796875,
-0.0182647705078125,
-0.0034389495849609375,
-0.01155853271484375,
-0.0244140625,
0.01155853271484375,
0.01055908203125,
0.00041794776916503906,
-0.01422882080078125,
-0.0115814208984375,
0.008209228515625,
-0.015869140625,
-0.0176849365234375,
-0.006534576416015625,
-0.01396942138671875,
0.00954437255859375,
-0.01229095458984375,
-0.00036072731018066406,
0.014556884765625,
0.005329132080078125,
-0.025726318359375,
-0.0035800933837890625,
-0.0216522216796875,
0.002277374267578125,
-0.024444580078125,
0.020751953125,
-0.017791748046875,
0.012481689453125,
-0.0020198822021484375,
0.0302581787109375,
0.0028514862060546875,
0.021240234375,
-0.01262664794921875,
0.0123443603515625,
-0.021209716796875,
-0.01093292236328125,
0.0062408447265625,
0.0054931640625,
-0.0113067626953125,
-0.041351318359375,
-0.01160430908203125,
0.01322174072265625,
0.0227508544921875,
-0.017242431640625,
0.0192413330078125,
0.0035037994384765625,
0.0391845703125,
-0.00841522216796875,
0.00003629922866821289,
-0.0234222412109375,
0.03253173828125,
0.00910186767578125,
0.00391387939453125,
0.00720977783203125,
-0.004241943359375,
0.048980712890625,
-0.00023233890533447266,
0.0028133392333984375,
0.0028171539306640625,
0.0210418701171875,
0.033416748046875,
0.0014858245849609375,
0.00548553466796875,
0.032470703125,
-0.004299163818359375,
0.01282501220703125,
0.00368499755859375,
-0.005992889404296875,
0.00553131103515625,
-0.007411956787109375,
0.0017795562744140625,
-0.01690673828125,
-0.01236724853515625,
0.0101165771484375,
0.0289154052734375,
0.00848388671875,
-0.0238800048828125,
-0.00836944580078125,
-0.01177215576171875,
0.0144195556640625,
0.0007524490356445312,
0.0046539306640625,
-0.01552581787109375,
0.02557373046875,
-0.0030841827392578125,
0.01422119140625,
-0.016845703125,
0.004795074462890625,
0.0005688667297363281,
0.0113372802734375,
0.0128173828125,
-0.006908416748046875,
-0.0033740997314453125,
-0.030975341796875,
0.0086669921875,
0.00959014892578125,
0.005123138427734375,
-0.0182952880859375,
-0.0231475830078125,
-0.027099609375,
-0.02447509765625,
0.012542724609375,
0.010009765625,
-0.021759033203125,
0.00914764404296875,
0.0130462646484375,
-0.01177215576171875,
0.0016450881958007812,
0.0026645660400390625,
0.0016269683837890625,
-0.0114593505859375,
0.0121612548828125,
0.005016326904296875,
0.00452423095703125,
0.0191650390625,
-0.0455322265625,
0.0266571044921875,
-0.005237579345703125,
-0.023468017578125,
-0.0200347900390625,
-0.0027599334716796875,
-0.0158538818359375,
0.01476287841796875,
-0.0269622802734375,
0.005126953125,
0.00766754150390625,
-0.007472991943359375,
0.0221099853515625,
0.01035308837890625,
0.0027942657470703125,
0.006412506103515625,
-0.0477294921875,
0.01235198974609375,
-0.02056884765625,
-0.03497314453125,
-0.04132080078125,
0.0174102783203125,
-0.0254058837890625,
-0.01105499267578125,
-0.0282745361328125,
-0.00543212890625,
-0.0226593017578125,
-0.006023406982421875,
0.001834869384765625,
0.0097503662109375,
-0.0038166046142578125,
-0.01708984375,
0.010955810546875,
-0.00318145751953125,
-0.0035800933837890625,
0.0183563232421875,
-0.0248565673828125,
0.009368896484375,
-0.038848876953125,
-0.00960540771484375,
-0.027618408203125,
-0.01145172119140625,
-0.018218994140625,
-0.010223388671875,
0.0220489501953125,
-0.00656890869140625,
0.019561767578125,
-0.0024509429931640625,
-0.0016937255859375,
-0.00414276123046875,
-0.01087188720703125,
0.02288818359375,
-0.0217437744140625,
0.000050187110900878906,
0.021484375,
-0.003398895263671875,
-0.02069091796875,
-0.0211944580078125,
-0.0017633438110351562,
0.0032329559326171875,
0.015350341796875,
-0.006633758544921875,
-0.0129852294921875,
0.019439697265625,
-0.0171051025390625,
-0.05010986328125,
0.00482177734375,
-0.01446533203125,
0.001552581787109375,
-0.0168914794921875,
-0.0219573974609375,
-0.00821685791015625,
-0.02105712890625,
-0.04486083984375,
-0.016998291015625,
-0.0167999267578125,
0.00940704345703125,
-0.0174102783203125,
-0.03082275390625,
-0.006450653076171875,
-0.0064239501953125,
0.0005507469177246094,
-0.038604736328125,
0.00258636474609375,
0.011383056640625,
-0.01397705078125,
0.00972747802734375,
-0.039093017578125,
-0.00046133995056152344,
-0.01335906982421875,
-0.005931854248046875,
0.01318359375,
-0.0023174285888671875,
-0.014923095703125,
0.0115509033203125,
0.0120086669921875,
-0.06365966796875,
0.0196380615234375,
0.01131439208984375,
-0.01380157470703125,
0.0250244140625,
0.0009508132934570312,
0.004741668701171875,
0.0205535888671875,
-0.0018253326416015625,
0.013275146484375,
0.032928466796875,
0.0076141357421875,
-0.00615692138671875,
0.0285797119140625,
-0.0175933837890625,
0.010589599609375,
-0.0023708343505859375,
-0.0286712646484375,
0.0251312255859375,
0.02252197265625,
0.005794525146484375,
0.0293731689453125,
0.0276336669921875,
0.00746917724609375,
0.00688934326171875,
-0.0200653076171875,
-0.034149169921875,
-0.0312042236328125,
-0.0361328125,
-0.005123138427734375,
0.0303802490234375,
0.00838470458984375,
0.00432586669921875,
-0.07318115234375,
-0.002590179443359375,
-0.0079193115234375,
0.011474609375,
0.00274658203125,
-0.0008745193481445312,
-0.0010995864868164062,
-0.01027679443359375,
0.0310211181640625,
0.0120391845703125,
-0.00968170166015625,
0.0066070556640625,
-0.047943115234375,
-0.00983428955078125,
-0.031890869140625,
-0.03509521484375,
0.00203704833984375,
0.01549530029296875,
0.0273590087890625,
-0.0224151611328125,
-0.0084381103515625,
0.0028629302978515625,
0.01067352294921875,
-0.01812744140625,
0.0184326171875,
0.0027942657470703125,
-0.0026035308837890625,
0.02081298828125,
0.01093292236328125,
-0.038116455078125,
0.01922607421875,
0.036834716796875,
0.0614013671875,
-0.0115203857421875,
-0.04473876953125,
-0.0026035308837890625,
-0.03515625,
0.0033969879150390625,
-0.0037212371826171875,
0.011993408203125,
0.0237579345703125,
0.03369140625,
-0.032958984375,
0.01678466796875,
-0.0250701904296875,
-0.005767822265625,
-0.0250244140625,
0.01538848876953125,
-0.0199432373046875,
0.01328277587890625,
0.0262908935546875,
0.0159454345703125,
0.0219573974609375,
0.017547607421875,
-0.042449951171875,
0.025177001953125,
0.0068206787109375,
0.03631591796875,
-0.0256805419921875,
0.003246307373046875,
-0.0227508544921875,
-0.037628173828125,
-0.01454925537109375,
0.00019347667694091797,
-0.0179595947265625,
0.024169921875,
0.0126953125,
0.01084136962890625,
0.0007834434509277344,
0.01094818115234375,
-0.03607177734375,
-0.0096893310546875,
-0.01470184326171875,
-0.005352020263671875,
0.007785797119140625,
-0.044403076171875,
0.01226806640625,
-0.0017547607421875,
0.0190582275390625,
0.031036376953125,
0.0156707763671875,
-0.0005769729614257812,
0.01220703125,
-0.00658416748046875,
-0.025115966796875,
-0.00568389892578125,
0.0003190040588378906,
-0.033172607421875,
0.00830841064453125,
-0.024749755859375,
0.04864501953125,
0.03997802734375,
-0.001529693603515625,
0.014984130859375,
0.0184173583984375,
-0.004665374755859375,
-0.006160736083984375,
0.041748046875,
0.038421630859375,
-0.037689208984375,
-0.0015039443969726562,
0.0196533203125,
-0.018798828125,
0.00211334228515625,
0.002437591552734375,
0.02337646484375,
-0.03240966796875,
0.0295867919921875,
0.027252197265625,
-0.00966644287109375,
-0.0235137939453125,
-0.0171356201171875,
-0.00170135498046875,
-0.0273895263671875,
-0.0033473968505859375,
-0.00873565673828125,
0.0003371238708496094,
-0.04156494140625,
0.007190704345703125,
-0.04638671875,
-0.041900634765625,
0.01580810546875,
0.034637451171875,
0.0007681846618652344,
-0.010223388671875,
-0.023468017578125,
-0.0238800048828125,
0.020721435546875,
0.0105438232421875,
-0.002635955810546875,
-0.0189666748046875,
0.0129547119140625,
0.01221466064453125,
0.019012451171875,
0.01482391357421875,
0.00994110107421875,
-0.0350341796875,
0.051544189453125,
0.012054443359375,
0.01241302490234375,
0.0009136199951171875,
0.010162353515625,
-0.0011959075927734375,
0.003753662109375,
0.039764404296875,
0.0012054443359375,
0.0032596588134765625,
-0.01540374755859375,
0.007205963134765625,
0.022125244140625,
0.006664276123046875,
0.00351715087890625,
-0.01192474365234375,
0.018585205078125,
-0.006256103515625,
0.007030487060546875,
0.0184478759765625,
-0.048828125,
-0.005706787109375,
0.048583984375,
0.01435089111328125,
-0.02911376953125,
-0.01219940185546875,
0.0128326416015625,
-0.0044708251953125,
0.022125244140625,
0.00562286376953125,
-0.0012140274047851562,
-0.0029850006103515625,
0.01995849609375,
-0.02264404296875,
0.0199737548828125,
-0.0209808349609375,
0.02899169921875,
0.051055908203125,
-0.0206146240234375,
-0.0129547119140625,
-0.00640106201171875,
-0.004772186279296875,
-0.01142120361328125,
-0.0162811279296875,
-0.00009894371032714844,
-0.02020263671875,
0.0152587890625,
-0.0026378631591796875,
-0.0034580230712890625,
0.04693603515625,
0.02978515625,
-0.00450897216796875,
0.036346435546875,
-0.004180908203125,
-0.0098876953125,
0.0269012451171875,
-0.00616455078125,
0.01512908935546875,
0.004573822021484375,
0.02325439453125,
0.0284271240234375,
0.02374267578125,
-0.0005927085876464844,
0.027618408203125,
0.005939483642578125,
-0.0357666015625,
0.013397216796875,
0.0033016204833984375,
0.0286407470703125,
0.0185089111328125,
0.020721435546875,
-0.0057220458984375,
0.01441192626953125,
-0.02386474609375,
0.036865234375,
0.0032978057861328125,
-0.00539398193359375,
-0.0298004150390625,
0.0127716064453125,
-0.01044464111328125,
-0.006710052490234375,
-0.000949859619140625,
0.0215606689453125,
-0.0283966064453125,
-0.002124786376953125,
0.0089263916015625,
0.006561279296875,
-0.007610321044921875,
0.0135040283203125,
-0.0289459228515625,
0.0036296844482421875,
-0.031524658203125,
0.0157623291015625,
-0.0210723876953125,
-0.017852783203125,
-0.0020160675048828125,
-0.017181396484375,
-0.0179595947265625,
0.0022487640380859375,
0.0023136138916015625,
-0.01337432861328125,
0.00986480712890625,
-0.0092926025390625,
-0.00667572021484375,
0.0101165771484375,
-0.0023517608642578125,
0.02154541015625,
-0.038543701171875,
-0.00563812255859375,
-0.045684814453125,
-0.0111236572265625,
-0.01788330078125,
-0.005458831787109375,
0.01236724853515625,
-0.01085662841796875,
-0.0033664703369140625,
0.0007829666137695312,
-0.01043701171875,
-0.01033782958984375,
-0.005298614501953125,
0.028350830078125,
-0.0132293701171875,
0.00760650634765625,
0.007106781005859375,
0.026702880859375,
0.0092010498046875,
-0.029876708984375,
0.033660888671875,
0.0091400146484375,
0.00936126708984375,
-0.0618896484375,
-0.0301055908203125,
0.002437591552734375,
-0.00595855712890625,
-0.01837158203125,
-0.0236358642578125,
-0.0212860107421875,
0.009429931640625,
-0.031768798828125,
-0.008880615234375,
-0.00968170166015625,
-0.010650634765625,
-0.02081298828125,
-0.026275634765625,
0.02880859375,
0.01776123046875,
0.010040283203125,
0.0006809234619140625,
-0.042755126953125,
0.004985809326171875,
-0.0130462646484375,
-0.0083465576171875,
-0.0176544189453125,
0.0386962890625,
0.01168060302734375,
-0.0171356201171875,
0.014007568359375,
-0.027801513671875,
-0.032806396484375,
-0.01010894775390625,
0.0237884521484375,
0.00409698486328125,
0.01103973388671875,
0.028533935546875,
-0.0231170654296875,
0.0020885467529296875,
-0.0181121826171875,
0.0015077590942382812,
-0.01525115966796875,
0.00418853759765625,
0.0006699562072753906,
-0.0172119140625,
-0.00839996337890625,
-0.02392578125,
-0.02667236328125,
-0.00936126708984375,
-0.005046844482421875,
-0.0093994140625,
0.0210418701171875,
0.008209228515625,
-0.027801513671875,
0.01593017578125,
0.0298004150390625,
-0.0032634735107421875,
0.00608062744140625,
-0.00571441650390625,
0.006561279296875,
-0.014373779296875,
-0.0243377685546875,
-0.0213775634765625,
-0.016815185546875,
0.00496673583984375,
0.017547607421875,
-0.00402069091796875,
-0.033172607421875,
-0.01361846923828125,
-0.023956298828125,
-0.0034332275390625,
-0.018768310546875,
0.0093841552734375,
0.0247802734375,
-0.03033447265625,
-0.004383087158203125,
0.0254974365234375,
0.006031036376953125,
-0.022979736328125,
-0.03485107421875,
-0.00685882568359375,
-0.0001227855682373047,
0.00284576416015625,
0.0032291412353515625,
0.0188446044921875,
-0.0288238525390625,
0.018310546875,
0.006183624267578125,
-0.01174163818359375,
0.0035247802734375,
-0.00914764404296875,
-0.00009340047836303711,
0.01381683349609375,
-0.01007080078125,
0.0009751319885253906,
0.007724761962890625,
-0.003330230712890625,
0.0293731689453125,
0.0311126708984375,
0.026336669921875,
0.01056671142578125,
-0.002593994140625,
0.020721435546875,
-0.005916595458984375,
-0.0243988037109375,
0.01397705078125,
0.030670166015625,
-0.00504302978515625,
-0.00815582275390625,
-0.020782470703125,
0.0166168212890625,
-0.0215911865234375,
0.01474761962890625,
-0.01490020751953125,
0.01018524169921875,
-0.02783203125,
0.01555633544921875,
-0.0013093948364257812,
0.0128631591796875,
0.01371002197265625,
-0.0210418701171875,
0.007450103759765625,
-0.0007677078247070312,
-0.05059814453125,
0.052581787109375,
-0.00214385986328125,
0.0021686553955078125,
-0.0022602081298828125,
0.0124969482421875,
-0.0220947265625,
0.03460693359375,
-0.005908966064453125,
-0.01849365234375,
-0.0211334228515625,
0.0111846923828125,
-0.016387939453125,
0.020050048828125,
-0.01354217529296875,
-0.006877899169921875,
0.02423095703125,
0.0307159423828125,
-0.00604248046875,
-0.0219268798828125,
0.0254364013671875,
-0.029998779296875,
0.0180511474609375,
-0.0384521484375,
0.005588531494140625,
-0.0308074951171875,
-0.00901031494140625,
0.00396728515625,
0.0200653076171875,
-0.0004489421844482422,
-0.0318603515625,
0.0260772705078125,
0.0024261474609375,
0.00640869140625,
0.036590576171875,
-0.032470703125,
-0.021484375,
0.015869140625,
-0.030242919921875,
0.00032138824462890625,
-0.0203094482421875,
-0.022003173828125,
-0.0019407272338867188,
0.006275177001953125,
-0.009979248046875,
0.01425933837890625,
0.003482818603515625,
-0.016387939453125,
0.05303955078125,
0.007404327392578125,
0.01088714599609375,
-0.01155853271484375,
0.0161895751953125,
-0.01611328125,
-0.010162353515625,
-0.02764892578125,
-0.01263427734375,
-0.0117034912109375,
-0.044677734375,
0.005615234375,
-0.0161590576171875,
0.0083465576171875,
-0.0019350051879882812,
0.04254150390625,
-0.01078033447265625,
0.01446533203125,
-0.00804901123046875,
0.029632568359375,
0.0014934539794921875,
-0.0175323486328125,
-0.0052642822265625,
-0.01116180419921875,
-0.01084136962890625,
0.035400390625,
-0.0172119140625,
-0.00421905517578125,
-0.02606201171875,
0.00572967529296875,
-0.00020956993103027344,
0.0115203857421875,
-0.03253173828125,
0.03466796875,
-0.01617431640625,
0.00650787353515625,
-0.007274627685546875,
0.0128021240234375,
-0.04046630859375,
0.004688262939453125,
-0.0222930908203125,
-0.0013017654418945312,
-0.008758544921875,
-0.02691650390625,
0.005214691162109375,
-0.0181884765625,
0.0191650390625,
0.00844573974609375,
0.0180206298828125,
0.01242828369140625,
0.0175323486328125,
-0.0008730888366699219,
-0.014007568359375,
0.0218505859375,
0.003021240234375,
-0.015716552734375,
-0.019683837890625,
-0.0045013427734375,
0.01702880859375,
0.040069580078125,
-0.0192413330078125,
-0.0245361328125,
0.005077362060546875,
-0.01739501953125,
-0.009765625,
-0.01265716552734375,
0.0030517578125,
-0.011627197265625,
-0.0169525146484375,
-0.002872467041015625,
0.0147247314453125,
0.0104522705078125,
-0.0081329345703125,
0.0120849609375,
-0.019561767578125,
-0.0252838134765625,
0.00732421875,
0.01207733154296875,
-0.00811004638671875,
-0.004119873046875,
-0.00945281982421875,
0.0233154296875,
-0.00681304931640625,
0.0015058517456054688,
0.0157318115234375,
0.00653076171875,
-0.01458740234375,
-0.003498077392578125,
-0.006984710693359375,
-0.0029926300048828125,
-0.0033779144287109375,
-0.004650115966796875,
-0.001331329345703125,
-0.000514984130859375,
-0.0186767578125,
0.01507568359375,
0.00946807861328125,
0.0325927734375,
0.004398345947265625,
-0.0006341934204101562,
-0.0010099411010742188,
0.034332275390625,
0.0083770751953125,
-0.004459381103515625,
-0.0014047622680664062,
0.0021877288818359375,
-0.00516510009765625,
-0.0168914794921875,
0.03143310546875,
-0.0265655517578125,
0.01412200927734375,
-0.0087127685546875,
0.005970001220703125,
-0.01229095458984375,
0.029998779296875,
0.04571533203125,
-0.00872039794921875,
0.0139923095703125,
-0.0081634521484375,
-0.003658294677734375,
-0.0140838623046875,
-0.004852294921875,
0.004726409912109375,
0.0251922607421875,
-0.015899658203125,
-0.00998687744140625,
-0.0063629150390625,
0.01380157470703125,
-0.01018524169921875,
0.01934814453125,
-0.016998291015625,
-0.0218048095703125,
-0.01224517822265625,
0.0252532958984375,
0.00974273681640625,
0.0190887451171875,
-0.003421783447265625,
-0.020660400390625,
-0.0142822265625,
-0.0027217864990234375,
0.0322265625,
0.00766754150390625,
-0.020416259765625,
-0.07147216796875,
0.005535125732421875,
0.02978515625,
-0.0173492431640625,
-0.0110626220703125,
0.01181793212890625,
-0.014129638671875,
-0.003658294677734375,
-0.0213623046875,
0.01140594482421875,
0.00762176513671875,
0.001773834228515625,
-0.0228729248046875,
-0.01715087890625,
-0.0080108642578125,
-0.002162933349609375,
-0.031494140625,
-0.0038471221923828125,
-0.0209808349609375,
-0.010101318359375,
0.005680084228515625,
-0.009796142578125,
0.0203857421875,
-0.01861572265625,
0.00952911376953125,
0.00998687744140625,
0.0003733634948730469,
0.0295562744140625,
-0.0164794921875,
0.00036072731018066406,
-0.011505126953125,
-0.00926971435546875,
0.016845703125,
-0.040252685546875,
-0.0206756591796875,
0.006122589111328125,
-0.0181121826171875,
0.04608154296875,
-0.0006585121154785156,
-0.02520751953125,
0.0149078369140625,
0.0299072265625,
0.00368499755859375,
0.056365966796875,
0.01122283935546875,
-0.00910186767578125,
0.0200347900390625,
0.035430908203125,
0.0001811981201171875,
0.007381439208984375,
0.0264892578125,
-0.02740478515625,
-0.00672149658203125,
-0.0009527206420898438,
-0.0004799365997314453,
-0.01364898681640625,
0.00507354736328125,
0.01007080078125,
0.00940704345703125,
0.0295562744140625,
0.0158538818359375,
0.01751708984375,
-0.00930023193359375,
-0.002902984619140625,
0.04327392578125,
0.005096435546875,
-0.02423095703125,
-0.031707763671875,
-0.0102996826171875,
-0.01172637939453125,
0.0210418701171875,
0.0003924369812011719,
-0.0161590576171875,
-0.020904541015625,
0.00168609619140625,
-0.0093994140625,
0.0196075439453125,
-0.0026721954345703125,
-0.0096435546875,
-0.037506103515625,
-0.01093292236328125,
0.022216796875,
-0.0266265869140625,
0.00313568115234375,
-0.00043845176696777344,
-0.004474639892578125,
-0.007793426513671875,
0.019256591796875,
-0.00917816162109375,
0.013824462890625,
0.0161285400390625,
-0.0259857177734375,
-0.004863739013671875,
-0.0189056396484375,
0.00360870361328125,
-0.0007810592651367188,
0.0009603500366210938,
0.0186309814453125,
0.0032939910888671875,
0.0165557861328125,
0.005764007568359375,
-0.00894927978515625,
-0.0002665519714355469,
0.034820556640625,
-0.005523681640625,
-0.00978851318359375,
-0.0200653076171875,
-0.02362060546875,
-0.0009150505065917969,
-0.01959228515625,
-0.00963592529296875,
-0.0021724700927734375,
-0.0131683349609375,
0.0007729530334472656,
0.0462646484375,
-0.01546478271484375,
0.0010013580322265625,
-0.021759033203125,
0.01169586181640625,
-0.0101776123046875,
-0.002288818359375,
-0.00792694091796875,
-0.0184478759765625,
-0.01322174072265625,
-0.0272064208984375,
0.033172607421875,
-0.0021915435791015625,
-0.0058746337890625,
-0.01177215576171875,
-0.02374267578125,
0.037841796875,
-0.04833984375,
0.026580810546875,
-0.003082275390625,
-0.01458740234375,
-0.00348663330078125,
-0.03759765625,
0.0171966552734375,
0.0433349609375,
0.004638671875,
-0.0269012451171875,
-0.0226593017578125,
0.006511688232421875,
-0.039825439453125,
0.04083251953125,
-0.0131378173828125,
-0.0345458984375,
-0.031646728515625,
-0.017852783203125,
-0.0180816650390625,
0.02447509765625,
0.029571533203125,
0.005664825439453125,
0.005092620849609375,
0.0029449462890625,
-0.0281982421875,
0.014190673828125,
-0.0157470703125,
-0.0015268325805664062,
0.003345489501953125,
0.01082611083984375,
-0.0176544189453125,
0.019927978515625,
-0.0033245086669921875,
0.0202789306640625,
-0.0033626556396484375,
-0.020751953125,
0.03558349609375,
-0.0193634033203125,
-0.0084075927734375,
0.01447296142578125,
-0.03076171875,
-0.005832672119140625,
-0.017578125,
-0.00540924072265625,
0.0223388671875,
0.029937744140625,
0.0147705078125,
0.0011377334594726562,
0.035980224609375,
0.02044677734375,
-0.0245361328125,
-0.0105438232421875,
-0.0220794677734375,
-0.0142669677734375,
-0.03045654296875,
-0.01136016845703125,
-0.035186767578125,
0.00583648681640625,
-0.00988006591796875,
0.00958251953125,
0.015899658203125,
0.00302886962890625,
0.00818634033203125,
0.0276336669921875,
-0.0084228515625,
0.00435638427734375,
0.004558563232421875,
0.0218658447265625,
0.0041656494140625,
0.02789306640625,
-0.007541656494140625,
0.029266357421875,
-0.0166778564453125,
-0.0245208740234375,
0.0055999755859375,
-0.001789093017578125,
0.0096893310546875,
-0.010711669921875,
-0.0196380615234375,
0.006763458251953125,
-0.023895263671875,
0.00031495094299316406,
0.0022411346435546875,
0.041351318359375,
-0.0088348388671875,
-0.01251220703125,
-0.00830841064453125,
-0.0078582763671875,
-0.0189971923828125,
-0.013427734375,
0.001155853271484375,
-0.01097869873046875,
0.0097503662109375,
-0.0023746490478515625,
-0.00012803077697753906,
-0.007110595703125,
0.0013246536254882812,
-0.0142974853515625,
0.02764892578125,
0.01265716552734375,
-0.0018129348754882812,
-0.01160430908203125,
-0.0091552734375,
0.03265380859375,
-0.04400634765625,
-0.0245819091796875,
-0.00933837890625,
-0.01104736328125,
-0.0061492919921875,
-0.00942230224609375,
-0.0068206787109375,
-0.00024044513702392578,
-0.001102447509765625,
0.041046142578125,
0.006496429443359375,
-0.027252197265625,
-0.004550933837890625,
-0.0311126708984375,
0.0157623291015625,
0.0299835205078125,
0.0198822021484375,
-0.00716400146484375,
-0.0180816650390625,
-0.002971649169921875,
-0.028350830078125,
0.00254058837890625,
-0.04217529296875,
0.0222015380859375,
0.0245513916015625,
-0.013519287109375,
0.004901885986328125,
0.0146942138671875,
0.0104522705078125,
-0.017486572265625,
0.0067291259765625,
-0.005153656005859375,
-0.007373809814453125,
0.00815582275390625,
-0.0107574462890625,
0.0161285400390625,
-0.0147552490234375,
-0.0284423828125,
0.016357421875,
0.02838134765625,
0.031280517578125,
0.0255126953125,
0.044921875,
-0.0171661376953125,
-0.02508544921875,
0.0023975372314453125,
0.018463134765625,
-0.0029659271240234375,
0.03143310546875,
0.0240936279296875,
-0.01389312744140625,
-0.032257080078125,
-0.001972198486328125,
-0.01271820068359375,
-0.01543426513671875,
-0.01519775390625,
-0.0281982421875,
0.0139617919921875,
-0.004665374755859375,
0.04083251953125,
-0.0179443359375,
0.0061187744140625,
-0.0111846923828125,
0.030029296875,
0.00687408447265625,
0.0106658935546875,
-0.019805908203125,
-0.0128936767578125,
0.018463134765625,
0.037322998046875,
-0.036376953125,
-0.039093017578125,
-0.007595062255859375,
0.0211181640625,
-0.041717529296875,
0.008941650390625,
0.036529541015625,
-0.02984619140625,
0.003963470458984375,
-0.01087188720703125,
-0.0173187255859375,
-0.0164947509765625,
-0.0064239501953125,
0.017059326171875,
-0.020782470703125,
-0.0261688232421875,
-0.006458282470703125,
0.0054473876953125,
0.039093017578125,
-0.0491943359375,
-0.0283355712890625,
0.01329803466796875,
0.0279998779296875,
0.0258941650390625,
-0.016510009765625,
0.017242431640625,
0.01157379150390625,
-0.01202392578125,
0.014007568359375,
0.0289306640625,
0.0125274658203125,
-0.0168609619140625,
0.0255889892578125,
-0.007904052734375,
-0.0249176025390625,
0.00457763671875,
0.004413604736328125,
-0.04522705078125,
-0.010772705078125,
-0.0178070068359375,
-0.0115509033203125,
0.01751708984375,
0.0188751220703125,
0.0248870849609375,
-0.0131072998046875,
0.0000959634780883789,
0.0251312255859375,
-0.00992584228515625,
0.0009722709655761719,
-0.0017900466918945312,
0.0014810562133789062,
0.047271728515625,
0.00676727294921875,
-0.0145263671875,
-0.01177978515625,
0.007610321044921875,
-0.01171875,
0.019195556640625,
0.046142578125,
0.0340576171875,
0.0162200927734375,
0.015289306640625,
0.0419921875,
-0.00881195068359375,
0.00420379638671875,
0.007293701171875,
0.00013530254364013672,
-0.0277557373046875,
-0.006572723388671875,
0.0176849365234375,
-0.0231475830078125,
-0.0361328125,
0.0008320808410644531,
-0.0031604766845703125,
0.0247955322265625,
0.0014963150024414062,
-0.035369873046875,
0.016998291015625,
0.061279296875,
0.0258026123046875,
-0.0372314453125,
-0.004909515380859375,
-0.0294036865234375,
-0.00209808349609375,
0.0252685546875,
-0.025146484375,
0.022857666015625,
-0.004119873046875,
-0.037322998046875,
-0.03985595703125,
-0.029571533203125,
-0.02203369140625,
0.0156707763671875,
0.006404876708984375,
0.002849578857421875,
-0.0012140274047851562,
0.039764404296875,
0.030853271484375,
-0.00975799560546875,
-0.00774383544921875,
-0.01241302490234375,
-0.00603485107421875,
-0.056549072265625,
0.0191650390625,
0.0189361572265625,
0.030975341796875,
0.00019156932830810547,
-0.00446319580078125,
-0.0234222412109375,
-0.0208282470703125,
-0.004871368408203125,
-0.0207366943359375,
0.006877899169921875,
0.0174713134765625,
-0.01348876953125,
0.0025348663330078125,
0.0028438568115234375,
-0.023468017578125,
0.006252288818359375,
0.0203704833984375,
-0.002925872802734375,
0.038055419921875,
-0.0012416839599609375,
0.0112457275390625,
-0.0199127197265625,
0.030853271484375,
-0.007495880126953125,
0.01235198974609375,
-0.03240966796875,
-0.003353118896484375,
0.00437164306640625,
0.013580322265625,
0.0169677734375,
-0.01047515869140625,
0.01398468017578125,
-0.019683837890625,
0.0137786865234375,
-0.02099609375,
0.020355224609375,
-0.005340576171875,
0.0180511474609375,
-0.0116729736328125,
-0.01806640625,
-0.0008273124694824219,
-0.016571044921875,
0.0085296630859375,
-0.004390716552734375,
-0.03717041015625,
0.0035858154296875,
-0.0140533447265625,
0.0004096031188964844,
-0.021759033203125,
0.02728271484375,
-0.046844482421875,
0.0260009765625,
0.003734588623046875,
0.0214080810546875,
0.0000795125961303711,
0.03411865234375,
0.0025806427001953125,
0.008331298828125,
0.0095672607421875,
0.0034618377685546875,
-0.053985595703125,
-0.0226593017578125,
0.00997161865234375,
-0.007724761962890625,
-0.009765625,
-0.029632568359375,
-0.0032939910888671875,
-0.0026416778564453125,
0.025634765625,
-0.0130157470703125,
-0.0103607177734375,
-0.0000057220458984375,
-0.00734710693359375,
-0.017974853515625,
-0.004589080810546875,
-0.01372528076171875,
-0.031707763671875,
0.004589080810546875,
0.01345062255859375,
0.03436279296875,
0.0096282958984375,
-0.0191650390625,
-0.001468658447265625,
-0.0005540847778320312,
0.00746917724609375,
0.00582122802734375,
-0.0153656005859375,
-0.0265350341796875,
0.01065826416015625,
-0.00989532470703125,
-0.032745361328125,
0.02508544921875,
0.0203399658203125,
0.01226043701171875,
-0.0013074874877929688,
0.0086212158203125,
-0.035980224609375,
-0.0148468017578125,
0.034088134765625,
0.00737762451171875,
0.0148468017578125,
-0.0031261444091796875,
0.0124664306640625,
0.041290283203125,
-0.0022716522216796875,
0.024017333984375,
-0.01064300537109375,
-0.0005755424499511719,
0.0188140869140625,
-0.04168701171875,
0.00453948974609375,
0.01538848876953125,
0.0292816162109375,
0.018707275390625,
-0.03411865234375,
-0.007617950439453125,
-0.00914764404296875,
-0.0016126632690429688,
-0.01554107666015625,
0.028839111328125,
-0.01543426513671875,
-0.00823974609375,
0.0277099609375,
0.01507568359375,
-0.0038623809814453125,
0.0037326812744140625,
0.04351806640625,
-0.045440673828125,
-0.00888824462890625,
0.041107177734375,
-0.01134490966796875,
0.032470703125,
-0.0079498291015625,
0.0251617431640625,
0.01171875,
-0.002536773681640625,
0.01006317138671875,
-0.005756378173828125,
-0.01064300537109375,
0.01039886474609375,
-0.01316070556640625,
-0.01556396484375,
0.01194000244140625,
-0.0035247802734375,
0.011932373046875,
-0.01462554931640625,
-0.00865936279296875,
0.00009143352508544922,
-0.0090789794921875,
0.01480865478515625,
-0.005001068115234375,
0.031707763671875,
-0.005535125732421875,
0.052032470703125,
0.0060577392578125,
-0.025177001953125,
-0.006237030029296875,
0.0355224609375,
0.00555419921875,
-0.01418304443359375,
0.019989013671875,
-0.0057373046875,
-0.01318359375,
-0.006458282470703125,
0.0224151611328125,
0.031402587890625,
0.0149993896484375,
-0.005603790283203125,
-0.0013952255249023438,
0.006465911865234375,
0.01548004150390625,
0.006900787353515625,
0.01464080810546875,
0.016448974609375,
0.0180511474609375,
0.039337158203125,
0.029693603515625,
-0.002597808837890625,
-0.03656005859375,
0.01490020751953125,
0.01531982421875,
-0.0177764892578125,
-0.028106689453125,
-0.020416259765625,
-0.0136260986328125,
0.01088714599609375,
0.006885528564453125,
0.0119781494140625,
-0.0217132568359375,
-0.01070404052734375,
-0.0158538818359375,
-0.006603240966796875,
0.025238037109375,
-0.0179901123046875,
0.01029205322265625,
0.0197296142578125,
-0.0018777847290039062,
0.0206146240234375,
-0.00672149658203125,
-0.029754638671875,
0.01419830322265625,
-0.018310546875,
-0.0044097900390625,
-0.005916595458984375,
-0.0308990478515625,
-0.004215240478515625,
-0.0038661956787109375,
0.04840087890625,
0.016693115234375,
-0.01271820068359375,
-0.0255126953125,
-0.00432586669921875,
0.00637054443359375,
0.033935546875,
-0.00885772705078125,
0.00687408447265625,
-0.00833892822265625,
0.033935546875,
0.038116455078125,
0.018218994140625,
0.006267547607421875,
0.01385498046875,
-0.003597259521484375,
-0.00580596923828125,
-0.003757476806640625,
-0.01064300537109375,
-0.01617431640625,
0.0167694091796875,
-0.007965087890625,
0.00007802248001098633,
0.001972198486328125,
-0.0218658447265625,
-0.019989013671875,
-0.0231781005859375,
-0.01422882080078125,
0.01922607421875,
-0.037689208984375,
-0.006229400634765625,
0.0191650390625,
0.007678985595703125,
0.0279541015625,
0.0513916015625,
0.0247650146484375,
0.0164947509765625,
-0.004520416259765625,
-0.0005059242248535156,
-0.0033817291259765625,
0.00782012939453125,
0.009613037109375,
0.0155487060546875,
0.0274810791015625,
-0.0191497802734375,
0.001220703125,
-0.00894927978515625,
0.019805908203125,
-0.0048065185546875,
0.015838623046875,
0.01995849609375,
-0.034149169921875,
0.0012407302856445312,
0.030029296875,
-0.0170135498046875,
-0.02410888671875,
-0.0054779052734375,
0.00626373291015625,
0.0274200439453125,
0.00856781005859375,
-0.02227783203125,
0.0167083740234375,
-0.0283203125,
0.00127410888671875,
0.03875732421875,
-0.01062774658203125,
0.0157012939453125,
-0.00524139404296875,
0.02410888671875,
-0.002460479736328125,
-0.004634857177734375,
-0.006099700927734375,
0.0063323974609375,
-0.012847900390625,
0.034515380859375,
-0.018798828125,
0.01142120361328125,
0.006198883056640625,
-0.0190277099609375,
0.01422119140625,
-0.013671875,
-0.017852783203125,
-0.023406982421875,
-0.01090240478515625,
0.0072784423828125,
0.0003848075866699219,
-0.04638671875,
-0.01366424560546875,
0.00998687744140625,
-0.01222991943359375,
-0.013031005859375,
0.020843505859375,
0.027435302734375,
-0.0335693359375,
0.01343536376953125,
0.01043701171875,
0.0190887451171875,
0.01519775390625,
-0.0030460357666015625,
-0.0261383056640625,
0.0139923095703125,
0.01226806640625,
-0.0110626220703125,
0.0160675048828125,
-0.02032470703125,
0.04315185546875,
-0.01520538330078125,
-0.0032596588134765625,
0.0263671875,
-0.01297760009765625,
-0.0191802978515625,
-0.0290985107421875,
0.0109710693359375,
0.0255279541015625,
0.0180816650390625,
-0.01531219482421875,
-0.01519012451171875,
-0.00037741661071777344,
0.005054473876953125,
0.007022857666015625,
0.002574920654296875,
-0.01488494873046875,
0.0124664306640625,
-0.0123748779296875,
0.0222625732421875,
0.00034880638122558594,
-0.047210693359375,
-0.00333404541015625,
-0.0249786376953125,
-0.016326904296875,
0.020294189453125,
0.026092529296875,
0.0240478515625,
0.016448974609375,
-0.01226806640625,
0.00782012939453125,
-0.007381439208984375,
0.0291595458984375,
-0.01561737060546875,
-0.0179901123046875,
-0.002597808837890625,
-0.01187896728515625,
0.00408935546875,
-0.027374267578125,
-0.03350830078125,
0.0311737060546875,
0.01352691650390625,
0.0305328369140625,
-0.00922393798828125,
0.005260467529296875,
-0.013336181640625,
0.02630615234375,
0.02410888671875,
-0.007678985595703125,
0.0047454833984375,
0.01352691650390625,
0.057220458984375,
0.0267333984375,
0.0166473388671875,
0.01049041748046875,
0.0022983551025390625,
0.01274871826171875,
-0.0555419921875,
-0.0152130126953125,
0.040435791015625,
0.01474761962890625,
0.01052093505859375,
0.01024627685546875,
-0.002155303955078125,
0.035858154296875,
-0.0277862548828125,
-0.03021240234375,
0.009063720703125,
-0.0008916854858398438,
-0.019439697265625,
0.0104522705078125,
-0.0017290115356445312,
0.0550537109375,
-0.003391265869140625,
-0.0004119873046875,
-0.0197601318359375,
-0.017730712890625,
0.0132904052734375,
0.004070281982421875,
-0.006076812744140625,
-0.00870513916015625,
-0.007724761962890625,
-0.01374053955078125,
0.007183074951171875,
-0.0016336441040039062,
-0.01059722900390625,
0.0172271728515625,
0.0012569427490234375,
0.0009508132934570312,
-0.0413818359375,
-0.00036263465881347656,
-0.0213775634765625,
0.0142059326171875,
0.004360198974609375,
-0.032623291015625,
-0.0450439453125,
0.017333984375,
-0.0012845993041992188,
-0.007740020751953125,
-0.0151214599609375,
-0.0347900390625,
-0.01090240478515625,
0.025177001953125,
-0.027801513671875,
-0.0279541015625,
-0.0024433135986328125,
-0.0399169921875,
-0.036285400390625,
-0.006298065185546875,
0.0020656585693359375,
-0.0229949951171875,
0.02386474609375,
0.00027298927307128906,
-0.00142669677734375,
-0.021697998046875,
-0.028106689453125,
-0.0029144287109375,
-0.007343292236328125,
0.014068603515625,
-0.0186614990234375,
0.0028247833251953125,
0.05078125,
-0.0204925537109375,
-0.00290679931640625,
0.029327392578125,
0.0234527587890625,
-0.001354217529296875,
-0.05609130859375,
-0.004390716552734375,
0.0133209228515625,
0.05377197265625,
0.025543212890625,
-0.0080718994140625,
-0.0164337158203125,
0.005092620849609375,
0.0006527900695800781,
0.0141754150390625,
0.0237579345703125,
0.01309967041015625,
-0.0243072509765625,
-0.0013904571533203125,
-0.00827789306640625,
0.00701904296875,
-0.00067901611328125,
0.004978179931640625,
0.005802154541015625,
0.0191650390625,
0.00846099853515625,
-0.00539398193359375,
0.0015401840209960938,
-0.026123046875,
0.006866455078125,
-0.0117034912109375,
-0.0006532669067382812,
0.01183319091796875,
0.003925323486328125,
-0.02294921875,
-0.0146636962890625,
0.0116729736328125,
0.01412200927734375,
0.0186309814453125,
0.01727294921875,
-0.01407623291015625,
-0.01328277587890625,
0.0021076202392578125,
0.0159912109375,
-0.0007643699645996094,
-0.011932373046875,
0.007335662841796875,
0.01061248779296875,
0.00727081298828125,
-0.01232147216796875,
-0.019683837890625,
-0.0232696533203125,
-0.0028781890869140625,
-0.0116424560546875,
-0.029327392578125,
-0.0019330978393554688,
0.026763916015625,
-0.0038280487060546875,
-0.00864410400390625,
0.0352783203125,
0.051666259765625,
-0.00577545166015625,
-0.02349853515625,
-0.015777587890625,
-0.0246734619140625,
-0.047393798828125,
0.0007843971252441406,
0.011474609375,
0.0077972412109375,
-0.0133819580078125,
0.0008635520935058594,
0.0014171600341796875,
-0.0036163330078125,
-0.0139617919921875,
-0.001651763916015625,
-0.0215606689453125,
0.0333251953125,
0.01500701904296875,
-0.01267242431640625,
0.0247802734375,
0.005558013916015625,
0.0094451904296875,
-0.003795623779296875,
-0.033721923828125,
-0.0006594657897949219,
-0.0287322998046875,
-0.0031261444091796875,
0.018707275390625,
-0.0164794921875,
0.019927978515625,
-0.0086669921875,
-0.007221221923828125,
0.00557708740234375,
0.01218414306640625,
0.035614013671875,
-0.01477813720703125,
0.0002841949462890625,
-0.02252197265625,
0.02484130859375,
-0.006397247314453125,
-0.007904052734375,
-0.006587982177734375,
0.023193359375,
0.01522064208984375,
0.010650634765625,
0.01500701904296875,
-0.01511383056640625,
0.0125579833984375,
-0.0246734619140625,
0.028656005859375,
0.01824951171875,
-0.0023956298828125,
-0.00318145751953125,
0.0036220550537109375,
-0.01172637939453125,
0.01421356201171875,
-0.018280029296875,
0.002101898193359375,
0.017578125,
0.0260162353515625,
-0.0137786865234375,
-0.004772186279296875,
0.0206298828125,
0.0263519287109375,
0.0303497314453125,
0.007068634033203125,
0.0007014274597167969,
-0.0036716461181640625,
0.004032135009765625,
-0.0102691650390625,
0.01214599609375,
-0.00699615478515625,
0.0041656494140625,
0.004627227783203125,
-0.0112457275390625,
0.006496429443359375,
0.040679931640625,
-0.03692626953125,
-0.03521728515625,
0.026611328125,
0.0231781005859375,
-0.0001474618911743164,
-0.00931549072265625,
-0.00612640380859375,
-0.01004791259765625,
-0.01776123046875,
0.0330810546875,
0.00865936279296875,
0.023223876953125,
-0.0004870891571044922,
0.00856781005859375,
0.0149688720703125,
-0.00408935546875,
0.020660400390625,
0.03643798828125,
0.005496978759765625,
0.0091400146484375,
0.0325927734375,
-0.01071929931640625,
0.0284271240234375,
0.0081939697265625,
-0.0194549560546875,
0.0138092041015625,
0.005130767822265625,
0.00659942626953125,
0.022308349609375,
-0.0148773193359375,
0.0272216796875,
0.0027904510498046875,
-0.046142578125,
-0.00458526611328125,
-0.03436279296875,
0.00339508056640625,
-0.014404296875,
-0.004192352294921875,
0.02435302734375,
0.00037288665771484375,
0.037872314453125,
0.009521484375,
0.00044727325439453125,
-0.0258331298828125,
-0.01904296875,
-0.00005996227264404297,
0.01131439208984375,
-0.00803375244140625,
-0.0220947265625,
-0.034515380859375,
-0.0175323486328125,
0.02532958984375,
0.01316070556640625,
-0.002300262451171875,
0.02532958984375,
-0.036102294921875,
-0.002685546875,
0.0250396728515625,
0.0224609375,
-0.0017976760864257812,
-0.01136016845703125,
0.036712646484375,
-0.007572174072265625,
0.024810791015625,
-0.016876220703125,
-0.02020263671875,
0.032745361328125,
0.006763458251953125,
-0.0134735107421875,
-0.030975341796875,
0.00726318359375,
-0.0241546630859375,
0.01537322998046875,
0.004688262939453125,
0.0012569427490234375,
0.00640106201171875,
0.007167816162109375,
-0.00604248046875,
-0.002689361572265625,
0.003620147705078125,
0.015838623046875,
0.00701141357421875,
0.0083160400390625,
-0.032440185546875,
0.04461669921875,
0.0297698974609375,
-0.01248931884765625,
0.0277252197265625,
-0.0007266998291015625,
0.034210205078125,
-0.005733489990234375,
-0.009857177734375,
-0.00621795654296875,
-0.01178741455078125,
-0.01457977294921875,
0.01328277587890625,
0.01503753662109375,
0.0119781494140625,
0.0192413330078125,
0.0230560302734375,
-0.00426483154296875,
-0.0182647705078125,
-0.006519317626953125,
-0.004482269287109375,
-0.028533935546875,
0.0222015380859375,
-0.03643798828125,
0.0183258056640625,
-0.03717041015625,
0.037078857421875,
-0.01206207275390625,
0.00011467933654785156,
0.0016937255859375,
0.0250091552734375,
-0.01230621337890625,
0.0287322998046875,
-0.012176513671875,
-0.00016391277313232422,
-0.031402587890625,
-0.01052093505859375,
-0.0037689208984375,
0.00293731689453125,
0.005268096923828125,
0.040557861328125,
-0.0009412765502929688,
-0.0006427764892578125,
-0.0111846923828125,
0.040069580078125,
-0.0021991729736328125,
0.0169525146484375,
0.0190277099609375,
0.01116180419921875,
0.0259246826171875,
-0.00785064697265625,
-0.0242156982421875,
0.0211334228515625,
-0.01255035400390625,
-0.01129150390625,
0.00783538818359375,
-0.006580352783203125,
0.024993896484375,
-0.0236053466796875,
-0.0169219970703125,
0.027435302734375,
0.00007456541061401367,
-0.0217132568359375,
-0.009857177734375,
-0.004535675048828125,
0.01076507568359375,
-0.053863525390625,
0.0000470280647277832,
-0.037750244140625,
0.019134521484375,
-0.0127716064453125,
-0.02203369140625,
0.007442474365234375,
0.0279388427734375,
0.0406494140625,
0.00469207763671875,
0.00894927978515625,
0.0016012191772460938,
0.007770538330078125,
-0.01276397705078125,
0.0029468536376953125,
-0.0196685791015625,
0.00662994384765625,
-0.0162200927734375,
-0.01494598388671875,
0.0055084228515625,
0.01428985595703125,
-0.0158843994140625,
-0.016448974609375,
-0.01361083984375,
0.022216796875,
-0.0196380615234375,
0.0011377334594726562,
0.032806396484375,
0.01035308837890625,
-0.0088653564453125,
0.016815185546875,
0.006832122802734375,
0.00263214111328125,
-0.0113677978515625,
-0.0256500244140625,
0.02642822265625,
-0.00763702392578125,
-0.0169219970703125,
0.0038852691650390625,
0.003856658935546875,
-0.0301513671875,
0.0294342041015625,
0.00284576416015625,
-0.00543975830078125,
0.0255889892578125,
-0.01071929931640625,
0.019989013671875,
-0.005748748779296875,
0.01044464111328125,
-0.01372528076171875,
-0.0013904571533203125,
0.00040411949157714844,
0.030426025390625,
0.004329681396484375,
0.0599365234375,
-0.00963592529296875,
0.000850677490234375,
0.0141754150390625,
-0.0174713134765625,
0.0018854141235351562,
0.01383209228515625,
0.03857421875,
0.0277252197265625,
-0.00955963134765625,
-0.03338623046875,
-0.006237030029296875,
-0.03375244140625,
0.01325225830078125,
0.0251312255859375,
-0.019317626953125,
0.01432037353515625,
-0.0026912689208984375,
0.03192138671875,
-0.0128631591796875,
0.01776123046875,
-0.00894927978515625,
0.002521514892578125,
-0.0117950439453125,
0.01800537109375,
0.018951416015625,
-0.00382232666015625,
0.0138092041015625,
-0.0277862548828125,
-0.005870819091796875,
0.0176544189453125,
-0.006740570068359375,
-0.01529693603515625,
-0.0472412109375,
0.0269012451171875,
0.027801513671875,
-0.0019664764404296875,
0.0172271728515625,
0.004665374755859375,
-0.0284576416015625,
-0.004058837890625,
0.0038700103759765625,
-0.00225067138671875,
-0.0094757080078125,
0.036163330078125,
-0.0168609619140625,
0.0200347900390625,
-0.022308349609375,
0.03912353515625,
0.0077362060546875,
-0.0025272369384765625,
0.0170745849609375,
-0.029693603515625,
0.01007080078125,
-0.00750732421875,
0.02642822265625,
0.006137847900390625,
-0.0088043212890625,
0.01418304443359375,
0.00920867919921875,
0.01284027099609375,
0.015106201171875,
-0.0003345012664794922,
-0.035247802734375,
-0.043853759765625,
0.0108489990234375,
0.011505126953125,
-0.021575927734375,
0.02984619140625,
-0.0032634735107421875,
-0.0231781005859375,
0.0078125,
0.0122833251953125,
-0.0228729248046875,
0.0255279541015625,
0.027740478515625,
0.036865234375,
0.052154541015625,
-0.01812744140625,
-0.0085296630859375,
-0.01224517822265625,
-0.0035648345947265625,
0.0165252685546875,
-0.0172119140625,
-0.005962371826171875,
0.007183074951171875,
-0.02978515625,
-0.0015020370483398438,
-0.01544189453125,
0.0208282470703125,
0.0010843276977539062,
0.00948333740234375,
-0.0196380615234375,
0.00638580322265625,
0.040313720703125,
0.01104736328125,
-0.01351165771484375,
0.006465911865234375,
0.036865234375,
0.026153564453125,
0.003482818603515625,
0.00992584228515625,
-0.014892578125,
0.02099609375,
0.0287933349609375,
-0.0261077880859375,
0.007755279541015625,
-0.0016279220581054688,
0.03387451171875,
0.00487518310546875,
-0.00701141357421875,
0.006168365478515625,
-0.0206146240234375,
-0.00554656982421875,
-0.00362396240234375,
-0.01947021484375,
0.005184173583984375,
0.007282257080078125,
-0.01154327392578125,
0.0120849609375,
0.03570556640625,
0.006732940673828125,
-0.018707275390625,
-0.0002665519714355469,
0.004062652587890625,
0.0008306503295898438,
-0.01076507568359375,
0.00501251220703125,
0.01181793212890625,
0.0100555419921875,
-0.00711822509765625,
-0.04827880859375,
-0.03326416015625,
0.0142364501953125,
0.00986480712890625,
-0.018829345703125,
-0.029754638671875,
-0.00653076171875,
-0.006465911865234375,
-0.0019931793212890625,
-0.0350341796875,
-0.018524169921875,
-0.0006432533264160156,
-0.0009126663208007812,
0.014007568359375,
-0.0308837890625,
0.0190277099609375,
0.0049285888671875,
-0.007381439208984375,
0.0157623291015625,
-0.0103607177734375,
0.041534423828125,
0.00966644287109375,
0.0139007568359375,
-0.04638671875,
-0.005840301513671875,
0.03863525390625,
0.0103759765625,
-0.0281829833984375,
0.00521087646484375,
0.0241241455078125,
0.0021991729736328125,
0.03448486328125,
-0.0166015625,
0.01708984375,
0.0005259513854980469,
0.0098876953125,
0.033355712890625,
-0.0281219482421875,
0.0252532958984375,
-0.0162200927734375,
-0.0195465087890625,
0.0262908935546875,
-0.017181396484375,
0.00606536865234375,
0.01904296875,
-0.0064697265625,
0.0172119140625,
-0.007564544677734375,
-0.0179290771484375,
0.005306243896484375,
0.0229949951171875,
0.00395965576171875,
-0.00991058349609375,
-0.040069580078125,
-0.01123046875,
0.0255584716796875,
0.0218048095703125,
0.0225982666015625,
0.004032135009765625,
-0.008453369140625,
0.00917816162109375,
0.0011625289916992188,
-0.033233642578125,
0.0033740997314453125,
0.01262664794921875,
-0.00724029541015625,
-0.003353118896484375,
0.007305145263671875,
0.00579833984375,
-0.0357666015625,
0.0103912353515625,
-0.03582763671875,
-0.0260009765625,
-0.0166778564453125,
0.03558349609375,
0.014678955078125,
0.0019273757934570312,
0.0196685791015625,
0.027557373046875,
0.0289459228515625,
0.038909912109375,
-0.0086517333984375,
0.0170440673828125,
-0.06585693359375,
-0.01253509521484375,
0.0182037353515625,
0.0014619827270507812,
-0.0121612548828125,
-0.0237884521484375,
-0.0022487640380859375,
0.0275421142578125,
-0.023773193359375,
-0.00936126708984375,
0.01302337646484375,
0.0018663406372070312,
0.0199737548828125,
-0.031402587890625,
-0.0014219284057617188,
-0.005229949951171875,
0.01509857177734375,
0.004024505615234375,
-0.00205230712890625,
-0.014556884765625,
0.01995849609375,
0.02581787109375,
-0.0335693359375,
0.0240325927734375,
-0.005428314208984375,
0.0018587112426757812,
0.0033016204833984375,
0.0026092529296875,
0.01291656494140625,
0.0140380859375,
-0.0016298294067382812,
-0.01561737060546875,
-0.0081939697265625,
0.00739288330078125,
0.016448974609375,
-0.0228271484375,
-0.005794525146484375,
0.01134490966796875,
-0.006500244140625,
0.0166015625,
-0.0195770263671875,
-0.05047607421875,
-0.0090789794921875,
0.0107269287109375,
-0.0098114013671875,
-0.0005779266357421875,
0.059844970703125,
0.034576416015625,
-0.0276947021484375,
-0.0003666877746582031,
0.014068603515625,
-0.015289306640625,
-0.0177764892578125,
-0.026275634765625,
0.01384735107421875,
0.042724609375,
0.0014314651489257812,
-0.016448974609375,
-0.026641845703125,
0.0169830322265625,
-0.0067901611328125,
0.00016570091247558594,
0.0128021240234375,
-0.015899658203125,
0.0132904052734375,
-0.0145721435546875,
-0.000812530517578125,
-0.032958984375,
-0.0215301513671875,
0.002811431884765625,
-0.032806396484375,
-0.00015532970428466797,
0.010406494140625,
0.01081085205078125,
-0.03204345703125,
-0.029571533203125,
-0.00119781494140625,
-0.025604248046875,
-0.01045989990234375,
-0.0236968994140625,
0.0012311935424804688,
-0.006793975830078125,
0.0044097900390625,
0.01404571533203125,
0.00536346435546875,
0.0251617431640625,
-0.010986328125,
-0.05950927734375,
-0.013397216796875,
-0.01009368896484375,
-0.00372314453125,
0.00940704345703125,
0.010223388671875,
0.02410888671875,
-0.0084075927734375,
-0.00958251953125,
-0.01485443115234375,
0.01800537109375,
-0.01654052734375,
-0.062164306640625,
0.00342559814453125,
-0.0119781494140625,
-0.013916015625,
0.0369873046875,
0.002391815185546875,
0.0303955078125,
0.0269012451171875,
-0.01297760009765625,
0.0276336669921875,
0.01023101806640625,
-0.01296234130859375,
-0.047210693359375,
-0.004497528076171875,
0.0105438232421875,
0.007320404052734375,
0.0261993408203125,
-0.0173492431640625,
-0.01435089111328125,
-0.0184478759765625,
-0.0263214111328125,
0.0003483295440673828,
0.0201416015625,
0.042144775390625,
-0.025665283203125,
-0.0091705322265625,
-0.02545166015625,
0.007389068603515625
] |
ours_480
|
It is well-known that the circumradius \(R\) and inradius \(r\) are \(\frac{65}{8}\) and \(4\) respectively. By Euler's formula, we have that \(OI' = d = \sqrt{R^2 - 2Rr} = \frac{\sqrt{65}}{8}\), where \(I'\) denotes the incenter. Notice that if an inclusive circle with center \(P\) has radius \(x\), then \(OP = R - x\), \(I'P = x - r\), which implies \(OP + I'P = R - r\). Thus, \(\mathcal{I}\) is an ellipse with foci \(O\) and \(I'\) and major axis \(R - r\). The minor axis of this ellipse is \(\sqrt{(R - r)^2 - d^2} = \sqrt{r^2} = r\), which means that \(I = \pi(R - r)r = \frac{33}{2} \pi\).
Similarly, if an exclusive circle has center \(P\) and radius \(x\), then \(OP = R - x\), \(I'P = x + r\), which implies \(OP + IP = R + r\). Thus, \(\mathcal{E}\) is an ellipse with foci \(O\) and \(I'\) and major axis \(R + r\). The minor axis of this ellipse is \(\sqrt{(R + r)^2 - d^2} = \sqrt{r^2 + 4Rr}\), which means that \(E = \pi(R + r) \sqrt{r^2 + 4Rr} = \frac{97 \sqrt{146}}{8} \pi\).
Therefore, the ratio is equal to \(\frac{132}{97 \sqrt{146}}\), and its square is \(\frac{8712}{686857}\), so our answer is \(\boxed{1558057}\).
|
1558057
|
{
"competition": "us_comps",
"dataset": "Ours",
"posts": null,
"source": "OMOFall18Solns.md"
}
|
In triangle \(ABC\), \(AB = 13\), \(BC = 14\), \(CA = 15\). Let \(\Omega\) and \(\omega\) be the circumcircle and incircle of \(ABC\) respectively. Among all circles that are tangent to both \(\Omega\) and \(\omega\), call those that contain \(\omega\) inclusive and those that do not contain \(\omega\) exclusive. Let \(\mathcal{I}\) and \(\mathcal{E}\) denote the set of centers of inclusive circles and exclusive circles respectively, and let \(I\) and \(E\) be the area of the regions enclosed by \(\mathcal{I}\) and \(\mathcal{E}\) respectively. The ratio \(\frac{I}{E}\) can be expressed as \(\sqrt{\frac{m}{n}}\), where \(m\) and \(n\) are relatively prime positive integers. Compute \(100m + n\).
|
[
"/Mathematics/Geometry/Curves/AlgebraicCurves/Ellipse",
"/Mathematics/Geometry/Curves/PlaneCurves/AlgebraicCurves",
"/Mathematics/Geometry/Curves/PlaneCurves/ConicSections",
"/Mathematics/Geometry/GeneralGeometry/Center",
"/Mathematics/Geometry/GeneralGeometry/EuclideanGeometry",
"/Mathematics/Geometry/GeneralGeometry/Geometry",
"/Mathematics/Geometry/PlaneGeometry/Circles/Circle",
"/Mathematics/Geometry/PlaneGeometry/Circles/Circle-CircleTangents",
"/Mathematics/Geometry/PlaneGeometry/Circles/Circumcenter",
"/Mathematics/Geometry/PlaneGeometry/Circles/Incenter",
"/Mathematics/Geometry/PlaneGeometry/Circles/Radius",
"/Mathematics/Geometry/PlaneGeometry/Circles/TangentCircles",
"/Mathematics/Geometry/PlaneGeometry/Triangles/TriangleCenters",
"/Mathematics/Geometry/PlaneGeometry/Triangles/TriangleCircles",
"/Mathematics/Geometry/PlaneGeometry/Triangles/TriangleConics"
] |
Identify that the centers of circles tangent to both given circles form ellipses whose foci are the two circle centers and whose major axis equals the sum (or difference) of the radii.
|
[
-0.000011265277862548828,
-0.01535797119140625,
0.01055908203125,
0.0251007080078125,
0.00013649463653564453,
0.025421142578125,
0.00811767578125,
0.0234527587890625,
0.00318145751953125,
-0.033782958984375,
0.0185394287109375,
0.0007510185241699219,
-0.006008148193359375,
0.03973388671875,
-0.01268768310546875,
-0.0070953369140625,
-0.014312744140625,
-0.03924560546875,
0.0239715576171875,
0.0003490447998046875,
-0.0073089599609375,
0.0036983489990234375,
-0.06414794921875,
0.0246124267578125,
-0.01503753662109375,
-0.021331787109375,
-0.01096343994140625,
-0.01190948486328125,
0.0007619857788085938,
0.0035610198974609375,
0.00817108154296875,
-0.01412200927734375,
0.02655029296875,
0.0033893585205078125,
0.00008165836334228516,
0.0201873779296875,
0.022003173828125,
0.001873016357421875,
-0.0214385986328125,
-0.02642822265625,
-0.0008525848388671875,
0.04022216796875,
-0.0136871337890625,
-0.0017309188842773438,
-0.005832672119140625,
0.004787445068359375,
0.00675201416015625,
0.010498046875,
-0.00426483154296875,
0.01263427734375,
0.00905609130859375,
0.018829345703125,
-0.01450347900390625,
-0.0036334991455078125,
-0.0022411346435546875,
-0.060760498046875,
0.00469207763671875,
-0.00266265869140625,
-0.0193634033203125,
0.002040863037109375,
0.00336456298828125,
0.01947021484375,
0.00897216796875,
-0.00983428955078125,
0.0006031990051269531,
-0.00820159912109375,
-0.0185699462890625,
-0.0210723876953125,
-0.005859375,
0.0109710693359375,
0.0236968994140625,
-0.03375244140625,
0.0159454345703125,
0.019439697265625,
0.029998779296875,
-0.00911712646484375,
-0.01025390625,
0.006610870361328125,
0.0007901191711425781,
0.005985260009765625,
-0.01096343994140625,
0.004486083984375,
0.005828857421875,
-0.0285797119140625,
0.01251220703125,
-0.02606201171875,
0.002498626708984375,
-0.00001239776611328125,
0.03143310546875,
-0.003322601318359375,
-0.0019378662109375,
0.0296478271484375,
-0.00968170166015625,
-0.0032405853271484375,
0.0033054351806640625,
0.0084991455078125,
0.0031375885009765625,
-0.0105743408203125,
-0.0181732177734375,
-0.0017423629760742188,
-0.01483154296875,
-0.0087127685546875,
0.0109100341796875,
-0.026397705078125,
-0.0014524459838867188,
-0.0139923095703125,
0.00759124755859375,
0.0005636215209960938,
0.0092315673828125,
-0.00902557373046875,
0.0092620849609375,
-0.0259857177734375,
0.029205322265625,
0.027069091796875,
0.0030879974365234375,
-0.021270751953125,
0.03631591796875,
-0.00991058349609375,
-0.0165252685546875,
-0.0243072509765625,
0.0004992485046386719,
0.006977081298828125,
0.020721435546875,
0.006214141845703125,
0.00887298583984375,
-0.007404327392578125,
0.00850677490234375,
-0.01947021484375,
-0.036285400390625,
-0.005092620849609375,
0.040771484375,
0.01454925537109375,
-0.0423583984375,
-0.016204833984375,
-0.0458984375,
-0.0029239654541015625,
0.0009126663208007812,
0.003368377685546875,
-0.02276611328125,
-0.00977325439453125,
-0.0010156631469726562,
0.004665374755859375,
0.0016956329345703125,
-0.06402587890625,
0.004650115966796875,
-0.01061248779296875,
-0.01335906982421875,
0.0089263916015625,
0.002552032470703125,
0.0069427490234375,
0.002918243408203125,
-0.0145721435546875,
-0.00914764404296875,
0.00255584716796875,
-0.006084442138671875,
-0.006008148193359375,
0.01100921630859375,
0.0037441253662109375,
0.00012755393981933594,
0.01161956787109375,
-0.0062103271484375,
-0.0166015625,
-0.003719329833984375,
0.007030487060546875,
0.00713348388671875,
-0.01189422607421875,
0.01326751708984375,
-0.006549835205078125,
-0.0010051727294921875,
0.0020694732666015625,
-0.007167816162109375,
0.003261566162109375,
0.00881195068359375,
-0.0018854141235351562,
0.0132598876953125,
0.0019311904907226562,
-0.01224517822265625,
0.02288818359375,
-0.00951385498046875,
0.017669677734375,
-0.00018155574798583984,
-0.01433563232421875,
0.0287628173828125,
-0.0139923095703125,
0.013763427734375,
0.017578125,
0.01049041748046875,
0.0130462646484375,
0.0140838623046875,
0.00905609130859375,
-0.005523681640625,
-0.0104827880859375,
-0.0061798095703125,
0.005870819091796875,
0.01861572265625,
0.00399017333984375,
-0.012847900390625,
0.02496337890625,
0.034027099609375,
0.00238037109375,
-0.010711669921875,
-0.0090179443359375,
0.0301666259765625,
-0.006450653076171875,
-0.000054895877838134766,
0.006134033203125,
-0.0166778564453125,
-0.004680633544921875,
-0.009979248046875,
0.0127410888671875,
-0.0014715194702148438,
0.0249176025390625,
-0.0024776458740234375,
-0.0023555755615234375,
-0.017578125,
-0.0136566162109375,
-0.01000213623046875,
0.01296234130859375,
0.0001862049102783203,
-0.01947021484375,
-0.0014467239379882812,
-0.002513885498046875,
0.01079559326171875,
-0.032958984375,
-0.0172271728515625,
0.0207366943359375,
-0.002048492431640625,
-0.0079803466796875,
0.00428009033203125,
0.0015840530395507812,
0.0022144317626953125,
-0.0092315673828125,
-0.0009469985961914062,
0.00807952880859375,
-0.016510009765625,
-0.014739990234375,
-0.05560302734375,
-0.0011243820190429688,
0.004909515380859375,
-0.01336669921875,
0.040313720703125,
-0.002643585205078125,
0.012054443359375,
-0.0039520263671875,
0.0023193359375,
-0.0027561187744140625,
0.0229644775390625,
-0.0237884521484375,
0.00637054443359375,
-0.01085662841796875,
-0.0192413330078125,
0.0265960693359375,
-0.0035247802734375,
-0.015655517578125,
-0.004970550537109375,
0.00460052490234375,
0.019775390625,
0.0212554931640625,
-0.0004177093505859375,
0.0029087066650390625,
-0.0090179443359375,
-0.0222015380859375,
-0.004878997802734375,
-0.0073394775390625,
-0.0106048583984375,
0.0216064453125,
0.018096923828125,
0.0135040283203125,
0.0127716064453125,
-0.0005431175231933594,
0.05584716796875,
-0.0228424072265625,
-0.021759033203125,
0.00885772705078125,
-0.0101165771484375,
-0.0298614501953125,
-0.000579833984375,
-0.0005311965942382812,
0.016571044921875,
0.0006728172302246094,
0.0291290283203125,
-0.021759033203125,
0.01009368896484375,
0.01361846923828125,
0.0027904510498046875,
0.0020694732666015625,
0.00800323486328125,
-0.036346435546875,
-0.004302978515625,
0.015472412109375,
0.00946807861328125,
0.02191162109375,
-0.0233612060546875,
0.0024852752685546875,
0.0292510986328125,
-0.00606536865234375,
-0.0008640289306640625,
0.01088714599609375,
0.00977325439453125,
0.0285491943359375,
0.0245819091796875,
-0.01097869873046875,
-0.005657196044921875,
0.005130767822265625,
0.02655029296875,
0.005619049072265625,
-0.004901885986328125,
-0.01172637939453125,
-0.0110015869140625,
-0.0155792236328125,
0.0148162841796875,
0.007740020751953125,
-0.0183563232421875,
0.00862884521484375,
-0.0423583984375,
-0.023040771484375,
0.006504058837890625,
0.00644683837890625,
-0.007503509521484375,
0.01390838623046875,
0.003814697265625,
0.0094451904296875,
0.005954742431640625,
0.005428314208984375,
0.019378662109375,
-0.016143798828125,
0.004150390625,
-0.00281524658203125,
-0.0130157470703125,
0.038787841796875,
-0.003810882568359375,
0.00262451171875,
-0.005237579345703125,
-0.015228271484375,
0.0080413818359375,
0.01531219482421875,
0.0150604248046875,
0.01284027099609375,
0.0135345458984375,
0.01335906982421875,
0.006084442138671875,
0.012176513671875,
0.0330810546875,
-0.069091796875,
-0.014556884765625,
0.0203704833984375,
-0.023468017578125,
-0.008148193359375,
-0.01441192626953125,
-0.04119873046875,
0.0158233642578125,
0.0189056396484375,
0.031463623046875,
0.026641845703125,
-0.01142120361328125,
-0.006359100341796875,
0.00008445978164672852,
0.005306243896484375,
0.0025806427001953125,
-0.00499725341796875,
0.0226593017578125,
-0.0083465576171875,
-0.0220794677734375,
0.034088134765625,
0.00015234947204589844,
0.0006504058837890625,
-0.0355224609375,
-0.01251983642578125,
-0.0457763671875,
-0.01157379150390625,
-0.0032501220703125,
-0.0082244873046875,
0.008331298828125,
0.0016584396362304688,
0.0247802734375,
-0.01690673828125,
-0.023590087890625,
0.0171661376953125,
-0.017486572265625,
0.005962371826171875,
-0.019805908203125,
-0.005405426025390625,
0.00202178955078125,
0.027557373046875,
-0.01285552978515625,
0.00757598876953125,
0.0249176025390625,
-0.035797119140625,
0.007755279541015625,
-0.0026721954345703125,
-0.0130462646484375,
0.0263824462890625,
-0.007266998291015625,
-0.013763427734375,
-0.0209503173828125,
-0.0247802734375,
-0.00868988037109375,
0.00524139404296875,
0.0307769775390625,
-0.039520263671875,
-0.0540771484375,
0.021697998046875,
0.027618408203125,
0.0133209228515625,
-0.00658416748046875,
-0.00476837158203125,
-0.033447265625,
0.01433563232421875,
-0.0009589195251464844,
0.022705078125,
0.00246429443359375,
0.015869140625,
0.0024089813232421875,
-0.01444244384765625,
-0.031829833984375,
0.01276397705078125,
-0.0170440673828125,
0.0001329183578491211,
-0.021697998046875,
-0.0310211181640625,
0.013397216796875,
-0.01214599609375,
0.019744873046875,
-0.0117034912109375,
0.0233917236328125,
-0.00406646728515625,
-0.008331298828125,
0.0380859375,
-0.003307342529296875,
-0.01641845703125,
0.01555633544921875,
-0.034271240234375,
-0.0123138427734375,
0.0343017578125,
-0.01477813720703125,
0.0140228271484375,
0.006443023681640625,
-0.0009984970092773438,
0.016021728515625,
0.005329132080078125,
-0.0233917236328125,
0.0041961669921875,
0.024200439453125,
0.01007080078125,
0.0165863037109375,
0.01611328125,
0.0207977294921875,
-0.00908660888671875,
-0.0293731689453125,
0.0251617431640625,
-0.0172271728515625,
-0.005706787109375,
-0.0080718994140625,
-0.04327392578125,
-0.0012493133544921875,
0.024932861328125,
0.037872314453125,
-0.03387451171875,
-0.0312347412109375,
0.01477813720703125,
-0.001064300537109375,
0.018463134765625,
-0.007404327392578125,
0.0189056396484375,
-0.00897979736328125,
-0.0010223388671875,
0.001163482666015625,
0.028472900390625,
-0.02471923828125,
0.012542724609375,
-0.0116119384765625,
-0.003326416015625,
-0.00004678964614868164,
-0.0217437744140625,
-0.028045654296875,
0.02899169921875,
-0.019195556640625,
-0.0091400146484375,
-0.0070648193359375,
0.01340484619140625,
-0.00600433349609375,
0.00279998779296875,
-0.00676727294921875,
-0.007411956787109375,
0.0144500732421875,
0.0182647705078125,
0.0202789306640625,
-0.004566192626953125,
-0.04437255859375,
-0.040496826171875,
-0.007678985595703125,
0.0173797607421875,
-0.0182647705078125,
-0.005413055419921875,
-0.024627685546875,
-0.0294189453125,
0.01342010498046875,
0.0055999755859375,
0.024932861328125,
0.0023632049560546875,
0.015594482421875,
-0.022247314453125,
-0.00823974609375,
-0.0182342529296875,
0.0167388916015625,
-0.035675048828125,
0.04791259765625,
-0.005687713623046875,
0.0168609619140625,
-0.0135498046875,
-0.0037860870361328125,
0.01436614990234375,
0.03094482421875,
-0.035888671875,
0.033935546875,
-0.0087127685546875,
-0.0079803466796875,
-0.0016803741455078125,
0.01560211181640625,
0.07012939453125,
-0.036163330078125,
0.01910400390625,
0.0230865478515625,
0.031890869140625,
0.012969970703125,
0.00919342041015625,
-0.0005078315734863281,
-0.0164337158203125,
0.02093505859375,
-0.01751708984375,
-0.034942626953125,
-0.0231781005859375,
-0.038330078125,
0.006221771240234375,
-0.04168701171875,
0.03167724609375,
0.0124053955078125,
-0.005542755126953125,
0.0034580230712890625,
-0.005619049072265625,
-0.01137542724609375,
0.007404327392578125,
0.004909515380859375,
-0.031768798828125,
-0.0125732421875,
-0.02044677734375,
-0.01617431640625,
-0.0239715576171875,
-0.0309906005859375,
-0.003818511962890625,
0.0209503173828125,
0.015838623046875,
-0.0526123046875,
0.00579071044921875,
-0.04736328125,
-0.006229400634765625,
-0.030975341796875,
0.0274658203125,
-0.005977630615234375,
0.0196685791015625,
0.0243682861328125,
0.01181793212890625,
0.0330810546875,
-0.0267181396484375,
-0.015869140625,
0.0218658447265625,
0.0069122314453125,
-0.004802703857421875,
-0.00543212890625,
-0.03240966796875,
0.0126495361328125,
-0.02203369140625,
0.0268707275390625,
0.00860595703125,
0.05084228515625,
-0.01136016845703125,
-0.003818511962890625,
0.022857666015625,
0.032684326171875,
-0.040252685546875,
0.028106689453125,
0.0162811279296875,
-0.0234832763671875,
-0.01519012451171875,
-0.022918701171875,
0.0105133056640625,
0.0308837890625,
-0.010498046875,
0.0080413818359375,
-0.00940704345703125,
-0.012237548828125,
-0.004638671875,
0.0161895751953125,
-0.0263214111328125,
-0.0014371871948242188,
-0.0307464599609375,
0.026153564453125,
0.003955841064453125,
0.03668212890625,
0.004787445068359375,
-0.043792724609375,
-0.0015192031860351562,
-0.016021728515625,
0.040771484375,
0.008453369140625,
-0.01446533203125,
-0.0167083740234375,
-0.007732391357421875,
0.00995635986328125,
0.0259857177734375,
-0.008148193359375,
0.0238037109375,
-0.026336669921875,
0.0070037841796875,
0.0034046173095703125,
-0.0211944580078125,
-0.0213470458984375,
0.0096893310546875,
-0.00569915771484375,
-0.01305389404296875,
0.00548553466796875,
0.025482177734375,
-0.00771331787109375,
-0.010345458984375,
0.0035552978515625,
-0.0028076171875,
-0.007236480712890625,
-0.047698974609375,
-0.005859375,
-0.0418701171875,
-0.048309326171875,
0.0110321044921875,
-0.037750244140625,
-0.0264129638671875,
-0.03350830078125,
-0.019805908203125,
0.031982421875,
0.0172882080078125,
-0.007366180419921875,
-0.045257568359375,
0.006107330322265625,
0.006954193115234375,
0.041351318359375,
-0.0557861328125,
-0.006473541259765625,
-0.0106658935546875,
-0.02496337890625,
-0.01490020751953125,
0.005901336669921875,
0.0219268798828125,
-0.02374267578125,
0.0203094482421875,
0.0308837890625,
0.0186767578125,
0.0135040283203125,
-0.035430908203125,
-0.036895751953125,
-0.023223876953125,
0.047760009765625,
0.0184478759765625,
-0.004550933837890625,
0.0067138671875,
0.006137847900390625,
0.00945281982421875,
0.024322509765625,
0.01369476318359375,
-0.040771484375,
-0.0192718505859375,
0.00429534912109375,
0.0335693359375,
-0.01137542724609375,
-0.00867462158203125,
0.018463134765625,
-0.0104522705078125,
-0.007694244384765625,
0.0308074951171875,
-0.034088134765625,
-0.007770538330078125,
-0.00385284423828125,
0.0186614990234375,
0.01183319091796875,
0.032196044921875,
0.0312042236328125,
-0.00626373291015625,
-0.002201080322265625,
0.044830322265625,
-0.0002727508544921875,
-0.017486572265625,
0.0157318115234375,
-0.0135040283203125,
-0.003917694091796875,
0.047821044921875,
-0.0258026123046875,
-0.014892578125,
-0.0265045166015625,
-0.01654052734375,
0.02130126953125,
-0.01580810546875,
-0.00888824462890625,
-0.0047760009765625,
0.0166473388671875,
-0.018890380859375,
0.0102081298828125,
-0.01215362548828125,
0.0153350830078125,
-0.01435089111328125,
-0.0193939208984375,
0.01200103759765625,
-0.04400634765625,
-0.00026917457580566406,
-0.044891357421875,
-0.0205230712890625,
-0.029449462890625,
0.0166473388671875,
-0.0246734619140625,
-0.0222015380859375,
-0.0033206939697265625,
-0.0015478134155273438,
-0.0162506103515625,
-0.00201416015625,
-0.025360107421875,
-0.00042939186096191406,
0.00440216064453125,
-0.018768310546875,
0.004207611083984375,
-0.01291656494140625,
-0.01277923583984375,
-0.0234527587890625,
-0.04278564453125,
0.0079803466796875,
-0.0183868408203125,
-0.0027751922607421875,
0.0005893707275390625,
-0.016693115234375,
0.0029926300048828125,
-0.00218963623046875,
-0.0235748291015625,
-0.019378662109375,
0.0030994415283203125,
0.01523590087890625,
0.0234832763671875,
-0.033905029296875,
0.004322052001953125,
0.00005060434341430664,
0.0236358642578125,
-0.006832122802734375,
-0.00920867919921875,
0.0015745162963867188,
0.0232391357421875,
-0.002063751220703125,
0.051055908203125,
0.016143798828125,
-0.01898193359375,
-0.0265045166015625,
-0.0027751922607421875,
-0.00252532958984375,
-0.007266998291015625,
-0.0058135986328125,
0.0277862548828125,
0.01250457763671875,
-0.0208740234375,
-0.0029449462890625,
0.01995849609375,
-0.0265045166015625,
-0.00841522216796875,
-0.01812744140625,
0.0237579345703125,
-0.034393310546875,
-0.04156494140625,
0.0012273788452148438,
-0.00748443603515625,
0.002529144287109375,
0.0254974365234375,
-0.0054168701171875,
0.0261993408203125,
0.00872039794921875,
-0.0190887451171875,
-0.0211334228515625,
0.0128631591796875,
0.00450897216796875,
-0.00624847412109375,
0.007183074951171875,
0.01430511474609375,
0.0233306884765625,
-0.01529693603515625,
-0.0258331298828125,
-0.006656646728515625,
-0.005542755126953125,
0.0218963623046875,
-0.0006966590881347656,
0.0227203369140625,
0.0009822845458984375,
0.0150909423828125,
0.010009765625,
-0.008758544921875,
-0.0198974609375,
-0.00024390220642089844,
-0.0223236083984375,
-0.0022106170654296875,
-0.0118865966796875,
0.012664794921875,
-0.003414154052734375,
-0.0172576904296875,
0.012969970703125,
0.0244903564453125,
-0.0006685256958007812,
-0.0064239501953125,
0.0054473876953125,
-0.0173797607421875,
-0.0009288787841796875,
0.01168060302734375,
0.01551055908203125,
0.020416259765625,
0.01392364501953125,
-0.00726318359375,
-0.026336669921875,
-0.00206756591796875,
-0.0160064697265625,
0.0102691650390625,
-0.01256561279296875,
-0.031097412109375,
0.0207061767578125,
-0.030426025390625,
-0.013916015625,
-0.042694091796875,
0.0018663406372070312,
0.00649261474609375,
-0.01080322265625,
0.027252197265625,
0.01473236083984375,
0.03692626953125,
-0.0239410400390625,
-0.0202484130859375,
0.01055908203125,
-0.0042572021484375,
0.0251922607421875,
-0.00604248046875,
0.01313018798828125,
-0.019439697265625,
-0.03717041015625,
0.01934814453125,
-0.0151214599609375,
-0.006694793701171875,
0.024810791015625,
0.0176544189453125,
-0.029754638671875,
-0.0051727294921875,
-0.00012993812561035156,
0.034332275390625,
-0.005504608154296875,
-0.006107330322265625,
0.018035888671875,
-0.03558349609375,
0.0284271240234375,
0.01084136962890625,
-0.00339508056640625,
0.005672454833984375,
0.0005741119384765625,
0.00513458251953125,
-0.024078369140625,
0.01006317138671875,
-0.03216552734375,
0.007534027099609375,
0.0242919921875,
0.0185089111328125,
0.01361083984375,
0.00693511962890625,
-0.0248260498046875,
0.0506591796875,
-0.00730133056640625,
0.037628173828125,
-0.016876220703125,
0.00705718994140625,
-0.00710296630859375,
0.0121612548828125,
0.025115966796875,
0.0265350341796875,
0.033782958984375,
0.040740966796875,
-0.00004595518112182617,
0.01558685302734375,
-0.022796630859375,
-0.035797119140625,
-0.018157958984375,
0.007160186767578125,
0.0228729248046875,
-0.0023517608642578125,
-0.0200347900390625,
-0.00045180320739746094,
-0.0035648345947265625,
0.020904541015625,
-0.028411865234375,
-0.0019216537475585938,
-0.025177001953125,
0.05157470703125,
-0.01180267333984375,
0.006565093994140625,
-0.0240325927734375,
-0.021026611328125,
-0.0196685791015625,
-0.0010194778442382812,
0.015289306640625,
0.01351165771484375,
-0.0179443359375,
-0.008819580078125,
-0.00826263427734375,
-0.01531982421875,
0.0188446044921875,
0.00919342041015625,
0.051055908203125,
-0.0297698974609375,
0.018524169921875,
0.0219879150390625,
0.00821685791015625,
-0.01229095458984375,
0.006832122802734375,
-0.01470947265625,
-0.004970550537109375,
-0.00603485107421875,
0.0145111083984375,
0.0014801025390625,
0.0257415771484375,
-0.007781982421875,
-0.00922393798828125,
0.003925323486328125,
-0.00974273681640625,
0.01222991943359375,
-0.01520538330078125,
-0.057861328125,
0.020660400390625,
0.0115966796875,
0.02960205078125,
0.00506591796875,
-0.00539398193359375,
-0.00848388671875,
-0.0043792724609375,
-0.00537872314453125,
-0.03515625,
-0.003894805908203125,
-0.0286407470703125,
-0.00991058349609375,
-0.009918212890625,
0.01107025146484375,
0.00795745849609375,
-0.004791259765625,
0.01433563232421875,
-0.0115203857421875,
-0.0036773681640625,
0.0078277587890625,
-0.0276031494140625,
0.005321502685546875,
-0.008056640625,
-0.01055908203125,
-0.006198883056640625,
-0.0032958984375,
-0.003143310546875,
-0.0010213851928710938,
0.03546142578125,
0.0106658935546875,
0.0056304931640625,
0.0224151611328125,
0.0171051025390625,
-0.0145263671875,
0.024658203125,
0.0004925727844238281,
0.02508544921875,
0.0384521484375,
0.012847900390625,
0.02783203125,
-0.013702392578125,
0.01082611083984375,
-0.037506103515625,
0.004047393798828125,
-0.020111083984375,
0.0082550048828125,
0.0200347900390625,
0.0198211669921875,
0.0052490234375,
0.037261962890625,
-0.0004799365997314453,
-0.0399169921875,
0.035614013671875,
0.01277923583984375,
0.0005893707275390625,
0.00496673583984375,
-0.0045318603515625,
0.02545166015625,
-0.0110931396484375,
0.0206756591796875,
-0.02935791015625,
0.00371551513671875,
0.0211944580078125,
0.0019855499267578125,
0.010406494140625,
-0.008209228515625,
0.042999267578125,
0.0009775161743164062,
-0.03662109375,
0.0185394287109375,
-0.00473785400390625,
-0.0572509765625,
0.004184722900390625,
0.0195770263671875,
-0.01160430908203125,
0.0225830078125,
-0.022308349609375,
-0.021820068359375,
0.00494384765625,
0.01189422607421875,
0.021331787109375,
-0.008209228515625,
0.01172637939453125,
0.0035305023193359375,
0.01094818115234375,
-0.019378662109375,
0.01255035400390625,
-0.00867462158203125,
0.0133209228515625,
-0.0175933837890625,
0.0340576171875,
-0.00984954833984375,
-0.01401519775390625,
-0.04632568359375,
-0.042327880859375,
0.00496673583984375,
-0.01093292236328125,
-0.0272979736328125,
-0.022674560546875,
0.0229339599609375,
0.0269622802734375,
-0.008544921875,
0.053680419921875,
-0.009368896484375,
-0.020294189453125,
-0.002201080322265625,
-0.002498626708984375,
0.0019464492797851562,
-0.005039215087890625,
0.045013427734375,
-0.00001817941665649414,
-0.006252288818359375,
0.00754547119140625,
0.01300048828125,
-0.0178985595703125,
-0.0241546630859375,
0.0208892822265625,
-0.004436492919921875,
0.005462646484375,
-0.002201080322265625,
0.01276397705078125,
-0.005367279052734375,
0.00811767578125,
-0.0282440185546875,
0.03204345703125,
0.01776123046875,
0.0322265625,
0.004245758056640625,
-0.024993896484375,
0.01134490966796875,
0.01230621337890625,
0.04248046875,
-0.061798095703125,
0.0178375244140625,
-0.04144287109375,
0.00872802734375,
-0.0113525390625,
-0.007076263427734375,
0.004848480224609375,
0.01873779296875,
0.026611328125,
-0.034210205078125,
-0.01256561279296875,
-0.00020051002502441406,
0.00817108154296875,
-0.006626129150390625,
-0.01126861572265625,
0.0313720703125,
-0.039276123046875,
-0.0099334716796875,
-0.0017528533935546875,
-0.01318359375,
0.020050048828125,
-0.02899169921875,
-0.0118560791015625,
0.0278778076171875,
0.007419586181640625,
0.00943756103515625,
-0.0310211181640625,
0.0231170654296875,
0.0013265609741210938,
0.00010275840759277344,
0.01312255859375,
-0.001224517822265625,
0.005512237548828125,
0.03668212890625,
-0.0211181640625,
0.02740478515625,
0.044586181640625,
0.021087646484375,
0.0139923095703125,
0.010284423828125,
0.041778564453125,
0.00930023193359375,
0.033355712890625,
0.0230865478515625,
-0.019012451171875,
-0.03204345703125,
0.0141448974609375,
-0.006755828857421875,
-0.0097503662109375,
0.00018656253814697266,
0.02008056640625,
0.02447509765625,
-0.0045013427734375,
-0.0186767578125,
-0.0215301513671875,
-0.037384033203125,
-0.012969970703125,
-0.0014019012451171875,
-0.0011749267578125,
-0.00397491455078125,
0.0229949951171875,
-0.00481414794921875,
0.025543212890625,
0.006175994873046875,
-0.0081329345703125,
0.0178680419921875,
-0.006038665771484375,
-0.007843017578125,
0.0018444061279296875,
0.0187530517578125,
0.026641845703125,
-0.0028591156005859375,
-0.0055694580078125,
-0.016998291015625,
0.01236724853515625,
0.010650634765625,
-0.0179443359375,
0.0008087158203125,
-0.0246734619140625,
-0.01042938232421875,
0.01166534423828125,
0.0190582275390625,
-0.06390380859375,
-0.0103759765625,
-0.019866943359375,
-0.00215911865234375,
-0.009735107421875,
0.025543212890625,
0.0121612548828125,
-0.00711822509765625,
-0.0008168220520019531,
-0.00330352783203125,
-0.00415802001953125,
-0.0036983489990234375,
-0.034576416015625,
-0.035003662109375,
-0.0166778564453125,
0.0213470458984375,
-0.00872039794921875,
-0.0294036865234375,
0.0023059844970703125,
0.0164947509765625,
0.0521240234375,
-0.017669677734375,
0.01358795166015625,
0.01557159423828125,
0.02850341796875,
-0.0157318115234375,
0.035247802734375,
-0.00490570068359375,
0.00009679794311523438,
0.0148773193359375,
0.019683837890625,
-0.00957489013671875,
0.041656494140625,
-0.0206451416015625,
-0.01715087890625,
0.0095977783203125,
0.01332855224609375,
-0.038299560546875,
0.0036907196044921875,
0.022308349609375,
-0.0072479248046875,
-0.0031108856201171875,
-0.0380859375,
-0.02020263671875,
-0.01087188720703125,
-0.0023956298828125,
-0.00864410400390625,
-0.017486572265625,
0.024566650390625,
-0.014404296875,
0.010101318359375,
0.00959014892578125,
0.0194244384765625,
-0.031585693359375,
-0.0216064453125,
-0.019927978515625,
-0.02349853515625,
-0.002407073974609375,
-0.0110931396484375,
-0.0293731689453125,
-0.00348663330078125,
-0.001132965087890625,
0.01678466796875,
-0.005931854248046875,
0.0211181640625,
-0.044189453125,
0.0245513916015625,
0.0026988983154296875,
-0.000568389892578125,
0.0111846923828125,
-0.0103759765625,
0.00875091552734375,
-0.0023593902587890625,
-0.03216552734375,
-0.0145416259765625,
-0.0004563331604003906,
-0.01306915283203125,
-0.00782012939453125,
0.04266357421875,
0.023956298828125,
-0.0121612548828125,
-0.01299285888671875,
0.0177001953125,
-0.01885986328125,
0.0215606689453125,
-0.01073455810546875,
0.0178985595703125,
0.047119140625,
0.01406097412109375,
0.0030345916748046875,
0.03533935546875,
-0.01331329345703125,
-0.057159423828125,
0.00977325439453125,
0.0183563232421875,
-0.035736083984375,
0.006084442138671875,
0.005390167236328125,
-0.01055908203125,
-0.0093231201171875,
-0.0028667449951171875,
0.01812744140625,
-0.0236053466796875,
-0.0232696533203125,
-0.0005540847778320312,
-0.01480865478515625,
0.0369873046875,
-0.016387939453125,
0.0279998779296875,
-0.007503509521484375,
-0.021942138671875,
-0.0093994140625,
0.007030487060546875,
-0.00010347366333007812,
0.00897979736328125,
0.006137847900390625,
-0.01529693603515625,
-0.0023174285888671875,
-0.0012569427490234375,
-0.00859832763671875,
-0.0234527587890625,
-0.0018568038940429688,
-0.00684356689453125,
0.01146697998046875,
0.0538330078125,
0.01265716552734375,
0.0099639892578125,
0.032501220703125,
0.0009946823120117188,
-0.01084136962890625,
0.0300750732421875,
0.0284423828125,
0.01290130615234375,
0.0277252197265625,
-0.01519775390625,
-0.005847930908203125,
-0.0027637481689453125,
-0.00196075439453125,
0.0200042724609375,
0.0129547119140625,
-0.00695037841796875,
-0.0106964111328125,
-0.009185791015625,
0.003139495849609375,
0.01367950439453125,
-0.0035991668701171875,
0.01505279541015625,
0.0106353759765625,
0.0252227783203125,
0.0203094482421875,
0.037017822265625,
0.01149749755859375,
-0.03411865234375,
-0.00908660888671875,
0.0155181884765625,
0.035064697265625,
-0.0267181396484375,
0.007160186767578125,
-0.0143585205078125,
0.0158233642578125,
-0.016326904296875,
-0.015625,
-0.0004696846008300781,
-0.007350921630859375,
-0.0122528076171875,
0.000732421875,
0.0049285888671875,
-0.0015382766723632812,
0.0223846435546875,
-0.00757598876953125,
0.0107269287109375,
0.0174102783203125,
-0.03216552734375,
0.0008139610290527344,
0.0012540817260742188,
-0.0256805419921875,
0.01947021484375,
0.00518798828125,
0.0175018310546875,
-0.0263671875,
0.007843017578125,
-0.0147857666015625,
-0.0119781494140625,
-0.0146484375,
-0.0128631591796875,
-0.00756072998046875,
-0.019683837890625,
-0.01416015625,
0.0090789794921875,
-0.0124969482421875,
-0.0022296905517578125,
-0.0146026611328125,
0.0214080810546875,
0.01256561279296875,
0.00699615478515625,
-0.0128631591796875,
-0.012664794921875,
0.0196380615234375,
0.023345947265625,
-0.0216522216796875,
0.021148681640625,
0.01165771484375,
0.004886627197265625,
-0.04132080078125,
0.0341796875,
-0.0236053466796875,
-0.01409149169921875,
0.0145416259765625,
-0.007495880126953125,
0.013763427734375,
0.0156402587890625,
-0.0416259765625,
-0.0225982666015625,
-0.00023877620697021484,
0.042877197265625,
0.00286102294921875,
0.038665771484375,
0.0268402099609375,
0.02606201171875,
0.030548095703125,
0.0269622802734375,
0.0288543701171875,
0.02423095703125,
-0.0036602020263671875,
-0.0010328292846679688,
-0.009979248046875,
-0.01776123046875,
-0.034881591796875,
0.0097503662109375,
-0.00690460205078125,
-0.00644683837890625,
0.04339599609375,
0.00485992431640625,
-0.00612640380859375,
-0.0031833648681640625,
-0.0016393661499023438,
0.004085540771484375,
0.0240020751953125,
-0.020233154296875,
0.00902557373046875,
-0.03265380859375,
0.0008683204650878906,
0.0233917236328125,
0.003444671630859375,
-0.04461669921875,
-0.004730224609375,
-0.02386474609375,
0.0083160400390625,
0.006366729736328125,
-0.01142120361328125,
0.0169677734375,
0.0116119384765625,
-0.01214599609375,
0.01104736328125,
-0.01580810546875,
-0.01561737060546875,
-0.00785064697265625,
0.0038242340087890625,
-0.0063629150390625,
-0.01146697998046875,
0.006191253662109375,
-0.00580596923828125,
-0.0136871337890625,
0.0100860595703125,
0.0282440185546875,
0.0186920166015625,
0.022064208984375,
-0.01132965087890625,
-0.0098114013671875,
-0.0233154296875,
-0.035919189453125,
0.0014390945434570312,
-0.04803466796875,
-0.017852783203125,
-0.012664794921875,
-0.005664825439453125,
-0.003025054931640625,
-0.0012426376342773438,
0.0082855224609375,
-0.03411865234375,
-0.0038700103759765625,
0.00933074951171875,
-0.0167083740234375,
0.01251220703125,
0.001514434814453125,
-0.039337158203125,
-0.0220489501953125,
-0.01204681396484375,
-0.0162506103515625,
-0.003772735595703125,
0.00562286376953125,
0.01092529296875,
0.0108795166015625,
0.0276336669921875,
0.0037937164306640625,
0.0404052734375,
-0.004558563232421875,
0.002742767333984375,
0.0208740234375,
0.012725830078125,
-0.0151519775390625,
-0.0199127197265625,
-0.001384735107421875,
0.026580810546875,
0.01666259765625,
-0.006195068359375,
-0.00537109375,
0.0032176971435546875,
-0.034698486328125,
-0.01934814453125,
-0.012908935546875,
0.01495361328125,
-0.005458831787109375,
-0.01502227783203125,
0.0136566162109375,
0.0094757080078125,
-0.0221099853515625,
-0.05810546875,
0.006195068359375,
-0.005382537841796875,
0.0281829833984375,
-0.0182037353515625,
-0.0002486705780029297,
-0.0038394927978515625,
0.03717041015625,
-0.01158905029296875,
-0.0269317626953125,
-0.00009268522262573242,
-0.01409149169921875,
0.01059722900390625,
0.037200927734375,
-0.0330810546875,
0.0171356201171875,
0.050994873046875,
-0.005260467529296875,
-0.00762939453125,
-0.0027713775634765625,
-0.024261474609375,
0.015594482421875,
-0.0065460205078125,
0.0094451904296875,
-0.01474761962890625,
-0.006839752197265625,
0.0161285400390625,
0.0067291259765625,
-0.011077880859375,
0.0018444061279296875,
-0.0196075439453125,
-0.005588531494140625,
0.03131103515625,
0.0195465087890625,
0.02252197265625,
0.0018520355224609375,
-0.032867431640625,
-0.01678466796875,
-0.0227813720703125,
-0.0203857421875,
0.0160369873046875,
-0.00272369384765625,
0.03424072265625,
-0.003681182861328125,
0.04205322265625,
-0.0181121826171875,
-0.0155792236328125,
-0.014068603515625,
-0.0011463165283203125,
0.0117950439453125,
0.0188140869140625,
-0.005420684814453125,
-0.0002467632293701172,
0.023193359375,
-0.0261077880859375,
0.01140594482421875,
-0.005161285400390625,
-0.0185699462890625,
-0.01102447509765625,
-0.0019216537475585938,
0.0152130126953125,
0.03045654296875,
0.0162506103515625,
0.02484130859375,
0.0272979736328125,
-0.010040283203125,
0.0131988525390625,
-0.0035076141357421875,
-0.02923583984375,
0.0174713134765625,
-0.0175018310546875,
-0.00921630859375,
0.01488494873046875,
-0.01338958740234375,
-0.005084991455078125,
-0.017669677734375,
0.0039005279541015625,
-0.0186920166015625,
0.00539398193359375,
0.003582000732421875,
0.0270233154296875,
-0.017547607421875,
0.000247955322265625,
0.025970458984375,
0.032012939453125,
0.02264404296875,
0.014495849609375,
0.030731201171875,
0.003520965576171875,
-0.02276611328125,
0.04095458984375,
-0.007434844970703125,
-0.004833221435546875,
-0.004634857177734375,
0.0064239501953125,
0.00458526611328125,
-0.0001055598258972168,
0.052825927734375,
-0.0193939208984375,
-0.0115203857421875,
-0.004413604736328125,
0.043701171875,
-0.025177001953125,
-0.0002307891845703125,
-0.032745361328125,
-0.01161956787109375,
0.006084442138671875,
0.0225982666015625,
-0.009796142578125,
-0.0036163330078125,
-0.0024700164794921875,
0.003780364990234375,
-0.02508544921875,
-0.045745849609375,
0.01328277587890625,
0.02587890625,
-0.01139068603515625,
-0.0171051025390625,
-0.000972747802734375,
-0.00628662109375,
0.001888275146484375,
-0.00047397613525390625,
0.0029430389404296875,
0.01148223876953125,
0.036895751953125,
0.00809478759765625,
-0.016632080078125,
0.019378662109375,
-0.024261474609375,
0.0016679763793945312,
-0.00933074951171875,
0.00934600830078125,
0.0199432373046875,
0.006458282470703125,
0.00782012939453125,
0.00299835205078125,
0.012176513671875,
-0.01444244384765625,
0.0400390625,
-0.0101470947265625,
0.01390838623046875,
0.0018434524536132812,
-0.01513671875,
0.034210205078125,
-0.03204345703125,
-0.0223236083984375,
0.0088653564453125,
-0.004238128662109375,
-0.037872314453125,
0.0054779052734375,
-0.0015230178833007812,
0.0087890625,
0.0157318115234375,
-0.0187225341796875,
0.0153656005859375,
0.01206207275390625,
-0.00015234947204589844,
0.0181732177734375,
-0.00621795654296875,
0.037811279296875,
0.0024623870849609375,
-0.00881195068359375,
0.004764556884765625,
0.007659912109375,
-0.0128326416015625,
0.02032470703125,
-0.01074981689453125,
-0.00127410888671875,
-0.0244598388671875,
-0.0234832763671875,
-0.0164794921875,
0.0024242401123046875,
0.038909912109375,
0.01092529296875,
-0.0235137939453125,
0.0013799667358398438,
0.0007367134094238281,
0.031341552734375,
0.02685546875,
0.01364898681640625,
0.0058441162109375,
0.0201568603515625,
0.01438140869140625,
-0.04119873046875,
-0.00872802734375,
-0.0047760009765625,
-0.01502227783203125,
0.00458526611328125,
-0.0185394287109375,
-0.022857666015625,
0.0127716064453125,
-0.0235748291015625,
0.00885009765625,
-0.004425048828125,
0.0357666015625,
-0.04644775390625,
0.006439208984375,
-0.0112152099609375,
0.0131378173828125,
-0.0175018310546875,
-0.00696563720703125,
0.0272979736328125,
-0.00461578369140625,
0.018524169921875,
-0.02001953125,
-0.0012540817260742188,
0.00888824462890625,
-0.0103607177734375,
-0.01708984375,
0.0034923553466796875,
0.010711669921875,
-0.0198211669921875,
-0.0027008056640625,
0.0016527175903320312,
0.006664276123046875,
-0.016571044921875,
-0.0008955001831054688,
0.01593017578125,
-0.00872802734375,
0.007205963134765625,
-0.002941131591796875,
-0.03594970703125,
-0.01483154296875,
-0.002346038818359375,
0.006122589111328125,
-0.03662109375,
0.005428314208984375,
-0.0004551410675048828,
0.03271484375,
-0.00244903564453125,
0.02752685546875,
0.0135650634765625,
-0.0243377685546875,
0.01324462890625,
0.0112457275390625,
0.0280303955078125,
0.03790283203125,
-0.008880615234375,
-0.01312255859375,
0.0271759033203125,
-0.0187835693359375,
-0.024444580078125,
0.026397705078125,
-0.0126800537109375,
0.017791748046875,
0.0098114013671875,
-0.0084686279296875,
0.00966644287109375,
-0.0467529296875,
0.0033931732177734375,
-0.006999969482421875,
-0.009613037109375,
-0.036224365234375,
0.0019283294677734375,
-0.0237274169921875,
0.00830078125,
0.0186309814453125,
0.024017333984375,
-0.0104827880859375,
-0.022369384765625,
-0.0299072265625,
-0.0214996337890625,
-0.0065155029296875,
0.0102081298828125,
0.035430908203125,
-0.01318359375,
0.04150390625,
-0.05035400390625,
0.0106964111328125,
0.0238800048828125,
0.00870513916015625,
0.01136016845703125,
-0.05108642578125,
-0.01096343994140625,
0.009368896484375,
-0.038116455078125,
0.01012420654296875,
-0.01105499267578125,
-0.002376556396484375,
0.0279693603515625,
0.0123291015625,
0.0281524658203125,
0.032958984375,
-0.00618743896484375,
0.0167083740234375,
0.0128936767578125,
-0.00237274169921875,
0.01824951171875,
-0.002597808837890625,
-0.0173492431640625,
0.0011434555053710938,
0.00484466552734375,
-0.005779266357421875,
-0.0045166015625,
0.0016450881958007812,
0.02667236328125,
0.0040130615234375,
0.00030612945556640625,
-0.0027484893798828125,
-0.03253173828125,
0.0142974853515625,
0.0048828125,
0.01110076904296875,
-0.032928466796875,
-0.033538818359375,
0.0186767578125,
0.007450103759765625,
0.0126953125,
0.0027790069580078125,
-0.002288818359375,
-0.017791748046875,
0.0133819580078125,
0.03997802734375,
0.00009334087371826172,
0.01157379150390625,
-0.00428009033203125,
0.037811279296875,
0.02569580078125,
-0.012969970703125,
-0.006526947021484375,
-0.0103759765625,
0.0070037841796875,
-0.01334381103515625,
0.0153656005859375,
0.01503753662109375,
0.0140380859375,
-0.0015087127685546875,
-0.0195159912109375,
-0.0276336669921875,
-0.03436279296875,
0.0115966796875,
0.0020732879638671875,
-0.010955810546875,
-0.038116455078125,
0.003940582275390625,
0.006809234619140625,
0.00737762451171875,
0.01332855224609375,
0.00225067138671875,
0.019989013671875,
-0.0108184814453125,
0.031707763671875,
-0.006725311279296875,
-0.031158447265625,
-0.006488800048828125,
0.0188140869140625,
-0.01302337646484375,
-0.00262451171875,
0.02618408203125,
-0.0278778076171875,
0.00939178466796875,
0.0164794921875,
-0.00948333740234375,
0.01296234130859375,
-0.023193359375,
-0.00301361083984375,
-0.007289886474609375,
-0.006359100341796875,
-0.01398468017578125,
0.00669097900390625,
-0.006633758544921875,
0.006359100341796875,
-0.021240234375,
-0.034423828125,
-0.0296783447265625,
-0.03826904296875,
-0.00830841064453125,
-0.006649017333984375,
0.00778961181640625,
0.0202178955078125,
0.031890869140625,
0.007434844970703125,
-0.0458984375,
-0.011322021484375,
0.0029964447021484375,
-0.0037593841552734375,
-0.0250701904296875,
-0.00005829334259033203,
-0.0013933181762695312,
0.0029144287109375,
-0.003063201904296875,
0.044464111328125,
-0.002033233642578125,
0.01116180419921875,
0.036712646484375,
-0.008941650390625,
0.0265350341796875,
0.0152587890625,
-0.0015993118286132812,
0.0016870498657226562,
-0.0159454345703125,
0.0036525726318359375,
0.00872039794921875,
0.0242462158203125,
-0.0121002197265625,
0.0160675048828125,
-0.025299072265625,
0.01396942138671875,
-0.010009765625,
0.0174407958984375,
0.0177459716796875,
-0.0136871337890625,
-0.00775146484375,
0.01372528076171875,
-0.001529693603515625,
-0.0080413818359375,
0.0035724639892578125,
0.0110015869140625,
-0.0225372314453125,
-0.01216888427734375,
0.004016876220703125,
-0.0008883476257324219,
-0.00231170654296875,
-0.0003643035888671875,
-0.01515960693359375,
-0.0161895751953125,
-0.045379638671875,
0.0041656494140625,
0.03021240234375,
0.032073974609375,
-0.0207061767578125,
-0.00020778179168701172,
0.03173828125,
0.0033416748046875,
-0.0083465576171875,
0.0086212158203125,
-0.00909423828125,
0.020172119140625,
0.006320953369140625,
-0.00811767578125,
-0.01479339599609375,
0.02264404296875,
0.005512237548828125,
0.00009047985076904297,
0.0075225830078125,
0.00362396240234375,
0.00662994384765625,
0.0017938613891601562,
-0.00949859619140625,
0.0178375244140625,
-0.0309600830078125,
0.0283355712890625,
-0.03253173828125,
0.01146697998046875,
-0.0228424072265625,
0.016143798828125,
0.01154327392578125,
-0.007457733154296875,
-0.00974273681640625,
0.020599365234375,
0.00457000732421875,
0.01030731201171875,
-0.013824462890625,
-0.0361328125,
-0.0054779052734375,
0.017852783203125,
-0.0007948875427246094,
-0.0016460418701171875,
-0.021575927734375,
0.016876220703125,
-0.0099639892578125,
-0.008819580078125,
0.0256195068359375,
-0.007648468017578125,
0.0243682861328125,
-0.0058441162109375,
0.027862548828125,
-0.0020542144775390625,
0.01116180419921875,
-0.004047393798828125,
0.0125579833984375,
0.00820159912109375,
0.0151824951171875,
-0.0285186767578125,
0.00662994384765625,
0.0001678466796875,
-0.0180816650390625,
0.0113067626953125,
-0.005115509033203125,
-0.01788330078125,
-0.020263671875,
-0.002742767333984375,
-0.011749267578125,
-0.05487060546875,
-0.006927490234375,
-0.03460693359375,
0.0098876953125,
0.004970550537109375,
-0.040313720703125,
-0.00505828857421875,
-0.006504058837890625,
-0.01824951171875,
0.003932952880859375,
-0.0034542083740234375,
-0.003849029541015625,
0.0191802978515625,
0.007343292236328125,
0.0078125,
0.0177764892578125,
0.0406494140625,
0.01287078857421875,
-0.0031528472900390625,
-0.038726806640625,
-0.004730224609375,
0.000926971435546875,
0.01959228515625,
0.0098419189453125,
-0.01540374755859375,
-0.003780364990234375,
-0.0262908935546875,
-0.00626373291015625,
-0.01434326171875,
0.004451751708984375,
0.0262451171875,
0.032623291015625,
-0.00666046142578125,
-0.0121612548828125,
0.0174407958984375,
0.0007567405700683594,
-0.035430908203125,
0.01397705078125,
-0.004364013671875,
-0.01251220703125,
-0.0057373046875,
0.0278167724609375,
-0.044921875,
0.015899658203125,
-0.0026683807373046875,
0.0004630088806152344,
0.005649566650390625,
0.0266265869140625,
-0.0003330707550048828,
-0.035919189453125,
0.0004169940948486328,
0.0018053054809570312,
0.0130157470703125,
0.01593017578125,
-0.0021114349365234375,
-0.00435638427734375,
-0.001781463623046875,
0.00354766845703125,
0.003429412841796875,
0.020355224609375,
-0.0026988983154296875,
0.0372314453125,
0.0095672607421875,
-0.02655029296875,
-0.00920867919921875,
-0.0055389404296875,
-0.0340576171875,
0.0352783203125,
-0.01540374755859375,
0.018341064453125,
0.016754150390625,
0.005298614501953125,
0.029083251953125,
-0.00003784894943237305,
-0.01302337646484375,
-0.002777099609375,
0.0014867782592773438,
0.0006747245788574219,
-0.00728607177734375,
-0.034393310546875,
-0.0200653076171875,
-0.017669677734375,
-0.024993896484375,
-0.0185394287109375,
0.01178741455078125,
-0.0124053955078125,
-0.019439697265625,
-0.000029087066650390625,
-0.032012939453125,
0.03778076171875,
0.015838623046875,
-0.022003173828125,
0.0144195556640625,
0.0119781494140625,
0.0128326416015625,
0.00572967529296875,
-0.004032135009765625,
-0.0006017684936523438,
-0.0008349418640136719,
-0.00336456298828125,
0.0059051513671875,
0.01641845703125,
0.00524139404296875,
0.020050048828125,
0.029693603515625,
-0.034576416015625,
0.019805908203125,
0.0012788772583007812,
0.0123748779296875,
-0.026611328125,
-0.0082855224609375,
-0.0195770263671875,
0.00011235475540161133,
0.00016796588897705078,
-0.03997802734375,
-0.00672149658203125,
0.01068878173828125,
-0.0033969879150390625,
0.0161590576171875,
0.00025010108947753906,
0.00714874267578125,
-0.012725830078125,
-0.005611419677734375,
0.006397247314453125,
0.004314422607421875,
-0.01136016845703125,
-0.0020122528076171875,
-0.007404327392578125,
0.018798828125,
-0.005275726318359375,
-0.02862548828125,
0.011749267578125,
0.02154541015625,
-0.035400390625,
-0.01123046875,
-0.02740478515625,
-0.005603790283203125,
-0.0265350341796875,
-0.0255279541015625,
0.0017747879028320312,
0.014007568359375,
0.0202789306640625,
-0.047210693359375,
-0.01739501953125,
0.0144500732421875,
-0.015533447265625,
-0.041748046875,
-0.0360107421875,
0.00510406494140625,
0.0133514404296875,
0.008331298828125,
-0.0010805130004882812,
-0.00960540771484375,
0.0265655517578125,
-0.01119232177734375,
-0.0012350082397460938,
-0.01210784912109375,
0.011932373046875,
0.024200439453125,
0.0182342529296875,
-0.01593017578125,
0.004657745361328125,
0.01081085205078125,
0.01415252685546875,
-0.0304107666015625,
-0.029815673828125,
0.000820159912109375,
-0.02862548828125,
0.01009368896484375,
0.00727081298828125,
-0.0247039794921875,
0.0186614990234375,
0.004364013671875,
0.01806640625,
-0.02655029296875,
-0.0145111083984375,
0.0093841552734375,
-0.0189361572265625,
-0.005886077880859375,
0.030670166015625,
-0.00429534912109375,
0.0102996826171875,
0.0228424072265625,
0.0161590576171875,
0.0215606689453125,
0.0013599395751953125,
0.025299072265625,
0.0023956298828125,
-0.0112457275390625,
0.0008182525634765625,
-0.018157958984375,
0.007476806640625,
-0.009735107421875,
0.01334381103515625,
-0.0027790069580078125,
-0.0301513671875,
-0.004749298095703125,
-0.00826263427734375,
0.0025272369384765625,
0.00917816162109375,
0.007633209228515625,
0.020416259765625,
0.007678985595703125,
0.0015201568603515625,
0.023284912109375,
0.044097900390625,
-0.002437591552734375,
0.00411224365234375,
-0.0077056884765625,
-0.043731689453125,
0.00946807861328125,
0.016998291015625,
-0.0176544189453125,
0.01337432861328125,
-0.00864410400390625,
0.01263427734375,
0.005908966064453125,
0.0207672119140625,
0.00951385498046875,
-0.00391387939453125,
0.01386260986328125,
0.004177093505859375,
0.00890350341796875,
-0.012054443359375,
-0.0253448486328125,
-0.0024738311767578125,
-0.0251007080078125,
-0.00318145751953125,
-0.0020809173583984375,
-0.007778167724609375,
-0.0181427001953125,
0.003604888916015625,
0.0164794921875,
0.01580810546875,
0.024200439453125,
-0.031463623046875,
-0.01430511474609375,
0.004100799560546875,
0.017181396484375,
-0.011749267578125,
0.00524139404296875,
0.0157318115234375,
0.0210418701171875,
-0.0182037353515625,
0.041412353515625,
0.0285186767578125,
-0.00250244140625,
0.0001595020294189453,
-0.00853729248046875,
-0.0140533447265625,
0.04693603515625,
-0.0174713134765625,
0.004119873046875,
0.019805908203125,
0.003993988037109375,
0.004329681396484375,
0.001941680908203125,
0.0260772705078125,
0.01023101806640625,
-0.0112762451171875,
0.0211944580078125,
0.017608642578125,
-0.004009246826171875,
-0.030548095703125,
-0.00135040283203125,
-0.0041961669921875,
-0.0017709732055664062,
-0.0177001953125,
0.0258026123046875,
-0.042144775390625,
0.009521484375,
0.0130462646484375,
-0.007503509521484375,
0.024749755859375,
0.037872314453125,
0.0081329345703125,
-0.01377105712890625,
-0.01134490966796875,
-0.032379150390625,
0.03302001953125,
-0.00665283203125,
-0.000438690185546875,
0.0252685546875,
0.0185699462890625,
0.0309600830078125,
0.011810302734375,
0.026611328125,
0.0034275054931640625,
0.0625,
0.0234527587890625,
0.0145416259765625,
0.01505279541015625,
0.0154571533203125,
-0.010223388671875,
0.019622802734375,
-0.032928466796875,
0.0236968994140625,
-0.0009102821350097656,
0.018768310546875,
-0.0107421875,
0.032745361328125,
-0.002864837646484375,
-0.0335693359375,
0.021575927734375,
0.003932952880859375,
0.041778564453125,
-0.002475738525390625,
-0.0271453857421875,
-0.005634307861328125,
0.0026912689208984375,
-0.0128936767578125,
-0.0251007080078125,
-0.0002758502960205078,
-0.01152801513671875,
-0.01311492919921875,
-0.00426483154296875,
-0.033782958984375,
0.0013151168823242188,
0.0086212158203125,
-0.00949859619140625,
-0.03857421875,
-0.034088134765625,
-0.00374603271484375,
0.031341552734375,
0.009735107421875,
0.002567291259765625,
-0.031524658203125,
0.016510009765625,
0.0195770263671875,
0.0097808837890625,
0.00011754035949707031,
0.011749267578125,
0.00865936279296875,
0.00605010986328125,
0.01438140869140625,
-0.01611328125,
-0.0123138427734375,
-0.027984619140625,
0.000033915042877197266,
-0.004695892333984375,
-0.03857421875,
0.03271484375,
0.00118255615234375,
-0.0218963623046875,
-0.0009174346923828125,
0.0306396484375,
-0.006420135498046875,
0.0209808349609375,
-0.01947021484375,
0.031768798828125,
0.005924224853515625,
0.003108978271484375,
0.031829833984375,
0.02880859375,
0.034576416015625,
0.00128173828125,
0.042449951171875,
0.00860595703125,
-0.007152557373046875,
0.007221221923828125,
-0.01519775390625,
-0.0242462158203125,
0.0092620849609375,
-0.01348876953125,
-0.0743408203125,
-0.0132598876953125,
0.0263824462890625,
0.0215606689453125,
-0.0279388427734375,
0.0092926025390625,
-0.006938934326171875,
-0.0203094482421875,
-0.017486572265625,
-0.034698486328125,
0.00809478759765625,
0.0066680908203125,
0.01043701171875,
-0.017913818359375,
-0.056365966796875,
0.009033203125,
-0.00827789306640625,
-0.034454345703125,
0.00914764404296875,
-0.003387451171875,
-0.01366424560546875,
0.040924072265625,
-0.00807952880859375,
-0.01395416259765625,
0.00630950927734375,
-0.0265960693359375,
0.0401611328125,
-0.0173492431640625,
-0.0247650146484375,
0.00021600723266601562,
0.00930023193359375,
-0.01473236083984375,
0.029083251953125,
-0.0018644332885742188,
0.002635955810546875,
0.006023406982421875,
0.047271728515625,
0.021148681640625,
-0.00963592529296875,
0.040802001953125,
0.0093841552734375,
0.0285797119140625,
-0.01221466064453125,
-0.005886077880859375,
0.004634857177734375,
-0.0290985107421875,
-0.007022857666015625,
0.00585174560546875,
-0.0192413330078125,
-0.026153564453125,
-0.01529693603515625,
-0.0227203369140625,
-0.00567626953125,
0.00878143310546875,
-0.004016876220703125,
-0.0257720947265625,
0.009246826171875,
-0.0081024169921875,
0.0308685302734375,
-0.047210693359375,
-0.010528564453125,
0.046295166015625,
0.00606536865234375,
0.059600830078125,
0.00998687744140625,
-0.024169921875,
0.006412506103515625,
0.005268096923828125,
0.030120849609375,
0.026885986328125,
0.00907135009765625,
0.0231781005859375,
0.0024394989013671875,
0.016143798828125,
0.0216522216796875,
-0.0210418701171875,
0.0159759521484375,
0.011810302734375,
-0.0232391357421875,
0.0189056396484375,
-0.02459716796875,
0.016082763671875,
0.00800323486328125,
0.0102386474609375,
0.047607421875,
0.00386810302734375,
0.033935546875,
0.01549530029296875,
-0.01904296875,
-0.01253509521484375,
0.00878143310546875,
0.00995635986328125,
-0.00501251220703125,
0.032745361328125,
0.00676727294921875,
0.0170135498046875,
-0.0306854248046875,
-0.0292816162109375,
0.033172607421875,
-0.011993408203125,
0.02410888671875,
0.0100860595703125,
-0.0134735107421875,
0.032440185546875,
-0.017059326171875,
-0.028717041015625,
0.0166473388671875,
-0.034210205078125,
0.00455474853515625,
-0.00798797607421875,
0.0217437744140625,
-0.030609130859375,
-0.0236968994140625,
0.012847900390625,
0.01568603515625,
0.01351165771484375,
-0.015472412109375,
0.0164642333984375,
0.007427215576171875,
0.004863739013671875,
0.0188751220703125,
0.005603790283203125,
-0.013092041015625,
0.027191162109375,
0.005870819091796875,
0.0255126953125,
0.00001990795135498047,
-0.017120361328125,
0.01003265380859375,
0.0404052734375,
-0.00812530517578125,
0.00579833984375,
0.0343017578125,
-0.0006766319274902344,
0.02008056640625,
0.0153350830078125,
0.0169525146484375,
0.0164947509765625,
0.04205322265625,
-0.0281524658203125,
0.015594482421875,
-0.02789306640625,
-0.004608154296875,
-0.025054931640625,
-0.0038700103759765625,
-0.02459716796875,
-0.0016727447509765625,
0.01434326171875,
-0.01131439208984375,
0.0060272216796875,
0.0249176025390625,
-0.0225372314453125,
-0.00507354736328125,
0.005313873291015625,
0.01837158203125,
-0.00525665283203125,
0.017547607421875,
-0.0306549072265625,
-0.01111602783203125,
-0.0206756591796875,
0.046112060546875,
0.016448974609375,
-0.0217742919921875,
0.04400634765625,
-0.0177764892578125,
0.016265869140625,
-0.04205322265625,
-0.0241241455078125,
-0.023345947265625,
0.0024776458740234375,
-0.01480865478515625,
0.0035800933837890625,
0.0197296142578125,
-0.0122528076171875,
-0.0050048828125,
0.003154754638671875,
-0.029632568359375,
-0.0290985107421875,
-0.0210723876953125,
-0.0182647705078125,
-0.00832366943359375,
0.00524139404296875,
-0.052978515625,
-0.028778076171875,
-0.0263824462890625,
0.0063629150390625,
-0.03765869140625,
-0.0271453857421875,
0.0125274658203125,
-0.0228424072265625,
-0.00833892822265625,
0.00528717041015625,
0.0283050537109375,
0.0030460357666015625,
-0.0288543701171875,
-0.03216552734375,
-0.03204345703125,
0.0194244384765625,
-0.003917694091796875,
-0.013092041015625,
-0.0251007080078125,
0.002452850341796875,
0.016326904296875,
0.0142364501953125,
0.011749267578125,
-0.005901336669921875,
-0.0293426513671875,
-0.05029296875,
0.006099700927734375,
0.02764892578125,
0.0179901123046875,
0.00284576416015625,
-0.0029659271240234375,
-0.00750732421875,
-0.00524139404296875,
0.00665283203125,
0.0269317626953125,
0.0018596649169921875,
-0.03216552734375,
-0.0032196044921875,
-0.01287841796875,
0.013641357421875,
-0.00484466552734375,
-0.0010824203491210938,
0.0225982666015625,
0.00649261474609375,
0.0004379749298095703,
0.029876708984375,
0.0138702392578125,
0.0113525390625,
-0.00959014892578125,
0.0080108642578125,
0.00001430511474609375,
0.0038356781005859375,
0.0239410400390625,
-0.003017425537109375,
-0.0301055908203125,
-0.0260162353515625,
-0.002719879150390625,
-0.0167694091796875,
0.003002166748046875,
0.00490570068359375,
-0.033721923828125,
0.0035228729248046875,
0.000050127506256103516,
0.019866943359375,
0.0194549560546875,
-0.00428009033203125,
0.01319122314453125,
0.0218505859375,
-0.00765228271484375,
0.019439697265625,
0.0034427642822265625
] |
ours_481
|
After the first two exchanges, Iris will have a \(\frac{1}{2}\)-kilogram piece and a \(\frac{1}{4}\)-kilogram piece, while Rosabel will have a \(\frac{1}{4}\)-kilogram piece. After that, Iris's largest piece will always exceed half of her total when it's her turn since her total amount of pie decreases each time, while Rosabel's largest piece will never exceed half of her total since her total amount of pie increases each time. So Iris will always cut the largest piece she has, while Rosabel will never need to do so.
When there are 2017 pieces in total, there will have been 2016 exchanges so far. Iris's largest piece will have a mass of \(\frac{\left(2^{2015}+1\right) / 3}{2^{2015}}\) kilograms (which is half of the amount of the pie she has after she gives pie to Iris for the 1008th time), while Rosabel's largest piece will have a mass of \(\frac{1}{4}\) kilograms. Therefore, we have \(m=\frac{2^{2015}+1}{3}\), \(n=2^{2015}\), \(p=1\), \(q=4\), and thus \(m+n+p+q=\frac{2^{2017}+16}{3} \equiv \frac{2+16}{3}=6 \pmod{2017}\).
\(\boxed{6}\)
|
6
|
{
"competition": "us_comps",
"dataset": "Ours",
"posts": null,
"source": "OMOFall18Solns.md"
}
|
Iris does not know what to do with her 1-kilogram pie, so she decides to share it with her friend Rosabel. Starting with Iris, they take turns to give exactly half of the total amount of pie (by mass) they possess to the other person. Since both of them prefer to have as few pieces of pie as possible, they use the following strategy: During each person's turn, she orders the pieces of pie that she has in a line from left to right in increasing order by mass, and starts giving the pieces of pie to the other person beginning from the left. If she encounters a piece that exceeds the remaining mass to give, she cuts it up into two pieces and gives the appropriately sized piece to the other person.
When the pie has been cut into a total of 2017 pieces, the largest piece that Iris has is \(\frac{m}{n}\) kilograms, and the largest piece that Rosabel has is \(\frac{p}{q}\) kilograms, where \(m, n, p, q\) are positive integers satisfying \(\operatorname{gcd}(m, n)=\operatorname{gcd}(p, q)=1\). Compute the remainder when \(m+n+p+q\) is divided by 2017.
|
[
"/Mathematics/DiscreteMathematics/Combinatorics/GeneralCombinatorics",
"/Mathematics/DiscreteMathematics/GeneralDiscreteMathematics/ConcreteMath",
"/Mathematics/DiscreteMathematics/GeneralDiscreteMathematics/ConcreteMathematics",
"/Mathematics/DiscreteMathematics/GeneralDiscreteMathematics/DiscreteMath",
"/Mathematics/DiscreteMathematics/GeneralDiscreteMathematics/DiscreteMathematics",
"/Mathematics/NumberTheory/Congruences/Congruence",
"/Mathematics/NumberTheory/Congruences/CongruenceEquation",
"/Mathematics/NumberTheory/Congruences/Congruent",
"/Mathematics/NumberTheory/Congruences/FermatsLittleTheorem",
"/Mathematics/NumberTheory/Congruences/Mod",
"/Mathematics/NumberTheory/Congruences/ModularArithmetic",
"/Mathematics/NumberTheory/Congruences/Residue",
"/Mathematics/NumberTheory/GeneralNumberTheory/ElementaryMethods",
"/Mathematics/NumberTheory/GeneralNumberTheory/ElementaryNumberTheory",
"/Mathematics/NumberTheory/RationalNumbers/RationalNumber"
] |
Notice that Iris’s pie amount strictly decreases each turn while Rosabel’s strictly increases, so only Iris ever needs to cut her largest piece, giving a predictable binary‑splitting pattern.
|
[
-0.00015282630920410156,
-0.01470947265625,
0.03570556640625,
-0.01018524169921875,
-0.00019550323486328125,
0.007472991943359375,
0.0128326416015625,
-0.0110015869140625,
0.0005965232849121094,
0.0274200439453125,
0.020751953125,
-0.0240936279296875,
-0.0005316734313964844,
-0.00748443603515625,
-0.017669677734375,
-0.02972412109375,
-0.030426025390625,
-0.01169586181640625,
0.0155792236328125,
-0.0015840530395507812,
-0.01457977294921875,
-0.01702880859375,
-0.0182647705078125,
0.027313232421875,
-0.0118560791015625,
-0.040283203125,
-0.014068603515625,
0.03887939453125,
0.019317626953125,
-0.0196075439453125,
-0.051116943359375,
0.005840301513671875,
0.02008056640625,
-0.006195068359375,
-0.00531005859375,
0.00408935546875,
-0.025543212890625,
-0.00267791748046875,
-0.01065826416015625,
-0.00759124755859375,
0.00679779052734375,
0.061767578125,
-0.006549835205078125,
0.0120086669921875,
-0.016326904296875,
0.01026153564453125,
-0.0022487640380859375,
0.0003552436828613281,
0.00020694732666015625,
-0.00601959228515625,
-0.004253387451171875,
0.005222320556640625,
0.01079559326171875,
-0.00649261474609375,
-0.0577392578125,
-0.09320068359375,
-0.0009007453918457031,
0.0002371072769165039,
0.0153350830078125,
-0.020263671875,
0.00968170166015625,
0.01464080810546875,
-0.006137847900390625,
0.0031681060791015625,
-0.0030841827392578125,
-0.007106781005859375,
-0.016510009765625,
0.0170135498046875,
0.002044677734375,
-0.004886627197265625,
0.043701171875,
-0.002552032470703125,
-0.0284881591796875,
0.0253753662109375,
0.0184478759765625,
-0.01727294921875,
-0.0188140869140625,
0.0091705322265625,
0.01425933837890625,
0.007049560546875,
0.01016998291015625,
0.0274505615234375,
0.0127410888671875,
0.01364898681640625,
0.0006570816040039062,
-0.0235595703125,
-0.00792694091796875,
0.0033359527587890625,
0.02410888671875,
-0.018402099609375,
0.00713348388671875,
-0.00901031494140625,
0.036712646484375,
-0.0078125,
0.0018377304077148438,
-0.016510009765625,
0.01303863525390625,
0.002086639404296875,
-0.0219268798828125,
0.004791259765625,
-0.0012197494506835938,
-0.0016584396362304688,
-0.0036144256591796875,
-0.00630950927734375,
-0.04833984375,
-0.0068511962890625,
-0.0126190185546875,
-0.00861358642578125,
-0.00165557861328125,
0.01409149169921875,
-0.0189971923828125,
0.0081024169921875,
0.01233673095703125,
0.0005831718444824219,
-0.01116180419921875,
-0.0014247894287109375,
-0.005817413330078125,
-0.0206298828125,
-0.00275421142578125,
0.017242431640625,
-0.001377105712890625,
0.006664276123046875,
-0.01532745361328125,
0.002197265625,
0.006572723388671875,
-0.016204833984375,
-0.01261138916015625,
-0.0021114349365234375,
0.0191497802734375,
0.023101806640625,
0.0182342529296875,
-0.0203399658203125,
-0.040771484375,
-0.0236053466796875,
-0.051544189453125,
-0.012451171875,
0.01090240478515625,
-0.004932403564453125,
-0.0025177001953125,
0.002620697021484375,
0.013580322265625,
-0.01081085205078125,
0.00003331899642944336,
0.0235748291015625,
-0.0303497314453125,
0.038604736328125,
0.0265960693359375,
-0.031707763671875,
0.0032711029052734375,
-0.007534027099609375,
0.01120758056640625,
-0.0037899017333984375,
0.0269317626953125,
0.005199432373046875,
-0.016510009765625,
0.00023984909057617188,
0.0321044921875,
0.0310211181640625,
-0.022216796875,
0.00220489501953125,
-0.01983642578125,
-0.012908935546875,
-0.032501220703125,
0.02850341796875,
-0.00981903076171875,
0.00370025634765625,
0.0028591156005859375,
0.00020742416381835938,
0.00750732421875,
0.01259613037109375,
0.004894256591796875,
-0.0267333984375,
-0.01174163818359375,
-0.00899505615234375,
-0.0044708251953125,
0.00875091552734375,
-0.005985260009765625,
-0.0023345947265625,
-0.00568389892578125,
0.0011920928955078125,
0.0273590087890625,
0.00267791748046875,
-0.0200347900390625,
0.006374359130859375,
-0.0259857177734375,
0.005218505859375,
-0.003177642822265625,
0.010284423828125,
0.0180206298828125,
0.020294189453125,
-0.025543212890625,
-0.01654052734375,
0.0038166046142578125,
0.006069183349609375,
-0.006618499755859375,
-0.018585205078125,
-0.03643798828125,
0.0302581787109375,
0.0245361328125,
-0.016082763671875,
0.01194000244140625,
0.010009765625,
-0.0286102294921875,
0.000995635986328125,
0.01166534423828125,
-0.006748199462890625,
-0.00200653076171875,
0.0033664703369140625,
0.01538848876953125,
0.01479339599609375,
0.0144500732421875,
-0.0035190582275390625,
-0.0036067962646484375,
-0.0219879150390625,
-0.018341064453125,
-0.00537872314453125,
-0.0167083740234375,
-0.002658843994140625,
0.01153564453125,
-0.0270233154296875,
0.00027871131896972656,
0.00795745849609375,
-0.01317596435546875,
-0.0024261474609375,
-0.0081329345703125,
-0.0028667449951171875,
0.0173797607421875,
-0.005809783935546875,
-0.0037441253662109375,
0.0205841064453125,
0.03692626953125,
0.007259368896484375,
-0.04541015625,
-0.0123291015625,
-0.0135498046875,
-0.00626373291015625,
0.00879669189453125,
-0.0018987655639648438,
0.0147247314453125,
-0.0021839141845703125,
0.0024585723876953125,
-0.0179443359375,
0.004375457763671875,
0.0039043426513671875,
-0.0175628662109375,
0.0133819580078125,
-0.0016031265258789062,
0.0009398460388183594,
0.0163726806640625,
0.0006089210510253906,
-0.0183868408203125,
0.00818634033203125,
-0.014068603515625,
-0.0007786750793457031,
-0.016937255859375,
0.0026454925537109375,
-0.0014705657958984375,
0.00492095947265625,
-0.01528167724609375,
0.0174102783203125,
0.0009851455688476562,
-0.0156707763671875,
-0.007541656494140625,
-0.015380859375,
-0.0028533935546875,
-0.023895263671875,
-0.01290130615234375,
0.004184722900390625,
0.0124053955078125,
0.00910186767578125,
0.0215301513671875,
-0.0162353515625,
-0.0252838134765625,
0.009521484375,
0.0235443115234375,
-0.025115966796875,
0.0033740997314453125,
0.0012578964233398438,
-0.001079559326171875,
-0.0035552978515625,
0.00579071044921875,
-0.023590087890625,
0.0003936290740966797,
0.01079559326171875,
0.00305938720703125,
0.0275115966796875,
0.018218994140625,
0.00156402587890625,
0.0079803466796875,
0.0115509033203125,
0.004161834716796875,
0.01224517822265625,
-0.0318603515625,
-0.004581451416015625,
0.030670166015625,
-0.041290283203125,
-0.0012369155883789062,
0.0311126708984375,
0.0160675048828125,
-0.00823211669921875,
-0.00002872943878173828,
0.0017385482788085938,
-0.005321502685546875,
0.0122833251953125,
0.00800323486328125,
0.03118896484375,
-0.006336212158203125,
0.0167999267578125,
-0.0254058837890625,
0.00440216064453125,
0.01373291015625,
0.003833770751953125,
-0.007167816162109375,
0.00511932373046875,
-0.047576904296875,
-0.02239990234375,
0.01068878173828125,
0.0112152099609375,
0.00476837158203125,
0.007221221923828125,
-0.0115814208984375,
0.0472412109375,
-0.03460693359375,
0.00508880615234375,
0.002712249755859375,
-0.0004487037658691406,
0.02337646484375,
0.0084381103515625,
-0.02850341796875,
0.004535675048828125,
-0.054412841796875,
-0.013641357421875,
-0.01849365234375,
0.00946044921875,
-0.005626678466796875,
0.022705078125,
0.0002409219741821289,
-0.006275177001953125,
0.014495849609375,
-0.0039520263671875,
-0.0285491943359375,
0.01546478271484375,
0.004947662353515625,
-0.052764892578125,
-0.02099609375,
0.0181884765625,
-0.006305694580078125,
0.0120391845703125,
0.00946044921875,
0.0279693603515625,
0.01033782958984375,
0.004489898681640625,
0.034515380859375,
0.020904541015625,
0.0034847259521484375,
0.01369476318359375,
0.0004813671112060547,
0.0262451171875,
-0.004787445068359375,
0.00896453857421875,
0.01507568359375,
0.0183563232421875,
-0.0304718017578125,
-0.00563812255859375,
0.0016603469848632812,
-0.0238800048828125,
-0.0300445556640625,
0.0274505615234375,
-0.028533935546875,
-0.0063934326171875,
-0.00386810302734375,
-0.00872039794921875,
0.009796142578125,
0.0020351409912109375,
-0.047698974609375,
0.0075836181640625,
-0.01462554931640625,
0.01554107666015625,
0.01690673828125,
0.0064239501953125,
-0.01367950439453125,
0.031036376953125,
0.01456451416015625,
0.045257568359375,
-0.035308837890625,
-0.003070831298828125,
0.01198577880859375,
-0.00168609619140625,
-0.04669189453125,
0.0062103271484375,
-0.0220947265625,
-0.01120758056640625,
-0.0092620849609375,
-0.005001068115234375,
-0.017822265625,
-0.01258087158203125,
-0.007427215576171875,
0.01922607421875,
0.029693603515625,
-0.0081329345703125,
-0.00955963134765625,
-0.007030487060546875,
-0.01387786865234375,
0.0192108154296875,
0.01262664794921875,
0.0013246536254882812,
-0.01529693603515625,
0.0206298828125,
-0.00556182861328125,
0.034942626953125,
-0.0025882720947265625,
-0.0180816650390625,
0.00911712646484375,
0.00811767578125,
0.0045166015625,
-0.0052490234375,
0.01065826416015625,
0.00852203369140625,
-0.04412841796875,
0.00933074951171875,
-0.002056121826171875,
-0.034759521484375,
0.022491455078125,
-0.00016760826110839844,
0.0096588134765625,
0.017242431640625,
-0.0132293701171875,
0.038818359375,
-0.027679443359375,
0.0187835693359375,
0.0025501251220703125,
-0.006450653076171875,
-0.00289154052734375,
0.0005898475646972656,
0.01220703125,
-0.018218994140625,
-0.013641357421875,
0.0110626220703125,
-0.0171661376953125,
0.0217437744140625,
-0.006122589111328125,
-0.01165771484375,
-0.0025386810302734375,
-0.00789642333984375,
-0.0322265625,
0.012847900390625,
0.0238800048828125,
0.015472412109375,
-0.031768798828125,
0.03448486328125,
-0.031646728515625,
0.0019550323486328125,
0.012847900390625,
-0.0034885406494140625,
0.006954193115234375,
0.0246734619140625,
-0.0005178451538085938,
0.0073089599609375,
-0.01346588134765625,
-0.0023441314697265625,
-0.006134033203125,
-0.0026264190673828125,
-0.02362060546875,
-0.00966644287109375,
-0.02398681640625,
-0.00585174560546875,
-0.002910614013671875,
0.0133209228515625,
0.024658203125,
0.03497314453125,
0.00435638427734375,
0.004253387451171875,
0.0281219482421875,
-0.00327301025390625,
-0.044464111328125,
0.01357269287109375,
-0.0003287792205810547,
0.0218658447265625,
-0.0143890380859375,
-0.0026607513427734375,
-0.0009531974792480469,
0.022216796875,
-0.00743865966796875,
0.058807373046875,
0.0054168701171875,
0.0303955078125,
0.007328033447265625,
-0.003215789794921875,
0.0040740966796875,
0.0177001953125,
-0.01088714599609375,
0.0257568359375,
-0.0193328857421875,
-0.004962921142578125,
-0.04473876953125,
0.00998687744140625,
-0.001964569091796875,
-0.008758544921875,
0.00850677490234375,
-0.00812530517578125,
-0.002956390380859375,
-0.045562744140625,
-0.031219482421875,
0.0298614501953125,
-0.007965087890625,
-0.00518035888671875,
0.0147247314453125,
-0.045074462890625,
0.0134124755859375,
-0.02191162109375,
0.0012226104736328125,
0.03558349609375,
0.0010042190551757812,
-0.0380859375,
-0.01306915283203125,
-0.00807952880859375,
0.0203704833984375,
0.01537322998046875,
0.01268768310546875,
0.0338134765625,
-0.024383544921875,
0.043060302734375,
0.053619384765625,
0.007266998291015625,
0.0022602081298828125,
0.0013360977172851562,
0.006336212158203125,
0.0203704833984375,
-0.00650787353515625,
0.018768310546875,
0.00540924072265625,
-0.01428985595703125,
-0.0033893585205078125,
-0.01629638671875,
-0.01751708984375,
0.007228851318359375,
0.01453399658203125,
0.01012420654296875,
-0.0069122314453125,
-0.0118255615234375,
-0.01381683349609375,
-0.0214080810546875,
0.00830841064453125,
-0.030975341796875,
-0.0307464599609375,
-0.044830322265625,
0.0010995864868164062,
0.009918212890625,
-0.041229248046875,
-0.038055419921875,
0.0165557861328125,
0.0206451416015625,
0.00048422813415527344,
0.0094757080078125,
-0.038482666015625,
0.032257080078125,
-0.0221710205078125,
-0.0133209228515625,
0.00679779052734375,
-0.006336212158203125,
0.01221466064453125,
0.0009374618530273438,
0.0130767822265625,
0.0279541015625,
0.0250244140625,
-0.0191497802734375,
-0.01824951171875,
-0.004238128662109375,
0.004848480224609375,
-0.0614013671875,
0.0119171142578125,
-0.01102447509765625,
0.007190704345703125,
-0.014984130859375,
-0.03155517578125,
-0.00757598876953125,
0.0012912750244140625,
0.0101470947265625,
-0.0199737548828125,
-0.004993438720703125,
0.020660400390625,
0.0101470947265625,
0.00005620718002319336,
0.0047149658203125,
0.0183258056640625,
-0.0085601806640625,
0.0258941650390625,
0.00829315185546875,
0.0185394287109375,
0.0208282470703125,
-0.0277862548828125,
0.0158233642578125,
0.004978179931640625,
-0.00406646728515625,
-0.03485107421875,
-0.026123046875,
-0.0126190185546875,
0.00994110107421875,
0.000016450881958007812,
0.0033931732177734375,
-0.003627777099609375,
-0.023101806640625,
0.0247039794921875,
0.0240325927734375,
-0.0240936279296875,
0.0155792236328125,
-0.019439697265625,
0.010955810546875,
-0.0023555755615234375,
0.026092529296875,
0.005523681640625,
-0.003818511962890625,
0.00542449951171875,
0.01287078857421875,
0.0149078369140625,
0.0014657974243164062,
-0.00399017333984375,
-0.01329803466796875,
0.02227783203125,
-0.0214691162109375,
-0.02056884765625,
0.002376556396484375,
0.000514984130859375,
0.01389312744140625,
0.00897979736328125,
-0.006954193115234375,
-0.006267547607421875,
-0.031829833984375,
0.0203704833984375,
-0.0438232421875,
-0.0222015380859375,
-0.0108795166015625,
0.0049285888671875,
-0.02264404296875,
-0.0005426406860351562,
-0.0033130645751953125,
0.0207061767578125,
0.001979827880859375,
0.0110015869140625,
-0.0089263916015625,
0.00408935546875,
0.0252838134765625,
-0.01303863525390625,
-0.03985595703125,
-0.00864410400390625,
-0.004642486572265625,
-0.0037059783935546875,
-0.00731658935546875,
0.0008692741394042969,
-0.002613067626953125,
0.00440216064453125,
-0.0014066696166992188,
0.003021240234375,
0.006122589111328125,
-0.00473785400390625,
-0.0123291015625,
0.00337982177734375,
-0.02972412109375,
0.042144775390625,
-0.0194091796875,
0.006603240966796875,
0.022552490234375,
-0.03961181640625,
0.0092010498046875,
-0.03936767578125,
0.0032863616943359375,
-0.03411865234375,
0.01776123046875,
0.01611328125,
0.02423095703125,
0.01441192626953125,
-0.01947021484375,
0.0226593017578125,
-0.0293426513671875,
0.0037631988525390625,
-0.00018644332885742188,
-0.00836181640625,
-0.01323699951171875,
0.0205230712890625,
-0.001949310302734375,
0.0137786865234375,
0.019073486328125,
0.058197021484375,
-0.0018548965454101562,
0.004062652587890625,
0.00594329833984375,
0.004486083984375,
0.0296173095703125,
0.004734039306640625,
-0.0287628173828125,
0.004413604736328125,
0.018035888671875,
-0.0242919921875,
0.0180816650390625,
0.0018558502197265625,
-0.00414276123046875,
0.0273590087890625,
-0.0288848876953125,
-0.0236358642578125,
0.022979736328125,
0.031158447265625,
-0.01097869873046875,
0.0215301513671875,
-0.017364501953125,
-0.0186920166015625,
-0.00624847412109375,
-0.0005860328674316406,
0.01441192626953125,
-0.0457763671875,
0.0267791748046875,
-0.008575439453125,
-0.009368896484375,
0.0119781494140625,
0.0058746337890625,
0.009552001953125,
0.016693115234375,
-0.00640869140625,
0.016204833984375,
0.0216217041015625,
-0.001678466796875,
-0.051849365234375,
-0.0015964508056640625,
-0.013916015625,
-0.0096588134765625,
0.0169677734375,
-0.002422332763671875,
0.005016326904296875,
-0.03594970703125,
-0.024139404296875,
-0.0117950439453125,
-0.046600341796875,
0.0247955322265625,
0.03338623046875,
0.0297088623046875,
-0.054931640625,
-0.032745361328125,
-0.00104522705078125,
-0.03497314453125,
0.0238800048828125,
-0.01175689697265625,
0.0631103515625,
0.0167999267578125,
0.0279541015625,
0.01279449462890625,
0.00585174560546875,
0.005260467529296875,
-0.0224151611328125,
-0.026702880859375,
0.015167236328125,
0.0127410888671875,
0.046966552734375,
0.03985595703125,
-0.016998291015625,
-0.0191650390625,
-0.0189361572265625,
-0.0032253265380859375,
0.007625579833984375,
-0.00316619873046875,
-0.039520263671875,
0.0255126953125,
-0.04510498046875,
-0.01168060302734375,
0.0011348724365234375,
0.0272369384765625,
-0.00007611513137817383,
0.024078369140625,
-0.01019287109375,
0.0106353759765625,
0.00528717041015625,
0.039093017578125,
0.0208740234375,
-0.00689697265625,
0.0287628173828125,
0.0005183219909667969,
0.01409149169921875,
0.01324462890625,
-0.04119873046875,
-0.007190704345703125,
0.0040740966796875,
-0.0157012939453125,
-0.0009751319885253906,
0.0142974853515625,
-0.00807952880859375,
-0.0096282958984375,
0.0318603515625,
0.007526397705078125,
0.004199981689453125,
-0.057586669921875,
0.016448974609375,
-0.008392333984375,
0.034881591796875,
0.026336669921875,
0.01137542724609375,
-0.004772186279296875,
0.008697509765625,
0.00818634033203125,
0.01435089111328125,
-0.006580352783203125,
0.004001617431640625,
0.0010995864868164062,
0.009674072265625,
0.01080322265625,
0.012237548828125,
-0.01427459716796875,
0.001468658447265625,
-0.0087432861328125,
0.028656005859375,
0.0028209686279296875,
-0.0238037109375,
0.0279388427734375,
0.007320404052734375,
-0.01788330078125,
0.04315185546875,
0.015167236328125,
-0.002895355224609375,
-0.001628875732421875,
-0.0015764236450195312,
0.00864410400390625,
-0.01140594482421875,
0.040191650390625,
-0.02178955078125,
0.01203155517578125,
-0.0301361083984375,
-0.0204010009765625,
-0.0250091552734375,
-0.006725311279296875,
-0.0027217864990234375,
0.0245361328125,
0.02239990234375,
-0.01235198974609375,
0.03411865234375,
0.00562286376953125,
-0.03448486328125,
-0.01123809814453125,
-0.0020751953125,
0.0006127357482910156,
-0.016021728515625,
0.01216888427734375,
-0.0213470458984375,
-0.03375244140625,
-0.004970550537109375,
0.0010786056518554688,
0.01409149169921875,
0.00788116455078125,
0.01024627685546875,
-0.018707275390625,
0.030731201171875,
-0.0247802734375,
0.0204620361328125,
-0.01377105712890625,
0.01020050048828125,
0.030731201171875,
0.0022430419921875,
0.0227203369140625,
0.00962066650390625,
0.027008056640625,
-0.007488250732421875,
-0.0145721435546875,
-0.01091766357421875,
-0.039398193359375,
0.002071380615234375,
-0.0166473388671875,
0.046356201171875,
-0.0309906005859375,
0.01422119140625,
0.0144805908203125,
-0.005519866943359375,
0.0210418701171875,
0.0032520294189453125,
0.00640869140625,
-0.0050048828125,
-0.00991058349609375,
0.00714111328125,
-0.007480621337890625,
-0.0001748800277709961,
0.021240234375,
-0.004711151123046875,
0.0045013427734375,
0.0015249252319335938,
0.0181121826171875,
0.035400390625,
-0.0138092041015625,
-0.017791748046875,
0.01439666748046875,
-0.00015556812286376953,
-0.0023746490478515625,
-0.0209808349609375,
0.00872802734375,
0.0165863037109375,
0.0095672607421875,
0.01029205322265625,
-0.006206512451171875,
0.021942138671875,
0.017059326171875,
0.039337158203125,
0.0189361572265625,
-0.02777099609375,
0.020965576171875,
0.0139923095703125,
-0.0305633544921875,
-0.0072174072265625,
0.004913330078125,
0.0101165771484375,
0.0032863616943359375,
0.019683837890625,
-0.036651611328125,
-0.03155517578125,
-0.012054443359375,
-0.0025501251220703125,
0.007648468017578125,
-0.0177459716796875,
0.020660400390625,
0.0148468017578125,
0.0201873779296875,
-0.007579803466796875,
0.00273895263671875,
0.0196990966796875,
0.003376007080078125,
0.021575927734375,
0.0186614990234375,
0.00719451904296875,
-0.004032135009765625,
0.01812744140625,
-0.0173492431640625,
0.01422882080078125,
-0.0170745849609375,
-0.01273345947265625,
0.0145416259765625,
-0.0272064208984375,
0.02215576171875,
-0.0261383056640625,
0.021575927734375,
0.0006847381591796875,
0.001392364501953125,
-0.0192413330078125,
0.01039886474609375,
0.01483154296875,
-0.00231170654296875,
0.0007038116455078125,
0.04632568359375,
-0.0164642333984375,
-0.0265655517578125,
0.005336761474609375,
-0.0054779052734375,
0.0118865966796875,
0.00576019287109375,
0.006988525390625,
-0.01318359375,
-0.0187530517578125,
0.000507354736328125,
-0.01336669921875,
0.00009548664093017578,
-0.040069580078125,
0.04095458984375,
-0.009033203125,
-0.0248870849609375,
-0.0140228271484375,
-0.004673004150390625,
-0.01284027099609375,
-0.00463104248046875,
0.00885772705078125,
-0.007709503173828125,
-0.02935791015625,
-0.007465362548828125,
-0.0082550048828125,
0.041595458984375,
0.04534912109375,
0.019073486328125,
0.045013427734375,
0.00464630126953125,
-0.0281829833984375,
-0.0078887939453125,
-0.0157318115234375,
-0.0208587646484375,
0.01507568359375,
-0.01715087890625,
-0.01026153564453125,
0.01143646240234375,
0.0433349609375,
0.01222991943359375,
-0.0306854248046875,
0.025146484375,
-0.03521728515625,
0.0089874267578125,
-0.006805419921875,
0.03070068359375,
0.0087127685546875,
-0.0250091552734375,
0.016510009765625,
-0.023681640625,
0.00577545166015625,
0.0247955322265625,
0.0010309219360351562,
0.0197601318359375,
0.0058441162109375,
-0.018341064453125,
0.0032672882080078125,
-0.006175994873046875,
0.046051025390625,
0.020660400390625,
-0.037933349609375,
-0.0031719207763671875,
-0.007587432861328125,
-0.00806427001953125,
-0.00347137451171875,
-0.00658416748046875,
-0.0294342041015625,
0.01494598388671875,
0.01519012451171875,
0.021148681640625,
-0.0232086181640625,
0.0032958984375,
-0.00365447998046875,
0.01898193359375,
-0.02490234375,
0.00559234619140625,
0.0086517333984375,
-0.004306793212890625,
-0.04345703125,
-0.002834320068359375,
0.01201629638671875,
0.003261566162109375,
-0.0343017578125,
-0.031890869140625,
-0.01204681396484375,
-0.0175628662109375,
-0.0090789794921875,
0.016876220703125,
0.034942626953125,
0.0216064453125,
-0.018707275390625,
-0.03863525390625,
0.02105712890625,
-0.0190277099609375,
-0.01123809814453125,
-0.030609130859375,
-0.0052032470703125,
0.035919189453125,
-0.03729248046875,
0.0032520294189453125,
-0.00482177734375,
0.018096923828125,
0.0159912109375,
-0.0010404586791992188,
0.004817962646484375,
-0.0018568038940429688,
-0.01629638671875,
0.017852783203125,
-0.01403045654296875,
-0.0022525787353515625,
0.01415252685546875,
0.037139892578125,
-0.028076171875,
-0.0000022649765014648438,
0.01493072509765625,
0.00992584228515625,
0.0239410400390625,
-0.0190582275390625,
-0.00531768798828125,
0.0216217041015625,
0.0290679931640625,
-0.024017333984375,
-0.0189971923828125,
-0.033660888671875,
0.006805419921875,
0.003086090087890625,
-0.01375579833984375,
0.0270233154296875,
0.01021575927734375,
0.00030350685119628906,
-0.037689208984375,
0.0054779052734375,
0.01117706298828125,
-0.00640869140625,
0.00518035888671875,
0.00555419921875,
-0.0036296844482421875,
0.0026340484619140625,
-0.0032196044921875,
0.00997161865234375,
-0.002231597900390625,
-0.0210418701171875,
-0.039215087890625,
0.0272979736328125,
0.0008535385131835938,
0.03466796875,
-0.04498291015625,
-0.0023040771484375,
0.0072784423828125,
-0.00789642333984375,
0.0016012191772460938,
0.01537322998046875,
0.013824462890625,
0.006103515625,
0.014007568359375,
-0.019989013671875,
-0.0286865234375,
0.027740478515625,
-0.0139007568359375,
0.0313720703125,
0.01165008544921875,
0.030120849609375,
-0.0013742446899414062,
-0.0129547119140625,
-0.0150604248046875,
-0.0229949951171875,
0.0025501251220703125,
0.02947998046875,
-0.0258026123046875,
0.00730133056640625,
-0.01215362548828125,
0.001506805419921875,
-0.0008454322814941406,
0.0033416748046875,
0.009765625,
-0.0233917236328125,
-0.041290283203125,
-0.020294189453125,
-0.0292510986328125,
-0.01500701904296875,
-0.003047943115234375,
0.0279998779296875,
-0.0251007080078125,
-0.025421142578125,
0.0259246826171875,
-0.0034694671630859375,
0.00634765625,
-0.0023365020751953125,
-0.0141754150390625,
0.01074981689453125,
-0.010345458984375,
0.0275421142578125,
0.005306243896484375,
-0.00311279296875,
0.01210784912109375,
0.0189056396484375,
-0.009063720703125,
0.003551483154296875,
0.0038471221923828125,
-0.0204925537109375,
0.01401519775390625,
-0.01093292236328125,
0.00579833984375,
-0.0005359649658203125,
0.0016078948974609375,
0.007511138916015625,
0.00682830810546875,
-0.0244903564453125,
0.031097412109375,
-0.00997161865234375,
0.0066680908203125,
0.0027751922607421875,
-0.02203369140625,
0.0002837181091308594,
-0.004360198974609375,
0.039459228515625,
0.0248565673828125,
0.00748443603515625,
0.0068511962890625,
0.01554107666015625,
-0.02044677734375,
-0.0112762451171875,
0.0209197998046875,
0.03582763671875,
-0.01268768310546875,
0.004444122314453125,
0.0042572021484375,
0.0011157989501953125,
-0.042999267578125,
-0.0006537437438964844,
-0.037841796875,
-0.0079193115234375,
-0.0005741119384765625,
0.0069122314453125,
-0.0109405517578125,
-0.006099700927734375,
-0.0024738311767578125,
-0.0086669921875,
-0.0233917236328125,
0.008514404296875,
-0.01398468017578125,
0.01552581787109375,
0.0033092498779296875,
0.016510009765625,
0.00814056396484375,
0.00759124755859375,
0.00823211669921875,
0.008819580078125,
0.01042938232421875,
0.006534576416015625,
0.0200347900390625,
0.0017728805541992188,
-0.00937652587890625,
-0.023223876953125,
0.0057830810546875,
0.028350830078125,
-0.0259552001953125,
-0.0079193115234375,
0.0340576171875,
0.0210723876953125,
-0.012969970703125,
-0.00914764404296875,
-0.0266265869140625,
0.0021877288818359375,
0.01152801513671875,
0.01580810546875,
-0.00904083251953125,
0.00945281982421875,
-0.038848876953125,
0.0254974365234375,
-0.018310546875,
0.0289154052734375,
0.01532745361328125,
0.00414276123046875,
0.037109375,
-0.007843017578125,
-0.004856109619140625,
-0.0178680419921875,
-0.00341796875,
-0.0015153884887695312,
-0.00608062744140625,
-0.003543853759765625,
-0.018096923828125,
-0.005443572998046875,
0.008453369140625,
-0.0033092498779296875,
-0.0379638671875,
0.039764404296875,
-0.0249176025390625,
0.00807952880859375,
0.00482177734375,
0.00615692138671875,
-0.021148681640625,
0.01068115234375,
-0.005462646484375,
-0.00923919677734375,
-0.0111083984375,
0.012420654296875,
-0.02313232421875,
0.0008091926574707031,
0.01312255859375,
0.0235137939453125,
0.0013561248779296875,
-0.00399017333984375,
-0.0006761550903320312,
-0.02130126953125,
-0.0206298828125,
-0.007320404052734375,
-0.01165771484375,
0.003559112548828125,
-0.0276336669921875,
-0.0208282470703125,
-0.0192718505859375,
-0.0113067626953125,
-0.0260772705078125,
-0.03912353515625,
0.02813720703125,
0.01226806640625,
0.00025463104248046875,
-0.00460052490234375,
-0.0259552001953125,
-0.01346588134765625,
-0.0217742919921875,
-0.02392578125,
0.002346038818359375,
0.00978851318359375,
-0.0030879974365234375,
0.0166473388671875,
-0.00388336181640625,
-0.025543212890625,
0.0065460205078125,
0.00809478759765625,
0.003078460693359375,
0.0521240234375,
-0.0208740234375,
0.00011217594146728516,
-0.0260162353515625,
-0.0146484375,
0.0114288330078125,
0.00470733642578125,
-0.0269927978515625,
0.003871917724609375,
0.0210723876953125,
0.012908935546875,
-0.048980712890625,
-0.0310516357421875,
-0.01482391357421875,
0.005695343017578125,
-0.0303802490234375,
-0.01039886474609375,
-0.01165008544921875,
0.005435943603515625,
0.00717926025390625,
0.029693603515625,
-0.005615234375,
0.004596710205078125,
-0.007251739501953125,
0.015380859375,
0.004962921142578125,
0.005161285400390625,
-0.040679931640625,
-0.0217132568359375,
-0.0007181167602539062,
-0.0232391357421875,
-0.043731689453125,
-0.02301025390625,
0.00817108154296875,
0.01934814453125,
-0.042755126953125,
-0.0148162841796875,
-0.01464080810546875,
0.00502777099609375,
0.0194549560546875,
0.03277587890625,
0.02398681640625,
-0.002811431884765625,
-0.0182037353515625,
0.0005216598510742188,
0.006595611572265625,
0.01248931884765625,
-0.042083740234375,
0.016937255859375,
-0.011505126953125,
0.0017824172973632812,
0.0094757080078125,
0.0147552490234375,
0.0003376007080078125,
0.0034046173095703125,
0.003971099853515625,
-0.033660888671875,
0.006893157958984375,
-0.040374755859375,
-0.01407623291015625,
0.019378662109375,
-0.02008056640625,
0.060028076171875,
0.0021114349365234375,
0.023590087890625,
0.01139068603515625,
-0.007671356201171875,
-0.00035071372985839844,
0.0430908203125,
-0.0162200927734375,
-0.01488494873046875,
0.0159454345703125,
0.006885528564453125,
-0.036529541015625,
0.033203125,
0.00308990478515625,
-0.006420135498046875,
0.00887298583984375,
-0.00991058349609375,
0.00537872314453125,
0.024627685546875,
-0.030914306640625,
-0.024566650390625,
-0.01617431640625,
0.0019626617431640625,
-0.0229034423828125,
0.0142059326171875,
-0.0110931396484375,
-0.0201263427734375,
0.044342041015625,
-0.017974853515625,
0.0005903244018554688,
-0.011016845703125,
-0.01059722900390625,
0.02618408203125,
0.02178955078125,
-0.0333251953125,
-0.0115203857421875,
0.00998687744140625,
-0.01560211181640625,
-0.00753021240234375,
0.0338134765625,
-0.00894927978515625,
-0.01171875,
-0.01544952392578125,
-0.01132965087890625,
0.0105438232421875,
-0.018768310546875,
-0.01800537109375,
-0.030059814453125,
-0.01324462890625,
0.01436614990234375,
0.018524169921875,
0.002410888671875,
-0.016510009765625,
-0.0313720703125,
-0.0200958251953125,
0.0102081298828125,
0.0179290771484375,
0.0032024383544921875,
0.005214691162109375,
0.0220184326171875,
0.0152130126953125,
0.03656005859375,
0.002033233642578125,
0.017669677734375,
0.045135498046875,
0.040283203125,
0.017608642578125,
-0.0282135009765625,
0.022125244140625,
-0.0161895751953125,
-0.007171630859375,
-0.00408172607421875,
-0.0092620849609375,
-0.01031494140625,
-0.019287109375,
-0.0247344970703125,
0.0013093948364257812,
-0.00333404541015625,
-0.036895751953125,
-0.0222015380859375,
-0.03143310546875,
0.00254058837890625,
-0.0251617431640625,
0.03009033203125,
0.0260467529296875,
-0.00377655029296875,
0.0260162353515625,
-0.0298919677734375,
0.0157318115234375,
0.004756927490234375,
-0.00740814208984375,
0.018218994140625,
-0.025146484375,
-0.04022216796875,
0.01345062255859375,
0.01049041748046875,
0.00426483154296875,
0.0186309814453125,
-0.01033782958984375,
0.004863739013671875,
-0.01293182373046875,
0.01216888427734375,
0.03204345703125,
-0.007625579833984375,
0.01654052734375,
-0.0017385482788085938,
0.031494140625,
-0.01433563232421875,
0.007595062255859375,
-0.016937255859375,
-0.005130767822265625,
-0.0147552490234375,
-0.0071258544921875,
0.0059356689453125,
0.004718780517578125,
0.00826263427734375,
-0.01181793212890625,
-0.0008597373962402344,
0.0007781982421875,
0.0202178955078125,
0.01088714599609375,
0.0203094482421875,
0.0181427001953125,
0.02117919921875,
-0.043792724609375,
-0.01438140869140625,
-0.03411865234375,
-0.0204315185546875,
0.0196533203125,
0.03057861328125,
0.0074005126953125,
-0.000048995018005371094,
0.0172576904296875,
0.0035572052001953125,
-0.0087890625,
0.004291534423828125,
-0.00702667236328125,
-0.003360748291015625,
0.0164031982421875,
-0.019134521484375,
0.011016845703125,
0.004047393798828125,
-0.0006937980651855469,
-0.0008306503295898438,
-0.0174102783203125,
-0.0236053466796875,
-0.01548004150390625,
-0.004169464111328125,
0.03839111328125,
-0.0214385986328125,
-0.01242828369140625,
0.02783203125,
0.0010528564453125,
-0.01358795166015625,
0.00675201416015625,
-0.019866943359375,
-0.03692626953125,
-0.006343841552734375,
-0.005695343017578125,
0.043914794921875,
0.0007309913635253906,
-0.017974853515625,
-0.0121917724609375,
0.0204010009765625,
-0.00818634033203125,
0.0036716461181640625,
-0.004364013671875,
0.015625,
-0.0104827880859375,
0.00580596923828125,
-0.00968170166015625,
-0.01873779296875,
-0.0263824462890625,
-0.0007276535034179688,
0.0173187255859375,
-0.0233917236328125,
-0.021514892578125,
0.01222991943359375,
-0.0082244873046875,
-0.022552490234375,
0.00896453857421875,
0.00453948974609375,
-0.0236053466796875,
0.013275146484375,
-0.0008392333984375,
0.006378173828125,
-0.01385498046875,
-0.00661468505859375,
0.01247406005859375,
0.0221710205078125,
-0.0087127685546875,
0.01546478271484375,
-0.01537322998046875,
-0.0006227493286132812,
-0.00782012939453125,
0.00548553466796875,
-0.0238800048828125,
0.0136260986328125,
0.0208587646484375,
-0.007259368896484375,
0.022003173828125,
0.0236358642578125,
-0.01169586181640625,
0.0188446044921875,
-0.0062408447265625,
0.035919189453125,
0.00274658203125,
-0.0189666748046875,
0.0264892578125,
0.0158843994140625,
-0.00836181640625,
0.03253173828125,
-0.00626373291015625,
0.01129913330078125,
-0.034759521484375,
0.04351806640625,
0.012969970703125,
-0.007419586181640625,
-0.0253753662109375,
-0.03466796875,
-0.003448486328125,
-0.005584716796875,
0.033660888671875,
-0.020172119140625,
-0.0723876953125,
-0.0116119384765625,
0.0309295654296875,
-0.011505126953125,
0.02435302734375,
0.0171356201171875,
0.00936126708984375,
0.020965576171875,
0.0008673667907714844,
-0.02032470703125,
-0.02215576171875,
0.010101318359375,
0.0082550048828125,
0.0006418228149414062,
-0.0027618408203125,
0.01172637939453125,
-0.01763916015625,
-0.0002913475036621094,
0.004550933837890625,
-0.0257415771484375,
0.0088958740234375,
0.0011425018310546875,
-0.052032470703125,
-0.0019512176513671875,
0.029541015625,
0.0384521484375,
0.02679443359375,
-0.006866455078125,
0.0155792236328125,
-0.01093292236328125,
-0.0188140869140625,
-0.00585174560546875,
0.024200439453125,
-0.0181427001953125,
0.006298065185546875,
-0.0220947265625,
-0.0033550262451171875,
-0.004207611083984375,
0.0006079673767089844,
0.0244903564453125,
0.01074981689453125,
-0.01190948486328125,
0.0096893310546875,
-0.02410888671875,
0.0273590087890625,
-0.0167236328125,
-0.0198211669921875,
0.0165252685546875,
-0.00449371337890625,
0.0182342529296875,
0.00604248046875,
0.02069091796875,
0.0078582763671875,
0.031829833984375,
0.01216888427734375,
0.0014543533325195312,
-0.01274871826171875,
0.0289154052734375,
0.02685546875,
-0.012176513671875,
0.000507354736328125,
0.018463134765625,
0.042724609375,
0.0236053466796875,
-0.004558563232421875,
0.0347900390625,
-0.0175933837890625,
-0.019561767578125,
0.00917816162109375,
-0.03289794921875,
-0.0106353759765625,
0.0399169921875,
0.0208282470703125,
-0.018585205078125,
0.0177154541015625,
-0.04248046875,
0.013763427734375,
0.00504302978515625,
0.0237274169921875,
-0.00823211669921875,
0.03533935546875,
-0.0244293212890625,
-0.0088958740234375,
0.01192474365234375,
-0.044677734375,
-0.01320648193359375,
0.0208740234375,
0.03594970703125,
-0.001560211181640625,
0.0003802776336669922,
0.00861358642578125,
-0.005100250244140625,
-0.0245361328125,
-0.00406646728515625,
-0.00856781005859375,
0.023468017578125,
-0.0240631103515625,
-0.020599365234375,
-0.0255584716796875,
-0.04583740234375,
-0.021148681640625,
0.01641845703125,
0.0007929801940917969,
0.003326416015625,
-0.01214599609375,
0.0046539306640625,
0.00304412841796875,
0.034912109375,
0.0138092041015625,
-0.01311492919921875,
-0.0208282470703125,
-0.008270263671875,
0.0191802978515625,
-0.01308441162109375,
-0.0037078857421875,
-0.05682373046875,
0.015777587890625,
-0.003681182861328125,
-0.027618408203125,
-0.0220184326171875,
0.00986480712890625,
-0.028594970703125,
0.00405120849609375,
-0.0008082389831542969,
0.032623291015625,
0.00711822509765625,
-0.0033969879150390625,
0.0234222412109375,
-0.004230499267578125,
-0.0225830078125,
0.017608642578125,
0.03753662109375,
0.017974853515625,
-0.0147705078125,
0.0283050537109375,
0.00504302978515625,
0.030548095703125,
-0.0120086669921875,
0.005069732666015625,
-0.026336669921875,
0.028228759765625,
-0.0093231201171875,
0.0040130615234375,
-0.0016040802001953125,
-0.0302734375,
0.0186614990234375,
0.021728515625,
-0.047821044921875,
0.00444793701171875,
-0.0196685791015625,
-0.032012939453125,
0.028533935546875,
-0.021331787109375,
-0.0170745849609375,
-0.01416015625,
-0.0042877197265625,
0.0124664306640625,
0.004871368408203125,
0.0306854248046875,
0.0164031982421875,
-0.0290069580078125,
-0.0178680419921875,
0.0017910003662109375,
-0.0091705322265625,
-0.019256591796875,
0.0068206787109375,
-0.0272216796875,
-0.0234527587890625,
-0.0101318359375,
0.03985595703125,
-0.0124664306640625,
0.0017681121826171875,
-0.002925872802734375,
-0.005260467529296875,
0.005229949951171875,
-0.0011129379272460938,
-0.012054443359375,
0.0216064453125,
-0.0239105224609375,
-0.032257080078125,
0.031951904296875,
-0.02496337890625,
-0.017486572265625,
-0.034698486328125,
0.028656005859375,
-0.014251708984375,
-0.006038665771484375,
-0.004077911376953125,
0.032867431640625,
0.0060272216796875,
-0.01079559326171875,
0.003765106201171875,
-0.0257568359375,
0.022796630859375,
0.01139068603515625,
-0.0222930908203125,
0.02349853515625,
0.0022373199462890625,
-0.01007080078125,
-0.0202789306640625,
-0.0174560546875,
0.00801849365234375,
-0.039031982421875,
-0.0297698974609375,
0.0186309814453125,
-0.0281524658203125,
0.019317626953125,
-0.003643035888671875,
-0.006732940673828125,
-0.0013093948364257812,
-0.005580902099609375,
-0.0150604248046875,
0.01476287841796875,
0.03460693359375,
0.00804901123046875,
-0.01364898681640625,
0.0112457275390625,
0.0276031494140625,
0.0178985595703125,
-0.003383636474609375,
0.002452850341796875,
0.00244903564453125,
0.0167236328125,
0.0174407958984375,
-0.00014913082122802734,
0.0206298828125,
0.001544952392578125,
0.002208709716796875,
-0.006305694580078125,
-0.015625,
0.01468658447265625,
0.0213775634765625,
-0.0150604248046875,
-0.0001747608184814453,
0.00384521484375,
-0.0155181884765625,
0.00803375244140625,
-0.01415252685546875,
0.0022068023681640625,
-0.01045989990234375,
0.01096343994140625,
0.0025920867919921875,
-0.0020542144775390625,
0.01959228515625,
-0.0192718505859375,
-0.000438690185546875,
-0.029144287109375,
-0.0211334228515625,
0.00873565673828125,
0.0008492469787597656,
-0.00644683837890625,
0.01348114013671875,
0.01488494873046875,
0.00670623779296875,
0.002948760986328125,
0.01043701171875,
-0.0243682861328125,
0.011993408203125,
0.01751708984375,
-0.026611328125,
0.01708984375,
-0.0038356781005859375,
-0.003780364990234375,
-0.001148223876953125,
-0.01386260986328125,
-0.004009246826171875,
-0.0177764892578125,
0.0206756591796875,
-0.0217132568359375,
-0.02960205078125,
0.02703857421875,
0.007083892822265625,
0.049468994140625,
-0.0207366943359375,
-0.01824951171875,
0.02130126953125,
-0.029541015625,
-0.013916015625,
0.00034928321838378906,
0.01522064208984375,
-0.00139617919921875,
-0.0015659332275390625,
0.0014524459838867188,
-0.0285797119140625,
0.006732940673828125,
0.01397705078125,
0.0184478759765625,
0.0008368492126464844,
0.0173797607421875,
-0.0011682510375976562,
0.0128631591796875,
0.00623321533203125,
0.0105133056640625,
0.031341552734375,
0.0284271240234375,
-0.032806396484375,
0.006351470947265625,
0.004711151123046875,
0.0033721923828125,
0.028778076171875,
-0.0023784637451171875,
-0.004207611083984375,
0.00030994415283203125,
0.008026123046875,
0.0017061233520507812,
0.0181884765625,
-0.0050811767578125,
0.00836181640625,
0.00004410743713378906,
-0.00731658935546875,
-0.0012617111206054688,
-0.0017719268798828125,
0.0196990966796875,
-0.00782012939453125,
0.0112762451171875,
0.0112457275390625,
0.023895263671875,
-0.012847900390625,
0.01340484619140625,
0.0233917236328125,
0.00902557373046875,
-0.0114898681640625,
0.0095367431640625,
-0.01355743408203125,
-0.0005497932434082031,
-0.001644134521484375,
0.0095672607421875,
0.00527191162109375,
0.0309600830078125,
0.0038013458251953125,
-0.01184844970703125,
0.01012420654296875,
0.004444122314453125,
0.0210723876953125,
-0.0016736984252929688,
0.01166534423828125,
-0.032501220703125,
-0.026702880859375,
0.0107269287109375,
0.00730133056640625,
0.0139007568359375,
-0.0220489501953125,
0.0208740234375,
-0.01410675048828125,
-0.00745391845703125,
-0.0068359375,
-0.018096923828125,
-0.0023956298828125,
-0.0026569366455078125,
-0.007904052734375,
0.0069580078125,
-0.016632080078125,
-0.00682830810546875,
-0.06781005859375,
-0.0203094482421875,
-0.00896453857421875,
0.0226287841796875,
0.0108489990234375,
-0.0011882781982421875,
-0.0156707763671875,
0.03076171875,
0.01617431640625,
-0.0130767822265625,
0.038299560546875,
0.00464630126953125,
0.01114654541015625,
0.00037479400634765625,
-0.037139892578125,
0.035369873046875,
0.015411376953125,
-0.0294036865234375,
-0.00765228271484375,
0.01117706298828125,
0.027557373046875,
-0.0435791015625,
-0.029998779296875,
0.0099639892578125,
0.01053619384765625,
0.0082244873046875,
0.0023784637451171875,
-0.0009937286376953125,
0.004467010498046875,
0.01419830322265625,
0.0206756591796875,
-0.0169677734375,
0.02166748046875,
0.0106353759765625,
0.010833740234375,
-0.013641357421875,
0.02398681640625,
-0.022918701171875,
-0.007732391357421875,
-0.0201416015625,
-0.002826690673828125,
-0.005680084228515625,
-0.018218994140625,
-0.00566864013671875,
0.024078369140625,
0.0014896392822265625,
0.00589752197265625,
0.0000718832015991211,
-0.0112457275390625,
-0.01099395751953125,
-0.055145263671875,
-0.04791259765625,
0.01035308837890625,
-0.023895263671875,
-0.02874755859375,
-0.03955078125,
-0.0288238525390625,
-0.0279541015625,
-0.0191802978515625,
-0.004222869873046875,
-0.002689361572265625,
0.01290130615234375,
0.0167999267578125,
-0.0263519287109375,
0.0011606216430664062,
-0.00865936279296875,
0.0092620849609375,
-0.0160675048828125,
-0.004238128662109375,
-0.0033168792724609375,
-0.01326751708984375,
-0.004497528076171875,
0.004642486572265625,
-0.031982421875,
0.00614166259765625,
-0.0131072998046875,
-0.00296783447265625,
0.00705718994140625,
0.0305938720703125,
0.0012493133544921875,
0.00687408447265625,
-0.01108551025390625,
0.00701141357421875,
0.017547607421875,
0.004856109619140625,
0.0243682861328125,
-0.0260467529296875,
-0.0379638671875,
-0.00957489013671875,
0.00041937828063964844,
0.0247955322265625,
-0.00992584228515625,
0.0066070556640625,
0.003337860107421875,
-0.004116058349609375,
-0.00458526611328125,
0.006259918212890625,
0.010223388671875,
0.01380157470703125,
-0.035125732421875,
-0.00823211669921875,
-0.020782470703125,
0.0044097900390625,
0.0170745849609375,
-0.01275634765625,
-0.01039886474609375,
0.0008654594421386719,
0.014739990234375,
-0.024383544921875,
-0.000732421875,
-0.00917816162109375,
-0.04302978515625,
0.00040531158447265625,
0.01102447509765625,
0.01445770263671875,
0.0011339187622070312,
-0.03851318359375,
0.007465362548828125,
-0.01226043701171875,
0.02490234375,
-0.0035457611083984375,
0.0141143798828125,
0.0086517333984375,
0.012603759765625,
-0.01214599609375,
0.0042572021484375,
0.0077667236328125,
-0.02947998046875,
0.0103302001953125,
-0.006313323974609375,
0.0014791488647460938,
-0.006092071533203125,
0.007747650146484375,
-0.0101776123046875,
0.0006442070007324219,
-0.03106689453125,
0.0004911422729492188,
0.014739990234375,
0.00699615478515625,
0.0182952880859375,
0.037445068359375,
-0.01739501953125,
-0.012115478515625,
0.0167694091796875,
-0.00386810302734375,
-0.020172119140625,
-0.0132598876953125,
0.053436279296875,
0.012481689453125,
-0.004543304443359375,
0.00603485107421875,
-0.0217437744140625,
0.00872802734375,
0.0562744140625,
0.0016927719116210938,
0.008026123046875,
-0.033355712890625,
-0.01445770263671875,
0.002544403076171875,
0.0020294189453125,
0.0029354095458984375,
0.01490020751953125,
0.00798797607421875,
0.0301513671875,
-0.008087158203125,
0.028076171875,
-0.0201568603515625,
-0.039306640625,
-0.02813720703125,
-0.0142364501953125,
0.0199432373046875,
0.0479736328125,
0.035797119140625,
-0.0284423828125,
-0.01910400390625,
0.0162200927734375,
0.0076141357421875,
-0.025482177734375,
-0.03314208984375,
0.01320648193359375,
0.006866455078125,
0.01537322998046875,
0.0271453857421875,
0.004253387451171875,
0.02197265625,
-0.01006317138671875,
0.0234527587890625,
-0.01432037353515625,
0.0009851455688476562,
0.0303802490234375,
0.00870513916015625,
-0.0111846923828125,
0.01421356201171875,
-0.0026340484619140625,
-0.0111541748046875,
-0.015655517578125,
0.0177764892578125,
-0.02178955078125,
0.0205230712890625,
-0.02142333984375,
0.026214599609375,
0.0025653839111328125,
0.056549072265625,
0.0223541259765625,
0.053009033203125,
-0.034759521484375,
-0.00438690185546875,
-0.0027332305908203125,
-0.00411224365234375,
0.0009703636169433594,
0.0211944580078125,
-0.032623291015625,
0.01776123046875,
-0.0159759521484375,
-0.004062652587890625,
0.031768798828125,
-0.036834716796875,
0.032073974609375,
-0.018096923828125,
-0.004383087158203125,
-0.005962371826171875,
-0.016357421875,
-0.01226043701171875,
0.00571441650390625,
0.037750244140625,
0.0033416748046875,
0.01526641845703125,
0.016693115234375,
-0.00033926963806152344,
-0.0032215118408203125,
0.0238189697265625,
0.0009298324584960938,
-0.021026611328125,
0.0038242340087890625,
0.0005497932434082031,
-0.020904541015625,
0.0053863525390625,
-0.019683837890625,
-0.0007796287536621094,
-0.003993988037109375,
-0.043487548828125,
0.005458831787109375,
0.00391387939453125,
0.03192138671875,
0.005672454833984375,
-0.0016489028930664062,
-0.01110076904296875,
-0.0186614990234375,
0.0196685791015625,
-0.032257080078125,
-0.0248870849609375,
0.00800323486328125,
-0.004138946533203125,
-0.00399017333984375,
-0.0000546574592590332,
-0.01308441162109375,
-0.01128387451171875,
0.0307464599609375,
0.00458526611328125,
-0.017242431640625,
-0.031646728515625,
0.01195526123046875,
-0.0156402587890625,
-0.01137542724609375,
-0.007518768310546875,
0.0207061767578125,
-0.00559234619140625,
-0.03125,
0.01003265380859375,
0.0218353271484375,
-0.058013916015625,
-0.003017425537109375,
0.0594482421875,
-0.01471710205078125,
0.037017822265625,
0.01503753662109375,
0.0067901611328125,
0.0024547576904296875,
0.051605224609375,
-0.02081298828125,
0.022186279296875,
0.0225067138671875,
-0.0259857177734375,
-0.01708984375,
-0.004974365234375,
0.02410888671875,
-0.06549072265625,
-0.0023097991943359375,
0.0209808349609375,
-0.0051727294921875,
-0.00847625732421875,
0.01038360595703125,
-0.0033664703369140625,
-0.046539306640625,
-0.0230865478515625,
-0.02020263671875,
-0.00780487060546875,
-0.004486083984375,
0.01302337646484375,
0.0230255126953125,
-0.0297393798828125,
0.035186767578125,
0.0241851806640625,
-0.02105712890625,
0.0014638900756835938,
-0.015899658203125,
-0.006572723388671875,
-0.0110015869140625,
-0.0033779144287109375,
0.0149688720703125,
0.0250701904296875,
0.00829315185546875,
0.0012493133544921875,
-0.01898193359375,
-0.0078125,
0.003437042236328125,
0.00394439697265625,
0.01219940185546875,
0.007099151611328125,
-0.0079193115234375,
0.037078857421875,
-0.02911376953125,
0.0154266357421875,
0.006214141845703125,
-0.0022373199462890625,
0.0027484893798828125,
0.004322052001953125,
0.0139312744140625,
-0.01256561279296875,
0.0204620361328125,
-0.0240936279296875,
-0.00131988525390625,
0.007305145263671875,
-0.042572021484375,
0.00004190206527709961,
-0.0115966796875,
-0.006496429443359375,
-0.0095367431640625,
-0.036712646484375,
0.000022172927856445312,
0.0259857177734375,
-0.004669189453125,
0.03564453125,
-0.01093292236328125,
-0.0133514404296875,
0.0116424560546875,
-0.019195556640625,
-0.01092529296875,
-0.007038116455078125,
0.048736572265625,
0.0196685791015625,
-0.007549285888671875,
0.01206207275390625,
-0.0083160400390625,
0.023956298828125,
-0.0197601318359375,
-0.00458526611328125,
-0.01099395751953125,
0.004123687744140625,
-0.01654052734375,
-0.017547607421875,
-0.00102996826171875,
-0.0102996826171875,
0.00231170654296875,
-0.001644134521484375,
-0.0009160041809082031,
-0.025482177734375,
0.0173797607421875,
-0.01556396484375,
-0.0129852294921875,
-0.0263824462890625,
0.0113067626953125,
-0.005828857421875,
-0.017333984375,
-0.01049041748046875,
-0.01490020751953125,
0.025543212890625,
-0.005840301513671875,
-0.004184722900390625,
-0.0369873046875,
0.03271484375,
0.006317138671875,
0.036163330078125,
0.015655517578125,
-0.0094146728515625,
-0.0187530517578125,
0.0191802978515625,
0.0294952392578125,
0.01488494873046875,
0.0030536651611328125,
0.0386962890625,
-0.007312774658203125,
-0.0004830360412597656,
-0.0214996337890625,
-0.050933837890625,
0.01242828369140625,
0.028533935546875,
0.037811279296875,
0.016510009765625,
-0.003631591796875,
0.00785064697265625,
-0.003055572509765625,
-0.039581298828125,
-0.017578125,
-0.0160064697265625,
0.004913330078125,
0.016845703125,
0.0090484619140625,
-0.029510498046875,
-0.0036602020263671875,
-0.00127410888671875,
0.006732940673828125,
-0.0038967132568359375,
-0.0033130645751953125,
0.0243682861328125,
-0.0211029052734375,
0.0316162109375,
0.00982666015625,
0.041900634765625,
-0.0328369140625,
-0.004047393798828125,
0.0245208740234375,
0.003551483154296875,
-0.01275634765625,
-0.0016717910766601562,
-0.0237579345703125,
0.0033779144287109375,
-0.0140380859375,
-0.019073486328125,
-0.016845703125,
-0.00745391845703125,
-0.0010738372802734375,
-0.00940704345703125,
0.032684326171875,
-0.005199432373046875,
-0.049530029296875,
0.0133514404296875,
-0.0304107666015625,
0.005252838134765625,
-0.0198974609375,
-0.00936126708984375,
0.00031113624572753906,
-0.040802001953125,
0.014617919921875,
-0.00836944580078125,
0.0003571510314941406,
-0.01511383056640625,
-0.0263519287109375,
-0.0120086669921875,
-0.0015649795532226562,
0.01824951171875,
0.0295562744140625,
-0.0197296142578125,
-0.01096343994140625,
-0.004924774169921875,
-0.0170135498046875,
0.00795745849609375,
0.03253173828125,
0.0010652542114257812,
0.0197906494140625,
-0.023834228515625,
-0.038818359375,
-0.01334381103515625,
0.0143280029296875,
-0.008453369140625,
-0.009307861328125,
0.060638427734375,
0.00182342529296875,
0.027801513671875,
0.0250244140625,
-0.007740020751953125,
0.00914764404296875,
-0.0248870849609375,
0.037750244140625,
-0.0206756591796875,
-0.0110931396484375,
-0.0018358230590820312,
0.0079803466796875,
0.0262908935546875,
0.04058837890625,
0.0032634735107421875,
0.0015954971313476562,
-0.0133209228515625,
0.005107879638671875,
-0.0193023681640625,
0.0009412765502929688,
-0.010772705078125,
0.0026683807373046875,
0.04388427734375,
-0.00455474853515625,
0.03125,
0.006198883056640625,
-0.0196990966796875,
0.041473388671875,
-0.0190887451171875,
0.025726318359375,
0.029541015625,
-0.0292510986328125,
-0.007232666015625,
-0.0005807876586914062,
-0.037628173828125,
0.013580322265625,
-0.0035686492919921875,
0.0103759765625,
-0.0253143310546875,
-0.04534912109375,
-0.023834228515625,
0.0055389404296875,
0.0106964111328125,
-0.007404327392578125,
0.01215362548828125,
0.0085906982421875,
-0.0323486328125,
-0.039276123046875,
-0.00262451171875,
0.0157012939453125,
-0.0100555419921875,
0.0202178955078125,
0.01226806640625,
0.005550384521484375,
0.031280517578125,
-0.01885986328125,
-0.00954437255859375,
-0.0258941650390625,
0.036376953125,
-0.043609619140625,
0.01256561279296875,
0.0058135986328125,
-0.026519775390625,
-0.027008056640625,
0.045806884765625,
-0.016021728515625,
0.0374755859375,
-0.0200347900390625,
0.01329803466796875,
0.0031986236572265625,
-0.026611328125,
-0.00464630126953125,
-0.01316070556640625,
-0.00012934207916259766,
-0.043731689453125,
0.044403076171875,
0.0156707763671875,
-0.045013427734375,
0.00843048095703125,
0.0107574462890625,
-0.00214385986328125,
0.004817962646484375,
0.0020313262939453125,
-0.00775909423828125,
0.0120086669921875,
0.0238037109375,
-0.01175689697265625,
-0.025787353515625,
-0.0110626220703125,
0.053436279296875,
-0.01239013671875,
-0.040679931640625,
0.020782470703125,
-0.005954742431640625,
-0.01107025146484375,
0.01479339599609375,
-0.00986480712890625,
-0.03961181640625,
0.039642333984375,
-0.0168609619140625,
0.0279693603515625,
0.01300811767578125,
-0.028106689453125,
-0.0032901763916015625,
-0.00838470458984375,
-0.00782012939453125,
-0.0190582275390625,
-0.04248046875,
0.013763427734375,
0.01317596435546875,
-0.0107574462890625,
-0.04779052734375,
-0.035614013671875,
-0.0008254051208496094,
-0.022003173828125,
-0.0033321380615234375,
-0.0008988380432128906,
-0.005298614501953125,
-0.045074462890625,
-0.00983428955078125,
-0.011138916015625,
-0.01253509521484375,
0.0211334228515625,
-0.02630615234375,
-0.01255035400390625,
0.009613037109375,
-0.0019369125366210938,
-0.04522705078125,
-0.004302978515625,
0.0207366943359375,
-0.0165863037109375,
-0.003917694091796875,
0.0187225341796875,
0.0015392303466796875,
0.004528045654296875,
-0.04827880859375,
-0.00112152099609375,
-0.00868988037109375,
0.032073974609375,
-0.0100860595703125,
-0.002716064453125,
0.03851318359375,
-0.031951904296875,
0.006893157958984375,
-0.001979827880859375,
-0.0233154296875,
0.01300048828125,
-0.0281219482421875,
0.01274871826171875,
-0.01377105712890625,
0.01526641845703125,
0.018035888671875,
0.00936126708984375,
-0.01247406005859375,
-0.0123138427734375,
0.00341796875,
0.01389312744140625,
-0.0069122314453125,
-0.01337432861328125,
-0.0039043426513671875,
-0.017120361328125,
0.005146026611328125,
-0.010772705078125,
0.022979736328125,
0.0211334228515625,
0.000629425048828125,
0.0073699951171875,
-0.0007338523864746094,
0.0012140274047851562,
0.01239776611328125,
0.0200347900390625,
0.016357421875,
-0.01611328125,
-0.019073486328125,
-0.00530242919921875,
0.01157379150390625,
0.004337310791015625,
-0.03076171875,
0.01485443115234375,
-0.01052093505859375,
0.02044677734375,
0.01062774658203125
] |
ours_482
|
Linearity of expectation and grid symmetry means we can calculate \(24^{2} E[L]\), where \(L\) is the amount of kilojoules consumed by a single lightbulb. Notice that after all \(48\) toggles, each light will have been toggled precisely twice, so it will be off.
Consider any specific lightbulb: it is toggled on at time \(t_{1}\) and off at time \(t_{2}\). Any other of the \(46\) toggles is equally likely to be before \(t_{1}\), after \(t_{2}\), or in between, so by linearity of expectation there are an expected \(\frac{46}{3}\) toggles in between \(t_{1}\) and \(t_{2}\); adding one gives an expected \(\frac{49}{3}\) minutes between \(t_{1}\) and \(t_{2}\). Therefore, the expected value is just \(24^{2} \cdot \frac{49}{3} = 9408\).
\(\boxed{9408}\)
|
9408
|
{
"competition": "us_comps",
"dataset": "Ours",
"posts": null,
"source": "OMOFall18Solns.md"
}
|
Jay has a \(24 \times 24\) grid of lights, all of which are initially off. Each of the \(48\) rows and columns has a switch that toggles all the lights in that row and column, respectively, i.e., it switches lights that are on to off and lights that are off to on. Jay toggles each of the \(48\) rows and columns exactly once, such that after each toggle he waits for one minute before the next toggle. Each light uses no energy while off and \(1\) kiloJoule of energy per minute while on. To express his creativity, Jay chooses to toggle the rows and columns in a random order. Compute the expected value of the total amount of energy in kiloJoules which has been expended by all the lights after all \(48\) toggles.
|
[
"/Mathematics/DiscreteMathematics/Combinatorics/GeneralCombinatorics",
"/Mathematics/DiscreteMathematics/GeneralDiscreteMathematics/DiscreteMath",
"/Mathematics/DiscreteMathematics/GeneralDiscreteMathematics/DiscreteMathematics",
"/Mathematics/DiscreteMathematics/GeneralDiscreteMathematics/FiniteMathematics",
"/Mathematics/ProbabilityandStatistics/Probability"
] |
Compute the expected on‑time of a bulb by finding the expected number of steps between its two toggles in a random permutation of the 48 switches.
|
[
0.0000762939453125,
-0.0037593841552734375,
0.0360107421875,
-0.007579803466796875,
0.00045609474182128906,
-0.0111083984375,
0.0300140380859375,
-0.0220184326171875,
0.0039215087890625,
0.01346588134765625,
0.00787353515625,
-0.0178070068359375,
-0.0009517669677734375,
0.0163726806640625,
0.016876220703125,
-0.040252685546875,
0.0194549560546875,
0.00649261474609375,
0.0129241943359375,
0.00044155120849609375,
-0.0157928466796875,
-0.012908935546875,
-0.0677490234375,
0.0031585693359375,
-0.0034942626953125,
-0.052093505859375,
-0.0177154541015625,
0.0246734619140625,
-0.0016431808471679688,
0.01611328125,
-0.04052734375,
0.003917694091796875,
0.05780029296875,
0.01013946533203125,
-0.003582000732421875,
0.0086822509765625,
0.050018310546875,
0.0018863677978515625,
-0.033416748046875,
0.017120361328125,
-0.006988525390625,
0.0064239501953125,
0.002330780029296875,
0.003170013427734375,
-0.005222320556640625,
0.0182647705078125,
0.0004229545593261719,
-0.0023174285888671875,
-0.00901031494140625,
-0.0333251953125,
-0.0060577392578125,
0.00836181640625,
0.01497650146484375,
-0.010284423828125,
-0.01148223876953125,
-0.0120849609375,
-0.022003173828125,
0.00478363037109375,
0.00823974609375,
-0.00409698486328125,
-0.002529144287109375,
0.018402099609375,
-0.0024356842041015625,
-0.01041412353515625,
0.0005183219909667969,
-0.0041351318359375,
0.0016145706176757812,
0.0230865478515625,
-0.00492095947265625,
-0.0154876708984375,
-0.03363037109375,
0.0016031265258789062,
-0.005474090576171875,
0.0229034423828125,
0.038787841796875,
-0.01525115966796875,
-0.0046539306640625,
0.001491546630859375,
-0.006732940673828125,
0.012115478515625,
-0.01264190673828125,
0.0043487548828125,
0.00769805908203125,
-0.03985595703125,
0.0062408447265625,
0.0013675689697265625,
-0.0087890625,
-0.0015306472778320312,
0.00997161865234375,
-0.003932952880859375,
0.0009660720825195312,
0.0248870849609375,
-0.0035152435302734375,
-0.0103302001953125,
-0.00293731689453125,
0.01123809814453125,
0.00803375244140625,
-0.01074981689453125,
-0.0163726806640625,
0.004482269287109375,
-0.0028514862060546875,
-0.005184173583984375,
0.0194549560546875,
-0.0004849433898925781,
-0.02838134765625,
0.0094146728515625,
-0.00977325439453125,
-0.00848388671875,
-0.0207366943359375,
0.002429962158203125,
0.0167694091796875,
0.00011748075485229492,
0.01593017578125,
0.0251617431640625,
0.003841400146484375,
-0.021636962890625,
-0.0214996337890625,
-0.02789306640625,
0.006984710693359375,
0.01277923583984375,
0.0005288124084472656,
0.0107574462890625,
0.0089569091796875,
0.01407623291015625,
0.01007080078125,
-0.0031719207763671875,
-0.00609588623046875,
-0.01457977294921875,
0.03411865234375,
0.01483917236328125,
-0.0191650390625,
0.015106201171875,
0.0108795166015625,
-0.00498199462890625,
-0.055572509765625,
0.00531768798828125,
-0.030914306640625,
-0.021026611328125,
0.0080413818359375,
-0.004245758056640625,
0.0122222900390625,
-0.0172882080078125,
0.00701141357421875,
-0.0199127197265625,
-0.0248565673828125,
0.0633544921875,
0.013336181640625,
-0.044525146484375,
0.01551055908203125,
0.0142669677734375,
-0.0215606689453125,
0.0099945068359375,
0.011199951171875,
0.00423431396484375,
-0.0086517333984375,
0.0038547515869140625,
0.0032176971435546875,
-0.01236724853515625,
-0.0009465217590332031,
0.004337310791015625,
0.005474090576171875,
-0.0063629150390625,
-0.0082244873046875,
0.0577392578125,
-0.01073455810546875,
-0.00027561187744140625,
0.002407073974609375,
0.02044677734375,
-0.0092010498046875,
0.01513671875,
0.00260162353515625,
-0.0262603759765625,
-0.007343292236328125,
-0.0020351409912109375,
-0.010467529296875,
-0.00927734375,
0.0208282470703125,
0.0135498046875,
0.01186370849609375,
0.0149993896484375,
0.0183258056640625,
-0.04205322265625,
-0.0218048095703125,
0.01824951171875,
0.002048492431640625,
-0.00728607177734375,
-0.0090789794921875,
-0.013763427734375,
0.0128173828125,
-0.00846099853515625,
0.0107269287109375,
0.01207733154296875,
0.005222320556640625,
-0.011016845703125,
-0.00720977783203125,
0.01309967041015625,
-0.00995635986328125,
-0.01611328125,
0.0253448486328125,
0.005615234375,
0.01421356201171875,
0.0028705596923828125,
0.01309967041015625,
0.0076141357421875,
0.01552581787109375,
-0.02008056640625,
-0.0243988037109375,
-0.01032257080078125,
0.01812744140625,
0.0025920867919921875,
0.002269744873046875,
-0.00621795654296875,
0.0020999908447265625,
-0.015411376953125,
0.0037288665771484375,
0.0100555419921875,
0.01274871826171875,
-0.0018339157104492188,
0.0141754150390625,
0.01058197021484375,
-0.01218414306640625,
-0.0086212158203125,
-0.023651123046875,
-0.01139068603515625,
-0.043731689453125,
-0.00371551513671875,
0.0208892822265625,
-0.00970458984375,
0.0009617805480957031,
0.0003859996795654297,
0.00725555419921875,
0.026519775390625,
-0.0111083984375,
-0.00701141357421875,
-0.01213836669921875,
0.01148223876953125,
-0.032958984375,
-0.0243377685546875,
-0.0037384033203125,
-0.033294677734375,
0.0260467529296875,
-0.00347137451171875,
0.0072784423828125,
0.00855255126953125,
-0.0013828277587890625,
0.0160980224609375,
-0.00951385498046875,
0.012725830078125,
0.018585205078125,
-0.004665374755859375,
-0.0229339599609375,
0.01763916015625,
-0.00853729248046875,
-0.007965087890625,
-0.01459503173828125,
-0.0083160400390625,
0.003910064697265625,
-0.004425048828125,
-0.020111083984375,
-0.036590576171875,
-0.0147705078125,
0.024017333984375,
0.0229644775390625,
-0.0008444786071777344,
-0.00421905517578125,
-0.03607177734375,
0.0195465087890625,
-0.01194000244140625,
-0.00461578369140625,
0.01180267333984375,
-0.0147552490234375,
0.01308441162109375,
-0.007228851318359375,
0.00811767578125,
0.004093170166015625,
-0.0191192626953125,
0.0176239013671875,
-0.0014467239379882812,
0.016448974609375,
-0.00836944580078125,
0.0208892822265625,
-0.0117340087890625,
-0.01096343994140625,
0.003292083740234375,
0.01198577880859375,
0.0224609375,
0.0287933349609375,
-0.0145263671875,
-0.01396942138671875,
0.0089111328125,
-0.0007419586181640625,
0.0211029052734375,
-0.0038909912109375,
-0.0168914794921875,
0.035797119140625,
-0.052520751953125,
0.0188446044921875,
-0.0078277587890625,
0.0182647705078125,
0.00897216796875,
0.011505126953125,
0.00844573974609375,
-0.0256195068359375,
0.0150909423828125,
0.0216217041015625,
0.00981903076171875,
-0.00044846534729003906,
0.007678985595703125,
-0.000006735324859619141,
-0.019134521484375,
0.0195159912109375,
-0.01247406005859375,
0.00928497314453125,
-0.010284423828125,
0.003875732421875,
-0.010040283203125,
0.018829345703125,
0.00875091552734375,
-0.00783538818359375,
-0.0270233154296875,
-0.006122589111328125,
-0.00043892860412597656,
0.0131378173828125,
0.01214599609375,
0.0239715576171875,
0.00313568115234375,
0.01129150390625,
0.0179595947265625,
-0.0511474609375,
0.0272674560546875,
-0.0225830078125,
-0.00164794921875,
-0.01216888427734375,
0.00888824462890625,
-0.0233612060546875,
0.0079345703125,
0.003383636474609375,
-0.0133056640625,
0.0118408203125,
0.003719329833984375,
-0.01375579833984375,
0.00725555419921875,
0.00974273681640625,
-0.00514984130859375,
-0.0253143310546875,
0.02056884765625,
0.052764892578125,
-0.00021278858184814453,
0.00783538818359375,
0.0081329345703125,
0.016876220703125,
-0.007427215576171875,
0.006092071533203125,
0.0123443603515625,
-0.0230865478515625,
0.00711822509765625,
0.00934600830078125,
0.006809234619140625,
-0.01393890380859375,
0.0110931396484375,
0.02545166015625,
-0.00848388671875,
0.004962921142578125,
-0.005413055419921875,
-0.00027060508728027344,
-0.0013217926025390625,
-0.0302734375,
0.01422882080078125,
-0.048248291015625,
0.006877899169921875,
-0.010955810546875,
0.0028533935546875,
-0.0032939910888671875,
0.0245513916015625,
-0.0421142578125,
0.005218505859375,
-0.00428009033203125,
-0.007659912109375,
0.00897216796875,
-0.004924774169921875,
0.007572174072265625,
0.0479736328125,
-0.005580902099609375,
0.032196044921875,
-0.00768280029296875,
0.00707244873046875,
-0.040924072265625,
-0.0115814208984375,
-0.048797607421875,
0.02191162109375,
-0.0255584716796875,
-0.035736083984375,
-0.00443267822265625,
0.0213165283203125,
0.00823974609375,
0.00531005859375,
-0.0036754608154296875,
-0.006622314453125,
0.01419830322265625,
-0.01268768310546875,
-0.044158935546875,
-0.0086212158203125,
-0.000629425048828125,
-0.0188140869140625,
0.006496429443359375,
-0.006015777587890625,
-0.015380859375,
-0.01019287109375,
-0.004978179931640625,
0.01346588134765625,
0.0019063949584960938,
0.00830841064453125,
0.01543426513671875,
-0.0009450912475585938,
-0.011566162109375,
-0.0048370361328125,
-0.011077880859375,
0.03289794921875,
-0.003047943115234375,
0.02093505859375,
-0.0504150390625,
-0.00750732421875,
0.031585693359375,
-0.00943756103515625,
0.012298583984375,
-0.00585174560546875,
-0.0148162841796875,
0.054107666015625,
-0.0150299072265625,
0.0092010498046875,
0.00702667236328125,
-0.01303863525390625,
0.051422119140625,
0.01317596435546875,
0.02734375,
0.0372314453125,
0.03662109375,
-0.0002777576446533203,
-0.0195770263671875,
0.01282501220703125,
0.0099945068359375,
0.0241241455078125,
-0.0122222900390625,
-0.0022068023681640625,
0.024688720703125,
-0.00618743896484375,
0.02447509765625,
0.01812744140625,
-0.0168914794921875,
0.050445556640625,
-0.036651611328125,
0.0264434814453125,
0.01462554931640625,
0.004726409912109375,
0.005062103271484375,
0.01910400390625,
0.000713348388671875,
0.0166778564453125,
-0.006298065185546875,
0.008636474609375,
0.0245361328125,
-0.0160980224609375,
0.029876708984375,
0.026885986328125,
-0.037200927734375,
0.001750946044921875,
0.00330352783203125,
-0.0130615234375,
0.0543212890625,
0.000005543231964111328,
-0.00946044921875,
-0.0345458984375,
0.029998779296875,
-0.01873779296875,
-0.01995849609375,
0.03265380859375,
0.032623291015625,
0.01290130615234375,
-0.0279998779296875,
-0.05224609375,
-0.0025959014892578125,
0.03460693359375,
-0.0196075439453125,
0.004642486572265625,
-0.01148223876953125,
0.0162506103515625,
0.02899169921875,
0.0119171142578125,
0.0170745849609375,
-0.0211029052734375,
-0.021728515625,
0.050537109375,
-0.0117645263671875,
-0.00975799560546875,
0.004161834716796875,
0.006755828857421875,
0.006908416748046875,
-0.0078125,
-0.03912353515625,
-0.018585205078125,
0.017181396484375,
0.0208892822265625,
-0.0218505859375,
0.03851318359375,
0.017913818359375,
0.0125274658203125,
0.036712646484375,
-0.0290679931640625,
-0.0058441162109375,
0.0048065185546875,
0.004657745361328125,
-0.003986358642578125,
0.04656982421875,
-0.038970947265625,
0.044891357421875,
0.02105712890625,
0.034454345703125,
-0.00745391845703125,
-0.028564453125,
0.022369384765625,
0.02001953125,
-0.0156097412109375,
0.0100555419921875,
-0.0006208419799804688,
-0.040374755859375,
-0.00010025501251220703,
-0.0190277099609375,
-0.0191497802734375,
-0.0245819091796875,
0.0307159423828125,
-0.0215301513671875,
-0.0173187255859375,
0.006191253662109375,
0.0012273788452148438,
-0.0114593505859375,
0.012115478515625,
0.01873779296875,
-0.02874755859375,
0.00984954833984375,
0.00945281982421875,
0.004344940185546875,
-0.005428314208984375,
0.0238800048828125,
0.002288818359375,
-0.0158233642578125,
-0.0023326873779296875,
0.0296783447265625,
-0.0027561187744140625,
-0.025360107421875,
-0.00548553466796875,
0.0242462158203125,
-0.006244659423828125,
-0.0201263427734375,
0.009368896484375,
-0.04083251953125,
0.016754150390625,
-0.021636962890625,
-0.00966644287109375,
0.0243988037109375,
-0.01617431640625,
-0.037506103515625,
0.0213775634765625,
0.036529541015625,
0.049346923828125,
0.0175323486328125,
0.0113372802734375,
-0.0037746429443359375,
0.0027599334716796875,
0.023223876953125,
-0.0266265869140625,
-0.011505126953125,
-0.0245819091796875,
0.004779815673828125,
-0.0078125,
-0.0039520263671875,
-0.0004546642303466797,
-0.00787353515625,
0.0024871826171875,
0.000225067138671875,
-0.016082763671875,
-0.005832672119140625,
0.01152801513671875,
-0.0163116455078125,
0.00557708740234375,
0.00630950927734375,
-0.0026340484619140625,
0.018798828125,
0.023162841796875,
-0.0023250579833984375,
-0.00699615478515625,
-0.00868988037109375,
0.04248046875,
0.005176544189453125,
-0.00677490234375,
0.0117950439453125,
-0.03363037109375,
-0.0190887451171875,
-0.01514434814453125,
-0.005077362060546875,
-0.007686614990234375,
0.0006246566772460938,
-0.009857177734375,
-0.034820556640625,
0.018402099609375,
0.0039825439453125,
-0.03289794921875,
0.005611419677734375,
0.001903533935546875,
-0.03375244140625,
-0.0037212371826171875,
0.0271453857421875,
0.00909423828125,
-0.0225830078125,
-0.004802703857421875,
0.03680419921875,
-0.02276611328125,
0.015838623046875,
-0.02142333984375,
0.0274200439453125,
-0.026702880859375,
-0.0194854736328125,
-0.02813720703125,
0.0290679931640625,
-0.00732421875,
-0.021240234375,
0.0023632049560546875,
0.0017671585083007812,
-0.0291748046875,
0.0190887451171875,
0.01097869873046875,
-0.016326904296875,
0.00384521484375,
0.0149688720703125,
-0.0081939697265625,
-0.00905609130859375,
0.007007598876953125,
-0.02862548828125,
0.0328369140625,
0.00537872314453125,
0.016632080078125,
0.0128326416015625,
0.0254058837890625,
-0.00949859619140625,
-0.03533935546875,
0.016082763671875,
0.0015268325805664062,
0.01030731201171875,
0.0341796875,
-0.038116455078125,
-0.003116607666015625,
-0.0026264190673828125,
-0.0302734375,
-0.030364990234375,
0.025909423828125,
-0.014495849609375,
-0.01352691650390625,
0.01485443115234375,
0.00020647048950195312,
-0.0086212158203125,
-0.007183074951171875,
0.0131378173828125,
-0.006221771240234375,
-0.0048828125,
-0.006534576416015625,
-0.0484619140625,
-0.048309326171875,
0.00426483154296875,
-0.003971099853515625,
0.01336669921875,
-0.0091705322265625,
0.00844573974609375,
-0.01296234130859375,
-0.006427764892578125,
0.0155029296875,
-0.004367828369140625,
-0.006145477294921875,
0.01059722900390625,
-0.029022216796875,
-0.00870513916015625,
0.0154571533203125,
-0.01611328125,
0.0157470703125,
0.0235443115234375,
-0.01076507568359375,
0.044677734375,
-0.0241546630859375,
-0.019195556640625,
-0.0236053466796875,
0.03240966796875,
-0.0260772705078125,
-0.031890869140625,
0.0131988525390625,
0.0063018798828125,
0.0013561248779296875,
-0.00008094310760498047,
-0.01806640625,
0.01540374755859375,
0.00598907470703125,
-0.0207672119140625,
0.03076171875,
0.0007691383361816406,
-0.032958984375,
0.055999755859375,
-0.0151824951171875,
0.0295867919921875,
-0.0274200439453125,
-0.040679931640625,
-0.01490020751953125,
-0.0242156982421875,
0.003307342529296875,
0.0017423629760742188,
0.021514892578125,
-0.0138702392578125,
-0.00942230224609375,
-0.0245513916015625,
-0.0193939208984375,
0.016998291015625,
0.0194854736328125,
-0.003108978271484375,
-0.0110626220703125,
-0.011505126953125,
0.0263824462890625,
-0.040496826171875,
-0.002452850341796875,
0.034149169921875,
-0.0159912109375,
-0.006427764892578125,
-0.0296783447265625,
-0.020843505859375,
0.0005459785461425781,
0.0157318115234375,
-0.01357269287109375,
-0.020965576171875,
-0.01175689697265625,
-0.041259765625,
-0.0293426513671875,
0.01568603515625,
-0.00530242919921875,
-0.03656005859375,
-0.0173492431640625,
0.0233612060546875,
-0.0181884765625,
-0.0178070068359375,
-0.038482666015625,
-0.00560760498046875,
-0.007965087890625,
0.0033054351806640625,
0.026702880859375,
-0.0203094482421875,
-0.0119781494140625,
0.00826263427734375,
0.01509857177734375,
0.00003600120544433594,
-0.0124664306640625,
-0.00923919677734375,
-0.0115814208984375,
0.04571533203125,
-0.00893402099609375,
0.0046234130859375,
0.011627197265625,
-0.0260162353515625,
0.03668212890625,
-0.0330810546875,
0.0013208389282226562,
0.002197265625,
0.0262451171875,
0.0023097991943359375,
0.0102081298828125,
0.0011739730834960938,
0.022064208984375,
-0.058563232421875,
-0.01439666748046875,
0.05303955078125,
0.0051116943359375,
0.00716400146484375,
0.004947662353515625,
-0.035888671875,
-0.018768310546875,
0.012115478515625,
-0.0196075439453125,
0.0057525634765625,
-0.0209197998046875,
-0.0390625,
-0.04437255859375,
-0.01202392578125,
0.01372528076171875,
0.0310821533203125,
-0.03662109375,
-0.0190887451171875,
-0.0180511474609375,
0.021392822265625,
0.0011949539184570312,
-0.001422882080078125,
-0.0295562744140625,
0.0015821456909179688,
0.004058837890625,
0.0186767578125,
-0.038726806640625,
0.0257415771484375,
0.030303955078125,
0.00392913818359375,
-0.01146697998046875,
-0.0115509033203125,
0.0193023681640625,
-0.01322174072265625,
0.0264129638671875,
0.03497314453125,
0.0017642974853515625,
-0.01065826416015625,
0.022491455078125,
0.0032558441162109375,
-0.0052947998046875,
-0.0207672119140625,
-0.01007843017578125,
-0.0187530517578125,
0.002727508544921875,
0.0154876708984375,
0.02081298828125,
0.0011892318725585938,
0.039398193359375,
0.0164337158203125,
0.01174163818359375,
0.0124969482421875,
0.0236053466796875,
0.01441192626953125,
-0.00341796875,
0.01947021484375,
0.037200927734375,
-0.018890380859375,
-0.044921875,
-0.01220703125,
0.0004451274871826172,
-0.0006194114685058594,
0.0283966064453125,
-0.0235443115234375,
-0.01094818115234375,
0.0204315185546875,
-0.012969970703125,
-0.0057373046875,
-0.0008845329284667969,
0.0033702850341796875,
0.0290679931640625,
-0.00799560546875,
-0.00501251220703125,
-0.0024929046630859375,
-0.00006574392318725586,
0.02490234375,
-0.0004856586456298828,
0.03594970703125,
0.01458740234375,
0.00537872314453125,
0.007701873779296875,
-0.0216827392578125,
-0.0103607177734375,
0.006481170654296875,
0.002643585205078125,
0.05181884765625,
-0.0092315673828125,
0.01247406005859375,
-0.03546142578125,
0.0335693359375,
-0.00047659873962402344,
-0.02398681640625,
-0.017364501953125,
-0.0158233642578125,
-0.006526947021484375,
-0.0037174224853515625,
-0.04119873046875,
0.0367431640625,
-0.00530242919921875,
0.0192108154296875,
0.02313232421875,
0.0271148681640625,
0.0206756591796875,
0.035400390625,
-0.0275421142578125,
0.001308441162109375,
0.0011358261108398438,
0.0428466796875,
0.030242919921875,
-0.017822265625,
-0.021453857421875,
0.01406097412109375,
-0.0007433891296386719,
0.0083160400390625,
-0.0311431884765625,
-0.050872802734375,
0.0250091552734375,
0.007213592529296875,
-0.031463623046875,
0.0144195556640625,
-0.00432586669921875,
0.028900146484375,
-0.0164794921875,
-0.0104827880859375,
0.00363922119140625,
-0.0340576171875,
-0.04345703125,
-0.01593017578125,
-0.0108184814453125,
-0.042572021484375,
0.005214691162109375,
0.01045989990234375,
0.045440673828125,
-0.0038547515869140625,
0.0184783935546875,
-0.00565338134765625,
0.01043701171875,
0.0105438232421875,
0.00038361549377441406,
-0.0222015380859375,
-0.0300750732421875,
0.007419586181640625,
-0.0010881423950195312,
0.0015573501586914062,
-0.01953125,
0.022796630859375,
0.0181884765625,
-0.0023899078369140625,
0.0193634033203125,
0.01184844970703125,
-0.03790283203125,
0.032928466796875,
-0.036041259765625,
0.0316162109375,
-0.032867431640625,
-0.039459228515625,
-0.005786895751953125,
-0.004344940185546875,
-0.02899169921875,
0.0262298583984375,
0.0128173828125,
0.0018644332885742188,
0.0011377334594726562,
0.01268768310546875,
0.0117034912109375,
-0.016265869140625,
-0.00266265869140625,
0.0106048583984375,
0.0298614501953125,
-0.0159759521484375,
0.0207672119140625,
-0.002185821533203125,
-0.01070404052734375,
-0.0210113525390625,
0.01483154296875,
-0.004589080810546875,
-0.022552490234375,
-0.01470947265625,
0.01271820068359375,
-0.014495849609375,
0.0190887451171875,
-0.04541015625,
-0.01230621337890625,
-0.01373291015625,
0.00980377197265625,
0.0069732666015625,
-0.0160064697265625,
-0.0055999755859375,
-0.02227783203125,
-0.032989501953125,
0.0229034423828125,
-0.045745849609375,
0.01453399658203125,
-0.0215911865234375,
0.01267242431640625,
0.004100799560546875,
0.0036640167236328125,
0.00809478759765625,
0.01358795166015625,
-0.0006117820739746094,
0.0002353191375732422,
-0.0286102294921875,
-0.02294921875,
-0.0169525146484375,
0.040924072265625,
-0.00856781005859375,
-0.0261383056640625,
0.0193939208984375,
0.0159149169921875,
-0.027862548828125,
-0.00472259521484375,
0.004398345947265625,
-0.01369476318359375,
0.01056671142578125,
-0.030059814453125,
-0.01259613037109375,
-0.0248565673828125,
0.04144287109375,
-0.00911712646484375,
-0.0192718505859375,
0.0224761962890625,
0.01309967041015625,
0.0244140625,
-0.023834228515625,
-0.00414276123046875,
-0.04364013671875,
-0.00323486328125,
0.023834228515625,
0.004878997802734375,
-0.00907135009765625,
0.0169830322265625,
0.00832366943359375,
-0.013427734375,
0.0211334228515625,
-0.0511474609375,
-0.0032825469970703125,
-0.003265380859375,
-0.0176544189453125,
-0.0009183883666992188,
-0.005329132080078125,
0.021026611328125,
-0.0029773712158203125,
-0.02337646484375,
-0.016998291015625,
0.034820556640625,
0.0273284912109375,
-0.014739990234375,
-0.044586181640625,
-0.00421905517578125,
-0.0258331298828125,
-0.019775390625,
-0.0421142578125,
-0.01119232177734375,
0.007091522216796875,
0.0013751983642578125,
-0.0157318115234375,
0.00772857666015625,
0.036956787109375,
-0.00016164779663085938,
0.014556884765625,
-0.03375244140625,
0.00649261474609375,
-0.001277923583984375,
-0.01189422607421875,
0.002933502197265625,
0.0012807846069335938,
-0.0025310516357421875,
0.0000883936882019043,
-0.0256500244140625,
-0.0034236907958984375,
-0.001678466796875,
0.0305023193359375,
0.002452850341796875,
0.0248260498046875,
-0.031768798828125,
-0.007122039794921875,
0.04534912109375,
0.004039764404296875,
0.01038360595703125,
0.0024967193603515625,
0.0299835205078125,
-0.03448486328125,
-0.0028553009033203125,
0.0024566650390625,
-0.019805908203125,
-0.0034313201904296875,
-0.01971435546875,
0.0477294921875,
0.0333251953125,
0.02569580078125,
-0.0256500244140625,
-0.005859375,
-0.00794219970703125,
-0.004940032958984375,
0.0006909370422363281,
-0.0321044921875,
0.013153076171875,
0.0113067626953125,
0.018768310546875,
-0.0235748291015625,
0.03143310546875,
-0.01224517822265625,
-0.0185546875,
-0.0033721923828125,
0.003139495849609375,
-0.002246856689453125,
0.02020263671875,
-0.005046844482421875,
0.016448974609375,
0.00107574462890625,
0.0236663818359375,
-0.05487060546875,
-0.01010894775390625,
-0.0006723403930664062,
0.0164337158203125,
-0.0018529891967773438,
-0.0196380615234375,
-0.0166015625,
0.005603790283203125,
-0.0001150369644165039,
0.023101806640625,
-0.004924774169921875,
0.0081634521484375,
-0.00004750490188598633,
0.004085540771484375,
0.032928466796875,
-0.01248931884765625,
-0.0038585662841796875,
-0.01029205322265625,
0.0094146728515625,
0.0352783203125,
0.0172576904296875,
-0.0112152099609375,
0.018646240234375,
0.01273345947265625,
-0.0028972625732421875,
0.03515625,
-0.00592803955078125,
-0.0150604248046875,
-0.0213623046875,
0.00991058349609375,
0.046600341796875,
0.002277374267578125,
-0.0205841064453125,
-0.01459503173828125,
-0.01479339599609375,
-0.06121826171875,
-0.01690673828125,
0.0043182373046875,
-0.007022857666015625,
0.054168701171875,
0.007343292236328125,
0.02349853515625,
0.01239013671875,
-0.004550933837890625,
-0.025238037109375,
-0.004436492919921875,
0.0215606689453125,
0.03350830078125,
-0.0408935546875,
0.04510498046875,
0.0209197998046875,
0.007568359375,
-0.032073974609375,
0.0034923553466796875,
0.025970458984375,
0.0152130126953125,
0.030303955078125,
-0.009002685546875,
0.0197296142578125,
-0.0077667236328125,
-0.0281829833984375,
-0.0219268798828125,
0.00823211669921875,
-0.028778076171875,
0.00560760498046875,
-0.016326904296875,
0.0665283203125,
-0.01068878173828125,
-0.0293121337890625,
0.04473876953125,
-0.03680419921875,
-0.00379180908203125,
-0.023284912109375,
-0.019378662109375,
-0.007068634033203125,
-0.0095977783203125,
0.005062103271484375,
-0.007762908935546875,
-0.00030732154846191406,
-0.0196533203125,
0.0168914794921875,
-0.00152587890625,
-0.0084991455078125,
-0.008056640625,
0.0007500648498535156,
-0.0009012222290039062,
-0.023895263671875,
-0.01082611083984375,
-0.0280609130859375,
-0.003025054931640625,
0.00786590576171875,
0.0218048095703125,
0.0153350830078125,
-0.01515960693359375,
0.020660400390625,
-0.01641845703125,
-0.0430908203125,
-0.009063720703125,
-0.0169677734375,
0.0301971435546875,
0.0193939208984375,
0.0093231201171875,
0.0182647705078125,
-0.0028896331787109375,
0.0185546875,
-0.01462554931640625,
-0.02996826171875,
-0.01201629638671875,
0.002239227294921875,
0.02032470703125,
-0.012847900390625,
-0.00189971923828125,
-0.024261474609375,
-0.0008444786071777344,
0.0207672119140625,
0.005584716796875,
0.0136566162109375,
-0.001361846923828125,
0.006072998046875,
0.007259368896484375,
0.0013427734375,
-0.0210418701171875,
-0.0024623870849609375,
0.00042057037353515625,
-0.0155487060546875,
0.0175933837890625,
-0.00885009765625,
-0.00890350341796875,
0.0282745361328125,
0.0011167526245117188,
0.0243682861328125,
-0.03045654296875,
0.013031005859375,
-0.000019788742065429688,
-0.0036144256591796875,
-0.0202789306640625,
-0.00850677490234375,
-0.045867919921875,
0.051666259765625,
0.0012226104736328125,
0.027984619140625,
-0.0172271728515625,
-0.03192138671875,
-0.00896453857421875,
-0.013824462890625,
0.0556640625,
0.0273590087890625,
-0.01763916015625,
0.0413818359375,
0.001560211181640625,
0.00490570068359375,
-0.005123138427734375,
-0.0139617919921875,
-0.002773284912109375,
-0.01043701171875,
0.0236663818359375,
0.0027675628662109375,
-0.01561737060546875,
-0.0232086181640625,
0.0142669677734375,
0.007678985595703125,
-0.0261383056640625,
0.016876220703125,
-0.003879547119140625,
-0.0103302001953125,
0.0229644775390625,
-0.0245513916015625,
0.0181884765625,
0.003936767578125,
0.00283050537109375,
0.00007218122482299805,
0.03204345703125,
-0.00322723388671875,
-0.0205535888671875,
-0.01145172119140625,
0.0238800048828125,
0.0005517005920410156,
-0.0098419189453125,
-0.01483917236328125,
0.01387786865234375,
-0.005413055419921875,
-0.0362548828125,
-0.02154541015625,
-0.0081634521484375,
-0.00914764404296875,
-0.006587982177734375,
-0.0017490386962890625,
0.007904052734375,
0.0241546630859375,
0.01727294921875,
-0.0040740966796875,
0.023956298828125,
0.0132904052734375,
0.006671905517578125,
0.0186004638671875,
-0.0252532958984375,
-0.0180816650390625,
0.01543426513671875,
0.0102996826171875,
0.000499725341796875,
-0.00052642822265625,
-0.0144500732421875,
-0.0172882080078125,
-0.00795745849609375,
-0.039154052734375,
-0.00048065185546875,
-0.0008759498596191406,
0.006069183349609375,
-0.01175689697265625,
0.00218963623046875,
-0.007480621337890625,
-0.0179595947265625,
0.006626129150390625,
-0.0102996826171875,
0.01190948486328125,
-0.010406494140625,
0.0265655517578125,
0.01103973388671875,
-0.02227783203125,
0.0211029052734375,
-0.002635955810546875,
-0.0231475830078125,
-0.0301513671875,
-0.0386962890625,
0.03271484375,
0.026275634765625,
-0.008575439453125,
-0.00724029541015625,
0.00043082237243652344,
0.031280517578125,
0.022216796875,
-0.007720947265625,
0.033660888671875,
0.012939453125,
0.0168609619140625,
-0.005466461181640625,
0.00148773193359375,
-0.0135345458984375,
-0.0114898681640625,
0.040740966796875,
-0.00646209716796875,
0.0175018310546875,
0.0221099853515625,
0.0138397216796875,
-0.01910400390625,
-0.003108978271484375,
0.004505157470703125,
-0.0273895263671875,
-0.0003604888916015625,
0.010589599609375,
0.002460479736328125,
0.01285552978515625,
-0.01554107666015625,
0.0233612060546875,
0.00027108192443847656,
-0.005962371826171875,
-0.0089263916015625,
-0.0228118896484375,
-0.0254058837890625,
0.0204315185546875,
-0.007232666015625,
0.0022525787353515625,
0.007610321044921875,
-0.005115509033203125,
-0.045928955078125,
0.01470184326171875,
0.01453399658203125,
-0.0126800537109375,
-0.0254058837890625,
-0.008941650390625,
-0.0194091796875,
0.017242431640625,
-0.0323486328125,
-0.0158233642578125,
0.0166473388671875,
0.01522064208984375,
0.03179931640625,
0.003719329833984375,
-0.00445556640625,
0.008819580078125,
0.036834716796875,
-0.01276397705078125,
-0.005710601806640625,
-0.0038127899169921875,
-0.0070648193359375,
-0.018096923828125,
-0.011810302734375,
-0.00643157958984375,
-0.0035915374755859375,
-0.0307769775390625,
-0.018798828125,
0.0198974609375,
-0.0240020751953125,
-0.022796630859375,
-0.004150390625,
-0.0218658447265625,
0.00511932373046875,
-0.0173492431640625,
-0.04034423828125,
-0.0078277587890625,
-0.00684356689453125,
0.0038547515869140625,
-0.017791748046875,
0.034698486328125,
-0.0177764892578125,
0.033416748046875,
-0.01467132568359375,
-0.0208892822265625,
0.01427459716796875,
-0.01515960693359375,
-0.007778167724609375,
-0.007686614990234375,
-0.01003265380859375,
0.0032825469970703125,
0.01058197021484375,
-0.0159454345703125,
-0.01031494140625,
-0.0023193359375,
0.037445068359375,
0.001953125,
-0.054107666015625,
0.040130615234375,
-0.004512786865234375,
-0.020233154296875,
-0.0016374588012695312,
-0.00444793701171875,
0.0066680908203125,
-0.01248931884765625,
-0.0219879150390625,
-0.015716552734375,
0.0220947265625,
-0.0291900634765625,
-0.01727294921875,
-0.0237884521484375,
0.003170013427734375,
0.0056915283203125,
0.008453369140625,
0.033905029296875,
-0.016204833984375,
0.0022220611572265625,
0.0072021484375,
0.0112457275390625,
-0.0283966064453125,
0.00395965576171875,
-0.01070404052734375,
-0.023712158203125,
-0.01232147216796875,
0.0157928466796875,
0.019012451171875,
0.0036258697509765625,
0.003910064697265625,
0.0157318115234375,
-0.022216796875,
-0.0280914306640625,
0.002933502197265625,
-0.0133819580078125,
-0.0196685791015625,
0.0023956298828125,
0.00679779052734375,
-0.0133209228515625,
0.0016317367553710938,
0.01548004150390625,
0.0003027915954589844,
-0.018585205078125,
-0.016204833984375,
0.01214599609375,
0.010467529296875,
-0.03759765625,
-0.008514404296875,
-0.005184173583984375,
-0.029022216796875,
0.023468017578125,
0.0204925537109375,
-0.0016584396362304688,
-0.0135040283203125,
-0.00960540771484375,
0.00867462158203125,
0.0022945404052734375,
-0.019439697265625,
0.0008883476257324219,
-0.0247039794921875,
0.01593017578125,
0.00003522634506225586,
-0.01177215576171875,
-0.002872467041015625,
0.0003268718719482422,
-0.0202178955078125,
0.0019197463989257812,
0.0025920867919921875,
0.0196075439453125,
-0.005336761474609375,
-0.0031833648681640625,
-0.0264129638671875,
-0.0006389617919921875,
-0.043792724609375,
-0.01029205322265625,
0.036407470703125,
-0.0069427490234375,
-0.021087646484375,
0.00861358642578125,
-0.016357421875,
-0.037353515625,
-0.0236053466796875,
-0.0023021697998046875,
-0.0018033981323242188,
-0.0024318695068359375,
0.0056610107421875,
-0.0276336669921875,
-0.0238494873046875,
-0.002590179443359375,
-0.02166748046875,
0.007160186767578125,
0.0020751953125,
0.0006508827209472656,
-0.0025386810302734375,
0.01418304443359375,
0.021392822265625,
0.01320648193359375,
-0.0288543701171875,
0.02197265625,
0.04925537109375,
-0.00799560546875,
-0.032470703125,
-0.0255584716796875,
-0.02349853515625,
0.017425537109375,
-0.0187835693359375,
-0.012176513671875,
-0.01438140869140625,
-0.02215576171875,
0.0162200927734375,
-0.00704193115234375,
-0.0128326416015625,
0.01995849609375,
-0.0186920166015625,
-0.01139068603515625,
-0.01139068603515625,
0.0040130615234375,
0.0194549560546875,
0.01300048828125,
-0.0095062255859375,
0.005512237548828125,
-0.01486968994140625,
-0.0218048095703125,
0.0188751220703125,
0.0092010498046875,
-0.0404052734375,
-0.017486572265625,
-0.0203857421875,
0.001026153564453125,
0.005214691162109375,
0.00487518310546875,
0.0141143798828125,
-0.01519775390625,
0.00835418701171875,
-0.0026454925537109375,
0.01067352294921875,
0.01873779296875,
0.0190277099609375,
-0.01934814453125,
-0.006900787353515625,
-0.01177978515625,
-0.025177001953125,
0.0281524658203125,
0.007755279541015625,
0.011932373046875,
0.0219573974609375,
-0.0009164810180664062,
0.033050537109375,
-0.005405426025390625,
-0.01399993896484375,
-0.006755828857421875,
-0.02203369140625,
-0.01461029052734375,
-0.01157379150390625,
-0.027557373046875,
-0.0115203857421875,
0.0016498565673828125,
0.0355224609375,
0.0147247314453125,
-0.00606536865234375,
0.01473236083984375,
-0.00286865234375,
0.0223236083984375,
-0.010345458984375,
0.03082275390625,
0.0288543701171875,
0.0225982666015625,
0.021697998046875,
0.0205230712890625,
0.006542205810546875,
-0.012359619140625,
-0.032501220703125,
-0.0011043548583984375,
-0.01407623291015625,
0.039642333984375,
0.0037136077880859375,
0.024139404296875,
-0.01160430908203125,
-0.00803375244140625,
0.0253753662109375,
0.02386474609375,
-0.0195465087890625,
0.0189208984375,
0.00722503662109375,
-0.0126953125,
-0.006366729736328125,
-0.002513885498046875,
0.0128631591796875,
-0.005817413330078125,
0.0229949951171875,
-0.019439697265625,
-0.02630615234375,
-0.0267486572265625,
0.03228759765625,
0.0159149169921875,
0.01210784912109375,
0.01194000244140625,
-0.036590576171875,
-0.02203369140625,
0.005741119384765625,
0.016326904296875,
0.034271240234375,
-0.0027599334716796875,
-0.004787445068359375,
-0.0200042724609375,
0.006343841552734375,
-0.0008144378662109375,
-0.0020732879638671875,
-0.0147705078125,
0.009613037109375,
0.003948211669921875,
0.006595611572265625,
0.021087646484375,
-0.01529693603515625,
0.03985595703125,
-0.0178070068359375,
0.0164031982421875,
0.024078369140625,
-0.037628173828125,
0.0289306640625,
-0.0078887939453125,
0.0298919677734375,
0.0168609619140625,
0.021881103515625,
0.00537872314453125,
-0.001068115234375,
-0.0057830810546875,
0.018096923828125,
-0.004302978515625,
0.0265350341796875,
0.007007598876953125,
-0.02166748046875,
0.007480621337890625,
-0.0302734375,
0.0255126953125,
-0.0162811279296875,
0.0104827880859375,
0.0230560302734375,
-0.0157318115234375,
-0.0496826171875,
-0.0389404296875,
0.0211181640625,
-0.01654052734375,
-0.007091522216796875,
0.059173583984375,
0.037109375,
-0.005947113037109375,
-0.020599365234375,
0.0281829833984375,
0.0110626220703125,
-0.0223236083984375,
-0.01477813720703125,
-0.029266357421875,
-0.0154266357421875,
-0.01983642578125,
-0.01239776611328125,
0.01206207275390625,
0.0352783203125,
0.00940704345703125,
0.0028076171875,
-0.01526641845703125,
-0.007633209228515625,
0.0173187255859375,
-0.0003581047058105469,
0.004764556884765625,
-0.0093231201171875,
0.0091094970703125,
-0.049835205078125,
-0.014434814453125,
-0.01039886474609375,
0.00748443603515625,
-0.01479339599609375,
-0.007427215576171875,
0.01690673828125,
-0.011688232421875,
-0.00872039794921875,
-0.006580352783203125,
-0.0000788569450378418,
-0.040374755859375,
-0.0103302001953125,
-0.01837158203125,
-0.012359619140625,
-0.0438232421875,
0.033172607421875,
-0.009490966796875,
0.0159454345703125,
-0.01001739501953125,
0.01282501220703125,
-0.0309295654296875,
-0.007328033447265625,
0.00004035234451293945,
-0.0009851455688476562,
0.030792236328125,
0.026123046875,
-0.0031604766845703125,
-0.0201263427734375,
0.011932373046875,
-0.00426483154296875,
0.01305389404296875,
-0.002044677734375,
0.01397705078125,
0.0220489501953125,
-0.010772705078125,
-0.023406982421875,
0.00971221923828125,
-0.046112060546875,
-0.0131072998046875,
0.032257080078125,
-0.02532958984375,
-0.0125274658203125,
0.017974853515625,
0.0083465576171875,
-0.004894256591796875,
0.019287109375,
0.01849365234375,
-0.03314208984375,
-0.00982666015625,
0.025634765625,
0.01203155517578125,
-0.00957489013671875,
-0.01181793212890625,
0.019500732421875,
0.0275115966796875,
0.00432586669921875,
0.0118255615234375,
-0.0111083984375,
0.01331329345703125,
-0.01348876953125,
0.0118865966796875,
0.0160675048828125,
-0.0124053955078125,
0.017822265625,
-0.001247406005859375,
0.035003662109375,
-0.0298004150390625,
-0.008819580078125,
0.0111083984375,
0.0264129638671875,
0.0223541259765625,
0.00804901123046875,
-0.0173492431640625,
-0.004344940185546875,
0.005550384521484375,
-0.0340576171875,
0.0278167724609375,
-0.0159759521484375,
0.0062255859375,
0.006984710693359375,
0.003787994384765625,
0.00859832763671875,
0.0176849365234375,
-0.00025272369384765625,
0.00920867919921875,
-0.003955841064453125,
-0.006023406982421875,
-0.019134521484375,
0.001682281494140625,
0.0221710205078125,
-0.005157470703125,
0.00571441650390625,
0.0196685791015625,
0.0028934478759765625,
0.0202484130859375,
-0.00839996337890625,
0.0258026123046875,
0.01267242431640625,
0.0325927734375,
-0.005649566650390625,
0.01064300537109375,
-0.00402069091796875,
0.0090789794921875,
-0.012664794921875,
-0.00717926025390625,
0.018310546875,
0.01806640625,
-0.01378631591796875,
0.03680419921875,
-0.03997802734375,
-0.00408172607421875,
0.0178985595703125,
0.0194549560546875,
0.00870513916015625,
-0.0034008026123046875,
-0.01267242431640625,
0.0018930435180664062,
0.0011053085327148438,
0.0012378692626953125,
-0.001934051513671875,
-0.002155303955078125,
-0.0164794921875,
-0.0089569091796875,
0.006938934326171875,
0.01506805419921875,
0.0002295970916748047,
-0.0012388229370117188,
-0.01148223876953125,
0.047332763671875,
0.0006756782531738281,
-0.0014066696166992188,
0.027496337890625,
-0.03826904296875,
0.02630615234375,
-0.033935546875,
0.00481414794921875,
0.022613525390625,
0.016815185546875,
0.00423431396484375,
-0.001735687255859375,
0.0176544189453125,
0.0004220008850097656,
-0.0160064697265625,
-0.015228271484375,
0.0246429443359375,
0.030975341796875,
-0.00727081298828125,
0.0055084228515625,
-0.00937652587890625,
0.0129241943359375,
0.0202178955078125,
-0.0294036865234375,
-0.063720703125,
0.00893402099609375,
0.023712158203125,
0.005405426025390625,
-0.008026123046875,
-0.04779052734375,
0.0287933349609375,
0.0170745849609375,
0.0113525390625,
-0.01166534423828125,
-0.021148681640625,
0.007343292236328125,
-0.0196380615234375,
0.010955810546875,
-0.0299835205078125,
0.01715087890625,
-0.009063720703125,
0.00988006591796875,
0.028656005859375,
-0.01361083984375,
-0.006504058837890625,
0.03070068359375,
-0.0098724365234375,
0.004222869873046875,
-0.004375457763671875,
-0.01363372802734375,
-0.0250701904296875,
-0.0175018310546875,
-0.00022304058074951172,
-0.002796173095703125,
0.0018777847290039062,
0.0009579658508300781,
0.003513336181640625,
0.009521484375,
0.032196044921875,
0.0045928955078125,
-0.0239715576171875,
-0.007572174072265625,
-0.0209197998046875,
-0.024383544921875,
-0.0005741119384765625,
0.03619384765625,
0.0116729736328125,
-0.01165008544921875,
-0.01739501953125,
0.01506805419921875,
0.01107025146484375,
-0.0037326812744140625,
-0.0006365776062011719,
0.0246124267578125,
-0.004669189453125,
-0.00095367431640625,
-0.00008827447891235352,
-0.001888275146484375,
-0.0079498291015625,
0.020233154296875,
0.0203094482421875,
0.01187896728515625,
0.010833740234375,
0.01100921630859375,
-0.009033203125,
0.013153076171875,
0.02081298828125,
-0.04412841796875,
0.005245208740234375,
-0.007396697998046875,
0.00537109375,
0.0176544189453125,
0.01432037353515625,
0.0189666748046875,
0.018096923828125,
-0.00397491455078125,
-0.004184722900390625,
-0.0209503173828125,
-0.004291534423828125,
-0.031341552734375,
0.00494384765625,
-0.01064300537109375,
-0.0029468536376953125,
0.0033245086669921875,
0.0247955322265625,
-0.018310546875,
0.01544189453125,
0.0095977783203125,
0.00431060791015625,
0.00960540771484375,
0.0121002197265625,
-0.006404876708984375,
0.01496124267578125,
-0.0289764404296875,
-0.038726806640625,
-0.01134490966796875,
0.021942138671875,
-0.0155792236328125,
0.006893157958984375,
-0.00832366943359375,
0.0182037353515625,
-0.004985809326171875,
-0.0182952880859375,
-0.002025604248046875,
0.011932373046875,
0.0160675048828125,
0.011688232421875,
0.00824737548828125,
-0.01012420654296875,
-0.01311492919921875,
-0.0191497802734375,
0.027557373046875,
0.0022182464599609375,
0.0017881393432617188,
-0.0019893646240234375,
0.0033054351806640625,
0.0093536376953125,
-0.0095367431640625,
0.0135650634765625,
-0.00809478759765625,
0.0017490386962890625,
-0.005855560302734375,
0.002605438232421875,
-0.009521484375,
0.0257415771484375,
-0.011383056640625,
0.00656890869140625,
0.00479888916015625,
-0.01654052734375,
0.01019287109375,
-0.0091094970703125,
-0.0045318603515625,
-0.031341552734375,
-0.026824951171875,
-0.0013628005981445312,
0.0220947265625,
0.036529541015625,
0.01006317138671875,
-0.017822265625,
0.046051025390625,
0.005741119384765625,
0.011444091796875,
0.00679779052734375,
-0.03399658203125,
-0.04095458984375,
0.0093994140625,
-0.00579833984375,
0.01152801513671875,
-0.04718017578125,
-0.033782958984375,
-0.0009241104125976562,
0.0009741783142089844,
-0.00421142578125,
0.01557159423828125,
-0.0003666877746582031,
0.0276947021484375,
-0.022247314453125,
-0.014373779296875,
-0.006298065185546875,
0.044189453125,
0.0036602020263671875,
-0.001781463623046875,
-0.0029315948486328125,
-0.03131103515625,
0.016448974609375,
0.02850341796875,
-0.01812744140625,
0.002407073974609375,
-0.003604888916015625,
0.0057373046875,
-0.005859375,
0.0207672119140625,
-0.00699615478515625,
0.0084991455078125,
-0.01300811767578125,
-0.005962371826171875,
-0.0077362060546875,
0.03277587890625,
-0.0015478134155273438,
-0.03582763671875,
-0.0181427001953125,
0.00284576416015625,
0.01812744140625,
0.047760009765625,
0.0193634033203125,
-0.01042938232421875,
0.0164031982421875,
0.01222991943359375,
-0.0177001953125,
0.002056121826171875,
0.00783538818359375,
-0.005908966064453125,
-0.005645751953125,
-0.0103912353515625,
-0.05975341796875,
-0.035980224609375,
-0.004608154296875,
-0.0238494873046875,
0.0040435791015625,
-0.021636962890625,
-0.002422332763671875,
0.00498199462890625,
-0.00980377197265625,
0.016448974609375,
-0.0226287841796875,
-0.02862548828125,
-0.0152740478515625,
0.006694793701171875,
-0.006198883056640625,
-0.0180511474609375,
-0.01316070556640625,
0.0241851806640625,
0.0174560546875,
0.01334381103515625,
0.0226593017578125,
0.0146026611328125,
-0.0009899139404296875,
-0.024078369140625,
0.007221221923828125,
0.0296478271484375,
0.005306243896484375,
-0.003414154052734375,
-0.0130462646484375,
-0.02349853515625,
0.0423583984375,
0.021392822265625,
-0.0010776519775390625,
-0.0028228759765625,
-0.0163726806640625,
-0.0170440673828125,
0.0191192626953125,
0.0291900634765625,
-0.003353118896484375,
0.022796630859375,
0.0002701282501220703,
0.016265869140625,
0.00759124755859375,
0.03118896484375,
0.0018815994262695312,
-0.00982666015625,
-0.004085540771484375,
0.004184722900390625,
0.0251617431640625,
0.0034313201904296875,
-0.0106201171875,
0.012115478515625,
0.0225677490234375,
-0.0229644775390625,
0.028564453125,
0.0085296630859375,
-0.006404876708984375,
-0.01126861572265625,
-0.00396728515625,
-0.03497314453125,
0.00007212162017822266,
-0.0262603759765625,
0.03460693359375,
-0.02801513671875,
0.01165008544921875,
-0.00461578369140625,
-0.003662109375,
-0.01383209228515625,
-0.0080108642578125,
0.0226898193359375,
0.033599853515625,
0.009979248046875,
-0.01494598388671875,
-0.01476287841796875,
-0.00594329833984375,
0.0186309814453125,
-0.014404296875,
-0.04144287109375,
-0.0021190643310546875,
-0.0007081031799316406,
0.01300048828125,
0.01377105712890625,
0.030059814453125,
0.0002090930938720703,
-0.019287109375,
0.0164031982421875,
-0.00653839111328125,
-0.0151824951171875,
-0.020843505859375,
0.0013189315795898438,
-0.015716552734375,
-0.00814056396484375,
0.00803375244140625,
0.013763427734375,
-0.02587890625,
-0.00531768798828125,
-0.0119476318359375,
-0.0206146240234375,
-0.001689910888671875,
0.0220794677734375,
0.0008916854858398438,
0.0038814544677734375,
0.01003265380859375,
0.0142974853515625,
-0.019012451171875,
0.030731201171875,
0.00617218017578125,
0.030059814453125,
-0.031463623046875,
-0.0048065185546875,
-0.00968170166015625,
-0.036224365234375,
-0.0135040283203125,
0.01450347900390625,
0.014251708984375,
-0.00995635986328125,
-0.0132598876953125,
0.002384185791015625,
-0.0235748291015625,
-0.0095672607421875,
-0.028717041015625,
0.00003057718276977539,
-0.00698089599609375,
0.0183563232421875,
0.002887725830078125,
-0.019805908203125,
-0.007354736328125,
0.00820159912109375,
0.004116058349609375,
0.0372314453125,
0.0115814208984375,
0.0214080810546875,
0.0034770965576171875,
0.017913818359375,
-0.0255889892578125,
-0.00933074951171875,
0.0014467239379882812,
-0.01065826416015625,
-0.0206451416015625,
0.00490570068359375,
-0.024444580078125,
0.0188446044921875,
0.020843505859375,
-0.006374359130859375,
-0.01189422607421875,
-0.00040340423583984375,
0.0032215118408203125,
0.034271240234375,
-0.037628173828125,
-0.0013561248779296875,
-0.00867462158203125,
0.003223419189453125,
-0.01544189453125,
0.006679534912109375,
-0.00565338134765625,
0.004489898681640625,
0.0018453598022460938,
-0.033050537109375,
0.009552001953125,
-0.0301513671875,
0.00643157958984375,
0.00006240606307983398,
-0.0220489501953125,
0.0005092620849609375,
0.01378631591796875,
0.016448974609375,
-0.005901336669921875,
-0.039764404296875,
0.0079498291015625,
-0.00061798095703125,
0.04608154296875,
0.019378662109375,
-0.00843048095703125,
0.00487518310546875,
0.016937255859375,
0.006626129150390625,
-0.02691650390625,
0.0014171600341796875,
-0.01654052734375,
0.005889892578125,
0.01309967041015625,
0.004146575927734375,
-0.001674652099609375,
0.0112762451171875,
0.00992584228515625,
0.011810302734375,
0.0211181640625,
0.0006146430969238281,
-0.03594970703125,
-0.032562255859375,
-0.019866943359375,
-0.0048065185546875,
0.0177459716796875,
-0.0029125213623046875,
0.028076171875,
0.02734375,
-0.0224761962890625,
0.0008177757263183594,
0.0219573974609375,
0.0031337738037109375,
0.034027099609375,
0.0012254714965820312,
-0.0165557861328125,
0.02154541015625,
-0.0528564453125,
0.0472412109375,
-0.0163421630859375,
0.003215789794921875,
-0.016326904296875,
0.0220947265625,
0.00995635986328125,
-0.00235748291015625,
0.0015106201171875,
0.009979248046875,
-0.0124359130859375,
-0.01320648193359375,
0.0224151611328125,
-0.004726409912109375,
0.017669677734375,
0.007579803466796875,
-0.01654052734375,
0.02978515625,
-0.007495880126953125,
0.01160430908203125,
-0.0084991455078125,
0.0034618377685546875,
-0.00991058349609375,
-0.0330810546875,
-0.01528167724609375,
-0.041473388671875,
0.0276641845703125,
-0.0498046875,
-0.02520751953125,
-0.0030384063720703125,
-0.0006780624389648438,
0.0036067962646484375,
0.0183563232421875,
-0.0241241455078125,
-0.03936767578125,
0.00830078125,
-0.007415771484375,
-0.010162353515625,
0.01556396484375,
0.0092926025390625,
0.003582000732421875,
0.004787445068359375,
0.0020809173583984375,
-0.0062408447265625,
0.0277099609375,
0.02294921875,
-0.0164642333984375,
0.02294921875,
0.002170562744140625,
-0.00521087646484375,
-0.048248291015625,
-0.01169586181640625,
-0.0123291015625,
0.00521087646484375,
0.0164031982421875,
-0.00823211669921875,
-0.01806640625,
0.017913818359375,
-0.01354217529296875,
0.0157012939453125,
-0.00997161865234375,
0.001605987548828125,
0.0168304443359375,
0.0017995834350585938,
0.00688934326171875,
-0.01247406005859375,
-0.00858306884765625,
0.054107666015625,
0.002227783203125,
-0.0003616809844970703,
0.01171112060546875,
0.0232086181640625,
0.0157012939453125,
-0.034271240234375,
-0.01166534423828125,
-0.0223541259765625,
-0.003421783447265625,
-0.01371002197265625,
0.0250396728515625,
0.00669097900390625,
0.012054443359375,
0.0110321044921875,
0.042755126953125,
-0.015869140625,
-0.0123748779296875,
0.035552978515625,
0.0130615234375,
0.008453369140625,
-0.017974853515625,
-0.013916015625,
-0.004364013671875,
-0.000021755695343017578,
0.01494598388671875,
-0.0167236328125,
0.0283660888671875,
-0.005893707275390625,
-0.02099609375,
-0.051055908203125,
-0.02178955078125,
0.02178955078125,
-0.0104217529296875,
0.02020263671875,
-0.0035247802734375,
-0.0035724639892578125,
0.0182037353515625,
-0.0238189697265625,
-0.0027313232421875,
-0.04248046875,
-0.00571441650390625,
0.00913238525390625,
0.01140594482421875,
0.0210113525390625,
-0.0174407958984375,
0.01361083984375,
0.0019063949584960938,
0.01611328125,
-0.0019025802612304688,
-0.0462646484375,
0.0004324913024902344,
0.01453399658203125,
-0.0009603500366210938,
-0.00778961181640625,
-0.006206512451171875,
0.00806427001953125,
-0.02593994140625,
0.020355224609375,
0.0312347412109375,
0.005008697509765625,
0.048431396484375,
-0.034576416015625,
-0.0078582763671875,
-0.00042629241943359375,
-0.004306793212890625,
-0.014495849609375,
-0.0033893585205078125,
-0.017974853515625,
-0.033447265625,
-0.049835205078125,
-0.007228851318359375,
-0.00827789306640625,
-0.01415252685546875,
0.0037174224853515625,
0.0241546630859375,
0.031402587890625,
-0.0034046173095703125,
0.0202484130859375,
0.002582550048828125,
0.00125885009765625,
0.015625,
0.00131988525390625,
-0.0173187255859375,
-0.0093231201171875,
-0.002422332763671875,
-0.01088714599609375,
0.0018024444580078125,
-0.02935791015625,
0.00738525390625,
-0.0013217926025390625,
0.0280914306640625,
0.0308074951171875,
-0.00472259521484375,
0.0023136138916015625,
0.05535888671875,
0.032501220703125,
0.0137176513671875,
-0.00423431396484375,
-0.0207977294921875,
0.00921630859375,
-0.0107879638671875,
0.00624847412109375,
-0.02178955078125,
-0.0013256072998046875,
-0.008819580078125,
0.0362548828125,
0.0167999267578125,
-0.0103302001953125,
0.0172119140625,
0.0177764892578125,
-0.0023822784423828125,
-0.021942138671875,
-0.012664794921875,
-0.039337158203125,
0.01161956787109375,
0.0008893013000488281,
-0.018218994140625,
-0.0225067138671875,
-0.01195526123046875,
-0.023895263671875,
0.009979248046875,
-0.031829833984375,
0.0269775390625,
0.020904541015625,
-0.015899658203125,
-0.0014629364013671875,
0.042083740234375,
-0.022979736328125,
-0.0019140243530273438,
-0.0006475448608398438,
0.0004963874816894531,
-0.03173828125,
-0.01806640625,
-0.003116607666015625,
0.02972412109375,
0.0128631591796875,
0.00402069091796875,
-0.0072479248046875,
0.0013380050659179688,
-0.03277587890625,
-0.038299560546875,
0.04437255859375,
-0.035003662109375,
-0.01039886474609375,
-0.02227783203125,
-0.00901031494140625,
-0.0018281936645507812,
0.051666259765625,
0.001789093017578125,
0.003173828125,
-0.040802001953125,
0.00848388671875,
0.0276947021484375,
-0.0261688232421875,
0.0276336669921875,
-0.0094146728515625,
0.00577545166015625,
0.01403045654296875,
-0.021453857421875,
0.03192138671875,
0.005706787109375,
-0.010162353515625,
0.01038360595703125,
0.0221710205078125,
0.02227783203125,
-0.01480865478515625,
-0.0004305839538574219,
-0.053192138671875,
0.011383056640625,
-0.0166778564453125,
0.01849365234375,
-0.0016565322875976562,
-0.05841064453125,
-0.0165863037109375,
-0.0187225341796875,
0.011199951171875,
-0.034210205078125,
0.0157012939453125,
0.0082855224609375,
0.00760650634765625,
0.005153656005859375,
-0.0128936767578125,
0.048248291015625,
-0.0225067138671875,
-0.0237884521484375,
0.0279998779296875,
0.021331787109375,
-0.034820556640625,
-0.0229644775390625,
-0.0263671875,
-0.01236724853515625,
0.0185394287109375,
0.0245819091796875,
0.005889892578125,
0.00511932373046875,
0.01113128662109375,
0.01507568359375,
0.0301513671875,
0.0010242462158203125,
0.0301361083984375,
0.0173187255859375,
-0.022735595703125,
-0.009063720703125,
-0.007083892822265625,
-0.039031982421875,
-0.0156707763671875,
0.0056304931640625,
-0.0245208740234375,
-0.01190185546875,
-0.0011301040649414062,
-0.00015342235565185547,
-0.06317138671875,
-0.01514434814453125,
0.01129150390625,
-0.00576019287109375,
0.0151824951171875,
-0.010955810546875,
-0.01375579833984375,
-0.0170440673828125,
0.0056610107421875,
-0.038818359375,
-0.00394439697265625,
-0.0187225341796875,
0.0165252685546875,
-0.00814056396484375,
0.00614166259765625,
0.005435943603515625,
-0.0196075439453125,
-0.0310821533203125,
-0.02398681640625,
0.007259368896484375,
0.0200042724609375,
-0.00145721435546875,
-0.00927734375,
0.033111572265625,
-0.03729248046875,
0.0182037353515625,
0.01251220703125,
0.0070953369140625,
-0.00432586669921875,
-0.032501220703125,
-0.007549285888671875,
-0.00003361701965332031,
0.0120697021484375,
0.02154541015625,
-0.0225067138671875,
-0.0016880035400390625,
-0.0205535888671875,
-0.0059356689453125,
-0.004070281982421875,
0.0177001953125,
0.0211334228515625,
-0.01367950439453125,
0.041290283203125,
-0.007598876953125,
0.026123046875,
0.0087738037109375,
0.024505615234375,
0.0030612945556640625,
-0.0154266357421875,
0.0020999908447265625,
-0.0195770263671875,
-0.0014810562133789062,
0.041778564453125,
-0.00634002685546875,
0.006622314453125,
-0.007770538330078125,
-0.0194854736328125,
0.00841522216796875,
0.0035877227783203125,
-0.00621795654296875,
-0.01027679443359375,
-0.009063720703125,
0.0019550323486328125,
0.018341064453125
] |
ours_483
|
The slopes of lines \(AB, BC, CD, DA, AC, BD\) are \(-\frac{2}{5}, \frac{1}{3}, 1, \frac{5}{8}, 4, \frac{7}{3}\) respectively. By Desargues' Involution Theorem, \(\left(-\frac{2}{5}, 1; \frac{1}{3}, \frac{5}{8}; 4, \frac{7}{3}\right)\) are pairs of an involution \(f\). This involution satisfies \((x+y)(x+f(y))=c\) for some constants \(x, c\).
Solving for \(x, c\), we have \(\left(x+\frac{2}{5}\right)(x-1)=\left(x-\frac{1}{3}\right)\left(x-\frac{5}{8}\right)=c\), giving \(x=\frac{73}{43}\) and \(c=\frac{2706}{1849}\).
If the desired slope is \(s=f\left(\frac{20}{17}\right)\), then \(\left(\frac{73}{43}-\frac{20}{17}\right)\left(\frac{73}{43}-s\right)=\frac{2706}{1849}\). Solving this, we find \(s=-\frac{141}{127}\).
Thus, \(m=141\) and \(n=127\), so \(100m+n = 100 \times 141 + 127 = 14227\).
\(\boxed{14227}\)
|
14227
|
{
"competition": "us_comps",
"dataset": "Ours",
"posts": null,
"source": "OMOFall18Solns.md"
}
|
A hyperbola in the coordinate plane passing through the points \((2,5), (7,3), (1,1)\), and \((10,10)\) has an asymptote of slope \(\frac{20}{17}\). The slope of its other asymptote can be expressed in the form \(-\frac{m}{n}\), where \(m\) and \(n\) are relatively prime positive integers. Compute \(100m+n\).
|
[
"/Mathematics/Algebra/AlgebraicCurves/AlgebraicCurve",
"/Mathematics/Algebra/AlgebraicCurves/AlgebraicGeometry",
"/Mathematics/Algebra/AlgebraicCurves/Hyperbola",
"/Mathematics/Algebra/AlgebraicCurves/QuadraticCurve",
"/Mathematics/Algebra/AlgebraicEquations/AlgebraicEquation",
"/Mathematics/Geometry/CoordinateGeometry/AnalyticGeometry",
"/Mathematics/Geometry/CoordinateGeometry/Cartesian",
"/Mathematics/Geometry/CoordinateGeometry/CartesianCoordinateSystem",
"/Mathematics/Geometry/CoordinateGeometry/CartesianPlane",
"/Mathematics/Geometry/Curves/AlgebraicCurves",
"/Mathematics/Geometry/Curves/PlaneCurves",
"/Mathematics/Geometry/PlaneGeometry/MiscellaneousPlaneGeometry",
"/Mathematics/Geometry/PlaneGeometry/PlaneCurves",
"/Mathematics/Geometry/ProjectiveGeometry/GeneralProjectiveGeometry"
] |
Apply Desargues' Involution Theorem to the six slopes formed by the four points, creating an involution that maps the given asymptote slope to the other one.
|
[
-0.0002205371856689453,
-0.057830810546875,
0.047119140625,
-0.006793975830078125,
-0.0006284713745117188,
0.01513671875,
0.024627685546875,
0.032867431640625,
0.00272369384765625,
0.0265960693359375,
0.0008187294006347656,
0.050628662109375,
-0.005092620849609375,
0.0190582275390625,
-0.019378662109375,
0.01111602783203125,
-0.0183868408203125,
-0.01140594482421875,
0.0400390625,
-0.0028209686279296875,
-0.01074981689453125,
0.0079498291015625,
-0.040008544921875,
0.0321044921875,
-0.0019502639770507812,
0.0237884521484375,
-0.01128387451171875,
-0.01372528076171875,
-0.0166015625,
-0.01727294921875,
0.01059722900390625,
0.0015077590942382812,
-0.0022373199462890625,
-0.0117340087890625,
-0.0017948150634765625,
-0.01220703125,
0.002971649169921875,
-0.0012264251708984375,
-0.03314208984375,
-0.0220489501953125,
-0.00267791748046875,
0.005809783935546875,
-0.016754150390625,
0.0137786865234375,
-0.0015821456909179688,
0.0222930908203125,
-0.017822265625,
-0.004974365234375,
0.0016469955444335938,
-0.010040283203125,
-0.00414276123046875,
0.0168609619140625,
-0.0175628662109375,
-0.0170745849609375,
-0.01091766357421875,
-0.050018310546875,
-0.01026153564453125,
0.0028247833251953125,
-0.0018129348754882812,
0.025726318359375,
0.0017232894897460938,
-0.0112457275390625,
0.01503753662109375,
-0.0035247802734375,
-0.0068817138671875,
-0.01197052001953125,
0.00814056396484375,
-0.049224853515625,
0.0141754150390625,
0.0049285888671875,
0.019134521484375,
-0.00347900390625,
-0.00555419921875,
0.028167724609375,
0.024749755859375,
-0.00672149658203125,
-0.00832366943359375,
0.01113128662109375,
-0.01163482666015625,
0.01056671142578125,
0.00397491455078125,
0.00452423095703125,
0.012298583984375,
-0.020843505859375,
0.02410888671875,
-0.02667236328125,
-0.034088134765625,
0.00981903076171875,
0.023040771484375,
-0.00032901763916015625,
0.0016279220581054688,
0.053466796875,
0.0013875961303710938,
0.006103515625,
0.007488250732421875,
0.0121307373046875,
0.0096893310546875,
-0.004730224609375,
-0.0161285400390625,
0.002719879150390625,
-0.0207061767578125,
-0.01099395751953125,
-0.0140838623046875,
-0.006710052490234375,
0.004405975341796875,
-0.00727081298828125,
-0.012542724609375,
0.008819580078125,
0.002285003662109375,
-0.003528594970703125,
0.022491455078125,
0.007740020751953125,
0.0224456787109375,
0.0103607177734375,
0.0161285400390625,
-0.0079345703125,
0.0291900634765625,
-0.0037631988525390625,
0.0030269622802734375,
-0.01715087890625,
0.0008015632629394531,
0.0060577392578125,
-0.0258636474609375,
-0.0016069412231445312,
-0.0120849609375,
0.0023365020751953125,
-0.0029582977294921875,
-0.0052032470703125,
-0.0265350341796875,
0.01311492919921875,
0.016143798828125,
-0.007282257080078125,
-0.0121307373046875,
-0.043243408203125,
-0.046417236328125,
0.0269317626953125,
-0.02349853515625,
-0.002666473388671875,
0.0152587890625,
-0.005161285400390625,
-0.00040650367736816406,
-0.011444091796875,
0.004413604736328125,
-0.0318603515625,
0.0295257568359375,
-0.051025390625,
0.006877899169921875,
0.01006317138671875,
0.0005388259887695312,
-0.00946807861328125,
0.02197265625,
-0.0029430389404296875,
0.00801849365234375,
-0.0017576217651367188,
-0.01062774658203125,
0.00783538818359375,
0.01076507568359375,
-0.005222320556640625,
-0.01220703125,
0.008819580078125,
0.0033092498779296875,
0.00829315185546875,
0.024200439453125,
0.0191192626953125,
-0.0023593902587890625,
-0.0013637542724609375,
-0.008819580078125,
0.0139312744140625,
-0.00951385498046875,
0.0244598388671875,
-0.0027866363525390625,
-0.0052490234375,
0.01092529296875,
-0.0311279296875,
0.0216522216796875,
0.019500732421875,
-0.005695343017578125,
0.00965118408203125,
0.0038166046142578125,
0.0215301513671875,
-0.0035495758056640625,
-0.0250701904296875,
-0.0229034423828125,
0.00714874267578125,
0.0006361007690429688,
-0.0038013458251953125,
-0.016754150390625,
0.01241302490234375,
0.0101318359375,
0.0380859375,
-0.004138946533203125,
-0.0121917724609375,
-0.0177154541015625,
0.00904083251953125,
-0.0083770751953125,
-0.0125274658203125,
-0.01447296142578125,
-0.0036907196044921875,
-0.033447265625,
0.026763916015625,
-0.004734039306640625,
0.003864288330078125,
0.014404296875,
-0.01200103759765625,
0.01800537109375,
0.00803375244140625,
0.004161834716796875,
-0.01192474365234375,
-0.0029964447021484375,
0.0034027099609375,
0.0309600830078125,
0.00428009033203125,
-0.0134124755859375,
-0.035003662109375,
-0.00986480712890625,
-0.0019435882568359375,
-0.031707763671875,
-0.006816864013671875,
0.0237579345703125,
0.00922393798828125,
0.0018682479858398438,
-0.01331329345703125,
0.00021767616271972656,
-0.027557373046875,
0.01033782958984375,
0.0174407958984375,
-0.004642486572265625,
0.006008148193359375,
-0.00414276123046875,
0.0022602081298828125,
0.0233154296875,
0.0105438232421875,
0.0013036727905273438,
-0.01093292236328125,
-0.00746917724609375,
-0.0191650390625,
-0.053985595703125,
-0.00024068355560302734,
0.01611328125,
0.006069183349609375,
-0.0200042724609375,
-0.0177459716796875,
0.01447296142578125,
-0.005901336669921875,
0.0174102783203125,
-0.00499725341796875,
0.018402099609375,
-0.01381683349609375,
0.00572967529296875,
-0.0290985107421875,
-0.01500701904296875,
0.01354217529296875,
0.0009570121765136719,
-0.0223236083984375,
0.01047515869140625,
-0.00225830078125,
0.0099334716796875,
-0.0311431884765625,
-0.006801605224609375,
0.0280303955078125,
0.0054168701171875,
0.0091094970703125,
0.0017795562744140625,
-0.00719451904296875,
-0.002838134765625,
0.0288238525390625,
0.01180267333984375,
0.01120758056640625,
0.010345458984375,
-0.01290130615234375,
0.0301971435546875,
-0.018402099609375,
-0.008331298828125,
0.00875091552734375,
0.004436492919921875,
-0.01513671875,
-0.00601959228515625,
0.002384185791015625,
0.01311492919921875,
-0.007396697998046875,
-0.00412750244140625,
-0.01097869873046875,
-0.0257720947265625,
0.0020542144775390625,
-0.014984130859375,
-0.0160064697265625,
0.00971221923828125,
-0.00634002685546875,
-0.0128326416015625,
-0.00537872314453125,
0.00945281982421875,
-0.031829833984375,
0.007389068603515625,
-0.0196533203125,
0.018707275390625,
0.0014810562133789062,
0.0184478759765625,
0.01415252685546875,
0.00406646728515625,
-0.0164337158203125,
0.027862548828125,
-0.013671875,
-0.00644683837890625,
-0.01093292236328125,
0.0159759521484375,
0.034393310546875,
0.0221710205078125,
0.006443023681640625,
-0.0171356201171875,
0.0057525634765625,
0.002445220947265625,
-0.0049285888671875,
-0.004734039306640625,
-0.0088043212890625,
-0.004932403564453125,
-0.020965576171875,
-0.01380157470703125,
0.025634765625,
-0.0278167724609375,
0.033050537109375,
0.01052093505859375,
0.04339599609375,
0.02862548828125,
0.0207366943359375,
0.00894927978515625,
-0.01009368896484375,
-0.0011615753173828125,
0.0020046234130859375,
-0.0004000663757324219,
0.02593994140625,
-0.0166778564453125,
0.00589752197265625,
0.0177154541015625,
-0.008636474609375,
0.032196044921875,
0.01512908935546875,
-0.0026988983154296875,
0.0254669189453125,
-0.032684326171875,
0.003993988037109375,
0.007335662841796875,
-0.016082763671875,
0.0294647216796875,
-0.0291748046875,
-0.036529541015625,
0.00569915771484375,
-0.043304443359375,
-0.00785064697265625,
0.019805908203125,
-0.018524169921875,
0.040740966796875,
-0.006938934326171875,
-0.01947021484375,
0.0011949539184570312,
-0.0294189453125,
0.006572723388671875,
-0.024322509765625,
-0.0014400482177734375,
-0.01100921630859375,
0.031951904296875,
-0.01256561279296875,
-0.00974273681640625,
-0.0207366943359375,
0.01499176025390625,
-0.026336669921875,
-0.041839599609375,
0.0008549690246582031,
0.017364501953125,
-0.01125335693359375,
0.002410888671875,
-0.0207366943359375,
0.010711669921875,
0.00746917724609375,
0.0259246826171875,
0.01049041748046875,
0.029571533203125,
0.00824737548828125,
0.0235443115234375,
-0.0013256072998046875,
-0.0017099380493164062,
-0.004550933837890625,
0.022003173828125,
-0.0026493072509765625,
0.0130615234375,
-0.025360107421875,
0.005863189697265625,
0.01532745361328125,
-0.036163330078125,
-0.0237884521484375,
-0.0038967132568359375,
-0.006557464599609375,
-0.0003459453582763672,
-0.006610870361328125,
-0.022369384765625,
-0.039886474609375,
-0.0076141357421875,
-0.0022068023681640625,
0.0265655517578125,
0.05096435546875,
-0.017059326171875,
-0.027679443359375,
-0.0024585723876953125,
-0.031646728515625,
-0.0293731689453125,
0.028045654296875,
-0.007167816162109375,
-0.0004761219024658203,
-0.01056671142578125,
0.003078460693359375,
-0.0283050537109375,
0.00939178466796875,
0.04498291015625,
-0.01253509521484375,
-0.0019311904907226562,
-0.0199127197265625,
0.018646240234375,
0.0252685546875,
0.0040435791015625,
-0.0116729736328125,
-0.00940704345703125,
-0.0205841064453125,
-0.01213836669921875,
-0.00629425048828125,
0.0045928955078125,
-0.0024776458740234375,
0.030029296875,
-0.0070648193359375,
0.0220184326171875,
-0.0014848709106445312,
0.0208892822265625,
-0.024749755859375,
0.0085601806640625,
-0.020721435546875,
0.003204345703125,
0.00390625,
-0.0054931640625,
0.052490234375,
-0.00765228271484375,
-0.0126190185546875,
0.0111236572265625,
-0.0101776123046875,
-0.03875732421875,
0.013763427734375,
0.0016641616821289062,
0.006633758544921875,
-0.0233154296875,
-0.0072784423828125,
0.007427215576171875,
0.00496673583984375,
0.00931549072265625,
-0.0168304443359375,
0.01265716552734375,
0.044952392578125,
-0.03271484375,
0.00873565673828125,
0.01428985595703125,
0.0224456787109375,
0.006622314453125,
-0.048248291015625,
0.0014276504516601562,
0.007160186767578125,
-0.0100860595703125,
-0.02496337890625,
0.00003039836883544922,
-0.0038127899169921875,
0.01561737060546875,
-0.0087127685546875,
0.0243988037109375,
0.002399444580078125,
0.01006317138671875,
0.0164794921875,
-0.0290985107421875,
-0.01009368896484375,
-0.00572967529296875,
-0.033172607421875,
0.0030517578125,
0.01279449462890625,
0.0087127685546875,
-0.0069427490234375,
0.01435089111328125,
0.0012149810791015625,
0.0201568603515625,
0.0004355907440185547,
-0.053802490234375,
0.006534576416015625,
0.053680419921875,
-0.0044708251953125,
0.005634307861328125,
-0.04766845703125,
0.006740570068359375,
0.0241546630859375,
0.0155792236328125,
-0.0274810791015625,
-0.01482391357421875,
-0.0007619857788085938,
-0.01471710205078125,
0.01849365234375,
0.00395965576171875,
-0.007354736328125,
-0.02099609375,
-0.0033054351806640625,
-0.05889892578125,
-0.007762908935546875,
-0.0236663818359375,
0.00902557373046875,
-0.0056304931640625,
-0.01149749755859375,
-0.01446533203125,
0.01062774658203125,
-0.00797271728515625,
0.028961181640625,
0.012664794921875,
0.038482666015625,
0.0013103485107421875,
0.03131103515625,
0.00539398193359375,
0.001056671142578125,
-0.03167724609375,
0.022247314453125,
0.0236053466796875,
-0.01690673828125,
-0.0212249755859375,
0.007602691650390625,
0.0010023117065429688,
0.0242767333984375,
-0.0011568069458007812,
0.00855255126953125,
-0.00740814208984375,
-0.004550933837890625,
0.0154266357421875,
0.00754547119140625,
-0.01055145263671875,
-0.0640869140625,
0.034942626953125,
-0.047027587890625,
-0.005954742431640625,
-0.004909515380859375,
-0.0212860107421875,
0.01311492919921875,
-0.0109100341796875,
-0.01348876953125,
-0.03363037109375,
-0.0028438568115234375,
-0.02899169921875,
0.00319671630859375,
-0.0103302001953125,
0.00661468505859375,
0.0205230712890625,
-0.0177154541015625,
0.035003662109375,
0.0224151611328125,
0.004268646240234375,
-0.0094451904296875,
-0.00836944580078125,
-0.0201568603515625,
-0.017333984375,
-0.0308074951171875,
-0.031280517578125,
0.003936767578125,
0.02783203125,
0.0121002197265625,
-0.0010986328125,
0.024505615234375,
0.0148162841796875,
0.011688232421875,
-0.0150146484375,
-0.01210784912109375,
-0.0236968994140625,
0.018524169921875,
-0.04437255859375,
0.005451202392578125,
0.005878448486328125,
-0.0220794677734375,
0.015777587890625,
0.020416259765625,
0.0024394989013671875,
-0.046142578125,
0.01788330078125,
-0.007778167724609375,
-0.0199127197265625,
0.035308837890625,
0.031494140625,
0.0330810546875,
0.0031528472900390625,
0.00453948974609375,
-0.005405426025390625,
-0.02630615234375,
-0.0200347900390625,
0.01464080810546875,
-0.00409698486328125,
-0.00392913818359375,
0.0037670135498046875,
-0.00865936279296875,
0.0164642333984375,
0.01611328125,
-0.001369476318359375,
0.0218353271484375,
-0.005825042724609375,
0.00037932395935058594,
0.00653839111328125,
0.0498046875,
-0.02032470703125,
-0.00856781005859375,
0.00101470947265625,
-0.052337646484375,
-0.01436614990234375,
-0.0292205810546875,
0.049713134765625,
0.01125335693359375,
0.022003173828125,
-0.0325927734375,
-0.0078887939453125,
-0.0240325927734375,
0.001861572265625,
-0.0042724609375,
0.01776123046875,
0.012481689453125,
-0.0180511474609375,
-0.0277862548828125,
0.0010099411010742188,
0.0024166107177734375,
0.01165008544921875,
-0.04046630859375,
0.04974365234375,
0.0060882568359375,
0.0271759033203125,
-0.0107421875,
-0.02728271484375,
0.01251983642578125,
-0.0013952255249023438,
-0.01837158203125,
-0.028472900390625,
-0.01462554931640625,
0.01580810546875,
-0.01708984375,
-0.056732177734375,
-0.0303802490234375,
0.0015058517456054688,
0.0095367431640625,
-0.0013179779052734375,
0.0096282958984375,
0.0114288330078125,
0.035919189453125,
-0.0214385986328125,
0.043548583984375,
0.00615692138671875,
-0.0297088623046875,
-0.0229949951171875,
-0.0209503173828125,
0.026611328125,
-0.0267791748046875,
-0.01549530029296875,
0.00408935546875,
0.044708251953125,
-0.003429412841796875,
-0.0017442703247070312,
0.005344390869140625,
0.0169219970703125,
0.0194549560546875,
-0.002361297607421875,
-0.009002685546875,
-0.01702880859375,
0.0004246234893798828,
0.0419921875,
-0.02117919921875,
-0.00835418701171875,
-0.044586181640625,
-0.03314208984375,
0.00733184814453125,
-0.01904296875,
0.00518035888671875,
0.0168304443359375,
0.002063751220703125,
0.0164031982421875,
0.0174102783203125,
-0.01331329345703125,
0.00030684471130371094,
0.0262908935546875,
0.0439453125,
0.004177093505859375,
0.0083160400390625,
-0.024261474609375,
0.00893402099609375,
-0.00811004638671875,
0.004180908203125,
0.04168701171875,
-0.006534576416015625,
0.0296478271484375,
0.033447265625,
0.035797119140625,
-0.0076904296875,
0.0088653564453125,
-0.037200927734375,
0.01312255859375,
0.006198883056640625,
-0.0176544189453125,
0.01427459716796875,
-0.019073486328125,
-0.03143310546875,
-0.0278472900390625,
0.0088348388671875,
-0.022216796875,
0.0161285400390625,
-0.0197906494140625,
-0.0273590087890625,
-0.01361846923828125,
0.0005922317504882812,
0.0145111083984375,
-0.0007910728454589844,
0.004856109619140625,
-0.04962158203125,
-0.029937744140625,
-0.0267181396484375,
-0.00390625,
-0.003055572509765625,
-0.01509857177734375,
0.0044708251953125,
-0.01213836669921875,
-0.023956298828125,
-0.001079559326171875,
-0.0008344650268554688,
-0.00652313232421875,
-0.0213165283203125,
-0.035430908203125,
0.00234222412109375,
0.019805908203125,
-0.00916290283203125,
-0.02655029296875,
-0.01523590087890625,
0.01149749755859375,
-0.00801849365234375,
-0.009124755859375,
0.0012111663818359375,
0.003917694091796875,
-0.007122039794921875,
-0.0224761962890625,
0.00910186767578125,
-0.01509857177734375,
0.00548553466796875,
0.0182952880859375,
0.0293426513671875,
0.00832366943359375,
-0.00018274784088134766,
-0.022125244140625,
0.01053619384765625,
-0.0211181640625,
0.01678466796875,
-0.0186767578125,
-0.0125732421875,
0.004764556884765625,
-0.0012416839599609375,
0.01029205322265625,
0.0116119384765625,
-0.049468994140625,
-0.0187835693359375,
0.00785064697265625,
0.0082855224609375,
0.0025310516357421875,
0.00463104248046875,
-0.01029205322265625,
-0.0235748291015625,
0.038970947265625,
-0.0007538795471191406,
-0.00824737548828125,
0.0037212371826171875,
-0.046875,
-0.023345947265625,
-0.017120361328125,
-0.050140380859375,
-0.004512786865234375,
-0.0162506103515625,
0.0175323486328125,
-0.00930023193359375,
-0.00719451904296875,
0.02325439453125,
-0.00667572021484375,
-0.0176239013671875,
-0.021270751953125,
0.02398681640625,
0.00899505615234375,
-0.03570556640625,
0.0159454345703125,
0.037384033203125,
-0.033966064453125,
-0.021087646484375,
0.01122283935546875,
-0.0015649795532226562,
-0.0024776458740234375,
0.006694793701171875,
0.0086517333984375,
0.042694091796875,
0.0350341796875,
0.0029296875,
-0.0189056396484375,
-0.0255584716796875,
0.0014104843139648438,
-0.0034008026123046875,
-0.0067291259765625,
-0.014923095703125,
-0.006755828857421875,
-0.00803375244140625,
0.0147247314453125,
-0.0046844482421875,
0.0096588134765625,
-0.00035953521728515625,
-0.00682830810546875,
-0.0001430511474609375,
0.02886962890625,
-0.012542724609375,
0.0203857421875,
-0.008209228515625,
-0.003124237060546875,
-0.021514892578125,
0.0107421875,
0.00038814544677734375,
-0.023345947265625,
0.004669189453125,
0.0011072158813476562,
0.006725311279296875,
0.0022907257080078125,
-0.0215301513671875,
0.03521728515625,
0.020599365234375,
0.010772705078125,
-0.015289306640625,
-0.0007262229919433594,
-0.0262603759765625,
-0.0210113525390625,
0.00629425048828125,
0.0296630859375,
-0.0061492919921875,
-0.025115966796875,
-0.0182037353515625,
0.00649261474609375,
0.00368499755859375,
-0.006038665771484375,
-0.00292205810546875,
0.0032501220703125,
-0.0025768280029296875,
0.02490234375,
0.004390716552734375,
-0.0005512237548828125,
0.042449951171875,
0.02593994140625,
0.0170440673828125,
-0.02203369140625,
-0.028533935546875,
0.0078887939453125,
0.01105499267578125,
0.0103302001953125,
0.042877197265625,
0.048858642578125,
-0.0009431838989257812,
0.0202178955078125,
0.00899505615234375,
0.0193939208984375,
0.01904296875,
0.01568603515625,
-0.0007557868957519531,
-0.0261077880859375,
0.0286712646484375,
-0.03125,
0.01023101806640625,
-0.0115966796875,
-0.0262908935546875,
-0.024627685546875,
0.002498626708984375,
-0.009185791015625,
0.018829345703125,
-0.01528167724609375,
-0.0080718994140625,
-0.0156707763671875,
0.0026645660400390625,
0.0017137527465820312,
0.060028076171875,
0.0189361572265625,
-0.0082855224609375,
0.00969696044921875,
0.022735595703125,
0.02996826171875,
0.0308837890625,
-0.032501220703125,
-0.0025157928466796875,
0.0153961181640625,
-0.003337860107421875,
-0.0037326812744140625,
-0.01007080078125,
0.03662109375,
0.01280975341796875,
-0.031219482421875,
0.00661468505859375,
0.016815185546875,
0.00627899169921875,
-0.03515625,
0.015716552734375,
-0.0283050537109375,
-0.0171356201171875,
-0.021820068359375,
-0.004604339599609375,
0.005550384521484375,
-0.025360107421875,
-0.00931549072265625,
-0.03009033203125,
0.0165557861328125,
0.00815582275390625,
-0.009765625,
0.00452423095703125,
-0.01097869873046875,
0.00560760498046875,
0.00441741943359375,
-0.0287322998046875,
0.007076263427734375,
-0.038482666015625,
0.01325225830078125,
0.00350189208984375,
-0.005397796630859375,
0.02276611328125,
-0.00800323486328125,
0.00528717041015625,
-0.04376220703125,
0.0316162109375,
-0.007541656494140625,
0.0033321380615234375,
0.00785064697265625,
0.006603240966796875,
-0.0294189453125,
-0.00440216064453125,
0.00527191162109375,
-0.036895751953125,
-0.008148193359375,
-0.0286102294921875,
0.01849365234375,
-0.00250244140625,
-0.0237884521484375,
-0.0220947265625,
-0.0190582275390625,
-0.060882568359375,
-0.0281829833984375,
0.054107666015625,
-0.056488037109375,
-0.0189971923828125,
0.0207366943359375,
0.031524658203125,
0.01031494140625,
0.01141357421875,
0.00298309326171875,
0.01555633544921875,
-0.02447509765625,
0.0191192626953125,
-0.0004305839538574219,
-0.01305389404296875,
-0.0145416259765625,
-0.0207672119140625,
-0.0008077621459960938,
0.002407073974609375,
-0.040283203125,
-0.01342010498046875,
0.0309906005859375,
-0.0078125,
0.0305328369140625,
-0.00304412841796875,
-0.003261566162109375,
0.01047515869140625,
-0.013580322265625,
-0.0273284912109375,
0.041351318359375,
0.032501220703125,
-0.0150909423828125,
-0.01155853271484375,
-0.0025482177734375,
-0.0235595703125,
-0.036041259765625,
-0.034027099609375,
-0.0184783935546875,
0.0258636474609375,
0.0187530517578125,
-0.004207611083984375,
0.038848876953125,
0.02325439453125,
-0.035125732421875,
-0.03179931640625,
-0.008026123046875,
0.0146026611328125,
-0.019134521484375,
-0.0234527587890625,
-0.00986480712890625,
0.01244354248046875,
-0.02001953125,
-0.002590179443359375,
-0.021881103515625,
-0.036773681640625,
0.017608642578125,
-0.01108551025390625,
0.031524658203125,
-0.0183563232421875,
-0.0031642913818359375,
-0.020843505859375,
-0.0023326873779296875,
0.00597381591796875,
0.00559234619140625,
-0.01198577880859375,
-0.01062774658203125,
0.0251617431640625,
0.01387786865234375,
0.027984619140625,
-0.0150909423828125,
0.0455322265625,
0.0254058837890625,
-0.0006694793701171875,
0.01122283935546875,
0.033111572265625,
0.00001138448715209961,
-0.027923583984375,
-0.00844573974609375,
0.0028209686279296875,
0.007205963134765625,
0.0237884521484375,
0.03826904296875,
-0.01324462890625,
-0.0065460205078125,
-0.0109710693359375,
-0.02154541015625,
-0.0174713134765625,
-0.0289306640625,
-0.008331298828125,
-0.026458740234375,
-0.034820556640625,
0.0089874267578125,
0.033111572265625,
0.0180511474609375,
0.0223236083984375,
-0.006526947021484375,
0.00986480712890625,
-0.018341064453125,
0.0400390625,
-0.0235595703125,
-0.028350830078125,
-0.022705078125,
0.030303955078125,
0.0221099853515625,
0.00516510009765625,
-0.0016813278198242188,
0.0300140380859375,
-0.01654052734375,
0.0167083740234375,
-0.004085540771484375,
0.01003265380859375,
0.0182952880859375,
-0.0250396728515625,
-0.01202392578125,
-0.01160430908203125,
0.0091400146484375,
-0.019317626953125,
0.0267333984375,
-0.0299835205078125,
0.0017566680908203125,
0.032806396484375,
0.00846099853515625,
0.01161956787109375,
0.031951904296875,
0.0004336833953857422,
0.0101776123046875,
-0.01149749755859375,
0.0042877197265625,
0.0162811279296875,
0.02362060546875,
-0.0241851806640625,
-0.014404296875,
-0.019561767578125,
0.061431884765625,
-0.0343017578125,
-0.032989501953125,
-0.01274871826171875,
-0.023101806640625,
0.037109375,
-0.015472412109375,
0.005870819091796875,
-0.027008056640625,
0.021942138671875,
-0.0215606689453125,
-0.0056304931640625,
-0.0311126708984375,
-0.04498291015625,
0.0238189697265625,
0.01355743408203125,
0.02947998046875,
-0.02099609375,
0.042449951171875,
0.00008547306060791016,
0.00812530517578125,
-0.042510986328125,
-0.0127716064453125,
-0.0005335807800292969,
0.0142669677734375,
0.02471923828125,
-0.0208587646484375,
0.009368896484375,
0.021270751953125,
0.033905029296875,
-0.05645751953125,
0.0094146728515625,
0.0272979736328125,
0.022674560546875,
0.0207977294921875,
-0.0027141571044921875,
-0.00988006591796875,
-0.010284423828125,
-0.01178741455078125,
-0.0125885009765625,
0.016693115234375,
0.01751708984375,
0.00275421142578125,
0.0160980224609375,
0.0081634521484375,
0.00913238525390625,
-0.004398345947265625,
0.0016345977783203125,
-0.0294647216796875,
-0.0297088623046875,
-0.019439697265625,
0.01157379150390625,
0.0146484375,
-0.01021575927734375,
0.0155487060546875,
0.0263519287109375,
-0.015869140625,
0.0380859375,
-0.00286102294921875,
-0.0117645263671875,
-0.0023937225341796875,
0.0262451171875,
0.026153564453125,
0.0154876708984375,
-0.0274658203125,
-0.006633758544921875,
0.026519775390625,
-0.0005955696105957031,
0.0025539398193359375,
0.02093505859375,
0.00312042236328125,
-0.005619049072265625,
0.009124755859375,
-0.027679443359375,
0.01096343994140625,
-0.0166778564453125,
-0.0034198760986328125,
-0.0148773193359375,
-0.0157623291015625,
0.0220947265625,
0.018768310546875,
-0.01471710205078125,
0.025970458984375,
-0.003726959228515625,
0.045318603515625,
-0.0184783935546875,
0.01371002197265625,
-0.0214996337890625,
0.0044403076171875,
0.007450103759765625,
-0.023590087890625,
-0.004184722900390625,
-0.0136260986328125,
-0.004100799560546875,
0.000038504600524902344,
0.0019588470458984375,
0.006458282470703125,
-0.01318359375,
0.004283905029296875,
-0.018798828125,
-0.016021728515625,
-0.004261016845703125,
-0.040130615234375,
-0.0008745193481445312,
0.00433349609375,
-0.00989532470703125,
-0.0078277587890625,
0.022308349609375,
0.01113128662109375,
-0.0281524658203125,
0.005340576171875,
-0.0250244140625,
0.0053558349609375,
0.006072998046875,
0.0004799365997314453,
0.01319122314453125,
0.025360107421875,
0.0035419464111328125,
0.032440185546875,
-0.0285797119140625,
-0.0180511474609375,
0.0301055908203125,
0.020416259765625,
-0.025543212890625,
0.017852783203125,
-0.0028400421142578125,
0.005138397216796875,
-0.023162841796875,
-0.024627685546875,
-0.016021728515625,
0.00024211406707763672,
-0.02264404296875,
0.00934600830078125,
-0.033111572265625,
0.0122528076171875,
-0.01593017578125,
0.00885772705078125,
-0.01369476318359375,
0.0009531974792480469,
0.0041046142578125,
-0.004436492919921875,
-0.0301513671875,
-0.007068634033203125,
0.00811004638671875,
0.0019683837890625,
0.0198211669921875,
0.00707244873046875,
0.0037975311279296875,
-0.00365447998046875,
-0.037322998046875,
-0.0290985107421875,
0.0237274169921875,
-0.0252685546875,
0.030853271484375,
-0.0264129638671875,
-0.0211029052734375,
-0.0223236083984375,
-0.006267547607421875,
0.0487060546875,
-0.005985260009765625,
0.00202178955078125,
-0.00628662109375,
0.0141448974609375,
-0.005374908447265625,
0.0203094482421875,
-0.019287109375,
0.0085906982421875,
-0.022796630859375,
-0.00420379638671875,
-0.0007762908935546875,
0.0260467529296875,
-0.008331298828125,
-0.01435089111328125,
0.021240234375,
-0.0341796875,
0.0209808349609375,
0.00714874267578125,
-0.03704833984375,
0.0218505859375,
-0.0103912353515625,
-0.01024627685546875,
-0.0226287841796875,
0.0033931732177734375,
-0.01055908203125,
-0.016937255859375,
-0.00970458984375,
-0.00012052059173583984,
0.0264129638671875,
-0.018463134765625,
-0.0172576904296875,
0.00830078125,
-0.0027008056640625,
-0.00623321533203125,
-0.0026721954345703125,
0.0026988983154296875,
-0.0035839080810546875,
0.005706787109375,
0.0018358230590820312,
0.02130126953125,
0.0200347900390625,
-0.03741455078125,
0.022552490234375,
0.00923919677734375,
-0.0096282958984375,
0.051971435546875,
0.03717041015625,
0.0097808837890625,
-0.03216552734375,
-0.048492431640625,
-0.0295257568359375,
-0.01015472412109375,
-0.006114959716796875,
0.032745361328125,
0.01123046875,
-0.01043701171875,
-0.04278564453125,
-0.035614013671875,
0.0032958984375,
0.03326416015625,
0.0038661956787109375,
-0.00846099853515625,
-0.016845703125,
0.006015777587890625,
-0.024017333984375,
0.023773193359375,
0.00711822509765625,
0.04058837890625,
0.00531005859375,
0.004505157470703125,
0.031463623046875,
0.00026416778564453125,
-0.00733184814453125,
-0.01036834716796875,
0.0017948150634765625,
0.023529052734375,
0.01129150390625,
-0.04632568359375,
-0.010162353515625,
0.01580810546875,
-0.0203704833984375,
-0.0102386474609375,
0.00753021240234375,
-0.004047393798828125,
-0.01029205322265625,
0.01467132568359375,
0.03521728515625,
-0.040374755859375,
-0.015411376953125,
-0.0238037109375,
-0.025360107421875,
0.00673675537109375,
0.00795745849609375,
-0.00860595703125,
0.0007009506225585938,
-0.01125335693359375,
0.006931304931640625,
-0.0091400146484375,
-0.022308349609375,
-0.00399017333984375,
0.004528045654296875,
-0.01003265380859375,
-0.02923583984375,
0.02142333984375,
-0.0104217529296875,
-0.00823211669921875,
-0.011260986328125,
0.0046844482421875,
0.0206756591796875,
0.004718780517578125,
0.0294189453125,
-0.00864410400390625,
-0.047149658203125,
-0.0178985595703125,
-0.0013608932495117188,
-0.0218353271484375,
0.0013151168823242188,
-0.01500701904296875,
-0.036346435546875,
0.0235137939453125,
0.00804901123046875,
-0.0137481689453125,
0.037109375,
0.028045654296875,
0.0006914138793945312,
0.0399169921875,
-0.00925445556640625,
0.01348876953125,
0.0034389495849609375,
0.02276611328125,
0.0018262863159179688,
0.0100250244140625,
0.0106048583984375,
0.0167236328125,
-0.041900634765625,
-0.024200439453125,
0.030181884765625,
0.007282257080078125,
-0.0214691162109375,
-0.0091400146484375,
0.0128631591796875,
-0.00395965576171875,
-0.034576416015625,
0.00301361083984375,
-0.0291900634765625,
-0.013153076171875,
0.0246429443359375,
0.004695892333984375,
-0.0124359130859375,
-0.004688262939453125,
-0.00386810302734375,
-0.0183868408203125,
-0.0175628662109375,
0.00946807861328125,
-0.0159759521484375,
0.014739990234375,
0.021209716796875,
0.0239410400390625,
-0.0003616809844970703,
-0.0012006759643554688,
0.00789642333984375,
0.01934814453125,
-0.00011026859283447266,
-0.007518768310546875,
-0.005184173583984375,
0.016845703125,
-0.005039215087890625,
-0.0126800537109375,
-0.022613525390625,
-0.0038299560546875,
0.00971221923828125,
-0.0126800537109375,
-0.0011396408081054688,
-0.02960205078125,
0.0169525146484375,
0.031494140625,
0.035400390625,
-0.004474639892578125,
-0.00951385498046875,
-0.00492095947265625,
-0.00875091552734375,
0.01087188720703125,
-0.0166168212890625,
0.0130462646484375,
0.0116424560546875,
-0.0419921875,
-0.01000213623046875,
-0.01342010498046875,
0.0008592605590820312,
-0.0165863037109375,
-0.031829833984375,
0.01200103759765625,
-0.007236480712890625,
-0.006214141845703125,
-0.00940704345703125,
-0.006954193115234375,
-0.00966644287109375,
-0.01020050048828125,
-0.0011959075927734375,
-0.00473785400390625,
-0.0100860595703125,
-0.0106201171875,
0.004581451416015625,
-0.01499176025390625,
-0.00853729248046875,
0.0126495361328125,
0.0242919921875,
-0.02130126953125,
-0.0032444000244140625,
0.0037403106689453125,
0.006298065185546875,
0.0021114349365234375,
-0.0021877288818359375,
-0.0042877197265625,
0.04791259765625,
-0.003803253173828125,
-0.00923919677734375,
-0.01739501953125,
0.02764892578125,
-0.00589752197265625,
0.01473236083984375,
-0.01174163818359375,
0.005992889404296875,
-0.0005502700805664062,
0.01526641845703125,
-0.0059051513671875,
0.0201873779296875,
0.004482269287109375,
0.00809478759765625,
-0.0279083251953125,
0.006927490234375,
-0.033172607421875,
-0.0228424072265625,
0.005313873291015625,
0.00749969482421875,
0.0015192031860351562,
0.043426513671875,
-0.020660400390625,
-0.0115509033203125,
-0.00015473365783691406,
0.006977081298828125,
-0.0005931854248046875,
0.024383544921875,
-0.0091094970703125,
0.007808685302734375,
-0.0031108856201171875,
-0.019287109375,
-0.0005660057067871094,
0.0247039794921875,
-0.0191650390625,
-0.0254974365234375,
-0.0333251953125,
-0.006412506103515625,
-0.004299163818359375,
-0.002521514892578125,
-0.0033702850341796875,
0.0164337158203125,
-0.04864501953125,
0.006072998046875,
0.0038433074951171875,
0.00739288330078125,
-0.0021076202392578125,
-0.0084228515625,
-0.046600341796875,
-0.01389312744140625,
0.0106353759765625,
0.0178985595703125,
0.00217437744140625,
-0.041656494140625,
-0.00830078125,
0.0008707046508789062,
-0.029571533203125,
0.0178375244140625,
-0.007160186767578125,
0.005031585693359375,
-0.01126861572265625,
0.001922607421875,
-0.045074462890625,
0.0055389404296875,
0.0012140274047851562,
-0.00754547119140625,
-0.0009832382202148438,
-0.0060882568359375,
-0.007053375244140625,
-0.0097808837890625,
0.03497314453125,
0.0015611648559570312,
0.016143798828125,
-0.02154541015625,
0.000980377197265625,
0.042510986328125,
-0.005908966064453125,
-0.030303955078125,
-0.00501251220703125,
-0.019622802734375,
0.0341796875,
0.0190582275390625,
-0.01873779296875,
0.0023441314697265625,
0.00978851318359375,
0.00012826919555664062,
0.0300750732421875,
-0.01503753662109375,
0.00003981590270996094,
0.00971221923828125,
-0.00003337860107421875,
-0.00952911376953125,
-0.023040771484375,
-0.03839111328125,
0.0066070556640625,
0.0174407958984375,
-0.0103302001953125,
-0.03729248046875,
0.005840301513671875,
-0.0155181884765625,
-0.0035152435302734375,
-0.00391387939453125,
-0.0023403167724609375,
0.0138092041015625,
-0.0030422210693359375,
0.049072265625,
0.016815185546875,
0.00921630859375,
0.013031005859375,
-0.022705078125,
-0.01203155517578125,
-0.01515960693359375,
0.0170135498046875,
0.01264190673828125,
0.004547119140625,
-0.008148193359375,
-0.0245208740234375,
0.0198516845703125,
0.0014925003051757812,
-0.01197052001953125,
0.024658203125,
0.022552490234375,
-0.023712158203125,
0.0016269683837890625,
0.0295562744140625,
0.011932373046875,
0.0018310546875,
-0.001434326171875,
0.01055908203125,
0.02850341796875,
-0.0091400146484375,
0.003971099853515625,
0.00615692138671875,
-0.00620269775390625,
0.019134521484375,
0.006305694580078125,
0.011260986328125,
0.00411224365234375,
-0.0212860107421875,
0.01024627685546875,
0.040252685546875,
0.0188446044921875,
0.0206146240234375,
-0.0045928955078125,
0.025970458984375,
-0.0311737060546875,
0.0164337158203125,
-0.014068603515625,
0.042236328125,
-0.01568603515625,
-0.00402069091796875,
0.004840850830078125,
-0.018890380859375,
-0.0182647705078125,
-0.01529693603515625,
0.0099334716796875,
0.01444244384765625,
0.00989532470703125,
-0.006999969482421875,
0.002948760986328125,
-0.00244140625,
-0.01433563232421875,
-0.0026264190673828125,
0.01001739501953125,
-0.01003265380859375,
0.005889892578125,
0.003814697265625,
0.0032405853271484375,
0.0181884765625,
0.0193634033203125,
0.00797271728515625,
-0.005214691162109375,
0.03094482421875,
0.0137786865234375,
0.060302734375,
0.0284881591796875,
-0.006313323974609375,
0.032440185546875,
0.0079193115234375,
-0.01092529296875,
0.007709503173828125,
0.0389404296875,
0.015777587890625,
0.011962890625,
-0.023468017578125,
-0.0110626220703125,
-0.022918701171875,
-0.012176513671875,
0.0014734268188476562,
-0.011474609375,
0.0204010009765625,
-0.0435791015625,
-0.011871337890625,
-0.00618743896484375,
0.01384735107421875,
-0.007411956787109375,
0.01027679443359375,
0.015533447265625,
-0.01540374755859375,
-0.0122833251953125,
-0.004047393798828125,
-0.043975830078125,
0.0093994140625,
-0.0218658447265625,
0.005916595458984375,
0.01248931884765625,
-0.0152435302734375,
0.0039005279541015625,
0.0204315185546875,
0.0325927734375,
-0.00843048095703125,
-0.0092315673828125,
-0.005611419677734375,
-0.0163726806640625,
0.017669677734375,
0.00603485107421875,
0.02667236328125,
-0.0261993408203125,
0.03924560546875,
0.0172271728515625,
0.02166748046875,
-0.0188140869140625,
0.021484375,
-0.04986572265625,
0.0177001953125,
-0.028076171875,
-0.00887298583984375,
-0.0080108642578125,
0.0036144256591796875,
0.0238800048828125,
0.01739501953125,
-0.029205322265625,
-0.004795074462890625,
0.0149078369140625,
-0.0253143310546875,
-0.0299530029296875,
0.0022144317626953125,
0.021026611328125,
-0.0246734619140625,
0.005496978759765625,
0.01593017578125,
-0.03765869140625,
-0.0206146240234375,
-0.00579833984375,
-0.0085296630859375,
0.01030731201171875,
0.006427764892578125,
0.04364013671875,
0.01837158203125,
-0.01049041748046875,
-0.0092926025390625,
0.0094757080078125,
0.047698974609375,
0.0048675537109375,
0.003253936767578125,
-0.03253173828125,
0.017120361328125,
0.027374267578125,
-0.035552978515625,
-0.01134490966796875,
-0.0226593017578125,
-0.01184844970703125,
0.0016565322875976562,
-0.008514404296875,
0.021240234375,
0.003376007080078125,
0.009674072265625,
0.01216888427734375,
0.00555419921875,
-0.006366729736328125,
0.0330810546875,
0.00899505615234375,
0.004009246826171875,
0.0228424072265625,
0.017913818359375,
-0.0182647705078125,
-0.0222015380859375,
-0.041900634765625,
0.029998779296875,
-0.03411865234375,
-0.0020847320556640625,
0.0079193115234375,
0.0129852294921875,
-0.00743865966796875,
0.003635406494140625,
0.022979736328125,
0.033447265625,
-0.01175689697265625,
-0.0006966590881347656,
-0.00543975830078125,
-0.03448486328125,
0.03485107421875,
-0.016357421875,
0.00836181640625,
-0.0016117095947265625,
-0.00200653076171875,
-0.00838470458984375,
-0.00864410400390625,
0.01114654541015625,
0.03167724609375,
0.004077911376953125,
0.0098724365234375,
-0.019073486328125,
-0.032989501953125,
0.0054168701171875,
0.0182342529296875,
0.01080322265625,
0.033111572265625,
-0.02435302734375,
0.031463623046875,
0.0228271484375,
-0.01154327392578125,
0.025634765625,
-0.0169219970703125,
-0.027679443359375,
0.006664276123046875,
0.0096893310546875,
0.00707244873046875,
-0.0152740478515625,
0.006839752197265625,
-0.0335693359375,
-0.039947509765625,
-0.01470184326171875,
-0.0149688720703125,
-0.01367950439453125,
0.0237579345703125,
-0.022491455078125,
0.033294677734375,
0.0276031494140625,
0.018798828125,
0.009063720703125,
0.005565643310546875,
0.023193359375,
0.011566162109375,
-0.015869140625,
-0.01412200927734375,
0.00738525390625,
0.008819580078125,
0.0313720703125,
0.01010894775390625,
0.0011796951293945312,
-0.02325439453125,
0.01136016845703125,
-0.005340576171875,
0.0015411376953125,
0.01025390625,
0.01110076904296875,
-0.007061004638671875,
-0.036102294921875,
-0.015869140625,
0.00455474853515625,
-0.019195556640625,
0.01548004150390625,
0.00421142578125,
0.0028533935546875,
0.0210418701171875,
-0.006984710693359375,
0.00009113550186157227,
0.01593017578125,
-0.0162200927734375,
0.005584716796875,
0.03778076171875,
0.021209716796875,
-0.0188140869140625,
-0.010711669921875,
-0.0176849365234375,
-0.0026702880859375,
0.00458526611328125,
0.01375579833984375,
0.0311126708984375,
-0.006923675537109375,
-0.0232391357421875,
0.0033664703369140625,
-0.032623291015625,
-0.0073699951171875,
-0.0275115966796875,
-0.0008306503295898438,
0.00992584228515625,
0.027252197265625,
-0.016632080078125,
-0.023193359375,
-0.0079193115234375,
-0.029754638671875,
0.03875732421875,
-0.04913330078125,
-0.006359100341796875,
0.042633056640625,
0.00495147705078125,
0.003265380859375,
-0.030548095703125,
-0.015625,
-0.012603759765625,
0.026214599609375,
0.007843017578125,
-0.0099029541015625,
-0.005054473876953125,
0.0099029541015625,
0.02911376953125,
0.0258026123046875,
-0.0294189453125,
0.0231170654296875,
0.0200347900390625,
0.006343841552734375,
-0.00617218017578125,
0.0240325927734375,
-0.005645751953125,
-0.0126800537109375,
-0.0240325927734375,
-0.005062103271484375,
0.01349639892578125,
0.0003185272216796875,
-0.0085906982421875,
-0.0014638900756835938,
-0.0100555419921875,
0.00848388671875,
-0.0007166862487792969,
0.01190948486328125,
0.0077667236328125,
-0.056182861328125,
0.01409149169921875,
0.02484130859375,
-0.0242919921875,
0.019287109375,
-0.02783203125,
-0.0013494491577148438,
-0.0224761962890625,
-0.004436492919921875,
0.00424957275390625,
-0.0151824951171875,
-0.0136566162109375,
-0.026153564453125,
-0.004032135009765625,
-0.00815582275390625,
-0.015472412109375,
-0.0218353271484375,
0.00986480712890625,
0.01526641845703125,
-0.01055145263671875,
0.043243408203125,
-0.005153656005859375,
0.051116943359375,
-0.00604248046875,
-0.00452423095703125,
-0.011962890625,
0.0401611328125,
-0.020721435546875,
0.0149383544921875,
0.005039215087890625,
0.0131683349609375,
0.01515960693359375,
0.0038509368896484375,
0.0101470947265625,
-0.007259368896484375,
-0.0399169921875,
0.01568603515625,
-0.016632080078125,
0.0019521713256835938,
0.002521514892578125,
0.016510009765625,
-0.0126953125,
-0.020233154296875,
-0.0174560546875,
0.0521240234375,
-0.00522613525390625,
-0.0167083740234375,
-0.0226593017578125,
-0.0089263916015625,
-0.0111236572265625,
0.004764556884765625,
-0.00931549072265625,
0.0094451904296875,
-0.01210784912109375,
0.03900146484375,
0.0089569091796875,
0.0189666748046875,
0.0288238525390625,
-0.0126953125,
0.0084991455078125,
-0.0160369873046875,
0.01971435546875,
0.0003142356872558594,
0.035186767578125,
0.038299560546875,
0.0257720947265625,
-0.0394287109375,
0.0253753662109375,
-0.036712646484375,
0.0310821533203125,
-0.01568603515625,
0.005794525146484375,
-0.0193634033203125,
0.00730133056640625,
0.00809478759765625,
-0.018463134765625,
0.005069732666015625,
-0.029541015625,
0.00047588348388671875,
0.0015611648559570312,
-0.026123046875,
0.0266571044921875,
-0.027587890625,
-0.00807952880859375,
0.00724029541015625,
0.00945281982421875,
0.01849365234375,
0.0021266937255859375,
-0.01251983642578125,
-0.037322998046875,
-0.0222930908203125,
-0.0144805908203125,
-0.00884246826171875,
-0.03289794921875,
0.0016632080078125,
-0.0243377685546875,
0.023101806640625,
0.019775390625,
-0.022125244140625,
0.020355224609375,
-0.017974853515625,
-0.01169586181640625,
-0.04217529296875,
-0.0304412841796875,
-0.004741668701171875,
-0.013092041015625,
-0.00040650367736816406,
-0.0138397216796875,
-0.0462646484375,
0.005756378173828125,
0.00778961181640625,
-0.010833740234375,
0.01543426513671875,
-0.00785064697265625,
-0.004608154296875,
0.0019855499267578125,
0.0290069580078125,
0.0066680908203125,
-0.0076141357421875,
0.0015544891357421875,
0.0262298583984375,
-0.00838470458984375,
-0.02880859375,
0.0219879150390625,
-0.0498046875,
0.0195770263671875,
0.0164794921875,
0.0022830963134765625,
0.0075225830078125,
0.02178955078125,
-0.007755279541015625,
-0.023590087890625,
0.00441741943359375,
-0.00495147705078125,
0.032562255859375,
0.0165863037109375,
0.032379150390625,
0.01702880859375,
0.00978851318359375,
0.032501220703125,
0.0240325927734375,
0.0333251953125,
-0.007293701171875,
0.006805419921875,
0.01019287109375,
-0.00711822509765625,
-0.006732940673828125,
-0.02001953125,
-0.036285400390625,
-0.0028820037841796875,
-0.020416259765625,
0.0278167724609375,
0.020660400390625,
-0.0175323486328125,
0.007778167724609375,
-0.03680419921875,
-0.037261962890625,
0.0010557174682617188,
0.01364898681640625,
-0.055267333984375,
0.00072479248046875,
-0.005519866943359375,
-0.0174407958984375,
-0.01422882080078125,
0.02435302734375,
-0.0189361572265625,
-0.0205841064453125,
-0.00447845458984375,
-0.024261474609375,
0.01189422607421875,
0.00609588623046875,
0.0413818359375,
0.027008056640625,
0.007801055908203125,
-0.0159912109375,
-0.0032596588134765625,
0.03338623046875,
0.0153656005859375,
0.014739990234375,
0.01690673828125,
-0.03485107421875,
0.01139068603515625,
-0.0012769699096679688,
0.0180206298828125,
0.005626678466796875,
0.041046142578125,
0.00943756103515625,
-0.01213836669921875,
0.0234527587890625,
-0.0089263916015625,
0.02618408203125,
-0.025390625,
0.0271759033203125,
-0.0283050537109375,
0.0031681060791015625,
0.004085540771484375,
0.00951385498046875,
-0.01380157470703125,
0.0026035308837890625,
0.024658203125,
-0.005939483642578125,
0.022735595703125,
0.016448974609375,
0.01568603515625,
0.01236724853515625,
0.0007548332214355469,
-0.00792694091796875,
0.0122528076171875,
-0.002960205078125,
0.0009374618530273438,
-0.0234375,
0.010284423828125,
0.0011196136474609375,
0.0125885009765625,
-0.0038814544677734375,
0.0231781005859375,
0.0269317626953125,
-0.007381439208984375,
0.009429931640625,
-0.0246429443359375,
-0.0238189697265625,
-0.0251922607421875,
0.0010280609130859375,
0.030120849609375,
-0.0016498565673828125,
-0.018096923828125,
0.0033111572265625,
0.02825927734375,
-0.00028252601623535156,
-0.029449462890625,
0.0017385482788085938,
-0.0036678314208984375,
0.0104217529296875,
0.0094757080078125,
0.005023956298828125,
0.01239776611328125,
0.024017333984375,
0.0161285400390625,
0.01122283935546875,
0.0090484619140625,
0.0147552490234375,
-0.0186614990234375,
0.0164794921875,
0.0306549072265625,
-0.0009255409240722656,
-0.004566192626953125,
0.004749298095703125,
-0.0033359527587890625,
0.004489898681640625,
-0.01904296875,
-0.00167083740234375,
0.0264434814453125,
-0.0112457275390625,
-0.005367279052734375,
0.0228118896484375,
-0.00984954833984375,
-0.038421630859375,
0.00385284423828125,
0.0011930465698242188,
0.018218994140625,
0.0008869171142578125,
0.02581787109375,
-0.0215911865234375,
-0.0255279541015625,
0.003208160400390625,
-0.006114959716796875,
0.0128631591796875,
-0.003612518310546875,
0.0008916854858398438,
0.0034732818603515625,
0.00506591796875,
0.020660400390625,
-0.029571533203125,
0.01392364501953125,
-0.0029697418212890625,
0.05218505859375,
-0.024383544921875,
0.0211944580078125,
0.0233001708984375,
-0.009796142578125,
-0.01454925537109375,
0.010986328125,
-0.0009198188781738281,
0.0335693359375,
-0.0089874267578125,
0.0271148681640625,
0.01172637939453125,
0.03399658203125,
-0.00891876220703125,
-0.007045745849609375,
0.0634765625,
-0.01160430908203125,
0.018798828125,
0.007232666015625,
-0.0297088623046875,
0.03424072265625,
-0.004154205322265625,
-0.0262908935546875,
0.0200042724609375,
-0.0173492431640625,
0.005931854248046875,
-0.004886627197265625,
-0.01438140869140625,
-0.00981903076171875,
-0.0194091796875,
-0.01485443115234375,
0.029876708984375,
0.01483917236328125,
0.005840301513671875,
0.00528717041015625,
0.0151214599609375,
-0.02032470703125,
0.006351470947265625,
-0.03936767578125,
0.0096893310546875,
-0.0011386871337890625,
-0.00002962350845336914,
-0.00514984130859375,
-0.014678955078125,
0.01303863525390625,
0.0308685302734375,
-0.039398193359375,
0.00785064697265625,
-0.00568389892578125,
0.00550079345703125,
-0.019439697265625,
0.023040771484375,
0.0121002197265625,
-0.01161956787109375,
0.03515625,
-0.023406982421875,
0.002101898193359375,
0.006465911865234375,
-0.0010223388671875,
0.0101165771484375,
0.032257080078125,
0.0002422332763671875,
-0.0267333984375,
0.016510009765625,
-0.0225830078125,
-0.013275146484375,
-0.01031494140625,
-0.022735595703125,
-0.0233306884765625,
-0.0037631988525390625,
-0.02569580078125,
-0.03448486328125,
0.0181732177734375,
-0.007648468017578125,
-0.01206207275390625,
0.045440673828125,
-0.037017822265625,
0.037567138671875,
0.0235595703125,
-0.002899169921875,
0.01715087890625,
0.0018444061279296875,
-0.01108551025390625,
-0.0160369873046875,
-0.006626129150390625,
0.0142822265625,
0.004978179931640625,
-0.005313873291015625,
0.0253448486328125,
-0.001392364501953125,
0.026763916015625,
-0.01953125,
-0.00162506103515625,
0.01091766357421875,
0.00885009765625,
0.0082550048828125,
0.0129241943359375,
-0.038787841796875,
-0.0262451171875,
-0.01555633544921875,
0.0011892318725585938,
0.029815673828125,
0.0308990478515625,
0.0296478271484375,
-0.03338623046875,
0.006099700927734375,
-0.033294677734375,
0.005496978759765625,
0.03363037109375,
0.025238037109375,
0.01422882080078125,
-0.0303192138671875,
-0.0157012939453125,
-0.0208892822265625,
-0.01540374755859375,
0.003650665283203125,
0.004711151123046875,
-0.007122039794921875,
0.01348876953125,
0.03509521484375,
-0.01517486572265625,
-0.005130767822265625,
-0.00653076171875,
0.0189056396484375,
0.0146942138671875,
0.036773681640625,
-0.02032470703125,
-0.01194000244140625,
0.01044464111328125,
0.0133514404296875,
-0.00746917724609375,
0.004241943359375,
-0.00897979736328125,
0.0147247314453125,
0.00836944580078125,
-0.0291748046875,
-0.017669677734375,
-0.0075225830078125,
0.0118255615234375,
-0.0159149169921875,
-0.000019848346710205078,
0.0059814453125,
0.01216888427734375,
0.01226806640625,
-0.0061187744140625,
0.0255889892578125,
-0.01229095458984375,
-0.0223846435546875,
0.0105133056640625,
0.0086212158203125,
-0.0161285400390625,
0.0006585121154785156,
0.0182952880859375,
-0.00044226646423339844,
-0.009063720703125,
-0.0007181167602539062,
0.008758544921875,
0.0017423629760742188,
-0.01384735107421875,
-0.00428009033203125,
-0.002948760986328125,
0.0110931396484375,
-0.00115203857421875,
0.0273895263671875,
0.0238037109375,
0.011993408203125,
0.00714874267578125,
0.002887725830078125,
-0.0234527587890625,
-0.04010009765625,
-0.02178955078125,
0.000911712646484375,
0.020843505859375,
0.0152740478515625,
-0.00830078125,
-0.035491943359375,
0.00736236572265625,
-0.0023288726806640625,
-0.02606201171875,
0.007640838623046875,
-0.006519317626953125,
0.020294189453125,
0.020263671875,
-0.0026760101318359375,
-0.0159454345703125,
0.006183624267578125,
-0.0122833251953125,
-0.0011348724365234375,
0.0015287399291992188,
-0.00939178466796875,
-0.008056640625,
0.00033092498779296875,
0.0036163330078125,
-0.00826263427734375,
0.005615234375,
-0.02374267578125,
0.021942138671875,
0.00490570068359375,
-0.0157623291015625,
0.004756927490234375,
0.01971435546875,
-0.0011053085327148438,
-0.0280609130859375,
0.0023345947265625,
-0.00841522216796875,
-0.00324249267578125,
0.016571044921875,
-0.010284423828125,
0.031982421875,
-0.007640838623046875,
0.01413726806640625,
-0.0022411346435546875,
-0.01085662841796875,
-0.0276336669921875,
0.006381988525390625,
0.0083465576171875,
-0.00785064697265625,
0.0121002197265625,
-0.00933074951171875,
-0.013092041015625,
-0.038177490234375,
-0.021026611328125,
-0.00812530517578125,
-0.018890380859375,
-0.0312347412109375,
0.0026035308837890625,
-0.034271240234375,
-0.01253509521484375,
0.028289794921875,
-0.00885772705078125,
0.0140228271484375,
-0.003726959228515625,
-0.0007262229919433594,
-0.0188140869140625,
0.04608154296875,
-0.0189666748046875,
-0.0195465087890625,
-0.0115966796875,
0.00006151199340820312,
0.01525115966796875,
0.01137542724609375,
-0.01494598388671875,
0.01367950439453125,
0.01258087158203125,
0.0127105712890625,
0.027069091796875,
-0.0233917236328125,
-0.00412750244140625,
0.0173492431640625,
0.0244598388671875,
-0.0031566619873046875,
-0.01061248779296875,
0.0196990966796875,
0.0146942138671875,
0.025634765625,
0.030670166015625,
-0.0007472038269042969,
0.005489349365234375,
0.01551055908203125,
-0.0183563232421875,
-0.028778076171875,
0.00960540771484375,
0.001735687255859375,
0.0189208984375,
0.0303955078125,
0.02130126953125,
0.004383087158203125,
0.016143798828125,
-0.0027828216552734375,
0.00962066650390625,
0.0177001953125,
-0.00868988037109375,
-0.01107025146484375,
-0.02252197265625,
0.0182647705078125,
0.0093841552734375,
-0.03277587890625,
0.0127716064453125,
-0.025299072265625,
0.0090179443359375,
0.00914764404296875,
-0.007221221923828125,
-0.00644683837890625,
0.01593017578125,
0.00360870361328125,
-0.0198516845703125,
-0.0103912353515625,
0.0195465087890625,
0.01430511474609375,
-0.0243682861328125,
0.02764892578125,
0.0298004150390625,
-0.042388916015625,
-0.0012769699096679688,
0.01165008544921875,
-0.0228424072265625,
0.0261688232421875,
-0.004474639892578125,
-0.01470947265625,
0.009796142578125,
0.01885986328125,
-0.0250701904296875,
-0.00283050537109375,
0.0374755859375,
-0.0015382766723632812,
0.009552001953125,
-0.0198211669921875,
-0.01904296875,
-0.01534271240234375,
0.021636962890625,
-0.006084442138671875,
-0.007259368896484375,
-0.0116729736328125,
0.01494598388671875,
-0.02984619140625,
0.006866455078125,
0.0011272430419921875,
0.01137542724609375,
0.006099700927734375,
-0.00620269775390625,
0.03228759765625,
0.01715087890625,
-0.00934600830078125,
0.0211639404296875,
-0.034271240234375,
-0.0230865478515625,
0.018951416015625,
0.0151519775390625,
-0.0292205810546875,
-0.0293426513671875,
-0.043975830078125,
0.0294952392578125,
0.004772186279296875,
-0.0311737060546875,
-0.00785064697265625,
0.0178985595703125,
-0.00794219970703125,
0.0197296142578125,
0.001262664794921875,
-0.01531219482421875,
-0.0034198760986328125,
0.0386962890625,
0.016326904296875,
0.02838134765625,
0.01175689697265625,
0.015960693359375,
0.01169586181640625,
0.00010895729064941406,
-0.03411865234375,
-0.022064208984375,
0.027252197265625,
-0.01476287841796875,
0.02001953125,
-0.0300750732421875,
-0.0254974365234375,
-0.0452880859375,
0.0246734619140625,
-0.0095062255859375,
-0.00446319580078125,
-0.0238800048828125,
-0.01207733154296875,
-0.006744384765625,
-0.018035888671875,
0.027587890625,
0.0010652542114257812,
-0.0207366943359375,
0.038330078125,
0.02679443359375,
0.005924224853515625,
-0.030670166015625,
0.034942626953125,
-0.0132293701171875,
-0.0285797119140625,
0.0219268798828125,
-0.020965576171875,
-0.0250244140625,
-0.0215301513671875,
-0.024627685546875,
-0.0080108642578125,
0.006305694580078125,
0.01110076904296875,
-0.0496826171875,
-0.01490020751953125,
0.00031065940856933594,
-0.0290069580078125,
0.01146697998046875,
0.005889892578125,
-0.01788330078125,
0.0004239082336425781,
0.00493621826171875,
0.015594482421875,
-0.0027942657470703125,
-0.0013294219970703125,
-0.0293731689453125,
-0.016937255859375,
0.0033702850341796875,
-0.03558349609375,
-0.005985260009765625,
0.017303466796875,
0.0141448974609375,
0.0322265625,
-0.0159759521484375,
0.019256591796875,
0.0218505859375,
0.009918212890625,
-0.0245819091796875,
0.018402099609375,
-0.0253753662109375,
0.01216888427734375,
0.0105743408203125,
-0.0408935546875,
-0.0128326416015625,
0.036224365234375,
-0.004718780517578125,
0.025970458984375,
-0.0117340087890625,
-0.0251922607421875,
-0.013214111328125,
0.0210113525390625,
-0.0259857177734375,
-0.0028228759765625,
0.0084228515625,
-0.0004208087921142578,
0.0313720703125
] |
ours_484
|
Call a pair of stations $(i, j)$ bad if there are no passengers going from station $i$ to $j$. First, we consider the least number of passengers that are on the bus between station $1009$ and $1010$. Suppose that there is $i \leq 1009$ and $j \geq 1010$ such that $(i, j)$ is bad, then by the problem statement all such bad $\left(i^{\prime}, j^{\prime}\right)$ must have $i^{\prime}=i$ or $j^{\prime}=j$ or the good group $i, i^{\prime}, j, j^{\prime}$ violates the condition. Moreover, not both $i^{\prime}=i$ and $j^{\prime}=j$ can happen for the two different bad pairs because they will again form a good group that violates the condition. This means that all such bad pairs have the same $i$ or all have the same $j$, meaning that there are at most $1009$ bad pairs. This means that the number of passengers on the bus must be at least $1009^{2}-1009=1017072$.
We now show that $N=1017072$ is possible. Suppose that for each pair $(i, j)$ such that $1 \leq i<j \leq 2017$, there is a passenger from station $i$ to $j$. Then on the trip from station $s$ to $s+1(s=1,2, \ldots, 2017)$, there will be $s(2017-s) \leq 1008 \cdot 1009=N$ passengers on the bus, so the bus can carry all of them.
\(\boxed{1017072}\)
|
1017072
|
{
"competition": "us_comps",
"dataset": "Ours",
"posts": null,
"source": "OMOFall18Solns.md"
}
|
On Lineland there are $2018$ bus stations numbered $1$ through $2018$ from left to right. A self-driving bus that can carry at most $N$ passengers starts from station $1$ and drives all the way to station $2018$, while making a stop at each bus station. Each passenger that gets on the bus at station $i$ will get off at station $j$ for some $j>i$ (the value of $j$ may vary over different passengers). Call any group of four distinct stations $i_{1}, i_{2}, j_{1}, j_{2}$ with $i_{u}<j_{v}$ for all $u, v \in\{1,2\}$ a good group. Suppose that in any good group $i_{1}, i_{2}, j_{1}, j_{2}$, there is a passenger who boards at station $i_{1}$ and de-boards at station $j_{1}$, or there is a passenger who boards at station $i_{2}$ and de-boards at station $j_{2}$, or both scenarios occur. Compute the minimum possible value of $N$.
|
[
"/Mathematics/DiscreteMathematics/Combinatorics/CombinatorialOptimization",
"/Mathematics/DiscreteMathematics/Combinatorics/GeneralCombinatorics",
"/Mathematics/DiscreteMathematics/GeneralDiscreteMathematics/DiscreteMath",
"/Mathematics/DiscreteMathematics/GeneralDiscreteMathematics/DiscreteMathematics"
] |
All missing origin‑destination pairs must share a common station, limiting their number to at most 1009 and giving the lower bound on the bus capacity.
|
[
0.00021028518676757812,
-0.024749755859375,
-0.0010013580322265625,
0.00754547119140625,
0.0008311271667480469,
0.019989013671875,
0.0321044921875,
-0.02703857421875,
0.0162811279296875,
-0.040008544921875,
0.052154541015625,
-0.020294189453125,
0.00615692138671875,
-0.0003597736358642578,
-0.004604339599609375,
0.0160064697265625,
0.040618896484375,
0.020294189453125,
-0.008026123046875,
-0.0027828216552734375,
-0.01507568359375,
-0.0030269622802734375,
-0.0085601806640625,
0.0212554931640625,
-0.01342010498046875,
-0.04718017578125,
-0.025787353515625,
0.010009765625,
-0.0023860931396484375,
-0.042205810546875,
-0.0638427734375,
-0.005596160888671875,
-0.0008473396301269531,
-0.0360107421875,
0.0022449493408203125,
0.016571044921875,
-0.0091400146484375,
-0.0026569366455078125,
-0.0171051025390625,
-0.0089263916015625,
-0.005580902099609375,
-0.0137786865234375,
0.0183563232421875,
0.0018358230590820312,
-0.01483154296875,
0.0180511474609375,
0.008392333984375,
0.00667572021484375,
-0.006069183349609375,
-0.0099639892578125,
-0.0007271766662597656,
0.0034885406494140625,
0.0041656494140625,
-0.006458282470703125,
-0.03387451171875,
-0.07110595703125,
-0.006801605224609375,
-0.0001647472381591797,
0.002758026123046875,
0.002960205078125,
0.003993988037109375,
-0.016021728515625,
0.03240966796875,
-0.004177093505859375,
-0.0028591156005859375,
-0.0037479400634765625,
0.006435394287109375,
0.035430908203125,
0.009063720703125,
-0.028900146484375,
-0.030670166015625,
-0.0217132568359375,
-0.03546142578125,
0.0120391845703125,
0.00860595703125,
-0.0269775390625,
-0.00858306884765625,
-0.00046372413635253906,
-0.0181884765625,
-0.0142059326171875,
0.02777099609375,
0.0150909423828125,
0.0025959014892578125,
-0.006622314453125,
0.0003676414489746094,
0.0254058837890625,
0.01275634765625,
-0.01183319091796875,
0.0026416778564453125,
-0.00991058349609375,
-0.009979248046875,
-0.011474609375,
0.0132293701171875,
-0.01265716552734375,
-0.005893707275390625,
-0.001285552978515625,
-0.0059661865234375,
-0.0201568603515625,
-0.00621795654296875,
0.00702667236328125,
-0.0041961669921875,
0.0128021240234375,
0.030487060546875,
0.0040740966796875,
-0.04278564453125,
-0.015869140625,
-0.016693115234375,
-0.003681182861328125,
-0.028045654296875,
0.005374908447265625,
0.007080078125,
-0.0084075927734375,
0.035919189453125,
-0.0011072158813476562,
-0.0204315185546875,
-0.0030117034912109375,
-0.0103759765625,
-0.0082550048828125,
0.00710296630859375,
0.0146636962890625,
0.0036907196044921875,
0.0222320556640625,
0.007167816162109375,
0.00684356689453125,
0.0065155029296875,
-0.0242156982421875,
0.0093841552734375,
-0.0119171142578125,
0.00844573974609375,
0.0159759521484375,
-0.004093170166015625,
0.006748199462890625,
-0.038848876953125,
-0.004169464111328125,
-0.0295562744140625,
-0.006359100341796875,
0.00272369384765625,
-0.00811767578125,
0.023193359375,
-0.014556884765625,
0.00868988037109375,
-0.012237548828125,
-0.00899505615234375,
0.01404571533203125,
-0.01194000244140625,
-0.01371002197265625,
-0.006175994873046875,
-0.052734375,
0.01788330078125,
-0.0022525787353515625,
-0.010467529296875,
-0.006519317626953125,
0.0125732421875,
-0.01519775390625,
-0.0046844482421875,
0.015350341796875,
0.00363922119140625,
0.0015249252319335938,
-0.013519287109375,
-0.009613037109375,
0.0119476318359375,
-0.0131683349609375,
-0.00385284423828125,
0.033203125,
-0.01045989990234375,
0.01361846923828125,
-0.0021343231201171875,
-0.01197052001953125,
-0.0021343231201171875,
0.0045318603515625,
0.0009102821350097656,
-0.0185546875,
0.01312255859375,
-0.014495849609375,
-0.018157958984375,
-0.0034885406494140625,
0.0047760009765625,
0.00189208984375,
0.0025234222412109375,
0.0128936767578125,
0.00177001953125,
-0.016387939453125,
0.038421630859375,
0.0016222000122070312,
0.0080108642578125,
0.015869140625,
-0.0082855224609375,
0.01392364501953125,
0.019378662109375,
0.015777587890625,
0.00804901123046875,
0.017974853515625,
0.0080413818359375,
-0.001567840576171875,
-0.006198883056640625,
-0.0010423660278320312,
-0.01084136962890625,
0.0235443115234375,
0.018463134765625,
0.0091552734375,
0.01641845703125,
-0.000286102294921875,
-0.031890869140625,
-0.0011425018310546875,
0.0149993896484375,
-0.0090179443359375,
0.0018243789672851562,
-0.0035190582275390625,
-0.0012102127075195312,
-0.0011072158813476562,
0.0038661956787109375,
0.00978851318359375,
-0.0198211669921875,
0.019775390625,
-0.0010118484497070312,
0.00693511962890625,
-0.005466461181640625,
-0.004489898681640625,
0.003414154052734375,
-0.0523681640625,
0.01409912109375,
0.0007958412170410156,
-0.006458282470703125,
-0.0029754638671875,
-0.03662109375,
0.0015859603881835938,
0.005218505859375,
0.00904083251953125,
0.007617950439453125,
0.01328277587890625,
0.0364990234375,
-0.01030731201171875,
-0.00972747802734375,
-0.004299163818359375,
-0.0172271728515625,
0.003757476806640625,
0.006122589111328125,
-0.005645751953125,
0.0129547119140625,
0.0014791488647460938,
0.0225830078125,
-0.004077911376953125,
-0.007709503173828125,
-0.0018672943115234375,
-0.0240631103515625,
-0.0036334991455078125,
0.00830078125,
0.00447845458984375,
0.0209197998046875,
-0.009185791015625,
-0.028778076171875,
0.005741119384765625,
-0.00226593017578125,
0.0029354095458984375,
-0.0026912689208984375,
0.0013017654418945312,
0.0004405975341796875,
-0.00516510009765625,
-0.0052490234375,
-0.034515380859375,
-0.01483917236328125,
-0.0256805419921875,
0.00019049644470214844,
0.0026702880859375,
-0.0003249645233154297,
0.00576019287109375,
-0.00786590576171875,
-0.00543212890625,
0.004383087158203125,
0.0010099411010742188,
0.067626953125,
-0.00966644287109375,
-0.00823974609375,
0.0184326171875,
-0.0023784637451171875,
-0.0323486328125,
-0.005306243896484375,
0.01468658447265625,
-0.0052337646484375,
-0.005054473876953125,
0.01496124267578125,
-0.0328369140625,
-0.006465911865234375,
0.0152130126953125,
0.01474761962890625,
-0.0013856887817382812,
-0.03009033203125,
-0.0021228790283203125,
-0.01276397705078125,
-0.005992889404296875,
0.01084136962890625,
0.0012521743774414062,
-0.0037784576416015625,
-0.00222015380859375,
0.0225372314453125,
-0.0462646484375,
0.0217742919921875,
0.006744384765625,
0.01348876953125,
-0.0240936279296875,
0.024658203125,
-0.013214111328125,
0.009185791015625,
0.0159149169921875,
-0.00786590576171875,
0.045379638671875,
0.00006669759750366211,
0.01329803466796875,
-0.00424957275390625,
-0.0011320114135742188,
-0.00787353515625,
-0.0015306472778320312,
0.02264404296875,
-0.0066375732421875,
-0.003108978271484375,
-0.0309600830078125,
-0.02044677734375,
0.0205078125,
0.0006489753723144531,
-0.0264129638671875,
0.0421142578125,
0.01180267333984375,
-0.021392822265625,
0.0070343017578125,
0.005695343017578125,
0.018341064453125,
0.004291534423828125,
0.02337646484375,
-0.0233612060546875,
0.04827880859375,
-0.025421142578125,
0.0177459716796875,
-0.007114410400390625,
-0.007293701171875,
-0.0168609619140625,
0.02313232421875,
-0.01074981689453125,
0.0145416259765625,
0.010986328125,
-0.0034427642822265625,
-0.0006170272827148438,
-0.01242828369140625,
-0.0270843505859375,
0.0006985664367675781,
0.013214111328125,
0.0025043487548828125,
-0.0194854736328125,
-0.0111236572265625,
-0.0239410400390625,
0.01374053955078125,
0.0037841796875,
0.0173492431640625,
0.006008148193359375,
0.0045013427734375,
-0.03570556640625,
0.01351165771484375,
-0.00811004638671875,
0.01087188720703125,
0.01262664794921875,
0.052825927734375,
0.002849578857421875,
0.0016374588012695312,
-0.00928497314453125,
-0.027679443359375,
0.00693511962890625,
-0.037506103515625,
0.0031108856201171875,
0.01354217529296875,
-0.0303802490234375,
-0.00891876220703125,
-0.0050811767578125,
-0.0323486328125,
-0.0034160614013671875,
-0.02691650390625,
-0.05548095703125,
0.002895355224609375,
-0.005702972412109375,
-0.0001348257064819336,
-0.0171966552734375,
-0.0105438232421875,
0.0196533203125,
0.022491455078125,
0.006011962890625,
0.03375244140625,
-0.035888671875,
-0.0150909423828125,
-0.004383087158203125,
-0.017669677734375,
0.00824737548828125,
0.0110321044921875,
-0.00884246826171875,
-0.051116943359375,
-0.009185791015625,
0.020050048828125,
0.01296234130859375,
-0.007259368896484375,
-0.004253387451171875,
0.01293182373046875,
0.03436279296875,
-0.0146331787109375,
-0.019775390625,
0.00536346435546875,
-0.000446319580078125,
0.037567138671875,
0.0005083084106445312,
-0.0185394287109375,
-0.0232696533203125,
-0.02728271484375,
-0.0009870529174804688,
0.01611328125,
0.00616455078125,
-0.0177154541015625,
0.0187530517578125,
0.0157012939453125,
0.010162353515625,
-0.0006413459777832031,
0.017242431640625,
0.034759521484375,
-0.05816650390625,
0.013031005859375,
0.00977325439453125,
-0.0330810546875,
0.00243377685546875,
-0.00897216796875,
0.022064208984375,
0.0301971435546875,
-0.0122833251953125,
0.04510498046875,
0.0202178955078125,
0.029296875,
0.0026988983154296875,
0.0008368492126464844,
-0.00701141357421875,
0.033905029296875,
0.01058197021484375,
0.0076904296875,
0.0030078887939453125,
0.0007214546203613281,
-0.019195556640625,
0.020111083984375,
0.0119171142578125,
-0.013580322265625,
0.03765869140625,
-0.01995849609375,
-0.02911376953125,
0.001041412353515625,
0.024017333984375,
0.00824737548828125,
-0.004802703857421875,
0.0159912109375,
-0.040283203125,
-0.0212249755859375,
-0.0009784698486328125,
0.00305938720703125,
0.01165008544921875,
0.044219970703125,
-0.005985260009765625,
-0.007266998291015625,
-0.04437255859375,
-0.028656005859375,
-0.00867462158203125,
-0.017669677734375,
-0.016082763671875,
-0.013885498046875,
-0.01386260986328125,
-0.01354217529296875,
-0.005462646484375,
0.02716064453125,
0.015380859375,
0.00043010711669921875,
-0.00235748291015625,
-0.0232086181640625,
0.00479888916015625,
0.007099151611328125,
-0.04046630859375,
0.029632568359375,
-0.0011692047119140625,
0.029998779296875,
-0.01303863525390625,
-0.0166473388671875,
-0.01348876953125,
0.020751953125,
0.0017805099487304688,
0.07122802734375,
0.0021228790283203125,
0.00010991096496582031,
0.035308837890625,
0.0238800048828125,
0.0284423828125,
-0.0268096923828125,
-0.0013828277587890625,
0.017333984375,
-0.02545166015625,
-0.03350830078125,
0.004669189453125,
-0.01291656494140625,
0.0029735565185546875,
-0.018402099609375,
0.0137481689453125,
-0.01033782958984375,
-0.0080108642578125,
0.0096893310546875,
-0.00423431396484375,
0.016632080078125,
-0.002567291259765625,
0.020782470703125,
-0.019134521484375,
-0.016265869140625,
-0.00885009765625,
-0.011993408203125,
0.0044097900390625,
0.01068878173828125,
0.0103302001953125,
-0.031646728515625,
-0.0229339599609375,
-0.048187255859375,
0.046234130859375,
0.0067291259765625,
0.037445068359375,
-0.0024509429931640625,
-0.0236663818359375,
0.029571533203125,
0.0258026123046875,
-0.0115814208984375,
-0.0176849365234375,
-0.01132965087890625,
0.032562255859375,
-0.0347900390625,
0.02508544921875,
0.010772705078125,
-0.003276824951171875,
-0.0177001953125,
0.034210205078125,
-0.005657196044921875,
-0.01383209228515625,
0.0250701904296875,
0.0007681846618652344,
0.00821685791015625,
-0.00385284423828125,
0.00272369384765625,
-0.006103515625,
0.015655517578125,
0.005100250244140625,
-0.006107330322265625,
-0.0125579833984375,
-0.00247955322265625,
0.023956298828125,
-0.005458831787109375,
-0.0019388198852539062,
0.027069091796875,
0.00029158592224121094,
0.03033447265625,
-0.003765106201171875,
-0.00159454345703125,
0.0051727294921875,
0.0254058837890625,
0.006130218505859375,
0.022613525390625,
0.032684326171875,
0.01013946533203125,
0.003414154052734375,
0.01241302490234375,
0.004726409912109375,
-0.00453948974609375,
0.00406646728515625,
-0.005092620849609375,
0.00836944580078125,
0.01366424560546875,
-0.015960693359375,
-0.0224151611328125,
-0.028656005859375,
-0.01751708984375,
-0.00940704345703125,
-0.0139007568359375,
-0.0225677490234375,
-0.0240325927734375,
-0.0133209228515625,
-0.00738525390625,
-0.0260772705078125,
-0.0231781005859375,
0.008056640625,
0.01131439208984375,
-0.004383087158203125,
0.00640869140625,
0.029449462890625,
0.00665283203125,
0.00424957275390625,
0.01276397705078125,
-0.005397796630859375,
0.01490020751953125,
0.00023686885833740234,
0.019622802734375,
0.0289306640625,
0.0214691162109375,
0.00711822509765625,
-0.044891357421875,
0.0269012451171875,
-0.019195556640625,
0.007022857666015625,
-0.034759521484375,
-0.0264892578125,
-0.00753021240234375,
-0.0201263427734375,
0.002414703369140625,
-0.0121917724609375,
-0.0035724639892578125,
-0.00923919677734375,
0.0252685546875,
-0.0016269683837890625,
-0.0029163360595703125,
0.01308441162109375,
-0.00799560546875,
0.0117340087890625,
-0.0032711029052734375,
0.02508544921875,
-0.0011625289916992188,
-0.018585205078125,
-0.024749755859375,
-0.01511383056640625,
0.0207977294921875,
-0.0305938720703125,
-0.00893402099609375,
-0.01934814453125,
0.021820068359375,
0.006282806396484375,
0.0090789794921875,
0.0026035308837890625,
-0.0394287109375,
0.0143280029296875,
-0.002277374267578125,
-0.0046234130859375,
-0.0157012939453125,
0.01409149169921875,
0.0061187744140625,
0.000995635986328125,
-0.035491943359375,
-0.007480621337890625,
-0.002628326416015625,
0.01340484619140625,
-0.01033782958984375,
-0.02349853515625,
0.01326751708984375,
0.0165252685546875,
-0.03936767578125,
-0.010467529296875,
-0.01435089111328125,
-0.00885009765625,
-0.0080718994140625,
-0.01381683349609375,
0.0164947509765625,
-0.03363037109375,
-0.054168701171875,
-0.01593017578125,
0.024932861328125,
-0.00904083251953125,
-0.01812744140625,
0.00843048095703125,
-0.0069732666015625,
0.03277587890625,
0.0028839111328125,
0.0361328125,
0.033416748046875,
-0.0038814544677734375,
0.04022216796875,
-0.0293121337890625,
0.0151519775390625,
0.009796142578125,
0.0123443603515625,
0.0009889602661132812,
0.03192138671875,
0.0025730133056640625,
-0.028076171875,
-0.0021572113037109375,
0.00849151611328125,
0.0188140869140625,
-0.029327392578125,
-0.0066070556640625,
-0.00943756103515625,
0.022552490234375,
0.0014019012451171875,
0.0015897750854492188,
0.0292205810546875,
0.05670166015625,
-0.0238189697265625,
0.035980224609375,
-0.0265350341796875,
0.01031494140625,
0.0023345947265625,
-0.006938934326171875,
0.0225830078125,
-0.0105743408203125,
-0.0010328292846679688,
-0.02545166015625,
0.0125274658203125,
0.012237548828125,
-0.00862884521484375,
0.01953125,
-0.0030918121337890625,
-0.038055419921875,
-0.0028553009033203125,
-0.0020885467529296875,
-0.005245208740234375,
0.01032257080078125,
-0.005279541015625,
0.0261993408203125,
-0.030426025390625,
-0.02557373046875,
0.027130126953125,
-0.0294952392578125,
0.00983428955078125,
-0.0196380615234375,
-0.00868988037109375,
-0.0172882080078125,
-0.001995086669921875,
0.005275726318359375,
-0.021026611328125,
-0.01016998291015625,
0.01357269287109375,
0.00812530517578125,
-0.00835418701171875,
-0.04815673828125,
0.015869140625,
0.013397216796875,
-0.023834228515625,
0.01561737060546875,
0.009490966796875,
-0.0244140625,
-0.0270538330078125,
-0.055877685546875,
-0.0250396728515625,
-0.0018358230590820312,
-0.019927978515625,
-0.0276336669921875,
0.01025390625,
-0.028106689453125,
-0.04461669921875,
0.01461029052734375,
-0.030670166015625,
-0.00133514404296875,
-0.0066986083984375,
0.033233642578125,
0.0005640983581542969,
0.0169219970703125,
-0.0129241943359375,
-0.012176513671875,
-0.007843017578125,
0.0172882080078125,
-0.006923675537109375,
-0.03240966796875,
0.0198211669921875,
0.007659912109375,
0.011627197265625,
0.036224365234375,
-0.025177001953125,
-0.014190673828125,
0.0006055831909179688,
-0.0036563873291015625,
-0.0071868896484375,
-0.037261962890625,
0.0092620849609375,
-0.02789306640625,
-0.00403594970703125,
-0.034454345703125,
0.004566192626953125,
0.0122528076171875,
0.010284423828125,
-0.02471923828125,
-0.0104827880859375,
-0.0050811767578125,
-0.0202484130859375,
-0.034393310546875,
-0.01300048828125,
0.03485107421875,
0.000743865966796875,
-0.00759124755859375,
0.0038909912109375,
-0.0279388427734375,
-0.0085906982421875,
-0.0139007568359375,
-0.0186920166015625,
-0.020599365234375,
-0.004047393798828125,
-0.030548095703125,
0.03607177734375,
0.0005106925964355469,
0.0017910003662109375,
0.0208740234375,
-0.0261688232421875,
0.01197052001953125,
0.0019197463989257812,
0.009307861328125,
0.0098114013671875,
0.01229095458984375,
0.000713348388671875,
-0.0050506591796875,
0.0023479461669921875,
0.018096923828125,
-0.01377105712890625,
-0.002346038818359375,
-0.01000213623046875,
-0.0032138824462890625,
-0.0085906982421875,
-0.00030994415283203125,
0.0277099609375,
0.022003173828125,
-0.0032215118408203125,
0.0092926025390625,
-0.0180206298828125,
-0.0122528076171875,
0.0019168853759765625,
0.01678466796875,
0.0130615234375,
0.045867919921875,
-0.032440185546875,
-0.0174102783203125,
0.0032558441162109375,
0.000347137451171875,
0.007488250732421875,
0.0024356842041015625,
0.0166168212890625,
0.003936767578125,
0.0308380126953125,
-0.027801513671875,
-0.0208587646484375,
-0.02667236328125,
0.0011510848999023438,
-0.012054443359375,
0.0198211669921875,
0.00782012939453125,
0.00485992431640625,
-0.010162353515625,
0.015777587890625,
-0.0054931640625,
0.00481414794921875,
0.0069580078125,
0.00855255126953125,
0.0321044921875,
-0.007671356201171875,
-0.04315185546875,
0.0128631591796875,
-0.0173797607421875,
0.00959014892578125,
0.00907135009765625,
-0.016937255859375,
0.01177978515625,
-0.051513671875,
0.0036067962646484375,
0.0242462158203125,
-0.00397491455078125,
0.033172607421875,
-0.00441741943359375,
0.027496337890625,
-0.0309600830078125,
-0.0044403076171875,
0.00713348388671875,
0.01129150390625,
-0.0117340087890625,
0.0140228271484375,
-0.0226593017578125,
-0.049835205078125,
-0.028656005859375,
-0.0394287109375,
0.0268402099609375,
-0.001079559326171875,
0.033203125,
-0.0237579345703125,
-0.0037670135498046875,
-0.0190582275390625,
0.022064208984375,
-0.00434112548828125,
0.0164031982421875,
-0.00027489662170410156,
0.0087738037109375,
0.0159149169921875,
0.0184173583984375,
0.03070068359375,
-0.015899658203125,
0.0005583763122558594,
-0.003932952880859375,
-0.009490966796875,
0.0194854736328125,
-0.0302886962890625,
0.006511688232421875,
0.0404052734375,
-0.01157379150390625,
-0.019683837890625,
0.007732391357421875,
0.00946807861328125,
0.0174407958984375,
-0.00681304931640625,
-0.01236724853515625,
-0.00627899169921875,
-0.0028839111328125,
-0.006435394287109375,
-0.0016431808471679688,
0.01837158203125,
-0.030242919921875,
-0.0291900634765625,
0.0295257568359375,
-0.028076171875,
-0.026214599609375,
-0.01044464111328125,
-0.00815582275390625,
0.037200927734375,
0.033355712890625,
-0.0278167724609375,
0.0094451904296875,
-0.004375457763671875,
0.007720947265625,
-0.01508331298828125,
-0.0079803466796875,
0.0177001953125,
0.0262603759765625,
0.0156402587890625,
-0.034454345703125,
-0.005336761474609375,
0.0012140274047851562,
0.03448486328125,
0.00429534912109375,
0.034149169921875,
0.02227783203125,
-0.01129913330078125,
-0.005611419677734375,
-0.016143798828125,
0.020263671875,
0.0032978057861328125,
0.00409698486328125,
0.0028247833251953125,
-0.0225830078125,
0.02801513671875,
0.0135345458984375,
0.0243072509765625,
-0.0172882080078125,
0.0253143310546875,
0.00640869140625,
0.01071929931640625,
-0.006855010986328125,
0.0023403167724609375,
0.01499176025390625,
-0.005786895751953125,
-0.012603759765625,
0.017669677734375,
-0.00391387939453125,
0.00011974573135375977,
0.01763916015625,
0.003787994384765625,
-0.0138397216796875,
-0.00659942626953125,
-0.038665771484375,
-0.01666259765625,
-0.035980224609375,
0.01141357421875,
-0.01189422607421875,
0.01351165771484375,
-0.0014095306396484375,
0.01371002197265625,
-0.01080322265625,
-0.0173187255859375,
-0.039306640625,
-0.0081787109375,
-0.0120391845703125,
-0.0160980224609375,
-0.071044921875,
-0.007843017578125,
0.00001239776611328125,
0.023834228515625,
0.0029087066650390625,
-0.0006837844848632812,
0.035614013671875,
-0.02093505859375,
-0.03533935546875,
0.00110626220703125,
-0.0048828125,
-0.032745361328125,
-0.0015954971313476562,
-0.007244110107421875,
-0.0452880859375,
-0.0135650634765625,
0.03436279296875,
-0.0091552734375,
-0.047821044921875,
-0.0014753341674804688,
0.0164337158203125,
0.0269012451171875,
-0.0009026527404785156,
-0.0036678314208984375,
0.0071868896484375,
-0.00917816162109375,
0.0028839111328125,
-0.0294036865234375,
-0.01374053955078125,
0.00238800048828125,
0.01318359375,
0.010650634765625,
-0.0049591064453125,
0.0198516845703125,
0.0147705078125,
-0.004344940185546875,
0.0290985107421875,
-0.00954437255859375,
-0.0235137939453125,
0.0067901611328125,
0.0106353759765625,
-0.006099700927734375,
0.0151824951171875,
-0.0288848876953125,
0.0283660888671875,
-0.0013628005981445312,
0.0078887939453125,
0.00843048095703125,
0.00615692138671875,
-0.004245758056640625,
-0.0092620849609375,
-0.000507354736328125,
0.0116119384765625,
-0.0289764404296875,
0.0022125244140625,
0.004680633544921875,
-0.0257415771484375,
0.006290435791015625,
-0.01284027099609375,
0.0247039794921875,
-0.035430908203125,
-0.00804901123046875,
-0.0013074874877929688,
0.005889892578125,
0.01302337646484375,
-0.0028839111328125,
0.005779266357421875,
0.0032367706298828125,
-0.0005736351013183594,
-0.037353515625,
-0.005321502685546875,
-0.0301513671875,
-0.027740478515625,
0.0220947265625,
-0.0029315948486328125,
-0.03399658203125,
-0.0184326171875,
-0.02484130859375,
-0.0109710693359375,
0.0000807642936706543,
0.00681304931640625,
-0.016845703125,
0.0186920166015625,
-0.0066375732421875,
0.0170745849609375,
0.0085296630859375,
-0.018646240234375,
-0.0379638671875,
-0.0068511962890625,
0.0394287109375,
-0.053253173828125,
-0.0264434814453125,
0.002910614013671875,
0.00787353515625,
0.0004897117614746094,
-0.0236358642578125,
-0.01959228515625,
0.036895751953125,
0.0156402587890625,
-0.0330810546875,
-0.0271453857421875,
0.01471710205078125,
0.0179443359375,
0.00433349609375,
0.00019991397857666016,
0.007335662841796875,
0.0452880859375,
0.0271148681640625,
-0.0104217529296875,
0.01873779296875,
0.005428314208984375,
-0.022552490234375,
0.0308837890625,
0.001216888427734375,
0.007579803466796875,
0.010101318359375,
-0.005588531494140625,
-0.0014104843139648438,
-0.01424407958984375,
0.0018453598022460938,
-0.063232421875,
-0.01219940185546875,
0.008697509765625,
0.0229034423828125,
-0.0006761550903320312,
-0.0171661376953125,
-0.0292205810546875,
-0.02557373046875,
0.0025272369384765625,
0.0167388916015625,
0.023223876953125,
0.01218414306640625,
0.0031452178955078125,
-0.0099029541015625,
-0.01352691650390625,
0.01178741455078125,
-0.0094451904296875,
-0.0015010833740234375,
0.01444244384765625,
0.03387451171875,
-0.0013074874877929688,
-0.00838470458984375,
0.00946044921875,
-0.0276641845703125,
-0.036224365234375,
0.0161895751953125,
0.018035888671875,
-0.007503509521484375,
-0.0251312255859375,
0.0168914794921875,
-0.0316162109375,
-0.0159759521484375,
-0.01218414306640625,
0.00047326087951660156,
-0.015228271484375,
-0.02099609375,
-0.047271728515625,
0.0099639892578125,
0.02374267578125,
0.044189453125,
0.013275146484375,
0.0229034423828125,
0.01381683349609375,
-0.035247802734375,
-0.019775390625,
-0.0249786376953125,
-0.025360107421875,
0.036529541015625,
-0.022125244140625,
0.01433563232421875,
-0.01239013671875,
0.0015544891357421875,
-0.0091705322265625,
0.0137939453125,
-0.042694091796875,
0.0101165771484375,
0.049346923828125,
-0.0279998779296875,
-0.0199432373046875,
0.01043701171875,
-0.039947509765625,
-0.0226287841796875,
-0.01214599609375,
0.01873779296875,
-0.00506591796875,
-0.01210784912109375,
0.046234130859375,
-0.004276275634765625,
-0.051239013671875,
0.020843505859375,
-0.00788116455078125,
-0.0091400146484375,
-0.0189971923828125,
0.005741119384765625,
0.003322601318359375,
-0.01235198974609375,
0.02911376953125,
0.004673004150390625,
0.0212249755859375,
-0.027191162109375,
0.03558349609375,
0.01044464111328125,
-0.03179931640625,
0.00785064697265625,
-0.0325927734375,
-0.00279998779296875,
0.0158843994140625,
0.017425537109375,
-0.03692626953125,
-0.0307769775390625,
-0.002765655517578125,
0.004497528076171875,
-0.0384521484375,
-0.01009368896484375,
0.000732421875,
0.0174560546875,
-0.0277862548828125,
0.019195556640625,
-0.0022735595703125,
0.020751953125,
0.0140228271484375,
0.0266876220703125,
-0.01512908935546875,
0.0009069442749023438,
-0.005107879638671875,
-0.009979248046875,
-0.0421142578125,
-0.00814056396484375,
-0.007488250732421875,
-0.004241943359375,
0.0234527587890625,
-0.0029125213623046875,
-0.0035419464111328125,
-0.0269775390625,
-0.0306854248046875,
0.0017518997192382812,
0.0008440017700195312,
-0.0005831718444824219,
0.01103973388671875,
0.003604888916015625,
-0.0140380859375,
0.004199981689453125,
0.0248870849609375,
0.0050048828125,
0.0177764892578125,
0.0230712890625,
-0.021209716796875,
-0.006137847900390625,
0.0223236083984375,
-0.00720977783203125,
-0.00782012939453125,
0.013458251953125,
-0.006740570068359375,
0.0224151611328125,
0.005901336669921875,
-0.03778076171875,
0.00794219970703125,
-0.0021762847900390625,
0.001239776611328125,
-0.024200439453125,
-0.016326904296875,
-0.0031604766845703125,
0.00020551681518554688,
0.00811004638671875,
-0.0294647216796875,
0.033294677734375,
0.00742340087890625,
-0.007568359375,
0.0242767333984375,
0.0230255126953125,
-0.0174713134765625,
-0.01032257080078125,
-0.0296783447265625,
-0.00313568115234375,
0.024261474609375,
0.0149688720703125,
0.00287628173828125,
-0.0019397735595703125,
-0.00737762451171875,
0.02642822265625,
0.034515380859375,
-0.0277099609375,
0.0301666259765625,
0.0240478515625,
0.0009503364562988281,
0.0161590576171875,
-0.0033321380615234375,
0.007171630859375,
-0.0225067138671875,
0.002185821533203125,
0.00826263427734375,
0.02423095703125,
-0.0182647705078125,
-0.0426025390625,
-0.0177154541015625,
0.00896453857421875,
-0.005767822265625,
-0.0196075439453125,
-0.0080718994140625,
0.03466796875,
-0.01038360595703125,
0.0033092498779296875,
-0.0180511474609375,
0.0180511474609375,
-0.006992340087890625,
-0.0009341239929199219,
-0.00705718994140625,
-0.0076446533203125,
0.0139312744140625,
0.0037403106689453125,
-0.00373077392578125,
0.032135009765625,
-0.001766204833984375,
0.0007143020629882812,
-0.01064300537109375,
-0.014251708984375,
-0.0014600753784179688,
-0.0159759521484375,
-0.021240234375,
0.013275146484375,
0.0275726318359375,
-0.001861572265625,
-0.0208740234375,
-0.0241546630859375,
-0.0040283203125,
0.0222930908203125,
0.0173187255859375,
-0.005096435546875,
0.01229095458984375,
0.0131072998046875,
-0.01384735107421875,
0.01224517822265625,
-0.01418304443359375,
0.0188446044921875,
0.0116729736328125,
-0.00801849365234375,
0.0118408203125,
0.00995635986328125,
-0.0137481689453125,
-0.0104827880859375,
0.003570556640625,
-0.0187835693359375,
-0.028961181640625,
-0.015899658203125,
0.0073394775390625,
0.031982421875,
-0.01435089111328125,
-0.0085601806640625,
0.00855255126953125,
0.00688934326171875,
0.027984619140625,
-0.00034999847412109375,
0.0183563232421875,
-0.005252838134765625,
0.0010242462158203125,
-0.0151214599609375,
-0.006359100341796875,
0.013702392578125,
-0.0128326416015625,
0.021697998046875,
-0.0005345344543457031,
0.04290771484375,
0.023101806640625,
-0.01508331298828125,
-0.033782958984375,
0.01273345947265625,
-0.0295867919921875,
-0.0140533447265625,
-0.03485107421875,
0.0108795166015625,
-0.00792694091796875,
0.00811004638671875,
-0.00909423828125,
0.024932861328125,
-0.00392913818359375,
-0.0037250518798828125,
0.02899169921875,
-0.0007815361022949219,
-0.01352691650390625,
0.042083740234375,
-0.0355224609375,
0.01361846923828125,
0.00658416748046875,
0.016082763671875,
-0.033966064453125,
0.0130615234375,
-0.00211334228515625,
-0.054412841796875,
0.03125,
0.0024871826171875,
-0.009857177734375,
0.03875732421875,
-0.02716064453125,
-0.0209197998046875,
-0.0042266845703125,
-0.0034542083740234375,
0.01389312744140625,
-0.0014371871948242188,
0.0218505859375,
-0.03326416015625,
-0.0014009475708007812,
-0.03924560546875,
0.05682373046875,
-0.0236053466796875,
0.001773834228515625,
-0.0208892822265625,
-0.00836944580078125,
-0.0180206298828125,
-0.02215576171875,
0.0220794677734375,
0.00787353515625,
0.01531982421875,
0.041259765625,
-0.0030155181884765625,
-0.005001068115234375,
-0.00466156005859375,
-0.0184173583984375,
0.007778167724609375,
-0.0217742919921875,
-0.0248870849609375,
-0.00872039794921875,
0.003330230712890625,
-0.0251312255859375,
0.0401611328125,
-0.0182037353515625,
0.005584716796875,
-0.01165771484375,
0.0039825439453125,
-0.01085662841796875,
-0.004150390625,
-0.01227569580078125,
-0.0169677734375,
-0.01401519775390625,
-0.0152130126953125,
0.0006036758422851562,
0.0177459716796875,
0.004611968994140625,
0.007381439208984375,
0.044036865234375,
-0.0102691650390625,
0.00521087646484375,
-0.010009765625,
-0.01800537109375,
-0.0011377334594726562,
0.0164337158203125,
0.01415252685546875,
0.02020263671875,
-0.00679779052734375,
-0.0159454345703125,
-0.00267791748046875,
-0.0010118484497070312,
-0.0303497314453125,
0.00930023193359375,
-0.00519561767578125,
-0.0030956268310546875,
-0.0511474609375,
0.0037212371826171875,
0.032379150390625,
-0.0114288330078125,
-0.0153656005859375,
-0.01311492919921875,
0.00989532470703125,
0.03875732421875,
-0.00885772705078125,
-0.0118560791015625,
-0.01201629638671875,
-0.01221466064453125,
-0.0012912750244140625,
-0.0187835693359375,
-0.0256195068359375,
-0.0202484130859375,
-0.053741455078125,
0.003459930419921875,
-0.02008056640625,
0.005523681640625,
0.004085540771484375,
0.036346435546875,
0.0013685226440429688,
-0.03125,
-0.01433563232421875,
0.012969970703125,
0.034576416015625,
0.0111541748046875,
-0.013336181640625,
-0.002994537353515625,
-0.00292205810546875,
-0.005245208740234375,
0.0189971923828125,
-0.0201568603515625,
0.00081634521484375,
0.0003204345703125,
-0.0031108856201171875,
0.023345947265625,
0.0160980224609375,
0.0007457733154296875,
-0.010009765625,
-0.0182037353515625,
-0.002166748046875,
-0.035888671875,
0.0021209716796875,
-0.0021953582763671875,
0.0170135498046875,
0.00013506412506103516,
0.007144927978515625,
-0.011932373046875,
0.019256591796875,
0.013153076171875,
-0.03594970703125,
-0.0159759521484375,
-0.004390716552734375,
0.0015850067138671875,
-0.0109405517578125,
0.00766754150390625,
-0.0260009765625,
0.0084991455078125,
-0.040435791015625,
-0.0012607574462890625,
-0.0224456787109375,
-0.026153564453125,
-0.00876617431640625,
0.0177001953125,
0.01495361328125,
-0.018890380859375,
-0.0283355712890625,
-0.0018701553344726562,
0.0209503173828125,
-0.0011167526245117188,
-0.00010150671005249023,
0.01120758056640625,
-0.00960540771484375,
-0.00864410400390625,
0.045440673828125,
0.01331329345703125,
-0.007350921630859375,
-0.0306243896484375,
0.0202178955078125,
-0.0264892578125,
-0.005649566650390625,
-0.039093017578125,
0.03076171875,
0.0010509490966796875,
0.004093170166015625,
0.0017795562744140625,
-0.0169830322265625,
-0.0188751220703125,
-0.009063720703125,
-0.01192474365234375,
-0.0278472900390625,
-0.00244903564453125,
-0.0352783203125,
0.00946807861328125,
-0.0189666748046875,
0.010467529296875,
0.01056671142578125,
-0.0002589225769042969,
-0.02398681640625,
-0.004688262939453125,
0.00196075439453125,
0.0278778076171875,
0.0391845703125,
0.003173828125,
-0.0105438232421875,
0.0028438568115234375,
0.0016469955444335938,
0.030487060546875,
0.006011962890625,
-0.00780487060546875,
0.01129913330078125,
0.01139068603515625,
-0.0052490234375,
0.027313232421875,
-0.00391387939453125,
0.01027679443359375,
-0.017364501953125,
0.00653839111328125,
0.005496978759765625,
0.037567138671875,
-0.01311492919921875,
-0.005584716796875,
0.01885986328125,
-0.006946563720703125,
0.007038116455078125,
0.00795745849609375,
0.006343841552734375,
0.0066680908203125,
0.0068359375,
-0.00004088878631591797,
-0.0204925537109375,
0.0166015625,
-0.0170440673828125,
0.0208587646484375,
-0.00696563720703125,
-0.0234375,
-0.021026611328125,
-0.00881195068359375,
0.046478271484375,
0.0217132568359375,
0.00998687744140625,
0.0056610107421875,
-0.01043701171875,
-0.0222625732421875,
0.0038852691650390625,
0.027862548828125,
0.036041259765625,
-0.0103302001953125,
-0.0024127960205078125,
0.0254364013671875,
-0.034698486328125,
0.01003265380859375,
0.0300750732421875,
-0.01385498046875,
-0.015655517578125,
0.01432037353515625,
-0.00963592529296875,
0.03778076171875,
0.0089569091796875,
0.041259765625,
0.0099639892578125,
-0.005123138427734375,
0.006694793701171875,
0.02935791015625,
0.053741455078125,
-0.01445770263671875,
-0.0174560546875,
-0.01129150390625,
0.0268096923828125,
0.0059814453125,
-0.01366424560546875,
-0.00041937828063964844,
0.037872314453125,
-0.0034885406494140625,
-0.0060577392578125,
-0.0021915435791015625,
-0.00970458984375,
0.035247802734375,
0.015167236328125,
0.0116729736328125,
0.00015485286712646484,
-0.011627197265625,
-0.0129547119140625,
0.0010404586791992188,
-0.00244140625,
0.0244598388671875,
-0.02783203125,
0.00907135009765625,
-0.0179595947265625,
0.0013856887817382812,
0.01114654541015625,
0.036895751953125,
0.00982666015625,
0.0192718505859375,
-0.0164031982421875,
-0.01432037353515625,
-0.00366973876953125,
0.0006070137023925781,
0.052215576171875,
-0.01800537109375,
0.01355743408203125,
0.033721923828125,
-0.026214599609375,
0.004848480224609375,
0.00638580322265625,
0.01522064208984375,
0.0501708984375,
0.021759033203125,
-0.013458251953125,
0.00010246038436889648,
-0.015106201171875,
0.0131072998046875,
0.01171112060546875,
-0.0035247802734375,
0.0406494140625,
0.00189971923828125,
-0.02734375,
-0.04522705078125,
0.00708770751953125,
0.0116729736328125,
0.015777587890625,
0.0222320556640625,
-0.01035308837890625,
0.006519317626953125,
-0.036865234375,
0.00690460205078125,
0.03009033203125,
0.01025390625,
-0.005199432373046875,
0.002658843994140625,
-0.025543212890625,
-0.0071258544921875,
-0.00951385498046875,
0.006534576416015625,
-0.033599853515625,
-0.022125244140625,
-0.0244140625,
-0.0240631103515625,
-0.007488250732421875,
-0.0037326812744140625,
-0.0172119140625,
0.0124664306640625,
0.00664520263671875,
-0.004039764404296875,
-0.00487518310546875,
-0.00591278076171875,
0.019927978515625,
0.014678955078125,
0.0195159912109375,
-0.004871368408203125,
-0.0219573974609375,
-0.048828125,
-0.031768798828125,
-0.026275634765625,
0.038970947265625,
0.003200531005859375,
-0.0177459716796875,
0.0205841064453125,
-0.00725555419921875,
0.006351470947265625,
-0.00556182861328125,
-0.0177154541015625,
-0.00554656982421875,
0.019256591796875,
0.009429931640625,
-0.00678253173828125,
-0.005870819091796875,
-0.004245758056640625,
-0.033599853515625,
0.004505157470703125,
0.0137481689453125,
0.0311431884765625,
0.00405120849609375,
-0.00983428955078125,
0.00954437255859375,
0.01219940185546875,
-0.0002028942108154297,
0.0281524658203125,
0.0168914794921875,
-0.036163330078125,
0.02410888671875,
-0.0081024169921875,
0.046783447265625,
-0.01009368896484375,
-0.0004978179931640625,
0.01416015625,
-0.00435638427734375,
0.007297515869140625,
0.015625,
-0.006450653076171875,
-0.023773193359375,
0.0345458984375,
-0.046478271484375,
-0.031402587890625,
0.0273590087890625,
0.0175933837890625,
0.0084686279296875,
0.01000213623046875,
0.01226043701171875,
-0.025970458984375,
-0.060791015625,
0.038330078125,
-0.01175689697265625,
0.0055389404296875,
-0.0188446044921875,
-0.00374603271484375,
-0.0126495361328125,
0.0300140380859375,
0.0111541748046875,
0.01462554931640625,
0.035980224609375,
-0.03057861328125,
0.0330810546875,
0.0213470458984375,
-0.0116424560546875,
0.0031337738037109375,
-0.0083160400390625,
0.0195770263671875,
-0.006816864013671875,
-0.021270751953125,
-0.00235748291015625,
-0.0099334716796875,
0.00803375244140625,
-0.0045166015625,
0.0176239013671875,
0.006793975830078125,
-0.006214141845703125,
-0.0020732879638671875,
0.0213470458984375,
0.0308074951171875,
0.01169586181640625,
0.004802703857421875,
-0.00927734375,
0.0269012451171875,
0.0018939971923828125,
-0.00864410400390625,
0.005077362060546875,
0.00955963134765625,
0.0095672607421875,
-0.0208740234375,
-0.00083160400390625,
0.0194549560546875,
-0.023712158203125,
0.00911712646484375,
-0.00899505615234375,
-0.0026950836181640625,
0.00637054443359375,
-0.0098419189453125,
-0.019287109375,
-0.0204925537109375,
0.004589080810546875,
0.0032501220703125,
0.00513458251953125,
0.047760009765625,
0.0200042724609375,
-0.040985107421875,
0.005222320556640625,
-0.0112457275390625,
0.00763702392578125,
-0.012481689453125,
0.0202484130859375,
0.0139007568359375,
0.0136871337890625,
0.004367828369140625,
0.01039886474609375,
0.00002664327621459961,
0.0094757080078125,
-0.0154266357421875,
-0.00743865966796875,
-0.0139007568359375,
0.006988525390625,
0.020111083984375,
0.013946533203125,
-0.006015777587890625,
0.006420135498046875,
-0.01541900634765625,
-0.0152587890625,
0.007537841796875,
-0.014984130859375,
-0.01207733154296875,
0.01142120361328125,
-0.01427459716796875,
0.0235595703125,
-0.021209716796875,
0.0016498565673828125,
0.006923675537109375,
-0.007259368896484375,
0.007495880126953125,
-0.00817108154296875,
0.020172119140625,
-0.01788330078125,
0.0125885009765625,
0.02276611328125,
0.022308349609375,
-0.0103759765625,
-0.0197906494140625,
-0.0150909423828125,
0.018585205078125,
0.0110321044921875,
-0.04345703125,
-0.0276336669921875,
-0.00931549072265625,
-0.004390716552734375,
0.005046844482421875,
-0.0245819091796875,
0.01219940185546875,
-0.0007390975952148438,
0.035430908203125,
-0.0107879638671875,
-0.0079345703125,
0.050811767578125,
0.019561767578125,
0.017059326171875,
-0.0008487701416015625,
-0.0294952392578125,
0.017852783203125,
-0.0084381103515625,
-0.01678466796875,
-0.04974365234375,
0.00644683837890625,
-0.0019159317016601562,
0.013519287109375,
0.01442718505859375,
0.0112457275390625,
0.01300048828125,
-0.0168609619140625,
-0.001613616943359375,
0.01313018798828125,
-0.00473785400390625,
-0.01477813720703125,
0.01230621337890625,
0.00688934326171875,
-0.0552978515625,
0.0258026123046875,
0.012969970703125,
-0.042510986328125,
-0.0149688720703125,
0.0201568603515625,
0.01708984375,
0.004489898681640625,
0.00020384788513183594,
0.01244354248046875,
-0.0234222412109375,
0.01383209228515625,
-0.0092926025390625,
-0.0153961181640625,
-0.022308349609375,
0.015899658203125,
-0.0135498046875,
-0.0015516281127929688,
0.0078582763671875,
-0.0200653076171875,
-0.0112152099609375,
-0.01885986328125,
-0.011260986328125,
-0.01187896728515625,
0.01399993896484375,
-0.02947998046875,
0.006732940673828125,
0.032501220703125,
0.0240020751953125,
0.006465911865234375,
-0.0157318115234375,
0.0174560546875,
-0.013275146484375,
-0.0302581787109375,
0.0191650390625,
-0.0022678375244140625,
0.023529052734375,
0.0225677490234375,
-0.0374755859375,
-0.0191497802734375,
-0.040802001953125,
0.00022137165069580078,
0.006526947021484375,
0.002803802490234375,
0.002712249755859375,
0.01168060302734375,
-0.00968170166015625,
-0.0021820068359375,
0.0175323486328125,
-0.003894805908203125,
0.0114288330078125,
-0.01384735107421875,
0.01171112060546875,
-0.0159912109375,
0.0030536651611328125,
-0.0037078857421875,
0.0022563934326171875,
-0.02337646484375,
0.021514892578125,
-0.00921630859375,
-0.01157379150390625,
-0.03485107421875,
-0.00742340087890625,
-0.005428314208984375,
0.0280609130859375,
0.023773193359375,
0.0506591796875,
0.005405426025390625,
0.003681182861328125,
-0.007320404052734375,
0.00827789306640625,
0.00511932373046875,
0.00948333740234375,
0.01303863525390625,
-0.020233154296875,
0.0158233642578125,
-0.006824493408203125,
-0.01007843017578125,
-0.02862548828125,
-0.00677490234375,
0.04266357421875,
-0.01302337646484375,
-0.0067596435546875,
-0.00017201900482177734,
-0.005405426025390625,
-0.012847900390625,
-0.0093231201171875,
0.02740478515625,
-0.013580322265625,
-0.003131866455078125,
-0.0245361328125,
0.01425933837890625,
-0.0164947509765625,
0.0021381378173828125,
-0.003879547119140625,
-0.017364501953125,
-0.006595611572265625,
0.0186920166015625,
-0.00748443603515625,
-0.019744873046875,
-0.01111602783203125,
-0.034027099609375,
-0.01136016845703125,
-0.0347900390625,
0.005832672119140625,
-0.01009368896484375,
-0.0093536376953125,
0.00725555419921875,
-0.0027103424072265625,
0.00830841064453125,
-0.036346435546875,
-0.029571533203125,
-0.0201416015625,
0.0178680419921875,
-0.0183563232421875,
0.0217742919921875,
-0.02764892578125,
-0.0264129638671875,
0.00872802734375,
0.0015649795532226562,
-0.02032470703125,
-0.00228118896484375,
0.01332855224609375,
0.0467529296875,
0.0096588134765625,
0.016632080078125,
-0.00856781005859375,
0.01381683349609375,
-0.01151275634765625,
-0.0176239013671875,
-0.03399658203125,
-0.0533447265625,
0.0008530616760253906,
0.032440185546875,
-0.0305633544921875,
0.0295562744140625,
-0.008575439453125,
-0.03106689453125,
0.001789093017578125,
0.012725830078125,
-0.015380859375,
0.01384735107421875,
-0.00899505615234375,
0.00853729248046875,
0.01377105712890625,
-0.00579833984375,
-0.01727294921875,
-0.0008535385131835938,
-0.0108489990234375,
-0.01898193359375,
0.0203704833984375,
0.03497314453125,
0.01078033447265625,
0.0030536651611328125,
-0.0113372802734375,
0.01291656494140625,
-0.006542205810546875,
0.0164947509765625,
-0.02484130859375,
0.004283905029296875,
-0.043701171875,
0.0278167724609375,
-0.00893402099609375,
0.00373077392578125,
0.018829345703125,
-0.005313873291015625,
-0.0175323486328125,
0.01605224609375,
-0.0057830810546875,
-0.00746917724609375,
0.00323486328125,
-0.00341033935546875,
-0.026947021484375,
-0.0263519287109375,
0.0222320556640625,
0.02001953125,
0.00962066650390625,
-0.0274658203125,
0.018310546875,
0.058074951171875,
-0.00673675537109375,
0.0034008026123046875,
0.02557373046875,
0.0151824951171875,
-0.031982421875,
-0.024993896484375,
-0.0245361328125,
0.0281982421875,
0.007297515869140625,
-0.01096343994140625,
0.006694793701171875,
0.0006055831909179688,
-0.016265869140625,
0.029296875,
0.0019483566284179688,
-0.001399993896484375,
-0.020111083984375,
0.0128631591796875,
0.01702880859375,
-0.01007843017578125,
0.03802490234375,
0.0142974853515625,
-0.0059051513671875,
0.0005011558532714844,
0.005764007568359375,
0.01468658447265625,
0.006130218505859375,
-0.0233612060546875,
0.051025390625,
-0.00058746337890625,
0.0124053955078125,
0.0174407958984375,
0.0016164779663085938,
0.011871337890625,
0.062347412109375,
-0.0282745361328125,
-0.01708984375,
-0.0231170654296875,
-0.002811431884765625,
-0.0177001953125,
0.0285186767578125,
-0.0165863037109375,
0.006565093994140625,
0.004024505615234375,
0.01016998291015625,
-0.04876708984375,
0.0223846435546875,
-0.006656646728515625,
-0.04132080078125,
-0.016815185546875,
0.006847381591796875,
0.03228759765625,
-0.01953125,
-0.0081329345703125,
-0.0174102783203125,
-0.0186309814453125,
0.004940032958984375,
0.004550933837890625,
0.007904052734375,
-0.011749267578125,
0.009002685546875,
-0.00937652587890625,
0.019287109375,
0.050628662109375,
0.0105743408203125,
-0.0023975372314453125,
-0.005367279052734375,
0.038177490234375,
-0.00994873046875,
-0.0170135498046875,
0.00098419189453125,
-0.0018558502197265625,
-0.02197265625,
-0.008148193359375,
0.0243988037109375,
-0.018463134765625,
-0.003658294677734375,
0.018463134765625,
-0.019500732421875,
-0.0177459716796875,
-0.028106689453125,
0.0216064453125,
0.0193328857421875,
0.00788116455078125,
0.0204925537109375,
0.022491455078125,
0.01538848876953125,
-0.00977325439453125,
-0.02288818359375,
-0.00724029541015625,
0.00867462158203125,
0.01073455810546875,
-0.01157379150390625,
-0.017181396484375,
-0.020599365234375,
-0.01053619384765625,
0.01416015625,
0.014739990234375,
0.0269012451171875,
-0.004245758056640625,
0.0218505859375,
-0.00817108154296875,
-0.0005574226379394531,
0.0167388916015625,
0.01035308837890625,
0.0040283203125,
0.00896453857421875,
-0.0205078125,
0.024658203125,
-0.007259368896484375,
-0.00846099853515625,
0.035736083984375,
-0.0161895751953125,
0.0152587890625,
-0.0038433074951171875,
0.0126953125,
0.01108551025390625,
-0.01328277587890625,
-0.0528564453125,
0.0213775634765625,
-0.03704833984375,
-0.0120086669921875,
-0.007518768310546875,
0.057220458984375,
0.0158843994140625,
-0.02728271484375,
-0.01318359375,
0.018463134765625,
0.035186767578125,
0.0099945068359375,
-0.032073974609375,
-0.0218505859375,
0.01995849609375,
0.00948333740234375,
0.0084991455078125,
-0.00687408447265625,
-0.0181732177734375,
-0.00862884521484375,
0.0081787109375,
-0.0153656005859375,
-0.0106964111328125,
0.0019283294677734375,
0.031585693359375,
-0.00909423828125,
-0.0036106109619140625,
0.0193023681640625,
0.032135009765625,
0.02301025390625,
0.023223876953125,
-0.0063934326171875,
0.0297698974609375,
-0.0310516357421875,
0.033935546875,
0.0164947509765625,
-0.00989532470703125,
0.0196075439453125,
0.045379638671875,
0.0210418701171875,
-0.032989501953125,
0.023529052734375,
0.0022716522216796875,
0.039825439453125,
0.01218414306640625,
0.00768280029296875,
0.01242828369140625,
0.0084991455078125,
-0.0110321044921875,
-0.0158538818359375,
-0.03826904296875,
0.037628173828125,
-0.0174560546875,
-0.025054931640625,
0.02447509765625,
-0.01067352294921875,
-0.032623291015625,
-0.01515960693359375,
-0.00787353515625,
0.022125244140625,
-0.0029926300048828125,
-0.00965118408203125,
0.0281524658203125,
-0.01438140869140625,
0.0257110595703125,
-0.0286865234375,
-0.003887176513671875,
0.04693603515625,
-0.01108551025390625,
0.037689208984375,
-0.0038127899169921875,
0.004741668701171875,
0.0245208740234375,
0.016021728515625,
-0.01122283935546875,
-0.007495880126953125,
0.005199432373046875,
-0.0192108154296875,
-0.013519287109375,
0.0017137527465820312,
-0.00846099853515625,
-0.0283050537109375,
-0.0030384063720703125,
0.00691986083984375,
-0.00778961181640625,
0.00970458984375,
0.01306915283203125,
0.0172271728515625,
0.032073974609375,
-0.0178070068359375,
0.02105712890625,
-0.056793212890625,
-0.0009403228759765625,
-0.0058135986328125,
0.0036468505859375,
0.00487518310546875,
-0.00646209716796875,
0.03741455078125,
0.0029010772705078125,
0.0003705024719238281,
0.0276641845703125,
0.006206512451171875,
0.007511138916015625,
-0.041290283203125,
0.0024013519287109375,
0.00818634033203125,
0.02020263671875,
0.00243377685546875,
0.0086669921875,
-0.006755828857421875,
0.0168304443359375,
0.01708984375,
0.031341552734375,
0.0174560546875,
0.00443267822265625,
-0.0278167724609375,
0.012237548828125,
0.05224609375,
-0.044189453125,
-0.01361083984375,
-0.006748199462890625,
0.005130767822265625,
-0.007404327392578125,
0.010406494140625,
0.005313873291015625,
0.00841522216796875,
-0.01337432861328125,
0.0237579345703125,
-0.00562286376953125,
-0.004535675048828125,
0.01367950439453125,
0.0203704833984375,
-0.0200653076171875,
-0.024261474609375,
0.012908935546875,
0.0205230712890625,
-0.027130126953125,
0.012359619140625,
-0.0204010009765625,
0.0186004638671875,
0.014923095703125,
-0.031890869140625,
-0.0020656585693359375,
0.01140594482421875,
0.005558013916015625,
-0.020782470703125,
-0.005664825439453125,
0.009429931640625,
0.005748748779296875,
0.00795745849609375,
0.01348876953125,
0.00849151611328125,
-0.0273895263671875,
0.025177001953125,
0.003749847412109375,
-0.044830322265625,
-0.0264892578125,
-0.042755126953125,
-0.0005331039428710938,
0.00772857666015625,
0.022247314453125,
-0.002178192138671875,
0.0026111602783203125,
0.0263671875,
0.01253509521484375,
-0.0131072998046875,
-0.02313232421875,
-0.00568389892578125,
0.038177490234375,
0.01450347900390625,
-0.01300048828125,
-0.02398681640625,
0.02960205078125,
0.0013170242309570312,
0.035552978515625,
0.0020599365234375,
0.01352691650390625,
-0.01611328125,
-0.01561737060546875,
0.035430908203125,
-0.0232696533203125,
-0.003086090087890625,
-0.020050048828125,
-0.0305633544921875,
0.017974853515625,
-0.020416259765625,
0.00848388671875,
-0.0062713623046875,
-0.0061187744140625,
-0.003826141357421875,
0.024169921875,
-0.03436279296875,
-0.0216217041015625,
-0.009246826171875,
-0.006290435791015625,
0.0017910003662109375,
-0.01155853271484375,
0.00614166259765625,
-0.02252197265625,
0.01320648193359375,
0.00974273681640625,
0.00501251220703125,
0.0119781494140625,
-0.01342010498046875,
0.0194549560546875,
0.0019931793212890625,
0.0105438232421875,
-0.024993896484375,
-0.02288818359375,
0.006130218505859375,
-0.0030994415283203125,
0.00888824462890625,
-0.001697540283203125,
0.044189453125,
0.007495880126953125,
-0.0338134765625,
-0.0085601806640625,
-0.006420135498046875,
-0.0191802978515625,
0.0109100341796875,
0.007450103759765625,
0.0193634033203125,
0.032562255859375,
-0.0169677734375,
-0.00019812583923339844,
-0.0047607421875,
0.006786346435546875,
0.031646728515625,
-0.038055419921875,
0.03607177734375,
0.0205841064453125,
0.0188140869140625,
0.0099029541015625,
-0.03118896484375,
0.02392578125,
-0.0164642333984375,
-0.0155487060546875,
-0.0014715194702148438,
-0.0203399658203125,
0.00897979736328125,
0.0162353515625,
0.0164031982421875,
0.041168212890625,
-0.003932952880859375,
-0.0005631446838378906,
-0.01033782958984375,
0.00521087646484375,
-0.039825439453125,
0.037628173828125,
0.0020580291748046875,
-0.00923919677734375,
0.0234527587890625,
-0.01702880859375,
0.0184478759765625,
-0.0180816650390625,
-0.00710296630859375,
0.0007863044738769531,
0.01142120361328125,
0.054840087890625,
0.014678955078125,
-0.0036716461181640625,
-0.00215911865234375,
-0.00508880615234375,
-0.00998687744140625,
0.00867462158203125,
0.00689697265625,
0.02880859375,
-0.037139892578125,
-0.0191497802734375,
0.0013027191162109375,
-0.0112762451171875,
0.028045654296875,
-0.0202789306640625,
-0.00617218017578125,
-0.004390716552734375,
-0.006870269775390625,
0.0015840530395507812,
-0.005847930908203125,
0.0068817138671875,
-0.015167236328125,
0.0120697021484375,
-0.0148773193359375,
0.0061492919921875,
0.055511474609375,
-0.00873565673828125,
-0.006683349609375,
-0.021453857421875,
0.04632568359375,
-0.0218353271484375,
-0.045440673828125,
0.01043701171875,
-0.032562255859375,
-0.0010042190551757812,
0.01027679443359375,
-0.00360107421875,
-0.01439666748046875,
0.0295257568359375,
-0.01482391357421875,
0.009521484375,
0.01180267333984375,
0.029693603515625,
-0.0224151611328125,
-0.017547607421875,
-0.0271453857421875,
0.00579071044921875,
0.0176544189453125,
-0.03021240234375,
-0.007457733154296875,
0.00238800048828125,
-0.0008044242858886719,
-0.012664794921875,
-0.0278167724609375,
0.00785064697265625,
0.0120086669921875,
0.0161285400390625,
-0.027862548828125,
-0.0026874542236328125,
-0.047149658203125,
-0.001888275146484375,
-0.032257080078125,
-0.0220184326171875,
0.00698089599609375,
0.00815582275390625,
0.003360748291015625,
0.0142364501953125,
-0.0244293212890625,
-0.01012420654296875,
-0.0012807846069335938,
0.0020694732666015625,
0.0153350830078125,
0.01482391357421875,
-0.004573822021484375,
-0.00023257732391357422,
0.028076171875,
0.034881591796875,
-0.01108551025390625,
-0.01763916015625,
-0.0234222412109375,
-0.0088043212890625,
0.0002269744873046875,
-0.03338623046875,
-0.006137847900390625,
-0.0258026123046875,
0.005481719970703125,
0.009429931640625,
-0.003269195556640625,
-0.039520263671875,
-0.044281005859375,
-0.003772735595703125,
-0.0032196044921875,
0.0406494140625,
0.005863189697265625,
-0.0157470703125,
0.033447265625,
-0.005214691162109375,
0.025238037109375,
-0.0142974853515625,
0.0138092041015625,
-0.0020904541015625,
-0.030609130859375,
-0.01471710205078125,
0.0032863616943359375,
-0.04620361328125,
-0.030364990234375,
-0.00933074951171875,
0.01296234130859375,
-0.0035953521728515625,
0.0110321044921875,
0.006443023681640625,
-0.0022182464599609375,
0.0325927734375,
-0.043304443359375,
-0.00698089599609375,
-0.01323699951171875,
-0.05517578125,
-0.0090179443359375,
-0.031707763671875,
0.03582763671875,
0.0284881591796875,
0.032318115234375,
-0.0150604248046875,
-0.01279449462890625,
0.021514892578125,
-0.026580810546875,
0.00386810302734375,
0.0291595458984375,
0.0031299591064453125,
0.0168304443359375,
-0.0008034706115722656,
-0.0126190185546875,
-0.0004551410675048828,
0.0234222412109375,
-0.0254669189453125,
0.01172637939453125,
0.0122528076171875,
0.0172271728515625,
-0.00119781494140625,
0.029815673828125,
0.0004906654357910156,
0.023895263671875,
0.00850677490234375,
-0.008758544921875,
-0.0167999267578125,
-0.0206756591796875,
0.01065826416015625,
0.041717529296875,
-0.0272216796875,
0.008331298828125,
0.01580810546875,
-0.002960205078125,
-0.004150390625
] |
ours_485
|
Suppose that it is currently player 1's turn and let \(D = P - C\), where \(P\) is the number of presents and \(C\) is the number of pieces of coal. Let \(P_i (i = 2, 0, -2)\) be the probability that player 1 wins when it is their turn and \(D = i\).
Suppose that \(D = -2\). If player 1 does not receive a present, then player 2 receives one immediately after, so \(P_{-2} = \frac{1}{2}\).
Suppose that \(D = 0\). There is a \(\frac{1}{2}\) chance that player 1 receives a present and wins. There is a \(\frac{1}{4}\) chance that both player 1 and player 2 do not receive presents right now. Consider a Cartesian grid where Santa begins at \((0,2)\) and moves one unit in the positive \(x\) direction if he gives a present and the positive \(y\) direction if he gives coal. Move Santa in this pattern until he goes back to player 1. Then Santa will stop somewhere on the line \(x+y=10\) such that \(|x-y| \leq 3\) for all positions that Santa is in. We can apply modified Pascal counting to count the number of ways that Santa can arrive at each of \((4,6), (5,5), (6,4)\). We do this by starting with 1 at \((1,1)\) and applying the usual Pascal counting except at a border point along \(y = x \pm 3\), their value is doubled when added to get to a neighboring point. This works because the probability that Santa takes the path that is followed along this doubling is 1 rather than \(\frac{1}{2}\) (which would be the probability for regular paths). Doing this gets us the following Pascal counting:
So the probability that Santa ends up at \((4,6)\) is \(\frac{126}{256}\), \((5,5)\) is \(\frac{85}{256}\), \((6,4)\) is \(\frac{45}{256}\). These states represent \(D = -2, 0, 2\) respectively, so
\[
P_0 = \frac{1}{2} + \frac{1}{4}\left(\frac{126}{256} P_{-2} + \frac{85}{256} P_0 + \frac{45}{256} P_2\right).
\]
Suppose that \(D = 2\). From the same logic as above, it suffices to do Pascal counting except starting at \((1,1)\) this time. Doing this gets us the following Pascal counting:
So the probability that Santa ends up at \((4,6)\) is \(\frac{85}{256}\), \((5,5)\) is \(\frac{86}{256}\), \((6,4)\) is \(\frac{86}{256}\). These states represent \(D = -2, 0, 2\) respectively, so
\[
P_2 = \frac{1}{2} + \frac{1}{4}\left(\frac{85}{256} P_{-2} + \frac{86}{256} P_0 + \frac{85}{256} P_2\right).
\]
We can solve this system of equations to deduce that \(P_0 = \frac{9185}{14274}\). Since the initial state is \(D = 0\), we have that \(p = P_0\) and hence \(100m+n = 932774\).
\(\boxed{932774}\)
|
932774
|
{
"competition": "us_comps",
"dataset": "Ours",
"posts": null,
"source": "OMOFall18Solns.md"
}
|
Players \(1, 2, \ldots, 10\) are playing a game on Christmas. Santa visits each player's house according to a set of rules:
- Santa first visits player 1. After visiting player \(i\), Santa visits player \(i+1\), where player \(11\) is the same as player 1.
- Every time Santa visits someone, he gives them either a present or a piece of coal (but not both).
- The absolute difference between the number of presents and pieces of coal that Santa has given out is at most 3 at every point in time.
- If Santa has a choice between giving out a present and a piece of coal, he chooses with equal probability.
Let \(p\) be the probability that player 1 gets a present before player 2 does. If \(p=\frac{m}{n}\) for relatively prime positive integers \(m\) and \(n\), then compute \(100m+n\).
|
[
"/Mathematics/DiscreteMathematics/Combinatorics/BinomialCoefficients",
"/Mathematics/DiscreteMathematics/Combinatorics/Enumeration",
"/Mathematics/DiscreteMathematics/Combinatorics/GeneralCombinatorics",
"/Mathematics/DiscreteMathematics/Combinatorics/LatticePathsandPolygons",
"/Mathematics/DiscreteMathematics/GeneralDiscreteMathematics/DiscreteMath",
"/Mathematics/DiscreteMathematics/GeneralDiscreteMathematics/DiscreteMathematics",
"/Mathematics/ProbabilityandStatistics/Probability/ConditionalProbability",
"/Mathematics/ProbabilityandStatistics/Probability/TotalProbabilityTheorem",
"/Mathematics/ProbabilityandStatistics/RandomWalks/RandomWalk",
"/Mathematics/ProbabilityandStatistics/RandomWalks/RandomWalk1-Dimensional"
] |
Translate the gifting process into a constrained lattice random walk and count reachable states with a modified Pascal triangle to obtain transition probabilities.
|
[
0.000001430511474609375,
0.020111083984375,
0.0256195068359375,
-0.004398345947265625,
0.00014078617095947266,
0.007648468017578125,
0.0384521484375,
-0.01551055908203125,
0.0008134841918945312,
-0.009063720703125,
0.0195465087890625,
-0.028045654296875,
-0.0032482147216796875,
-0.054534912109375,
-0.046173095703125,
-0.0180511474609375,
0.00489044189453125,
0.010589599609375,
-0.028594970703125,
0.00092315673828125,
-0.00855255126953125,
-0.055938720703125,
-0.0229949951171875,
0.0172882080078125,
-0.018035888671875,
-0.021392822265625,
-0.0117950439453125,
0.01444244384765625,
0.031768798828125,
-0.0016031265258789062,
-0.05694580078125,
-0.00748443603515625,
0.0015249252319335938,
-0.0226898193359375,
0.0028324127197265625,
0.021514892578125,
0.0175933837890625,
-0.004344940185546875,
0.024078369140625,
0.00390625,
-0.004947662353515625,
0.04052734375,
-0.0052032470703125,
0.01141357421875,
-0.01806640625,
-0.00267791748046875,
-0.01190948486328125,
0.037109375,
-0.004589080810546875,
-0.00539398193359375,
-0.00809478759765625,
0.01351165771484375,
-0.015655517578125,
-0.0120697021484375,
-0.01397705078125,
-0.07989501953125,
0.0130157470703125,
-0.01404571533203125,
0.016204833984375,
-0.03485107421875,
0.01120758056640625,
-0.015777587890625,
0.021820068359375,
-0.010406494140625,
0.0006690025329589844,
-0.00380706787109375,
-0.002353668212890625,
-0.020172119140625,
-0.00859832763671875,
-0.007480621337890625,
0.038543701171875,
0.0166168212890625,
-0.033905029296875,
0.017913818359375,
0.0204315185546875,
-0.011077880859375,
-0.01486968994140625,
-0.0044403076171875,
0.0226287841796875,
-0.00469207763671875,
0.005519866943359375,
0.01302337646484375,
-0.01148223876953125,
0.0108795166015625,
0.0021114349365234375,
0.02813720703125,
0.0057373046875,
-0.0105438232421875,
0.01090240478515625,
0.002857208251953125,
-0.0007243156433105469,
0.01751708984375,
0.0217437744140625,
0.0128936767578125,
0.0033321380615234375,
-0.01446533203125,
-0.0010633468627929688,
-0.00788116455078125,
-0.026092529296875,
0.007843017578125,
-0.01293182373046875,
-0.0056610107421875,
0.03070068359375,
0.00487518310546875,
-0.044708251953125,
0.00920867919921875,
-0.0202789306640625,
-0.001567840576171875,
-0.003215789794921875,
-0.0056915283203125,
-0.00567626953125,
0.004344940185546875,
0.0523681640625,
-0.02349853515625,
-0.0032978057861328125,
0.01128387451171875,
0.013671875,
-0.023040771484375,
-0.0316162109375,
0.00870513916015625,
-0.002819061279296875,
0.00817108154296875,
-0.013671875,
0.004650115966796875,
-0.0009455680847167969,
0.0377197265625,
-0.0171356201171875,
0.00023603439331054688,
0.01210784912109375,
0.00418853759765625,
0.021942138671875,
0.01239776611328125,
-0.039398193359375,
-0.01861572265625,
-0.05035400390625,
0.01352691650390625,
0.01415252685546875,
-0.007434844970703125,
0.00449371337890625,
-0.0111846923828125,
0.00792694091796875,
-0.017822265625,
0.00189208984375,
-0.0014142990112304688,
-0.0179595947265625,
0.007568359375,
-0.0190277099609375,
-0.05029296875,
-0.0115814208984375,
0.003261566162109375,
-0.0178680419921875,
-0.0114288330078125,
0.01477813720703125,
0.0115203857421875,
-0.0171966552734375,
0.0205841064453125,
0.0167999267578125,
0.010711669921875,
-0.005367279052734375,
0.0142974853515625,
-0.0092620849609375,
-0.0118408203125,
-0.00749969482421875,
0.0222930908203125,
-0.00939178466796875,
-0.005023956298828125,
-0.0004267692565917969,
-0.0196685791015625,
-0.00441741943359375,
-0.0006527900695800781,
0.004638671875,
0.02001953125,
-0.00835418701171875,
-0.004520416259765625,
-0.01195526123046875,
0.01422882080078125,
-0.0196380615234375,
-0.026702880859375,
-0.0011835098266601562,
0.016021728515625,
0.003871917724609375,
-0.03973388671875,
0.0109405517578125,
-0.0047454833984375,
-0.0188446044921875,
0.02093505859375,
-0.006053924560546875,
0.00890350341796875,
0.0192413330078125,
0.016571044921875,
0.007595062255859375,
0.00554656982421875,
-0.0056610107421875,
0.00937652587890625,
-0.0010709762573242188,
-0.005176544189453125,
-0.00852203369140625,
0.002735137939453125,
0.030120849609375,
-0.0024700164794921875,
0.026123046875,
0.000021636486053466797,
-0.04461669921875,
0.0032596588134765625,
0.0037994384765625,
0.002593994140625,
-0.003543853759765625,
0.0024204254150390625,
0.00389862060546875,
-0.00649261474609375,
0.0001819133758544922,
-0.00629425048828125,
0.004230499267578125,
-0.00609588623046875,
0.00923919677734375,
0.0028820037841796875,
-0.002193450927734375,
0.004169464111328125,
-0.0005884170532226562,
-0.02801513671875,
-0.0093841552734375,
0.007656097412109375,
0.0045623779296875,
-0.0065155029296875,
-0.021881103515625,
0.0163421630859375,
0.00013649463653564453,
0.0025882720947265625,
-0.0151519775390625,
0.0037841796875,
0.048614501953125,
0.00145721435546875,
-0.0188446044921875,
-0.0033111572265625,
0.01245880126953125,
-0.00815582275390625,
-0.008270263671875,
0.00272369384765625,
0.0233917236328125,
0.0003924369812011719,
0.0416259765625,
0.0017795562744140625,
0.01139068603515625,
0.0110626220703125,
-0.00756072998046875,
-0.00690460205078125,
0.01166534423828125,
-0.003772735595703125,
0.005458831787109375,
-0.006748199462890625,
0.0005311965942382812,
-0.0029163360595703125,
-0.0064239501953125,
0.007404327392578125,
0.0142669677734375,
-0.03350830078125,
-0.00690460205078125,
-0.0192718505859375,
0.00441741943359375,
-0.01312255859375,
-0.006015777587890625,
-0.01183319091796875,
-0.015411376953125,
-0.01617431640625,
0.021728515625,
-0.007282257080078125,
0.037933349609375,
0.00164031982421875,
-0.0140533447265625,
-0.01407623291015625,
0.04248046875,
-0.0118865966796875,
-0.036895751953125,
0.020782470703125,
0.03277587890625,
-0.003818511962890625,
-0.005039215087890625,
0.01055145263671875,
-0.01416015625,
-0.00809478759765625,
0.002399444580078125,
-0.0218658447265625,
-0.0382080078125,
0.0165557861328125,
0.00909423828125,
-0.0028324127197265625,
-0.0187530517578125,
-0.0168914794921875,
-0.0198974609375,
0.00321197509765625,
-0.0003676414489746094,
0.01412200927734375,
-0.00678253173828125,
-0.0131988525390625,
-0.01611328125,
-0.0298309326171875,
0.0158843994140625,
0.004413604736328125,
0.0216827392578125,
-0.00798797607421875,
0.0177001953125,
0.0026092529296875,
0.01629638671875,
0.0190582275390625,
-0.00249481201171875,
0.040985107421875,
-0.0049896240234375,
-0.0030651092529296875,
0.021881103515625,
-0.0345458984375,
0.0193939208984375,
0.00429534912109375,
0.0169525146484375,
0.01275634765625,
0.0098724365234375,
-0.0367431640625,
0.00817108154296875,
0.022430419921875,
-0.02130126953125,
0.0276947021484375,
0.01097869873046875,
-0.00902557373046875,
-0.009979248046875,
0.00862884521484375,
0.01486968994140625,
-0.0005068778991699219,
-0.0180511474609375,
0.0038318634033203125,
-0.03485107421875,
0.0100555419921875,
-0.024383544921875,
-0.00417327880859375,
0.0179290771484375,
-0.0229644775390625,
-0.018463134765625,
0.036773681640625,
0.0163726806640625,
0.0170135498046875,
0.000888824462890625,
0.01180267333984375,
-0.0149993896484375,
-0.01123046875,
0.0016775131225585938,
-0.0239410400390625,
-0.0009212493896484375,
0.009307861328125,
-0.00020945072174072266,
-0.0183563232421875,
-0.0143585205078125,
0.0316162109375,
0.0222320556640625,
0.0284576416015625,
0.0035247802734375,
-0.00833892822265625,
-0.0208740234375,
0.01004791259765625,
0.012939453125,
0.00745391845703125,
-0.01995849609375,
0.0285186767578125,
0.002803802490234375,
0.003124237060546875,
0.0191802978515625,
-0.02606201171875,
0.01103973388671875,
-0.026763916015625,
-0.0236968994140625,
0.019256591796875,
-0.0287933349609375,
-0.0225830078125,
-0.01519012451171875,
0.00824737548828125,
0.01457977294921875,
-0.0020885467529296875,
-0.0296173095703125,
0.01218414306640625,
0.0160369873046875,
0.0263824462890625,
-0.0264129638671875,
0.014862060546875,
-0.002483367919921875,
0.0343017578125,
0.0158233642578125,
0.025054931640625,
-0.0251617431640625,
-0.0180206298828125,
0.03509521484375,
-0.029815673828125,
-0.0201263427734375,
-0.004169464111328125,
-0.007080078125,
0.02789306640625,
0.01300048828125,
0.0013322830200195312,
0.01934814453125,
-0.026092529296875,
-0.0035305023193359375,
0.01611328125,
0.040252685546875,
-0.013885498046875,
0.016204833984375,
-0.018463134765625,
-0.02874755859375,
0.0270538330078125,
-0.005237579345703125,
-0.0114593505859375,
0.0023975372314453125,
-0.0208282470703125,
0.0071868896484375,
0.00836181640625,
-0.026641845703125,
0.0034637451171875,
0.0083160400390625,
0.0105743408203125,
0.01461029052734375,
-0.00418853759765625,
0.00405120849609375,
0.0295562744140625,
-0.048675537109375,
-0.031402587890625,
0.00891876220703125,
-0.0294189453125,
-0.02099609375,
0.00878143310546875,
0.01039886474609375,
0.0243072509765625,
-0.007648468017578125,
0.02581787109375,
-0.0360107421875,
-0.0098876953125,
-0.0170440673828125,
-0.00978851318359375,
-0.006641387939453125,
0.0106964111328125,
0.00600433349609375,
0.03955078125,
-0.0009613037109375,
-0.0016527175903320312,
-0.017669677734375,
0.01202392578125,
0.0138702392578125,
-0.0216217041015625,
0.01033782958984375,
-0.023468017578125,
-0.00839996337890625,
0.0286865234375,
-0.0014982223510742188,
0.01523590087890625,
-0.040985107421875,
0.0170440673828125,
-0.0288848876953125,
0.01202392578125,
-0.0007724761962890625,
0.00933837890625,
-0.0012960433959960938,
0.03271484375,
0.0286865234375,
-0.03497314453125,
-0.02801513671875,
0.0022373199462890625,
-0.0306854248046875,
0.0184478759765625,
0.0198516845703125,
-0.016326904296875,
0.01418304443359375,
0.00348663330078125,
-0.042938232421875,
0.0037326812744140625,
0.0191802978515625,
0.036468505859375,
0.0020465850830078125,
-0.02008056640625,
-0.0236358642578125,
-0.0350341796875,
-0.05279541015625,
0.01904296875,
-0.0306396484375,
0.01334381103515625,
-0.030029296875,
-0.024169921875,
0.043670654296875,
-0.0005373954772949219,
-0.0146484375,
0.057891845703125,
0.01110076904296875,
-0.0011167526245117188,
0.0150604248046875,
0.025787353515625,
-0.006725311279296875,
-0.0340576171875,
0.007686614990234375,
0.03662109375,
-0.0259857177734375,
-0.050201416015625,
-0.01520538330078125,
-0.01285552978515625,
-0.008819580078125,
0.006267547607421875,
-0.01419830322265625,
-0.02239990234375,
0.00492095947265625,
0.002307891845703125,
0.0271759033203125,
0.01560211181640625,
0.005283355712890625,
0.0034275054931640625,
0.02252197265625,
0.0153350830078125,
-0.0238494873046875,
-0.01861572265625,
-0.005748748779296875,
0.01192474365234375,
0.017974853515625,
-0.027984619140625,
-0.006458282470703125,
-0.01061248779296875,
0.036895751953125,
-0.0293121337890625,
0.0174407958984375,
0.027008056640625,
-0.021820068359375,
0.006275177001953125,
0.041290283203125,
-0.0123291015625,
-0.0189056396484375,
-0.004795074462890625,
-0.0013666152954101562,
-0.001049041748046875,
-0.00244903564453125,
0.0283660888671875,
0.01337432861328125,
-0.0016393661499023438,
0.009002685546875,
-0.03131103515625,
-0.002384185791015625,
-0.0026378631591796875,
0.01139068603515625,
-0.035980224609375,
-0.01221466064453125,
0.0184173583984375,
-0.01971435546875,
-0.01001739501953125,
0.0035228729248046875,
0.02691650390625,
0.0131683349609375,
-0.0272064208984375,
0.003604888916015625,
0.0088348388671875,
-0.0168609619140625,
0.0161590576171875,
-0.021087646484375,
0.0296630859375,
0.030426025390625,
-0.01358795166015625,
-0.0092926025390625,
0.00888824462890625,
-0.032928466796875,
0.01235198974609375,
-0.0136871337890625,
0.0031795501708984375,
-0.039154052734375,
0.0011186599731445312,
0.007602691650390625,
-0.030975341796875,
-0.020050048828125,
0.015716552734375,
-0.0180816650390625,
0.01387786865234375,
0.0179290771484375,
-0.05438232421875,
-0.005252838134765625,
0.01947021484375,
-0.0161895751953125,
0.01104736328125,
0.0033969879150390625,
-0.004413604736328125,
-0.01352691650390625,
-0.0169219970703125,
-0.0126953125,
-0.0149078369140625,
-0.00850677490234375,
0.0127716064453125,
0.0013589859008789062,
0.007049560546875,
0.0311279296875,
0.017730712890625,
0.0252838134765625,
-0.006565093994140625,
0.027130126953125,
0.00716400146484375,
-0.0076446533203125,
-0.0166015625,
0.042388916015625,
-0.006305694580078125,
-0.01548004150390625,
-0.046173095703125,
0.00249481201171875,
0.00049591064453125,
0.01045989990234375,
-0.0155792236328125,
-0.01160430908203125,
0.0164642333984375,
-0.0237274169921875,
-0.004329681396484375,
-0.01537322998046875,
0.0229339599609375,
0.014678955078125,
0.039764404296875,
-0.00794219970703125,
-0.00916290283203125,
0.0095062255859375,
0.008392333984375,
-0.0021514892578125,
-0.006534576416015625,
0.027374267578125,
0.0234832763671875,
-0.0090484619140625,
0.01340484619140625,
-0.0272064208984375,
-0.032379150390625,
0.018798828125,
0.00359344482421875,
0.0225067138671875,
-0.0188446044921875,
-0.0230712890625,
-0.00799560546875,
-0.0026226043701171875,
-0.0269622802734375,
0.0275115966796875,
-0.0008559226989746094,
-0.01184844970703125,
-0.038543701171875,
0.036102294921875,
-0.03338623046875,
-0.0211944580078125,
-0.01430511474609375,
0.027801513671875,
0.01062774658203125,
0.00945281982421875,
-0.0289154052734375,
-0.0006012916564941406,
0.0157012939453125,
0.032135009765625,
-0.04400634765625,
-0.0176239013671875,
-0.005947113037109375,
0.034210205078125,
0.0269317626953125,
-0.0312042236328125,
-0.0010423660278320312,
0.00714111328125,
-0.0004417896270751953,
0.01593017578125,
-0.0154876708984375,
-0.029205322265625,
-0.010589599609375,
-0.005767822265625,
-0.006069183349609375,
0.022674560546875,
-0.01392364501953125,
0.01096343994140625,
0.008209228515625,
0.0198211669921875,
0.003986358642578125,
-0.018524169921875,
-0.043182373046875,
0.01776123046875,
-0.01088714599609375,
0.0230712890625,
-0.001346588134765625,
0.0182342529296875,
-0.01910400390625,
0.01003265380859375,
0.0204010009765625,
0.043914794921875,
0.035186767578125,
-0.0080413818359375,
-0.006755828857421875,
0.01001739501953125,
0.031097412109375,
-0.00943756103515625,
0.0204925537109375,
0.033599853515625,
-0.0335693359375,
0.0133514404296875,
0.0301361083984375,
0.0023136138916015625,
-0.0238494873046875,
0.01551055908203125,
0.00267791748046875,
0.01270294189453125,
0.0309295654296875,
-0.01331329345703125,
0.038818359375,
0.02349853515625,
-0.0193328857421875,
0.018341064453125,
-0.01279449462890625,
-0.038421630859375,
0.01611328125,
0.031158447265625,
-0.0045623779296875,
0.0129547119140625,
0.020294189453125,
0.0300750732421875,
-0.00907135009765625,
0.00600433349609375,
0.01438140869140625,
-0.01149749755859375,
-0.0247955322265625,
0.0012769699096679688,
-0.030364990234375,
-0.0081787109375,
0.010650634765625,
-0.015411376953125,
-0.0240325927734375,
-0.0005159378051757812,
-0.0233306884765625,
0.0345458984375,
-0.000698089599609375,
-0.04132080078125,
-0.003757476806640625,
-0.01114654541015625,
-0.015289306640625,
0.00922393798828125,
0.0038547515869140625,
-0.0190277099609375,
-0.045806884765625,
-0.01157379150390625,
-0.0028476715087890625,
-0.0189056396484375,
0.0175933837890625,
0.038818359375,
-0.03997802734375,
-0.0250396728515625,
0.0007348060607910156,
0.00563812255859375,
-0.0645751953125,
0.01334381103515625,
0.0273895263671875,
0.041351318359375,
-0.0150146484375,
0.033721923828125,
-0.0084686279296875,
-0.0004992485046386719,
0.0244293212890625,
0.019989013671875,
0.007720947265625,
0.03564453125,
0.01168060302734375,
0.01275634765625,
-0.0308380126953125,
-0.042205810546875,
0.00685882568359375,
-0.0245208740234375,
0.0262603759765625,
-0.004291534423828125,
-0.055206298828125,
0.0269622802734375,
-0.0163421630859375,
-0.0007290840148925781,
-0.00788116455078125,
0.01207733154296875,
0.0173187255859375,
0.04852294921875,
0.025482177734375,
-0.03741455078125,
-0.01543426513671875,
0.0032558441162109375,
0.027099609375,
-0.0380859375,
-0.0038013458251953125,
0.017303466796875,
-0.0428466796875,
0.00572967529296875,
-0.0249176025390625,
-0.02984619140625,
-0.0252532958984375,
0.007781982421875,
-0.0277862548828125,
-0.0250396728515625,
0.00859832763671875,
-0.027069091796875,
-0.017791748046875,
0.0024585723876953125,
-0.0059051513671875,
0.0225982666015625,
-0.026031494140625,
0.006481170654296875,
-0.001529693603515625,
0.0275726318359375,
0.0027942657470703125,
-0.007320404052734375,
-0.04473876953125,
-0.031951904296875,
0.0024204254150390625,
-0.01953125,
0.00598907470703125,
-0.002017974853515625,
0.012176513671875,
-0.00885772705078125,
-0.033905029296875,
-0.00830078125,
0.00951385498046875,
0.034515380859375,
-0.014923095703125,
-0.00392913818359375,
0.0180816650390625,
0.001659393310546875,
0.011444091796875,
0.0220489501953125,
-0.006671905517578125,
0.01444244384765625,
-0.01047515869140625,
-0.0098114013671875,
-0.0213470458984375,
0.00443267822265625,
0.0014486312866210938,
0.0087127685546875,
-0.0135650634765625,
-0.01548004150390625,
0.0181121826171875,
0.0168609619140625,
-0.009796142578125,
-0.033905029296875,
-0.04669189453125,
-0.0188751220703125,
0.01446533203125,
0.0265960693359375,
-0.0021572113037109375,
-0.01145172119140625,
0.004154205322265625,
-0.016265869140625,
-0.02081298828125,
-0.0202789306640625,
-0.00659942626953125,
-0.020751953125,
0.0176239013671875,
-0.00759124755859375,
-0.00177001953125,
0.020263671875,
-0.002532958984375,
0.01399993896484375,
0.00759124755859375,
0.039794921875,
-0.005596160888671875,
0.005649566650390625,
-0.0202484130859375,
-0.0063934326171875,
0.02386474609375,
-0.0185699462890625,
0.039825439453125,
0.0019683837890625,
0.0189666748046875,
0.0090789794921875,
0.0311737060546875,
0.052520751953125,
0.0146484375,
-0.030517578125,
-0.0237579345703125,
0.0097808837890625,
-0.01445770263671875,
0.0281524658203125,
-0.03289794921875,
-0.00910186767578125,
0.0076751708984375,
-0.0144805908203125,
-0.0033550262451171875,
-0.0013227462768554688,
0.0101470947265625,
0.006565093994140625,
0.0140838623046875,
0.0014104843139648438,
0.01531219482421875,
-0.021514892578125,
-0.0104522705078125,
0.040496826171875,
0.018310546875,
-0.0011463165283203125,
0.00225830078125,
-0.004878997802734375,
-0.007671356201171875,
-0.006046295166015625,
0.0028858184814453125,
-0.005367279052734375,
0.028564453125,
0.03265380859375,
-0.0263519287109375,
-0.006927490234375,
0.00006455183029174805,
0.0271759033203125,
-0.004161834716796875,
0.005748748779296875,
-0.030303955078125,
0.0280914306640625,
-0.006633758544921875,
-0.011474609375,
0.0211029052734375,
-0.0106658935546875,
-0.006927490234375,
-0.0068511962890625,
-0.018707275390625,
-0.0014371871948242188,
0.0037136077880859375,
-0.03680419921875,
-0.041748046875,
-0.01470184326171875,
-0.00646209716796875,
-0.0005769729614257812,
-0.005001068115234375,
0.01214599609375,
0.031524658203125,
0.0310516357421875,
0.01273345947265625,
-0.02520751953125,
-0.0006551742553710938,
0.031402587890625,
0.0290985107421875,
-0.006740570068359375,
0.0241851806640625,
0.0153350830078125,
-0.00644683837890625,
-0.009368896484375,
0.00013875961303710938,
0.0033111572265625,
-0.0160980224609375,
0.01364898681640625,
0.007389068603515625,
-0.00496673583984375,
-0.0018262863159179688,
-0.02362060546875,
0.0226593017578125,
0.00689697265625,
0.00926971435546875,
0.0135345458984375,
0.0004508495330810547,
0.00995635986328125,
0.011993408203125,
0.028076171875,
-0.0027828216552734375,
-0.0034847259521484375,
0.0267791748046875,
-0.0254364013671875,
0.0029506683349609375,
0.018707275390625,
-0.0143585205078125,
-0.0005240440368652344,
-0.004467010498046875,
-0.0222625732421875,
0.005970001220703125,
-0.0250396728515625,
-0.0171356201171875,
-0.01654052734375,
0.00243377685546875,
0.0026493072509765625,
-0.032257080078125,
0.0009160041809082031,
0.01666259765625,
-0.018585205078125,
-0.01317596435546875,
0.007518768310546875,
-0.006946563720703125,
-0.017974853515625,
-0.017333984375,
0.031707763671875,
0.0419921875,
0.018707275390625,
0.0006618499755859375,
0.0279388427734375,
0.01520538330078125,
-0.03973388671875,
0.006561279296875,
-0.00879669189453125,
-0.0435791015625,
0.0080108642578125,
-0.007556915283203125,
-0.006404876708984375,
0.02471923828125,
0.049224853515625,
-0.0030231475830078125,
-0.048980712890625,
0.00782012939453125,
0.0256805419921875,
-0.0164794921875,
-0.0174102783203125,
0.0255126953125,
0.01519775390625,
-0.0014257431030273438,
0.007843017578125,
-0.0156402587890625,
0.0262603759765625,
0.025360107421875,
0.010589599609375,
0.004077911376953125,
0.00420379638671875,
-0.0043182373046875,
-0.0135498046875,
-0.01702880859375,
-0.003871917724609375,
0.01442718505859375,
-0.0312347412109375,
0.00970458984375,
0.006038665771484375,
-0.0146636962890625,
0.030181884765625,
-0.0287933349609375,
0.0013294219970703125,
-0.003162384033203125,
0.0046234130859375,
0.0165557861328125,
-0.0013074874877929688,
0.003131866455078125,
0.009674072265625,
-0.0102386474609375,
-0.0258026123046875,
-0.00926971435546875,
0.0006241798400878906,
0.0015716552734375,
-0.02557373046875,
0.0219879150390625,
0.0055999755859375,
-0.0016069412231445312,
-0.022735595703125,
-0.0212860107421875,
0.0229034423828125,
-0.004367828369140625,
-0.03936767578125,
-0.0006084442138671875,
0.011749267578125,
0.005893707275390625,
0.0155792236328125,
-0.006771087646484375,
0.0181121826171875,
0.002105712890625,
0.0133056640625,
0.015899658203125,
-0.0045166015625,
0.0227813720703125,
0.0165863037109375,
0.009521484375,
-0.00567626953125,
0.0179290771484375,
0.026519775390625,
-0.0170440673828125,
-0.021575927734375,
-0.04974365234375,
-0.0005345344543457031,
0.01824951171875,
-0.03204345703125,
-0.01065826416015625,
0.01497650146484375,
-0.00281524658203125,
-0.0089263916015625,
-0.038848876953125,
0.03759765625,
0.0215606689453125,
0.0032405853271484375,
-0.01062774658203125,
0.00798797607421875,
0.039825439453125,
0.02996826171875,
-0.0149993896484375,
-0.02947998046875,
-0.041900634765625,
0.02362060546875,
-0.054412841796875,
-0.004974365234375,
0.0032863616943359375,
-0.017120361328125,
0.0112762451171875,
-0.04608154296875,
0.010986328125,
0.0223388671875,
-0.033966064453125,
-0.0100250244140625,
0.0185546875,
0.024871826171875,
-0.01641845703125,
-0.0303955078125,
0.0207366943359375,
-0.0076904296875,
0.0007004737854003906,
-0.0204925537109375,
0.015106201171875,
0.02459716796875,
0.024871826171875,
-0.00007659196853637695,
-0.0187225341796875,
-0.0014495849609375,
0.003917694091796875,
-0.0443115234375,
-0.001605987548828125,
0.0226898193359375,
0.034027099609375,
0.030792236328125,
-0.0008473396301269531,
-0.01139068603515625,
0.0401611328125,
0.0085296630859375,
0.019775390625,
-0.015380859375,
0.05096435546875,
-0.0035839080810546875,
0.00013530254364013672,
-0.008819580078125,
-0.031829833984375,
0.0300140380859375,
0.06451416015625,
-0.0167694091796875,
-0.01509857177734375,
0.004978179931640625,
-0.00806427001953125,
-0.0038471221923828125,
0.0196685791015625,
-0.0218963623046875,
0.0101776123046875,
-0.038909912109375,
-0.017425537109375,
-0.03765869140625,
0.00829315185546875,
-0.0248260498046875,
-0.01134490966796875,
-0.0022296905517578125,
-0.0029964447021484375,
0.02972412109375,
-0.0018434524536132812,
0.007175445556640625,
-0.0364990234375,
-0.01190948486328125,
-0.0137786865234375,
-0.005260467529296875,
0.0202789306640625,
0.0017194747924804688,
0.000010132789611816406,
0.02313232421875,
-0.0037059783935546875,
-0.0052032470703125,
-0.0026760101318359375,
0.014190673828125,
-0.015655517578125,
-0.0111083984375,
-0.005443572998046875,
-0.012054443359375,
-0.027435302734375,
-0.005298614501953125,
-0.020355224609375,
0.0124053955078125,
-0.00514984130859375,
0.048614501953125,
-0.00423431396484375,
0.007904052734375,
0.026611328125,
0.00030350685119628906,
-0.006591796875,
-0.0008454322814941406,
-0.0084381103515625,
-0.0206146240234375,
-0.01666259765625,
0.04339599609375,
0.0260772705078125,
0.010101318359375,
-0.0192108154296875,
0.0379638671875,
0.00399017333984375,
0.0019855499267578125,
-0.00937652587890625,
-0.015777587890625,
-0.007266998291015625,
-0.0251312255859375,
0.050628662109375,
-0.018463134765625,
-0.00739288330078125,
0.0136566162109375,
0.0123443603515625,
-0.003753662109375,
0.005184173583984375,
0.00423431396484375,
-0.00850677490234375,
-0.020416259765625,
0.01403045654296875,
-0.00942230224609375,
0.002841949462890625,
0.043121337890625,
-0.0030918121337890625,
-0.00415802001953125,
-0.0303802490234375,
0.01033782958984375,
-0.003314971923828125,
0.01447296142578125,
-0.0004379749298095703,
0.01268768310546875,
0.0007801055908203125,
0.01043701171875,
0.0129241943359375,
0.0157012939453125,
-0.01275634765625,
-0.004199981689453125,
0.0005288124084472656,
-0.007411956787109375,
0.0147857666015625,
-0.00946044921875,
-0.02569580078125,
-0.01360321044921875,
-0.01012420654296875,
-0.033416748046875,
0.046966552734375,
0.0204620361328125,
-0.004119873046875,
-0.017059326171875,
0.00832366943359375,
-0.0124359130859375,
0.00649261474609375,
-0.007793426513671875,
-0.008087158203125,
0.019073486328125,
-0.00864410400390625,
0.006427764892578125,
-0.0089263916015625,
-0.026580810546875,
-0.00904083251953125,
0.0209503173828125,
0.01483154296875,
0.040374755859375,
-0.0038433074951171875,
-0.00908660888671875,
-0.01137542724609375,
-0.0191802978515625,
0.0233306884765625,
0.01055908203125,
-0.0042724609375,
0.0265960693359375,
0.008880615234375,
-0.007068634033203125,
-0.0125732421875,
-0.0249786376953125,
-0.0007357597351074219,
0.0207672119140625,
0.0265350341796875,
-0.045745849609375,
0.0295257568359375,
-0.00125885009765625,
-0.004955291748046875,
0.00772857666015625,
0.0019207000732421875,
-0.0153350830078125,
-0.0024967193603515625,
-0.0264892578125,
0.032470703125,
-0.01495361328125,
0.0089263916015625,
-0.01351165771484375,
0.035064697265625,
-0.001094818115234375,
-0.003200531005859375,
0.00006759166717529297,
-0.02313232421875,
0.027984619140625,
0.00864410400390625,
-0.0173187255859375,
-0.01580810546875,
-0.005558013916015625,
-0.012969970703125,
0.002788543701171875,
0.0244140625,
-0.042266845703125,
0.0015687942504882812,
0.00872802734375,
-0.01922607421875,
-0.0011911392211914062,
0.020721435546875,
0.030670166015625,
0.017608642578125,
0.01751708984375,
0.0350341796875,
0.00833892822265625,
0.0007033348083496094,
0.0112152099609375,
-0.0545654296875,
0.001384735107421875,
-0.0352783203125,
-0.007099151611328125,
0.006259918212890625,
0.01366424560546875,
-0.018280029296875,
-0.005584716796875,
-0.003448486328125,
0.002376556396484375,
0.023529052734375,
-0.0038909912109375,
0.00937652587890625,
0.032928466796875,
0.0011568069458007812,
0.00945281982421875,
0.0257415771484375,
0.011138916015625,
0.0035419464111328125,
0.0174560546875,
0.007183074951171875,
0.0211334228515625,
0.00714874267578125,
-0.00902557373046875,
-0.00846099853515625,
0.0034847259521484375,
0.0056915283203125,
0.0023441314697265625,
-0.02655029296875,
0.0103302001953125,
-0.0045166015625,
0.01036834716796875,
0.010040283203125,
-0.00567626953125,
0.022674560546875,
0.0426025390625,
-0.0003685951232910156,
-0.001140594482421875,
-0.01122283935546875,
-0.01617431640625,
-0.0037593841552734375,
-0.00301361083984375,
0.0039215087890625,
-0.00652313232421875,
0.0042572021484375,
0.004909515380859375,
0.01137542724609375,
0.018890380859375,
-0.0018711090087890625,
-0.048370361328125,
0.03021240234375,
-0.0069732666015625,
-0.017333984375,
0.0196533203125,
0.0025386810302734375,
-0.0160675048828125,
-0.0180816650390625,
0.0036182403564453125,
0.018951416015625,
0.0026397705078125,
-0.010986328125,
0.017547607421875,
-0.034576416015625,
0.008544921875,
0.01457977294921875,
-0.0128021240234375,
-0.0003025531768798828,
0.01557159423828125,
0.03179931640625,
-0.0223388671875,
0.01450347900390625,
0.029266357421875,
-0.026763916015625,
0.006534576416015625,
-0.0057830810546875,
-0.01197052001953125,
0.025909423828125,
-0.008575439453125,
0.0219879150390625,
0.01580810546875,
-0.018310546875,
0.0062713623046875,
0.027374267578125,
0.030364990234375,
0.0009255409240722656,
-0.006103515625,
-0.0018148422241210938,
0.039154052734375,
-0.01458740234375,
0.0008544921875,
-0.007289886474609375,
0.00380706787109375,
-0.00910186767578125,
-0.046112060546875,
-0.008087158203125,
-0.0305328369140625,
0.0064697265625,
0.016387939453125,
0.00647735595703125,
-0.0016317367553710938,
0.016265869140625,
0.0137481689453125,
-0.019287109375,
-0.0187835693359375,
-0.0198516845703125,
-0.02410888671875,
-0.056488037109375,
-0.0268707275390625,
0.03778076171875,
-0.01157379150390625,
0.0017614364624023438,
-0.0233612060546875,
-0.010345458984375,
0.01241302490234375,
-0.006114959716796875,
-0.01947021484375,
0.0013875961303710938,
0.0025959014892578125,
-0.0086822509765625,
-0.0005412101745605469,
-0.00792694091796875,
0.00838470458984375,
-0.0211029052734375,
0.0179595947265625,
-0.01812744140625,
-0.0160675048828125,
0.037322998046875,
-0.0030364990234375,
-0.020263671875,
0.00940704345703125,
0.005657196044921875,
0.00910186767578125,
0.01389312744140625,
-0.038238525390625,
-0.0294647216796875,
-0.019744873046875,
0.020233154296875,
0.016632080078125,
-0.045745849609375,
-0.0006313323974609375,
-0.033050537109375,
-0.003597259521484375,
-0.0135040283203125,
-0.00980377197265625,
-0.0186309814453125,
-0.003955841064453125,
0.016632080078125,
0.00760650634765625,
-0.0185699462890625,
0.002971649169921875,
-0.00510406494140625,
-0.039886474609375,
-0.00017189979553222656,
0.0015697479248046875,
-0.01007843017578125,
-0.01395416259765625,
0.0084991455078125,
0.025299072265625,
-0.0174102783203125,
0.0171051025390625,
-0.013336181640625,
0.0163726806640625,
0.0085601806640625,
0.01058197021484375,
-0.01244354248046875,
0.01534271240234375,
-0.012847900390625,
-0.0000718832015991211,
0.01080322265625,
0.041015625,
0.0284423828125,
0.006381988525390625,
0.01041412353515625,
0.005077362060546875,
-0.022308349609375,
0.00778961181640625,
0.0091094970703125,
-0.0016851425170898438,
-0.0182037353515625,
-0.00524139404296875,
-0.006439208984375,
-0.003665924072265625,
-0.016571044921875,
-0.03375244140625,
-0.0095977783203125,
-0.046295166015625,
0.003978729248046875,
0.03143310546875,
-0.024749755859375,
-0.020263671875,
0.012725830078125,
-0.0117034912109375,
-0.0214691162109375,
-0.03826904296875,
-0.01111602783203125,
-0.0183258056640625,
0.0222015380859375,
0.0015382766723632812,
-0.0169830322265625,
-0.01076507568359375,
-0.00850677490234375,
0.006290435791015625,
-0.01439666748046875,
0.002170562744140625,
0.0017614364624023438,
0.01006317138671875,
0.0017852783203125,
-0.0057220458984375,
-0.01558685302734375,
0.02801513671875,
0.007091522216796875,
-0.0017652511596679688,
-0.032135009765625,
-0.0482177734375,
0.006237030029296875,
0.00905609130859375,
0.0036468505859375,
0.0107879638671875,
0.00927734375,
-0.00199127197265625,
-0.0178070068359375,
0.01332855224609375,
-0.02496337890625,
0.0117034912109375,
0.0161590576171875,
0.006641387939453125,
-0.0037517547607421875,
0.02459716796875,
-0.0311737060546875,
0.0211029052734375,
-0.005504608154296875,
0.006778717041015625,
-0.007411956787109375,
-0.0031452178955078125,
-0.01528167724609375,
0.022796630859375,
0.0247955322265625,
-0.0163726806640625,
0.00554656982421875,
-0.02093505859375,
-0.0252227783203125,
-0.0041046142578125,
0.00392913818359375,
0.0025768280029296875,
0.027557373046875,
0.017181396484375,
-0.017852783203125,
0.00772857666015625,
-0.0277099609375,
0.0157318115234375,
0.003292083740234375,
0.022064208984375,
0.02825927734375,
-0.0209808349609375,
0.00621795654296875,
-0.0009264945983886719,
-0.005504608154296875,
-0.0081787109375,
0.005786895751953125,
-0.0028171539306640625,
-0.00848388671875,
-0.006107330322265625,
-0.0146331787109375,
-0.0103607177734375,
0.0015811920166015625,
0.01488494873046875,
0.0269775390625,
-0.0111846923828125,
-0.0089111328125,
0.0068511962890625,
0.006465911865234375,
-0.0038852691650390625,
-0.006534576416015625,
0.0014705657958984375,
-0.00707244873046875,
0.017364501953125,
-0.0255126953125,
-0.0205535888671875,
-0.017578125,
0.00036144256591796875,
0.004825592041015625,
-0.0275115966796875,
-0.046417236328125,
0.0023708343505859375,
0.04638671875,
-0.0026760101318359375,
-0.0020542144775390625,
0.003879547119140625,
0.035125732421875,
0.0160369873046875,
-0.006946563720703125,
-0.01103973388671875,
-0.0210723876953125,
0.01131439208984375,
0.000896453857421875,
-0.0017690658569335938,
0.00304412841796875,
0.028472900390625,
-0.0028209686279296875,
0.00789642333984375,
0.02471923828125,
0.01058197021484375,
0.01678466796875,
0.01396942138671875,
-0.0292816162109375,
0.007598876953125,
-0.01512908935546875,
-0.0253143310546875,
0.004688262939453125,
0.007015228271484375,
0.022430419921875,
-0.03326416015625,
0.006900787353515625,
0.0160369873046875,
0.00791168212890625,
0.028594970703125,
0.016693115234375,
0.0029926300048828125,
-0.0261077880859375,
0.021270751953125,
-0.008514404296875,
0.0235443115234375,
0.00887298583984375,
0.007659912109375,
0.00609588623046875,
0.0078125,
0.0182342529296875,
-0.004428863525390625,
-0.0092315673828125,
0.03509521484375,
-0.013336181640625,
-0.0247344970703125,
0.01319122314453125,
0.01568603515625,
-0.0123291015625,
0.032379150390625,
-0.050445556640625,
-0.0271453857421875,
0.0008025169372558594,
0.0186309814453125,
-0.004825592041015625,
-0.00984954833984375,
0.0037403106689453125,
0.04345703125,
-0.0119476318359375,
-0.01496124267578125,
0.01324462890625,
0.03436279296875,
0.0233917236328125,
-0.00994873046875,
-0.0265655517578125,
-0.0006551742553710938,
0.0006313323974609375,
0.02874755859375,
-0.003704071044921875,
0.0009613037109375,
0.0394287109375,
-0.01654052734375,
0.0029582977294921875,
-0.040985107421875,
0.024993896484375,
0.0261993408203125,
0.023284912109375,
0.0252685546875,
-0.01690673828125,
-0.0039005279541015625,
-0.044769287109375,
-0.0082244873046875,
0.023223876953125,
-0.00862884521484375,
0.031646728515625,
-0.01325225830078125,
-0.031524658203125,
0.0277252197265625,
-0.007190704345703125,
0.029266357421875,
-0.003246307373046875,
0.02716064453125,
-0.01885986328125,
-0.00023746490478515625,
-0.03399658203125,
-0.0194549560546875,
0.0249176025390625,
0.0188140869140625,
0.03173828125,
-0.01318359375,
-0.043060302734375,
-0.00870513916015625,
0.00426483154296875,
0.00958251953125,
-0.015869140625,
-0.01407623291015625,
-0.018341064453125,
-0.0098419189453125,
-0.03900146484375,
-0.007167816162109375,
0.0098114013671875,
-0.0190277099609375,
0.01512908935546875,
0.0016183853149414062,
0.0182647705078125,
-0.0008063316345214844,
0.009735107421875,
-0.00711822509765625,
0.004726409912109375,
0.01568603515625,
0.028350830078125,
0.0108642578125,
0.0025310516357421875,
-0.0177001953125,
-0.0212249755859375,
-0.00959014892578125,
-0.01480865478515625,
0.0304107666015625,
0.01406097412109375,
-0.0162353515625,
0.0017385482788085938,
0.02496337890625,
0.00238800048828125,
0.015625,
0.0167999267578125,
-0.0176849365234375,
-0.0015668869018554688,
0.0019159317016601562,
-0.0406494140625,
-0.0262298583984375,
-0.010711669921875,
0.0201263427734375,
0.007595062255859375,
-0.0186614990234375,
0.007564544677734375,
-0.05853271484375,
-0.004486083984375,
0.0496826171875,
-0.0217437744140625,
0.00782012939453125,
-0.016571044921875,
-0.00955963134765625,
0.041015625,
0.0159454345703125,
0.003971099853515625,
0.01605224609375,
-0.0045623779296875,
-0.010101318359375,
-0.022430419921875,
-0.004772186279296875,
0.0305023193359375,
-0.01204681396484375,
-0.0105438232421875,
-0.05133056640625,
0.03656005859375,
0.0380859375,
0.012481689453125,
0.00740814208984375,
0.016448974609375,
-0.0183563232421875,
0.00034928321838378906,
0.033233642578125,
-0.007740020751953125,
-0.0083465576171875,
0.006534576416015625,
-0.03497314453125,
0.0213470458984375,
0.02325439453125,
0.0266571044921875,
-0.0224761962890625,
-0.00844573974609375,
-0.0165252685546875,
0.007476806640625,
0.02728271484375,
0.005847930908203125,
0.0133514404296875,
0.014739990234375,
0.022735595703125,
-0.0140228271484375,
-0.0116729736328125,
0.01322174072265625,
-0.036285400390625,
-0.00872039794921875,
-0.00635528564453125,
0.0078887939453125,
0.0094757080078125,
-0.01213836669921875,
0.010833740234375,
-0.027923583984375,
-0.008453369140625,
0.001483917236328125,
-0.004856109619140625,
-0.0003032684326171875,
0.007659912109375,
0.00807952880859375,
-0.02655029296875,
-0.035614013671875,
0.01678466796875,
-0.006298065185546875,
0.014801025390625,
-0.0037136077880859375,
-0.01788330078125,
-0.0028591156005859375,
0.0231170654296875,
-0.0003170967102050781,
0.006710052490234375,
0.00946807861328125,
0.01409149169921875,
0.010467529296875,
-0.0032939910888671875,
-0.01422119140625,
0.01110076904296875,
-0.0050048828125,
0.0238800048828125,
0.0178070068359375,
-0.00423431396484375,
-0.0249176025390625,
0.00858306884765625,
-0.0029239654541015625,
-0.00981903076171875,
-0.0016775131225585938,
0.007965087890625,
0.007266998291015625,
0.01227569580078125,
-0.0235137939453125,
0.000028192996978759766,
0.011627197265625,
-0.021636962890625,
0.0062255859375,
-0.01058197021484375,
-0.020538330078125,
0.0220947265625,
-0.01152801513671875,
-0.007049560546875,
0.0032520294189453125,
0.028778076171875,
0.0140228271484375,
0.0178070068359375,
0.004055023193359375,
0.01354217529296875,
-0.03466796875,
-0.0164337158203125,
-0.00305938720703125,
0.017547607421875,
0.0306396484375,
-0.0099945068359375,
0.0030651092529296875,
-0.03167724609375,
0.016937255859375,
-0.0168914794921875,
-0.0111083984375,
0.0171966552734375,
0.01418304443359375,
0.036865234375,
-0.0125885009765625,
0.01904296875,
0.044189453125,
0.012451171875,
0.01470184326171875,
-0.016021728515625,
-0.05902099609375,
-0.0006933212280273438,
0.0035495758056640625,
-0.034820556640625,
0.0013208389282226562,
-0.006092071533203125,
-0.0089874267578125,
-0.0028285980224609375,
0.01247406005859375,
-0.01526641845703125,
0.0275421142578125,
0.03253173828125,
0.00946807861328125,
0.01554107666015625,
0.006008148193359375,
-0.0237884521484375,
0.0120391845703125,
0.030548095703125,
-0.005153656005859375,
0.02410888671875,
0.00955963134765625,
-0.00905609130859375,
-0.01371002197265625,
-0.0074920654296875,
0.01195526123046875,
0.0208282470703125,
0.00646209716796875,
-0.001056671142578125,
-0.0095672607421875,
0.0124664306640625,
-0.01050567626953125,
-0.005222320556640625,
-0.005489349365234375,
-0.007724761962890625,
0.01467132568359375,
0.025848388671875,
-0.00933074951171875,
0.014007568359375,
-0.0002837181091308594,
0.00551605224609375,
0.00952911376953125,
0.0204620361328125,
0.007762908935546875,
-0.0016527175903320312,
0.013916015625,
0.047332763671875,
0.0155181884765625,
0.0014886856079101562,
0.004077911376953125,
0.006378173828125,
-0.004985809326171875,
0.0111846923828125,
0.00003892183303833008,
0.00925445556640625,
0.0250396728515625,
0.004245758056640625,
-0.0011720657348632812,
-0.001956939697265625,
-0.00804901123046875,
0.0088958740234375,
-0.0298614501953125,
0.0183563232421875,
0.004657745361328125,
0.0190582275390625,
0.02423095703125,
-0.0018863677978515625,
0.0003876686096191406,
-0.01036834716796875,
0.0115509033203125,
-0.0174407958984375,
0.0083160400390625,
-0.01467132568359375,
0.033782958984375,
-0.018341064453125,
0.004734039306640625,
-0.05560302734375,
0.021087646484375,
0.0200347900390625,
0.0222015380859375,
-0.0283050537109375,
0.0174407958984375,
-0.02239990234375,
-0.0077362060546875,
0.04193115234375,
0.038726806640625,
-0.0440673828125,
0.007228851318359375,
0.0008678436279296875,
-0.0181427001953125,
0.03814697265625,
0.0220184326171875,
-0.000637054443359375,
-0.00632476806640625,
-0.048675537109375,
-0.00274658203125,
-0.0103302001953125,
-0.041473388671875,
-0.028472900390625,
-0.00461578369140625,
0.00595855712890625,
0.00397491455078125,
-0.00487518310546875,
0.00820159912109375,
-0.0198516845703125,
0.0144195556640625,
-0.00881195068359375,
0.01026153564453125,
-0.009979248046875,
-0.0096588134765625,
0.026885986328125,
-0.00441741943359375,
0.00791168212890625,
-0.01177215576171875,
-0.0234527587890625,
0.003173828125,
-0.0205078125,
0.006927490234375,
0.0024547576904296875,
-0.033538818359375,
-0.01953125,
-0.0185546875,
0.035888671875,
0.0201568603515625,
0.035400390625,
-0.0187530517578125,
-0.00490570068359375,
0.0369873046875,
-0.004253387451171875,
-0.046051025390625,
-0.0247650146484375,
-0.029022216796875,
0.0260162353515625,
0.032379150390625,
0.02557373046875,
0.00337982177734375,
-0.0188140869140625,
-0.029571533203125,
-0.01000213623046875,
-0.003971099853515625,
-0.0291290283203125,
0.0106353759765625,
0.01287078857421875,
0.002902984619140625,
0.01010894775390625,
0.01702880859375,
-0.028411865234375,
-0.0110626220703125,
-0.043975830078125,
-0.033538818359375,
-0.026092529296875,
-0.0267333984375,
0.01523590087890625,
-0.0169525146484375,
0.01092529296875,
0.016571044921875,
-0.031768798828125,
0.004459381103515625,
0.0308837890625,
-0.00749969482421875,
-0.00859832763671875,
0.0174407958984375,
-0.038055419921875,
0.042083740234375,
0.0217132568359375,
0.005321502685546875,
-0.012908935546875,
-0.0013341903686523438,
-0.015960693359375,
0.009002685546875,
0.0229034423828125,
0.045166015625,
0.005405426025390625,
0.01546478271484375,
0.0165252685546875,
0.00946807861328125,
0.01947021484375,
0.00446319580078125,
0.0160064697265625,
-0.0350341796875,
-0.00047850608825683594,
-0.0079193115234375,
0.00830078125,
0.0021533966064453125,
-0.01041412353515625,
-0.0003466606140136719,
0.00804901123046875,
0.0163116455078125,
-0.01523590087890625,
-0.021026611328125,
0.0113983154296875,
-0.0113525390625,
0.00959014892578125,
-0.02978515625,
-0.0230560302734375,
-0.0209503173828125,
0.0032634735107421875,
-0.005893707275390625,
0.016265869140625,
-0.002105712890625,
0.0233154296875,
-0.0106048583984375,
0.01093292236328125,
0.0032329559326171875,
0.0024166107177734375,
-0.0038623809814453125,
-0.019012451171875,
0.00534820556640625,
0.0204010009765625,
0.003509521484375,
-0.01450347900390625,
0.016265869140625,
-0.0261077880859375,
-0.006191253662109375,
0.01009368896484375,
-0.0062103271484375,
-0.0117340087890625,
0.04443359375,
0.0175628662109375,
0.0173492431640625,
0.0188140869140625,
0.01107025146484375,
-0.0117645263671875,
-0.01287078857421875,
-0.00826263427734375,
-0.00508880615234375,
-0.007587432861328125,
0.01210784912109375,
-0.006008148193359375,
0.0114288330078125,
0.00015735626220703125,
-0.00411224365234375,
0.0004444122314453125,
0.04473876953125,
-0.032012939453125,
0.0195770263671875,
-0.052825927734375,
0.02294921875,
-0.00916290283203125,
0.021728515625,
-0.0093994140625,
0.00019073486328125,
0.04278564453125,
0.0199127197265625,
-0.038177490234375,
0.01488494873046875,
-0.0114593505859375,
-0.00006014108657836914,
-0.01678466796875,
-0.012939453125,
-0.004016876220703125,
-0.0114593505859375,
0.0233306884765625,
-0.02630615234375,
-0.0245513916015625,
0.01168060302734375,
0.0007066726684570312,
-0.0469970703125,
0.005016326904296875,
-0.0167694091796875,
-0.004337310791015625,
-0.0162353515625,
0.020843505859375,
-0.0093231201171875,
0.0196533203125,
0.0072174072265625,
0.0394287109375,
0.01062774658203125,
0.00896453857421875,
0.027496337890625,
-0.00780487060546875,
-0.016845703125,
-0.0250396728515625,
0.006938934326171875,
0.01235198974609375,
-0.0167236328125,
0.016021728515625,
-0.011962890625,
0.0235595703125,
-0.024932861328125,
0.005458831787109375,
-0.0411376953125,
0.0137481689453125,
-0.01800537109375,
0.005428314208984375,
-0.0252838134765625,
0.026580810546875,
0.02001953125,
0.008331298828125,
0.007465362548828125,
-0.006351470947265625,
-0.023834228515625,
0.0228424072265625,
-0.005462646484375,
0.0243377685546875,
0.0191497802734375,
-0.01202392578125,
0.007556915283203125,
-0.0130462646484375,
-0.0191497802734375,
-0.02349853515625,
-0.01543426513671875,
0.0262451171875,
0.0178985595703125,
0.021636962890625,
-0.0176544189453125,
-0.01016998291015625,
-0.0340576171875,
0.0020809173583984375,
0.006137847900390625,
0.0085601806640625,
-0.005077362060546875,
-0.02630615234375,
0.02069091796875,
0.01458740234375,
0.004482269287109375,
-0.00835418701171875,
-0.013519287109375,
0.0119171142578125,
-0.0004284381866455078,
-0.0185699462890625,
0.0188140869140625,
0.0200653076171875,
0.023681640625,
-0.0153045654296875,
-0.0200958251953125,
0.004871368408203125,
0.0272979736328125,
0.0013895034790039062,
0.0119171142578125,
-0.0134124755859375,
-0.0157470703125,
0.0267791748046875,
-0.0152130126953125,
-0.0244140625,
-0.0274658203125,
-0.0111236572265625,
-0.0016956329345703125,
-0.020599365234375,
0.0077972412109375,
-0.042572021484375,
-0.00720977783203125,
-0.0200653076171875,
0.01245880126953125,
-0.022491455078125,
0.0251007080078125,
-0.017242431640625,
0.024383544921875,
-0.01236724853515625,
-0.00434112548828125,
-0.061309814453125,
-0.01959228515625,
0.0013418197631835938,
-0.00733184814453125,
-0.005962371826171875,
-0.00495147705078125,
0.00850677490234375,
0.00949859619140625,
-0.022796630859375,
-0.0313720703125,
0.032745361328125,
0.003490447998046875,
-0.0281829833984375,
0.004077911376953125,
0.0188446044921875,
-0.029693603515625,
-0.00951385498046875,
-0.00960540771484375,
0.01505279541015625,
0.0214385986328125,
-0.00836181640625,
0.04461669921875,
0.01424407958984375,
0.01006317138671875,
0.005481719970703125,
-0.0193328857421875,
0.00464630126953125,
-0.0301055908203125,
0.007022857666015625,
0.0016078948974609375,
0.00933837890625,
-0.0095062255859375,
0.031463623046875,
0.00004875659942626953,
0.0215301513671875,
-0.01258087158203125,
0.01450347900390625,
0.0135650634765625,
0.017852783203125,
-0.002658843994140625,
0.043548583984375,
-0.037109375,
0.0012960433959960938,
0.03497314453125,
-0.0286865234375,
0.033203125,
0.0038814544677734375,
-0.004932403564453125,
-0.00970458984375,
-0.00007611513137817383,
0.02166748046875,
-0.0129241943359375,
0.04150390625,
0.0180816650390625,
-0.0001068115234375,
0.01218414306640625,
-0.0072479248046875,
-0.019622802734375,
-0.01059722900390625,
0.0076751708984375,
-0.029449462890625,
0.013092041015625,
0.043975830078125,
-0.004673004150390625,
0.0134124755859375,
-0.005443572998046875,
0.02862548828125,
0.01165008544921875,
-0.01265716552734375,
0.00611114501953125,
-0.00795745849609375,
0.03271484375,
0.04144287109375,
-0.007678985595703125,
-0.00574493408203125,
-0.01447296142578125,
0.01253509521484375,
-0.018951416015625,
-0.0090484619140625,
0.0196685791015625,
0.000560760498046875,
-0.00341796875,
-0.0153350830078125,
0.0302886962890625,
-0.0087127685546875,
-0.0293121337890625,
-0.0086669921875,
-0.0299530029296875,
0.00954437255859375,
-0.02642822265625,
-0.0243682861328125,
0.026611328125,
-0.037200927734375,
0.0190582275390625,
-0.013153076171875,
0.016632080078125,
-0.0286102294921875,
-0.031646728515625,
0.0127410888671875,
-0.030364990234375,
-0.017547607421875,
-0.0330810546875,
-0.00858306884765625,
0.01332855224609375,
-0.019287109375,
0.0029354095458984375,
0.02618408203125,
-0.0168609619140625,
-0.0024967193603515625,
-0.050384521484375,
0.006801605224609375,
-0.003421783447265625,
0.0008478164672851562,
0.0263824462890625,
0.02496337890625,
-0.005672454833984375,
-0.01125335693359375,
0.013824462890625,
0.00998687744140625,
0.034149169921875,
0.0305938720703125,
-0.01226806640625,
-0.0245513916015625,
0.003833770751953125,
-0.03204345703125,
-0.01922607421875,
-0.00910186767578125,
0.01055145263671875,
-0.0182037353515625,
-0.021728515625,
-0.00431060791015625,
-0.004543304443359375,
0.003780364990234375,
-0.0117340087890625,
-0.049713134765625,
0.023101806640625,
0.00873565673828125,
-0.0009860992431640625,
-0.005573272705078125,
0.0262451171875,
0.0186920166015625,
0.0004813671112060547,
-0.0012369155883789062,
0.0016021728515625,
0.029022216796875,
-0.0079803466796875,
0.01493072509765625,
0.01690673828125,
0.015899658203125,
0.0008492469787597656,
-0.0033855438232421875,
0.018402099609375,
-0.0119781494140625,
-0.0172882080078125,
-0.007793426513671875,
-0.019378662109375,
-0.005985260009765625,
-0.019775390625,
-0.01494598388671875,
0.0139312744140625,
-0.00821685791015625,
0.01092529296875,
0.00506591796875,
0.027191162109375,
-0.0227203369140625,
-0.0222015380859375,
-0.01004791259765625,
0.00960540771484375,
0.01409912109375,
0.00852203369140625,
-0.0438232421875,
0.01009368896484375,
-0.023193359375,
0.0223388671875,
-0.027374267578125,
-0.0411376953125,
-0.022705078125,
0.027496337890625,
0.00952911376953125,
0.0208892822265625,
-0.0151519775390625,
-0.0239715576171875,
0.0026798248291015625,
0.027130126953125,
0.0224151611328125,
0.0322265625,
0.003925323486328125,
-0.01470947265625,
0.01329803466796875,
0.00946044921875,
-0.021942138671875,
0.00379180908203125,
-0.03143310546875,
0.0177459716796875,
0.033416748046875,
-0.0157470703125,
0.00799560546875,
0.01499176025390625,
0.033172607421875,
0.0186309814453125,
-0.01873779296875,
0.007354736328125,
-0.0019512176513671875,
0.004535675048828125,
-0.0023403167724609375,
-0.0131683349609375,
0.050079345703125,
-0.0002551078796386719,
0.0034732818603515625,
-0.0036106109619140625,
0.0010204315185546875,
0.0185394287109375,
0.0057220458984375,
-0.0018329620361328125,
-0.0216064453125,
0.0075531005859375,
-0.011383056640625,
0.00936126708984375,
0.007099151611328125,
-0.01299285888671875,
0.006839752197265625,
0.00519561767578125,
0.0291900634765625,
0.0328369140625,
-0.01233673095703125,
0.01163482666015625,
0.007602691650390625,
-0.0034942626953125,
0.0038547515869140625,
-0.0187530517578125,
-0.0312347412109375,
-0.0297698974609375,
-0.01806640625,
0.007740020751953125,
-0.0200347900390625,
0.00763702392578125,
-0.033782958984375,
0.015960693359375,
0.046417236328125,
-0.0003402233123779297,
-0.0024051666259765625,
0.0450439453125,
-0.0194549560546875,
-0.027618408203125,
-0.0017690658569335938,
0.0289459228515625,
-0.005401611328125,
-0.0169830322265625,
0.025238037109375,
0.0006766319274902344,
0.0443115234375,
0.01451873779296875,
0.00719451904296875,
-0.008026123046875,
0.026580810546875,
-0.02130126953125,
-0.0589599609375,
0.00585174560546875,
0.0173492431640625,
-0.01092529296875,
-0.0146636962890625,
0.025146484375,
-0.0104522705078125,
0.01149749755859375,
-0.0080108642578125,
-0.0199737548828125,
0.0039215087890625,
0.0299530029296875,
0.00689697265625,
-0.00250244140625,
-0.01277923583984375,
0.00870513916015625,
0.01503753662109375,
-0.03216552734375,
-0.0064239501953125,
-0.00112152099609375,
0.01442718505859375,
-0.0019054412841796875,
0.01605224609375,
-0.0058746337890625,
0.0213623046875,
0.00811004638671875,
-0.020172119140625,
-0.035614013671875,
-0.0294036865234375,
0.0167999267578125,
0.0095977783203125,
-0.01239013671875,
0.0285186767578125,
0.0231475830078125,
-0.0204315185546875,
0.023834228515625,
-0.0286407470703125,
0.004970550537109375,
0.01309967041015625,
0.01995849609375,
-0.0034694671630859375,
0.03594970703125,
0.0163421630859375,
0.0011434555053710938,
0.0306396484375,
-0.00829315185546875,
-0.01837158203125,
-0.00594329833984375,
-0.0267181396484375,
0.01262664794921875,
0.0184783935546875,
-0.0411376953125,
-0.0236663818359375,
0.005084991455078125,
-0.0239715576171875,
-0.0225677490234375,
0.036224365234375,
-0.01226806640625,
-0.036407470703125,
0.023345947265625,
0.023223876953125,
-0.00701141357421875,
-0.007122039794921875,
0.008392333984375,
0.0114288330078125,
-0.01078033447265625,
0.0125274658203125,
-0.037750244140625,
0.00885009765625,
-0.01108551025390625,
-0.034149169921875,
0.025726318359375,
-0.01531219482421875,
0.018798828125,
0.016845703125,
-0.0037841796875,
-0.0250701904296875,
0.0003371238708496094,
0.0160980224609375,
0.01097869873046875,
0.019683837890625,
0.0187225341796875,
-0.005023956298828125,
-0.00624847412109375,
0.00968170166015625,
0.01056671142578125,
0.0240631103515625,
-0.0023021697998046875,
0.024627685546875,
-0.01148223876953125,
-0.0177154541015625,
0.00698089599609375,
0.02093505859375,
-0.0003483295440673828,
-0.04132080078125,
-0.00156402587890625,
0.0221405029296875,
-0.0031871795654296875,
0.01485443115234375,
-0.03887939453125,
-0.0301513671875,
-0.005176544189453125,
0.01404571533203125,
0.0396728515625,
0.0056304931640625,
-0.00667572021484375,
0.00537872314453125,
-0.013427734375,
-0.0194549560546875,
0.0003170967102050781,
0.027191162109375,
-0.0161895751953125,
0.010894775390625,
0.001682281494140625,
0.00962066650390625,
0.0168609619140625,
0.01525115966796875,
-0.00504302978515625,
-0.00864410400390625,
0.0008120536804199219,
-0.00884246826171875,
0.032135009765625
] |
ours_486
|
The least possible number of tasty tuples is \(\boxed{4606}\).
Solution: For \( i = 1, \ldots, n \), let \( b_{i} \) be the number of \( a_{j} \) with \( a_{j} = n+1-i \). Note that \( b_{1} + b_{2} + \ldots + b_{n} = k \leq n \). This is also a bijection to the \( a_{i} \) because the \( k \)-tuples are ordered. We will say that an \( n \)-tuple \((b_{1}, b_{2}, \ldots, b_{n})\) of nonnegative integers is tasteful if the corresponding \( k \)-tuple of \( a_{i} \) is tasty. It suffices to count the tasteful \( n \)-tuples.
I claim that there are \(\frac{1}{n+2} \cdot \binom{2n+2}{n+1} - 2^{n}\) tasteful \( n \)-tuples. To prove this, we will establish that the setup is equivalent to the following:
i) \(\sum_{i=1}^{m} b_{i} \leq m\) for \( m = 1, 2, \ldots, n \) and ii) \(\max_{i=1,2,\ldots,n} b_{i} \geq 2\).
|
4606
|
{
"competition": "us_comps",
"dataset": "Ours",
"posts": null,
"source": "OMOFall18Solns.md"
}
|
For positive integers \( k, n \) with \( k \leq n \), we say that a \( k \)-tuple \((a_{1}, a_{2}, \ldots, a_{k})\) of positive integers is tasty if:
- There exists a \( k \)-element subset \( S \) of \([n]\) and a bijection \( f:[k] \rightarrow S \) with \( a_{x} \leq f(x) \) for each \( x \in [k] \).
- \( a_{x} = a_{y} \) for some distinct \( x, y \in [k] \).
- \( a_{i} \leq a_{j} \) for any \( i < j \).
For some positive integer \( n \), there are more than 2018 tasty tuples as \( k \) ranges through \( 2, 3, \ldots, n \). Compute the least possible number of tasty tuples there can be.
|
[
"/Mathematics/DiscreteMathematics/Combinatorics/BinomialCoefficients",
"/Mathematics/DiscreteMathematics/Combinatorics/CombinatorialIdentities",
"/Mathematics/DiscreteMathematics/Combinatorics/Enumeration",
"/Mathematics/DiscreteMathematics/GeneralDiscreteMathematics/DiscreteMath",
"/Mathematics/DiscreteMathematics/GeneralDiscreteMathematics/DiscreteMathematics",
"/Mathematics/DiscreteMathematics/GeneralDiscreteMathematics/FiniteMathematics"
] |
Encode each tasty tuple as a sequence (b_i) whose partial sums never exceed the index, then count such sequences using Catalan numbers and exclude those with all entries ≤1.
|
[
0.00004088878631591797,
0.015411376953125,
0.03973388671875,
0.0102386474609375,
0.00009202957153320312,
-0.00531005859375,
0.035247802734375,
-0.001766204833984375,
-0.006526947021484375,
0.0215911865234375,
0.0235595703125,
-0.046173095703125,
-0.0024433135986328125,
-0.0277099609375,
-0.0230560302734375,
-0.003936767578125,
0.028656005859375,
0.00972747802734375,
-0.00579071044921875,
-0.006023406982421875,
-0.005706787109375,
0.006076812744140625,
0.0139312744140625,
0.04144287109375,
-0.0176544189453125,
-0.00592041015625,
-0.01849365234375,
0.0238494873046875,
0.03125,
-0.01544189453125,
-0.0003845691680908203,
-0.0153350830078125,
0.02685546875,
-0.0287322998046875,
-0.0023517608642578125,
0.0219573974609375,
-0.005283355712890625,
-0.0152435302734375,
-0.024566650390625,
-0.07879638671875,
-0.0157012939453125,
0.0207977294921875,
0.003993988037109375,
-0.000286102294921875,
-0.032318115234375,
0.0134124755859375,
-0.0007452964782714844,
0.0004382133483886719,
-0.0167388916015625,
0.0168609619140625,
-0.007022857666015625,
0.023895263671875,
-0.017333984375,
0.001522064208984375,
-0.02239990234375,
-0.049468994140625,
0.00811004638671875,
-0.00267791748046875,
-0.00856781005859375,
-0.0218963623046875,
0.00333404541015625,
0.00922393798828125,
-0.004550933837890625,
-0.010650634765625,
0.00022327899932861328,
-0.0158538818359375,
-0.045166015625,
0.023101806640625,
0.00292205810546875,
-0.0281219482421875,
-0.0012464523315429688,
-0.0234832763671875,
-0.021697998046875,
0.034423828125,
0.04766845703125,
-0.0093231201171875,
-0.0068359375,
0.00016295909881591797,
-0.00756072998046875,
0.0189056396484375,
0.05157470703125,
0.002468109130859375,
-0.0146484375,
0.001277923583984375,
0.01280975341796875,
0.016632080078125,
-0.00872039794921875,
0.005611419677734375,
0.04718017578125,
-0.0158843994140625,
0.0090789794921875,
0.0029315948486328125,
-0.00379180908203125,
0.0114288330078125,
0.0015211105346679688,
-0.0008420944213867188,
0.03167724609375,
-0.01073455810546875,
-0.0035533905029296875,
-0.0004892349243164062,
-0.006610870361328125,
0.0148162841796875,
0.04669189453125,
0.0194854736328125,
-0.05255126953125,
-0.0189208984375,
-0.0113372802734375,
0.0011873245239257812,
-0.032623291015625,
-0.01165771484375,
-0.0002562999725341797,
0.024932861328125,
0.00772857666015625,
-0.0011072158813476562,
-0.02740478515625,
0.0160980224609375,
0.002468109130859375,
-0.01161956787109375,
-0.002544403076171875,
-0.0203399658203125,
0.00007164478302001953,
0.00496673583984375,
-0.0010919570922851562,
0.0025081634521484375,
-0.00542449951171875,
-0.02044677734375,
-0.023040771484375,
-0.035858154296875,
0.006404876708984375,
-0.00922393798828125,
0.0019989013671875,
0.0177459716796875,
-0.0467529296875,
-0.0283660888671875,
-0.0279388427734375,
0.00534820556640625,
-0.004299163818359375,
-0.00014829635620117188,
-0.0015459060668945312,
-0.016021728515625,
0.005779266357421875,
-0.0173492431640625,
-0.006916046142578125,
0.029571533203125,
-0.0255279541015625,
-0.00965118408203125,
-0.0036678314208984375,
-0.036895751953125,
0.004344940185546875,
0.01922607421875,
-0.003978729248046875,
0.0031642913818359375,
-0.01096343994140625,
0.00768280029296875,
0.0015344619750976562,
0.01509857177734375,
0.0038166046142578125,
0.0165557861328125,
-0.0046844482421875,
-0.01505279541015625,
-0.01076507568359375,
-0.0238800048828125,
-0.00872802734375,
0.0229034423828125,
-0.00421142578125,
0.0013151168823242188,
0.031036376953125,
-0.022491455078125,
0.0014171600341796875,
0.00127410888671875,
-0.01763916015625,
-0.00432586669921875,
-0.0019445419311523438,
0.0016574859619140625,
-0.0154571533203125,
-0.0143890380859375,
-0.0321044921875,
-0.0092010498046875,
0.00675201416015625,
0.0208892822265625,
0.015838623046875,
-0.0236053466796875,
-0.025299072265625,
0.0096282958984375,
0.0152130126953125,
-0.006137847900390625,
-0.0195465087890625,
0.0178375244140625,
0.013580322265625,
0.00437164306640625,
-0.005420684814453125,
0.0179290771484375,
-0.00992584228515625,
0.0036220550537109375,
-0.0019855499267578125,
-0.01088714599609375,
-0.0264892578125,
0.0190887451171875,
0.037017822265625,
-0.0023708343505859375,
0.01442718505859375,
-0.01012420654296875,
-0.0321044921875,
-0.01294708251953125,
-0.0024089813232421875,
-0.019195556640625,
-0.00725555419921875,
-0.01409912109375,
0.008056640625,
-0.016265869140625,
-0.0080108642578125,
-0.036041259765625,
-0.00882720947265625,
0.00189208984375,
-0.0184478759765625,
0.0102081298828125,
-0.01169586181640625,
0.0091094970703125,
-0.00829315185546875,
-0.06634521484375,
0.005519866943359375,
0.0018177032470703125,
-0.00933837890625,
-0.005977630615234375,
-0.0242156982421875,
0.0139007568359375,
-0.00634765625,
-0.01053619384765625,
0.011688232421875,
0.02191162109375,
0.01166534423828125,
0.01084136962890625,
-0.00495147705078125,
-0.0013074874877929688,
0.004100799560546875,
-0.0014438629150390625,
0.006923675537109375,
-0.01256561279296875,
0.01434326171875,
-0.01209259033203125,
0.0225067138671875,
-0.009735107421875,
-0.015045166015625,
-0.004032135009765625,
-0.01128387451171875,
-0.006954193115234375,
0.00927734375,
0.01276397705078125,
0.026611328125,
-0.01161956787109375,
-0.0237579345703125,
0.01152801513671875,
-0.0196533203125,
0.0094146728515625,
0.005527496337890625,
0.0018339157104492188,
-0.006679534912109375,
-0.0052947998046875,
-0.022979736328125,
-0.044586181640625,
-0.006252288818359375,
-0.0283966064453125,
0.001232147216796875,
-0.022064208984375,
0.0029621124267578125,
-0.0203704833984375,
-0.0122528076171875,
-0.019378662109375,
-0.01493072509765625,
0.006969451904296875,
0.037811279296875,
-0.0026912689208984375,
-0.00720977783203125,
0.00821685791015625,
0.01268768310546875,
-0.0018157958984375,
-0.0168609619140625,
0.007068634033203125,
-0.01409149169921875,
0.005947113037109375,
0.025543212890625,
-0.01837158203125,
0.005489349365234375,
0.0210113525390625,
-0.00820159912109375,
-0.0035953521728515625,
-0.0084075927734375,
-0.0159759521484375,
0.00021696090698242188,
0.02838134765625,
0.004543304443359375,
-0.01502227783203125,
-0.002628326416015625,
-0.00658416748046875,
0.01433563232421875,
-0.05206298828125,
0.00986480712890625,
-0.0069732666015625,
0.00585174560546875,
0.01300811767578125,
0.0340576171875,
-0.0030155181884765625,
0.00803375244140625,
0.0067291259765625,
-0.00011283159255981445,
0.0081329345703125,
-0.01593017578125,
0.015380859375,
-0.0237884521484375,
-0.0025386810302734375,
0.006931304931640625,
-0.01251220703125,
0.0034389495849609375,
-0.01369476318359375,
0.0146026611328125,
-0.023284912109375,
-0.019775390625,
0.0037975311279296875,
-0.0190582275390625,
0.0224761962890625,
0.0192108154296875,
-0.011016845703125,
0.0061187744140625,
-0.007904052734375,
-0.024444580078125,
-0.004901885986328125,
0.0008115768432617188,
0.038848876953125,
-0.02313232421875,
0.043914794921875,
-0.00998687744140625,
0.014434814453125,
-0.030731201171875,
0.00923919677734375,
-0.0377197265625,
-0.003292083740234375,
-0.0141754150390625,
-0.00421142578125,
0.010833740234375,
-0.007511138916015625,
0.017333984375,
-0.01690673828125,
-0.037384033203125,
-0.01284027099609375,
-0.0009036064147949219,
0.01110076904296875,
-0.007091522216796875,
-0.0027027130126953125,
-0.01229095458984375,
0.021270751953125,
0.0302886962890625,
-0.0006361007690429688,
0.022369384765625,
-0.0028057098388671875,
-0.002483367919921875,
0.01113128662109375,
-0.002056121826171875,
-0.0181732177734375,
-0.0163421630859375,
0.00742340087890625,
0.00266265869140625,
0.0189056396484375,
-0.00435638427734375,
-0.0038242340087890625,
-0.002704620361328125,
-0.0203857421875,
-0.015380859375,
-0.0013885498046875,
-0.032989501953125,
-0.014862060546875,
-0.01593017578125,
-0.026947021484375,
-0.0016918182373046875,
-0.0008835792541503906,
-0.04827880859375,
0.01203155517578125,
-0.0101776123046875,
-0.002292633056640625,
-0.018463134765625,
-0.0225677490234375,
0.01136016845703125,
0.01763916015625,
0.021026611328125,
0.0423583984375,
-0.0223388671875,
-0.01535797119140625,
0.0049285888671875,
-0.044097900390625,
-0.0232086181640625,
0.0191192626953125,
-0.0228271484375,
0.0017681121826171875,
-0.0070037841796875,
-0.00428009033203125,
0.0208892822265625,
-0.040863037109375,
-0.0014362335205078125,
0.022918701171875,
0.0284423828125,
-0.024871826171875,
-0.0215911865234375,
0.02447509765625,
-0.021820068359375,
0.0007257461547851562,
0.006237030029296875,
-0.02117919921875,
-0.0084991455078125,
-0.01934814453125,
-0.002777099609375,
0.01221466064453125,
0.006450653076171875,
-0.01473236083984375,
-0.00116729736328125,
-0.0147247314453125,
0.0158538818359375,
-0.021942138671875,
0.01070404052734375,
-0.03021240234375,
-0.04461669921875,
-0.0153961181640625,
0.00585174560546875,
-0.03369140625,
0.017333984375,
-0.042449951171875,
0.017120361328125,
0.00955963134765625,
-0.015380859375,
0.013519287109375,
0.0131683349609375,
0.016510009765625,
-0.0095977783203125,
-0.0022907257080078125,
-0.012725830078125,
0.0088043212890625,
-0.0008172988891601562,
0.039520263671875,
0.02288818359375,
0.0206756591796875,
0.0123748779296875,
0.04107666015625,
-0.0303955078125,
-0.01097869873046875,
-0.00753021240234375,
-0.0030651092529296875,
-0.0180206298828125,
0.016448974609375,
-0.005832672119140625,
-0.00521087646484375,
-0.02252197265625,
0.036376953125,
-0.023712158203125,
-0.00446319580078125,
-0.0196075439453125,
-0.02001953125,
-0.0191497802734375,
0.0275726318359375,
0.0166015625,
0.01593017578125,
-0.0016021728515625,
-0.031524658203125,
0.014801025390625,
-0.0219268798828125,
-0.01029205322265625,
-0.0199737548828125,
0.0077667236328125,
-0.0028972625732421875,
-0.01282501220703125,
0.039825439453125,
0.025360107421875,
0.009033203125,
0.006931304931640625,
-0.01508331298828125,
-0.00786590576171875,
0.0198516845703125,
-0.04339599609375,
0.0276336669921875,
-0.00016570091247558594,
0.0228424072265625,
-0.020538330078125,
-0.004680633544921875,
0.0227508544921875,
-0.006946563720703125,
0.00934600830078125,
0.060272216796875,
-0.005859375,
0.0103607177734375,
0.02496337890625,
0.005420684814453125,
-0.01031494140625,
-0.033111572265625,
0.0143280029296875,
0.0229644775390625,
-0.01381683349609375,
-0.00970458984375,
0.0034637451171875,
-0.040924072265625,
-0.0012645721435546875,
-0.025726318359375,
0.006221771240234375,
0.0014715194702148438,
0.0210723876953125,
-0.00974273681640625,
-0.014312744140625,
0.0124053955078125,
0.00925445556640625,
0.040771484375,
0.055419921875,
-0.037750244140625,
-0.01338958740234375,
-0.041778564453125,
-0.004909515380859375,
-0.00547027587890625,
0.0112457275390625,
-0.02886962890625,
-0.0213165283203125,
-0.032073974609375,
0.019989013671875,
-0.0033283233642578125,
0.02288818359375,
-0.01139068603515625,
-0.00604248046875,
-0.0010156631469726562,
0.047760009765625,
0.0023822784423828125,
-0.03564453125,
0.0189208984375,
0.006359100341796875,
-0.0186614990234375,
0.0256500244140625,
-0.0166778564453125,
-0.004238128662109375,
-0.05029296875,
0.0169219970703125,
0.003963470458984375,
-0.015533447265625,
0.007457733154296875,
-0.005702972412109375,
0.009552001953125,
-0.0013933181762695312,
0.006458282470703125,
0.00931549072265625,
0.0015010833740234375,
0.0166168212890625,
0.01092529296875,
-0.026153564453125,
0.0318603515625,
-0.009796142578125,
0.0033893585205078125,
0.00473785400390625,
0.0230712890625,
-0.024261474609375,
0.0109100341796875,
-0.0174407958984375,
-0.0004153251647949219,
-0.02606201171875,
-0.0030059814453125,
0.0122528076171875,
-0.0082244873046875,
0.018096923828125,
-0.01209259033203125,
0.02630615234375,
0.0283966064453125,
0.00818634033203125,
0.0231781005859375,
0.0199432373046875,
-0.023651123046875,
0.037567138671875,
-0.0089874267578125,
-0.0267486572265625,
-0.03106689453125,
-0.0287322998046875,
-0.0249786376953125,
0.0019855499267578125,
-0.027008056640625,
0.01561737060546875,
0.015533447265625,
-0.01091766357421875,
-0.008758544921875,
-0.0222930908203125,
-0.007602691650390625,
0.01557159423828125,
0.032470703125,
-0.0308685302734375,
0.01251983642578125,
0.057464599609375,
0.01275634765625,
0.00887298583984375,
-0.0023651123046875,
0.0322265625,
0.0004906654357910156,
-0.0217437744140625,
0.01453399658203125,
0.033233642578125,
0.0099945068359375,
0.00589752197265625,
-0.04376220703125,
0.0235137939453125,
-0.0233612060546875,
-0.0014867782592773438,
-0.01554107666015625,
-0.026123046875,
-0.0216522216796875,
0.014556884765625,
0.0248565673828125,
-0.014801025390625,
-0.00429534912109375,
-0.025054931640625,
-0.01019287109375,
-0.00710296630859375,
0.00037670135498046875,
0.0277557373046875,
-0.0071258544921875,
0.022857666015625,
0.004230499267578125,
0.04412841796875,
0.0023174285888671875,
-0.027557373046875,
0.0008487701416015625,
-0.011077880859375,
-0.02716064453125,
-0.0014820098876953125,
-0.008575439453125,
0.003997802734375,
0.0238494873046875,
0.0106658935546875,
0.01335906982421875,
0.0177001953125,
-0.0206146240234375,
-0.0040435791015625,
-0.0021152496337890625,
-0.004665374755859375,
-0.049560546875,
0.0166473388671875,
-0.0003800392150878906,
-0.00878143310546875,
-0.0032806396484375,
-0.0133819580078125,
0.003650665283203125,
0.0257720947265625,
-0.040008544921875,
0.0084228515625,
0.03533935546875,
0.024200439453125,
-0.05523681640625,
0.006938934326171875,
0.0175018310546875,
-0.0011463165283203125,
-0.007076263427734375,
-0.0034160614013671875,
-0.009124755859375,
-0.0113372802734375,
-0.0295257568359375,
-0.00902557373046875,
0.0282135009765625,
-0.00957489013671875,
0.0028629302978515625,
0.007404327392578125,
-0.035736083984375,
0.0198974609375,
0.00551605224609375,
0.0202484130859375,
-0.0006532669067382812,
0.0301055908203125,
0.0127105712890625,
-0.0305633544921875,
0.0110321044921875,
0.022979736328125,
-0.0140228271484375,
-0.00278472900390625,
-0.0238189697265625,
-0.0170440673828125,
-0.0009517669677734375,
0.0075531005859375,
0.004283905029296875,
0.0276031494140625,
-0.01092529296875,
-0.010284423828125,
-0.00815582275390625,
0.020843505859375,
0.038360595703125,
0.007015228271484375,
0.027313232421875,
0.020965576171875,
-0.0290985107421875,
0.028167724609375,
0.003078460693359375,
0.03509521484375,
-0.005645751953125,
0.0024166107177734375,
-0.01250457763671875,
0.00801849365234375,
0.010009765625,
-0.0338134765625,
0.0164947509765625,
0.005443572998046875,
0.00748443603515625,
0.0080413818359375,
0.006412506103515625,
-0.0059661865234375,
0.000476837158203125,
-0.0287628173828125,
0.001529693603515625,
0.0174560546875,
-0.0208740234375,
-0.0242767333984375,
-0.0214996337890625,
-0.0011749267578125,
0.0204620361328125,
-0.026611328125,
-0.0004112720489501953,
-0.00786590576171875,
-0.0043487548828125,
-0.026397705078125,
0.019012451171875,
-0.0291595458984375,
-0.01462554931640625,
-0.01169586181640625,
0.003261566162109375,
0.003173828125,
0.0085906982421875,
-0.019195556640625,
0.00904083251953125,
-0.0004911422729492188,
-0.01180267333984375,
0.017578125,
-0.04266357421875,
-0.0207366943359375,
-0.0235748291015625,
-0.047332763671875,
-0.006175994873046875,
-0.0202484130859375,
-0.0174713134765625,
-0.031402587890625,
-0.0014181137084960938,
-0.0029468536376953125,
-0.006038665771484375,
0.03387451171875,
-0.0306854248046875,
0.00027108192443847656,
-0.00024509429931640625,
0.025543212890625,
-0.005893707275390625,
0.00951385498046875,
-0.015899658203125,
0.0005664825439453125,
-0.00893402099609375,
0.010406494140625,
-0.0026836395263671875,
-0.01629638671875,
0.01727294921875,
0.0201568603515625,
0.001583099365234375,
0.0015106201171875,
-0.0034465789794921875,
-0.024139404296875,
-0.022003173828125,
0.015838623046875,
-0.00997161865234375,
-0.00824737548828125,
-0.0031261444091796875,
-0.030792236328125,
0.00421905517578125,
-0.04644775390625,
-0.002933502197265625,
-0.007740020751953125,
-0.03466796875,
-0.025146484375,
-0.0281982421875,
-0.04254150390625,
0.0217132568359375,
-0.04376220703125,
0.0008754730224609375,
0.0072479248046875,
0.0053253173828125,
-0.00804901123046875,
-0.004520416259765625,
-0.029052734375,
-0.02142333984375,
0.00791168212890625,
-0.0158843994140625,
-0.0259246826171875,
-0.000514984130859375,
-0.00844573974609375,
-0.0010318756103515625,
-0.0044403076171875,
-0.004863739013671875,
0.0080718994140625,
-0.0019235610961914062,
0.039154052734375,
0.00698089599609375,
-0.008331298828125,
0.0247802734375,
0.01523590087890625,
-0.01702880859375,
-0.01132965087890625,
-0.0283966064453125,
-0.005817413330078125,
-0.0159912109375,
-0.00390625,
0.00582122802734375,
0.00965118408203125,
0.0108642578125,
-0.00022685527801513672,
0.01467132568359375,
0.01502227783203125,
0.000008225440979003906,
0.032257080078125,
-0.005462646484375,
0.00649261474609375,
0.03204345703125,
0.01552581787109375,
0.014862060546875,
0.0416259765625,
-0.0306243896484375,
0.02008056640625,
-0.00555419921875,
-0.00569915771484375,
0.0169830322265625,
-0.01418304443359375,
0.0110015869140625,
-0.0275726318359375,
0.0007224082946777344,
-0.0212249755859375,
-0.00621795654296875,
-0.022796630859375,
-0.0014200210571289062,
-0.0077056884765625,
0.006439208984375,
0.0173187255859375,
0.0115814208984375,
0.003421783447265625,
0.004955291748046875,
-0.0290374755859375,
-0.0018701553344726562,
0.01280975341796875,
-0.01380157470703125,
0.02044677734375,
0.045196533203125,
-0.016265869140625,
-0.0269775390625,
-0.0059661865234375,
-0.006282806396484375,
0.00434112548828125,
-0.0298919677734375,
0.01474761962890625,
-0.0039043426513671875,
-0.009429931640625,
-0.0174713134765625,
-0.0023937225341796875,
-0.0026683807373046875,
-0.00604248046875,
-0.0035858154296875,
-0.0134124755859375,
0.021575927734375,
0.004878997802734375,
0.001338958740234375,
-0.002414703369140625,
0.0019168853759765625,
-0.0098876953125,
0.0037174224853515625,
-0.0182342529296875,
-0.0061187744140625,
0.00592041015625,
-0.033233642578125,
0.0252227783203125,
-0.0093231201171875,
-0.01372528076171875,
-0.0190277099609375,
0.0211944580078125,
-0.0094451904296875,
-0.00609588623046875,
-0.0004429817199707031,
0.01027679443359375,
-0.00359344482421875,
0.0579833984375,
0.023223876953125,
-0.012908935546875,
0.04974365234375,
0.02703857421875,
0.0128936767578125,
0.0283203125,
-0.041595458984375,
-0.0189056396484375,
-0.0184173583984375,
-0.0273895263671875,
-0.011383056640625,
0.0196685791015625,
-0.004047393798828125,
0.032257080078125,
-0.0479736328125,
0.0360107421875,
-0.0144195556640625,
0.00389862060546875,
-0.012969970703125,
0.0160980224609375,
0.0020656585693359375,
0.0009746551513671875,
-0.027862548828125,
-0.000007510185241699219,
-0.050872802734375,
-0.01436614990234375,
0.01265716552734375,
-0.0005950927734375,
0.060760498046875,
0.0238800048828125,
-0.02227783203125,
0.01316070556640625,
0.012969970703125,
-0.002899169921875,
0.0297698974609375,
-0.0196533203125,
0.0096435546875,
0.047149658203125,
0.0084686279296875,
-0.042633056640625,
0.00867462158203125,
0.01024627685546875,
0.0289306640625,
0.0222625732421875,
-0.0112762451171875,
0.00830841064453125,
-0.0053253173828125,
0.005596160888671875,
-0.0298004150390625,
0.0018110275268554688,
0.01192474365234375,
0.0160675048828125,
0.035797119140625,
-0.0290069580078125,
-0.01468658447265625,
-0.01160430908203125,
0.0113067626953125,
-0.030670166015625,
0.01459503173828125,
-0.01019287109375,
0.01479339599609375,
-0.02496337890625,
-0.0168914794921875,
0.004871368408203125,
0.01532745361328125,
0.0026454925537109375,
0.0025482177734375,
-0.00264739990234375,
0.016082763671875,
-0.01360321044921875,
0.0055389404296875,
0.004909515380859375,
0.031280517578125,
-0.041656494140625,
-0.049224853515625,
-0.00023984909057617188,
0.0257110595703125,
0.0255279541015625,
0.036712646484375,
0.0077972412109375,
0.01146697998046875,
0.00037932395935058594,
-0.0130157470703125,
-0.017425537109375,
-0.040771484375,
-0.00414276123046875,
-0.051055908203125,
-0.04315185546875,
-0.006069183349609375,
0.006683349609375,
0.0246124267578125,
-0.0003514289855957031,
0.0165863037109375,
0.006305694580078125,
-0.00246429443359375,
-0.04254150390625,
-0.0272979736328125,
0.04071044921875,
-0.031402587890625,
-0.0135955810546875,
0.007289886474609375,
-0.030303955078125,
0.001995086669921875,
0.0177764892578125,
-0.005451202392578125,
-0.0149078369140625,
0.0017900466918945312,
-0.0117645263671875,
-0.0018138885498046875,
0.0018434524536132812,
0.01007843017578125,
0.01953125,
-0.005725860595703125,
-0.006591796875,
-0.03826904296875,
-0.031463623046875,
-0.0006203651428222656,
0.031402587890625,
0.0288848876953125,
-0.009765625,
0.006664276123046875,
0.05377197265625,
-0.004695892333984375,
0.01064300537109375,
-0.01812744140625,
-0.051483154296875,
-0.004016876220703125,
-0.003757476806640625,
-0.016937255859375,
0.008392333984375,
0.01099395751953125,
0.01412200927734375,
-0.0038299560546875,
0.0043182373046875,
0.0195465087890625,
0.0049285888671875,
0.032012939453125,
-0.02191162109375,
-0.0167236328125,
-0.0088958740234375,
-0.01535797119140625,
0.011077880859375,
0.0008993148803710938,
-0.031036376953125,
-0.01160430908203125,
-0.0114898681640625,
0.0185394287109375,
-0.0307769775390625,
0.01251983642578125,
-0.0091552734375,
0.0269012451171875,
-0.0024871826171875,
-0.0267181396484375,
0.0175933837890625,
0.0027446746826171875,
-0.01190948486328125,
-0.03240966796875,
0.0216217041015625,
0.0026073455810546875,
0.0016832351684570312,
-0.033111572265625,
0.0211029052734375,
-0.032135009765625,
-0.0185546875,
-0.033050537109375,
-0.018280029296875,
-0.007175445556640625,
0.0130615234375,
0.01259613037109375,
0.01149749755859375,
-0.0180816650390625,
0.033355712890625,
-0.0062103271484375,
-0.0390625,
-0.01329803466796875,
0.0264739990234375,
0.0012731552124023438,
0.0051422119140625,
0.021728515625,
0.0085296630859375,
0.0174102783203125,
0.0008497238159179688,
-0.0134735107421875,
0.01247406005859375,
0.016387939453125,
0.0125732421875,
-0.00461578369140625,
0.0019025802612304688,
0.0282135009765625,
0.0052337646484375,
-0.00893402099609375,
-0.02105712890625,
0.01538848876953125,
0.02740478515625,
0.01282501220703125,
0.005340576171875,
0.001312255859375,
0.011993408203125,
-0.0199737548828125,
0.0096588134765625,
0.0146484375,
0.0218658447265625,
-0.01026153564453125,
-0.015380859375,
0.0028553009033203125,
0.01904296875,
0.0260772705078125,
-0.03924560546875,
0.00432586669921875,
0.0030612945556640625,
0.05426025390625,
-0.0004870891571044922,
-0.0185546875,
0.015533447265625,
-0.019378662109375,
-0.01251983642578125,
0.01190948486328125,
0.018646240234375,
-0.01320648193359375,
0.00982666015625,
0.032012939453125,
-0.0058746337890625,
0.0140228271484375,
-0.0172119140625,
0.003940582275390625,
0.01824951171875,
0.051177978515625,
-0.0161590576171875,
0.01025390625,
0.004558563232421875,
-0.007781982421875,
0.017181396484375,
0.011505126953125,
0.00733184814453125,
0.0132598876953125,
-0.0182647705078125,
0.005458831787109375,
-0.0158233642578125,
0.0008721351623535156,
0.01593017578125,
0.0160064697265625,
-0.04638671875,
-0.0279998779296875,
-0.01392364501953125,
-0.03057861328125,
-0.0190582275390625,
0.0175323486328125,
-0.0015411376953125,
-0.003856658935546875,
-0.00791168212890625,
-0.01434326171875,
-0.00170135498046875,
0.0169677734375,
-0.03863525390625,
0.02850341796875,
-0.0253753662109375,
-0.00397491455078125,
-0.0102386474609375,
0.0117645263671875,
0.013580322265625,
0.005123138427734375,
-0.0231475830078125,
-0.01334381103515625,
0.0262451171875,
-0.05120849609375,
0.0019388198852539062,
-0.0005335807800292969,
-0.00684356689453125,
-0.008697509765625,
0.02117919921875,
0.046234130859375,
0.0182037353515625,
-0.01214599609375,
0.005046844482421875,
-0.0077667236328125,
-0.0335693359375,
0.01528167724609375,
-0.003002166748046875,
-0.01354217529296875,
-0.01122283935546875,
-0.0014429092407226562,
0.0008158683776855469,
-0.019805908203125,
0.0264892578125,
0.0009493827819824219,
0.010711669921875,
-0.037567138671875,
0.047760009765625,
0.00754547119140625,
-0.0302581787109375,
-0.0221710205078125,
0.042877197265625,
0.015838623046875,
-0.004177093505859375,
0.025177001953125,
-0.022979736328125,
-0.043731689453125,
-0.011810302734375,
-0.006259918212890625,
0.0026683807373046875,
-0.006488800048828125,
-0.0010023117065429688,
-0.001697540283203125,
-0.01232147216796875,
0.0193634033203125,
-0.0214385986328125,
0.03961181640625,
-0.0024700164794921875,
0.035614013671875,
-0.0177459716796875,
-0.034088134765625,
-0.0019969940185546875,
0.00677490234375,
-0.031890869140625,
0.0180206298828125,
-0.001255035400390625,
-0.0323486328125,
-0.009063720703125,
-0.00649261474609375,
-0.030853271484375,
0.015472412109375,
-0.037445068359375,
0.01416015625,
0.01166534423828125,
-0.00844573974609375,
-0.002300262451171875,
0.039459228515625,
-0.0226898193359375,
-0.018890380859375,
0.0284423828125,
-0.006275177001953125,
-0.0069122314453125,
0.0160980224609375,
-0.030059814453125,
-0.001918792724609375,
-0.0224456787109375,
-0.033966064453125,
0.007137298583984375,
-0.0115203857421875,
0.0175933837890625,
0.0234222412109375,
0.02081298828125,
-0.050567626953125,
-0.0117340087890625,
0.043304443359375,
0.0172271728515625,
-0.005390167236328125,
-0.00521087646484375,
0.0181884765625,
0.01308441162109375,
-0.0116729736328125,
-0.031829833984375,
0.028106689453125,
0.0171051025390625,
-0.004276275634765625,
0.029876708984375,
0.0115203857421875,
-0.024505615234375,
-0.00035452842712402344,
-0.0259857177734375,
-0.032379150390625,
0.004489898681640625,
0.030029296875,
0.0040435791015625,
0.035308837890625,
-0.0186004638671875,
0.019195556640625,
0.021270751953125,
0.0263214111328125,
-0.0179443359375,
-0.010772705078125,
-0.0372314453125,
-0.0252227783203125,
-0.005313873291015625,
0.0305023193359375,
0.002277374267578125,
0.013702392578125,
0.01334381103515625,
-0.01456451416015625,
-0.0115203857421875,
0.007213592529296875,
0.0145111083984375,
-0.006439208984375,
0.0005664825439453125,
0.005474090576171875,
0.0013275146484375,
0.002536773681640625,
-0.0208587646484375,
-0.0004317760467529297,
-0.007625579833984375,
-0.0316162109375,
0.0116424560546875,
0.0171051025390625,
-0.008148193359375,
-0.0133209228515625,
0.0227203369140625,
-0.026397705078125,
-0.01233673095703125,
0.006439208984375,
-0.01546478271484375,
-0.00867462158203125,
0.0229339599609375,
-0.0113677978515625,
-0.0003197193145751953,
-0.034454345703125,
-0.0374755859375,
0.017242431640625,
0.0109405517578125,
-0.038848876953125,
-0.0352783203125,
0.0003097057342529297,
0.00257110595703125,
0.03265380859375,
-0.004276275634765625,
0.00769805908203125,
-0.036224365234375,
-0.0028057098388671875,
-0.0245361328125,
0.0058746337890625,
-0.0115203857421875,
-0.013519287109375,
-0.0052642822265625,
0.01428985595703125,
-0.0003533363342285156,
-0.009307861328125,
-0.007312774658203125,
-0.0272064208984375,
0.0072479248046875,
-0.00777435302734375,
-0.033416748046875,
-0.01788330078125,
-0.029205322265625,
0.0252227783203125,
-0.011810302734375,
-0.0012559890747070312,
-0.0006666183471679688,
0.02874755859375,
0.01158905029296875,
-0.0010547637939453125,
0.00983428955078125,
-0.01265716552734375,
-0.005695343017578125,
-0.007450103759765625,
-0.006252288818359375,
0.013031005859375,
-0.0174102783203125,
0.0243988037109375,
0.0042266845703125,
0.0082244873046875,
0.0027751922607421875,
0.0092620849609375,
-0.022308349609375,
0.02984619140625,
-0.0270843505859375,
-0.022613525390625,
0.00799560546875,
0.0201873779296875,
-0.00798797607421875,
-0.0287933349609375,
-0.01207733154296875,
0.043670654296875,
0.0267333984375,
0.0305023193359375,
0.0004642009735107422,
-0.02557373046875,
0.0108489990234375,
0.0374755859375,
-0.0133209228515625,
-0.0029582977294921875,
-0.032867431640625,
-0.016082763671875,
-0.02239990234375,
0.0005702972412109375,
0.023193359375,
-0.02984619140625,
0.01154327392578125,
0.0131378173828125,
0.007144927978515625,
0.01580810546875,
0.01091766357421875,
-0.01129150390625,
0.00695037841796875,
0.0148162841796875,
0.00777435302734375,
0.002918243408203125,
-0.006870269775390625,
-0.0159149169921875,
0.0178375244140625,
-0.04046630859375,
0.0413818359375,
0.032257080078125,
-0.012298583984375,
0.00577545166015625,
-0.0130615234375,
-0.01509857177734375,
-0.0206146240234375,
-0.0009784698486328125,
-0.0184478759765625,
-0.0128173828125,
0.04144287109375,
0.0017108917236328125,
-0.01030731201171875,
0.0246734619140625,
-0.01236724853515625,
0.00458526611328125,
-0.0389404296875,
-0.031036376953125,
-0.038238525390625,
-0.00909423828125,
0.00202178955078125,
0.0230560302734375,
0.0033321380615234375,
0.004852294921875,
-0.011199951171875,
-0.01203155517578125,
0.032501220703125,
0.01348876953125,
-0.034423828125,
0.02008056640625,
0.004474639892578125,
-0.0199127197265625,
0.018829345703125,
-0.002857208251953125,
-0.0142822265625,
0.01300811767578125,
0.0032253265380859375,
-0.0034027099609375,
-0.035919189453125,
-0.007747650146484375,
0.01456451416015625,
-0.0104522705078125,
-0.005352020263671875,
0.00949859619140625,
0.0238189697265625,
0.0021572113037109375,
-0.0037670135498046875,
-0.004413604736328125,
0.0018720626831054688,
-0.01428985595703125,
-0.0287017822265625,
-0.006244659423828125,
0.0052947998046875,
-0.01251983642578125,
-0.01453399658203125,
0.0216522216796875,
0.01107025146484375,
0.0116729736328125,
0.0066986083984375,
0.01497650146484375,
0.0235443115234375,
-0.02398681640625,
0.008514404296875,
-0.0103302001953125,
-0.0216522216796875,
0.0035037994384765625,
-0.0009655952453613281,
-0.02813720703125,
-0.018402099609375,
-0.0276947021484375,
-0.016754150390625,
-0.005115509033203125,
0.00909423828125,
0.0205230712890625,
0.01837158203125,
-0.022064208984375,
-0.0166473388671875,
0.007556915283203125,
-0.0073089599609375,
0.02679443359375,
0.00604248046875,
-0.0300140380859375,
0.0112457275390625,
-0.00926971435546875,
-0.0202484130859375,
-0.025299072265625,
-0.035369873046875,
-0.025970458984375,
-0.01230621337890625,
0.0109100341796875,
0.02337646484375,
0.01386260986328125,
-0.002429962158203125,
-0.0255279541015625,
-0.0291290283203125,
-0.032958984375,
-0.04595947265625,
-0.0288543701171875,
-0.00583648681640625,
0.036529541015625,
0.00936126708984375,
-0.0035953521728515625,
-0.004825592041015625,
0.026947021484375,
0.006427764892578125,
-0.03033447265625,
0.007389068603515625,
-0.01273345947265625,
-0.0093231201171875,
0.0038585662841796875,
0.01511383056640625,
0.0098114013671875,
0.0111083984375,
-0.030731201171875,
0.013336181640625,
0.0007352828979492188,
-0.0088958740234375,
-0.0271759033203125,
0.043426513671875,
0.00691986083984375,
-0.003009796142578125,
-0.00457000732421875,
-0.0105438232421875,
0.0110015869140625,
-0.01454925537109375,
0.0069580078125,
-0.046478271484375,
0.0017709732055664062,
-0.0038166046142578125,
0.0277557373046875,
0.003406524658203125,
0.0125274658203125,
0.0276336669921875,
-0.01531982421875,
0.016448974609375,
0.0189666748046875,
-0.01457977294921875,
-0.0067596435546875,
0.0340576171875,
-0.023284912109375,
0.01128387451171875,
-0.005153656005859375,
-0.0030345916748046875,
0.00983428955078125,
-0.026641845703125,
0.0009274482727050781,
-0.00017940998077392578,
0.006053924560546875,
0.0068206787109375,
-0.003978729248046875,
-0.01435089111328125,
0.025970458984375,
-0.00925445556640625,
-0.01210784912109375,
0.01078033447265625,
0.0030670166015625,
0.0299530029296875,
-0.0202484130859375,
-0.0159149169921875,
0.00676727294921875,
-0.008087158203125,
-0.01087188720703125,
0.00028514862060546875,
0.0208740234375,
-0.02593994140625,
-0.01393890380859375,
0.0120391845703125,
-0.0236358642578125,
0.025634765625,
-0.00131988525390625,
0.005008697509765625,
-0.0097503662109375,
0.00885772705078125,
0.0116424560546875,
0.0232696533203125,
0.0039005279541015625,
0.001003265380859375,
0.0218505859375,
0.00112152099609375,
-0.0097808837890625,
-0.01123809814453125,
0.0189971923828125,
0.024444580078125,
0.0179290771484375,
0.0118255615234375,
-0.0287017822265625,
0.0224609375,
-0.0013866424560546875,
0.0011758804321289062,
-0.00975799560546875,
0.0012302398681640625,
0.004268646240234375,
0.003597259521484375,
0.01007080078125,
0.044403076171875,
-0.0025310516357421875,
0.0185546875,
0.021728515625,
-0.0084991455078125,
0.018157958984375,
-0.02703857421875,
0.030303955078125,
-0.0131072998046875,
0.0045013427734375,
0.02294921875,
-0.007686614990234375,
0.0181884765625,
0.018402099609375,
-0.04779052734375,
-0.01605224609375,
0.0146331787109375,
-0.007659912109375,
0.0213470458984375,
0.01358795166015625,
0.0325927734375,
0.0229644775390625,
0.00325775146484375,
-0.0012884140014648438,
0.0167236328125,
-0.0032520294189453125,
-0.04168701171875,
-0.0164337158203125,
0.00536346435546875,
0.010589599609375,
0.0146331787109375,
0.0008587837219238281,
-0.0020198822021484375,
0.039031982421875,
0.002227783203125,
-0.019287109375,
-0.0184173583984375,
0.0209197998046875,
0.035919189453125,
0.007434844970703125,
0.0047760009765625,
0.01262664794921875,
-0.011627197265625,
0.0161590576171875,
-0.0046844482421875,
0.004535675048828125,
0.026397705078125,
-0.0001226663589477539,
0.01387786865234375,
-0.00982666015625,
-0.0126953125,
0.020904541015625,
-0.0031261444091796875,
-0.0189971923828125,
0.00281524658203125,
-0.0167694091796875,
-0.0108489990234375,
-0.011688232421875,
0.0034580230712890625,
0.032989501953125,
-0.0254669189453125,
0.00269317626953125,
0.022613525390625,
-0.00922393798828125,
-0.00928497314453125,
-0.01454925537109375,
0.033416748046875,
-0.0029430389404296875,
-0.01290130615234375,
-0.007770538330078125,
0.006130218505859375,
0.005123138427734375,
0.00909423828125,
0.00994873046875,
-0.0191802978515625,
0.02410888671875,
-0.01245880126953125,
-0.01532745361328125,
0.0007886886596679688,
-0.010650634765625,
-0.0092620849609375,
0.0090179443359375,
-0.02301025390625,
0.0038051605224609375,
-0.018829345703125,
-0.034027099609375,
0.0014123916625976562,
0.0012388229370117188,
-0.0162353515625,
-0.003108978271484375,
0.0024852752685546875,
-0.0509033203125,
0.00855255126953125,
-0.027801513671875,
0.029205322265625,
0.00014340877532958984,
0.01464080810546875,
0.0004324913024902344,
-0.0303955078125,
-0.002010345458984375,
-0.020751953125,
-0.0192413330078125,
0.01425933837890625,
0.0154876708984375,
0.00955963134765625,
0.00568389892578125,
0.00421142578125,
0.01157379150390625,
0.0284881591796875,
0.002910614013671875,
-0.0012655258178710938,
0.0233154296875,
-0.053741455078125,
-0.03900146484375,
-0.01132965087890625,
0.0263671875,
0.0213775634765625,
-0.01168060302734375,
0.03375244140625,
-0.01500701904296875,
0.007312774658203125,
-0.004505157470703125,
0.01342010498046875,
-0.01157379150390625,
0.0211181640625,
-0.0179595947265625,
-0.0270233154296875,
-0.006412506103515625,
0.0300445556640625,
0.0208892822265625,
0.0072021484375,
-0.0111541748046875,
0.041473388671875,
0.0196990966796875,
-0.0006213188171386719,
-0.020599365234375,
0.048431396484375,
-0.01444244384765625,
0.007640838623046875,
-0.0005769729614257812,
0.00482177734375,
0.0209197998046875,
0.007205963134765625,
-0.01219940185546875,
-0.0137786865234375,
-0.026580810546875,
0.020782470703125,
0.01201629638671875,
0.00435638427734375,
0.003997802734375,
0.0013637542724609375,
0.00030875205993652344,
0.0316162109375,
-0.045166015625,
-0.0296478271484375,
0.04290771484375,
-0.025054931640625,
-0.0029621124267578125,
0.0070037841796875,
0.0256805419921875,
-0.003780364990234375,
-0.044891357421875,
0.0012578964233398438,
-0.004558563232421875,
0.00995635986328125,
-0.0217437744140625,
-0.0199127197265625,
-0.004695892333984375,
0.02056884765625,
-0.0139923095703125,
0.019775390625,
0.008758544921875,
-0.0228118896484375,
0.021575927734375,
-0.0244140625,
0.0014791488647460938,
-0.00592803955078125,
-0.01195526123046875,
0.0235137939453125,
-0.0197906494140625,
-0.0024929046630859375,
0.0184173583984375,
-0.01558685302734375,
-0.01367950439453125,
-0.00699615478515625,
0.00927734375,
-0.01535797119140625,
-0.0005340576171875,
0.01033782958984375,
-0.006763458251953125,
0.02532958984375,
0.0091705322265625,
0.004058837890625,
-0.0177154541015625,
0.01409149169921875,
-0.0135498046875,
-0.0245208740234375,
-0.0234375,
-0.011322021484375,
-0.01294708251953125,
-0.00634765625,
0.0106353759765625,
0.0280914306640625,
-0.004150390625,
0.00998687744140625,
-0.02691650390625,
-0.020538330078125,
-0.0012359619140625,
-0.01065826416015625,
-0.039886474609375,
-0.0211181640625,
-0.02410888671875,
0.01467132568359375,
0.01373291015625,
0.0261993408203125,
0.0212249755859375,
-0.019317626953125,
0.0101165771484375,
-0.010101318359375,
0.0287628173828125,
-0.039398193359375,
0.03497314453125,
0.00856781005859375,
0.006710052490234375,
0.025421142578125,
0.004077911376953125,
0.0012235641479492188,
-0.002185821533203125,
-0.026275634765625,
-0.0108489990234375,
0.0066375732421875,
-0.063232421875,
-0.0023555755615234375,
0.0015554428100585938,
0.016815185546875,
-0.017547607421875,
-0.01232147216796875,
-0.0081329345703125,
0.006931304931640625,
-0.0312042236328125,
0.034332275390625,
-0.0015096664428710938,
-0.00809478759765625,
0.0298004150390625,
-0.022796630859375,
-0.057708740234375,
0.0015659332275390625,
-0.0174713134765625,
-0.0203704833984375,
-0.0268402099609375,
0.01172637939453125,
-0.019073486328125,
0.0008454322814941406,
0.002407073974609375,
0.03338623046875,
-0.0212554931640625,
-0.04443359375,
-0.00960540771484375,
0.0189056396484375,
-0.0086822509765625,
-0.0299072265625,
-0.0178375244140625,
0.0026836395263671875,
0.01496124267578125,
-0.0027484893798828125,
-0.032135009765625,
0.00943756103515625,
-0.01401519775390625,
0.035552978515625,
-0.01154327392578125,
-0.007205963134765625,
0.039520263671875,
0.00873565673828125,
-0.0183868408203125,
-0.01280975341796875,
-0.037139892578125,
-0.0009984970092773438,
0.01837158203125,
-0.037078857421875,
-0.0224761962890625,
0.00274658203125,
0.0256195068359375,
-0.00392913818359375,
0.0181121826171875,
0.0188446044921875,
0.00678253173828125,
0.0302734375,
-0.0005955696105957031,
0.01044464111328125,
-0.00527191162109375,
0.00862884521484375,
-0.004596710205078125,
-0.0034008026123046875,
-0.0227203369140625,
-0.0154266357421875,
-0.02569580078125,
-0.00698089599609375,
-0.00841522216796875,
0.045196533203125,
0.01122283935546875,
-0.0015249252319335938,
-0.0135345458984375,
0.0287322998046875,
-0.0158843994140625,
0.01136016845703125,
-0.0036296844482421875,
-0.034942626953125,
0.01355743408203125,
0.0087127685546875,
0.0009975433349609375,
0.00688934326171875,
0.0113372802734375,
0.0181121826171875,
0.006855010986328125,
-0.022705078125,
0.0137481689453125,
0.01247406005859375,
0.014373779296875,
0.0005059242248535156,
0.0139312744140625,
0.0272064208984375,
0.036285400390625,
0.0174560546875,
0.0018777847290039062,
0.048492431640625,
-0.036529541015625,
0.0008959770202636719,
0.0281829833984375,
-0.010772705078125,
0.01401519775390625,
0.01157379150390625,
-0.03826904296875,
-0.02337646484375,
0.0024890899658203125,
0.01221466064453125,
0.01473236083984375,
0.0013208389282226562,
0.005649566650390625,
-0.006195068359375,
0.0277862548828125,
-0.01366424560546875,
0.012786865234375,
-0.0078125,
0.0251922607421875,
-0.0257415771484375,
0.02740478515625,
-0.0305938720703125,
0.01093292236328125,
-0.0020046234130859375,
0.005340576171875,
-0.00620269775390625,
-0.0037136077880859375,
-0.00677490234375,
-0.0243377685546875,
-0.01462554931640625,
0.003406524658203125,
-0.0203094482421875,
0.006214141845703125,
0.00278472900390625,
0.01100921630859375,
-0.028228759765625,
-0.003856658935546875,
0.0296783447265625,
-0.0299835205078125,
-0.003948211669921875,
-0.00861358642578125,
-0.00547027587890625,
-0.00041365623474121094,
-0.01922607421875,
0.013458251953125,
-0.0032939910888671875,
-0.025115966796875,
0.00748443603515625,
0.041412353515625,
-0.032012939453125,
0.0117034912109375,
-0.008697509765625,
-0.00809478759765625,
-0.0081939697265625,
0.00525665283203125,
0.00024271011352539062,
0.013336181640625,
0.0164947509765625,
-0.01001739501953125,
0.02490234375,
0.001560211181640625,
0.00196075439453125,
-0.0182342529296875,
-0.0166168212890625,
0.0274200439453125,
-0.0164794921875,
-0.011962890625,
-0.010772705078125,
-0.0169830322265625,
-0.02880859375,
-0.0162811279296875,
-0.0216827392578125,
0.00296783447265625,
-0.0246429443359375,
-0.033935546875,
0.0160675048828125,
0.019317626953125,
-0.00943756103515625,
-0.019683837890625,
-0.032470703125,
-0.00997161865234375,
0.00128936767578125,
-0.0226593017578125,
0.0267791748046875,
0.00440216064453125,
-0.01351165771484375,
0.01334381103515625,
-0.002254486083984375,
0.004650115966796875,
0.0120391845703125,
0.031768798828125,
0.022979736328125,
-0.0284423828125,
0.015838623046875,
-0.00036597251892089844,
0.0203857421875,
0.0022678375244140625,
-0.044525146484375,
-0.0293121337890625,
-0.023956298828125,
-0.00443267822265625,
0.0243682861328125,
-0.021759033203125,
0.016357421875,
-0.007720947265625,
0.0016698837280273438,
0.00988006591796875,
0.007762908935546875,
-0.02740478515625,
0.003936767578125,
0.0163726806640625,
0.007720947265625,
0.0204925537109375,
0.027130126953125,
-0.04486083984375,
0.0128173828125,
0.0225067138671875,
0.0021915435791015625,
-0.0083770751953125,
0.05126953125,
-0.005458831787109375,
0.005084991455078125,
-0.023345947265625,
0.017181396484375,
0.004451751708984375,
0.005340576171875,
-0.03631591796875,
0.00035190582275390625,
-0.032745361328125,
-0.023529052734375,
0.0036773681640625,
-0.00843048095703125,
0.043914794921875,
-0.0226898193359375,
-0.0089263916015625,
-0.0027618408203125,
0.033477783203125,
-0.00018465518951416016,
-0.005489349365234375,
0.0012731552124023438,
-0.013671875,
-0.0246429443359375,
0.00397491455078125,
0.009613037109375,
0.01160430908203125,
-0.002025604248046875,
0.02001953125,
0.0290374755859375,
-0.010009765625,
0.0132293701171875,
0.0188140869140625,
-0.041412353515625,
-0.0167694091796875,
0.01192474365234375,
-0.00884246826171875,
-0.0201568603515625,
-0.00832366943359375,
-0.015350341796875,
-0.005279541015625,
-0.030548095703125,
-0.01329803466796875,
-0.0003209114074707031,
-0.0190582275390625,
-0.021392822265625,
-0.010650634765625,
-0.01153564453125,
0.00469207763671875,
0.0108489990234375,
0.021148681640625,
0.0287628173828125,
0.01519775390625,
0.009368896484375,
-0.005466461181640625,
-0.006481170654296875,
0.00004190206527709961,
-0.00525665283203125,
0.0277557373046875,
0.0015192031860351562,
0.0355224609375,
-0.0158233642578125,
0.0015115737915039062,
-0.004314422607421875,
0.054046630859375,
-0.022979736328125,
-0.005401611328125,
0.00768280029296875,
0.00012362003326416016,
-0.020751953125,
-0.0030841827392578125,
-0.0020732879638671875,
-0.0130462646484375,
0.01959228515625,
-0.0243377685546875,
-0.052947998046875,
0.01480865478515625,
-0.0057830810546875,
0.00958251953125,
-0.0224151611328125,
0.00070953369140625,
0.04046630859375,
0.01629638671875,
-0.0421142578125,
-0.025787353515625,
-0.01288604736328125,
0.0289154052734375,
0.01270294189453125,
0.01294708251953125,
-0.0281829833984375,
-0.00891876220703125,
-0.00969696044921875,
-0.0062255859375,
0.008331298828125,
-0.0210418701171875,
-0.0074615478515625,
0.00592041015625,
0.028167724609375,
-0.0117645263671875,
-0.003997802734375,
-0.0012111663818359375,
0.0227203369140625,
0.01690673828125,
-0.0263671875,
0.04327392578125,
0.0064849853515625,
-0.048065185546875,
-0.0162811279296875,
0.0095672607421875,
0.005008697509765625,
-0.0272216796875,
0.030975341796875,
-0.0236358642578125,
0.003376007080078125,
0.014373779296875,
0.01102447509765625,
-0.0054473876953125,
0.0045623779296875,
-0.00556182861328125,
0.0030307769775390625,
0.01282501220703125,
-0.00826263427734375,
0.0082244873046875,
-0.00913238525390625,
0.0137786865234375,
0.00824737548828125,
0.0240631103515625,
-0.0243377685546875,
0.00623321533203125,
-0.03515625,
-0.01052093505859375,
0.00659942626953125,
0.00646209716796875,
-0.0143585205078125,
0.0159454345703125,
0.000164031982421875,
-0.01177215576171875,
-0.012481689453125,
0.0029468536376953125,
0.0226898193359375,
-0.01375579833984375,
0.0278472900390625,
-0.0012235641479492188,
0.00383758544921875,
0.0081787109375,
-0.0009412765502929688,
0.00502777099609375,
0.006839752197265625,
-0.032623291015625,
0.0017852783203125,
-0.007595062255859375,
-0.009033203125,
-0.00858306884765625,
0.004314422607421875,
0.04052734375,
-0.0102386474609375,
-0.0002562999725341797,
-0.00289154052734375,
0.003391265869140625,
0.027862548828125,
-0.0017442703247070312,
0.0025157928466796875,
0.0009446144104003906,
0.01401519775390625,
0.0031528472900390625,
-0.027374267578125,
-0.05328369140625,
-0.0263214111328125,
0.01126861572265625,
-0.0160980224609375,
-0.026336669921875,
0.0005154609680175781,
0.0112152099609375,
0.018280029296875,
-0.03680419921875,
0.00128936767578125,
0.0304718017578125,
0.022186279296875,
-0.0013427734375,
0.0091552734375,
0.01922607421875,
-0.032440185546875,
0.004985809326171875,
0.0204925537109375,
0.03271484375,
0.0235137939453125,
0.033050537109375,
0.036102294921875,
-0.0200042724609375,
0.01194000244140625,
0.0008616447448730469,
0.0261688232421875,
-0.02435302734375,
-0.031341552734375,
-0.00867462158203125,
0.0128936767578125,
-0.01004791259765625,
0.01415252685546875,
-0.0228118896484375,
0.0223541259765625,
0.034088134765625,
-0.037109375,
0.0211181640625,
0.00861358642578125,
-0.0096282958984375,
0.0005235671997070312,
-0.031097412109375,
-0.008819580078125,
-0.01198577880859375,
-0.00580596923828125,
0.038299560546875,
0.000018298625946044922,
0.0193939208984375,
0.00803375244140625,
0.014434814453125,
0.033416748046875,
-0.03131103515625,
0.045166015625,
0.00669097900390625,
-0.0195770263671875,
0.00811004638671875,
0.00997161865234375,
-0.010894775390625,
0.0244598388671875,
-0.003025054931640625,
0.0198974609375,
-0.0004875659942626953,
0.0240936279296875,
0.0156097412109375,
-0.0160980224609375,
-0.004795074462890625,
0.02423095703125,
-0.00115203857421875,
0.047271728515625,
-0.0175933837890625,
0.0003972053527832031,
0.01364898681640625,
-0.0145416259765625,
-0.003246307373046875,
-0.048858642578125,
-0.00763702392578125,
-0.013275146484375,
-0.00818634033203125,
-0.009857177734375,
-0.050140380859375,
-0.00565338134765625,
0.03564453125,
0.0163116455078125,
0.0019073486328125,
0.01242828369140625,
-0.00927734375,
-0.007434844970703125,
-0.00965118408203125,
0.003124237060546875,
-0.0141143798828125,
0.0233917236328125,
0.01470947265625,
0.010009765625,
-0.0169219970703125,
0.0245819091796875,
-0.005401611328125,
0.004871368408203125,
-0.004581451416015625,
-0.005580902099609375,
0.0272064208984375,
-0.0023345947265625,
-0.0055084228515625,
0.0008101463317871094,
-0.031494140625,
0.0214080810546875,
0.00322723388671875,
-0.01010894775390625,
0.02374267578125,
0.01096343994140625,
0.0142364501953125,
0.0181732177734375,
0.00952911376953125,
-0.0036945343017578125,
0.01251983642578125,
0.0037746429443359375,
0.006603240966796875,
-0.02618408203125,
-0.0207366943359375,
0.01538848876953125,
-0.0100250244140625,
-0.0222930908203125,
-0.0186309814453125,
0.00656890869140625,
-0.0146331787109375,
-0.0219573974609375,
-0.0124359130859375,
-0.015777587890625,
0.016448974609375,
0.0168304443359375,
0.0025920867919921875,
-0.0293426513671875,
0.0175933837890625,
0.029876708984375,
-0.01383209228515625,
0.0128326416015625,
-0.005741119384765625,
0.0119476318359375,
-0.015472412109375,
-0.01397705078125,
-0.031707763671875,
-0.0016489028930664062,
0.0027561187744140625,
0.03277587890625,
0.002166748046875,
-0.0023555755615234375,
-0.0217437744140625,
0.0203094482421875,
0.004909515380859375,
-0.0302581787109375,
-0.01104736328125,
-0.001220703125,
0.04107666015625,
0.02056884765625,
0.002079010009765625,
-0.0399169921875,
0.0330810546875,
-0.007038116455078125,
-0.0166473388671875,
0.0031986236572265625,
0.0059356689453125,
-0.00762176513671875,
-0.0010118484497070312,
0.016693115234375,
-0.032928466796875,
0.0399169921875,
0.00836944580078125,
0.002086639404296875,
-0.00620269775390625,
-0.0261993408203125,
-0.004261016845703125,
-0.022674560546875,
0.0100555419921875,
0.00716400146484375,
0.0163421630859375,
-0.01336669921875,
0.0034008026123046875,
-0.0187530517578125,
0.0007557868957519531,
-0.00960540771484375,
-0.01132965087890625,
0.0222015380859375,
-0.01280975341796875,
-0.0166778564453125,
-0.0059356689453125,
0.012420654296875,
-0.0093994140625,
-0.031829833984375,
0.008758544921875,
-0.0158538818359375,
-0.025665283203125,
-0.01200103759765625,
-0.0258026123046875,
0.0186004638671875,
0.00925445556640625,
0.0236053466796875,
0.031768798828125,
0.007534027099609375,
0.005962371826171875,
-0.033050537109375,
-0.0024280548095703125,
0.01361846923828125,
0.0144805908203125,
0.01904296875,
0.00705718994140625,
0.024932861328125,
0.0021305084228515625,
-0.032012939453125,
-0.0118560791015625,
-0.0287322998046875,
0.0240631103515625,
0.0247650146484375,
0.0006909370422363281,
0.04278564453125,
0.01116943359375,
0.01340484619140625,
0.033294677734375,
-0.00891876220703125,
0.02618408203125,
-0.0243072509765625,
0.004985809326171875,
0.0226287841796875,
-0.03192138671875,
0.026885986328125,
0.005359649658203125,
0.01361083984375,
0.02923583984375,
-0.0036945343017578125,
-0.0028057098388671875,
-0.0079803466796875,
0.0117034912109375,
-0.01885986328125,
0.020263671875,
0.004070281982421875,
0.004528045654296875,
0.0225982666015625,
0.00827789306640625,
0.036773681640625,
-0.0161590576171875,
-0.01088714599609375,
0.0035076141357421875,
-0.0258331298828125,
0.0303192138671875,
0.0018939971923828125,
0.0009446144104003906,
-0.00799560546875,
0.031585693359375,
-0.011688232421875,
0.007785797119140625,
-0.003696441650390625,
0.0004870891571044922,
-0.01122283935546875,
0.012969970703125,
-0.0184326171875,
-0.01520538330078125,
0.0207672119140625,
-0.031951904296875,
-0.00611114501953125,
-0.0254669189453125,
0.0010433197021484375,
0.01264190673828125,
-0.0170745849609375,
0.0162506103515625,
-0.02093505859375,
-0.003490447998046875,
0.00904083251953125,
-0.0186614990234375,
0.03912353515625,
-0.0228729248046875,
-0.013092041015625,
-0.0167694091796875,
0.047149658203125,
0.007144927978515625,
-0.04010009765625,
0.0108489990234375,
-0.00988006591796875,
0.00948333740234375,
0.0251922607421875,
0.0169219970703125,
-0.0159149169921875,
0.0169677734375,
0.009063720703125,
-0.0017337799072265625,
-0.01001739501953125,
0.03948974609375,
-0.031982421875,
-0.01421356201171875,
0.0016937255859375,
0.004604339599609375,
-0.0019092559814453125,
-0.02130126953125,
0.0188446044921875,
0.00211334228515625,
-0.0024318695068359375,
-0.007022857666015625,
-0.0172882080078125,
0.0150146484375,
0.043731689453125,
0.039306640625,
-0.039794921875,
-0.032745361328125,
-0.0684814453125,
-0.00827789306640625,
-0.034393310546875,
0.0017576217651367188,
-0.003448486328125,
0.01297760009765625,
0.01837158203125,
-0.023406982421875,
-0.0267333984375,
-0.01015472412109375,
0.01190948486328125,
-0.0147552490234375,
-0.010284423828125,
0.0186004638671875,
0.0228118896484375,
0.01029205322265625,
0.00988006591796875,
-0.012786865234375,
0.00327301025390625,
-0.0167999267578125,
0.010040283203125,
-0.0026760101318359375,
0.01495361328125,
-0.031707763671875,
-0.0223236083984375,
0.0051116943359375,
-0.01107025146484375,
-0.0019683837890625,
0.0018320083618164062,
-0.019561767578125,
-0.0238189697265625,
0.0181732177734375,
0.02642822265625,
0.055206298828125,
-0.0280303955078125,
-0.0146636962890625,
0.00665283203125,
-0.01666259765625,
0.0184173583984375,
0.01898193359375,
0.021026611328125,
-0.0147552490234375,
-0.0255889892578125,
-0.00782012939453125,
0.00653076171875,
0.01140594482421875,
-0.0284423828125,
-0.049072265625,
0.021026611328125,
0.00028324127197265625,
-0.00559234619140625,
-0.0044708251953125,
0.03594970703125,
0.031951904296875,
-0.037689208984375,
0.0013551712036132812,
0.0115509033203125,
-0.01073455810546875,
0.00691986083984375,
-0.009429931640625,
0.026702880859375,
0.040679931640625,
0.036224365234375,
0.005123138427734375,
-0.003376007080078125,
-0.004253387451171875,
-0.02801513671875,
-0.000789642333984375,
-0.0162353515625,
0.037689208984375,
-0.004032135009765625,
-0.0017747879028320312,
0.007404327392578125,
0.007293701171875,
0.04083251953125,
0.025177001953125,
0.01535797119140625,
0.020050048828125,
0.015167236328125,
-0.0193023681640625,
-0.004558563232421875,
0.030364990234375,
-0.026702880859375,
-0.0149383544921875,
-0.0258941650390625,
-0.0273284912109375,
-0.0020885467529296875,
0.004375457763671875,
0.0128021240234375,
0.024505615234375,
0.0140228271484375,
0.0011749267578125,
0.0208587646484375,
-0.0161285400390625
] |
ours_487
|
Since \(\angle AEB = \frac{\pi}{2}\), we have that \( AENM \) is cyclic. Let \(\omega\) be the nine-point circle of \(\triangle ABC\). Note that \( N \) is the center of \(\omega\) and \( M \) and \( E \) are on \(\omega\). The radius of \(\omega\) is \(\frac{R}{2}\), where \( R \) is the circumradius of \(\triangle ABC\). Considering the concyclic points \( A, E, N, M \), we have \( MN = NE = \frac{R}{2} = 10 \) and \( AN = 17 \). Since \( AN > MN = NE \), it follows that \( A \) lies on the arc \( ME \) not containing \( N \) on \((AENM)\).
Applying Ptolemy's Theorem to cyclic quadrilateral \( AENM \), we have:
\[
17 \cdot EM = AN \cdot EM = AE \cdot NM + AM \cdot NE = 10(AE + AM).
\]
By the angle bisector theorem on \(\triangle AME\), \(\frac{MJ}{JE} = \frac{MA}{AE}\), so \( MJ = \frac{AM \cdot ME}{AM + AE} \).
By the angle bisector theorem on \(\triangle MAJ\), \(\frac{AI}{IJ} = \frac{AM}{MJ} = \frac{AM + AE}{ME} = \frac{17}{10}\). Thus,
\[
\frac{AI}{AJ} = \frac{AM + AE}{AM + AE + ME} = \frac{17}{27}.
\]
Therefore, \( 100m + n = 1727 \).
\(\boxed{1727}\)
|
1727
|
{
"competition": "us_comps",
"dataset": "Ours",
"posts": null,
"source": "OMOFall19Solns-2.md"
}
|
Let \( \triangle ABC \) be an acute triangle with circumcenter \( O \) and orthocenter \( H \). Let \( E \) be the intersection of \( BH \) and \( AC \), and let \( M \) and \( N \) be the midpoints of \( HB \) and \( HO \), respectively. Let \( I \) be the incenter of \( \triangle AEM \) and \( J \) be the intersection of \( ME \) and \( AI \). If \( AO = 20 \), \( AN = 17 \), and \(\angle ANM = 90^\circ\), then \(\frac{AI}{AJ} = \frac{m}{n}\) for relatively prime positive integers \( m \) and \( n \). Compute \( 100m + n \).
|
[
"/Mathematics/Geometry/GeneralGeometry/Bisector",
"/Mathematics/Geometry/GeneralGeometry/EuclideanGeometry",
"/Mathematics/Geometry/GeneralGeometry/Geometry",
"/Mathematics/Geometry/PlaneGeometry/Circles/Circumcenter",
"/Mathematics/Geometry/PlaneGeometry/Circles/Concyclic",
"/Mathematics/Geometry/PlaneGeometry/Circles/Incenter",
"/Mathematics/Geometry/PlaneGeometry/Circles/Nine-PointCircle",
"/Mathematics/Geometry/PlaneGeometry/Triangles/TriangleCenters",
"/Mathematics/Geometry/PlaneGeometry/Triangles/TriangleCircles",
"/Mathematics/Geometry/Points/Midpoint",
"/Mathematics/Geometry/Points/Point"
] |
Recognize that A, E, N, M are concyclic and apply Ptolemy’s theorem together with the angle‑bisector theorem to relate the segment lengths.
|
[
-0.00032711029052734375,
-0.0008554458618164062,
0.0592041015625,
0.042633056640625,
-0.000995635986328125,
0.0163116455078125,
0.0157318115234375,
0.026092529296875,
-0.0033779144287109375,
-0.0019483566284179688,
0.0077056884765625,
0.00852203369140625,
-0.00860595703125,
0.028839111328125,
0.0171661376953125,
-0.039276123046875,
0.043914794921875,
-0.01551055908203125,
0.0247955322265625,
-0.0008821487426757812,
-0.0030918121337890625,
-0.003643035888671875,
-0.0382080078125,
0.008056640625,
-0.01007080078125,
-0.0178985595703125,
-0.019439697265625,
0.0056304931640625,
-0.038055419921875,
0.04541015625,
-0.0038852691650390625,
0.010955810546875,
0.004718780517578125,
-0.005859375,
-0.0003216266632080078,
0.01363372802734375,
0.007236480712890625,
0.0015993118286132812,
-0.03594970703125,
-0.051849365234375,
0.008575439453125,
0.0143890380859375,
-0.016571044921875,
0.01134490966796875,
0.0193328857421875,
-0.0013380050659179688,
-0.0026416778564453125,
-0.0018863677978515625,
-0.0067291259765625,
-0.006855010986328125,
0.006687164306640625,
0.004535675048828125,
-0.046600341796875,
-0.01209259033203125,
-0.0178070068359375,
-0.0369873046875,
0.00479888916015625,
0.0002065896987915039,
0.0014190673828125,
0.0023670196533203125,
0.0028667449951171875,
0.036224365234375,
-0.01363372802734375,
-0.0084686279296875,
-0.0015668869018554688,
-0.0008387565612792969,
-0.039031982421875,
-0.0186614990234375,
-0.009796142578125,
-0.0017232894897460938,
0.051513671875,
-0.005767822265625,
0.008056640625,
0.00756072998046875,
0.0215606689453125,
0.001617431640625,
-0.0143585205078125,
-0.00731658935546875,
0.0026569366455078125,
-0.005519866943359375,
-0.01221466064453125,
0.0012340545654296875,
0.0129852294921875,
-0.01666259765625,
0.0088043212890625,
0.005435943603515625,
-0.019622802734375,
-0.0000527501106262207,
0.04156494140625,
-0.003997802734375,
0.00954437255859375,
-0.004520416259765625,
-0.0219573974609375,
0.0033245086669921875,
-0.008453369140625,
0.01837158203125,
0.02215576171875,
-0.02069091796875,
-0.0197601318359375,
-0.00673675537109375,
-0.017852783203125,
-0.018280029296875,
0.0267486572265625,
-0.0090484619140625,
0.0270538330078125,
-0.001804351806640625,
-0.003448486328125,
0.0157623291015625,
-0.0096588134765625,
-0.0027217864990234375,
0.01355743408203125,
0.0033721923828125,
0.031005859375,
0.01270294189453125,
0.01560211181640625,
-0.0282135009765625,
0.032562255859375,
0.0194244384765625,
0.0156707763671875,
0.0516357421875,
-0.0059814453125,
0.01291656494140625,
-0.01548004150390625,
0.012786865234375,
0.0054931640625,
-0.0114898681640625,
-0.0042572021484375,
-0.00377655029296875,
-0.036865234375,
0.00432586669921875,
0.006610870361328125,
0.00336456298828125,
-0.044921875,
-0.0301666259765625,
-0.0276641845703125,
0.0185089111328125,
-0.0183868408203125,
0.0129547119140625,
-0.0256195068359375,
0.0063323974609375,
-0.0009617805480957031,
-0.001800537109375,
0.00959014892578125,
-0.07843017578125,
0.006771087646484375,
-0.06671142578125,
-0.0019369125366210938,
-0.00991058349609375,
0.0004520416259765625,
0.007183074951171875,
-0.003063201904296875,
0.005863189697265625,
-0.006870269775390625,
-0.0002911090850830078,
-0.00524139404296875,
-0.0037593841552734375,
0.0174560546875,
0.021514892578125,
0.00725555419921875,
0.0081329345703125,
0.00984954833984375,
-0.01258087158203125,
-0.01122283935546875,
-0.00933837890625,
-0.0199432373046875,
-0.00135040283203125,
-0.031280517578125,
0.00716400146484375,
-0.0313720703125,
-0.00505828857421875,
-0.00876617431640625,
0.020416259765625,
0.0075836181640625,
-0.026153564453125,
0.011474609375,
0.00463104248046875,
-0.01561737060546875,
0.002410888671875,
-0.01458740234375,
0.027435302734375,
-0.004070281982421875,
-0.032135009765625,
-0.0033168792724609375,
0.01052093505859375,
0.002094268798828125,
0.0187530517578125,
0.00891876220703125,
0.0000960230827331543,
0.00841522216796875,
0.02716064453125,
-0.0015478134155273438,
-0.0167388916015625,
-0.00882720947265625,
-0.02716064453125,
0.0263519287109375,
0.00276947021484375,
-0.0115509033203125,
0.00797271728515625,
0.01117706298828125,
0.004116058349609375,
-0.002574920654296875,
-0.01326751708984375,
0.0123138427734375,
-0.00312042236328125,
-0.0220489501953125,
0.0014896392822265625,
-0.0004119873046875,
-0.01116180419921875,
-0.0032215118408203125,
0.0074615478515625,
0.015869140625,
0.031951904296875,
-0.00738525390625,
0.0025539398193359375,
-0.004528045654296875,
0.001628875732421875,
-0.015533447265625,
0.0211029052734375,
0.0007357597351074219,
0.015533447265625,
0.00891876220703125,
-0.0135040283203125,
0.0017862319946289062,
-0.0116119384765625,
-0.01812744140625,
0.00879669189453125,
-0.004703521728515625,
-0.013916015625,
-0.011322021484375,
-0.0014085769653320312,
0.01328277587890625,
0.00997161865234375,
-0.0098114013671875,
-0.003391265869140625,
0.0009984970092773438,
-0.01258087158203125,
-0.0289306640625,
0.002071380615234375,
0.003978729248046875,
-0.00006681680679321289,
0.034393310546875,
-0.0211944580078125,
-0.00007653236389160156,
-0.009246826171875,
-0.0011138916015625,
0.00409698486328125,
0.01137542724609375,
-0.01093292236328125,
-0.0163726806640625,
0.0007433891296386719,
-0.01320648193359375,
0.0193939208984375,
0.005634307861328125,
-0.0234832763671875,
-0.0034427642822265625,
0.01194000244140625,
-0.0013265609741210938,
-0.0011577606201171875,
-0.008026123046875,
0.01186370849609375,
0.0036678314208984375,
-0.0187225341796875,
-0.006160736083984375,
-0.0145111083984375,
-0.0070037841796875,
0.025634765625,
0.000293731689453125,
0.007762908935546875,
0.01287841796875,
-0.00749969482421875,
0.04962158203125,
-0.001003265380859375,
-0.0022983551025390625,
0.00679779052734375,
-0.01165008544921875,
-0.022247314453125,
-0.0186309814453125,
-0.005748748779296875,
0.00339508056640625,
0.01432037353515625,
0.0244140625,
-0.0244140625,
-0.026123046875,
0.0045623779296875,
-0.00232696533203125,
-0.01203155517578125,
-0.0117950439453125,
-0.05718994140625,
-0.015716552734375,
0.0175323486328125,
-0.0005736351013183594,
0.0299072265625,
0.0018033981323242188,
-0.006488800048828125,
0.046600341796875,
-0.0224151611328125,
0.00466156005859375,
-0.00594329833984375,
0.00635528564453125,
0.00931549072265625,
0.0246734619140625,
-0.0206298828125,
0.005062103271484375,
-0.006317138671875,
0.0196685791015625,
0.01291656494140625,
0.004913330078125,
0.01529693603515625,
-0.032562255859375,
0.00820159912109375,
-0.0019159317016601562,
0.0029773712158203125,
-0.00002205371856689453,
0.003398895263671875,
-0.0460205078125,
-0.015899658203125,
-0.012298583984375,
-0.00931549072265625,
-0.02020263671875,
0.01512908935546875,
0.00641632080078125,
0.01076507568359375,
0.010986328125,
0.0074310302734375,
0.0184173583984375,
-0.007587432861328125,
0.025726318359375,
-0.00006252527236938477,
0.026580810546875,
0.0323486328125,
-0.0206146240234375,
-0.003204345703125,
-0.01220703125,
-0.005863189697265625,
0.0313720703125,
0.004302978515625,
0.0090179443359375,
0.0055694580078125,
0.016510009765625,
0.0006642341613769531,
-0.00893402099609375,
0.026702880859375,
0.01494598388671875,
-0.0701904296875,
-0.0216827392578125,
0.01036834716796875,
-0.01751708984375,
-0.0020809173583984375,
-0.0099029541015625,
-0.031494140625,
0.0281829833984375,
-0.002696990966796875,
0.0231475830078125,
-0.0006837844848632812,
-0.0202178955078125,
-0.010528564453125,
0.0233612060546875,
0.002819061279296875,
-0.0157470703125,
0.0138092041015625,
0.0007977485656738281,
-0.02325439453125,
-0.02264404296875,
0.037872314453125,
-0.039642333984375,
-0.0011701583862304688,
-0.0216217041015625,
0.001384735107421875,
-0.028045654296875,
0.027496337890625,
0.003200531005859375,
-0.00710296630859375,
0.0278778076171875,
-0.014556884765625,
0.0009522438049316406,
0.023193359375,
-0.00861358642578125,
0.01837158203125,
-0.0301361083984375,
-0.00820159912109375,
-0.0027370452880859375,
-0.0225982666015625,
-0.01233673095703125,
0.020751953125,
-0.016448974609375,
0.01200103759765625,
0.018280029296875,
-0.046417236328125,
0.0009136199951171875,
-0.0007481575012207031,
-0.0206451416015625,
0.013092041015625,
-0.0069732666015625,
-0.0127410888671875,
-0.0374755859375,
0.00229644775390625,
-0.003932952880859375,
0.006572723388671875,
0.0213623046875,
-0.0117645263671875,
-0.054046630859375,
-0.004119873046875,
-0.01174163818359375,
0.0021762847900390625,
0.0137786865234375,
-0.010040283203125,
-0.0021190643310546875,
0.00867462158203125,
-0.01280975341796875,
0.0228729248046875,
-0.00614166259765625,
0.0184173583984375,
0.01380157470703125,
-0.0261993408203125,
-0.03509521484375,
0.016693115234375,
-0.012664794921875,
-0.02020263671875,
-0.009002685546875,
-0.007228851318359375,
0.0113983154296875,
-0.015228271484375,
0.025299072265625,
-0.018157958984375,
0.005229949951171875,
-0.0022735595703125,
-0.0031948089599609375,
0.048095703125,
-0.005176544189453125,
-0.003986358642578125,
0.0175323486328125,
0.0038623809814453125,
-0.007808685302734375,
0.016693115234375,
-0.007083892822265625,
0.00164794921875,
0.03424072265625,
0.003086090087890625,
-0.005481719970703125,
0.00841522216796875,
0.004985809326171875,
-0.019287109375,
0.0009398460388183594,
0.0023365020751953125,
0.0069122314453125,
0.0035572052001953125,
0.005710601806640625,
-0.0099639892578125,
0.01186370849609375,
0.0023670196533203125,
0.0095977783203125,
-0.0025653839111328125,
0.030853271484375,
-0.0269012451171875,
0.03399658203125,
0.0228118896484375,
0.0193634033203125,
-0.04583740234375,
-0.027252197265625,
0.04327392578125,
-0.01120758056640625,
0.0208892822265625,
-0.0010232925415039062,
0.0175323486328125,
-0.0296173095703125,
-0.026885986328125,
-0.014801025390625,
-0.00620269775390625,
0.0084228515625,
-0.0077667236328125,
-0.003475189208984375,
0.00276947021484375,
-0.00579833984375,
-0.042724609375,
-0.008270263671875,
0.0616455078125,
0.00354766845703125,
0.0035400390625,
-0.00951385498046875,
0.01560211181640625,
-0.0161590576171875,
-0.0092926025390625,
-0.01085662841796875,
0.00632476806640625,
-0.00972747802734375,
0.0151214599609375,
0.035736083984375,
0.0008807182312011719,
-0.0083160400390625,
-0.052398681640625,
0.002964019775390625,
0.0162811279296875,
0.01023101806640625,
-0.016571044921875,
-0.0416259765625,
-0.0142669677734375,
0.02789306640625,
0.01255035400390625,
0.012939453125,
-0.00844573974609375,
0.0207977294921875,
-0.044708251953125,
0.0026912689208984375,
0.0265960693359375,
0.00847625732421875,
-0.051025390625,
0.048492431640625,
-0.01534271240234375,
-0.0167083740234375,
0.01519775390625,
0.0059814453125,
0.01097869873046875,
0.0218658447265625,
-0.0014886856079101562,
0.0335693359375,
0.0240020751953125,
0.0010576248168945312,
0.00021207332611083984,
0.0178680419921875,
0.05230712890625,
-0.0205535888671875,
0.006221771240234375,
0.0138397216796875,
0.029052734375,
0.0202789306640625,
0.0187225341796875,
0.0047149658203125,
-0.01256561279296875,
0.041656494140625,
-0.003620147705078125,
-0.0010747909545898438,
-0.006481170654296875,
-0.04534912109375,
0.0114288330078125,
-0.0007038116455078125,
0.0234527587890625,
-0.0289154052734375,
-0.0221710205078125,
-0.004215240478515625,
-0.01458740234375,
-0.0300445556640625,
0.005855560302734375,
0.0011806488037109375,
-0.0133514404296875,
0.0261688232421875,
-0.0228271484375,
-0.017578125,
-0.00373077392578125,
0.017822265625,
0.0173492431640625,
-0.01238250732421875,
0.0027942657470703125,
-0.032867431640625,
0.0301055908203125,
-0.024627685546875,
0.006839752197265625,
-0.0288543701171875,
0.0184478759765625,
-0.0243988037109375,
0.028961181640625,
0.0298004150390625,
-0.01050567626953125,
0.031768798828125,
-0.024688720703125,
-0.01039886474609375,
0.000820159912109375,
0.0014629364013671875,
-0.01483154296875,
-0.015777587890625,
-0.06256103515625,
0.0119781494140625,
0.0013093948364257812,
-0.00982666015625,
0.0185394287109375,
0.0135650634765625,
-0.0217132568359375,
-0.0246429443359375,
0.0166778564453125,
0.01302337646484375,
0.00684356689453125,
0.03424072265625,
0.046112060546875,
-0.0009479522705078125,
-0.0096588134765625,
-0.007801055908203125,
0.01018524169921875,
0.0036754608154296875,
-0.003570556640625,
0.00521087646484375,
-0.016876220703125,
-0.00893402099609375,
-0.00502777099609375,
0.0128936767578125,
-0.00794219970703125,
-0.0084991455078125,
0.00189971923828125,
0.03076171875,
0.00963592529296875,
0.032135009765625,
0.0270538330078125,
-0.00016164779663085938,
-0.0117034912109375,
-0.029815673828125,
0.037506103515625,
-0.006084442138671875,
0.0274810791015625,
-0.031341552734375,
0.01224517822265625,
0.0187835693359375,
0.0055694580078125,
0.0044708251953125,
-0.0190582275390625,
-0.0171966552734375,
0.005077362060546875,
0.010894775390625,
0.01146697998046875,
0.0087127685546875,
0.006732940673828125,
-0.031463623046875,
-0.0237579345703125,
-0.0157318115234375,
0.01519012451171875,
0.0226287841796875,
0.0224151611328125,
-0.013671875,
-0.00862884521484375,
-0.0204315185546875,
-0.045684814453125,
0.017120361328125,
-0.032012939453125,
-0.038970947265625,
0.029052734375,
-0.0303192138671875,
0.005828857421875,
-0.01126861572265625,
-0.01461029052734375,
-0.00469970703125,
0.046875,
-0.003833770751953125,
-0.046051025390625,
-0.003662109375,
0.00984954833984375,
0.0098876953125,
-0.051300048828125,
-0.01152801513671875,
-0.0001361370086669922,
-0.0162506103515625,
-0.0089569091796875,
0.010498046875,
0.00656890869140625,
-0.005207061767578125,
0.0145721435546875,
0.027587890625,
0.038116455078125,
0.0229034423828125,
-0.027679443359375,
-0.0028133392333984375,
-0.00453948974609375,
0.04388427734375,
0.00594329833984375,
0.0029850006103515625,
-0.002559661865234375,
-0.0222625732421875,
0.004913330078125,
-0.00035309791564941406,
0.0154266357421875,
-0.04620361328125,
-0.0171356201171875,
0.0103912353515625,
0.036895751953125,
-0.004573822021484375,
-0.007411956787109375,
0.007293701171875,
-0.01485443115234375,
-0.02960205078125,
0.009674072265625,
-0.0311126708984375,
0.01934814453125,
0.00447845458984375,
0.003269195556640625,
0.0287322998046875,
-0.007625579833984375,
0.032501220703125,
0.01020050048828125,
-0.0056304931640625,
0.0791015625,
-0.007232666015625,
-0.007717132568359375,
0.0185394287109375,
0.0272064208984375,
-0.0236053466796875,
0.038360595703125,
-0.032958984375,
0.00408935546875,
-0.003414154052734375,
0.0175323486328125,
0.01157379150390625,
-0.023101806640625,
0.003871917724609375,
-0.0157012939453125,
0.0160675048828125,
0.0011081695556640625,
0.006145477294921875,
-0.031280517578125,
-0.007785797119140625,
-0.034423828125,
-0.0018939971923828125,
-0.0004992485046386719,
-0.055511474609375,
0.00940704345703125,
-0.045013427734375,
-0.0223236083984375,
-0.03363037109375,
-0.01324462890625,
-0.0379638671875,
-0.0310211181640625,
-0.01251220703125,
0.01113128662109375,
-0.006336212158203125,
0.001796722412109375,
-0.004486083984375,
-0.010955810546875,
0.0067901611328125,
-0.0270843505859375,
0.00400543212890625,
0.0272979736328125,
-0.0082244873046875,
-0.00962066650390625,
-0.0179290771484375,
0.012176513671875,
0.0239715576171875,
0.00138092041015625,
-0.01425933837890625,
0.0030994415283203125,
0.0161895751953125,
-0.0207061767578125,
-0.01398468017578125,
-0.055206298828125,
-0.016448974609375,
-0.0007042884826660156,
0.029876708984375,
-0.0194244384765625,
-0.01059722900390625,
-0.0009984970092773438,
-0.01113128662109375,
0.0027370452880859375,
-0.00980377197265625,
-0.0298309326171875,
0.021453857421875,
0.0027751922607421875,
0.022918701171875,
0.01259613037109375,
-0.025482177734375,
-0.030609130859375,
-0.0233917236328125,
0.0016756057739257812,
-0.0157470703125,
-0.019287109375,
-0.0024852752685546875,
-0.001194000244140625,
-0.0098114013671875,
-0.0032711029052734375,
0.0211334228515625,
-0.018096923828125,
-0.00035500526428222656,
0.0087432861328125,
0.0181427001953125,
-0.0025482177734375,
-0.019989013671875,
0.007568359375,
0.01247406005859375,
-0.01226043701171875,
0.0298919677734375,
-0.00916290283203125,
0.0012826919555664062,
0.00409698486328125,
-0.03936767578125,
-0.0012607574462890625,
0.015289306640625,
0.0009188652038574219,
0.02349853515625,
-0.002536773681640625,
-0.01290130615234375,
0.0260162353515625,
-0.053497314453125,
0.01190185546875,
0.006961822509765625,
0.00933837890625,
0.0226287841796875,
-0.006305694580078125,
0.0335693359375,
-0.005100250244140625,
0.0134429931640625,
-0.041107177734375,
-0.0224456787109375,
-0.046234130859375,
-0.0237274169921875,
0.0160369873046875,
-0.027313232421875,
-0.030303955078125,
-0.0021800994873046875,
-0.015228271484375,
0.006549835205078125,
0.00728607177734375,
0.035003662109375,
0.01415252685546875,
0.0220184326171875,
0.012725830078125,
-0.0283660888671875,
0.01654052734375,
0.0199737548828125,
-0.01035308837890625,
0.021331787109375,
-0.00522613525390625,
-0.010101318359375,
-0.0022563934326171875,
-0.00945281982421875,
-0.0122222900390625,
0.0283203125,
0.002552032470703125,
-0.0303802490234375,
0.016754150390625,
-0.0166778564453125,
-0.00829315185546875,
-0.009521484375,
-0.0229644775390625,
0.031463623046875,
0.0018215179443359375,
0.00754547119140625,
0.00522613525390625,
0.006122589111328125,
-0.003307342529296875,
-0.039398193359375,
-0.005584716796875,
-0.0112457275390625,
0.034820556640625,
0.00817108154296875,
-0.0019207000732421875,
-0.03082275390625,
-0.0154571533203125,
0.024627685546875,
-0.021942138671875,
-0.0010271072387695312,
0.02392578125,
0.049102783203125,
-0.0272979736328125,
-0.0284576416015625,
-0.02362060546875,
-0.012451171875,
0.00661468505859375,
0.0004887580871582031,
0.023773193359375,
-0.022216796875,
0.01450347900390625,
-0.0026454925537109375,
0.01043701171875,
0.0230255126953125,
0.004207611083984375,
0.005329132080078125,
-0.01439666748046875,
-0.00841522216796875,
-0.0011320114135742188,
0.0111541748046875,
0.03387451171875,
0.0154266357421875,
-0.0014944076538085938,
-0.01079559326171875,
0.0006575584411621094,
0.0296173095703125,
0.01313018798828125,
0.025634765625,
-0.0297088623046875,
-0.02239990234375,
0.032501220703125,
0.0295562744140625,
0.043975830078125,
-0.0110931396484375,
-0.00905609130859375,
0.04901123046875,
0.00632476806640625,
0.0318603515625,
-0.01383209228515625,
-0.00859832763671875,
0.018524169921875,
0.003997802734375,
0.008575439453125,
-0.0208282470703125,
-0.0002536773681640625,
-0.00418853759765625,
-0.0038585662841796875,
-0.01519012451171875,
-0.014495849609375,
-0.002918243408203125,
-0.0191650390625,
0.01715087890625,
-0.0065460205078125,
0.0243377685546875,
-0.0098724365234375,
-0.00408935546875,
-0.042205810546875,
-0.00554656982421875,
0.0295562744140625,
0.018280029296875,
-0.01105499267578125,
0.0026531219482421875,
-0.037017822265625,
-0.0100555419921875,
-0.01160430908203125,
0.01458740234375,
0.0176544189453125,
-0.005252838134765625,
0.022918701171875,
-0.003543853759765625,
0.037200927734375,
-0.0026187896728515625,
0.0040283203125,
-0.01959228515625,
-0.0061798095703125,
0.004878997802734375,
-0.0186004638671875,
0.0216064453125,
0.0087890625,
-0.025390625,
-0.024444580078125,
0.002559661865234375,
-0.0032901763916015625,
0.010833740234375,
0.004787445068359375,
-0.0250701904296875,
0.0223846435546875,
-0.0204315185546875,
0.0297088623046875,
-0.01537322998046875,
-0.0242767333984375,
-0.01458740234375,
0.03759765625,
0.0247039794921875,
-0.0225372314453125,
-0.0177459716796875,
-0.009368896484375,
-0.01027679443359375,
0.007381439208984375,
0.00003403425216674805,
0.0166015625,
-0.0176849365234375,
0.0220794677734375,
0.01861572265625,
0.0216827392578125,
0.01059722900390625,
-0.01560211181640625,
0.02081298828125,
0.0027618408203125,
0.025665283203125,
-0.0032367706298828125,
-0.0048980712890625,
-0.00907135009765625,
-0.0177459716796875,
-0.003414154052734375,
-0.0203704833984375,
-0.01032257080078125,
0.018157958984375,
0.0205078125,
0.01114654541015625,
0.00728607177734375,
-0.005329132080078125,
0.0004494190216064453,
0.04656982421875,
0.00641632080078125,
0.028656005859375,
0.014251708984375,
-0.0163116455078125,
-0.00307464599609375,
0.01509857177734375,
-0.028961181640625,
0.009246826171875,
0.0127716064453125,
0.021484375,
0.01558685302734375,
0.035247802734375,
0.006343841552734375,
-0.042510986328125,
0.018646240234375,
-0.0102691650390625,
0.00479888916015625,
-0.0186767578125,
0.01532745361328125,
0.0203704833984375,
-0.00791168212890625,
0.0250396728515625,
-0.0115203857421875,
-0.007648468017578125,
0.0264739990234375,
0.0185394287109375,
0.034515380859375,
-0.003116607666015625,
0.0018129348754882812,
0.00875091552734375,
-0.0205230712890625,
0.0054931640625,
-0.0144805908203125,
-0.018829345703125,
-0.038818359375,
0.0003750324249267578,
0.01383209228515625,
0.0177764892578125,
-0.0273895263671875,
-0.0257720947265625,
0.01776123046875,
-0.0016374588012695312,
0.006717681884765625,
-0.01861572265625,
0.00019466876983642578,
-0.004108428955078125,
0.012237548828125,
-0.01076507568359375,
0.0246734619140625,
-0.00115966796875,
0.01554107666015625,
-0.043701171875,
0.0121307373046875,
0.0137481689453125,
-0.0335693359375,
-0.030059814453125,
-0.02496337890625,
0.0302276611328125,
-0.01207733154296875,
-0.01522064208984375,
-0.0207366943359375,
0.03192138671875,
0.03192138671875,
-0.0243377685546875,
0.03546142578125,
-0.00910186767578125,
-0.006595611572265625,
0.00832366943359375,
0.00921630859375,
-0.0191497802734375,
-0.0168609619140625,
0.01611328125,
-0.0281219482421875,
-0.0106658935546875,
0.0022678375244140625,
-0.00406646728515625,
-0.002803802490234375,
-0.0014448165893554688,
0.007778167724609375,
-0.00406646728515625,
-0.00389862060546875,
-0.00434112548828125,
-0.0015401840209960938,
0.00579833984375,
0.036041259765625,
-0.018798828125,
-0.0152435302734375,
0.0003895759582519531,
0.00469970703125,
0.002685546875,
-0.0164031982421875,
0.01253509521484375,
0.01207733154296875,
0.0241851806640625,
-0.047698974609375,
0.0016870498657226562,
-0.017242431640625,
0.02874755859375,
-0.0160369873046875,
-0.00968170166015625,
0.0172271728515625,
0.0039825439453125,
0.0298919677734375,
-0.03228759765625,
-0.005367279052734375,
0.007167816162109375,
-0.004688262939453125,
-0.00017499923706054688,
-0.02447509765625,
0.013916015625,
-0.04876708984375,
0.0029296875,
-0.029266357421875,
-0.006587982177734375,
-0.01421356201171875,
-0.04010009765625,
0.005764007568359375,
0.02923583984375,
-0.0164031982421875,
-0.0177459716796875,
-0.034759521484375,
0.0394287109375,
-0.0205841064453125,
0.0078125,
-0.0268096923828125,
0.0033664703369140625,
-0.01123809814453125,
0.006343841552734375,
-0.023529052734375,
-0.006633758544921875,
0.0211334228515625,
0.0074615478515625,
0.00433349609375,
0.005176544189453125,
0.0117034912109375,
0.00936126708984375,
0.0303192138671875,
-0.01422119140625,
0.0007305145263671875,
-0.0457763671875,
0.0253448486328125,
0.009552001953125,
0.01364898681640625,
-0.004985809326171875,
0.00110626220703125,
0.036407470703125,
-0.000009655952453613281,
-0.026153564453125,
-0.030364990234375,
-0.0264739990234375,
-0.01364898681640625,
0.022796630859375,
-0.022918701171875,
-0.0160980224609375,
0.0103912353515625,
-0.01277923583984375,
0.037567138671875,
-0.0021533966064453125,
-0.0035724639892578125,
0.01091766357421875,
-0.022796630859375,
-0.027069091796875,
-0.00603485107421875,
-0.01959228515625,
0.0087127685546875,
-0.0036563873291015625,
0.0008144378662109375,
0.0030651092529296875,
0.0088958740234375,
0.0079345703125,
-0.002368927001953125,
-0.01354217529296875,
-0.01505279541015625,
-0.0067138671875,
-0.01482391357421875,
0.0220947265625,
-0.022613525390625,
-0.023101806640625,
0.0042877197265625,
-0.0133514404296875,
-0.0104522705078125,
0.04034423828125,
0.00390625,
-0.01019287109375,
-0.01519012451171875,
0.0013561248779296875,
0.01114654541015625,
-0.01418304443359375,
-0.00641632080078125,
-0.030029296875,
0.01959228515625,
0.0254364013671875,
0.0015230178833007812,
0.0024318695068359375,
-0.010650634765625,
0.02227783203125,
0.0016651153564453125,
-0.01033782958984375,
-0.0014600753784179688,
-0.00943756103515625,
0.03753662109375,
0.0195159912109375,
0.01413726806640625,
0.01409912109375,
-0.00801849365234375,
0.0242919921875,
0.0083160400390625,
-0.022064208984375,
0.0033721923828125,
0.01250457763671875,
-0.031982421875,
-0.0161590576171875,
0.00000864267349243164,
-0.01812744140625,
0.03607177734375,
0.0024261474609375,
-0.017669677734375,
-0.00027632713317871094,
-0.0032978057861328125,
-0.00855255126953125,
-0.01371002197265625,
-0.0377197265625,
-0.00714874267578125,
-0.014495849609375,
0.001239776611328125,
-0.0302276611328125,
0.03082275390625,
0.00902557373046875,
0.01119232177734375,
-0.01322174072265625,
-0.0214691162109375,
-0.046875,
-0.0255126953125,
-0.029449462890625,
0.0006999969482421875,
-0.04473876953125,
-0.0138702392578125,
0.0147705078125,
0.004611968994140625,
-0.0102691650390625,
0.0207977294921875,
-0.031463623046875,
0.03485107421875,
-0.01102447509765625,
-0.0007576942443847656,
0.01186370849609375,
-0.0273590087890625,
0.004756927490234375,
-0.025177001953125,
-0.00713348388671875,
0.001155853271484375,
-0.00653839111328125,
-0.038055419921875,
0.0382080078125,
0.010589599609375,
0.018035888671875,
-0.012908935546875,
-0.018707275390625,
-0.017974853515625,
0.00717926025390625,
0.0280914306640625,
-0.01348876953125,
0.01454925537109375,
0.0218505859375,
0.0306243896484375,
-0.0012798309326171875,
0.0248870849609375,
-0.0175323486328125,
-0.010467529296875,
0.0086212158203125,
0.034271240234375,
-0.05657958984375,
0.0023097991943359375,
0.01410675048828125,
0.00661468505859375,
0.0015230178833007812,
-0.0026988983154296875,
0.0246429443359375,
-0.036407470703125,
-0.05523681640625,
-0.01084136962890625,
-0.05523681640625,
0.0174713134765625,
0.0009055137634277344,
0.0034503936767578125,
-0.018768310546875,
-0.02337646484375,
-0.0005850791931152344,
-0.00983428955078125,
0.004154205322265625,
0.00890350341796875,
-0.00247955322265625,
0.002185821533203125,
-0.0183258056640625,
-0.01409149169921875,
0.004802703857421875,
-0.04107666015625,
-0.00031447410583496094,
-0.021881103515625,
0.016082763671875,
0.03021240234375,
0.01238250732421875,
0.007843017578125,
-0.0025234222412109375,
0.0229034423828125,
0.0034942626953125,
0.0292510986328125,
0.00202178955078125,
0.0261688232421875,
-0.0124053955078125,
-0.0067138671875,
0.0033245086669921875,
-0.003665924072265625,
0.004337310791015625,
0.005565643310546875,
0.0193939208984375,
-0.0138702392578125,
-0.015411376953125,
-0.02484130859375,
-0.0154571533203125,
0.034423828125,
0.003452301025390625,
0.007434844970703125,
0.003948211669921875,
0.0606689453125,
0.004756927490234375,
0.0467529296875,
0.0020732879638671875,
-0.03631591796875,
-0.02398681640625,
0.0223388671875,
0.0240478515625,
0.0012865066528320312,
-0.0008664131164550781,
-0.0162200927734375,
-0.0076141357421875,
-0.0275421142578125,
-0.0176849365234375,
-0.029876708984375,
0.0061187744140625,
0.0218658447265625,
-0.00748443603515625,
-0.0011768341064453125,
0.018524169921875,
0.00926971435546875,
-0.0104522705078125,
0.0081024169921875,
0.028076171875,
0.0006852149963378906,
0.0091552734375,
-0.0267181396484375,
-0.023681640625,
0.00527191162109375,
0.005847930908203125,
0.01221466064453125,
-0.0251922607421875,
-0.01470947265625,
0.005153656005859375,
-0.0135498046875,
-0.00551605224609375,
-0.0139312744140625,
-0.00841522216796875,
-0.01558685302734375,
-0.0153656005859375,
-0.0060882568359375,
-0.00030350685119628906,
0.01273345947265625,
-0.00347900390625,
0.024627685546875,
-0.00847625732421875,
-0.00472259521484375,
-0.005107879638671875,
-0.006305694580078125,
0.0025081634521484375,
-0.00901031494140625,
0.0006556510925292969,
0.01230621337890625,
0.0280914306640625,
0.005218505859375,
-0.025970458984375,
0.01522064208984375,
-0.0008153915405273438,
-0.0302734375,
0.007724761962890625,
0.026123046875,
0.0197601318359375,
0.048736572265625,
-0.029327392578125,
-0.01358795166015625,
0.01959228515625,
0.03411865234375,
0.005401611328125,
0.018341064453125,
0.00775909423828125,
-0.00909423828125,
0.02838134765625,
0.0038394927978515625,
-0.004970550537109375,
0.0006823539733886719,
-0.00119781494140625,
-0.0258331298828125,
-0.0249786376953125,
-0.022064208984375,
-0.023284912109375,
0.0152130126953125,
0.01593017578125,
-0.017852783203125,
0.01079559326171875,
-0.006622314453125,
-0.04193115234375,
0.0000845789909362793,
0.0017919540405273438,
0.01251220703125,
0.0200958251953125,
0.016143798828125,
-0.004852294921875,
-0.0181884765625,
0.0071258544921875,
0.0350341796875,
-0.0042266845703125,
0.0222015380859375,
-0.0157318115234375,
-0.00466156005859375,
-0.0102996826171875,
-0.003986358642578125,
0.0003781318664550781,
0.0291748046875,
0.02178955078125,
-0.00713348388671875,
0.02008056640625,
-0.0101776123046875,
-0.0194549560546875,
0.0225372314453125,
0.02362060546875,
-0.003177642822265625,
-0.012664794921875,
0.028472900390625,
0.035125732421875,
-0.0011854171752929688,
-0.006443023681640625,
0.0250091552734375,
0.0206146240234375,
0.002880096435546875,
-0.0213165283203125,
-0.01180267333984375,
-0.0020599365234375,
-0.01242828369140625,
-0.0149993896484375,
-0.021270751953125,
0.00856781005859375,
-0.00431060791015625,
0.005992889404296875,
-0.0203857421875,
-0.0133819580078125,
0.00958251953125,
-0.0068359375,
0.030059814453125,
-0.01259613037109375,
-0.0018415451049804688,
-0.01361083984375,
-0.0185546875,
0.0017538070678710938,
-0.005031585693359375,
-0.018951416015625,
0.014190673828125,
-0.031951904296875,
0.0164337158203125,
0.019683837890625,
0.029754638671875,
0.032958984375,
0.031524658203125,
0.0236053466796875,
-0.0040435791015625,
-0.008697509765625,
-0.0012369155883789062,
0.02447509765625,
-0.03363037109375,
-0.01271820068359375,
0.02081298828125,
0.0249786376953125,
0.004924774169921875,
0.02032470703125,
0.006755828857421875,
0.00026679039001464844,
-0.01290130615234375,
-0.0298309326171875,
-0.011688232421875,
0.00862884521484375,
-0.0035762786865234375,
-0.01104736328125,
-0.0026702880859375,
0.01409912109375,
-0.0149078369140625,
-0.0266265869140625,
0.004421234130859375,
0.020782470703125,
0.002353668212890625,
-0.00347137451171875,
0.01190185546875,
0.0157318115234375,
0.022735595703125,
-0.0124664306640625,
0.013153076171875,
-0.016876220703125,
0.01435089111328125,
0.0265960693359375,
-0.0033931732177734375,
0.005390167236328125,
-0.00669097900390625,
0.0404052734375,
0.003082275390625,
0.021209716796875,
-0.007556915283203125,
-0.03497314453125,
-0.0032329559326171875,
0.004177093505859375,
0.004886627197265625,
-0.01396942138671875,
-0.0160980224609375,
0.00612640380859375,
0.0250701904296875,
0.00109100341796875,
-0.027069091796875,
0.0129852294921875,
-0.005702972412109375,
0.005336761474609375,
-0.0037631988525390625,
0.0203094482421875,
0.0305328369140625,
-0.01499176025390625,
-0.05194091796875,
-0.006603240966796875,
-0.00717926025390625,
0.01971435546875,
0.03369140625,
0.007152557373046875,
0.00705718994140625,
0.038970947265625,
-0.0147705078125,
-0.015655517578125,
-0.0153961181640625,
-0.000015497207641601562,
0.01788330078125,
-0.0187835693359375,
0.00445556640625,
-0.0030975341796875,
0.015289306640625,
-0.0263671875,
0.0136566162109375,
-0.0042724609375,
0.0163726806640625,
-0.03631591796875,
0.007659912109375,
0.037628173828125,
0.0250091552734375,
0.01203155517578125,
0.025634765625,
0.0467529296875,
0.00028204917907714844,
0.0279693603515625,
-0.0009469985961914062,
0.0143585205078125,
0.017425537109375,
-0.01248931884765625,
0.01788330078125,
0.01023101806640625,
-0.00128173828125,
0.01458740234375,
0.0007619857788085938,
-0.002178192138671875,
0.0210723876953125,
0.032440185546875,
-0.0246429443359375,
0.00827789306640625,
-0.003620147705078125,
-0.0024623870849609375,
0.01480865478515625,
0.01190185546875,
0.0272979736328125,
-0.0005307197570800781,
0.00719451904296875,
0.01947021484375,
-0.0012769699096679688,
0.07464599609375,
-0.0000029802322387695312,
-0.0177001953125,
-0.0205078125,
-0.0117950439453125,
0.01885986328125,
-0.01038360595703125,
0.033203125,
-0.04315185546875,
-0.024658203125,
-0.00434112548828125,
0.059051513671875,
-0.00750732421875,
-0.0293731689453125,
-0.017578125,
-0.020751953125,
-0.01056671142578125,
-0.0008091926574707031,
-0.0191192626953125,
0.0032062530517578125,
-0.004138946533203125,
-0.0032672882080078125,
-0.01534271240234375,
0.005584716796875,
-0.009307861328125,
0.0004172325134277344,
-0.0071868896484375,
-0.0283203125,
0.0106353759765625,
-0.0088958740234375,
0.01024627685546875,
-0.0044097900390625,
0.001071929931640625,
0.042694091796875,
0.034637451171875,
-0.0075225830078125,
-0.021820068359375,
0.00760650634765625,
0.0026111602783203125,
-0.0199737548828125,
0.012237548828125,
-0.0013208389282226562,
0.005962371826171875,
-0.0302886962890625,
-0.033355712890625,
-0.0098724365234375,
-0.0189208984375,
-0.0261688232421875,
0.0261383056640625,
0.0321044921875,
-0.009796142578125,
0.0281982421875,
-0.02587890625,
0.0124053955078125,
-0.0259246826171875,
-0.0191192626953125,
0.0178375244140625,
0.01192474365234375,
-0.006381988525390625,
0.00980377197265625,
0.0015172958374023438,
0.0002522468566894531,
0.019866943359375,
0.021728515625,
-0.00726318359375,
-0.00988006591796875,
0.0030422210693359375,
0.0288543701171875,
-0.0020656585693359375,
-0.005184173583984375,
0.039093017578125,
-0.01033782958984375,
-0.00576019287109375,
0.01070404052734375,
-0.0010404586791992188,
-0.0150909423828125,
-0.01512908935546875,
-0.007732391357421875,
-0.01200103759765625,
-0.047821044921875,
-0.0243377685546875,
0.00015616416931152344,
0.0260772705078125,
-0.006504058837890625,
-0.039306640625,
-0.01268768310546875,
-0.02301025390625,
0.01276397705078125,
0.0199432373046875,
-0.0102691650390625,
0.004108428955078125,
-0.0262603759765625,
0.04644775390625,
0.0024967193603515625,
-0.006256103515625,
-0.0024929046630859375,
-0.0247802734375,
-0.0024204254150390625,
0.005229949951171875,
-0.0186614990234375,
0.0173187255859375,
0.01702880859375,
-0.008056640625,
0.018096923828125,
0.0157012939453125,
-0.01053619384765625,
0.0160369873046875,
0.0022716522216796875,
-0.01355743408203125,
0.00920867919921875,
0.007434844970703125,
0.017181396484375,
0.001934051513671875,
0.018768310546875,
-0.00311279296875,
-0.0211029052734375,
0.0007395744323730469,
0.01800537109375,
-0.041290283203125,
-0.01629638671875,
-0.00376129150390625,
-0.031951904296875,
0.0159759521484375,
-0.0010852813720703125,
-0.01593017578125,
0.02728271484375,
-0.00563812255859375,
-0.0030155181884765625,
0.004642486572265625,
0.0030651092529296875,
0.0004074573516845703,
-0.0286865234375,
-0.008270263671875,
0.01186370849609375,
-0.015960693359375,
-0.00870513916015625,
-0.0152435302734375,
0.01335906982421875,
0.005138397216796875,
0.010528564453125,
0.054351806640625,
-0.0205535888671875,
-0.014678955078125,
0.00536346435546875,
-0.0084228515625,
0.022125244140625,
0.01983642578125,
-0.03497314453125,
0.0053253173828125,
0.016632080078125,
0.0187835693359375,
-0.01506805419921875,
0.01904296875,
-0.056121826171875,
0.004032135009765625,
-0.0003371238708496094,
-0.019439697265625,
-0.005641937255859375,
-0.045440673828125,
-0.014923095703125,
0.017059326171875,
-0.006748199462890625,
0.003704071044921875,
-0.0120391845703125,
-0.0228729248046875,
-0.00506591796875,
0.0216217041015625,
0.0166778564453125,
-0.0268096923828125,
-0.0152587890625,
-0.004764556884765625,
-0.00864410400390625,
-0.0160675048828125,
0.015380859375,
0.0019683837890625,
-0.018768310546875,
0.00616455078125,
-0.040557861328125,
-0.00824737548828125,
0.00936126708984375,
-0.00672149658203125,
0.02874755859375,
-0.00206756591796875,
-0.0265045166015625,
-0.01378631591796875,
-0.029693603515625,
0.0246734619140625,
-0.0057830810546875,
0.00910186767578125,
0.01678466796875,
-0.025634765625,
0.005161285400390625,
0.0024166107177734375,
0.0182342529296875,
-0.006805419921875,
0.00274658203125,
-0.01490020751953125,
0.0220794677734375,
0.0221710205078125,
0.006977081298828125,
0.006317138671875,
-0.0034637451171875,
-0.01403045654296875,
0.003025054931640625,
-0.0179901123046875,
0.0019102096557617188,
-0.00885772705078125,
-0.0298919677734375,
0.00551605224609375,
0.00008678436279296875,
0.02520751953125,
-0.0155029296875,
0.00254058837890625,
-0.02313232421875,
-0.0132598876953125,
-0.0418701171875,
-0.0261077880859375,
0.00433349609375,
0.0186767578125,
-0.004547119140625,
0.0267791748046875,
0.0309295654296875,
-0.00496673583984375,
0.027984619140625,
-0.014801025390625,
0.029205322265625,
0.0270843505859375,
0.01261138916015625,
-0.033477783203125,
0.0034198760986328125,
-0.00501251220703125,
-0.0219268798828125,
0.0133056640625,
-0.0022869110107421875,
0.01033782958984375,
-0.00848388671875,
-0.02496337890625,
-0.034149169921875,
0.00634002685546875,
-0.003406524658203125,
0.0021533966064453125,
-0.0091552734375,
-0.0008854866027832031,
-0.01508331298828125,
-0.0011949539184570312,
0.0163421630859375,
0.00649261474609375,
-0.0169830322265625,
-0.02825927734375,
0.0080718994140625,
-0.009552001953125,
0.0244140625,
-0.0011529922485351562,
-0.030487060546875,
0.03704833984375,
0.007110595703125,
-0.00797271728515625,
-0.0316162109375,
-0.01039886474609375,
-0.028411865234375,
-0.0245361328125,
-0.0074920654296875,
0.0009860992431640625,
0.0164794921875,
-0.0087432861328125,
-0.0164337158203125,
-0.01039886474609375,
0.0073089599609375,
-0.0236358642578125,
-0.0013113021850585938,
0.0269927978515625,
-0.00878143310546875,
0.0010356903076171875,
-0.052490234375,
0.0005259513854980469,
-0.01904296875,
0.0223236083984375,
0.007305145263671875,
-0.024658203125,
0.01314544677734375,
0.01117706298828125,
0.01174163818359375,
-0.020660400390625,
-0.01296234130859375,
0.005504608154296875,
0.0121917724609375,
0.001842498779296875,
0.0020160675048828125,
0.0128631591796875,
-0.01407623291015625,
0.021240234375,
0.0248565673828125,
-0.0130767822265625,
0.0304412841796875,
0.043487548828125,
0.0020732879638671875,
0.01343536376953125,
0.0028553009033203125,
0.00714111328125,
0.0088348388671875,
-0.0194854736328125,
-0.0308990478515625,
0.01507568359375,
0.0018053054809570312,
-0.01125335693359375,
0.0035495758056640625,
0.0233154296875,
0.0129547119140625,
-0.01345062255859375,
-0.004291534423828125,
0.04425048828125,
-0.036102294921875,
-0.0125885009765625,
0.029296875,
0.032379150390625,
-0.00919342041015625,
0.0099639892578125,
0.005298614501953125,
-0.02886962890625,
-0.00806427001953125,
-0.0176544189453125,
-0.021392822265625,
-0.0188140869140625,
-0.003116607666015625,
-0.020965576171875,
0.0157623291015625,
-0.012847900390625,
0.0028057098388671875,
0.0189666748046875,
0.025054931640625,
-0.0009632110595703125,
0.005344390869140625,
-0.0024814605712890625,
0.0009560585021972656,
-0.01555633544921875,
-0.0172119140625,
0.0103302001953125,
0.0013895034790039062,
0.01424407958984375,
-0.0158233642578125,
0.03460693359375,
-0.0053863525390625,
0.01224517822265625,
0.00579833984375,
0.0030689239501953125,
-0.01373291015625,
-0.006084442138671875,
0.025787353515625,
-0.0064544677734375,
0.01983642578125,
-0.00864410400390625,
-0.00366973876953125,
-0.03887939453125,
0.01220703125,
-0.0179290771484375,
0.00820159912109375,
0.0125732421875,
-0.0268402099609375,
0.01287078857421875,
-0.00603485107421875,
-0.021728515625,
-0.0191650390625,
0.017303466796875,
0.007171630859375,
-0.01485443115234375,
0.0234375,
-0.00946807861328125,
0.00756072998046875,
-0.048431396484375,
0.025115966796875,
-0.01276397705078125,
-0.01947021484375,
0.028472900390625,
0.005687713623046875,
0.005336761474609375,
0.0114288330078125,
-0.0030517578125,
-0.01160430908203125,
0.01348114013671875,
-0.0269012451171875,
0.033935546875,
0.0105743408203125,
0.01197052001953125,
-0.0238800048828125,
0.001148223876953125,
-0.0016117095947265625,
-0.0140533447265625,
0.0011892318725585938,
0.0125885009765625,
-0.0165557861328125,
0.01001739501953125,
0.01873779296875,
-0.02886962890625,
-0.03961181640625,
0.0032196044921875,
-0.018768310546875,
0.004947662353515625,
-0.0195770263671875,
-0.01290130615234375,
-0.0130157470703125,
0.00955963134765625,
-0.046142578125,
-0.004375457763671875,
0.01331329345703125,
-0.0216522216796875,
-0.0198974609375,
0.005779266357421875,
0.00354766845703125,
0.023101806640625,
0.04510498046875,
0.031341552734375,
0.022003173828125,
-0.044189453125,
-0.02117919921875,
-0.0146026611328125,
0.0006046295166015625,
-0.0202178955078125,
-0.019866943359375,
-0.00125885009765625,
-0.007755279541015625,
-0.0130615234375,
0.0152130126953125,
-0.0005240440368652344,
0.01258087158203125,
0.01751708984375,
-0.01183319091796875,
0.0164642333984375,
0.016632080078125,
0.006740570068359375,
-0.024658203125,
-0.0084228515625,
0.0125274658203125,
-0.00893402099609375,
0.0171051025390625,
0.03314208984375,
-0.03448486328125,
0.052886962890625,
-0.00447845458984375,
0.0033016204833984375,
0.00652313232421875,
0.009674072265625,
-0.0047454833984375,
-0.0204010009765625,
0.05078125,
0.0167999267578125,
-0.0091705322265625,
-0.0021343231201171875,
-0.01114654541015625,
-0.0027332305908203125,
-0.01558685302734375,
-0.02899169921875,
0.0101318359375,
0.032196044921875,
-0.007404327392578125,
0.0250701904296875,
0.002490997314453125,
-0.01393890380859375,
-0.01507568359375,
0.0140838623046875,
-0.006381988525390625,
-0.0008845329284667969,
-0.0421142578125,
0.044158935546875,
0.004974365234375,
0.0068359375,
0.018798828125,
0.0129241943359375,
-0.029754638671875,
0.0195465087890625,
0.00786590576171875,
0.005413055419921875,
-0.00403594970703125,
-0.007640838623046875,
0.00789642333984375,
0.01067352294921875,
-0.023193359375,
-0.0307159423828125,
0.0238189697265625,
0.0189208984375,
-0.0079193115234375,
-0.034088134765625,
-0.0200347900390625,
0.0367431640625,
0.0053253173828125,
0.011993408203125,
-0.016082763671875,
-0.021453857421875,
0.0307159423828125,
0.0009679794311523438,
-0.05242919921875,
0.0076141357421875,
0.0228729248046875,
0.013580322265625,
0.0220489501953125,
0.0090179443359375,
-0.01134490966796875,
0.040771484375,
0.0035152435302734375,
-0.0280914306640625,
-0.019439697265625,
-0.01354217529296875,
0.0089111328125,
-0.0188446044921875,
-0.0102996826171875,
-0.01593017578125,
0.0242919921875,
-0.00244903564453125,
-0.0169677734375,
0.00279998779296875,
0.0014963150024414062,
-0.01450347900390625,
-0.025909423828125,
0.01079559326171875,
-0.01546478271484375,
-0.018402099609375,
-0.0328369140625,
-0.003253936767578125,
-0.01334381103515625,
-0.0254669189453125,
-0.0190582275390625,
-0.00897216796875,
-0.004070281982421875,
-0.024871826171875,
-0.01232147216796875,
0.01409912109375,
0.04473876953125,
-0.0174713134765625,
-0.024200439453125,
0.002849578857421875,
0.033172607421875,
-0.03668212890625,
-0.01262664794921875,
-0.0104827880859375,
0.0242462158203125,
0.03985595703125,
-0.01319122314453125,
-0.021942138671875,
0.01971435546875,
-0.0051422119140625,
-0.0271148681640625,
-0.0350341796875,
-0.0087738037109375,
-0.0159149169921875,
0.0010671615600585938,
-0.0084228515625,
0.0039825439453125,
0.01509857177734375,
0.023773193359375,
0.0013532638549804688,
-0.0008869171142578125,
0.01506805419921875,
-0.0212860107421875,
0.006107330322265625,
0.00423431396484375,
-0.0180206298828125,
0.025299072265625,
0.0122222900390625,
-0.024169921875,
-0.0191497802734375,
-0.00394439697265625,
-0.0100555419921875,
0.00804901123046875,
0.021575927734375,
-0.0222625732421875,
0.0279388427734375,
-0.00881195068359375,
0.0323486328125,
-0.030181884765625,
0.0170135498046875,
0.023468017578125,
-0.0308685302734375,
0.000060617923736572266,
0.00533294677734375,
0.0016193389892578125,
-0.021575927734375,
0.01032257080078125,
0.01158905029296875,
0.00942230224609375,
0.0079345703125,
0.0211029052734375,
-0.00194549560546875,
0.01372528076171875,
0.009674072265625,
-0.00937652587890625,
0.007266998291015625,
0.027496337890625,
0.03924560546875,
-0.01202392578125,
-0.039459228515625,
0.00262451171875,
0.004940032958984375,
0.0101165771484375,
0.0007982254028320312,
-0.016387939453125,
0.011749267578125,
-0.0149993896484375,
0.0355224609375,
0.005741119384765625,
0.0401611328125,
-0.007183074951171875,
0.00040721893310546875,
0.046875,
-0.045654296875,
0.003986358642578125,
0.020294189453125,
-0.048614501953125,
0.00872039794921875,
-0.03192138671875,
-0.0009274482727050781,
0.00011819601058959961,
0.002094268798828125,
0.001804351806640625,
0.005931854248046875,
0.00794219970703125,
0.004512786865234375,
0.0030612945556640625,
-0.00624847412109375,
-0.0016508102416992188,
0.0007214546203613281,
0.004673004150390625,
0.0013885498046875,
0.0091094970703125,
-0.0238494873046875,
-0.03704833984375,
0.0009975433349609375,
0.000972747802734375,
0.0048828125,
-0.002735137939453125,
0.017822265625,
-0.005893707275390625,
0.015045166015625,
0.01444244384765625,
-0.01062774658203125,
0.0107574462890625,
-0.00724029541015625,
0.0045318603515625,
-0.03265380859375,
0.01145172119140625,
0.034942626953125,
0.0080108642578125,
-0.0210418701171875,
-0.0146942138671875,
-0.0022125244140625,
0.019317626953125,
-0.01227569580078125,
0.045379638671875,
0.04315185546875,
-0.002986907958984375,
-0.007762908935546875,
-0.01366424560546875,
0.0005712509155273438,
-0.008270263671875,
-0.0027523040771484375,
-0.02093505859375,
0.001708984375,
-0.048431396484375,
0.0011072158813476562,
-0.0013170242309570312,
0.01439666748046875,
-0.031707763671875,
-0.045135498046875,
0.03131103515625,
-0.008270263671875,
0.0255126953125,
0.006641387939453125,
-0.03204345703125,
0.024566650390625,
-0.0034580230712890625,
0.01593017578125,
-0.0233306884765625,
-0.047149658203125,
-0.0195159912109375,
0.00418853759765625,
-0.01251983642578125,
-0.0141754150390625,
-0.015716552734375,
0.012176513671875,
0.0176544189453125,
0.0028514862060546875,
0.000743865966796875,
0.005390167236328125,
0.02789306640625,
0.0253448486328125,
-0.02093505859375,
-0.01351165771484375,
0.01557159423828125,
-0.04052734375,
0.036834716796875,
-0.022430419921875,
0.011810302734375,
-0.0273590087890625,
0.0218658447265625,
-0.0158538818359375,
-0.0021419525146484375,
-0.033905029296875,
-0.007061004638671875,
0.0011425018310546875,
-0.0243682861328125,
0.0181884765625,
-0.003917694091796875,
-0.027496337890625,
0.0055999755859375,
0.0169525146484375,
0.001827239990234375,
0.0088653564453125,
-0.024566650390625,
-0.049468994140625,
-0.0014047622680664062,
-0.0249176025390625,
-0.0006890296936035156,
-0.0134735107421875,
0.033477783203125,
-0.006237030029296875,
0.0030803680419921875,
-0.00458526611328125,
-0.020599365234375,
0.01206207275390625,
0.01593017578125,
-0.035980224609375,
-0.0093994140625,
0.006927490234375,
0.029327392578125,
0.0015382766723632812,
0.0120849609375,
-0.0208282470703125,
0.0193023681640625,
0.0228271484375,
0.0023212432861328125,
-0.004497528076171875,
0.0253143310546875,
-0.0072174072265625,
-0.009979248046875,
-0.0233001708984375,
-0.0167236328125,
0.0002713203430175781,
0.0141448974609375,
-0.0303955078125,
-0.019134521484375,
-0.0003190040588378906,
0.028717041015625,
-0.00696563720703125,
-0.0213775634765625,
0.005474090576171875,
0.0159149169921875,
0.00702667236328125,
0.045928955078125,
0.03338623046875,
0.0087890625,
0.0006208419799804688,
0.01617431640625,
-0.00749969482421875,
0.0159912109375,
0.032135009765625,
-0.0158233642578125,
0.0113525390625,
0.008270263671875,
0.00637054443359375,
-0.041656494140625,
0.0036449432373046875,
0.0291290283203125,
0.01126861572265625,
-0.03070068359375,
0.018768310546875,
-0.00399017333984375,
-0.031036376953125,
-0.00726318359375,
-0.008148193359375,
-0.03619384765625,
0.00836181640625,
0.0193328857421875,
-0.03155517578125,
-0.042449951171875,
-0.014495849609375,
0.0189666748046875,
0.01317596435546875,
0.01493072509765625,
-0.0008921623229980469,
0.004314422607421875,
0.01531219482421875,
-0.01293182373046875,
0.0251007080078125,
-0.004711151123046875,
-0.0272369384765625,
0.039764404296875,
-0.004917144775390625,
-0.002223968505859375,
-0.006755828857421875,
0.030364990234375,
0.00955963134765625,
0.0116729736328125,
-0.0157318115234375,
-0.012451171875,
0.0200347900390625,
0.01271820068359375,
0.0160064697265625,
-0.0015201568603515625,
-0.0129852294921875,
0.01258087158203125,
0.01214599609375,
-0.014678955078125,
-0.00811004638671875,
0.007007598876953125,
-0.016326904296875,
0.005489349365234375,
-0.01482391357421875,
-0.0111846923828125,
-0.0269012451171875,
-0.00861358642578125,
-0.0149688720703125,
-0.0270538330078125,
0.01073455810546875,
0.02838134765625,
-0.0304412841796875,
-0.01284027099609375,
-0.0253448486328125,
-0.0090484619140625,
-0.0156097412109375,
-0.0007166862487792969,
0.017364501953125,
0.0232391357421875,
0.029205322265625,
-0.018096923828125,
-0.023284912109375,
-0.003635406494140625,
0.00783538818359375,
0.03533935546875,
0.02203369140625,
-0.015716552734375,
0.03070068359375,
0.019134521484375,
0.01318359375,
0.008575439453125,
-0.0272064208984375,
-0.0153045654296875,
-0.00469207763671875,
-0.0103607177734375,
0.00899505615234375,
-0.0227203369140625,
-0.0020923614501953125,
0.0125274658203125,
0.007415771484375,
0.0697021484375,
0.00696563720703125,
0.01415252685546875,
0.01012420654296875,
-0.0244903564453125,
-0.01287078857421875,
-0.009307861328125,
-0.012115478515625,
0.034149169921875,
0.01361846923828125,
-0.00934600830078125,
0.01171875,
0.0035190582275390625,
-0.0269775390625,
0.00458526611328125,
-0.0223541259765625,
0.0200347900390625,
0.01248931884765625,
-0.0230255126953125,
0.02142333984375,
0.02569580078125,
-0.0282440185546875,
0.020050048828125,
-0.023468017578125,
-0.004123687744140625,
0.007415771484375,
-0.0019550323486328125,
-0.031158447265625,
-0.035888671875,
0.0288848876953125,
-0.0253753662109375,
-0.0015392303466796875,
0.025299072265625,
0.0268707275390625,
0.0013437271118164062,
0.0137786865234375,
0.0213165283203125,
-0.04144287109375,
-0.004795074462890625,
-0.0057373046875,
0.0211639404296875,
0.0063934326171875,
-0.01113128662109375,
-0.0037441253662109375,
0.01091766357421875,
0.01482391357421875,
0.0213165283203125,
-0.0401611328125,
0.01105499267578125,
0.0207061767578125,
0.034637451171875,
0.03009033203125,
0.004772186279296875,
0.0262451171875,
0.050537109375,
-0.01264190673828125,
0.026458740234375,
-0.0012645721435546875,
-0.00726318359375,
-0.027191162109375,
-0.0228118896484375,
-0.01126861572265625,
-0.0118560791015625,
0.007671356201171875,
0.00873565673828125,
0.0228729248046875,
0.01019287109375,
-0.032989501953125,
0.006404876708984375,
0.018402099609375,
0.005340576171875,
0.0246734619140625,
0.0024547576904296875,
0.00948333740234375,
-0.0213623046875,
0.0018930435180664062,
-0.00768280029296875,
0.01493072509765625,
-0.0125579833984375,
0.038177490234375,
0.0023250579833984375,
-0.0247650146484375,
-0.0227508544921875,
-0.036041259765625,
0.00466156005859375,
-0.0026226043701171875,
-0.0247650146484375,
-0.0222015380859375,
-0.005100250244140625,
-0.017303466796875,
0.0106201171875,
0.01297760009765625,
-0.0264739990234375,
-0.0204010009765625,
0.01305389404296875,
-0.0074005126953125,
-0.0007891654968261719,
0.015167236328125,
-0.043609619140625,
-0.05609130859375,
-0.021728515625,
0.0284881591796875,
-0.0210113525390625,
-0.01715087890625,
0.0045928955078125,
-0.005031585693359375,
0.002330780029296875,
-0.0018100738525390625,
-0.005458831787109375,
0.01568603515625,
-0.017486572265625,
-0.0114593505859375,
-0.01995849609375,
0.013916015625,
-0.012908935546875,
-0.01436614990234375,
-0.0096435546875,
0.0196990966796875,
-0.0008883476257324219,
-0.01451873779296875,
0.012481689453125,
-0.0247955322265625,
-0.0248870849609375,
-0.0509033203125,
0.020904541015625,
0.033172607421875,
-0.039093017578125,
-0.03533935546875,
0.00583648681640625,
-0.037261962890625,
-0.0254364013671875,
-0.0081787109375,
0.0009627342224121094,
0.01250457763671875,
-0.0202484130859375,
0.006359100341796875,
-0.0242462158203125,
0.01271820068359375,
-0.00146484375,
0.0030536651611328125,
0.01120758056640625,
0.013153076171875,
0.00659942626953125,
0.0241241455078125,
-0.0038356781005859375,
0.0259552001953125,
-0.004756927490234375,
-0.0165557861328125,
0.027862548828125,
0.00537872314453125,
-0.00232696533203125,
-0.006992340087890625,
-0.04180908203125,
0.00408935546875,
-0.026885986328125,
-0.016510009765625,
-0.02398681640625,
0.02764892578125,
-0.0236053466796875,
0.003421783447265625,
-0.005893707275390625,
0.006832122802734375,
0.0120849609375,
0.0173187255859375,
-0.0173797607421875,
0.007518768310546875,
0.01824951171875,
0.008026123046875,
0.003711700439453125
] |
ours_488
|
I claim the possible values of \(n\) are \(0, 4, 8, \ldots, 196\).
Note that if we ignore the rightmost column and the bottom row of the grid, then the rest of the grid can be partitioned into forty-nine \(2 \times 2\) squares. For any \(k=0,1, \ldots, 49\), choose any \(k\) of those \(2 \times 2\) squares, and color all the cells in those squares white, and color the cells in the other \(49-k\) of those squares, as well as the cells in the rightmost column and the bottom row of the grid, black. The result is a crossword puzzle with exactly \(4k\) white cells. It is not hard to see that this crossword puzzle is tasty. Thus \(4k\) is a possible value of \(n\), so \(0, 4, 8, \ldots, 196\) all are possible values of \(n\).
Now the other direction: suppose there is a tasty crossword puzzle with exactly \(n\) white squares. Label the rows \(1\) to \(15\) in order from top to bottom; label the columns \(1\) to \(15\) in order from left to right. Place the letter \(a\) in every square at the intersection of an odd-numbered row and an odd-numbered column; place the letter \(b\) in every square at the intersection of an odd-numbered row and an even-numbered column; place the letter \(c\) in every square at the intersection of an even-numbered row and an odd-numbered column; place the letter \(d\) in every square at the intersection of an even-numbered row and an even-numbered column. Let \(A\) be the number of white squares that contain the letter \(a\); define \(B, C\), and \(D\) analogously. Consider all horizontal words (words that are a subset of some row) in the grid; every such word consists of an even number of white squares (since the crossword puzzle is tasty), and every white square in the grid is in exactly one such word. Considering such words in odd-numbered rows, we get \(A=B\). A similar consideration of even-numbered rows yields that \(C=D\). Similar consideration of vertical words yields that \(A=C\) and \(B=D\). Thus \(A=B=C=D\). Then \(n=A+B+C+D=4D\). Now \(D\) is a nonnegative integer; furthermore, \(D\) is at most the total number of cells containing \(d\)'s in the grid, which is \(49\). Thus \(n\) is among \(0, 4, 8, \ldots, 196\), as desired.
Thus the possible values of \(n\) are \(0, 4, 8, \ldots, 196\), as claimed. Thus the answer is \(0+4+8+\cdots+196=4(1+2+\cdots+49)=4 \cdot \frac{49 \cdot 50}{2}=4900\).
\(\boxed{4900}\)
|
4900
|
{
"competition": "us_comps",
"dataset": "Ours",
"posts": null,
"source": "OMOFall19Solns-2.md"
}
|
Define a crossword puzzle to be a \(15 \times 15\) grid of squares, each of which is either black or white. In a crossword puzzle, define a word to be a sequence of one or more consecutive white squares in a row or column such that the squares immediately before and after the sequence are either black or nonexistent. (The latter case would occur if an end of a word coincides with an end of a row or column of the grid.) A crossword puzzle is tasty if every word consists of an even number of white squares. Compute the sum of all nonnegative integers \(n\) such that there exists a tasty crossword puzzle with exactly \(n\) white squares.
|
[
"/Mathematics/DiscreteMathematics/Combinatorics/Enumeration",
"/Mathematics/DiscreteMathematics/Combinatorics/GeneralCombinatorics",
"/Mathematics/DiscreteMathematics/GeneralDiscreteMathematics/DiscreteMath",
"/Mathematics/DiscreteMathematics/GeneralDiscreteMathematics/DiscreteMathematics",
"/Mathematics/RecreationalMathematics/Puzzles/Puzzle"
] |
Classify cells by row/column parity and show each parity class has the same number of white squares, so total white squares is a multiple of 4.
|
[
0.00010883808135986328,
0.0030117034912109375,
0.039886474609375,
-0.005428314208984375,
0.0005364418029785156,
-0.029571533203125,
0.018035888671875,
-0.029052734375,
0.004474639892578125,
-0.024688720703125,
0.0202178955078125,
-0.0157318115234375,
0.0010967254638671875,
0.0003304481506347656,
-0.036956787109375,
-0.040191650390625,
0.0205535888671875,
-0.0252685546875,
-0.0002455711364746094,
-0.00250244140625,
-0.00945281982421875,
-0.0133819580078125,
-0.03424072265625,
0.03619384765625,
0.00727081298828125,
-0.037109375,
-0.0205535888671875,
0.038909912109375,
0.0484619140625,
-0.019561767578125,
-0.0343017578125,
-0.026458740234375,
0.0140380859375,
-0.005321502685546875,
0.0073394775390625,
0.00725555419921875,
0.0202484130859375,
-0.004207611083984375,
0.0217132568359375,
-0.06878662109375,
-0.026397705078125,
-0.0005645751953125,
-0.0236663818359375,
-0.008514404296875,
0.023712158203125,
-0.0190582275390625,
0.0026798248291015625,
0.005229949951171875,
-0.043853759765625,
0.01348876953125,
-0.00432586669921875,
0.0189666748046875,
-0.000038564205169677734,
-0.0036907196044921875,
0.00406646728515625,
-0.0168914794921875,
0.00966644287109375,
0.007053375244140625,
0.013580322265625,
0.0096282958984375,
0.00533294677734375,
0.0201568603515625,
-0.0020122528076171875,
-0.038177490234375,
0.0005121231079101562,
-0.005031585693359375,
-0.0003495216369628906,
-0.0294342041015625,
-0.0020885467529296875,
0.0012531280517578125,
-0.0169219970703125,
0.01267242431640625,
-0.0182342529296875,
0.0157623291015625,
0.01284027099609375,
-0.0236968994140625,
0.00496673583984375,
0.022247314453125,
0.0279998779296875,
0.007740020751953125,
0.041595458984375,
-0.0131988525390625,
0.002166748046875,
-0.011749267578125,
0.01267242431640625,
-0.01197052001953125,
-0.0072174072265625,
0.0033702850341796875,
0.057281494140625,
-0.0249481201171875,
-0.00566864013671875,
0.01401519775390625,
0.00759124755859375,
0.0174560546875,
0.00415802001953125,
0.003459930419921875,
0.01483917236328125,
-0.00823211669921875,
-0.005367279052734375,
0.0175628662109375,
-0.00908660888671875,
0.0023555755615234375,
0.0272979736328125,
-0.0231475830078125,
-0.03863525390625,
-0.0157318115234375,
-0.0042572021484375,
-0.0033359527587890625,
-0.0071868896484375,
0.003997802734375,
-0.00196075439453125,
0.0083770751953125,
-0.00893402099609375,
0.00994110107421875,
-0.0295562744140625,
-0.007633209228515625,
0.0090789794921875,
-0.00876617431640625,
-0.0111236572265625,
-0.00704193115234375,
-0.0011091232299804688,
0.007450103759765625,
-0.0007863044738769531,
0.01812744140625,
-0.002902984619140625,
-0.042572021484375,
0.00510406494140625,
-0.00322723388671875,
0.020660400390625,
-0.0223388671875,
-0.0019397735595703125,
0.0147857666015625,
-0.02923583984375,
-0.0120697021484375,
-0.05401611328125,
-0.004955291748046875,
-0.005130767822265625,
-0.01514434814453125,
0.0079193115234375,
0.010650634765625,
0.0036830902099609375,
-0.0062408447265625,
0.0017633438110351562,
-0.011688232421875,
-0.01081085205078125,
0.0445556640625,
-0.00731658935546875,
-0.05029296875,
-0.0037078857421875,
0.0216827392578125,
0.0006628036499023438,
0.014373779296875,
-0.0036563873291015625,
0.01261138916015625,
-0.0114593505859375,
0.0035839080810546875,
0.004852294921875,
-0.0037593841552734375,
0.01493072509765625,
0.00153350830078125,
0.0037555694580078125,
-0.0045013427734375,
0.0030517578125,
0.046905517578125,
-0.0011014938354492188,
-0.004638671875,
0.01531982421875,
-0.010894775390625,
0.0228271484375,
0.0067901611328125,
0.005764007568359375,
-0.0244903564453125,
0.01151275634765625,
-0.0183868408203125,
0.01299285888671875,
0.0009312629699707031,
-0.0010957717895507812,
0.01302337646484375,
-0.01422882080078125,
0.0190582275390625,
0.0010671615600585938,
-0.0200347900390625,
0.0269317626953125,
0.006641387939453125,
-0.00013899803161621094,
0.0031452178955078125,
-0.006290435791015625,
0.0154876708984375,
0.00843048095703125,
0.01371002197265625,
-0.01898193359375,
0.018585205078125,
-0.01291656494140625,
0.01078033447265625,
-0.029693603515625,
-0.00762939453125,
0.0096893310546875,
-0.002429962158203125,
0.009490966796875,
0.0128326416015625,
0.00852203369140625,
-0.01099395751953125,
0.006275177001953125,
0.011962890625,
0.00603485107421875,
-0.010955810546875,
0.01020050048828125,
-0.010589599609375,
0.017730712890625,
-0.0012578964233398438,
-0.00511932373046875,
0.00530242919921875,
-0.0007877349853515625,
0.0208740234375,
-0.0185394287109375,
0.008697509765625,
-0.0134124755859375,
0.01354217529296875,
0.0310821533203125,
-0.052093505859375,
0.00870513916015625,
0.00856781005859375,
-0.015777587890625,
-0.0141754150390625,
-0.0207366943359375,
0.0170745849609375,
0.029083251953125,
-0.002780914306640625,
0.036865234375,
0.004367828369140625,
0.006145477294921875,
0.01556396484375,
0.01788330078125,
-0.0076904296875,
-0.01183319091796875,
0.003734588623046875,
-0.0188140869140625,
-0.0213470458984375,
-0.00384521484375,
-0.0079803466796875,
0.02294921875,
0.007503509521484375,
-0.0011415481567382812,
0.0014629364013671875,
0.01806640625,
0.00004017353057861328,
0.01306915283203125,
-0.00304412841796875,
-0.006595611572265625,
0.00908660888671875,
-0.0012712478637695312,
0.0019779205322265625,
-0.031707763671875,
-0.0016164779663085938,
-0.0189208984375,
-0.0173492431640625,
0.01149749755859375,
0.03125,
-0.0200653076171875,
-0.031829833984375,
-0.003948211669921875,
0.00952911376953125,
0.00844573974609375,
-0.0101318359375,
-0.004718780517578125,
-0.038787841796875,
0.0440673828125,
0.009185791015625,
-0.0173797607421875,
0.00371551513671875,
0.005950927734375,
0.005214691162109375,
-0.00389862060546875,
0.00959014892578125,
0.0251922607421875,
-0.02044677734375,
-0.002407073974609375,
0.004924774169921875,
0.003490447998046875,
0.00969696044921875,
0.01824951171875,
-0.03204345703125,
-0.0179290771484375,
-0.019073486328125,
-0.0022907257080078125,
-0.019134521484375,
0.0045318603515625,
-0.019134521484375,
-0.0094451904296875,
0.01552581787109375,
0.0098419189453125,
-0.0151214599609375,
-0.0038700103759765625,
-0.0250396728515625,
0.02569580078125,
-0.05206298828125,
-0.00490570068359375,
-0.007144927978515625,
0.005889892578125,
-0.0045928955078125,
0.0135345458984375,
0.0034084320068359375,
-0.017852783203125,
0.036468505859375,
0.0166473388671875,
0.036468505859375,
-0.00867462158203125,
-0.00489044189453125,
-0.0180816650390625,
-0.0002651214599609375,
0.0244903564453125,
-0.0161895751953125,
0.011932373046875,
-0.0033435821533203125,
0.02886962890625,
-0.0290069580078125,
0.0019893646240234375,
0.017547607421875,
-0.00447845458984375,
-0.00011843442916870117,
-0.0015954971313476562,
0.0157928466796875,
-0.0113372802734375,
0.00021016597747802734,
-0.01468658447265625,
-0.0012292861938476562,
0.017669677734375,
-0.0030155181884765625,
-0.033782958984375,
0.036529541015625,
-0.0270233154296875,
0.01947021484375,
-0.0069427490234375,
-0.0077667236328125,
-0.02490234375,
0.00238800048828125,
-0.00974273681640625,
0.000553131103515625,
0.016082763671875,
0.00881195068359375,
-0.005435943603515625,
-0.0012445449829101562,
-0.031158447265625,
0.0307464599609375,
-0.0015163421630859375,
0.00948333740234375,
0.0023860931396484375,
-0.0146484375,
-0.0011701583862304688,
-0.022003173828125,
-0.047515869140625,
0.025634765625,
-0.0183258056640625,
0.00940704345703125,
-0.044219970703125,
0.0168609619140625,
-0.0228424072265625,
-0.0164642333984375,
-0.0330810546875,
0.0160980224609375,
-0.0122528076171875,
0.01409912109375,
0.01251220703125,
0.01030731201171875,
0.029815673828125,
-0.02117919921875,
-0.019989013671875,
0.00356292724609375,
0.0024394989013671875,
-0.0300445556640625,
-0.00496673583984375,
-0.007480621337890625,
-0.0084686279296875,
0.002765655517578125,
-0.016998291015625,
0.005382537841796875,
-0.005176544189453125,
0.0144805908203125,
-0.0229644775390625,
-0.019683837890625,
-0.00728607177734375,
0.0127716064453125,
0.0198211669921875,
0.034698486328125,
-0.0196533203125,
-0.0005469322204589844,
-0.020111083984375,
-0.0110321044921875,
-0.0272674560546875,
0.0193023681640625,
0.006298065185546875,
0.045196533203125,
-0.01551055908203125,
0.0072174072265625,
0.016387939453125,
0.001613616943359375,
0.00433349609375,
0.006008148193359375,
0.036956787109375,
-0.03302001953125,
-0.032562255859375,
-0.0309600830078125,
-0.0114288330078125,
-0.00728607177734375,
-0.005649566650390625,
-0.006397247314453125,
0.005176544189453125,
-0.01018524169921875,
-0.00849151611328125,
0.00872039794921875,
0.032012939453125,
0.021881103515625,
-0.0117645263671875,
-0.01065826416015625,
0.01081085205078125,
-0.01471710205078125,
0.001300811767578125,
-0.01873779296875,
0.024200439453125,
-0.0179443359375,
-0.01016998291015625,
0.004352569580078125,
0.0275726318359375,
0.00678253173828125,
0.01061248779296875,
0.01006317138671875,
0.0006375312805175781,
0.043792724609375,
-0.00783538818359375,
0.00656890869140625,
0.003387451171875,
-0.0168914794921875,
0.0257110595703125,
0.02423095703125,
0.006683349609375,
0.0667724609375,
0.01242828369140625,
0.0260772705078125,
0.006015777587890625,
0.02386474609375,
-0.002506256103515625,
-0.0085601806640625,
-0.0274810791015625,
0.0088348388671875,
-0.00466156005859375,
0.0111541748046875,
-0.019622802734375,
0.0203399658203125,
-0.037200927734375,
0.0147552490234375,
-0.058990478515625,
0.006378173828125,
-0.0126953125,
-0.0101776123046875,
-0.0238494873046875,
0.0021381378173828125,
-0.00977325439453125,
-0.00860595703125,
-0.0258941650390625,
-0.03546142578125,
-0.01483154296875,
0.00771331787109375,
-0.0233917236328125,
-0.00719451904296875,
-0.01410675048828125,
0.0009746551513671875,
0.00177001953125,
-0.022064208984375,
0.0423583984375,
-0.007228851318359375,
0.0238037109375,
-0.01207733154296875,
0.00787353515625,
0.001251220703125,
-0.0098419189453125,
0.01016998291015625,
0.02294921875,
0.02252197265625,
-0.039154052734375,
-0.019927978515625,
0.01067352294921875,
-0.01078033447265625,
-0.030914306640625,
0.02459716796875,
0.014434814453125,
0.03131103515625,
-0.00244903564453125,
0.00920867919921875,
-0.0302276611328125,
0.0016679763793945312,
0.01230621337890625,
0.058868408203125,
-0.046539306640625,
-0.01227569580078125,
0.0033969879150390625,
-0.0010213851928710938,
0.0231475830078125,
-0.0169525146484375,
-0.039276123046875,
0.00038933753967285156,
-0.004863739013671875,
-0.00128173828125,
-0.0203094482421875,
-0.01470947265625,
0.0190582275390625,
0.006000518798828125,
0.06329345703125,
0.0038433074951171875,
0.037384033203125,
-0.0193634033203125,
-0.0111083984375,
0.00482177734375,
0.00799560546875,
-0.032318115234375,
0.021331787109375,
-0.0271148681640625,
0.03448486328125,
-0.00409698486328125,
-0.00037026405334472656,
0.007526397705078125,
0.021453857421875,
-0.0009450912475585938,
-0.01483154296875,
-0.0008554458618164062,
-0.007297515869140625,
-0.01230621337890625,
-0.0213623046875,
-0.030853271484375,
-0.0209197998046875,
0.0180816650390625,
-0.01325225830078125,
-0.0011930465698242188,
0.012786865234375,
0.01392364501953125,
0.0038013458251953125,
0.029052734375,
0.005832672119140625,
0.0269317626953125,
0.028350830078125,
0.02777099609375,
-0.0110626220703125,
-0.0333251953125,
0.04779052734375,
-0.0012540817260742188,
-0.0178680419921875,
-0.036224365234375,
0.0232696533203125,
0.0218353271484375,
-0.01239776611328125,
0.025146484375,
0.00394439697265625,
0.00962066650390625,
-0.041656494140625,
0.004955291748046875,
-0.026092529296875,
-0.00949859619140625,
0.001194000244140625,
-0.01496124267578125,
0.0190277099609375,
0.0259246826171875,
-0.0036563873291015625,
0.036529541015625,
0.01004791259765625,
0.025390625,
0.0261993408203125,
-0.0308380126953125,
-0.018218994140625,
-0.038238525390625,
-0.0079498291015625,
-0.050445556640625,
0.004306793212890625,
-0.0224456787109375,
0.009979248046875,
-0.01241302490234375,
-0.0206756591796875,
0.00452423095703125,
-0.0044097900390625,
-0.0205078125,
0.0021038055419921875,
-0.03912353515625,
0.007602691650390625,
-0.005947113037109375,
-0.02374267578125,
-0.0125885009765625,
0.0222320556640625,
-0.0281524658203125,
0.0220947265625,
0.0018053054809570312,
0.01277923583984375,
-0.0257568359375,
-0.004741668701171875,
0.031524658203125,
0.004001617431640625,
-0.017120361328125,
0.00762939453125,
-0.029754638671875,
-0.033355712890625,
-0.0204010009765625,
-0.007633209228515625,
0.0277862548828125,
0.0006384849548339844,
-0.010894775390625,
-0.0146636962890625,
0.0150909423828125,
0.0017681121826171875,
-0.0384521484375,
0.037322998046875,
0.002559661865234375,
-0.0030364990234375,
-0.04144287109375,
0.0209503173828125,
0.00933074951171875,
-0.0177001953125,
0.01120758056640625,
0.04296875,
-0.007038116455078125,
-0.003261566162109375,
-0.0032863616943359375,
0.03759765625,
-0.003505706787109375,
-0.003116607666015625,
-0.014373779296875,
0.0121612548828125,
0.0258636474609375,
0.0017671585083007812,
0.0172576904296875,
0.0253143310546875,
-0.0229644775390625,
0.0042266845703125,
0.018798828125,
-0.06707763671875,
-0.0195770263671875,
0.007061004638671875,
-0.0078887939453125,
-0.01508331298828125,
0.0108489990234375,
-0.01444244384765625,
0.03582763671875,
-0.0239715576171875,
-0.016876220703125,
0.005504608154296875,
0.00040531158447265625,
0.0116729736328125,
-0.00572967529296875,
-0.00472259521484375,
0.018707275390625,
-0.0010728836059570312,
0.00278472900390625,
-0.038543701171875,
0.0195159912109375,
-0.0396728515625,
-0.0063018798828125,
-0.040252685546875,
-0.0026378631591796875,
0.003376007080078125,
0.00913238525390625,
0.01055145263671875,
0.00951385498046875,
0.020751953125,
0.011138916015625,
0.037322998046875,
-0.003726959228515625,
0.000762939453125,
-0.0159759521484375,
-0.040802001953125,
-0.021759033203125,
-0.0006461143493652344,
0.023040771484375,
0.01287078857421875,
0.01088714599609375,
-0.019683837890625,
0.01397705078125,
-0.0164337158203125,
0.0125579833984375,
0.026519775390625,
0.01140594482421875,
-0.0074615478515625,
0.00019502639770507812,
0.028656005859375,
-0.004611968994140625,
-0.01270294189453125,
0.0194854736328125,
0.005641937255859375,
-0.00543212890625,
0.0391845703125,
-0.006221771240234375,
0.030181884765625,
-0.0252685546875,
0.0285186767578125,
-0.0205078125,
0.0208740234375,
0.0016069412231445312,
-0.0220947265625,
0.015045166015625,
-0.018524169921875,
-0.00766754150390625,
0.00750732421875,
0.0210723876953125,
-0.01021575927734375,
-0.013336181640625,
0.0218353271484375,
0.002368927001953125,
0.01120758056640625,
0.01568603515625,
-0.0250701904296875,
-0.012725830078125,
-0.0192718505859375,
-0.01349639892578125,
-0.02392578125,
0.031707763671875,
-0.01422882080078125,
0.0009250640869140625,
0.0015048980712890625,
-0.017333984375,
0.0043182373046875,
-0.0199432373046875,
0.035888671875,
-0.0103302001953125,
-0.0027713775634765625,
-0.0215606689453125,
-0.025146484375,
0.0308380126953125,
-0.01348876953125,
-0.03436279296875,
0.032012939453125,
-0.0367431640625,
-0.00794219970703125,
-0.0011920928955078125,
-0.0233154296875,
0.0168609619140625,
-0.003208160400390625,
-0.01541900634765625,
-0.03668212890625,
-0.0134124755859375,
-0.002208709716796875,
-0.0125732421875,
0.029632568359375,
-0.01593017578125,
-0.01462554931640625,
-0.01500701904296875,
0.0158233642578125,
-0.01091766357421875,
-0.0086669921875,
-0.0184173583984375,
-0.0209197998046875,
-0.01367950439453125,
-0.0242462158203125,
0.01180267333984375,
-0.0071258544921875,
0.0308990478515625,
0.03399658203125,
0.005413055419921875,
-0.00852203369140625,
-0.03985595703125,
0.0021495819091796875,
-0.0250701904296875,
0.0154266357421875,
-0.019622802734375,
0.001842498779296875,
0.0265350341796875,
-0.0195770263671875,
0.025177001953125,
-0.0269012451171875,
0.0229644775390625,
0.01318359375,
-0.046234130859375,
-0.0018758773803710938,
-0.0194854736328125,
-0.0304412841796875,
0.01273345947265625,
-0.06396484375,
-0.003452301025390625,
0.017578125,
0.033416748046875,
0.014739990234375,
0.0006699562072753906,
-0.0270843505859375,
0.0029621124267578125,
0.0308685302734375,
-0.028411865234375,
0.007114410400390625,
-0.005626678466796875,
-0.00878143310546875,
-0.00844573974609375,
-0.0259857177734375,
0.029541015625,
0.0015249252319335938,
-0.0247039794921875,
0.017303466796875,
-0.0276641845703125,
0.0443115234375,
0.0208587646484375,
0.01300811767578125,
-0.00553131103515625,
-0.0269317626953125,
-0.0291748046875,
0.01201629638671875,
-0.01094818115234375,
-0.0299530029296875,
0.0191192626953125,
0.00433349609375,
-0.0035152435302734375,
-0.038299560546875,
0.0095672607421875,
0.048858642578125,
-0.00971221923828125,
0.00969696044921875,
0.0079193115234375,
0.0160675048828125,
0.0146484375,
0.0248565673828125,
-0.009033203125,
-0.004119873046875,
-0.0048828125,
-0.008026123046875,
0.0180511474609375,
0.01715087890625,
-0.01318359375,
-0.00711822509765625,
0.0211029052734375,
-0.0286102294921875,
0.006011962890625,
-0.01270294189453125,
0.0136260986328125,
-0.01366424560546875,
-0.0181884765625,
-0.01134490966796875,
0.0140533447265625,
0.015838623046875,
0.015533447265625,
0.017791748046875,
0.00946044921875,
-0.0136260986328125,
0.00850677490234375,
-0.00415802001953125,
-0.00827789306640625,
0.007228851318359375,
0.0294036865234375,
-0.0269317626953125,
-0.016387939453125,
-0.00867462158203125,
0.018218994140625,
-0.033599853515625,
-0.01265716552734375,
-0.01129913330078125,
-0.018096923828125,
-0.0328369140625,
-0.01280975341796875,
0.0185699462890625,
0.006565093994140625,
-0.0013408660888671875,
0.0026378631591796875,
-0.016204833984375,
0.0093536376953125,
0.00267791748046875,
-0.01486968994140625,
0.0149993896484375,
0.0012369155883789062,
-0.00909423828125,
-0.0158233642578125,
0.0196075439453125,
-0.0197906494140625,
0.0075836181640625,
-0.0567626953125,
0.004207611083984375,
0.002197265625,
-0.04193115234375,
-0.0193634033203125,
0.0187835693359375,
-0.0261993408203125,
0.01114654541015625,
0.016632080078125,
0.02825927734375,
-0.035858154296875,
0.05126953125,
-0.01032257080078125,
-0.0217742919921875,
-0.018463134765625,
0.045166015625,
0.04541015625,
-0.04443359375,
-0.051116943359375,
-0.00502777099609375,
-0.022857666015625,
-0.0003197193145751953,
-0.01141357421875,
-0.01224517822265625,
0.022918701171875,
-0.0015802383422851562,
-0.00760650634765625,
0.0029811859130859375,
-0.004791259765625,
-0.0077362060546875,
-0.01349639892578125,
-0.0035228729248046875,
0.040618896484375,
-0.0196075439453125,
-0.020782470703125,
-0.0011568069458007812,
-0.03521728515625,
-0.0116424560546875,
-0.009307861328125,
-0.007007598876953125,
0.0233001708984375,
-0.00888824462890625,
0.00792694091796875,
0.0243988037109375,
-0.0101165771484375,
0.0200347900390625,
0.0214080810546875,
-0.031707763671875,
-0.021209716796875,
-0.0201568603515625,
-0.0281829833984375,
-0.036956787109375,
-0.00870513916015625,
0.01206207275390625,
0.033203125,
-0.0032558441162109375,
-0.0211334228515625,
-0.016448974609375,
-0.00406646728515625,
0.004909515380859375,
-0.035797119140625,
-0.0114593505859375,
-0.042449951171875,
-0.0026073455810546875,
-0.00673675537109375,
0.00760650634765625,
0.0029163360595703125,
-0.007144927978515625,
0.0145721435546875,
-0.005619049072265625,
-0.01519775390625,
-0.02874755859375,
0.01349639892578125,
0.0012865066528320312,
-0.0164794921875,
0.02484130859375,
0.0028820037841796875,
-0.0019426345825195312,
0.0120697021484375,
-0.00370025634765625,
0.04693603515625,
-0.0037136077880859375,
-0.0140380859375,
0.0106964111328125,
-0.0013475418090820312,
-0.05029296875,
-0.0093841552734375,
-0.0131072998046875,
0.01058197021484375,
-0.0017747879028320312,
0.0350341796875,
0.00032448768615722656,
0.033233642578125,
0.039031982421875,
0.004688262939453125,
0.0034580230712890625,
-0.0019435882568359375,
0.01047515869140625,
0.00020003318786621094,
0.007720947265625,
0.01019287109375,
0.019378662109375,
0.0141754150390625,
-0.034027099609375,
-0.0091552734375,
0.01155853271484375,
0.0028934478759765625,
-0.0265045166015625,
-0.0301666259765625,
0.0050201416015625,
-0.0103759765625,
-0.007965087890625,
0.04296875,
-0.015380859375,
0.038909912109375,
-0.002166748046875,
-0.00864410400390625,
-0.059844970703125,
0.0022220611572265625,
0.00506591796875,
-0.0018625259399414062,
-0.035858154296875,
0.0170440673828125,
0.0199127197265625,
-0.0201263427734375,
0.0093536376953125,
-0.03765869140625,
-0.01416778564453125,
0.0194854736328125,
0.0308074951171875,
0.037384033203125,
-0.003498077392578125,
0.01476287841796875,
-0.0175933837890625,
-0.026397705078125,
0.038543701171875,
0.0003483295440673828,
-0.05450439453125,
-0.002468109130859375,
-0.011474609375,
-0.0191802978515625,
0.0309906005859375,
-0.0195159912109375,
-0.006168365478515625,
0.01123046875,
0.002227783203125,
0.0265350341796875,
-0.006946563720703125,
-0.0025882720947265625,
-0.0016803741455078125,
-0.01013946533203125,
-0.0250244140625,
0.0215911865234375,
-0.006870269775390625,
-0.0093231201171875,
-0.0040283203125,
-0.01078033447265625,
0.0372314453125,
0.007785797119140625,
-0.0259246826171875,
-0.00019121170043945312,
0.0121307373046875,
0.0014619827270507812,
0.004337310791015625,
0.00962066650390625,
0.02593994140625,
0.025299072265625,
-0.017669677734375,
-0.0228271484375,
0.022613525390625,
-0.023101806640625,
-0.0163116455078125,
-0.004261016845703125,
0.0052947998046875,
-0.012420654296875,
-0.02911376953125,
-0.00684356689453125,
0.004344940185546875,
0.004138946533203125,
0.030120849609375,
0.032257080078125,
-0.01275634765625,
-0.06475830078125,
-0.00665283203125,
0.023681640625,
-0.0080413818359375,
-0.0172882080078125,
0.03778076171875,
0.037567138671875,
-0.01241302490234375,
-0.004314422607421875,
-0.001178741455078125,
0.0214385986328125,
0.01776123046875,
-0.035736083984375,
0.00746917724609375,
0.0254974365234375,
-0.026885986328125,
0.0088348388671875,
-0.020233154296875,
-0.03216552734375,
-0.0162811279296875,
-0.021392822265625,
-0.02362060546875,
0.0003955364227294922,
-0.0186309814453125,
0.007411956787109375,
-0.033111572265625,
-0.00009202957153320312,
0.02734375,
-0.04132080078125,
0.00372314453125,
-0.035125732421875,
0.0214691162109375,
0.025299072265625,
-0.02032470703125,
0.034637451171875,
-0.026885986328125,
0.0148468017578125,
-0.01499176025390625,
0.01352691650390625,
0.0077667236328125,
0.03204345703125,
0.0118560791015625,
0.0016326904296875,
-0.0014133453369140625,
0.005901336669921875,
-0.0305633544921875,
-0.0132293701171875,
0.01171875,
0.0124359130859375,
0.03668212890625,
-0.0018978118896484375,
0.01337432861328125,
0.005573272705078125,
0.0243377685546875,
0.004638671875,
-0.00994110107421875,
0.0286712646484375,
-0.018341064453125,
-0.01116180419921875,
-0.0292205810546875,
-0.004241943359375,
-0.006893157958984375,
0.02044677734375,
0.0237274169921875,
-0.01373291015625,
-0.01505279541015625,
0.00684356689453125,
0.0238494873046875,
0.0226287841796875,
0.00658416748046875,
0.0264739990234375,
-0.0278167724609375,
-0.06280517578125,
-0.0246429443359375,
-0.0068511962890625,
-0.032867431640625,
0.00778961181640625,
-0.036590576171875,
0.02215576171875,
0.0161590576171875,
-0.0257720947265625,
0.0136871337890625,
-0.017822265625,
-0.0341796875,
0.01049041748046875,
-0.00811004638671875,
0.03662109375,
-0.0165863037109375,
-0.00998687744140625,
-0.01215362548828125,
0.0079498291015625,
-0.0170745849609375,
-0.004184722900390625,
0.018157958984375,
-0.022491455078125,
0.0197601318359375,
0.020751953125,
-0.0220947265625,
-0.029632568359375,
-0.0135345458984375,
0.0110931396484375,
0.00666046142578125,
-0.0111541748046875,
-0.0105438232421875,
0.0230712890625,
-0.0325927734375,
0.0193328857421875,
-0.00974273681640625,
-0.03680419921875,
-0.01410675048828125,
-0.0043792724609375,
-0.029937744140625,
-0.02349853515625,
0.01215362548828125,
-0.020416259765625,
0.0032444000244140625,
-0.0172271728515625,
0.0264434814453125,
0.00904083251953125,
-0.00748443603515625,
-0.0311126708984375,
0.006725311279296875,
0.027679443359375,
-0.0325927734375,
-0.0143890380859375,
-0.030517578125,
-0.0110015869140625,
0.004177093505859375,
-0.0008325576782226562,
-0.00910186767578125,
-0.03363037109375,
0.005184173583984375,
-0.005023956298828125,
-0.0212554931640625,
-0.0030689239501953125,
-0.01947021484375,
-0.0029163360595703125,
-0.022857666015625,
0.0013360977172851562,
0.01177978515625,
-0.0269927978515625,
-0.004848480224609375,
0.00804901123046875,
-0.0044403076171875,
0.0213470458984375,
-0.0066070556640625,
-0.02825927734375,
-0.0189361572265625,
-0.00240325927734375,
-0.006206512451171875,
0.00476837158203125,
-0.00841522216796875,
0.010711669921875,
0.0300750732421875,
-0.003414154052734375,
-0.011505126953125,
-0.006023406982421875,
-0.00870513916015625,
-0.0302734375,
-0.02264404296875,
-0.0096893310546875,
0.01105499267578125,
-0.00211334228515625,
-0.0311431884765625,
0.01227569580078125,
-0.00449371337890625,
-0.028167724609375,
-0.0258636474609375,
0.01361846923828125,
0.0156402587890625,
0.0024623870849609375,
0.00008171796798706055,
-0.03582763671875,
-0.01560211181640625,
-0.003520965576171875,
0.010345458984375,
0.00997161865234375,
0.015289306640625,
-0.003200531005859375,
-0.0259857177734375,
0.011444091796875,
-0.034454345703125,
0.0234527587890625,
-0.01348114013671875,
-0.0119476318359375,
0.052490234375,
0.0098114013671875,
-0.0012540817260742188,
-0.0141143798828125,
-0.0201263427734375,
-0.00807952880859375,
-0.0251922607421875,
0.0267181396484375,
0.00836181640625,
0.05999755859375,
-0.0163421630859375,
-0.0005593299865722656,
0.011749267578125,
0.05181884765625,
0.0205230712890625,
-0.023834228515625,
-0.01776123046875,
-0.0037403106689453125,
-0.0218505859375,
0.004848480224609375,
-0.0291595458984375,
0.034423828125,
0.0166015625,
-0.0243988037109375,
-0.015228271484375,
-0.0224456787109375,
-0.00463104248046875,
0.0113983154296875,
0.0018634796142578125,
-0.0005497932434082031,
0.04302978515625,
0.0232696533203125,
-0.0188140869140625,
-0.01593017578125,
-0.01947021484375,
-0.01136016845703125,
0.01068115234375,
-0.0030498504638671875,
0.00534820556640625,
-0.001049041748046875,
0.03021240234375,
-0.040496826171875,
-0.0013446807861328125,
0.00626373291015625,
-0.01380157470703125,
-0.0002841949462890625,
-0.0019197463989257812,
-0.01525115966796875,
-0.044403076171875,
0.0011529922485351562,
0.01812744140625,
0.005161285400390625,
0.0235443115234375,
0.0012922286987304688,
-0.0249786376953125,
-0.029388427734375,
-0.024017333984375,
0.00818634033203125,
0.0121307373046875,
0.0211944580078125,
-0.0110931396484375,
-0.0261688232421875,
-0.013916015625,
-0.009368896484375,
-0.01349639892578125,
-0.0126190185546875,
-0.00789642333984375,
0.021148681640625,
-0.004428863525390625,
0.004703521728515625,
-0.0019626617431640625,
0.0035247802734375,
-0.03057861328125,
0.007472991943359375,
0.0035457611083984375,
-0.0139923095703125,
0.0108184814453125,
0.02984619140625,
0.0007243156433105469,
0.00803375244140625,
0.0165557861328125,
0.0179443359375,
0.012176513671875,
-0.006420135498046875,
0.018310546875,
0.01209259033203125,
0.00798797607421875,
-0.0006794929504394531,
-0.006114959716796875,
-0.01097869873046875,
-0.0241546630859375,
-0.00533294677734375,
0.0164794921875,
0.0109405517578125,
0.0423583984375,
0.007648468017578125,
-0.0217132568359375,
0.0193634033203125,
0.01336669921875,
-0.0162200927734375,
0.00495147705078125,
0.004070281982421875,
0.01090240478515625,
-0.0014095306396484375,
0.0034942626953125,
0.03594970703125,
0.013458251953125,
0.0204925537109375,
0.01131439208984375,
-0.0230712890625,
-0.004741668701171875,
0.032928466796875,
0.01080322265625,
0.00925445556640625,
-0.0025615692138671875,
0.0087127685546875,
0.0179443359375,
-0.015655517578125,
0.005313873291015625,
-0.03118896484375,
-0.0242462158203125,
0.00919342041015625,
-0.0211029052734375,
-0.01898193359375,
-0.0211334228515625,
0.0003077983856201172,
0.007183074951171875,
0.028289794921875,
0.04229736328125,
0.01445770263671875,
-0.004718780517578125,
-0.0030460357666015625,
0.04229736328125,
-0.0194091796875,
-0.0024471282958984375,
0.01235198974609375,
0.040618896484375,
0.01043701171875,
-0.013763427734375,
0.00839996337890625,
-0.00628662109375,
-0.019622802734375,
-0.0272979736328125,
-0.01641845703125,
0.0124053955078125,
0.005126953125,
-0.0217132568359375,
-0.003757476806640625,
-0.0008764266967773438,
-0.002712249755859375,
-0.0153350830078125,
-0.028839111328125,
-0.03082275390625,
-0.0003592967987060547,
0.0167694091796875,
0.03240966796875,
-0.0041046142578125,
0.044769287109375,
-0.010772705078125,
-0.0345458984375,
0.00811767578125,
0.005992889404296875,
-0.019561767578125,
0.01285552978515625,
-0.01093292236328125,
-0.0261077880859375,
-0.0006055831909179688,
-0.01092529296875,
-0.00836944580078125,
-0.0143890380859375,
0.00756072998046875,
0.030792236328125,
-0.035430908203125,
0.0233612060546875,
0.032073974609375,
-0.01026153564453125,
-0.025177001953125,
-0.016754150390625,
0.006313323974609375,
-0.01502227783203125,
-0.01462554931640625,
0.0015134811401367188,
0.01099395751953125,
0.0130157470703125,
-0.024932861328125,
-0.01239776611328125,
0.0142059326171875,
-0.0022373199462890625,
-0.0066986083984375,
-0.01111602783203125,
-0.03485107421875,
-0.01468658447265625,
0.01036834716796875,
-0.0152587890625,
0.01023101806640625,
0.00218963623046875,
0.0006804466247558594,
-0.0219268798828125,
0.014129638671875,
-0.01479339599609375,
0.0113525390625,
-0.021209716796875,
-0.04107666015625,
-0.01158905029296875,
-0.046966552734375,
-0.0226898193359375,
0.00838470458984375,
0.01214599609375,
0.01071929931640625,
-0.0028171539306640625,
0.0090789794921875,
0.007518768310546875,
0.0010089874267578125,
-0.0006012916564941406,
-0.0141143798828125,
-0.017120361328125,
0.0120086669921875,
0.00341033935546875,
0.00861358642578125,
-0.007354736328125,
-0.0289154052734375,
-0.00811004638671875,
0.01457977294921875,
0.03240966796875,
0.00568389892578125,
0.002445220947265625,
-0.01404571533203125,
-0.016754150390625,
0.008026123046875,
-0.02581787109375,
-0.0204620361328125,
0.03009033203125,
-0.01556396484375,
0.0166778564453125,
-0.006252288818359375,
-0.007274627685546875,
-0.0025005340576171875,
0.04473876953125,
-0.0056610107421875,
-0.024444580078125,
0.0033588409423828125,
-0.03466796875,
0.00740814208984375,
0.0085601806640625,
0.0047760009765625,
-0.0101318359375,
-0.026336669921875,
0.0069427490234375,
0.0193634033203125,
-0.0115966796875,
0.0088958740234375,
0.0112152099609375,
0.01580810546875,
-0.0028133392333984375,
-0.0379638671875,
0.006069183349609375,
-0.0157012939453125,
0.011627197265625,
0.01425933837890625,
-0.003177642822265625,
-0.0167236328125,
-0.0279388427734375,
-0.0223541259765625,
0.0106964111328125,
0.0149688720703125,
0.0206298828125,
0.0295257568359375,
-0.01548004150390625,
0.0186004638671875,
-0.0027217864990234375,
0.0018110275268554688,
0.016204833984375,
0.018951416015625,
-0.00579833984375,
-0.038604736328125,
-0.008209228515625,
0.00736236572265625,
0.011871337890625,
-0.017364501953125,
-0.0189971923828125,
-0.00811004638671875,
-0.019317626953125,
0.00940704345703125,
-0.00882720947265625,
-0.0263824462890625,
-0.0124664306640625,
-0.014495849609375,
-0.0029811859130859375,
-0.006282806396484375,
-0.0303497314453125,
0.044342041015625,
-0.005481719970703125,
0.0121002197265625,
0.0008378028869628906,
-0.02447509765625,
-0.006069183349609375,
0.0123748779296875,
0.043121337890625,
-0.0240936279296875,
0.007556915283203125,
-0.0184173583984375,
0.01462554931640625,
-0.00591278076171875,
-0.0009121894836425781,
0.0087127685546875,
-0.0275115966796875,
0.0191650390625,
0.0102081298828125,
-0.0133056640625,
0.013427734375,
-0.00366973876953125,
0.002170562744140625,
0.0003578662872314453,
-0.0096282958984375,
-0.01776123046875,
0.0051116943359375,
0.03668212890625,
0.00804901123046875,
0.0214080810546875,
-0.0169677734375,
0.0166778564453125,
-0.01229095458984375,
-0.02001953125,
-0.00025153160095214844,
-0.03924560546875,
-0.022125244140625,
-0.01364898681640625,
-0.0021839141845703125,
-0.01531982421875,
-0.025604248046875,
0.01922607421875,
0.05548095703125,
-0.04266357421875,
0.0180206298828125,
-0.05877685546875,
-0.0017213821411132812,
-0.0025157928466796875,
-0.00943756103515625,
-0.0023059844970703125,
0.0237579345703125,
0.0157623291015625,
-0.01464080810546875,
-0.0017910003662109375,
-0.00001996755599975586,
-0.00833892822265625,
0.01406097412109375,
-0.005580902099609375,
-0.0011196136474609375,
-0.00963592529296875,
-0.0014629364013671875,
0.00165557861328125,
-0.02532958984375,
0.00957489013671875,
-0.01311492919921875,
0.0202178955078125,
-0.002964019775390625,
0.00269317626953125,
0.01160430908203125,
-0.0163421630859375,
0.0007085800170898438,
-0.0027751922607421875,
0.0226287841796875,
-0.00476837158203125,
0.007244110107421875,
-0.0276947021484375,
-0.01506805419921875,
0.0283966064453125,
0.0096435546875,
0.005359649658203125,
0.01389312744140625,
0.01006317138671875,
-0.01490020751953125,
-0.0010395050048828125,
0.03570556640625,
0.022491455078125,
-0.01039886474609375,
-0.0008301734924316406,
0.00872039794921875,
0.0013647079467773438,
0.0286865234375,
-0.01090240478515625,
-0.03466796875,
0.045562744140625,
-0.0174713134765625,
0.00786590576171875,
0.02996826171875,
-0.01378631591796875,
0.0192413330078125,
-0.0017490386962890625,
0.006229400634765625,
-0.00508880615234375,
-0.03411865234375,
-0.013763427734375,
-0.01108551025390625,
0.044586181640625,
0.020263671875,
-0.0021648406982421875,
0.0316162109375,
-0.007724761962890625,
0.0180511474609375,
0.01187896728515625,
0.0211181640625,
-0.0153961181640625,
0.022796630859375,
0.003673553466796875,
-0.0018329620361328125,
0.007965087890625,
0.0211334228515625,
-0.0096588134765625,
0.041839599609375,
-0.007282257080078125,
-0.00948333740234375,
-0.03692626953125,
-0.013427734375,
0.01215362548828125,
-0.0023975372314453125,
0.0179901123046875,
-0.003002166748046875,
-0.0006766319274902344,
-0.043731689453125,
0.0101776123046875,
0.03448486328125,
0.0189361572265625,
-0.015289306640625,
-0.01149749755859375,
-0.00128173828125,
-0.0255279541015625,
-0.019378662109375,
-0.00150299072265625,
0.014923095703125,
0.0283050537109375,
0.0161590576171875,
0.029266357421875,
0.007785797119140625,
-0.003002166748046875,
0.01515960693359375,
0.006481170654296875,
-0.000014781951904296875,
-0.0131072998046875,
0.0323486328125,
-0.022491455078125,
-0.045257568359375,
-0.00029754638671875,
0.02294921875,
-0.00690460205078125,
-0.006908416748046875,
0.0380859375,
-0.0056915283203125,
-0.014312744140625,
0.01019287109375,
-0.029510498046875,
-0.051971435546875,
0.01074981689453125,
0.032562255859375,
0.01258087158203125,
-0.006256103515625,
0.0241546630859375,
0.027130126953125,
-0.01236724853515625,
-0.0184478759765625,
-0.006000518798828125,
-0.0093536376953125,
0.0058135986328125,
0.0002522468566894531,
0.0296478271484375,
0.029876708984375,
0.056121826171875,
-0.0159149169921875,
-0.027740478515625,
0.0021038055419921875,
0.030853271484375,
-0.0012655258178710938,
-0.0115203857421875,
0.01104736328125,
0.019561767578125,
-0.00139617919921875,
-0.0164031982421875,
-0.0024433135986328125,
-0.0325927734375,
-0.0255279541015625,
0.0113983154296875,
-0.019012451171875,
-0.023956298828125,
-0.0009107589721679688,
-0.01218414306640625,
0.0237274169921875,
0.02716064453125,
0.00821685791015625,
-0.0158233642578125,
0.0205230712890625,
0.007259368896484375,
-0.00004267692565917969,
0.00730133056640625,
-0.0184173583984375,
0.00934600830078125,
0.035003662109375,
0.01175689697265625,
-0.0007915496826171875,
-0.0012187957763671875,
0.0254669189453125,
-0.0141754150390625,
0.0184326171875,
-0.00797271728515625,
0.0008645057678222656,
0.0020313262939453125,
0.0032520294189453125,
0.016998291015625,
-0.036529541015625,
0.0016727447509765625,
0.019622802734375,
0.0106658935546875,
-0.014739990234375,
-0.00960540771484375,
-0.01470184326171875,
-0.0152130126953125,
-0.005462646484375,
0.01296234130859375,
0.03167724609375,
-0.01546478271484375,
-0.0050811767578125,
0.0120849609375,
-0.001277923583984375,
-0.0187530517578125,
-0.035125732421875,
-0.01611328125,
-0.00856781005859375,
0.0003273487091064453,
-0.0181121826171875,
-0.0120391845703125,
0.0135040283203125,
0.0276947021484375,
-0.004047393798828125,
-0.00467681884765625,
0.0129547119140625,
-0.0257110595703125,
-0.017333984375,
0.02423095703125,
-0.00025010108947753906,
-0.01485443115234375,
-0.0030918121337890625,
0.01739501953125,
0.02276611328125,
0.0261077880859375,
-0.001983642578125,
0.0187530517578125,
-0.023101806640625,
0.011505126953125,
0.0152130126953125,
-0.0225830078125,
0.019775390625,
-0.004425048828125,
-0.001049041748046875,
-0.0006132125854492188,
-0.01184844970703125,
0.003154754638671875,
0.01727294921875,
0.0043792724609375,
0.006618499755859375,
0.0195465087890625,
-0.00914764404296875,
-0.006633758544921875,
-0.022979736328125,
0.01131439208984375,
-0.01413726806640625,
0.008209228515625,
-0.01812744140625,
-0.02484130859375,
0.007770538330078125,
-0.0097808837890625,
0.034698486328125,
-0.01617431640625,
0.0111083984375,
-0.01297760009765625,
-0.04193115234375,
0.01476287841796875,
-0.0257415771484375,
-0.0460205078125,
0.01264190673828125,
-0.0022735595703125,
0.0006518363952636719,
0.0175323486328125,
0.0080413818359375,
0.006084442138671875,
-0.01309967041015625,
-0.005634307861328125,
0.020477294921875,
0.0198516845703125,
-0.0216827392578125,
-0.031402587890625,
0.004154205322265625,
-0.039337158203125,
0.00887298583984375,
0.002658843994140625,
-0.0672607421875,
-0.0011653900146484375,
0.002475738525390625,
0.0258941650390625,
-0.0284271240234375,
-0.00514984130859375,
0.01312255859375,
0.0009765625,
-0.0264434814453125,
-0.006656646728515625,
-0.0157623291015625,
-0.006053924560546875,
0.00434112548828125,
-0.0277862548828125,
-0.04022216796875,
0.0093994140625,
-0.0007734298706054688,
-0.0169830322265625,
0.03277587890625,
0.004421234130859375,
-0.004058837890625,
0.01378631591796875,
0.01285552978515625,
0.003406524658203125,
-0.0224151611328125,
0.0033931732177734375,
-0.004352569580078125,
0.0364990234375,
-0.0020732879638671875,
-0.0183868408203125,
-0.026275634765625,
0.002735137939453125,
-0.018646240234375,
0.0382080078125,
0.007717132568359375,
-0.0149383544921875,
0.004489898681640625,
0.01617431640625,
-0.0001125335693359375,
0.021636962890625,
-0.03057861328125,
-0.01152801513671875,
-0.007236480712890625,
0.0038604736328125,
0.0201416015625,
0.007755279541015625,
0.01224517822265625,
0.01509857177734375,
-0.0138092041015625,
0.0111083984375,
0.01360321044921875,
0.016082763671875,
0.0303802490234375,
0.0253448486328125,
-0.00664520263671875,
0.053680419921875,
0.0322265625,
0.0217132568359375,
-0.0104827880859375,
0.038482666015625,
-0.00392913818359375,
0.01849365234375,
0.031585693359375,
0.001110076904296875,
0.0099334716796875,
-0.006031036376953125,
-0.017242431640625,
0.00945281982421875,
-0.00899505615234375,
0.01470947265625,
0.0026454925537109375,
0.00815582275390625,
-0.032379150390625,
-0.004150390625,
0.01560211181640625,
-0.038665771484375,
-0.005695343017578125,
-0.053802490234375,
-0.006793975830078125,
-0.0009946823120117188,
0.0009160041809082031,
0.0131683349609375,
0.024505615234375,
0.022674560546875,
-0.0160369873046875,
0.011871337890625,
-0.0038623809814453125,
0.023651123046875,
-0.0055694580078125,
-0.043304443359375,
-0.0364990234375,
-0.0219573974609375,
-0.00595855712890625,
0.017822265625,
0.005825042724609375,
-0.0304718017578125,
-0.00551605224609375,
-0.0033702850341796875,
-0.048187255859375,
0.0224609375,
-0.00836944580078125,
-0.02001953125,
0.01092529296875,
-0.018829345703125,
0.005084991455078125,
-0.009674072265625,
0.0207977294921875,
0.01471710205078125,
-0.02294921875,
-0.031829833984375,
0.009002685546875,
-0.0116424560546875,
0.009735107421875,
-0.0035552978515625,
-0.0114593505859375,
-0.0004553794860839844,
0.02374267578125,
0.0194244384765625,
-0.003017425537109375,
-0.022247314453125,
0.014556884765625,
-0.0025310516357421875,
-0.0165557861328125,
-0.017059326171875,
-0.01104736328125,
-0.02490234375,
0.0197296142578125,
-0.0016469955444335938,
-0.024078369140625,
-0.017852783203125,
-0.00527191162109375,
-0.0188446044921875,
0.00594329833984375,
0.0234222412109375,
-0.0232086181640625,
0.01079559326171875,
0.03521728515625,
0.0026531219482421875,
-0.007537841796875,
-0.036407470703125,
-0.010040283203125,
0.0002770423889160156,
-0.006809234619140625,
0.002246856689453125,
-0.0216827392578125,
-0.0181121826171875,
0.0254364013671875,
0.0139007568359375,
0.008941650390625,
0.035919189453125,
-0.028961181640625,
0.04010009765625,
-0.01824951171875,
-0.00821685791015625,
0.0233306884765625,
0.0122833251953125,
-0.026702880859375,
-0.011444091796875,
-0.03594970703125,
-0.0246124267578125,
0.0161590576171875,
0.0124664306640625,
-0.042633056640625,
0.00826263427734375,
0.013763427734375,
-0.00464630126953125,
-0.01374053955078125,
0.0242919921875,
0.004520416259765625,
0.038787841796875,
0.00450897216796875,
-0.01250457763671875,
-0.0154266357421875,
0.033538818359375,
-0.01371002197265625,
-0.0256195068359375,
-0.00969696044921875,
0.0022563934326171875,
0.01544189453125,
0.0242462158203125,
0.014556884765625,
-0.00861358642578125,
-0.0191650390625,
-0.0196380615234375,
0.0240936279296875,
0.01120758056640625,
-0.0027370452880859375,
0.0047454833984375,
-0.0714111328125,
-0.00859832763671875,
-0.00739288330078125,
-0.035919189453125,
-0.00994873046875,
-0.0234222412109375,
-0.0174560546875,
0.00321197509765625,
-0.01114654541015625,
-0.006122589111328125,
0.018951416015625,
0.0222015380859375,
-0.020782470703125,
-0.010833740234375,
-0.006717681884765625,
-0.0019474029541015625,
-0.01342010498046875,
-0.03680419921875,
0.00024318695068359375,
0.00963592529296875,
0.00598907470703125,
-0.003173828125,
0.01006317138671875,
-0.017120361328125,
-0.020782470703125,
0.0084991455078125,
-0.0015897750854492188,
0.026123046875,
-0.0211334228515625,
-0.0165863037109375,
-0.01119232177734375,
-0.00646209716796875,
-0.00490570068359375,
-0.0136871337890625,
-0.0255279541015625,
0.023162841796875,
-0.00027298927307128906,
-0.00864410400390625,
0.0029621124267578125,
0.0308380126953125,
-0.0157318115234375,
0.039093017578125,
0.00959014892578125,
-0.0197296142578125,
-0.0364990234375,
-0.01123809814453125,
-0.030548095703125,
-0.01806640625,
-0.00958251953125,
0.0154876708984375,
0.021881103515625,
0.0156097412109375,
-0.030548095703125,
0.0123748779296875,
0.0243988037109375,
-0.01441192626953125,
0.040252685546875,
0.0196990966796875,
-0.004730224609375,
-0.01422882080078125,
0.01959228515625,
0.0172576904296875,
0.012054443359375,
0.0229949951171875,
-0.0210418701171875,
-0.01410675048828125,
0.00732421875,
-0.02484130859375,
-0.006927490234375,
-0.005657196044921875,
-0.01514434814453125,
-0.016021728515625,
0.0243377685546875,
0.026031494140625,
-0.0250396728515625,
-0.0111083984375,
0.0180816650390625,
-0.0013551712036132812,
-0.0099639892578125,
-0.0246124267578125,
0.01442718505859375,
-0.006267547607421875,
-0.00496673583984375,
0.01184844970703125,
-0.024261474609375,
0.00972747802734375,
-0.00675201416015625,
0.00968170166015625,
-0.0014743804931640625,
-0.026031494140625,
0.00890350341796875,
0.025421142578125,
-0.038330078125,
-0.007793426513671875,
0.0312347412109375,
-0.0010232925415039062,
-0.0212860107421875,
-0.01715087890625,
0.004955291748046875,
-0.01947021484375,
-0.01349639892578125,
0.04388427734375,
-0.0019235610961914062,
0.01453399658203125,
-0.01221466064453125,
0.0006113052368164062,
-0.00798797607421875,
0.0206451416015625,
-0.0098114013671875,
0.0020656585693359375,
-0.006519317626953125,
-0.00690460205078125,
-0.003391265869140625,
0.011322021484375,
-0.0222015380859375,
0.01403045654296875,
0.037567138671875,
0.03131103515625,
-0.004306793212890625,
-0.0228424072265625,
-0.0207366943359375,
0.0115509033203125,
-0.014801025390625,
0.0126953125,
0.005001068115234375,
0.0145263671875,
0.0238800048828125,
-0.0177001953125,
-0.03045654296875,
-0.0206451416015625,
-0.01097869873046875,
0.0108489990234375,
-0.01337432861328125,
0.029449462890625,
-0.0124969482421875,
0.00042366981506347656,
0.031524658203125,
0.0147552490234375,
0.00502777099609375,
-0.0382080078125,
0.01253509521484375,
0.004932403564453125,
-0.0125579833984375,
0.032318115234375,
0.03948974609375,
0.0125732421875,
-0.01171112060546875,
0.024749755859375,
0.018951416015625,
0.036895751953125,
-0.01364898681640625,
-0.024078369140625,
-0.018829345703125,
-0.004100799560546875,
-0.0157928466796875,
-0.005031585693359375,
-0.0175628662109375,
-0.031341552734375,
-0.0229034423828125,
-0.036773681640625,
-0.0058441162109375,
-0.055206298828125,
0.02056884765625,
-0.01203155517578125,
-0.015777587890625,
0.0015926361083984375,
0.005977630615234375,
0.0086822509765625,
-0.00988006591796875,
-0.03692626953125,
0.0007581710815429688,
-0.027008056640625,
0.030303955078125,
0.039031982421875,
-0.00691986083984375,
-0.005756378173828125,
0.010406494140625,
0.0496826171875,
-0.008544921875,
-0.010406494140625,
-0.010284423828125,
-0.0009136199951171875,
-0.01104736328125,
-0.02874755859375,
0.00847625732421875,
0.0231475830078125,
-0.00672149658203125,
0.0193023681640625,
-0.0274810791015625,
0.006015777587890625,
-0.021331787109375,
0.0205841064453125,
0.021636962890625,
0.0031719207763671875,
0.0065155029296875,
0.00644683837890625,
-0.00855255126953125,
0.00939178466796875,
-0.0231475830078125,
0.0013647079467773438,
0.00684356689453125,
-0.0194854736328125,
0.03033447265625,
-0.00937652587890625,
0.007526397705078125,
0.01557159423828125,
-0.05029296875,
0.022186279296875,
-0.00603485107421875,
-0.01406097412109375,
-0.0082244873046875,
0.01081085205078125,
-0.00334930419921875,
0.005615234375,
0.016204833984375,
0.009857177734375,
-0.0150909423828125,
-0.023895263671875,
0.03338623046875,
0.0044097900390625,
-0.01250457763671875,
0.036376953125,
-0.0177001953125,
-0.0004940032958984375,
0.0162353515625,
0.00624847412109375,
-0.003021240234375,
-0.0129241943359375,
-0.01092529296875,
-0.019256591796875,
-0.005023956298828125,
-0.036468505859375,
0.0055389404296875,
-0.02886962890625,
-0.0430908203125,
-0.002201080322265625,
0.044464111328125,
0.01434326171875,
0.0281524658203125,
-0.006778717041015625,
-0.039337158203125,
-0.006622314453125,
-0.023681640625,
0.007427215576171875,
-0.0045928955078125,
0.030426025390625,
-0.01132965087890625,
0.0308685302734375,
-0.0214996337890625,
-0.00164794921875,
0.00787353515625,
0.006221771240234375,
-0.02093505859375,
0.00510406494140625,
0.0211944580078125,
0.01751708984375,
-0.00275421142578125,
-0.01409912109375,
-0.01019287109375,
0.01113128662109375,
-0.007114410400390625,
-0.0004987716674804688,
-0.0006036758422851562,
-0.000240325927734375,
0.01119232177734375,
-0.01297760009765625,
-0.02630615234375,
-0.0015401840209960938,
0.0014505386352539062,
0.0145111083984375,
0.00778961181640625,
0.008819580078125,
-0.017333984375,
0.01335906982421875,
-0.005443572998046875,
-0.01517486572265625,
0.004093170166015625,
-0.031768798828125,
0.00411224365234375,
-0.0186920166015625,
0.00010186433792114258,
0.0006194114685058594,
-0.002674102783203125,
0.0026187896728515625,
-0.0271759033203125,
0.036956787109375,
0.0016965866088867188,
-0.0022678375244140625,
0.0428466796875,
-0.0063323974609375,
0.007434844970703125,
-0.01412200927734375,
0.0040740966796875,
-0.01026153564453125,
-0.02130126953125,
0.004627227783203125,
-0.01299285888671875,
0.021881103515625,
-0.0076904296875,
-0.0097808837890625,
0.004077911376953125,
-0.006622314453125,
-0.0106964111328125,
-0.002666473388671875,
-0.002277374267578125,
0.0203857421875,
0.0149078369140625,
0.02325439453125,
0.01763916015625,
-0.00637054443359375,
0.0187225341796875,
0.004302978515625,
0.015350341796875,
-0.0012273788452148438,
-0.0226898193359375,
-0.0095367431640625,
0.00574493408203125,
0.033599853515625,
-0.0209197998046875,
0.0208282470703125,
0.00930023193359375,
0.024688720703125,
0.00582122802734375,
-0.03851318359375,
0.002532958984375,
-0.01285552978515625,
0.003116607666015625,
-0.0115509033203125,
0.0241546630859375,
-0.016571044921875,
0.012481689453125,
-0.007472991943359375,
0.026702880859375,
0.01922607421875,
0.0017681121826171875,
0.01983642578125,
0.0031719207763671875,
-0.0035400390625,
0.01169586181640625,
0.0086822509765625,
-0.004344940185546875,
-0.0382080078125,
-0.0113983154296875,
-0.0159454345703125,
-0.0178070068359375,
-0.0022106170654296875,
0.0014600753784179688,
-0.003936767578125,
0.0070037841796875,
0.01511383056640625,
0.0136871337890625,
-0.0233917236328125,
-0.0189056396484375,
-0.01064300537109375,
0.00861358642578125,
-0.01146697998046875,
-0.0054168701171875,
-0.00865936279296875,
-0.0266571044921875,
0.01267242431640625,
-0.0099639892578125,
-0.033203125,
-0.004993438720703125,
-0.035980224609375,
0.01413726806640625,
0.00429534912109375,
-0.0257415771484375,
-0.01593017578125,
0.007312774658203125,
-0.00815582275390625,
0.0270233154296875,
-0.013275146484375,
0.016845703125,
-0.027191162109375,
-0.0126800537109375,
0.02301025390625,
-0.00608062744140625,
0.0107879638671875,
0.0123291015625,
0.0195465087890625,
0.029693603515625,
-0.022918701171875,
0.0033321380615234375,
-0.00791168212890625,
0.008697509765625,
0.0114288330078125,
-0.01131439208984375,
-0.03466796875,
-0.005718231201171875,
0.032196044921875,
0.0121002197265625,
0.0059661865234375,
-0.00560760498046875,
-0.007579803466796875,
-0.022247314453125,
-0.01142120361328125,
0.01013946533203125,
-0.01061248779296875,
-0.004673004150390625,
0.002960205078125,
-0.0204010009765625,
-0.03472900390625,
-0.0087127685546875,
0.0228118896484375,
-0.00142669677734375,
-0.0296630859375,
0.0068359375,
-0.022979736328125,
0.0178070068359375,
-0.00878143310546875,
0.0142974853515625,
0.023345947265625,
0.010894775390625,
-0.04248046875,
-0.0335693359375,
0.01255035400390625,
0.00254058837890625,
0.012176513671875,
-0.020050048828125,
-0.009307861328125,
-0.036041259765625,
0.04217529296875,
-0.022125244140625,
-0.01302337646484375,
-0.004638671875,
0.026580810546875,
-0.0196533203125,
-0.01016998291015625,
-0.007678985595703125,
-0.0202484130859375,
0.0008869171142578125,
0.0211029052734375,
-0.01448822021484375,
-0.006561279296875,
0.0240020751953125,
0.0025768280029296875,
-0.00028443336486816406,
-0.023956298828125,
0.0262908935546875,
-0.00933837890625,
-0.0130157470703125,
0.003986358642578125,
0.0269622802734375,
0.017425537109375,
0.00921630859375,
0.01161956787109375,
-0.016998291015625,
-0.0156707763671875,
0.007709503173828125,
-0.00521087646484375,
-0.0258636474609375,
0.0208892822265625,
0.01416015625,
-0.039306640625,
-0.0267333984375,
-0.017852783203125,
0.0128936767578125,
-0.035919189453125,
0.0189666748046875,
0.0010709762573242188,
0.03900146484375,
-0.0112457275390625,
-0.0272216796875,
-0.0323486328125,
-0.0195159912109375,
-0.00838470458984375,
-0.013458251953125,
-0.022064208984375,
0.03167724609375,
0.023834228515625,
-0.01482391357421875,
-0.011810302734375,
-0.01375579833984375,
-0.0049285888671875,
0.0011491775512695312,
-0.028533935546875,
0.00018131732940673828,
0.006244659423828125,
-0.0225830078125,
-0.04180908203125,
-0.00867462158203125,
-0.012542724609375,
-0.01329803466796875,
0.0157623291015625,
-0.01132965087890625,
-0.05712890625,
-0.004711151123046875,
-0.009429931640625,
0.0247344970703125,
0.00908660888671875,
-0.004451751708984375,
-0.02618408203125,
0.0027904510498046875,
-0.005802154541015625,
-0.01143646240234375,
-0.00043582916259765625,
-0.055694580078125,
0.0166778564453125,
0.00318145751953125,
0.01215362548828125,
0.025177001953125,
-0.00004673004150390625,
-0.011871337890625,
0.002536773681640625,
0.0005593299865722656,
0.006481170654296875,
-0.0210418701171875,
0.00974273681640625,
0.0267791748046875,
-0.05108642578125,
0.022491455078125,
0.01074981689453125,
0.0069427490234375,
0.0123748779296875,
-0.011505126953125,
0.00839996337890625,
0.0308380126953125,
0.0263519287109375,
-0.01050567626953125,
-0.0214691162109375,
-0.0244903564453125,
-0.0247802734375,
0.0076141357421875,
0.01145172119140625,
0.0002582073211669922,
0.010955810546875,
-0.0177001953125,
-0.0132293701171875,
-0.0160064697265625,
0.039093017578125,
-0.0008654594421386719,
0.0218658447265625,
-0.0003330707550048828,
0.01047515869140625,
-0.013397216796875,
0.007244110107421875,
0.0494384765625,
0.006221771240234375,
-0.022369384765625,
-0.00363922119140625,
-0.00893402099609375,
-0.00576019287109375,
-0.0198974609375,
0.01129150390625,
-0.0009851455688476562,
0.008575439453125,
-0.0185394287109375,
0.019287109375,
-0.00171661376953125
] |
ours_489
|
First, note that \( p > 2 \) is obvious. We claim \( q \mid p-1 \). If it doesn't, \( q \mid (p-1)^{q-1}-1 \) by Fermat's Little Theorem, so \( q \mid (2q)^{2p}-1 \), meaning \( q \mid -1 \), a contradiction. Now, we take cases on \( q \).
**Case 1: \( q = 2 \)**
The condition becomes \( p-2 \mid 4^{2p}-1 = 16^p-1 \). Note that \( 15 \mid 16^p-1 \). For any prime \( k \) dividing \( p-2 \) (which is odd since \( p > 2 \) is prime), \( k \mid 16^p-1 \), but since the order of \( 16 \pmod{k} \) divides \( k-1 \) and \( k-1 \leq p-3 < p \), the order must be \( 1 \), so \( k \mid 15 \). If \( k \) divides \(\frac{16^p-1}{15} = 16^{p-1} + \cdots + 16 + 1\), then \( 0 \equiv 16^{p-1} + \cdots + 16 + 1 \equiv 1 + \cdots + 1 + 1 = p \equiv 2 \pmod{k} \) (as \( 16 \equiv 1 \pmod{k} \) and \( p \equiv 2 \pmod{k} \)), contradicting \( k > 2 \). Thus, \( k \nmid \frac{16^p-1}{15} \). Then \(\gcd(p-2, \frac{16^p-1}{15}) = 1\), so since \( p-2 \mid 16^p-1 = \frac{16^p-1}{15} \cdot 15 \), we have \( p-2 \mid 15 \), so \( p \in \{3, 5, 7, 17\} \). All these can be seen to work.
**Case 2: \( q > 2 \)**
Since \( q-1 \) is even, we get \( p \mid (p-1)^{q-1}-1 \), so \( p \mid (2q-1)(2q+1) \). Since \( q \mid p-1 \), \( p > q+1 \), so \( 2p > 2q+2 > 2q+1 > 2q-1 \), and \( p \mid 2q-1 \) or \( p \mid 2q+1 \), so \( p \in \{2q-1, 2q+1\} \). Since \( q > 2 \) and \( q \mid p-1 \), this forces \( p = 2q+1 \). Then, the condition becomes
\[
(2q)^{q-1}-1 \mid (2q)^{2p}-1 \Rightarrow q-1 \mid 2p \Rightarrow q-1 \mid 2(2q+1) = 4(q-1) + 6
\]
so \( q-1 \mid 6 \), so \( q \in \{3, 7\} \). Since \( p = 2q+1 \) is also prime, the only solution from this case is \((p, q) = (7, 3)\). This can be seen to work.
For the answer extraction, the sum of possible values of \( pq \) is \( 2 \cdot 3 + 2 \cdot 5 + 2 \cdot 7 + 2 \cdot 17 + 3 \cdot 7 = 85 \).
\(\boxed{85}\)
|
85
|
{
"competition": "us_comps",
"dataset": "Ours",
"posts": null,
"source": "OMOFall19Solns-2.md"
}
|
Let \( p \) and \( q \) be prime numbers such that \((p-1)^{q-1}-1\) is a positive integer that divides \((2q)^{2p}-1\). Compute the sum of all possible values of \( pq \).
|
[
"/Mathematics/NumberTheory/Congruences/Congruence",
"/Mathematics/NumberTheory/Congruences/FermatsLittleTheorem",
"/Mathematics/NumberTheory/Congruences/ModularArithmetic",
"/Mathematics/NumberTheory/GeneralNumberTheory/ElementaryMethods",
"/Mathematics/NumberTheory/GeneralNumberTheory/ElementaryNumberTheory",
"/Mathematics/NumberTheory/GeneralNumberTheory/HigherArithmetic",
"/Mathematics/NumberTheory/GeneralNumberTheory/NumberTheory",
"/Mathematics/NumberTheory/PrimeNumbers/PrimeNumberProperties",
"/Mathematics/NumberTheory/PrimeNumbers/PrimeSumsandProducts"
] |
Use Fermat’s Little Theorem to force q | p−1 and then restrict p to the small candidates p∈{2q−1,2q+1}.
|
[
0.000013530254364013672,
-0.04095458984375,
-0.022491455078125,
-0.0034656524658203125,
0.00015413761138916016,
-0.0145416259765625,
0.029541015625,
0.01318359375,
0.01343536376953125,
0.0094757080078125,
0.010894775390625,
-0.040496826171875,
-0.0014142990112304688,
-0.036285400390625,
0.0010366439819335938,
0.033233642578125,
0.0249481201171875,
0.0256195068359375,
-0.01171875,
-0.0091094970703125,
-0.0005497932434082031,
-0.004974365234375,
-0.0335693359375,
0.0274658203125,
-0.005970001220703125,
-0.00952911376953125,
-0.014892578125,
-0.03289794921875,
0.007022857666015625,
0.03790283203125,
-0.0176849365234375,
-0.00574493408203125,
0.0386962890625,
-0.031524658203125,
-0.0015687942504882812,
0.0099945068359375,
0.01030731201171875,
-0.0015010833740234375,
-0.0011501312255859375,
-0.01511383056640625,
-0.0146636962890625,
0.025848388671875,
0.01116943359375,
0.0168609619140625,
0.023193359375,
0.0268402099609375,
0.0067901611328125,
-0.0006899833679199219,
0.0020008087158203125,
-0.00933074951171875,
-0.00989532470703125,
0.006603240966796875,
0.0009431838989257812,
-0.0007953643798828125,
-0.00820159912109375,
-0.06732177734375,
0.0136566162109375,
0.0011444091796875,
0.00467681884765625,
0.0099945068359375,
-0.004344940185546875,
-0.004665374755859375,
-0.008636474609375,
-0.0169219970703125,
-0.0087890625,
0.001277923583984375,
-0.0026187896728515625,
-0.0046539306640625,
-0.00424957275390625,
-0.0015649795532226562,
0.051361083984375,
0.0212860107421875,
0.00323486328125,
0.0192718505859375,
0.044158935546875,
-0.00347900390625,
-0.009429931640625,
-0.00830078125,
0.029388427734375,
0.03387451171875,
0.009002685546875,
0.033538818359375,
0.0214080810546875,
-0.01374053955078125,
0.0007891654968261719,
0.0076751708984375,
-0.0037689208984375,
0.0008330345153808594,
-0.011993408203125,
-0.006191253662109375,
0.00949859619140625,
0.03155517578125,
0.0027866363525390625,
0.0008931159973144531,
0.004673004150390625,
-0.01776123046875,
0.0164031982421875,
-0.00803375244140625,
-0.0219573974609375,
0.0094451904296875,
-0.0149383544921875,
-0.00981903076171875,
0.002887725830078125,
-0.0268402099609375,
-0.05914306640625,
-0.0020961761474609375,
-0.01482391357421875,
-0.01116180419921875,
-0.007694244384765625,
-0.0137481689453125,
0.011383056640625,
0.01500701904296875,
0.048126220703125,
0.007419586181640625,
0.0213165283203125,
0.0166473388671875,
0.03857421875,
0.026611328125,
0.0181121826171875,
-0.0245513916015625,
-0.00803375244140625,
0.0198211669921875,
-0.0146942138671875,
0.002254486083984375,
-0.0087890625,
-0.01514434814453125,
-0.016357421875,
-0.001888275146484375,
-0.017364501953125,
0.006702423095703125,
0.03125,
-0.0012140274047851562,
-0.0234832763671875,
-0.0175323486328125,
-0.052581787109375,
0.0193634033203125,
0.0036029815673828125,
-0.01096343994140625,
0.0109405517578125,
-0.016357421875,
-0.0036182403564453125,
-0.0157318115234375,
-0.004795074462890625,
0.00882720947265625,
0.0026721954345703125,
0.0200347900390625,
0.0009298324584960938,
-0.0297698974609375,
0.0085906982421875,
-0.018218994140625,
-0.00713348388671875,
-0.0124359130859375,
0.00922393798828125,
0.0006837844848632812,
-0.0142059326171875,
0.0115966796875,
0.015777587890625,
0.01483917236328125,
0.0045623779296875,
0.0062408447265625,
0.0231170654296875,
0.0017986297607421875,
-0.0027523040771484375,
0.026336669921875,
-0.017181396484375,
-0.005340576171875,
0.0180511474609375,
0.01432037353515625,
-0.013336181640625,
-0.0125732421875,
0.01334381103515625,
-0.006855010986328125,
-0.00806427001953125,
-0.0173797607421875,
-0.0223541259765625,
0.0025577545166015625,
-0.016326904296875,
0.0295257568359375,
-0.006256103515625,
0.005748748779296875,
-0.0025997161865234375,
-0.05145263671875,
0.00559234619140625,
-0.00927734375,
0.0048828125,
-0.03131103515625,
-0.01552581787109375,
0.005413055419921875,
0.00455474853515625,
0.01399993896484375,
-0.008880615234375,
0.01432037353515625,
-0.0035400390625,
0.010528564453125,
-0.0225372314453125,
-0.0164031982421875,
-0.01134490966796875,
-0.0035877227783203125,
0.007221221923828125,
0.0208740234375,
-0.0188446044921875,
0.0052032470703125,
0.019195556640625,
0.006603240966796875,
0.009918212890625,
0.0091552734375,
0.00975799560546875,
-0.0074920654296875,
-0.023529052734375,
0.00037217140197753906,
0.020233154296875,
-0.0014028549194335938,
0.01152801513671875,
-0.041290283203125,
-0.0184783935546875,
-0.00250244140625,
-0.01690673828125,
-0.005878448486328125,
-0.0024509429931640625,
-0.018829345703125,
-0.00164031982421875,
0.00598907470703125,
0.006702423095703125,
-0.00437164306640625,
-0.0037078857421875,
-0.0006918907165527344,
0.020263671875,
-0.0004799365997314453,
-0.0107421875,
-0.0021610260009765625,
0.0274810791015625,
0.004360198974609375,
-0.007358551025390625,
0.003307342529296875,
0.005641937255859375,
-0.007137298583984375,
-0.0270233154296875,
-0.001972198486328125,
0.01132965087890625,
-0.01377105712890625,
0.031494140625,
-0.01151275634765625,
0.0016527175903320312,
0.01409149169921875,
-0.00244140625,
-0.007843017578125,
0.020263671875,
-0.00890350341796875,
-0.01035308837890625,
-0.01904296875,
0.0028076171875,
-0.0099945068359375,
-0.005008697509765625,
-0.00724029541015625,
0.00466156005859375,
-0.007007598876953125,
0.01873779296875,
0.01253509521484375,
-0.0158233642578125,
0.00875091552734375,
-0.01367950439453125,
-0.059783935546875,
-0.00836181640625,
-0.0004756450653076172,
-0.00909423828125,
0.0170135498046875,
0.040374755859375,
-0.01523590087890625,
0.01120758056640625,
-0.007228851318359375,
0.0119171142578125,
-0.0137939453125,
0.0106964111328125,
-0.0128173828125,
0.00971221923828125,
-0.0023040771484375,
0.00749969482421875,
0.0044708251953125,
0.00545501708984375,
-0.0026798248291015625,
0.0008091926574707031,
-0.0125732421875,
-0.031097412109375,
0.020172119140625,
0.01641845703125,
-0.01093292236328125,
0.01885986328125,
-0.01551055908203125,
0.0019292831420898438,
-0.0012655258178710938,
-0.0113677978515625,
-0.0275115966796875,
-0.00893402099609375,
-0.00788116455078125,
0.041900634765625,
-0.00887298583984375,
-0.002666473388671875,
0.01511383056640625,
0.00475311279296875,
-0.01873779296875,
0.014434814453125,
-0.0006489753723144531,
-0.0196990966796875,
0.009063720703125,
0.00902557373046875,
0.0268707275390625,
0.0161285400390625,
0.0064697265625,
0.01256561279296875,
-0.0086822509765625,
-0.0034637451171875,
-0.0095062255859375,
-0.013824462890625,
0.0070953369140625,
-0.0110931396484375,
-0.0303497314453125,
-0.01145172119140625,
-0.0070343017578125,
-0.029144287109375,
0.01071929931640625,
0.0221710205078125,
-0.01459503173828125,
-0.0149688720703125,
0.022979736328125,
0.02294921875,
-0.0087890625,
0.0095672607421875,
0.008392333984375,
0.01007843017578125,
0.0190887451171875,
-0.055328369140625,
-0.002841949462890625,
0.0177154541015625,
-0.0159149169921875,
0.00719451904296875,
0.01934814453125,
-0.037506103515625,
0.01251220703125,
0.0025119781494140625,
0.0063018798828125,
0.00534820556640625,
-0.03643798828125,
0.038238525390625,
-0.0008306503295898438,
0.0029125213623046875,
0.028167724609375,
-0.02166748046875,
-0.01277923583984375,
-0.016204833984375,
-0.0154571533203125,
0.03253173828125,
0.010772705078125,
0.01361083984375,
-0.01416778564453125,
-0.047027587890625,
-0.0218505859375,
-0.01303863525390625,
0.0140380859375,
-0.0283203125,
0.0137481689453125,
0.0005369186401367188,
0.0124053955078125,
-0.008056640625,
-0.00998687744140625,
0.003864288330078125,
-0.019927978515625,
-0.01194000244140625,
0.00753021240234375,
-0.006938934326171875,
0.0185394287109375,
-0.0031337738037109375,
0.0022945404052734375,
0.003631591796875,
-0.014984130859375,
-0.032440185546875,
-0.0203857421875,
0.03192138671875,
-0.015777587890625,
0.031768798828125,
0.0128326416015625,
0.0145111083984375,
0.0194549560546875,
-0.02362060546875,
0.01910400390625,
-0.01232147216796875,
-0.01168060302734375,
-0.026153564453125,
-0.0004642009735107422,
-0.02349853515625,
0.023773193359375,
-0.0047454833984375,
0.003124237060546875,
-0.0145111083984375,
-0.00399017333984375,
0.0066070556640625,
0.00156402587890625,
-0.003528594970703125,
0.0210113525390625,
0.0518798828125,
-0.008819580078125,
-0.0006456375122070312,
-0.024078369140625,
-0.033203125,
0.00582122802734375,
0.01873779296875,
0.0020503997802734375,
-0.0219573974609375,
0.023193359375,
-0.01149749755859375,
0.00992584228515625,
0.0156402587890625,
-0.0220794677734375,
0.023193359375,
-0.007183074951171875,
0.01690673828125,
-0.01342010498046875,
0.0157470703125,
-0.0017538070678710938,
-0.0168914794921875,
-0.01885986328125,
-0.00518798828125,
-0.0028362274169921875,
-0.0044403076171875,
0.0170745849609375,
-0.007083892822265625,
0.038482666015625,
-0.0085906982421875,
0.0111083984375,
0.0252227783203125,
0.0096282958984375,
0.0012197494506835938,
-0.0008597373962402344,
-0.0059967041015625,
0.0251922607421875,
0.00867462158203125,
0.043304443359375,
0.0134735107421875,
-0.001758575439453125,
-0.0170745849609375,
0.022705078125,
-0.034271240234375,
-0.02374267578125,
-0.0132904052734375,
0.0108489990234375,
0.0031890869140625,
-0.0004410743713378906,
-0.007282257080078125,
0.002597808837890625,
-0.051910400390625,
0.0179290771484375,
-0.0052947998046875,
0.0031585693359375,
0.0005116462707519531,
-0.0010766983032226562,
0.0008502006530761719,
0.0191192626953125,
0.0299835205078125,
0.00885772705078125,
-0.01181793212890625,
0.0061798095703125,
-0.028472900390625,
0.01447296142578125,
0.01873779296875,
0.0253753662109375,
-0.0145111083984375,
0.02032470703125,
-0.020965576171875,
-0.001979827880859375,
0.02520751953125,
0.0224151611328125,
0.0023250579833984375,
-0.00958251953125,
0.0306549072265625,
-0.0115203857421875,
-0.03460693359375,
0.0270233154296875,
0.00982666015625,
0.0197906494140625,
-0.019500732421875,
0.00782012939453125,
0.031524658203125,
-0.00766754150390625,
-0.003063201904296875,
-0.0169219970703125,
0.00547027587890625,
0.0219573974609375,
0.00689697265625,
0.01155853271484375,
0.00850677490234375,
-0.0111541748046875,
0.013946533203125,
0.064697265625,
-0.0217132568359375,
0.002376556396484375,
-0.0279693603515625,
-0.0260009765625,
0.00220489501953125,
-0.0095672607421875,
-0.01025390625,
0.01519012451171875,
0.00884246826171875,
-0.0191192626953125,
-0.00231170654296875,
0.02294921875,
0.016937255859375,
-0.01479339599609375,
0.0266571044921875,
0.004177093505859375,
0.035614013671875,
-0.0208587646484375,
0.0287322998046875,
-0.0019779205322265625,
0.0271453857421875,
-0.04132080078125,
0.044586181640625,
0.0026111602783203125,
0.01184844970703125,
-0.0085906982421875,
0.00909423828125,
-0.0051116943359375,
-0.0172882080078125,
0.0191497802734375,
0.019561767578125,
0.016632080078125,
0.0290374755859375,
0.004566192626953125,
-0.0012273788452148438,
-0.0521240234375,
0.00579833984375,
0.001567840576171875,
-0.01538848876953125,
0.0145263671875,
0.01241302490234375,
-0.00913238525390625,
-0.040771484375,
0.00835418701171875,
0.003711700439453125,
0.0074462890625,
0.0086212158203125,
0.046142578125,
0.0269775390625,
-0.0230712890625,
0.0261688232421875,
0.0017175674438476562,
-0.006496429443359375,
-0.0200347900390625,
-0.0004482269287109375,
-0.018524169921875,
-0.0367431640625,
0.01525115966796875,
0.0222930908203125,
0.01396942138671875,
-0.00940704345703125,
0.0018625259399414062,
-0.01425933837890625,
0.0158843994140625,
0.005489349365234375,
0.0280914306640625,
-0.03692626953125,
-0.0136566162109375,
0.0306549072265625,
0.0208282470703125,
0.005889892578125,
-0.006267547607421875,
0.0007138252258300781,
-0.015533447265625,
0.01050567626953125,
-0.0150909423828125,
0.0030956268310546875,
-0.0177001953125,
0.00952911376953125,
-0.006603240966796875,
-0.0151519775390625,
-0.00974273681640625,
0.003719329833984375,
0.005466461181640625,
-0.016021728515625,
0.0021514892578125,
0.0235595703125,
-0.01422882080078125,
0.0164337158203125,
0.008270263671875,
0.036895751953125,
-0.0036830902099609375,
0.00838470458984375,
-0.0024509429931640625,
-0.00518798828125,
0.016143798828125,
0.0089263916015625,
0.00217437744140625,
-0.026885986328125,
-0.0113983154296875,
0.00616455078125,
0.0149383544921875,
0.0018634796142578125,
0.019744873046875,
0.0020961761474609375,
-0.02825927734375,
-0.007404327392578125,
0.01183319091796875,
0.0380859375,
0.038726806640625,
-0.025726318359375,
0.013519287109375,
-0.0068511962890625,
-0.00875091552734375,
-0.004276275634765625,
0.019775390625,
0.042144775390625,
-0.009368896484375,
-0.015869140625,
-0.01232147216796875,
0.0231781005859375,
0.00603485107421875,
0.0135498046875,
0.0193939208984375,
0.01395416259765625,
-0.01352691650390625,
0.0265350341796875,
-0.034088134765625,
-0.01116180419921875,
0.006046295166015625,
-0.0222320556640625,
0.025482177734375,
-0.01422882080078125,
-0.0093536376953125,
0.0253143310546875,
-0.01494598388671875,
0.006591796875,
0.0134735107421875,
-0.039154052734375,
0.029571533203125,
0.029937744140625,
-0.00557708740234375,
0.009124755859375,
0.0204620361328125,
-0.0089874267578125,
0.0225677490234375,
0.002536773681640625,
-0.00799560546875,
0.0207672119140625,
0.014373779296875,
0.0143890380859375,
-0.06353759765625,
0.01134490966796875,
0.00862884521484375,
0.0200958251953125,
0.0158538818359375,
-0.0265655517578125,
-0.0006914138793945312,
-0.014251708984375,
-0.0198516845703125,
-0.01200103759765625,
-0.0032749176025390625,
0.01509857177734375,
0.04315185546875,
0.02032470703125,
-0.021942138671875,
0.0282440185546875,
0.00035953521728515625,
-0.024139404296875,
0.015106201171875,
0.022125244140625,
-0.0071563720703125,
-0.073974609375,
0.005947113037109375,
0.015411376953125,
0.01297760009765625,
0.018585205078125,
-0.006847381591796875,
0.00878143310546875,
-0.0555419921875,
0.0188751220703125,
0.000009059906005859375,
-0.006336212158203125,
-0.004291534423828125,
0.006855010986328125,
-0.0272064208984375,
0.038787841796875,
0.0053253173828125,
0.0141448974609375,
-0.0195465087890625,
0.0228271484375,
-0.0005826950073242188,
0.0198516845703125,
0.01214599609375,
-0.044921875,
0.03131103515625,
0.0251922607421875,
0.0033130645751953125,
0.022216796875,
0.0103912353515625,
-0.005931854248046875,
-0.03021240234375,
-0.03997802734375,
-0.041046142578125,
0.022003173828125,
-0.009857177734375,
-0.00933837890625,
-0.005733489990234375,
0.034942626953125,
-0.0172119140625,
0.01708984375,
0.0175018310546875,
0.001316070556640625,
-0.002960205078125,
-0.0034637451171875,
0.009735107421875,
-0.033233642578125,
0.0126495361328125,
-0.046356201171875,
-0.01268768310546875,
0.005275726318359375,
-0.01491546630859375,
-0.004833221435546875,
0.0188140869140625,
0.01337432861328125,
0.00783538818359375,
-0.0260162353515625,
-0.0119476318359375,
-0.032470703125,
0.039276123046875,
-0.027435302734375,
0.004177093505859375,
0.009063720703125,
0.0209808349609375,
-0.0025005340576171875,
-0.0213623046875,
0.0191650390625,
0.020599365234375,
0.00702667236328125,
-0.010223388671875,
-0.0012035369873046875,
0.0010442733764648438,
-0.01299285888671875,
0.0150299072265625,
0.01459503173828125,
-0.0178070068359375,
-0.007904052734375,
0.0137176513671875,
0.012939453125,
0.01107025146484375,
0.004573822021484375,
0.004512786865234375,
0.0153961181640625,
0.029693603515625,
-0.004665374755859375,
-0.01123809814453125,
0.01123809814453125,
-0.0256805419921875,
0.023406982421875,
-0.0015087127685546875,
-0.02923583984375,
-0.05242919921875,
-0.024688720703125,
0.0025577545166015625,
0.020172119140625,
-0.047027587890625,
0.01233673095703125,
-0.00565338134765625,
-0.0230865478515625,
-0.0174713134765625,
0.0177459716796875,
0.03057861328125,
0.032745361328125,
-0.04034423828125,
-0.0227508544921875,
-0.0377197265625,
-0.034942626953125,
0.053955078125,
-0.041717529296875,
0.0234222412109375,
0.019500732421875,
0.0010519027709960938,
0.017547607421875,
-0.006565093994140625,
-0.044464111328125,
0.02301025390625,
0.045501708984375,
-0.012786865234375,
0.0308074951171875,
-0.002407073974609375,
0.0025882720947265625,
-0.006458282470703125,
0.011566162109375,
-0.01165771484375,
-0.03369140625,
-0.0226898193359375,
0.022003173828125,
-0.007297515869140625,
-0.006397247314453125,
0.0013113021850585938,
0.006816864013671875,
-0.0112152099609375,
-0.019439697265625,
0.00911712646484375,
0.00010877847671508789,
-0.014739990234375,
-0.0133056640625,
0.0206756591796875,
0.0080413818359375,
-0.0181121826171875,
-0.0265655517578125,
0.017730712890625,
0.02386474609375,
-0.0279693603515625,
-0.0178985595703125,
0.01142120361328125,
0.0189971923828125,
0.0311279296875,
-0.0009274482727050781,
-0.042266845703125,
-0.0369873046875,
0.00463104248046875,
0.01739501953125,
-0.0038394927978515625,
0.028564453125,
-0.00016319751739501953,
0.00611114501953125,
0.044677734375,
0.005458831787109375,
0.050201416015625,
0.01190185546875,
-0.008697509765625,
-0.0045928955078125,
0.0048980712890625,
-0.016326904296875,
0.00031304359436035156,
0.023040771484375,
0.002002716064453125,
-0.00988006591796875,
-0.002246856689453125,
-0.0030002593994140625,
-0.0012941360473632812,
-0.014404296875,
-0.00409698486328125,
-0.0034160614013671875,
-0.036590576171875,
-0.012969970703125,
0.0026378631591796875,
-0.00531768798828125,
0.018646240234375,
0.0274810791015625,
-0.02264404296875,
0.0109710693359375,
-0.00434112548828125,
-0.0161285400390625,
-0.006114959716796875,
0.0137939453125,
-0.008575439453125,
0.0163726806640625,
-0.01216888427734375,
-0.01097869873046875,
0.0085601806640625,
-0.045013427734375,
0.004604339599609375,
0.01438140869140625,
0.007526397705078125,
-0.01239776611328125,
0.0012979507446289062,
0.0278472900390625,
-0.0357666015625,
0.0009179115295410156,
0.0025272369384765625,
-0.003253936767578125,
0.0286865234375,
0.0228729248046875,
-0.0087432861328125,
-0.00820159912109375,
0.0005421638488769531,
0.0297698974609375,
0.001712799072265625,
-0.0233612060546875,
-0.0109100341796875,
0.01380157470703125,
0.0122833251953125,
0.03936767578125,
0.031646728515625,
-0.0170440673828125,
-0.0103759765625,
-0.011993408203125,
-0.03045654296875,
-0.0186920166015625,
-0.0188140869140625,
0.005275726318359375,
0.007598876953125,
0.0207366943359375,
0.023223876953125,
-0.020782470703125,
-0.00870513916015625,
0.01036834716796875,
0.00885772705078125,
-0.0193939208984375,
-0.0019817352294921875,
0.018768310546875,
0.00550079345703125,
-0.017059326171875,
0.0005841255187988281,
0.0195159912109375,
-0.0295867919921875,
-0.0163726806640625,
0.0197906494140625,
0.048828125,
0.0042572021484375,
-0.032501220703125,
-0.016265869140625,
-0.01708984375,
-0.0025787353515625,
-0.01824951171875,
0.002521514892578125,
-0.01483154296875,
-0.011932373046875,
-0.0241546630859375,
0.0022106170654296875,
-0.0226898193359375,
-0.011383056640625,
-0.0113677978515625,
-0.0372314453125,
0.005710601806640625,
0.0012121200561523438,
0.0328369140625,
-0.0172882080078125,
0.03863525390625,
-0.0171966552734375,
0.0181884765625,
0.0054931640625,
-0.016937255859375,
0.0250701904296875,
-0.03253173828125,
-0.00002086162567138672,
0.0018873214721679688,
0.01403045654296875,
-0.0221405029296875,
0.023590087890625,
0.0194854736328125,
-0.00492095947265625,
0.016754150390625,
0.019866943359375,
0.030426025390625,
-0.0004038810729980469,
-0.04052734375,
-0.026275634765625,
0.039947509765625,
0.043609619140625,
0.01313018798828125,
-0.0055084228515625,
-0.0203399658203125,
0.02569580078125,
-0.0179901123046875,
0.006473541259765625,
-0.001949310302734375,
-0.0073089599609375,
0.005893707275390625,
0.005641937255859375,
-0.0124664306640625,
0.0004096031188964844,
0.018035888671875,
-0.0006194114685058594,
0.0261077880859375,
-0.0282745361328125,
0.00406646728515625,
0.0165252685546875,
-0.044830322265625,
-0.019134521484375,
-0.0189361572265625,
0.02862548828125,
0.0226593017578125,
0.019622802734375,
0.0167083740234375,
-0.00965118408203125,
-0.018402099609375,
-0.0188751220703125,
-0.0034332275390625,
-0.0300445556640625,
0.0171661376953125,
0.017181396484375,
-0.0039215087890625,
0.0297698974609375,
0.0254058837890625,
0.00922393798828125,
-0.04168701171875,
0.009857177734375,
-0.004703521728515625,
-0.03070068359375,
-0.0007929801940917969,
-0.00861358642578125,
0.039581298828125,
-0.039093017578125,
0.0350341796875,
-0.003108978271484375,
-0.0105133056640625,
0.026885986328125,
0.01230621337890625,
0.003292083740234375,
-0.010894775390625,
0.01300811767578125,
-0.003849029541015625,
-0.01056671142578125,
0.008575439453125,
0.002002716064453125,
-0.0083465576171875,
0.0013551712036132812,
-0.01812744140625,
0.003437042236328125,
0.01491546630859375,
0.0106658935546875,
0.049591064453125,
0.01461029052734375,
-0.0222015380859375,
0.02215576171875,
-0.02728271484375,
-0.005451202392578125,
-0.028839111328125,
0.018646240234375,
0.0215606689453125,
0.0134124755859375,
0.0187530517578125,
-0.007541656494140625,
-0.039031982421875,
0.0305328369140625,
-0.00528717041015625,
-0.0286712646484375,
0.0128173828125,
-0.0234222412109375,
-0.0168304443359375,
-0.0233001708984375,
-0.0189666748046875,
0.01149749755859375,
0.0447998046875,
0.00738525390625,
-0.00453948974609375,
-0.033843994140625,
0.007709503173828125,
-0.0404052734375,
0.005954742431640625,
-0.024627685546875,
-0.01444244384765625,
-0.0140533447265625,
0.0228424072265625,
0.004352569580078125,
-0.0109405517578125,
0.00028133392333984375,
0.03619384765625,
0.0030803680419921875,
0.020660400390625,
0.0207672119140625,
-0.0018606185913085938,
0.0137176513671875,
-0.027313232421875,
-0.003475189208984375,
0.00846099853515625,
0.02215576171875,
-0.0233917236328125,
0.029205322265625,
-0.01059722900390625,
0.0229644775390625,
0.039794921875,
0.0083465576171875,
-0.004512786865234375,
-0.0007014274597167969,
-0.003200531005859375,
-0.0106353759765625,
0.01284027099609375,
-0.0305633544921875,
0.0124969482421875,
0.009124755859375,
-0.01134490966796875,
-0.0131378173828125,
-0.046173095703125,
-0.01433563232421875,
-0.03155517578125,
-0.01364898681640625,
0.003322601318359375,
-0.034423828125,
0.01024627685546875,
0.002429962158203125,
0.0384521484375,
0.004451751708984375,
-0.00450897216796875,
0.004375457763671875,
-0.007640838623046875,
0.005924224853515625,
-0.06109619140625,
0.056640625,
0.0181732177734375,
0.01224517822265625,
-0.0303955078125,
-0.0189056396484375,
-0.004913330078125,
-0.044036865234375,
-0.004550933837890625,
0.01560211181640625,
-0.00201416015625,
-0.0218658447265625,
0.006664276123046875,
0.016357421875,
0.01812744140625,
-0.0014209747314453125,
0.0196990966796875,
0.00238037109375,
0.024200439453125,
0.00318145751953125,
-0.00609588623046875,
-0.015533447265625,
0.01947021484375,
0.031158447265625,
0.003261566162109375,
-0.0345458984375,
-0.0242919921875,
-0.0015897750854492188,
-0.0033779144287109375,
0.03369140625,
0.002185821533203125,
0.036895751953125,
-0.004230499267578125,
0.0106964111328125,
-0.04034423828125,
-0.027069091796875,
-0.0211639404296875,
0.01065826416015625,
0.0171966552734375,
0.0062408447265625,
0.00347900390625,
0.004070281982421875,
-0.00623321533203125,
0.0291290283203125,
0.0161895751953125,
0.00780487060546875,
-0.038482666015625,
0.0113677978515625,
0.01334381103515625,
0.01222991943359375,
-0.01094818115234375,
-0.0307769775390625,
-0.01136016845703125,
0.01082611083984375,
0.0037670135498046875,
-0.02392578125,
0.02569580078125,
0.002716064453125,
-0.00650787353515625,
0.0009531974792480469,
-0.006290435791015625,
0.006000518798828125,
-0.00348663330078125,
-0.00550079345703125,
-0.0418701171875,
-0.014617919921875,
0.0286712646484375,
0.0187530517578125,
-0.01114654541015625,
0.007152557373046875,
-0.0262603759765625,
0.0010519027709960938,
-0.0036373138427734375,
0.01216888427734375,
-0.0217742919921875,
-0.010498046875,
-0.0097503662109375,
-0.005046844482421875,
-0.0234527587890625,
-0.0238494873046875,
-0.020294189453125,
0.027252197265625,
-0.033782958984375,
-0.0006489753723144531,
0.00921630859375,
0.031768798828125,
-0.029937744140625,
-0.013275146484375,
-0.03155517578125,
-0.03167724609375,
0.00722503662109375,
-0.0025787353515625,
-0.04443359375,
0.00550079345703125,
0.00455474853515625,
0.007476806640625,
-0.011444091796875,
0.00970458984375,
-0.0472412109375,
-0.015869140625,
0.007049560546875,
-0.039886474609375,
-0.01203155517578125,
-0.0083770751953125,
0.015960693359375,
-0.006793975830078125,
-0.042205810546875,
0.0213470458984375,
0.0037555694580078125,
0.007633209228515625,
-0.0142059326171875,
0.013275146484375,
-0.0009136199951171875,
0.005832672119140625,
-0.018890380859375,
-0.037139892578125,
0.006008148193359375,
0.00928497314453125,
-0.0004241466522216797,
-0.0033969879150390625,
-0.0287017822265625,
0.005462646484375,
-0.00823211669921875,
-0.007312774658203125,
0.0026493072509765625,
0.026031494140625,
-0.0002079010009765625,
-0.002460479736328125,
-0.0210723876953125,
-0.0103607177734375,
0.0048980712890625,
-0.0249786376953125,
0.01366424560546875,
-0.0093536376953125,
0.0214996337890625,
0.037506103515625,
0.023162841796875,
-0.036468505859375,
-0.0029201507568359375,
-0.005710601806640625,
0.011810302734375,
-0.027587890625,
0.007671356201171875,
0.0047760009765625,
-0.0545654296875,
0.053253173828125,
-0.00370025634765625,
-0.003154754638671875,
0.002353668212890625,
0.00067901611328125,
-0.0125274658203125,
0.032928466796875,
0.0012569427490234375,
-0.0213623046875,
0.0035915374755859375,
-0.004421234130859375,
-0.00131988525390625,
0.03875732421875,
-0.026611328125,
0.01218414306640625,
-0.0008134841918945312,
-0.04010009765625,
0.0295562744140625,
-0.023590087890625,
-0.016876220703125,
-0.007755279541015625,
-0.0213470458984375,
-0.0003306865692138672,
-0.00293731689453125,
0.006557464599609375,
-0.0159912109375,
0.01537322998046875,
-0.009765625,
-0.021881103515625,
0.0279998779296875,
-0.020416259765625,
0.00968170166015625,
0.0191497802734375,
-0.0265960693359375,
0.01236724853515625,
-0.0060577392578125,
0.0034637451171875,
-0.023345947265625,
0.01153564453125,
-0.028900146484375,
0.0047607421875,
-0.005161285400390625,
0.041412353515625,
0.01076507568359375,
-0.0043182373046875,
0.00983428955078125,
0.042877197265625,
-0.0068817138671875,
-0.0275115966796875,
-0.0022430419921875,
0.0018301010131835938,
0.0293731689453125,
-0.00676727294921875,
0.0014295578002929688,
-0.0048065185546875,
0.03753662109375,
-0.0045166015625,
-0.0290374755859375,
-0.01084136962890625,
-0.0217742919921875,
-0.0004553794860839844,
-0.013671875,
0.004840850830078125,
0.0292510986328125,
0.003391265869140625,
-0.0087890625,
0.01233673095703125,
-0.0107421875,
-0.02227783203125,
-0.0198822021484375,
-0.011688232421875,
0.0181121826171875,
-0.0141143798828125,
0.0241851806640625,
-0.015838623046875,
0.016876220703125,
-0.01415252685546875,
-0.01522064208984375,
-0.005901336669921875,
0.0259857177734375,
0.012451171875,
0.0006260871887207031,
-0.0028629302978515625,
0.00385284423828125,
0.0199432373046875,
-0.004047393798828125,
0.01303863525390625,
0.016876220703125,
-0.0017271041870117188,
0.00473785400390625,
-0.0294647216796875,
-0.050750732421875,
-0.02850341796875,
-0.039093017578125,
0.00751495361328125,
0.02777099609375,
-0.0007266998291015625,
0.00940704345703125,
0.02490234375,
-0.02178955078125,
-0.01273345947265625,
-0.0201568603515625,
0.00868988037109375,
-0.0008134841918945312,
0.0268096923828125,
-0.04022216796875,
-0.0021533966064453125,
-0.0278778076171875,
0.05987548828125,
-0.01885986328125,
0.020721435546875,
-0.0024356842041015625,
0.0049285888671875,
-0.042236328125,
0.058563232421875,
-0.01525115966796875,
0.00428009033203125,
-0.003021240234375,
0.0149688720703125,
-0.00980377197265625,
0.0265350341796875,
0.0401611328125,
-0.0186920166015625,
0.02374267578125,
0.00872802734375,
0.01538848876953125,
0.00827789306640625,
-0.0265960693359375,
-0.038299560546875,
-0.00991058349609375,
-0.0192718505859375,
0.008697509765625,
-0.00640106201171875,
0.00855255126953125,
-0.002964019775390625,
-0.01300811767578125,
-0.00455474853515625,
0.00634765625,
0.037384033203125,
0.0096435546875,
-0.00868988037109375,
-0.01497650146484375,
-0.007724761962890625,
0.004596710205078125,
0.0148162841796875,
-0.019012451171875,
0.0321044921875,
-0.0238189697265625,
-0.0241851806640625,
-0.01409149169921875,
-0.0118255615234375,
0.01161956787109375,
0.0041656494140625,
0.016204833984375,
-0.0155029296875,
0.00469207763671875,
-0.0231475830078125,
0.03570556640625,
-0.0234375,
-0.00379180908203125,
0.0285491943359375,
0.0139007568359375,
0.001018524169921875,
0.02691650390625,
0.00977325439453125,
0.0145721435546875,
0.0003414154052734375,
0.01058197021484375,
-0.0154571533203125,
0.00235748291015625,
-0.022491455078125,
-0.019866943359375,
-0.0142669677734375,
0.0181884765625,
0.004192352294921875,
0.0433349609375,
0.016815185546875,
0.0003609657287597656,
-0.01763916015625,
-0.019927978515625,
0.00087738037109375,
0.0298614501953125,
-0.005367279052734375,
-0.005992889404296875,
0.035400390625,
-0.013275146484375,
-0.0423583984375,
0.037933349609375,
-0.026123046875,
0.0225982666015625,
0.01351165771484375,
0.0189056396484375,
0.0203704833984375,
0.0205841064453125,
-0.01125335693359375,
-0.031646728515625,
0.03314208984375,
0.0152435302734375,
0.02520751953125,
-0.007076263427734375,
-0.0160980224609375,
-0.0094451904296875,
-0.005428314208984375,
0.007709503173828125,
0.0012521743774414062,
-0.0167999267578125,
0.0200347900390625,
0.0157470703125,
-0.0278472900390625,
0.03204345703125,
0.00013065338134765625,
0.03692626953125,
0.03741455078125,
-0.006793975830078125,
0.0193634033203125,
0.01042938232421875,
0.0032596588134765625,
-0.03839111328125,
-0.01180267333984375,
0.01142120361328125,
0.0592041015625,
0.0052032470703125,
-0.0034332275390625,
-0.0057525634765625,
-0.0099334716796875,
-0.008209228515625,
0.0203857421875,
0.0357666015625,
-0.003753662109375,
-0.0279693603515625,
0.0179443359375,
-0.0228729248046875,
0.0139007568359375,
-0.05572509765625,
-0.002986907958984375,
-0.0009393692016601562,
0.0239715576171875,
0.045166015625,
-0.0089263916015625,
-0.03521728515625,
0.0002970695495605469,
0.020294189453125,
-0.0165557861328125,
0.0018262863159179688,
-0.033721923828125,
-0.023223876953125,
-0.027862548828125,
-0.01195526123046875,
-0.0028591156005859375,
0.021728515625,
-0.04559326171875,
0.003936767578125,
-0.008209228515625,
-0.00970458984375,
-0.0020732879638671875,
0.016510009765625,
-0.005268096923828125,
0.0019502639770507812,
-0.0263519287109375,
0.037506103515625,
0.0225372314453125,
0.01136016845703125,
0.01016998291015625,
-0.00583648681640625,
-0.045806884765625,
0.01491546630859375,
0.005977630615234375,
0.041229248046875,
0.01214599609375,
-0.0063629150390625,
-0.023681640625,
-0.01482391357421875,
-0.0023345947265625,
0.04400634765625,
0.00965118408203125,
0.029571533203125,
-0.0162353515625,
0.00928497314453125,
-0.0181884765625,
-0.007282257080078125,
0.028289794921875,
-0.0031757354736328125,
-0.0246124267578125,
0.0250396728515625,
-0.0251617431640625,
-0.01181793212890625,
0.002628326416015625,
-0.0487060546875,
-0.01264190673828125,
-0.0030078887939453125,
-0.0106658935546875,
-0.0006132125854492188,
0.00801849365234375,
0.040924072265625,
0.00974273681640625,
-0.01800537109375,
0.002704620361328125,
0.007358551025390625,
-0.019805908203125,
-0.00732421875,
-0.0175933837890625,
0.010772705078125,
0.016204833984375,
0.0224761962890625,
-0.0159759521484375,
0.0063934326171875,
0.0236358642578125,
0.011962890625,
-0.0087890625,
-0.00989532470703125,
0.012298583984375,
-0.0256805419921875,
0.006580352783203125,
0.00881195068359375,
-0.009429931640625,
-0.02056884765625,
0.00037360191345214844,
-0.00504302978515625,
0.0137481689453125,
0.01007080078125,
0.01406097412109375,
0.022369384765625,
-0.01435089111328125,
0.0216522216796875,
-0.021026611328125,
-0.0005550384521484375,
0.00206756591796875,
-0.017059326171875,
0.0211029052734375,
0.01287841796875,
0.00379180908203125,
0.00946044921875,
0.0011157989501953125,
0.01495361328125,
0.014923095703125,
-0.027130126953125,
-0.015777587890625,
0.0167388916015625,
-0.003482818603515625,
0.02105712890625,
-0.000045418739318847656,
0.00762176513671875,
-0.006092071533203125,
-0.0006427764892578125,
0.0139923095703125,
0.004974365234375,
0.0136260986328125,
0.006908416748046875,
-0.0286865234375,
0.0234222412109375,
0.003444671630859375,
0.01116180419921875,
-0.0003886222839355469,
0.007415771484375,
-0.039794921875,
-0.0027103424072265625,
-0.03363037109375,
-0.012054443359375,
0.0018548965454101562,
-0.007022857666015625,
0.045623779296875,
-0.030242919921875,
-0.019317626953125,
0.0286407470703125,
-0.00592041015625,
0.01470947265625,
0.00235748291015625,
0.00508880615234375,
-0.0276947021484375,
0.00469970703125,
-0.01416778564453125,
0.019561767578125,
0.01654052734375,
-0.0082550048828125,
-0.00714874267578125,
0.0029773712158203125,
0.0282745361328125,
0.0232696533203125,
-0.022491455078125,
-0.0202484130859375,
0.0166473388671875,
0.0093841552734375,
0.0228271484375,
-0.01415252685546875,
-0.0209197998046875,
-0.0037841796875,
-0.010284423828125,
0.0194091796875,
0.01580810546875,
0.000637054443359375,
0.02862548828125,
-0.0055389404296875,
0.022216796875,
0.01113128662109375,
0.0131378173828125,
0.0361328125,
-0.0081634521484375,
0.03839111328125,
0.031494140625,
-0.0281829833984375,
-0.0155029296875,
-0.032806396484375,
0.008758544921875,
0.02178955078125,
-0.010894775390625,
-0.02447509765625,
0.0085906982421875,
0.00849151611328125,
-0.01378631591796875,
0.02069091796875,
0.00007218122482299805,
-0.026611328125,
0.01250457763671875,
-0.031402587890625,
0.0006418228149414062,
0.02105712890625,
-0.05242919921875,
-0.007396697998046875,
0.03558349609375,
-0.005207061767578125,
0.0041961669921875,
0.0149078369140625,
0.015594482421875,
-0.018951416015625,
0.035186767578125,
-0.01535797119140625,
-0.0078887939453125,
0.026123046875,
-0.01538848876953125,
0.006855010986328125,
0.00007838010787963867,
0.0271453857421875,
-0.00615692138671875,
0.0100555419921875,
0.038360595703125,
0.02069091796875,
0.0082855224609375,
-0.0199432373046875,
0.0273284912109375,
-0.007015228271484375,
-0.018096923828125,
-0.01165008544921875,
0.00200653076171875,
-0.01221466064453125,
-0.03656005859375,
0.03192138671875,
-0.0213470458984375,
0.0051116943359375,
0.014190673828125,
-0.006076812744140625,
0.006694793701171875,
-0.006290435791015625,
0.003780364990234375,
-0.00862884521484375,
-0.0189056396484375,
-0.01013946533203125,
0.0017213821411132812,
-0.02569580078125,
-0.033355712890625,
-0.01236724853515625,
0.01824951171875,
-0.006175994873046875,
0.0094451904296875,
0.055877685546875,
-0.014007568359375,
-0.00958251953125,
0.0095062255859375,
0.01102447509765625,
0.020660400390625,
0.03021240234375,
0.013397216796875,
-0.0236053466796875,
0.0089263916015625,
-0.0249786376953125,
0.004512786865234375,
0.0180816650390625,
-0.0295257568359375,
0.00832366943359375,
0.02081298828125,
-0.01123809814453125,
0.0119476318359375,
-0.0303802490234375,
-0.01026153564453125,
0.0186614990234375,
-0.0072479248046875,
-0.0164337158203125,
-0.03399658203125,
-0.01043701171875,
-0.00445556640625,
0.020477294921875,
-0.0012521743774414062,
0.00791168212890625,
-0.0172119140625,
-0.0232696533203125,
-0.0030002593994140625,
0.01375579833984375,
-0.044464111328125,
0.0026493072509765625,
-0.0079498291015625,
0.01214599609375,
0.006023406982421875,
0.0172271728515625,
0.01081085205078125,
-0.010528564453125,
0.040313720703125,
-0.001430511474609375,
0.005260467529296875,
0.005523681640625,
-0.01580810546875,
0.005374908447265625,
-0.03594970703125,
0.0031585693359375,
0.006313323974609375,
-0.01297760009765625,
0.038604736328125,
0.017852783203125,
-0.0296173095703125,
0.0021266937255859375,
-0.0017242431640625,
0.00388336181640625,
0.033416748046875,
0.02874755859375,
0.0216217041015625,
-0.00829315185546875,
-0.0264129638671875,
0.0294036865234375,
0.0086212158203125,
-0.0360107421875,
-0.004451751708984375,
-0.0012674331665039062,
-0.010894775390625,
-0.01226806640625,
0.016693115234375,
0.00038123130798339844,
-0.03900146484375,
0.0024566650390625,
-0.017303466796875,
-0.0201568603515625,
-0.0158843994140625,
-0.0212249755859375,
0.01357269287109375,
-0.01088714599609375,
-0.0018873214721679688,
0.031036376953125,
0.0285186767578125,
0.0287017822265625,
-0.006084442138671875,
0.022430419921875,
-0.0240631103515625,
0.0181121826171875,
-0.01502227783203125,
-0.009857177734375,
0.0079193115234375,
0.041778564453125,
0.0164642333984375,
0.01953125,
-0.0251312255859375,
-0.00511932373046875,
-0.017059326171875,
-0.0016222000122070312,
-0.01496124267578125,
-0.0083160400390625,
0.0289306640625,
0.003528594970703125,
0.0108795166015625,
-0.00908660888671875,
-0.0179595947265625,
0.0030078887939453125,
-0.005626678466796875,
0.005573272705078125,
-0.0066375732421875,
0.018341064453125,
0.019287109375,
0.01160430908203125,
-0.0003616809844970703,
0.01319122314453125,
-0.01464080810546875,
0.035430908203125,
-0.0123291015625,
-0.0189666748046875,
0.00913238525390625,
0.00262451171875,
-0.0017347335815429688,
0.0036563873291015625,
0.03265380859375,
0.0179443359375,
-0.01396942138671875,
-0.00905609130859375,
-0.03436279296875,
0.008270263671875,
-0.01006317138671875,
-0.02557373046875,
0.0225982666015625,
-0.020538330078125,
0.0301666259765625,
-0.0099945068359375,
-0.0226287841796875,
-0.028106689453125,
-0.01513671875,
-0.0033931732177734375,
-0.0163116455078125,
0.00736236572265625,
0.0345458984375,
-0.00647735595703125,
0.02056884765625,
-0.0196380615234375,
-0.006031036376953125,
-0.01279449462890625,
-0.007904052734375,
-0.004993438720703125,
-0.01561737060546875,
-0.0225982666015625,
-0.000164031982421875,
0.0159454345703125,
0.0267181396484375,
-0.000016689300537109375,
0.0185089111328125,
0.0170440673828125,
-0.00975799560546875,
-0.02239990234375,
-0.00801849365234375,
0.0017671585083007812,
0.0038909912109375,
-0.0054168701171875,
0.0011205673217773438,
0.005313873291015625,
-0.00733184814453125,
-0.021514892578125,
-0.003734588623046875,
-0.0299835205078125,
0.01494598388671875,
-0.016204833984375,
-0.01186370849609375,
-0.00817108154296875,
-0.036712646484375,
-0.031585693359375,
0.0075225830078125,
0.0021419525146484375,
0.00800323486328125,
0.0022144317626953125,
0.0178985595703125,
0.031158447265625,
0.00897216796875,
-0.00476837158203125,
-0.034454345703125,
-0.01885986328125,
0.01071929931640625,
-0.0246429443359375,
-0.0072021484375,
0.011962890625,
0.0014848709106445312,
0.0196380615234375,
-0.00354766845703125,
0.01016998291015625,
0.05413818359375,
0.00543975830078125,
-0.0095062255859375,
-0.00554656982421875,
0.02001953125,
0.0038318634033203125,
0.039947509765625,
-0.0283203125,
0.01462554931640625,
-0.0198516845703125,
-0.0137786865234375,
0.036041259765625,
0.006542205810546875,
0.0107421875,
0.00829315185546875,
-0.006320953369140625,
-0.010986328125,
-0.0012254714965820312,
-0.01036834716796875,
-0.033966064453125,
0.005649566650390625,
0.0002512931823730469,
-0.0242156982421875,
-0.00452423095703125,
0.005725860595703125,
-0.0223388671875,
-0.00823974609375,
-0.011016845703125,
-0.01378631591796875,
0.0085601806640625,
-0.01465606689453125,
-0.01198577880859375,
-0.0155029296875,
-0.006961822509765625,
0.026702880859375,
-0.020721435546875,
0.03253173828125,
0.00887298583984375,
0.0196685791015625,
-0.0043487548828125,
0.0021610260009765625,
0.019561767578125,
-0.00919342041015625,
-0.036407470703125,
0.0275421142578125,
-0.004566192626953125,
0.01236724853515625,
0.0024166107177734375,
0.001293182373046875,
0.035491943359375,
-0.020721435546875,
0.0169830322265625,
-0.026824951171875,
0.0008254051208496094,
0.0172576904296875,
-0.0013179779052734375,
0.002338409423828125,
0.034637451171875,
-0.000011444091796875,
-0.0194549560546875,
-0.01493072509765625,
0.00505828857421875,
-0.0027103424072265625,
0.00041174888610839844,
0.009979248046875,
-0.0015668869018554688,
-0.0100250244140625,
0.02545166015625,
-0.0220947265625,
-0.032928466796875,
0.0157623291015625,
0.00978851318359375,
-0.0241546630859375,
0.0015668869018554688,
0.0026912689208984375,
0.0004565715789794922,
-0.0026073455810546875,
0.006122589111328125,
-0.009918212890625,
0.016357421875,
-0.027099609375,
-0.0010652542114257812,
-0.049346923828125,
-0.01336669921875,
-0.0230865478515625,
0.012725830078125,
-0.029205322265625,
-0.0263671875,
-0.03076171875,
0.0031108856201171875,
-0.00814056396484375,
-0.01727294921875,
0.03863525390625,
0.033935546875,
-0.027801513671875,
0.028533935546875,
0.00342559814453125,
-0.01433563232421875,
-0.0144195556640625,
-0.00827789306640625,
-0.0196990966796875,
-0.024017333984375,
0.0034332275390625,
0.0361328125,
-0.0242156982421875,
-0.0010499954223632812,
-0.03326416015625,
0.00780487060546875,
0.005916595458984375,
0.0195159912109375,
-0.010284423828125,
0.032928466796875,
0.0007805824279785156,
-0.005496978759765625,
-0.004581451416015625,
0.026824951171875,
0.014404296875,
-0.03570556640625,
-0.0010166168212890625,
0.01019287109375,
0.0019435882568359375,
0.00786590576171875,
-0.006443023681640625,
0.0019741058349609375,
0.020904541015625,
0.01381683349609375,
0.053070068359375,
-0.01264190673828125,
-0.00576019287109375,
-0.0016279220581054688,
-0.02777099609375,
0.01824951171875,
-0.01136016845703125,
-0.0157928466796875,
0.02032470703125,
-0.005779266357421875,
-0.00585174560546875,
-0.02252197265625,
-0.01088714599609375,
-0.0255584716796875,
-0.0243072509765625,
-0.0117950439453125,
-0.0024166107177734375,
-0.02471923828125,
0.0285491943359375,
-0.024261474609375,
0.00910186767578125,
-0.035736083984375,
0.0135498046875,
0.0002853870391845703,
-0.0140228271484375,
0.046966552734375,
0.01094818115234375,
0.0067901611328125,
0.01419830322265625,
-0.005008697509765625,
-0.0012798309326171875,
-0.014434814453125,
-0.0193328857421875,
-0.00860595703125,
-0.01152801513671875,
-0.029144287109375,
0.01145172119140625,
0.006214141845703125,
-0.0307769775390625,
0.011688232421875,
-0.00258636474609375,
-0.0091552734375,
0.0238037109375,
0.0218048095703125,
-0.0019073486328125,
0.02984619140625,
-0.0010128021240234375,
-0.0322265625,
-0.0251312255859375,
0.03558349609375,
-0.00943756103515625,
0.004573822021484375,
0.029266357421875,
0.014312744140625,
0.0377197265625,
0.00841522216796875,
-0.0465087890625,
0.0102996826171875,
0.0439453125,
-0.0252685546875,
-0.0018177032470703125,
-0.00571441650390625,
-0.02484130859375,
0.004405975341796875,
0.00847625732421875,
-0.047607421875,
-0.00177764892578125,
-0.0016736984252929688,
-0.038604736328125,
0.0031032562255859375,
0.0350341796875,
-0.0022144317626953125,
0.0147705078125,
-0.042327880859375,
0.049346923828125,
-0.0245513916015625,
0.0211944580078125,
-0.005077362060546875,
-0.0120849609375,
-0.018157958984375,
-0.0001964569091796875,
0.03338623046875,
0.024566650390625,
-0.020843505859375,
-0.0034542083740234375,
0.01165771484375,
0.01514434814453125,
0.03466796875,
0.00766754150390625,
-0.01806640625,
0.009521484375,
0.07568359375,
-0.01226043701171875,
-0.0270233154296875,
-0.0172576904296875,
0.005889892578125,
0.00885009765625,
0.0268707275390625,
0.01013946533203125,
-0.023895263671875,
-0.03277587890625,
-0.00881195068359375,
0.00458526611328125,
0.01465606689453125,
-0.01439666748046875,
0.015960693359375,
-0.0140380859375,
0.02044677734375,
0.05096435546875,
-0.0013990402221679688,
-0.01375579833984375,
0.0122528076171875,
0.0012979507446289062,
0.004314422607421875,
0.00516510009765625,
-0.00952911376953125,
-0.018768310546875,
-0.0122222900390625,
-0.01251983642578125,
0.01849365234375,
0.0052642822265625,
0.01186370849609375,
0.0083465576171875,
-0.00560760498046875,
0.0144500732421875,
0.004180908203125,
-0.0169219970703125,
-0.0031452178955078125,
-0.0127410888671875,
0.011383056640625,
-0.0288238525390625,
0.0127716064453125,
0.0057220458984375,
-0.006832122802734375,
0.006999969482421875,
-0.004070281982421875,
-0.000865936279296875,
0.035736083984375,
-0.0106353759765625,
-0.0014944076538085938,
0.023162841796875,
-0.004306793212890625,
-0.006618499755859375,
-0.015350341796875,
-0.01641845703125,
-0.029937744140625,
0.005615234375,
0.03411865234375,
0.003322601318359375,
-0.002960205078125,
-0.0030651092529296875,
-0.00495147705078125,
0.018280029296875,
-0.01030731201171875,
-0.0234375,
-0.00439453125,
0.01548004150390625,
0.0145416259765625,
0.004215240478515625,
-0.01503753662109375,
0.007778167724609375,
0.0033206939697265625,
0.0098876953125,
0.01050567626953125,
-0.00872802734375,
-0.0007824897766113281,
0.0292205810546875,
-0.00504302978515625,
-0.00337982177734375,
-0.04437255859375,
0.0306396484375,
-0.004032135009765625,
-0.0186309814453125,
-0.004543304443359375,
0.002391815185546875,
-0.045928955078125,
0.01367950439453125,
0.008392333984375,
0.00067901611328125,
0.0191497802734375,
-0.00366973876953125,
0.015899658203125,
-0.01276397705078125,
0.0087432861328125,
-0.00315093994140625,
0.004337310791015625,
0.007083892822265625,
-0.0018291473388671875,
-0.004180908203125,
0.01375579833984375,
0.02264404296875,
0.00823974609375,
0.002094268798828125,
0.00041484832763671875,
-0.0184783935546875,
0.01317596435546875,
-0.0010547637939453125,
0.0005984306335449219,
-0.008392333984375,
-0.021240234375,
-0.00391387939453125,
0.0211639404296875,
-0.0003674030303955078,
0.0152740478515625,
0.0170745849609375,
-0.00799560546875,
0.052459716796875,
-0.0216217041015625,
-0.0252227783203125,
0.0223541259765625,
-0.01004791259765625,
0.0124053955078125,
0.0193634033203125,
-0.0143585205078125,
0.0220489501953125,
0.0111083984375,
0.038299560546875,
0.0277862548828125,
0.0149383544921875,
-0.0100250244140625,
0.0139007568359375,
-0.0037441253662109375,
-0.0181121826171875,
0.0026702880859375,
0.0096588134765625,
0.0325927734375,
-0.031219482421875,
-0.0012311935424804688,
0.00815582275390625,
-0.01348114013671875,
0.03875732421875,
0.0012712478637695312,
0.00438690185546875,
-0.01036834716796875,
-0.006946563720703125,
-0.01090240478515625,
0.01324462890625,
-0.02630615234375,
-0.0194549560546875,
0.0177764892578125,
-0.01064300537109375,
0.01386260986328125,
0.0116119384765625,
-0.0389404296875,
0.0051422119140625,
-0.0047760009765625,
0.01448822021484375,
0.0144500732421875,
-0.004154205322265625,
0.010101318359375,
0.01256561279296875,
-0.022430419921875,
-0.03485107421875,
0.005401611328125,
0.02392578125,
0.00695037841796875,
-0.00040531158447265625,
-0.0089569091796875,
0.006855010986328125,
-0.0289764404296875,
0.0162200927734375,
-0.0023479461669921875,
0.01107025146484375,
-0.040557861328125,
-0.026824951171875,
-0.003936767578125,
-0.01172637939453125,
0.01390838623046875,
-0.031036376953125,
0.000545501708984375,
-0.01561737060546875,
-0.00029015541076660156,
0.01904296875,
-0.014373779296875,
-0.0160980224609375,
-0.0245819091796875,
-0.0113067626953125,
0.0188751220703125,
-0.0004105567932128906,
-0.0171661376953125,
0.00689697265625,
0.02874755859375,
-0.00640869140625,
0.01030731201171875,
-0.00859832763671875,
0.0127105712890625,
0.03167724609375,
0.00803375244140625,
0.004558563232421875,
0.021270751953125,
0.0295867919921875,
-0.01302337646484375,
0.031463623046875,
0.02435302734375,
0.0002512931823730469,
0.00112152099609375,
-0.01204681396484375,
-0.033905029296875,
-0.0208282470703125,
-0.0347900390625,
0.014495849609375,
-0.00328826904296875,
0.039947509765625,
0.0244903564453125,
-0.029754638671875,
0.0218048095703125,
-0.031951904296875,
-0.0263671875,
-0.011627197265625,
-0.00734710693359375,
-0.004962921142578125,
-0.032562255859375,
0.0129241943359375,
0.020355224609375,
0.0009417533874511719,
0.002788543701171875,
0.0007338523864746094,
-0.0272064208984375,
0.0155181884765625,
0.00424957275390625,
-0.043182373046875,
0.027740478515625,
-0.0100860595703125,
-0.00759124755859375,
0.004749298095703125,
0.0027942657470703125,
0.0207061767578125,
-0.0233306884765625,
0.00873565673828125,
0.02679443359375,
-0.004642486572265625,
0.0141754150390625,
0.0265655517578125,
-0.030487060546875,
-0.019744873046875,
0.0135955810546875,
0.005931854248046875,
0.0023403167724609375,
0.016998291015625,
0.004062652587890625,
-0.0251312255859375,
-0.006610870361328125,
-0.0149383544921875,
-0.02001953125,
-0.007541656494140625,
-0.007232666015625,
-0.0096435546875,
-0.0033130645751953125,
-0.00757598876953125,
-0.0009098052978515625,
-0.00548553466796875,
0.0280914306640625,
-0.00567626953125,
-0.03546142578125,
0.01348876953125,
0.034210205078125,
0.01108551025390625,
-0.033416748046875,
-0.0242156982421875,
0.01303863525390625,
-0.0133209228515625,
0.01090240478515625,
-0.01462554931640625,
-0.0201873779296875,
-0.01641845703125,
-0.02593994140625,
-0.01273345947265625,
-0.0021877288818359375,
0.004779815673828125,
0.0153656005859375,
-0.01140594482421875,
0.0364990234375,
-0.0184783935546875,
0.011016845703125,
0.0413818359375,
-0.0193023681640625,
0.0185394287109375,
-0.01198577880859375,
0.0258636474609375,
0.0009531974792480469,
-0.02923583984375,
0.0157928466796875,
-0.01332855224609375,
-0.00823211669921875,
0.027099609375,
0.0037326812744140625,
0.0170745849609375,
0.01081085205078125,
0.0163421630859375,
-0.012298583984375,
0.029541015625,
-0.0166015625,
-0.01415252685546875,
0.008056640625,
-0.0063323974609375,
0.0030364990234375,
0.006622314453125,
-0.025482177734375,
0.0177459716796875,
0.0199432373046875,
0.0213623046875,
0.0192413330078125,
-0.02178955078125,
-0.0028438568115234375,
0.005001068115234375,
-0.032867431640625,
0.0278778076171875,
0.01242828369140625,
0.00984954833984375,
0.031982421875,
-0.016448974609375,
0.0015916824340820312,
0.046295166015625,
0.041961669921875,
-0.003826141357421875,
0.053131103515625,
0.004856109619140625,
0.0264892578125,
-0.049591064453125,
0.0007872581481933594,
0.0002529621124267578,
-0.01050567626953125,
-0.0008325576782226562,
-0.006053924560546875,
-0.0083160400390625,
0.032257080078125,
-0.031646728515625,
-0.01279449462890625,
-0.03143310546875,
0.0110321044921875,
-0.004627227783203125,
0.0241241455078125,
0.006275177001953125,
-0.029022216796875,
0.003437042236328125,
0.00926971435546875,
-0.0146636962890625,
0.0150299072265625,
0.0008783340454101562,
-0.0283203125,
-0.004131317138671875,
-0.023773193359375,
0.03338623046875,
-0.01099395751953125,
-0.0027370452880859375,
-0.026397705078125,
0.03521728515625,
0.01849365234375,
-0.007564544677734375,
0.01412200927734375,
0.032379150390625,
-0.0291748046875,
0.01561737060546875,
-0.0321044921875,
0.0061492919921875,
0.04449462890625,
-0.01049041748046875,
-0.039520263671875,
-0.0260772705078125,
-0.002407073974609375,
0.039154052734375,
-0.0181121826171875,
-0.0100250244140625,
-0.00925445556640625,
0.00934600830078125,
-0.01253509521484375,
-0.0139312744140625,
-0.0565185546875,
-0.02203369140625,
0.0220947265625,
-0.010223388671875,
-0.004894256591796875,
-0.0172271728515625,
0.021942138671875,
-0.03387451171875,
0.0110626220703125,
0.032135009765625,
-0.0298004150390625,
0.002719879150390625,
0.00775146484375,
0.01222991943359375,
-0.03643798828125,
-0.0280609130859375,
-0.0199737548828125,
-0.028533935546875,
0.006298065185546875,
0.023101806640625,
0.01421356201171875,
-0.01541900634765625,
-0.006656646728515625,
-0.0194091796875,
-0.00403594970703125,
0.0173492431640625,
0.0005869865417480469,
-0.006473541259765625,
0.0177154541015625,
-0.03472900390625,
-0.00916290283203125,
-0.03826904296875,
0.0144805908203125,
-0.0253448486328125,
-0.02459716796875,
-0.0130615234375,
-0.01538848876953125,
-0.00279998779296875,
-0.0215606689453125,
-0.007282257080078125,
-0.01230621337890625,
-0.0163726806640625,
0.0271759033203125,
0.005161285400390625,
0.012420654296875,
0.02911376953125,
-0.00954437255859375,
0.00937652587890625,
-0.0296630859375,
0.0031795501708984375,
-0.00437164306640625,
-0.045074462890625,
-0.0033550262451171875,
-0.015472412109375,
0.0201873779296875,
0.0048828125,
-0.005889892578125,
-0.00643157958984375,
-0.0249786376953125,
-0.028533935546875,
0.014251708984375,
-0.00836181640625,
0.01424407958984375,
-0.004085540771484375,
0.0275726318359375,
-0.004497528076171875,
0.0268707275390625,
0.00380706787109375,
-0.005859375,
-0.0172271728515625,
-0.01116943359375,
0.004589080810546875,
0.00008475780487060547,
-0.00217437744140625,
0.0170440673828125,
-0.005023956298828125,
-0.0109405517578125,
-0.007450103759765625,
-0.030364990234375,
-0.012115478515625,
0.024749755859375,
0.0028095245361328125,
-0.003391265869140625,
-0.0157318115234375,
-0.0098724365234375,
-0.026885986328125
] |
ours_490
|
Note that for all \(x\), if \(x, f(x), f^{2}(x), \ldots\) eventually cycles with period \(>1\), then taking \(S\) to be the numbers in this cycle gives a contradiction. However, since \(\{1,2, \ldots 2018\}\) and \(\{1,2,3, \ldots 2019\}\) are finite, that sequence must eventually cycle or terminate at 2019. Thus, that sequence eventually is constant or terminates.
Now, let \(g(x)\) be the constant value that \(x, f(x), f^{2}(x), \ldots\) eventually becomes (let \(g(x)=2019\) if that sequence ever reaches 2019, when it would terminate). Denote \(X=\{g(1), g(2), \ldots g(2018)\}\). If \(|X \cap\{1,2,3, \ldots 2018\}| \geq 2\), then taking \(S=|X \cap\{1,2,3, \ldots 2018\}|\) gives a contradiction. Thus, \(|X \cap\{1,2,3, \ldots 2018\}| \in\{0,1\}\). Also, \(X\) is nonempty.
Draw a directed graph with vertices labeled \(1,2, \ldots 2019\), such that there is an edge from \(x\) to \(f(x)\) for all \(x \in\{1,2,3, \ldots 2018\}\).
Case 1: \(X=\{2019\}\). In this case, if the directions of the graph are removed, there is a path from \(x\) to \(2019\) for all \(x \in\{1,2,3, \ldots 2019\}\), and there are no cycles, so the graph must be a tree. Also, every tree can be converted to an antibijection by directing each edge 'towards' (on the unique path to) 2019. By Cayley's formula, this gives \(2019^{2017}\) functions.
Case 2: \(X=\{c\}\) or \(\{c, 2019\}\) for some \(c \in\{1,2, \ldots 2018\}\). We claim that this can be bijected to the set of ordered pairs (tree on vertices \(\{1,2, \ldots, 2019\}\), choice of neighbor of 2019). We can create a function from each of these by drawing the tree, deleting the edge between \(2019\) and \(c\), and creating functions from the two resulting trees as done in Case 1 (taking \(c\) as the 'final value' of the tree with \(c\) in it). Similarly, we can create the trees from a function by drawing the graph then connecting \(c\) to 2019, so this is a bijection. To count these, note that each tree generates \(\operatorname{deg}(2019)\) functions. Counting this over all labelings of a fixed tree shows that this is \(\frac{2 \cdot 2018}{2019}\) on average (there are \(2018\) edges, each is counted twice), giving \(\frac{2 \cdot 2018}{2019} \cdot 2019^{2017}=2 \cdot 2018 \cdot 2019^{2016}\) functions by Cayley's.
Thus \(N=2019^{2017}+2 \cdot 2018 \cdot 2019^{2016}=3^{2016} \cdot 673^{2016} \cdot 5 \cdot 7 \cdot 173\), giving an answer of \(2016 \cdot 3+2016 + 673+5+7+173=1363001\).
\(\boxed{1363001}\)
|
1363001
|
{
"competition": "us_comps",
"dataset": "Ours",
"posts": null,
"source": "OMOFall19Solns-2.md"
}
|
For finite sets \(A\) and \(B\), call a function \(f: A \rightarrow B\) an antibijection if there does not exist a set \(S \subseteq A \cap B\) such that \(S\) has at least two elements and, for all \(s \in S\), there exists exactly one element \(s^{\prime}\) of \(S\) such that \(f\left(s^{\prime}\right)=s\). Let \(N\) be the number of antibijections from \(\{1,2,3, \ldots 2018\}\) to \(\{1,2,3, \ldots 2019\}\). Suppose \(N\) is written as the product of a collection of (not necessarily distinct) prime numbers. Compute the sum of the members of this collection.
|
[
"/Mathematics/DiscreteMathematics/Combinatorics/Enumeration",
"/Mathematics/DiscreteMathematics/Combinatorics/GeneralCombinatorics",
"/Mathematics/DiscreteMathematics/GeneralDiscreteMathematics/DiscreteMath",
"/Mathematics/DiscreteMathematics/GeneralDiscreteMathematics/DiscreteMathematics",
"/Mathematics/DiscreteMathematics/GeneralDiscreteMathematics/FiniteMathematics",
"/Mathematics/DiscreteMathematics/GraphTheory/DirectedGraphs",
"/Mathematics/DiscreteMathematics/GraphTheory/LabeledGraphs",
"/Mathematics/DiscreteMathematics/GraphTheory/Trees"
] |
Interpret the function as a directed graph and use the antibijection condition to force a cycle‑free (tree‑like) structure, then count such graphs with Cayley’s formula.
|
[
-0.00005352497100830078,
0.0026073455810546875,
0.044891357421875,
-0.029937744140625,
-0.00002866983413696289,
0.00788116455078125,
-0.006008148193359375,
0.0082855224609375,
0.0093994140625,
-0.01357269287109375,
0.042999267578125,
-0.0210418701171875,
-0.00011169910430908203,
-0.01525115966796875,
-0.033935546875,
-0.03521728515625,
0.07940673828125,
0.0198211669921875,
0.002288818359375,
-0.0038661956787109375,
-0.0156402587890625,
-0.0055999755859375,
-0.0010290145874023438,
0.040740966796875,
-0.003467559814453125,
-0.018707275390625,
-0.0206298828125,
0.0128936767578125,
-0.00467681884765625,
0.0008206367492675781,
-0.0111083984375,
-0.0192108154296875,
0.0214691162109375,
-0.0206146240234375,
0.0021076202392578125,
0.01354217529296875,
0.012725830078125,
-0.0008001327514648438,
-0.01538848876953125,
-0.0194854736328125,
-0.0233154296875,
-0.02325439453125,
0.0316162109375,
-0.0057373046875,
-0.0010633468627929688,
0.00467681884765625,
-0.0007419586181640625,
0.01178741455078125,
-0.004608154296875,
-0.01519775390625,
-0.007450103759765625,
0.0137786865234375,
-0.005527496337890625,
-0.0152587890625,
-0.04412841796875,
-0.050140380859375,
0.00826263427734375,
0.002498626708984375,
-0.0013284683227539062,
-0.022735595703125,
0.005039215087890625,
0.003978729248046875,
0.01068115234375,
-0.01439666748046875,
-0.00494384765625,
-0.020477294921875,
-0.004451751708984375,
0.01031494140625,
-0.00475311279296875,
-0.01007843017578125,
-0.00685882568359375,
-0.0132904052734375,
-0.00829315185546875,
0.006931304931640625,
0.0189361572265625,
-0.013671875,
-0.01288604736328125,
0.0118408203125,
0.0312042236328125,
0.0129547119140625,
0.03411865234375,
0.01134490966796875,
-0.00833892822265625,
-0.007350921630859375,
0.0211029052734375,
0.005542755126953125,
0.038330078125,
-0.00208282470703125,
0.035614013671875,
-0.007236480712890625,
-0.004703521728515625,
0.019805908203125,
-0.0023555755615234375,
0.0234832763671875,
0.00388336181640625,
0.0169219970703125,
0.0206451416015625,
-0.0146331787109375,
-0.0023632049560546875,
0.005916595458984375,
-0.006725311279296875,
-0.005462646484375,
0.031494140625,
0.0045013427734375,
-0.037078857421875,
-0.01354217529296875,
-0.0092620849609375,
0.0020389556884765625,
-0.01837158203125,
-0.02215576171875,
0.01093292236328125,
-0.0017557144165039062,
0.0279083251953125,
0.01201629638671875,
-0.0013561248779296875,
0.0155487060546875,
0.02447509765625,
0.004291534423828125,
-0.0004706382751464844,
-0.0092620849609375,
-0.0029315948486328125,
0.01531219482421875,
0.01490020751953125,
0.0198974609375,
0.00838470458984375,
-0.0222930908203125,
-0.016204833984375,
-0.0191497802734375,
-0.0098724365234375,
-0.00678253173828125,
0.02520751953125,
0.00853729248046875,
0.0124053955078125,
-0.0176239013671875,
-0.032684326171875,
-0.009521484375,
-0.00231170654296875,
0.0032520294189453125,
0.0213470458984375,
-0.01303863525390625,
0.00421142578125,
-0.0167388916015625,
-0.0019989013671875,
0.008514404296875,
-0.015716552734375,
0.017913818359375,
0.00325775146484375,
-0.0307159423828125,
0.01519775390625,
0.01177978515625,
0.0021076202392578125,
0.006565093994140625,
0.01425933837890625,
0.0018701553344726562,
0.010589599609375,
0.02056884765625,
-0.007122039794921875,
0.003536224365234375,
-0.00848388671875,
0.005168914794921875,
-0.0048065185546875,
-0.0177459716796875,
-0.00960540771484375,
0.01050567626953125,
-0.0180511474609375,
0.006328582763671875,
0.019805908203125,
-0.016082763671875,
-0.01523590087890625,
-0.008544921875,
0.0023021697998046875,
-0.01343536376953125,
0.01384735107421875,
-0.0218658447265625,
0.003093719482421875,
-0.00409698486328125,
-0.00957489013671875,
-0.004791259765625,
-0.0112457275390625,
0.044158935546875,
0.00006622076034545898,
-0.046173095703125,
-0.01042938232421875,
0.0162506103515625,
0.026092529296875,
0.0014295578002929688,
0.0011796951293945312,
0.0226593017578125,
0.037445068359375,
0.00849151611328125,
-0.006641387939453125,
-0.0265655517578125,
-0.0002627372741699219,
0.00757598876953125,
-0.0015783309936523438,
-0.015472412109375,
-0.019805908203125,
0.0265960693359375,
0.030975341796875,
0.0034694671630859375,
-0.013397216796875,
0.0010404586791992188,
0.00806427001953125,
-0.005889892578125,
0.01277923583984375,
0.005596160888671875,
0.016998291015625,
0.0005211830139160156,
-0.00582122802734375,
-0.01502227783203125,
-0.0038204193115234375,
-0.017822265625,
-0.014678955078125,
-0.0089569091796875,
-0.0108489990234375,
0.007137298583984375,
-0.026123046875,
-0.0020999908447265625,
0.003265380859375,
-0.047698974609375,
0.00354766845703125,
-0.0005893707275390625,
-0.0227203369140625,
-0.0034008026123046875,
-0.021240234375,
0.0019044876098632812,
0.0101776123046875,
-0.00566864013671875,
0.00911712646484375,
0.0045928955078125,
0.0019407272338867188,
-0.0023632049560546875,
-0.01509857177734375,
-0.00905609130859375,
-0.0067901611328125,
-0.00572967529296875,
0.01511383056640625,
-0.00646209716796875,
0.00556182861328125,
-0.0291290283203125,
0.0235748291015625,
-0.0174407958984375,
-0.009368896484375,
0.004878997802734375,
-0.0196380615234375,
-0.0009946823120117188,
0.01389312744140625,
0.0011587142944335938,
-0.003833770751953125,
-0.0198974609375,
0.0010652542114257812,
0.003566741943359375,
0.002532958984375,
0.0051727294921875,
0.0306854248046875,
-0.01739501953125,
-0.0087738037109375,
0.0216064453125,
-0.021087646484375,
-0.0128173828125,
-0.01001739501953125,
-0.0204315185546875,
-0.0015859603881835938,
-0.01209259033203125,
0.0006604194641113281,
0.003795623779296875,
0.015045166015625,
0.00867462158203125,
0.0095672607421875,
-0.00075531005859375,
0.0264739990234375,
-0.0282440185546875,
-0.006839752197265625,
0.01087188720703125,
-0.015716552734375,
-0.01424407958984375,
-0.01198577880859375,
-0.01441192626953125,
0.00656890869140625,
-0.0233917236328125,
0.0199127197265625,
-0.029693603515625,
-0.017608642578125,
0.01824951171875,
-0.002521514892578125,
-0.00873565673828125,
-0.00611114501953125,
-0.00731658935546875,
-0.01513671875,
-0.004547119140625,
0.0028667449951171875,
-0.0308074951171875,
-0.00189208984375,
-0.00978851318359375,
0.045318603515625,
-0.0243377685546875,
0.0179901123046875,
-0.0111236572265625,
0.012847900390625,
-0.0129852294921875,
0.01050567626953125,
-0.005001068115234375,
0.0110321044921875,
0.038238525390625,
0.005313873291015625,
0.025543212890625,
-0.00214385986328125,
0.002532958984375,
-0.052154541015625,
0.0024509429931640625,
-0.0205230712890625,
0.0007076263427734375,
0.0162506103515625,
0.004199981689453125,
0.006256103515625,
-0.01389312744140625,
-0.01265716552734375,
0.01021575927734375,
-0.0184478759765625,
0.0007619857788085938,
0.0328369140625,
0.0165252685546875,
-0.0158233642578125,
0.00592041015625,
0.0009312629699707031,
-0.00045680999755859375,
-0.004154205322265625,
0.00804901123046875,
-0.037689208984375,
0.06280517578125,
-0.0246429443359375,
0.0255279541015625,
-0.0257110595703125,
-0.00038623809814453125,
-0.00490570068359375,
0.0076904296875,
-0.004306793212890625,
-0.003635406494140625,
0.019775390625,
-0.028411865234375,
-0.0147857666015625,
0.004253387451171875,
-0.006183624267578125,
-0.000056684017181396484,
-0.0010099411010742188,
0.0028209686279296875,
-0.033233642578125,
-0.0293731689453125,
-0.0247955322265625,
-0.0065765380859375,
0.039306640625,
-0.001453399658203125,
-0.011810302734375,
0.0228729248046875,
-0.04644775390625,
0.01186370849609375,
-0.0419921875,
-0.0221710205078125,
-0.0092926025390625,
0.01528167724609375,
-0.002696990966796875,
0.016143798828125,
0.01136016845703125,
0.01265716552734375,
0.0184326171875,
-0.02044677734375,
-0.009796142578125,
-0.00907135009765625,
-0.046356201171875,
-0.01560211181640625,
-0.007778167724609375,
0.006549835205078125,
0.00727081298828125,
-0.0313720703125,
-0.029693603515625,
-0.002079010009765625,
0.0183868408203125,
0.00026416778564453125,
-0.036376953125,
-0.005146026611328125,
0.0163421630859375,
0.0379638671875,
-0.0205230712890625,
0.031494140625,
-0.03533935546875,
-0.00799560546875,
0.004486083984375,
-0.023956298828125,
-0.00849151611328125,
0.0006113052368164062,
-0.0176849365234375,
-0.007808685302734375,
-0.0032939910888671875,
0.0390625,
-0.0240020751953125,
-0.008697509765625,
0.002620697021484375,
0.0189056396484375,
0.039764404296875,
-0.035247802734375,
0.0073089599609375,
-0.04034423828125,
-0.00832366943359375,
0.021484375,
0.01251220703125,
0.006900787353515625,
-0.0183563232421875,
-0.013885498046875,
-0.01739501953125,
-0.01336669921875,
0.037322998046875,
0.0352783203125,
-0.0121307373046875,
-0.0073089599609375,
0.0379638671875,
-0.016021728515625,
0.0279388427734375,
-0.00235748291015625,
-0.050567626953125,
-0.00511932373046875,
-0.0281829833984375,
-0.0138397216796875,
0.0099639892578125,
-0.0198974609375,
0.0176239013671875,
0.01751708984375,
-0.00498199462890625,
0.01393890380859375,
0.0234375,
0.01488494873046875,
-0.0177001953125,
-0.025787353515625,
0.024993896484375,
0.0149078369140625,
0.0027599334716796875,
0.00920867919921875,
0.0003991127014160156,
0.0015277862548828125,
0.015289306640625,
0.03497314453125,
-0.0232696533203125,
-0.01331329345703125,
-0.0026226043701171875,
-0.004024505615234375,
-0.0058441162109375,
0.0005831718444824219,
0.018310546875,
-0.00482177734375,
-0.028411865234375,
0.0007448196411132812,
-0.0278778076171875,
0.0202484130859375,
-0.004207611083984375,
-0.0094757080078125,
0.00013506412506103516,
0.01873779296875,
0.021881103515625,
-0.033966064453125,
-0.017333984375,
-0.019805908203125,
-0.0018768310546875,
-0.02587890625,
0.000020802021026611328,
-0.01255035400390625,
-0.04339599609375,
-0.00011843442916870117,
0.00934600830078125,
-0.0020427703857421875,
0.037750244140625,
-0.01235198974609375,
-0.00264739990234375,
-0.021575927734375,
0.0206451416015625,
0.01229095458984375,
-0.028167724609375,
-0.0027027130126953125,
0.01425933837890625,
0.01332855224609375,
-0.0027675628662109375,
-0.0184326171875,
0.0164794921875,
-0.0181732177734375,
0.016265869140625,
0.06488037109375,
-0.0040283203125,
-0.005260467529296875,
0.03472900390625,
0.0218048095703125,
-0.033599853515625,
-0.030914306640625,
0.0028514862060546875,
0.004364013671875,
-0.019134521484375,
-0.007480621337890625,
0.002971649169921875,
-0.0182952880859375,
0.01534271240234375,
-0.01445770263671875,
0.00949859619140625,
0.01312255859375,
-0.00611114501953125,
-0.005092620849609375,
0.045745849609375,
0.0462646484375,
0.0154571533203125,
0.006744384765625,
0.05816650390625,
0.011322021484375,
0.0213775634765625,
-0.03179931640625,
0.003078460693359375,
-0.00489044189453125,
0.037994384765625,
-0.0083465576171875,
0.0012998580932617188,
-0.034942626953125,
0.002429962158203125,
0.0221099853515625,
-0.0294647216796875,
0.0110321044921875,
-0.040771484375,
0.01264190673828125,
0.01074981689453125,
-0.0012111663818359375,
-0.00855255126953125,
-0.0013055801391601562,
-0.00916290283203125,
-0.03619384765625,
0.0015039443969726562,
-0.00687408447265625,
-0.013580322265625,
-0.048553466796875,
0.0236053466796875,
-0.017730712890625,
-0.0170745849609375,
0.01654052734375,
0.00014543533325195312,
-0.03033447265625,
0.0006442070007324219,
0.0129241943359375,
0.0020961761474609375,
-0.00981903076171875,
0.00952911376953125,
0.01528167724609375,
-0.01214599609375,
-0.00875091552734375,
0.0025959014892578125,
-0.031463623046875,
0.004344940185546875,
0.02734375,
-0.00957489013671875,
-0.015960693359375,
0.018310546875,
-0.006298065185546875,
-0.0047760009765625,
0.0128631591796875,
0.008392333984375,
0.0133514404296875,
-0.0021343231201171875,
0.0124664306640625,
-0.039581298828125,
0.0416259765625,
0.0157318115234375,
-0.0222015380859375,
0.0229034423828125,
-0.00849151611328125,
0.0081939697265625,
0.0249481201171875,
-0.003955841064453125,
-0.012054443359375,
-0.016448974609375,
-0.0177459716796875,
-0.00841522216796875,
-0.01824951171875,
-0.0138397216796875,
0.01172637939453125,
-0.009429931640625,
-0.015960693359375,
0.016265869140625,
-0.0049591064453125,
0.027252197265625,
0.02001953125,
0.020416259765625,
-0.0064544677734375,
0.04864501953125,
0.016510009765625,
-0.00389862060546875,
0.01372528076171875,
0.035186767578125,
-0.01454925537109375,
0.008270263671875,
-0.00021529197692871094,
-0.01268768310546875,
0.002658843994140625,
0.018829345703125,
0.00009918212890625,
0.0273284912109375,
0.0033245086669921875,
-0.022064208984375,
-0.02435302734375,
0.012237548828125,
-0.020904541015625,
-0.0264129638671875,
0.008209228515625,
-0.004608154296875,
-0.0206146240234375,
-0.018280029296875,
0.021392822265625,
-0.0016927719116210938,
0.00449371337890625,
0.0026378631591796875,
-0.031951904296875,
0.0140380859375,
-0.0278167724609375,
0.024169921875,
0.0040740966796875,
-0.0146484375,
-0.012298583984375,
-0.016265869140625,
-0.01116943359375,
-0.00310516357421875,
0.019561767578125,
0.0070037841796875,
0.019256591796875,
-0.0173797607421875,
-0.0113677978515625,
0.044219970703125,
-0.039886474609375,
0.0097503662109375,
0.003307342529296875,
-0.01117706298828125,
-0.0216064453125,
0.019317626953125,
0.004154205322265625,
0.012451171875,
0.0013742446899414062,
-0.033782958984375,
0.023590087890625,
0.0128936767578125,
0.0029468536376953125,
0.01556396484375,
0.02093505859375,
0.04364013671875,
-0.0386962890625,
0.017120361328125,
0.005802154541015625,
-0.00457763671875,
-0.00930023193359375,
0.003673553466796875,
0.00688934326171875,
-0.01010894775390625,
-0.0231475830078125,
-0.0016527175903320312,
0.0279541015625,
0.0020198822021484375,
0.00763702392578125,
0.019622802734375,
-0.0289459228515625,
0.02337646484375,
-0.003704071044921875,
0.010284423828125,
-0.0002751350402832031,
0.0198516845703125,
-0.001682281494140625,
-0.03314208984375,
0.0214996337890625,
-0.0293731689453125,
-0.0310211181640625,
-0.01329803466796875,
0.0006279945373535156,
-0.015960693359375,
-0.0245819091796875,
-0.006999969482421875,
0.002033233642578125,
0.003711700439453125,
0.0030670166015625,
0.001781463623046875,
-0.00467681884765625,
0.002044677734375,
0.0277099609375,
0.037261962890625,
0.01116943359375,
0.03302001953125,
-0.0236663818359375,
0.051666259765625,
-0.0050201416015625,
-0.006687164306640625,
-0.0009059906005859375,
-0.00998687744140625,
0.0009517669677734375,
0.0067901611328125,
0.0035572052001953125,
-0.012939453125,
0.00458526611328125,
0.022369384765625,
-0.009674072265625,
0.014923095703125,
0.0258636474609375,
-0.002254486083984375,
0.010406494140625,
-0.00701141357421875,
-0.038177490234375,
0.0300445556640625,
0.004489898681640625,
0.028778076171875,
-0.00958251953125,
-0.02191162109375,
0.002132415771484375,
-0.0236053466796875,
0.021270751953125,
-0.017486572265625,
-0.01313018798828125,
-0.0126953125,
0.0269927978515625,
-0.023193359375,
-0.00902557373046875,
0.0169525146484375,
0.04547119140625,
0.00714874267578125,
-0.006458282470703125,
-0.00556182861328125,
0.0207977294921875,
0.0133056640625,
-0.0251007080078125,
-0.0006580352783203125,
-0.01702880859375,
-0.0041961669921875,
-0.033782958984375,
-0.025726318359375,
0.00605010986328125,
-0.00902557373046875,
-0.004825592041015625,
-0.0225067138671875,
-0.02008056640625,
-0.0293121337890625,
-0.01503753662109375,
0.01105499267578125,
-0.0186614990234375,
0.00843048095703125,
0.022796630859375,
0.02655029296875,
-0.02276611328125,
0.0179290771484375,
-0.0132904052734375,
-0.024261474609375,
-0.01212310791015625,
0.00994873046875,
-0.002880096435546875,
-0.0005316734313964844,
0.006885528564453125,
0.0243072509765625,
-0.0218658447265625,
-0.0024394989013671875,
-0.040924072265625,
0.01654052734375,
-0.0007615089416503906,
0.0089111328125,
-0.022796630859375,
-0.01107025146484375,
0.0234222412109375,
-0.045654296875,
-0.00893402099609375,
-0.0258941650390625,
-0.019866943359375,
-0.004528045654296875,
0.001293182373046875,
-0.0274810791015625,
-0.034698486328125,
-0.049957275390625,
0.0262603759765625,
-0.04864501953125,
0.0217132568359375,
0.016632080078125,
0.00946044921875,
0.00177001953125,
0.00438690185546875,
-0.030670166015625,
0.016754150390625,
0.033416748046875,
-0.01540374755859375,
-0.004985809326171875,
-0.0205078125,
-0.011566162109375,
-0.0103912353515625,
-0.0015621185302734375,
-0.003993988037109375,
0.01605224609375,
0.006378173828125,
0.005184173583984375,
0.00479888916015625,
0.0248565673828125,
0.0225372314453125,
-0.006008148193359375,
-0.034271240234375,
-0.012847900390625,
-0.00959014892578125,
-0.004360198974609375,
-0.020355224609375,
-0.021392822265625,
0.053619384765625,
0.02435302734375,
-0.02069091796875,
-0.044647216796875,
0.0305938720703125,
0.004878997802734375,
-0.003627777099609375,
0.0276336669921875,
-0.0018825531005859375,
0.0167999267578125,
0.0284423828125,
0.01531982421875,
-0.01268768310546875,
-0.0150146484375,
-0.02691650390625,
0.045867919921875,
-0.006031036376953125,
-0.00988006591796875,
0.034027099609375,
0.00445556640625,
0.023834228515625,
0.0005192756652832031,
0.031646728515625,
0.00946044921875,
-0.0235137939453125,
-0.0189208984375,
0.004573822021484375,
-0.0016765594482421875,
0.0203704833984375,
0.0281982421875,
0.0107421875,
-0.0379638671875,
0.006465911865234375,
-0.000018298625946044922,
0.00606536865234375,
0.00553131103515625,
0.00251007080078125,
0.0004394054412841797,
0.024200439453125,
-0.000530242919921875,
-0.013336181640625,
-0.016021728515625,
0.0196685791015625,
0.021209716796875,
-0.05511474609375,
0.0166168212890625,
-0.00284576416015625,
0.0058441162109375,
0.0072021484375,
0.01129913330078125,
-0.021728515625,
0.016265869140625,
0.031097412109375,
-0.004947662353515625,
-0.0208587646484375,
-0.0021514892578125,
0.015045166015625,
0.037261962890625,
0.00939178466796875,
-0.0149078369140625,
-0.0223388671875,
-0.00437164306640625,
-0.035919189453125,
0.03515625,
-0.02679443359375,
-0.0018815994262695312,
-0.0216064453125,
-0.00574493408203125,
0.000675201416015625,
0.02911376953125,
0.008636474609375,
-0.0044403076171875,
0.005321502685546875,
0.03851318359375,
0.01043701171875,
0.004215240478515625,
-0.01202392578125,
-0.00435638427734375,
0.0443115234375,
0.00667572021484375,
0.0305633544921875,
0.0224151611328125,
-0.0299835205078125,
-0.0161590576171875,
-0.00223541259765625,
-0.00942230224609375,
0.0009717941284179688,
0.044097900390625,
-0.0199432373046875,
0.0267333984375,
0.0064697265625,
-0.01403045654296875,
0.0077972412109375,
0.01203155517578125,
-0.0088043212890625,
0.04217529296875,
0.00016832351684570312,
0.009429931640625,
-0.01117706298828125,
-0.0012750625610351562,
-0.038238525390625,
0.0109405517578125,
-0.0009899139404296875,
0.02777099609375,
0.016876220703125,
0.013641357421875,
-0.0237884521484375,
0.0182342529296875,
-0.011688232421875,
0.0029449462890625,
-0.0146942138671875,
0.00012731552124023438,
-0.0078582763671875,
0.002445220947265625,
0.0019168853759765625,
-0.043701171875,
0.00330352783203125,
-0.003177642822265625,
0.0433349609375,
0.01381683349609375,
0.0251617431640625,
0.042236328125,
0.01519012451171875,
-0.01428985595703125,
-0.022674560546875,
0.021697998046875,
0.01401519775390625,
-0.00836944580078125,
-0.0215606689453125,
-0.0309600830078125,
-0.018585205078125,
0.035247802734375,
0.0284881591796875,
-0.017852783203125,
0.0239410400390625,
-0.0011920928955078125,
0.001857757568359375,
-0.021881103515625,
0.0072784423828125,
0.0001277923583984375,
0.018524169921875,
-0.0093231201171875,
0.024810791015625,
-0.034576416015625,
0.0134429931640625,
-0.0032062530517578125,
0.0114288330078125,
0.0019512176513671875,
0.0305633544921875,
-0.003993988037109375,
-0.007045745849609375,
-0.0220489501953125,
0.005062103271484375,
0.031402587890625,
0.008087158203125,
-0.00472259521484375,
0.0122833251953125,
-0.0028591156005859375,
-0.01806640625,
-0.04052734375,
-0.00762176513671875,
-0.0065460205078125,
0.00264739990234375,
-0.048370361328125,
0.0041656494140625,
-0.029083251953125,
0.0224761962890625,
-0.01873779296875,
0.0003790855407714844,
0.01654052734375,
-0.005970001220703125,
-0.01580810546875,
0.0160064697265625,
0.00212860107421875,
-0.0283660888671875,
-0.00409698486328125,
-0.0042572021484375,
-0.0292205810546875,
-0.01468658447265625,
0.0011796951293945312,
0.0140380859375,
-0.01322174072265625,
0.01299285888671875,
0.02581787109375,
-0.005489349365234375,
0.012481689453125,
0.01380157470703125,
0.01157379150390625,
-0.038970947265625,
-0.0036449432373046875,
-0.0142974853515625,
-0.04437255859375,
0.032318115234375,
-0.005229949951171875,
0.028411865234375,
-0.025787353515625,
0.01036834716796875,
0.038604736328125,
0.03375244140625,
0.036102294921875,
-0.000008761882781982422,
-0.0231475830078125,
0.0236358642578125,
-0.00479888916015625,
0.0106964111328125,
0.01409912109375,
-0.019378662109375,
0.02490234375,
0.0023193359375,
0.0027008056640625,
0.02679443359375,
-0.0031375885009765625,
-0.01218414306640625,
-0.007904052734375,
-0.01194000244140625,
-0.0007333755493164062,
-0.004314422607421875,
0.01611328125,
0.00997161865234375,
-0.0275115966796875,
-0.01251983642578125,
-0.0188751220703125,
0.018157958984375,
-0.0017156600952148438,
-0.0218505859375,
-0.02435302734375,
-0.01171112060546875,
-0.0231781005859375,
-0.01099395751953125,
0.026885986328125,
-0.025604248046875,
0.016571044921875,
-0.034820556640625,
-0.01366424560546875,
-0.03375244140625,
-0.018035888671875,
-0.00130462646484375,
0.00829315185546875,
-0.032440185546875,
-0.000054001808166503906,
-0.0120086669921875,
-0.0192718505859375,
-0.0038204193115234375,
-0.0018148422241210938,
-0.0167388916015625,
0.01251220703125,
-0.00572967529296875,
0.0210418701171875,
0.0167999267578125,
-0.0169219970703125,
-0.008697509765625,
0.0173492431640625,
0.05670166015625,
0.0007295608520507812,
-0.01302337646484375,
-0.007595062255859375,
0.015625,
0.0233306884765625,
-0.0095367431640625,
0.01346588134765625,
0.0325927734375,
-0.0164337158203125,
0.016357421875,
0.01531219482421875,
-0.004558563232421875,
-0.00909423828125,
-0.015289306640625,
-0.0164337158203125,
0.01499176025390625,
-0.007354736328125,
0.0252838134765625,
-0.01195526123046875,
0.004547119140625,
0.017333984375,
-0.02069091796875,
0.04486083984375,
0.008148193359375,
0.0288543701171875,
-0.003017425537109375,
0.0256195068359375,
-0.0254974365234375,
-0.0116424560546875,
0.02642822265625,
-0.06951904296875,
0.0196533203125,
0.0102081298828125,
0.036346435546875,
-0.01268768310546875,
-0.01433563232421875,
-0.01340484619140625,
-0.004901885986328125,
-0.00867462158203125,
-0.00818634033203125,
-0.01464080810546875,
-0.0208892822265625,
0.011474609375,
0.0010528564453125,
-0.0039825439453125,
0.016387939453125,
0.0026226043701171875,
-0.0031490325927734375,
-0.0096588134765625,
0.009857177734375,
-0.010833740234375,
0.0046539306640625,
-0.00582122802734375,
0.0301971435546875,
-0.028167724609375,
-0.01495361328125,
-0.0116119384765625,
0.0462646484375,
-0.032257080078125,
-0.004547119140625,
-0.0003139972686767578,
0.0035648345947265625,
0.007843017578125,
-0.0009717941284179688,
-0.059173583984375,
-0.0478515625,
-0.0213165283203125,
-0.015106201171875,
0.0232391357421875,
0.034942626953125,
0.00799560546875,
0.013763427734375,
-0.01103973388671875,
0.01161956787109375,
0.007732391357421875,
0.004974365234375,
-0.00797271728515625,
0.006488800048828125,
-0.014801025390625,
0.01082611083984375,
0.01039886474609375,
0.001220703125,
-0.024261474609375,
0.0081939697265625,
0.01219940185546875,
-0.0190887451171875,
0.01328277587890625,
-0.0263824462890625,
-0.00494384765625,
0.003475189208984375,
-0.015869140625,
-0.042999267578125,
-0.0260772705078125,
0.01611328125,
0.020172119140625,
0.0007901191711425781,
0.027496337890625,
0.0214385986328125,
-0.020233154296875,
0.030029296875,
-0.01560211181640625,
-0.010833740234375,
-0.01097869873046875,
-0.00876617431640625,
-0.007472991943359375,
-0.0221405029296875,
0.038909912109375,
0.007732391357421875,
0.01490020751953125,
0.003887176513671875,
0.01119232177734375,
0.003818511962890625,
-0.0246124267578125,
0.01422119140625,
0.007038116455078125,
0.05670166015625,
0.0169677734375,
0.00991058349609375,
0.014434814453125,
-0.0102386474609375,
0.00006753206253051758,
-0.0039005279541015625,
-0.00775146484375,
-0.012542724609375,
0.0001385211944580078,
-0.0257415771484375,
-0.040008544921875,
-0.0007190704345703125,
-0.024017333984375,
0.017425537109375,
0.0270538330078125,
-0.006855010986328125,
-0.026580810546875,
-0.0206756591796875,
-0.0010080337524414062,
0.007259368896484375,
-0.013580322265625,
0.007518768310546875,
-0.0281982421875,
0.0011768341064453125,
-0.016326904296875,
0.0121917724609375,
-0.0035572052001953125,
0.0054473876953125,
-0.0105133056640625,
-0.00012981891632080078,
-0.01068878173828125,
0.0047760009765625,
0.005573272705078125,
0.0159149169921875,
-0.0099029541015625,
-0.03704833984375,
-0.00305938720703125,
-0.005657196044921875,
-0.00710296630859375,
0.017791748046875,
-0.006855010986328125,
0.01873779296875,
-0.0077972412109375,
-0.03515625,
-0.0162811279296875,
-0.016998291015625,
0.030242919921875,
0.0169830322265625,
0.0117034912109375,
-0.037261962890625,
-0.019287109375,
-0.0180206298828125,
0.0144500732421875,
0.0013628005981445312,
-0.0144195556640625,
-0.0160064697265625,
-0.0162506103515625,
-0.0039825439453125,
-0.01800537109375,
0.0034198760986328125,
0.0113067626953125,
0.003849029541015625,
0.00966644287109375,
-0.005977630615234375,
-0.0164642333984375,
-0.01274871826171875,
-0.03656005859375,
-0.0082244873046875,
0.0011167526245117188,
0.00821685791015625,
-0.021697998046875,
0.0122222900390625,
0.0001512765884399414,
0.031982421875,
0.01348876953125,
0.0023956298828125,
0.04791259765625,
-0.007549285888671875,
-0.055419921875,
0.0016632080078125,
-0.0283355712890625,
0.0177154541015625,
-0.004207611083984375,
0.011932373046875,
-0.0032558441162109375,
0.01403045654296875,
-0.0084991455078125,
-0.0482177734375,
0.023468017578125,
-0.0177001953125,
0.015167236328125,
0.00756072998046875,
0.03607177734375,
0.00241851806640625,
-0.024688720703125,
-0.01085662841796875,
-0.0185394287109375,
0.00476837158203125,
0.0139007568359375,
-0.007843017578125,
-0.0228729248046875,
0.0218048095703125,
0.01163482666015625,
-0.0204620361328125,
0.0228729248046875,
0.0191650390625,
0.002902984619140625,
-0.004291534423828125,
-0.0217742919921875,
-0.0145721435546875,
0.02191162109375,
0.01030731201171875,
0.00534820556640625,
0.01557159423828125,
0.0301971435546875,
0.01271820068359375,
-0.0299530029296875,
-0.0011606216430664062,
-0.026641845703125,
0.046478271484375,
-0.01496124267578125,
-0.00818634033203125,
-0.047027587890625,
0.0168304443359375,
-0.027008056640625,
0.0007824897766113281,
-0.0116119384765625,
-0.01059722900390625,
-0.0240631103515625,
0.0129852294921875,
-0.03143310546875,
-0.0151824951171875,
-0.01511383056640625,
-0.047454833984375,
0.01311492919921875,
-0.019989013671875,
-0.01788330078125,
-0.0269012451171875,
0.00438690185546875,
0.0177001953125,
-0.0032138824462890625,
-0.014373779296875,
0.001605987548828125,
0.041473388671875,
0.01390838623046875,
0.006153106689453125,
0.038299560546875,
-0.01171112060546875,
-0.044158935546875,
-0.002727508544921875,
-0.019500732421875,
-0.0088348388671875,
0.0156097412109375,
0.0030155181884765625,
-0.00498199462890625,
0.01311492919921875,
0.029266357421875,
0.0214996337890625,
-0.01120758056640625,
-0.0117950439453125,
-0.024078369140625,
0.016632080078125,
-0.01320648193359375,
0.038238525390625,
-0.037841796875,
-0.0124359130859375,
-0.010894775390625,
0.0262908935546875,
0.0171661376953125,
0.033843994140625,
-0.00730133056640625,
-0.0186920166015625,
-0.01116180419921875,
0.042755126953125,
-0.0260772705078125,
-0.00566864013671875,
-0.0238494873046875,
0.004535675048828125,
-0.01849365234375,
0.004001617431640625,
0.042388916015625,
-0.045257568359375,
0.03204345703125,
0.0142059326171875,
0.0203704833984375,
0.0416259765625,
-0.01274871826171875,
-0.007843017578125,
0.0195465087890625,
0.013763427734375,
-0.0006794929504394531,
-0.0266876220703125,
0.0149688720703125,
-0.0130462646484375,
-0.0175628662109375,
-0.0250244140625,
0.00942230224609375,
0.02392578125,
0.0281829833984375,
-0.0107574462890625,
-0.0036983489990234375,
0.006404876708984375,
-0.0221099853515625,
-0.01206207275390625,
-0.0171051025390625,
0.01070404052734375,
0.00817108154296875,
-0.03533935546875,
-0.0047607421875,
0.00620269775390625,
0.0014200210571289062,
0.012115478515625,
-0.04901123046875,
-0.0253448486328125,
-0.01515960693359375,
-0.00922393798828125,
-0.0107269287109375,
0.04241943359375,
-0.00408172607421875,
0.0295562744140625,
0.003772735595703125,
-0.0124969482421875,
0.041259765625,
-0.0087738037109375,
-0.032318115234375,
-0.004825592041015625,
-0.019317626953125,
-0.0380859375,
-0.0034503936767578125,
-0.019439697265625,
-0.035369873046875,
0.0008325576782226562,
0.0252838134765625,
-0.032623291015625,
-0.00981903076171875,
0.00455474853515625,
-0.006137847900390625,
-0.012664794921875,
0.04119873046875,
0.02813720703125,
-0.00130462646484375,
0.019744873046875,
0.0142974853515625,
0.01519012451171875,
0.00543212890625,
-0.009368896484375,
-0.0215301513671875,
-0.0162506103515625,
-0.0174102783203125,
-0.0279998779296875,
0.0303955078125,
-0.00795745849609375,
0.00482177734375,
0.0103607177734375,
-0.0036182403564453125,
0.000034809112548828125,
0.037261962890625,
-0.0123748779296875,
-0.018585205078125,
-0.0279388427734375,
-0.0167999267578125,
-0.0100250244140625,
-0.0136871337890625,
-0.0188446044921875,
-0.0173797607421875,
-0.0132293701171875,
0.00341033935546875,
-0.0021877288818359375,
0.022979736328125,
0.00733184814453125,
0.042724609375,
0.00855255126953125,
0.0010194778442382812,
-0.00855255126953125,
0.00844573974609375,
0.017303466796875,
-0.0272674560546875,
0.01335906982421875,
0.0104217529296875,
-0.0091094970703125,
-0.01427459716796875,
0.0063934326171875,
-0.01451873779296875,
-0.031890869140625,
-0.01274871826171875,
0.003910064697265625,
0.021087646484375,
0.0322265625,
-0.0011148452758789062,
0.00949859619140625,
-0.0244140625,
-0.005596160888671875,
-0.0301971435546875,
-0.02105712890625,
-0.0043792724609375,
0.0231781005859375,
0.0032978057861328125,
-0.0011119842529296875,
-0.023895263671875,
0.02545166015625,
0.01294708251953125,
-0.01210784912109375,
0.004062652587890625,
-0.0217742919921875,
-0.0008749961853027344,
-0.01049041748046875,
-0.01407623291015625,
-0.01251220703125,
0.0297698974609375,
-0.0066070556640625,
0.01195526123046875,
-0.01445770263671875,
-0.00022602081298828125,
0.0095062255859375,
0.024444580078125,
-0.00800323486328125,
-0.0265350341796875,
-0.013763427734375,
-0.01371002197265625,
0.004665374755859375,
-0.0009593963623046875,
-0.014404296875,
-0.0185394287109375,
-0.0065765380859375,
-0.0204315185546875,
0.028533935546875,
0.0118255615234375,
0.0271453857421875,
-0.01593017578125,
0.00460052490234375,
0.01021575927734375,
-0.0259246826171875,
-0.002727508544921875,
0.022613525390625,
-0.0009031295776367188,
-0.041412353515625,
0.01031494140625,
-0.037445068359375,
0.01141357421875,
0.0294189453125,
-0.010040283203125,
0.01190185546875,
-0.00640869140625,
-0.01502227783203125,
0.02734375,
0.025054931640625,
-0.0254669189453125,
0.01454925537109375,
-0.00872802734375,
-0.00879669189453125,
-0.0148773193359375,
-0.007190704345703125,
0.004116058349609375,
0.00231170654296875,
0.0030155181884765625,
0.0042266845703125,
0.007965087890625,
-0.0015287399291992188,
0.00421905517578125,
0.01317596435546875,
-0.0095672607421875,
-0.00994873046875,
0.0009222030639648438,
-0.0108642578125,
0.00011026859283447266,
0.0029296875,
-0.0043487548828125,
-0.0487060546875,
0.026031494140625,
0.0025920867919921875,
-0.0016202926635742188,
0.000047206878662109375,
-0.00750732421875,
0.01499176025390625,
-0.0162353515625,
0.031646728515625,
0.028533935546875,
0.03857421875,
0.0102996826171875,
0.0010881423950195312,
-0.00643157958984375,
-0.0192413330078125,
0.021392822265625,
-0.002285003662109375,
-0.003204345703125,
0.0006537437438964844,
-0.032806396484375,
-0.00652313232421875,
-0.006984710693359375,
-0.01342010498046875,
-0.0176544189453125,
-0.01104736328125,
-0.0031566619873046875,
0.01030731201171875,
-0.006175994873046875,
-0.015777587890625,
-0.0213470458984375,
0.0167083740234375,
0.0003693103790283203,
0.03570556640625,
0.05218505859375,
0.01239776611328125,
0.0284271240234375,
0.0206451416015625,
-0.0204925537109375,
0.0015516281127929688,
0.0017232894897460938,
-0.027801513671875,
0.0194091796875,
-0.007358551025390625,
0.005092620849609375,
0.026214599609375,
0.002216339111328125,
-0.010345458984375,
-0.00600433349609375,
0.0260009765625,
-0.002079010009765625,
-0.044921875,
-0.004276275634765625,
0.0032558441162109375,
-0.004085540771484375,
-0.042205810546875,
-0.004108428955078125,
0.0282440185546875,
0.000028252601623535156,
-0.0205230712890625,
0.009796142578125,
0.0262298583984375,
0.01067352294921875,
0.0013942718505859375,
-0.01104736328125,
0.01270294189453125,
-0.02484130859375,
0.0002472400665283203,
0.0240020751953125,
0.006072998046875,
-0.0013608932495117188,
-0.0227203369140625,
-0.0178680419921875,
0.0022945404052734375,
-0.00335693359375,
0.026641845703125,
-0.006267547607421875,
-0.0035991668701171875,
0.00821685791015625,
-0.00821685791015625,
0.0241241455078125,
-0.0115966796875,
0.00196075439453125,
0.061279296875,
-0.0299224853515625,
-0.007122039794921875,
0.0224609375,
0.004131317138671875,
0.003528594970703125,
-0.0030460357666015625,
0.021636962890625,
0.0242156982421875,
-0.021697998046875,
-0.0212554931640625,
0.00492095947265625,
-0.019805908203125,
0.0016813278198242188,
0.004302978515625,
-0.023681640625,
0.0165252685546875,
-0.00738525390625,
-0.02508544921875,
0.03631591796875,
0.003505706787109375,
-0.006031036376953125,
-0.0026378631591796875,
0.00946807861328125,
-0.00417327880859375,
0.00039267539978027344,
-0.0246429443359375,
-0.0135345458984375,
-0.0060577392578125,
0.0138397216796875,
0.0156707763671875,
0.0212554931640625,
-0.03875732421875,
0.0335693359375,
0.0297088623046875,
0.0075836181640625,
0.01336669921875,
-0.00458526611328125,
-0.01015472412109375,
-0.00623321533203125,
0.0279541015625,
0.0104217529296875,
-0.02410888671875,
0.02203369140625,
0.027130126953125,
0.01012420654296875,
0.004787445068359375,
-0.0164947509765625,
0.0246124267578125,
-0.0244140625,
0.017822265625,
-0.002681732177734375,
0.00904083251953125,
-0.01441192626953125,
-0.04193115234375,
-0.00859832763671875,
0.020050048828125,
0.0029354095458984375,
-0.01241302490234375,
-0.0026340484619140625,
0.0286865234375,
-0.0120697021484375,
-0.025665283203125,
0.00757598876953125,
-0.026702880859375,
0.01171875,
0.0023345947265625,
-0.0264129638671875,
-0.017120361328125,
0.0132293701171875,
-0.0006222724914550781,
-0.006343841552734375,
-0.02557373046875,
0.05230712890625,
-0.00030875205993652344,
-0.006862640380859375,
-0.0029296875,
0.006229400634765625,
0.006214141845703125,
0.01265716552734375,
-0.015655517578125,
-0.0021190643310546875,
0.00872802734375,
-0.010284423828125,
0.027557373046875,
-0.00629425048828125,
-0.0154266357421875,
-0.007373809814453125,
0.016357421875,
0.010955810546875,
-0.0162200927734375,
-0.005947113037109375,
0.00911712646484375,
0.00754547119140625,
-0.0281829833984375,
-0.009429931640625,
0.004474639892578125,
-0.0009641647338867188,
-0.006336212158203125,
0.00861358642578125,
-0.0203399658203125,
0.022369384765625,
-0.03082275390625,
0.01904296875,
0.01690673828125,
-0.0084075927734375,
-0.00121307373046875,
-0.0200958251953125,
-0.0097198486328125,
0.04705810546875,
0.0002582073211669922,
0.0278167724609375,
0.00603485107421875,
-0.0084228515625,
0.044647216796875,
-0.0238189697265625,
0.008514404296875,
0.01509857177734375,
-0.012725830078125,
-0.0029582977294921875,
0.00473785400390625,
-0.03839111328125,
-0.0003361701965332031,
-0.005985260009765625,
-0.00446319580078125,
0.0031795501708984375,
-0.0153961181640625,
-0.003368377685546875,
0.024993896484375,
-0.035491943359375,
0.0537109375,
0.0231475830078125,
0.0022754669189453125,
0.01274871826171875,
-0.0260009765625,
0.01428985595703125,
-0.00034689903259277344,
-0.0179595947265625,
0.008453369140625,
0.0050811767578125,
-0.0021152496337890625,
-0.0269317626953125,
0.01348876953125,
0.0060882568359375,
-0.0274505615234375,
0.0023288726806640625,
-0.01345062255859375,
0.006439208984375,
0.0009899139404296875,
-0.00823211669921875,
-0.042633056640625,
0.001338958740234375,
-0.0254974365234375,
-0.01174163818359375,
0.0222320556640625,
0.0208587646484375,
0.0205535888671875,
-0.0172882080078125,
-0.01215362548828125,
-0.0002524852752685547,
0.01465606689453125,
-0.018646240234375,
0.003192901611328125,
0.0221710205078125,
0.006496429443359375,
0.0169219970703125,
-0.0005559921264648438,
-0.007068634033203125,
0.0007643699645996094,
0.01303863525390625,
0.01983642578125,
0.01410675048828125,
-0.00496673583984375,
0.0019588470458984375,
0.0168609619140625,
-0.0182647705078125,
-0.0191802978515625,
-0.01082611083984375,
0.0279083251953125,
0.0189666748046875,
-0.0113372802734375,
-0.00983428955078125,
0.01727294921875,
-0.0092620849609375,
0.0306854248046875,
-0.01187896728515625,
-0.0396728515625,
0.042083740234375,
-0.0049591064453125,
-0.01125335693359375,
-0.034393310546875,
0.007659912109375,
-0.0139312744140625,
-0.016265869140625,
-0.01727294921875,
-0.00399017333984375,
-0.00588226318359375,
-0.039520263671875,
0.0028171539306640625,
-0.010986328125,
0.0151824951171875,
-0.032958984375,
-0.004344940185546875,
-0.0182342529296875,
0.03350830078125,
0.00006633996963500977,
-0.0088348388671875,
0.055908203125,
-0.006259918212890625,
-0.003696441650390625,
-0.0027484893798828125,
0.0352783203125,
0.053924560546875,
-0.0108184814453125,
0.033416748046875,
-0.024169921875,
-0.0169677734375,
-0.00777435302734375,
-0.00044918060302734375,
0.0030670166015625,
0.01045989990234375,
0.00301361083984375,
0.006061553955078125,
0.00524139404296875,
0.017669677734375,
-0.01287841796875,
0.00948333740234375,
-0.0166778564453125,
0.02197265625,
-0.0167388916015625,
0.004669189453125,
-0.024261474609375,
-0.0012998580932617188,
-0.015869140625,
-0.02362060546875,
-0.0093994140625,
-0.01430511474609375,
-0.024139404296875,
0.0241851806640625,
0.02471923828125,
0.025604248046875,
-0.023956298828125,
-0.013885498046875,
0.03265380859375,
-0.02032470703125,
0.0282135009765625,
-0.0017976760864257812,
-0.019439697265625,
-0.0092010498046875,
0.0070037841796875,
0.007076263427734375,
-0.007671356201171875,
-0.0189361572265625,
0.009490966796875,
-0.01297760009765625,
-0.026824951171875,
0.005615234375,
-0.00881195068359375,
0.017486572265625,
-0.0008225440979003906,
0.0151824951171875,
0.0263824462890625,
-0.00138092041015625,
0.0152740478515625,
0.003978729248046875,
0.01137542724609375,
-0.01061248779296875,
-0.0199737548828125,
0.0194854736328125,
-0.010467529296875,
0.0240936279296875,
0.01374053955078125,
-0.035125732421875,
-0.0014276504516601562,
-0.00484466552734375,
0.05218505859375,
0.005401611328125,
-0.01013946533203125,
0.0201263427734375,
0.00899505615234375,
0.0023937225341796875,
0.0010318756103515625,
0.0200958251953125,
-0.0169219970703125,
0.0204925537109375,
-0.0128936767578125,
0.0064544677734375,
-0.00023543834686279297,
0.050201416015625,
-0.011138916015625,
-0.006221771240234375,
-0.01096343994140625,
0.01474761962890625,
0.0021305084228515625,
-0.04034423828125,
-0.01013946533203125,
-0.006313323974609375,
-0.0302734375,
0.029022216796875,
0.003875732421875,
0.045013427734375,
0.0196075439453125,
0.0006437301635742188,
-0.0016298294067382812,
0.0034503936767578125,
0.036590576171875,
-0.0017042160034179688,
0.0011129379272460938,
0.01483154296875,
0.0110321044921875,
0.01342010498046875,
-0.035369873046875,
-0.02532958984375,
0.021820068359375,
0.0240478515625,
-0.0162811279296875,
0.04986572265625,
-0.0003559589385986328,
0.0126953125,
-0.00586700439453125,
-0.00321197509765625,
0.0041961669921875,
-0.0014486312866210938,
0.013580322265625,
-0.008697509765625,
0.0250244140625,
-0.00920867919921875,
0.01177978515625,
-0.0071563720703125,
0.0019989013671875,
0.00708770751953125,
0.0166473388671875,
-0.0157470703125,
-0.0131988525390625,
-0.0163116455078125,
-0.0169219970703125,
-0.023895263671875,
-0.0284423828125,
-0.0060577392578125,
-0.0027065277099609375,
-0.0167999267578125,
0.00936126708984375,
-0.004207611083984375,
0.01367950439453125,
-0.0169830322265625,
-0.0224456787109375,
-0.036773681640625,
-0.01204681396484375,
-0.0128021240234375,
0.032989501953125,
-0.026336669921875,
-0.04339599609375,
0.011688232421875,
0.005107879638671875,
-0.0276336669921875,
0.01224517822265625,
0.0200958251953125,
0.032073974609375,
-0.028106689453125,
0.0302886962890625,
0.00537872314453125,
-0.00669097900390625,
-0.0252227783203125,
-0.01043701171875,
0.005825042724609375,
-0.0084228515625,
0.030181884765625,
0.037750244140625,
-0.0203857421875,
0.0270233154296875,
-0.031097412109375,
-0.01103973388671875,
0.01552581787109375,
-0.01348114013671875,
-0.0731201171875,
0.028045654296875,
-0.0190887451171875,
-0.003589630126953125,
0.01580810546875,
0.039215087890625,
-0.035736083984375,
-0.0107269287109375,
-0.0183563232421875,
0.012359619140625,
-0.0007786750793457031,
0.035552978515625,
0.0014848709106445312,
-0.01001739501953125,
0.012603759765625,
0.0271453857421875,
0.0027217864990234375,
-0.016082763671875,
-0.017333984375,
0.00858306884765625,
-0.033782958984375,
-0.003997802734375,
0.0003094673156738281,
-0.0250244140625,
0.052825927734375,
-0.0225372314453125,
-0.01812744140625,
0.00174713134765625,
0.026641845703125,
-0.0013561248779296875,
-0.023773193359375,
0.00018143653869628906,
-0.0011548995971679688,
-0.03961181640625,
0.0130157470703125,
0.005268096923828125,
-0.003971099853515625,
0.0008182525634765625,
0.0146026611328125,
0.03033447265625,
-0.0095977783203125,
0.00800323486328125,
0.03387451171875,
0.022186279296875,
-0.0003025531768798828,
-0.00400543212890625,
-0.0105133056640625,
0.0177764892578125,
-0.005924224853515625,
-0.018310546875,
-0.00730133056640625,
0.015869140625,
-0.0098876953125,
0.005931854248046875,
0.014068603515625,
0.0009379386901855469,
0.01398468017578125,
-0.00095367431640625,
0.0039825439453125,
0.016021728515625,
0.02459716796875,
-0.0088348388671875,
-0.0204925537109375,
0.0216522216796875,
0.0190277099609375,
0.0027828216552734375,
0.0014162063598632812,
-0.00434112548828125,
0.01202392578125,
0.0213623046875,
0.0126495361328125,
0.0164642333984375,
0.01328277587890625,
0.0118255615234375,
0.038726806640625,
-0.049896240234375,
-0.0042724609375,
0.004047393798828125,
0.0008187294006347656,
-0.0104827880859375,
-0.011688232421875,
-0.00701904296875,
0.0149993896484375,
0.0282745361328125,
-0.030914306640625,
-0.0162811279296875,
0.012542724609375,
0.013092041015625,
-0.00412750244140625,
-0.0574951171875,
0.0136871337890625,
0.01971435546875,
0.00011396408081054688,
-0.00908660888671875,
-0.0228271484375,
-0.0255889892578125,
0.0009756088256835938,
-0.006786346435546875,
-0.0029926300048828125,
0.0022258758544921875,
-0.0014400482177734375,
-0.019744873046875,
0.01483917236328125,
0.0170440673828125,
0.00004404783248901367,
0.0036144256591796875,
-0.01201629638671875,
0.06256103515625,
-0.0273590087890625,
-0.040618896484375,
0.0184783935546875,
0.0196075439453125,
0.024688720703125,
0.007625579833984375,
0.048187255859375,
-0.004791259765625,
-0.0230560302734375,
-0.003658294677734375,
0.0035228729248046875,
0.0041961669921875,
-0.020050048828125,
0.016998291015625,
-0.01161956787109375,
0.04345703125,
0.042236328125,
0.006923675537109375,
-0.00788116455078125,
0.035003662109375,
-0.0163116455078125,
0.01499176025390625,
0.0200958251953125,
-0.003658294677734375,
-0.00926971435546875,
0.0189971923828125,
-0.007297515869140625,
-0.0240020751953125,
0.0007610321044921875,
-0.007366180419921875,
-0.01074981689453125,
-0.02069091796875,
0.0245819091796875,
0.007965087890625,
0.036865234375,
0.00662994384765625,
0.000012755393981933594,
-0.00566864013671875,
-0.0272064208984375,
-0.03485107421875,
0.0181732177734375,
0.0053863525390625,
-0.02728271484375,
0.0004811286926269531,
-0.006195068359375,
-0.0009918212890625,
0.01047515869140625,
0.007450103759765625,
-0.0017919540405273438,
0.003986358642578125,
-0.00795745849609375,
-0.007297515869140625,
0.019439697265625,
-0.0240631103515625,
-0.0110015869140625,
0.017059326171875,
0.024383544921875,
-0.021942138671875,
-0.018280029296875,
0.000049591064453125,
0.0140380859375,
0.0237579345703125,
-0.0223846435546875,
-0.0039215087890625,
0.00656890869140625,
0.03076171875,
0.003269195556640625,
-0.01316070556640625,
-0.02294921875,
0.00019240379333496094,
-0.0198974609375,
-0.0147247314453125,
-0.01381683349609375,
-0.003925323486328125,
0.0030517578125,
-0.0025424957275390625,
-0.00952911376953125,
-0.0196075439453125,
0.0126495361328125,
0.015899658203125,
0.017822265625,
0.0033168792724609375,
0.040924072265625,
-0.032684326171875,
0.00879669189453125,
0.00939178466796875,
0.0309600830078125,
0.01291656494140625,
0.044464111328125,
0.0501708984375,
0.016021728515625,
0.0004253387451171875,
-0.027374267578125,
0.0224151611328125,
0.007617950439453125,
0.020538330078125,
0.0021877288818359375,
0.01483917236328125,
0.0023250579833984375,
0.046142578125,
-0.00024187564849853516,
0.01139068603515625,
-0.00859832763671875,
-0.027984619140625,
0.0233154296875,
-0.01349639892578125,
-0.0195465087890625,
0.0097198486328125,
-0.023529052734375,
-0.003948211669921875,
-0.01279449462890625,
-0.0233917236328125,
0.0191497802734375,
-0.0003578662872314453,
0.01349639892578125,
-0.008544921875,
0.0012559890747070312,
0.0275421142578125,
-0.0205535888671875,
0.03436279296875,
0.0258026123046875,
-0.006282806396484375,
0.0213470458984375,
0.01073455810546875,
-0.0165557861328125,
0.010955810546875,
-0.0024929046630859375,
-0.0106048583984375,
0.00986480712890625,
0.013031005859375,
0.0005168914794921875,
0.00974273681640625,
-0.002780914306640625,
0.029266357421875,
-0.0012054443359375,
0.013458251953125,
-0.0377197265625,
-0.004779815673828125,
0.0511474609375,
-0.021881103515625,
0.037353515625,
-0.024658203125,
-0.0030460357666015625,
-0.005619049072265625,
0.00795745849609375,
-0.0054473876953125,
-0.00836181640625,
0.032867431640625,
0.01447296142578125,
0.00841522216796875,
0.004241943359375,
-0.01413726806640625,
0.0119171142578125,
-0.01580810546875,
-0.002353668212890625,
0.004154205322265625,
-0.01474761962890625,
-0.0299072265625,
0.009979248046875,
-0.01171875,
0.021881103515625,
0.007633209228515625,
-0.004581451416015625,
0.01806640625,
0.00464630126953125,
-0.0272216796875,
-0.0122528076171875,
-0.0209808349609375,
-0.0225372314453125,
-0.016845703125,
-0.000797271728515625,
-0.01531982421875,
-0.0180816650390625,
0.0174102783203125,
0.0089111328125,
0.0146026611328125,
-0.027252197265625,
-0.0112152099609375,
-0.0261077880859375,
-0.04571533203125,
0.0177459716796875,
0.003086090087890625,
-0.004375457763671875,
-0.014923095703125,
-0.00800323486328125,
0.01251983642578125,
-0.0002772808074951172,
-0.028900146484375,
-0.006725311279296875,
0.016387939453125,
-0.0083465576171875,
-0.0144805908203125,
0.00704193115234375,
-0.004711151123046875,
0.00031256675720214844,
-0.00849151611328125,
0.0170745849609375,
0.020965576171875,
0.0010395050048828125,
0.024658203125,
0.0098114013671875,
0.020263671875,
-0.0119781494140625,
0.0307769775390625,
0.02734375,
-0.043426513671875,
-0.036590576171875,
-0.027862548828125,
-0.0116424560546875,
-0.01345062255859375,
-0.01983642578125,
-0.026947021484375,
-0.0092926025390625,
-0.0001589059829711914,
-0.002986907958984375,
-0.0118408203125,
-0.031524658203125,
-0.005229949951171875,
0.041046142578125,
-0.006061553955078125,
-0.043304443359375,
0.0022449493408203125,
0.0259246826171875,
0.00592041015625,
-0.007610321044921875,
0.00827789306640625,
-0.010528564453125,
0.01050567626953125,
0.01161956787109375,
-0.0065765380859375,
-0.01605224609375,
0.02996826171875,
-0.0249176025390625,
0.0217742919921875,
0.0184783935546875,
-0.015167236328125,
0.01267242431640625,
-0.0055694580078125,
-0.0275115966796875,
-0.0174407958984375,
-0.00445556640625,
-0.0285186767578125,
0.00923919677734375,
-0.00476837158203125,
0.004543304443359375,
0.01174163818359375,
-0.01392364501953125,
0.0204925537109375,
-0.02984619140625,
0.0020809173583984375,
0.029815673828125,
-0.01180267333984375,
0.01190948486328125,
0.00290679931640625,
0.00008368492126464844,
-0.00276947021484375,
-0.00785064697265625,
-0.0312042236328125,
-0.01058197021484375,
0.01062774658203125,
-0.0033016204833984375,
-0.0011463165283203125,
0.0126953125,
0.034088134765625,
-0.0198516845703125,
-0.032318115234375,
-0.01154327392578125,
0.0011301040649414062,
-0.03125,
-0.005329132080078125,
-0.0311737060546875,
0.002880096435546875,
0.00775909423828125,
-0.0124053955078125,
-0.0005850791931152344,
-0.0269622802734375,
0.02288818359375,
0.0210113525390625,
-0.0017747879028320312,
0.044891357421875,
0.01953125,
0.044525146484375,
0.005519866943359375,
-0.0168304443359375,
0.005687713623046875,
-0.0255126953125,
0.0182037353515625,
0.0244293212890625,
-0.0426025390625,
0.053009033203125,
-0.025177001953125,
0.0036602020263671875,
-0.0031375885009765625,
-0.01043701171875,
0.00328826904296875,
0.039154052734375,
0.04473876953125,
-0.030853271484375,
0.047393798828125,
-0.016876220703125,
-0.00305938720703125,
0.014190673828125,
0.01078033447265625,
0.01312255859375,
-0.028045654296875,
0.001972198486328125,
-0.0073699951171875,
0.01509857177734375,
0.028045654296875,
0.05419921875,
0.0017976760864257812,
0.0106201171875,
0.043670654296875,
-0.0016193389892578125,
0.0192718505859375,
-0.039520263671875,
-0.024688720703125,
-0.00569915771484375,
0.0076141357421875,
-0.01763916015625,
0.01175689697265625,
0.032745361328125,
-0.0193328857421875,
-0.006443023681640625,
-0.007152557373046875,
0.02752685546875,
-0.004077911376953125,
0.042938232421875,
0.005706787109375,
-0.0007829666137695312,
0.01493072509765625,
-0.01201629638671875,
0.006420135498046875,
0.0272216796875,
-0.0138092041015625,
0.0089569091796875,
-0.0085601806640625,
0.06756591796875,
0.0175323486328125,
-0.0308380126953125,
0.0168304443359375,
-0.0103759765625,
0.0001888275146484375,
-0.0005197525024414062,
-0.004482269287109375,
-0.035980224609375,
0.007518768310546875,
0.0026950836181640625,
-0.0198974609375,
-0.0181884765625,
0.042449951171875,
-0.01129913330078125,
-0.027069091796875,
-0.002338409423828125,
-0.003345489501953125,
0.01513671875,
-0.039642333984375,
-0.004222869873046875,
-0.022735595703125,
-0.0211334228515625,
0.01206207275390625,
-0.01580810546875,
0.0216827392578125,
0.0638427734375,
-0.0186614990234375,
0.007328033447265625,
-0.0146942138671875,
-0.054168701171875,
0.01314544677734375,
-0.039581298828125,
0.01922607421875,
0.029083251953125,
-0.0090484619140625,
-0.006626129150390625,
-0.0132598876953125,
-0.027801513671875,
0.02569580078125,
-0.0009222030639648438,
0.01202392578125,
0.0003204345703125,
0.0015087127685546875,
0.0173797607421875,
-0.0013990402221679688,
0.00467681884765625,
-0.0244293212890625,
-0.0200042724609375,
-0.00315093994140625,
-0.0181427001953125,
-0.023162841796875,
0.0092315673828125,
-0.011199951171875,
-0.0223846435546875,
-0.046112060546875,
0.01226806640625,
-0.0020580291748046875,
-0.019195556640625,
-0.020416259765625,
-0.0044708251953125,
-0.0004851818084716797,
0.02813720703125,
0.037261962890625,
0.01329803466796875,
-0.023712158203125,
0.01290130615234375,
0.0225982666015625,
0.01264190673828125,
-0.0031986236572265625,
-0.006397247314453125,
-0.00986480712890625,
-0.02935791015625,
-0.00008469820022583008,
-0.0218658447265625,
-0.0236358642578125,
-0.041473388671875,
-0.0158843994140625,
0.0016717910766601562,
0.00960540771484375,
0.03668212890625,
0.006378173828125,
-0.0007734298706054688,
0.0210418701171875,
-0.01776123046875,
0.0069732666015625,
0.00010401010513305664,
-0.03131103515625,
0.007122039794921875,
-0.0333251953125,
-0.0004253387451171875,
0.01235198974609375,
0.0237884521484375,
-0.0296783447265625,
0.0003368854522705078,
0.03515625,
-0.020965576171875,
0.01267242431640625,
-0.01540374755859375,
0.0019254684448242188,
0.0207366943359375,
0.0202484130859375,
0.0112457275390625,
-0.003387451171875,
0.016845703125,
0.002079010009765625,
0.0230560302734375,
0.0160369873046875,
0.00815582275390625,
-0.0010089874267578125,
-0.01511383056640625,
0.0283660888671875,
0.01103973388671875,
-0.032867431640625,
-0.005584716796875,
-0.016845703125,
-0.006969451904296875,
0.00299835205078125,
0.0158843994140625,
0.00799560546875,
0.01442718505859375,
0.0093841552734375,
0.0025482177734375,
-0.01641845703125
] |
ours_491
|
Solution. Taking \( a = b = 2 \) gives \( 432 \leq 16v + w \). By the Cauchy-Schwarz inequality, we have:
\[
62208 = \frac{432^{2}}{3} \leq \frac{(16v + w)^{2}}{(\sqrt{2})^{2} + 1^{2}} \leq (8\sqrt{2}v)^{2} + w^{2} = 128v^{2} + w^{2}
\]
We claim that \( 62208 \) can be achieved with \( v = 18 \) and \( w = 144 \). Note that:
\[
128 \cdot 18^{2} + 144^{2} = 62208
\]
We now show that this choice works. The inequality:
\[
\left(2^{a+b}+8\right)\left(3^{a}+3^{b}\right) \leq 18\left(12^{a-1}+12^{b-1}-2^{a+b-1}\right)+144
\]
is equivalent, after some algebra, to:
\[
\left(2^{a+b+1} + 16\right)\left(3^{a} + 3^{b} + 9\right) \leq 3\left(12^{a} + 12^{b} + 144\right)
\]
Now, \( 2^{a+b+1} \leq 4^{a} + 4^{b} \) by AM-GM, so it suffices to prove:
\[
\left(4^{a} + 4^{b} + 4^{2}\right)\left(3^{a} + 3^{b} + 3^{2}\right) \leq 3\left(12^{a} + 12^{b} + 12^{2}\right)
\]
which is true by Chebyshev's Inequality. Thus, the smallest possible value of \( 128v^{2} + w^{2} \) is \(\boxed{62208}\).
|
62208
|
{
"competition": "us_comps",
"dataset": "Ours",
"posts": null,
"source": "OMOFall19Solns-2.md"
}
|
Let \( v \) and \( w \) be real numbers such that, for all real numbers \( a \) and \( b \), the inequality
\[
\left(2^{a+b}+8\right)\left(3^{a}+3^{b}\right) \leq v\left(12^{a-1}+12^{b-1}-2^{a+b-1}\right)+w
\]
holds. Compute the smallest possible value of \( 128 v^{2}+w^{2} \).
|
[
"/Mathematics/Algebra/AlgebraicIdentities/AlgebraicIdentity",
"/Mathematics/Algebra/GeneralAlgebra/Algebra",
"/Mathematics/Algebra/LinearAlgebra"
] |
Apply Cauchy–Schwarz to the inequality obtained at a = b = 2, turning a linear bound on 16v + w into the quadratic bound 128v² + w².
|
[
-0.00003814697265625,
0.028106689453125,
0.06427001953125,
0.00213623046875,
-0.0005521774291992188,
0.0192108154296875,
0.01174163818359375,
0.0244140625,
0.00412750244140625,
-0.01306915283203125,
0.020233154296875,
-0.01158905029296875,
-0.0032100677490234375,
0.01131439208984375,
-0.002758026123046875,
0.0164947509765625,
0.01042938232421875,
0.0120849609375,
0.0157470703125,
-0.000499725341796875,
-0.01238250732421875,
-0.0150299072265625,
-0.037933349609375,
0.0004417896270751953,
-0.013519287109375,
0.005039215087890625,
-0.0201416015625,
-0.032470703125,
0.05352783203125,
0.02508544921875,
0.01456451416015625,
-0.003040313720703125,
-0.0279083251953125,
-0.029571533203125,
-0.0021991729736328125,
-0.01308441162109375,
0.01291656494140625,
-0.01010894775390625,
0.01233673095703125,
-0.0440673828125,
0.0013980865478515625,
0.01078033447265625,
-0.020233154296875,
-0.0051116943359375,
0.0073089599609375,
0.01389312744140625,
-0.006755828857421875,
-0.00641632080078125,
-0.012054443359375,
-0.00501251220703125,
-0.00494384765625,
0.0050048828125,
0.032867431640625,
-0.0089569091796875,
-0.027130126953125,
-0.04443359375,
0.0191497802734375,
0.0006346702575683594,
-0.012298583984375,
-0.038116455078125,
-0.008026123046875,
0.0113067626953125,
0.0168609619140625,
-0.01262664794921875,
-0.0015916824340820312,
-0.0061798095703125,
-0.0098876953125,
-0.01593017578125,
0.002353668212890625,
0.002666473388671875,
0.01543426513671875,
-0.004932403564453125,
-0.0105438232421875,
0.019775390625,
0.0010929107666015625,
-0.0102691650390625,
-0.0119476318359375,
0.0036983489990234375,
0.0087738037109375,
0.0191497802734375,
0.0221710205078125,
-0.009735107421875,
0.01000213623046875,
-0.0279388427734375,
0.0172119140625,
-0.0006518363952636719,
-0.038818359375,
0.007755279541015625,
0.01157379150390625,
-0.003925323486328125,
-0.01433563232421875,
0.004058837890625,
0.002227783203125,
-0.042327880859375,
-0.003345489501953125,
-0.01044464111328125,
0.003932952880859375,
-0.0019369125366210938,
-0.0109710693359375,
0.01215362548828125,
-0.0133819580078125,
-0.03125,
0.005157470703125,
-0.01032257080078125,
-0.03790283203125,
-0.00989532470703125,
-0.0169219970703125,
-0.007144927978515625,
-0.00537872314453125,
-0.0061187744140625,
0.0268096923828125,
-0.010986328125,
0.0275115966796875,
0.002384185791015625,
0.0036258697509765625,
-0.002086639404296875,
0.01068115234375,
0.0193328857421875,
-0.0094451904296875,
0.01270294189453125,
0.006473541259765625,
0.0007824897766113281,
-0.01459503173828125,
0.011138916015625,
-0.03466796875,
0.01537322998046875,
0.003997802734375,
-0.029541015625,
-0.017486572265625,
-0.0022430419921875,
0.00888824462890625,
0.01220703125,
-0.041656494140625,
-0.0198211669921875,
-0.048492431640625,
0.036376953125,
-0.013885498046875,
0.0057373046875,
-0.00998687744140625,
-0.01470184326171875,
-0.0095062255859375,
-0.00675201416015625,
0.003582000732421875,
0.017608642578125,
-0.022613525390625,
-0.02978515625,
0.0110015869140625,
0.0030689239501953125,
0.019287109375,
0.0124969482421875,
0.013946533203125,
0.0035858154296875,
-0.003765106201171875,
-0.0269317626953125,
0.005336761474609375,
0.0024242401123046875,
0.01100921630859375,
0.003238677978515625,
-0.032867431640625,
-0.007534027099609375,
-0.004123687744140625,
-0.0017032623291015625,
0.002658843994140625,
0.0036220550537109375,
-0.0024471282958984375,
-0.00848388671875,
-0.0007519721984863281,
-0.0142974853515625,
-0.026153564453125,
-0.0179595947265625,
0.0192718505859375,
0.00939178466796875,
-0.003681182861328125,
0.0025634765625,
-0.01171875,
0.01273345947265625,
-0.0073394775390625,
-0.015869140625,
-0.02008056640625,
0.026031494140625,
-0.0036029815673828125,
-0.023406982421875,
0.0279388427734375,
0.009002685546875,
-0.006679534912109375,
-0.008819580078125,
0.01229095458984375,
-0.0033588409423828125,
0.0308990478515625,
-0.00196075439453125,
-0.01375579833984375,
0.00017595291137695312,
-0.0020275115966796875,
-0.0074462890625,
-0.01422119140625,
0.0167083740234375,
-0.05224609375,
-0.020172119140625,
0.0081634521484375,
-0.0062255859375,
0.0035686492919921875,
-0.0160369873046875,
0.0015773773193359375,
0.0142059326171875,
0.0074615478515625,
-0.0021686553955078125,
0.00940704345703125,
-0.020233154296875,
-0.007740020751953125,
0.00623321533203125,
0.01110076904296875,
0.0165863037109375,
0.004756927490234375,
-0.01800537109375,
0.006664276123046875,
-0.016845703125,
-0.0012769699096679688,
-0.00760650634765625,
0.00826263427734375,
-0.05194091796875,
-0.0013523101806640625,
0.00445556640625,
0.00850677490234375,
-0.0034084320068359375,
-0.0245513916015625,
0.01507568359375,
0.010589599609375,
-0.0008783340454101562,
0.01047515869140625,
0.0039825439453125,
0.01323699951171875,
-0.0162811279296875,
0.00170135498046875,
0.00955963134765625,
-0.003082275390625,
-0.0059967041015625,
-0.021881103515625,
-0.0203857421875,
-0.0158233642578125,
0.005847930908203125,
0.0157470703125,
-0.0214385986328125,
0.006336212158203125,
0.0002503395080566406,
-0.0038127899169921875,
-0.0030651092529296875,
-0.0021495819091796875,
-0.0022144317626953125,
0.008880615234375,
0.014312744140625,
-0.01629638671875,
0.0196075439453125,
-0.009307861328125,
-0.0230560302734375,
-0.022369384765625,
-0.0037555694580078125,
0.012786865234375,
0.0218658447265625,
-0.01081085205078125,
0.00032067298889160156,
0.009490966796875,
-0.05316162109375,
0.01540374755859375,
-0.0027370452880859375,
0.0032958984375,
0.0357666015625,
0.04473876953125,
0.0294952392578125,
0.0034503936767578125,
-0.0031642913818359375,
0.061553955078125,
-0.01428985595703125,
0.01142120361328125,
-0.00499725341796875,
0.01763916015625,
-0.01068878173828125,
0.0087432861328125,
-0.0131683349609375,
0.0008254051208496094,
-0.0010404586791992188,
-0.005138397216796875,
-0.0280303955078125,
-0.0285797119140625,
-0.0037174224853515625,
0.0014486312866210938,
0.0089263916015625,
0.00469970703125,
-0.01055145263671875,
0.008087158203125,
0.0285491943359375,
0.0039005279541015625,
-0.0189971923828125,
-0.005779266357421875,
0.00677490234375,
0.07855224609375,
0.01535797119140625,
0.0008330345153808594,
0.007274627685546875,
0.004810333251953125,
0.0131378173828125,
0.0183258056640625,
-0.0029392242431640625,
-0.0042266845703125,
-0.017730712890625,
0.0063629150390625,
0.00806427001953125,
-0.0002455711364746094,
-0.0036468505859375,
0.0035953521728515625,
0.00579071044921875,
-0.0016155242919921875,
-0.005306243896484375,
-0.0024547576904296875,
-0.01229095458984375,
-0.041107177734375,
-0.0675048828125,
-0.0005850791931152344,
-0.0021991729736328125,
0.01190948486328125,
0.01340484619140625,
0.00495147705078125,
-0.001064300537109375,
-0.0014476776123046875,
0.0035800933837890625,
0.01080322265625,
-0.0038127899169921875,
-0.00040650367736816406,
0.0153656005859375,
0.01395416259765625,
0.00292205810546875,
-0.0322265625,
-0.0045013427734375,
-0.01468658447265625,
-0.0299530029296875,
0.007175445556640625,
-0.007167816162109375,
-0.0175323486328125,
0.02520751953125,
0.01561737060546875,
0.00047516822814941406,
-0.01377105712890625,
-0.03167724609375,
-0.01055908203125,
-0.05682373046875,
-0.0114898681640625,
0.0125885009765625,
0.0230712890625,
-0.00432586669921875,
0.034881591796875,
0.0011014938354492188,
0.042572021484375,
-0.0039825439453125,
-0.004863739013671875,
-0.0028057098388671875,
-0.0230560302734375,
0.01139068603515625,
-0.00403594970703125,
-0.0034961700439453125,
0.0469970703125,
0.0028858184814453125,
0.00324249267578125,
-0.01041412353515625,
-0.0158233642578125,
0.038604736328125,
-0.03399658203125,
0.003322601318359375,
-0.03045654296875,
0.0087890625,
0.0026988983154296875,
0.01186370849609375,
-0.0311737060546875,
-0.02264404296875,
0.00406646728515625,
-0.00276947021484375,
-0.0190277099609375,
0.0036029815673828125,
-0.00623321533203125,
0.00323486328125,
0.005931854248046875,
-0.017303466796875,
0.0047607421875,
0.007659912109375,
-0.034454345703125,
0.0216522216796875,
0.007785797119140625,
-0.0250396728515625,
-0.0027866363525390625,
-0.001041412353515625,
-0.028656005859375,
0.022796630859375,
0.00843048095703125,
0.01258087158203125,
-0.0017862319946289062,
0.005279541015625,
-0.027984619140625,
-0.04644775390625,
-0.0101776123046875,
0.0233306884765625,
0.034454345703125,
0.01073455810546875,
-0.0279693603515625,
0.002391815185546875,
-0.041412353515625,
-0.0114898681640625,
0.0228118896484375,
-0.0020275115966796875,
-0.0066986083984375,
0.015777587890625,
-0.01314544677734375,
0.006031036376953125,
-0.011566162109375,
-0.034820556640625,
0.01348114013671875,
-0.0246734619140625,
-0.015716552734375,
-0.00458526611328125,
0.0008168220520019531,
0.0009293556213378906,
-0.0286712646484375,
-0.0157470703125,
0.024139404296875,
-0.007717132568359375,
-0.006717681884765625,
-0.0088348388671875,
-0.01364898681640625,
0.0089111328125,
-0.0433349609375,
0.0085601806640625,
-0.01102447509765625,
-0.0268707275390625,
0.032745361328125,
-0.02001953125,
-0.00200653076171875,
0.02001953125,
-0.0057220458984375,
0.027008056640625,
0.006961822509765625,
0.01126861572265625,
-0.00931549072265625,
0.027862548828125,
-0.0195465087890625,
-0.00948333740234375,
-0.002002716064453125,
-0.0206298828125,
0.00818634033203125,
0.006656646728515625,
0.018218994140625,
0.0272369384765625,
0.00211334228515625,
-0.038421630859375,
0.005054473876953125,
-0.0035114288330078125,
0.0104522705078125,
-0.035430908203125,
-0.0281219482421875,
0.0140228271484375,
0.054412841796875,
-0.0151824951171875,
-0.03179931640625,
-0.0345458984375,
-0.0194091796875,
-0.003093719482421875,
0.029510498046875,
0.006671905517578125,
0.0218353271484375,
0.01322174072265625,
0.0105743408203125,
0.023193359375,
0.02923583984375,
0.047576904296875,
-0.00823211669921875,
-0.031341552734375,
0.001438140869140625,
0.013946533203125,
-0.0213775634765625,
0.0199432373046875,
0.00373077392578125,
0.026397705078125,
-0.0174102783203125,
-0.00687408447265625,
0.0179901123046875,
-0.01375579833984375,
-0.00238800048828125,
-0.0005102157592773438,
-0.0178070068359375,
-0.0031909942626953125,
0.032867431640625,
-0.00429534912109375,
0.0058746337890625,
-0.01549530029296875,
0.006015777587890625,
0.0462646484375,
-0.007251739501953125,
-0.045562744140625,
-0.0244598388671875,
-0.006710052490234375,
0.00119781494140625,
0.00653839111328125,
0.01236724853515625,
-0.046142578125,
0.004184722900390625,
0.0009012222290039062,
0.0219573974609375,
0.016448974609375,
-0.0025787353515625,
-0.0023097991943359375,
0.0044097900390625,
0.00881195068359375,
0.0034637451171875,
0.0007648468017578125,
0.039215087890625,
-0.01332855224609375,
-0.0007696151733398438,
-0.0150604248046875,
0.00235748291015625,
-0.0151519775390625,
0.0187835693359375,
-0.01024627685546875,
0.0221710205078125,
0.024078369140625,
-0.03082275390625,
0.01103973388671875,
0.054595947265625,
-0.020599365234375,
-0.02850341796875,
0.0053558349609375,
0.0194549560546875,
-0.0159912109375,
0.029510498046875,
-0.0083160400390625,
-0.01390838623046875,
0.0073394775390625,
-0.0218963623046875,
0.0044403076171875,
-0.053741455078125,
0.0013341903686523438,
-0.0011463165283203125,
-0.01273345947265625,
0.01383209228515625,
0.036895751953125,
-0.0204925537109375,
-0.025115966796875,
-0.0106964111328125,
-0.0211639404296875,
-0.01230621337890625,
0.0088653564453125,
0.0014057159423828125,
0.0071258544921875,
0.004100799560546875,
0.036651611328125,
0.0296630859375,
-0.00965118408203125,
-0.02276611328125,
0.0002868175506591797,
0.01055145263671875,
0.00909423828125,
-0.0208282470703125,
0.0362548828125,
-0.0218505859375,
0.031402587890625,
0.005130767822265625,
0.0230712890625,
0.01226043701171875,
0.00799560546875,
0.0160064697265625,
-0.0248565673828125,
0.01020050048828125,
-0.0211181640625,
-0.013671875,
-0.0303802490234375,
-0.0085906982421875,
-0.04156494140625,
-0.006610870361328125,
-0.020721435546875,
-0.02947998046875,
0.0103302001953125,
-0.04888916015625,
-0.0013599395751953125,
-0.0265350341796875,
-0.0035266876220703125,
0.021728515625,
0.0303192138671875,
0.0016469955444335938,
-0.02093505859375,
0.019927978515625,
0.0003895759582519531,
-0.04376220703125,
0.02032470703125,
-0.02069091796875,
0.00934600830078125,
-0.0014476776123046875,
-0.0030384063720703125,
0.01192474365234375,
-0.0003681182861328125,
0.004222869873046875,
-0.016357421875,
-0.0077362060546875,
0.0022068023681640625,
0.01108551025390625,
-0.0155487060546875,
0.04180908203125,
0.03460693359375,
-0.048248291015625,
0.005916595458984375,
0.00948333740234375,
0.0184326171875,
-0.030426025390625,
0.0012664794921875,
-0.004032135009765625,
0.00888824462890625,
-0.0050048828125,
0.0030460357666015625,
-0.05279541015625,
0.0086822509765625,
0.0143890380859375,
0.0158233642578125,
-0.025665283203125,
0.01000213623046875,
-0.0037212371826171875,
-0.002452850341796875,
-0.00861358642578125,
0.00647735595703125,
-0.0263214111328125,
0.0297393798828125,
-0.029815673828125,
-0.01390838623046875,
0.01922607421875,
-0.0258941650390625,
-0.005157470703125,
-0.0191650390625,
-0.0117950439453125,
0.0106201171875,
0.00849151611328125,
-0.0299530029296875,
-0.0110015869140625,
0.007640838623046875,
-0.01483154296875,
0.037811279296875,
-0.0204315185546875,
-0.006015777587890625,
0.0026874542236328125,
-0.001739501953125,
0.032012939453125,
-0.047821044921875,
-0.021148681640625,
-0.029632568359375,
-0.006427764892578125,
-0.042694091796875,
-0.005306243896484375,
-0.0279388427734375,
-0.0181884765625,
0.01438140869140625,
-0.0013723373413085938,
-0.00247955322265625,
0.0134429931640625,
-0.0034046173095703125,
-0.0100250244140625,
-0.0140838623046875,
0.00799560546875,
0.0005841255187988281,
0.025115966796875,
-0.01155853271484375,
0.007442474365234375,
0.0231475830078125,
-0.037872314453125,
-0.0082855224609375,
0.01532745361328125,
0.002452850341796875,
0.020721435546875,
-0.005680084228515625,
-0.001781463623046875,
-0.0151824951171875,
0.01354217529296875,
-0.004573822021484375,
-0.030731201171875,
0.04376220703125,
-0.03521728515625,
-0.032806396484375,
0.0160980224609375,
0.01354217529296875,
0.0213470458984375,
0.038909912109375,
0.030242919921875,
-0.0243072509765625,
0.01229095458984375,
-0.006969451904296875,
0.0078277587890625,
0.0223388671875,
-0.01617431640625,
0.00872039794921875,
0.011627197265625,
0.00316619873046875,
-0.0264434814453125,
0.02252197265625,
0.01250457763671875,
0.003314971923828125,
0.011932373046875,
0.01812744140625,
0.015716552734375,
0.005863189697265625,
-0.0253143310546875,
-0.0069427490234375,
0.00960540771484375,
-0.00704193115234375,
-0.025909423828125,
-0.016754150390625,
-0.0260772705078125,
0.021392822265625,
-0.00785064697265625,
0.00766754150390625,
-0.001094818115234375,
0.0228271484375,
-0.0066680908203125,
-0.006778717041015625,
-0.039794921875,
0.007549285888671875,
-0.01947021484375,
-0.0122222900390625,
0.0195770263671875,
0.01079559326171875,
0.0010852813720703125,
-0.00789642333984375,
0.01428985595703125,
0.02459716796875,
0.0285797119140625,
0.0283966064453125,
0.0019245147705078125,
-0.0177001953125,
-0.0252685546875,
0.03607177734375,
-0.0189666748046875,
-0.0162811279296875,
-0.028106689453125,
-0.007427215576171875,
0.0183868408203125,
-0.00818634033203125,
-0.005950927734375,
-0.04534912109375,
-0.03497314453125,
-0.015411376953125,
0.0250244140625,
-0.0109100341796875,
0.0017032623291015625,
-0.01221466064453125,
-0.032073974609375,
-0.01629638671875,
-0.014862060546875,
-0.0047454833984375,
-0.0215606689453125,
-0.01474761962890625,
-0.00559234619140625,
0.0139312744140625,
0.0089874267578125,
-0.064697265625,
-0.004856109619140625,
-0.005260467529296875,
-0.00965118408203125,
-0.02703857421875,
-0.01062774658203125,
0.03375244140625,
-0.0124359130859375,
-0.033172607421875,
-0.02484130859375,
-0.006229400634765625,
0.0017213821411132812,
-0.024871826171875,
-0.01274871826171875,
-0.042755126953125,
-0.022674560546875,
0.00638580322265625,
-0.01352691650390625,
-0.034027099609375,
-0.0304718017578125,
-0.03173828125,
0.0255889892578125,
-0.002414703369140625,
-0.030426025390625,
-0.017242431640625,
0.043975830078125,
0.00989532470703125,
0.01439666748046875,
0.0042266845703125,
-0.0171051025390625,
0.010528564453125,
0.0140533447265625,
-0.003265380859375,
-0.032440185546875,
0.006103515625,
0.054718017578125,
0.00582122802734375,
0.0287017822265625,
0.01036834716796875,
0.01190948486328125,
-0.0122833251953125,
-0.0034275054931640625,
0.0003955364227294922,
-0.017822265625,
-0.0161285400390625,
0.005466461181640625,
0.0240478515625,
-0.011322021484375,
-0.0016632080078125,
-0.031585693359375,
0.016265869140625,
-0.0009660720825195312,
-0.0234375,
0.0106353759765625,
0.008544921875,
0.0008821487426757812,
0.0205078125,
0.00687408447265625,
-0.00930023193359375,
-0.03009033203125,
-0.03594970703125,
0.03369140625,
-0.005893707275390625,
0.0115966796875,
0.02227783203125,
-0.0019073486328125,
0.0213623046875,
-0.01904296875,
0.017974853515625,
-0.0187530517578125,
0.01047515869140625,
-0.0333251953125,
0.0097503662109375,
0.0069732666015625,
-0.018646240234375,
0.01226043701171875,
0.0247344970703125,
0.00844573974609375,
-0.01137542724609375,
-0.03369140625,
0.0005040168762207031,
-0.0013055801391601562,
0.012115478515625,
-0.001239776611328125,
-0.0213165283203125,
-0.00005507469177246094,
-0.01026153564453125,
-0.0188751220703125,
-0.01470184326171875,
0.036651611328125,
-0.027191162109375,
-0.0172576904296875,
-0.0202789306640625,
-0.004344940185546875,
0.03277587890625,
-0.01043701171875,
0.015899658203125,
-0.002475738525390625,
0.027923583984375,
-0.045745849609375,
0.0088043212890625,
-0.00823974609375,
0.021392822265625,
-0.01171112060546875,
0.0181121826171875,
-0.0035247802734375,
0.0272064208984375,
-0.006061553955078125,
-0.0206756591796875,
-0.007488250732421875,
-0.00807952880859375,
0.0124053955078125,
0.0031147003173828125,
0.0197601318359375,
0.004413604736328125,
-0.004245758056640625,
0.013885498046875,
0.014190673828125,
-0.007167816162109375,
-0.002269744873046875,
0.01177215576171875,
0.057830810546875,
0.0234832763671875,
0.027252197265625,
0.002849578857421875,
0.0155792236328125,
-0.0275726318359375,
0.040618896484375,
-0.01427459716796875,
-0.0006031990051269531,
-0.03466796875,
0.0095062255859375,
-0.0153045654296875,
0.040435791015625,
-0.0261993408203125,
-0.0193939208984375,
-0.0202484130859375,
0.0031681060791015625,
-0.0013055801391601562,
-0.001190185546875,
-0.029083251953125,
0.0228271484375,
-0.006622314453125,
-0.0223846435546875,
-0.021728515625,
0.0163421630859375,
-0.0357666015625,
-0.0281982421875,
0.003627777099609375,
0.0253143310546875,
0.004077911376953125,
-0.0142822265625,
-0.009063720703125,
-0.033660888671875,
0.015777587890625,
0.0037078857421875,
0.0116424560546875,
-0.0135040283203125,
0.0233612060546875,
0.01500701904296875,
0.01441192626953125,
-0.0164642333984375,
-0.016143798828125,
-0.0187225341796875,
-0.00408172607421875,
-0.02435302734375,
0.0203399658203125,
0.018310546875,
0.007137298583984375,
-0.0089263916015625,
-0.01554107666015625,
-0.01401519775390625,
0.005619049072265625,
0.01226043701171875,
0.00926971435546875,
-0.046112060546875,
0.01244354248046875,
0.006717681884765625,
0.01021575927734375,
0.0006251335144042969,
0.01364898681640625,
0.0084991455078125,
0.004955291748046875,
0.0024089813232421875,
0.0007305145263671875,
-0.010650634765625,
-0.01285552978515625,
0.0322265625,
-0.000797271728515625,
0.0200042724609375,
0.0285186767578125,
-0.020843505859375,
-0.0017414093017578125,
-0.0013580322265625,
-0.0016374588012695312,
-0.021759033203125,
-0.0419921875,
0.0360107421875,
0.0222015380859375,
0.0360107421875,
0.0224151611328125,
-0.01358795166015625,
-0.0091094970703125,
0.00676727294921875,
-0.01143646240234375,
0.0163116455078125,
-0.0128631591796875,
0.017913818359375,
0.00275421142578125,
-0.0158233642578125,
-0.01045989990234375,
-0.0263824462890625,
0.025787353515625,
-0.03045654296875,
0.0136871337890625,
0.0217742919921875,
-0.01262664794921875,
0.0017805099487304688,
-0.0521240234375,
0.00215911865234375,
-0.051727294921875,
-0.007366180419921875,
0.01120758056640625,
-0.03692626953125,
0.0186767578125,
0.02752685546875,
0.024200439453125,
-0.02685546875,
-0.01873779296875,
-0.0202484130859375,
-0.01849365234375,
-0.00807952880859375,
0.0128173828125,
0.032501220703125,
-0.0010223388671875,
0.009002685546875,
-0.0199127197265625,
0.027984619140625,
0.0206146240234375,
-0.004817962646484375,
0.01476287841796875,
-0.006008148193359375,
-0.004650115966796875,
0.0169830322265625,
-0.0050048828125,
0.0019311904907226562,
-0.024658203125,
-0.040283203125,
-0.0022029876708984375,
0.01082611083984375,
0.005374908447265625,
-0.0007772445678710938,
-0.021331787109375,
0.028167724609375,
0.00797271728515625,
-0.0111083984375,
0.011077880859375,
-0.01462554931640625,
-0.00656890869140625,
0.0070953369140625,
0.0035858154296875,
-0.004001617431640625,
-0.028717041015625,
0.011932373046875,
0.0202484130859375,
-0.04412841796875,
0.0271453857421875,
0.02178955078125,
0.016845703125,
-0.00304412841796875,
-0.007396697998046875,
0.004425048828125,
0.0186920166015625,
0.01275634765625,
0.015350341796875,
0.00722503662109375,
-0.0030651092529296875,
-0.0206451416015625,
-0.030670166015625,
-0.003971099853515625,
-0.01473236083984375,
-0.02276611328125,
-0.01294708251953125,
-0.0243377685546875,
-0.003520965576171875,
0.0189361572265625,
-0.012359619140625,
0.0191802978515625,
0.031097412109375,
0.001522064208984375,
-0.001895904541015625,
0.01131439208984375,
0.0024547576904296875,
0.01263427734375,
0.00782012939453125,
0.016265869140625,
-0.006435394287109375,
0.0200347900390625,
0.00714111328125,
0.0224761962890625,
0.0091705322265625,
0.0217742919921875,
-0.0004527568817138672,
0.02081298828125,
-0.00798797607421875,
0.035003662109375,
0.0218658447265625,
-0.014678955078125,
-0.004436492919921875,
-0.027618408203125,
-0.0283966064453125,
0.0396728515625,
-0.0047607421875,
-0.0224609375,
-0.038665771484375,
-0.0210723876953125,
0.043487548828125,
-0.0199127197265625,
-0.04766845703125,
-0.00400543212890625,
-0.0084991455078125,
0.028411865234375,
-0.03515625,
-0.0099029541015625,
-0.0018644332885742188,
-0.01053619384765625,
0.0021457672119140625,
-0.021575927734375,
0.01139068603515625,
-0.03533935546875,
0.0333251953125,
0.01995849609375,
0.052642822265625,
-0.0229034423828125,
-0.0099334716796875,
-0.01641845703125,
-0.0307464599609375,
0.02191162109375,
0.002071380615234375,
-0.01904296875,
-0.00946044921875,
-0.00039315223693847656,
0.00032138824462890625,
0.0243988037109375,
-0.005084991455078125,
0.00841522216796875,
0.00995635986328125,
0.0137939453125,
0.007472991943359375,
-0.0270233154296875,
-0.017974853515625,
-0.0021419525146484375,
0.0117340087890625,
0.0216827392578125,
-0.006504058837890625,
-0.031402587890625,
0.022613525390625,
-0.03814697265625,
-0.0008459091186523438,
-0.00481414794921875,
0.00888824462890625,
-0.012847900390625,
-0.0038089752197265625,
-0.04217529296875,
-0.01959228515625,
-0.035675048828125,
-0.006328582763671875,
-0.006137847900390625,
-0.01264190673828125,
-0.0061187744140625,
0.0224761962890625,
0.0084381103515625,
-0.0279083251953125,
-0.0023288726806640625,
-0.0194244384765625,
-0.01438140869140625,
0.0255279541015625,
0.03839111328125,
0.0051116943359375,
0.0229949951171875,
-0.0026035308837890625,
0.0170745849609375,
-0.0012235641479492188,
0.013214111328125,
-0.01447296142578125,
0.00716400146484375,
-0.0006232261657714844,
0.01006317138671875,
-0.01611328125,
-0.006011962890625,
-0.0017671585083007812,
0.0019025802612304688,
0.0037078857421875,
-0.0426025390625,
-0.0204010009765625,
0.02459716796875,
-0.00836944580078125,
0.01153564453125,
-0.0021724700927734375,
-0.0020599365234375,
0.0162811279296875,
-0.01367950439453125,
0.02130126953125,
-0.0025081634521484375,
-0.0309600830078125,
0.0276031494140625,
-0.0096282958984375,
-0.039886474609375,
-0.01197052001953125,
0.002574920654296875,
0.0254058837890625,
-0.053863525390625,
0.0035800933837890625,
0.00420379638671875,
-0.004070281982421875,
-0.0217742919921875,
0.036712646484375,
0.00421142578125,
-0.00888824462890625,
0.029998779296875,
0.00530242919921875,
-0.0117034912109375,
0.0244598388671875,
0.007080078125,
-0.00023818016052246094,
0.01526641845703125,
-0.0211181640625,
-0.0384521484375,
0.0222930908203125,
-0.0122222900390625,
-0.0087432861328125,
0.01093292236328125,
0.0189666748046875,
-0.0167388916015625,
-0.032867431640625,
-0.0165252685546875,
0.0023059844970703125,
0.01366424560546875,
0.00035500526428222656,
-0.0287628173828125,
-0.000675201416015625,
-0.02374267578125,
-0.0020904541015625,
-0.019927978515625,
-0.00324249267578125,
-0.024322509765625,
0.01070404052734375,
-0.00768280029296875,
-0.0019626617431640625,
-0.04473876953125,
-0.0205841064453125,
0.037811279296875,
0.0281982421875,
-0.009979248046875,
0.017120361328125,
-0.0239715576171875,
0.0018138885498046875,
-0.0159149169921875,
-0.0018014907836914062,
0.0182952880859375,
-0.007488250732421875,
0.01312255859375,
-0.0031890869140625,
0.036407470703125,
0.007328033447265625,
0.03009033203125,
0.0014190673828125,
0.00949859619140625,
-0.02093505859375,
0.0272674560546875,
-0.0233306884765625,
-0.019134521484375,
0.00177764892578125,
-0.0186614990234375,
0.031524658203125,
0.0223541259765625,
-0.018524169921875,
-0.008819580078125,
0.0205535888671875,
-0.0128173828125,
-0.0013036727905273438,
0.00786590576171875,
0.0079803466796875,
0.0016164779663085938,
0.0187835693359375,
0.0010290145874023438,
-0.0011587142944335938,
0.00609588623046875,
0.027923583984375,
0.006145477294921875,
0.001811981201171875,
0.01898193359375,
-0.00199127197265625,
-0.02899169921875,
0.0013284683227539062,
-0.0548095703125,
0.03582763671875,
0.024017333984375,
0.0211181640625,
0.0009160041809082031,
-0.0212249755859375,
-0.00786590576171875,
-0.0023345947265625,
0.034637451171875,
-0.0238037109375,
-0.0029754638671875,
-0.0106201171875,
-0.0213775634765625,
0.005764007568359375,
-0.01212310791015625,
0.0166168212890625,
-0.017303466796875,
0.01084136962890625,
0.034637451171875,
0.019561767578125,
0.01184844970703125,
-0.00251007080078125,
0.0182647705078125,
-0.01190185546875,
-0.036956787109375,
0.037017822265625,
0.01500701904296875,
0.0177154541015625,
-0.01125335693359375,
-0.033050537109375,
0.005451202392578125,
-0.01490020751953125,
0.00626373291015625,
0.01861572265625,
0.0066375732421875,
-0.0240631103515625,
-0.01428985595703125,
0.01329803466796875,
0.0033397674560546875,
0.004344940185546875,
0.0024166107177734375,
-0.045074462890625,
0.020599365234375,
0.01523590087890625,
-0.006435394287109375,
0.0242462158203125,
-0.0248870849609375,
0.0198211669921875,
-0.0190277099609375,
-0.0189971923828125,
0.0274658203125,
-0.00548553466796875,
0.0034542083740234375,
-0.025848388671875,
-0.012451171875,
-0.00995635986328125,
-0.010589599609375,
-0.0187835693359375,
0.0031452178955078125,
-0.01479339599609375,
-0.007076263427734375,
0.0016469955444335938,
0.0032253265380859375,
0.007266998291015625,
0.018524169921875,
0.026885986328125,
-0.0059814453125,
-0.0021266937255859375,
0.011566162109375,
-0.0229339599609375,
-0.021636962890625,
-0.020050048828125,
-0.01410675048828125,
0.034332275390625,
-0.0127410888671875,
-0.0184478759765625,
-0.0027008056640625,
-0.01424407958984375,
-0.0186614990234375,
0.01024627685546875,
-0.05523681640625,
-0.0006146430969238281,
-0.0189971923828125,
-0.0018711090087890625,
-0.020843505859375,
0.0149078369140625,
-0.000009655952453613281,
0.0133819580078125,
-0.0010747909545898438,
0.0234832763671875,
-0.0233154296875,
-0.01468658447265625,
-0.0132598876953125,
0.05731201171875,
-0.038482666015625,
-0.0074005126953125,
0.005401611328125,
0.01123046875,
-0.03460693359375,
-0.0021724700927734375,
0.005046844482421875,
-0.020751953125,
0.0070648193359375,
0.01317596435546875,
-0.0084991455078125,
0.0021228790283203125,
-0.0343017578125,
-0.0277099609375,
0.023712158203125,
0.01959228515625,
0.00345611572265625,
0.0164794921875,
0.0045166015625,
-0.0467529296875,
-0.00861358642578125,
0.01157379150390625,
0.06640625,
0.018768310546875,
0.004718780517578125,
0.0026397705078125,
-0.0170745849609375,
-0.00010675191879272461,
-0.031280517578125,
0.0249176025390625,
-0.016510009765625,
0.007709503173828125,
0.0071258544921875,
-0.0019893646240234375,
-0.0006356239318847656,
0.0007929801940917969,
-0.01253509521484375,
0.0021762847900390625,
-0.0082550048828125,
-0.0333251953125,
-0.01346588134765625,
-0.01334381103515625,
0.007232666015625,
0.01529693603515625,
0.0017261505126953125,
-0.00806427001953125,
0.0330810546875,
-0.0225372314453125,
-0.03228759765625,
-0.01953125,
-0.027252197265625,
0.007659912109375,
0.0035991668701171875,
-0.01495361328125,
-0.0025463104248046875,
-0.004611968994140625,
-0.0233001708984375,
-0.0069732666015625,
0.0177001953125,
0.0181121826171875,
0.00913238525390625,
-0.013214111328125,
0.0202178955078125,
0.01367950439453125,
-0.01788330078125,
-0.0133819580078125,
-0.01183319091796875,
-0.0234375,
0.017333984375,
-0.00919342041015625,
0.013946533203125,
-0.018890380859375,
0.034393310546875,
0.00562286376953125,
0.0120697021484375,
-0.01514434814453125,
-0.003643035888671875,
0.032623291015625,
0.03521728515625,
-0.0003223419189453125,
-0.0206146240234375,
0.013946533203125,
0.00612640380859375,
0.0102691650390625,
0.019927978515625,
0.036376953125,
-0.035064697265625,
0.000038623809814453125,
0.006351470947265625,
-0.008941650390625,
-0.0011348724365234375,
-0.049774169921875,
-0.025421142578125,
0.005786895751953125,
-0.022735595703125,
0.004337310791015625,
0.0302581787109375,
0.030303955078125,
-0.0300750732421875,
0.03411865234375,
0.00524139404296875,
-0.020904541015625,
-0.02288818359375,
-0.017730712890625,
0.004253387451171875,
0.0192413330078125,
-0.058349609375,
-0.0222015380859375,
-0.032135009765625,
-0.0012216567993164062,
-0.00791168212890625,
-0.0054931640625,
0.0265960693359375,
-0.00750732421875,
-0.024658203125,
0.0118408203125,
-0.02484130859375,
0.00600433349609375,
-0.033538818359375,
0.0024662017822265625,
-0.00569915771484375,
0.058624267578125,
0.0755615234375,
-0.00989532470703125,
-0.004871368408203125,
0.002750396728515625,
0.027008056640625,
-0.0005521774291992188,
-0.0134429931640625,
-0.0283966064453125,
0.014984130859375,
0.0024127960205078125,
0.0204315185546875,
-0.0032176971435546875,
0.007442474365234375,
-0.0251922607421875,
-0.0102081298828125,
-0.0164794921875,
-0.0180206298828125,
-0.0005512237548828125,
0.03509521484375,
0.007724761962890625,
-0.00585174560546875,
-0.034942626953125,
0.0160980224609375,
-0.0003075599670410156,
-0.0020198822021484375,
-0.0254058837890625,
0.0126953125,
-0.0284576416015625,
0.00966644287109375,
-0.016632080078125,
0.0279083251953125,
0.04248046875,
-0.01206207275390625,
-0.029541015625,
0.0175323486328125,
0.0017261505126953125,
-0.00011551380157470703,
0.0214996337890625,
0.007843017578125,
-0.01373291015625,
0.02587890625,
-0.007762908935546875,
0.0142669677734375,
0.0224151611328125,
0.01055145263671875,
-0.028167724609375,
0.01468658447265625,
-0.017059326171875,
-0.0028781890869140625,
0.008514404296875,
-0.0010843276977539062,
-0.00891876220703125,
-0.0175933837890625,
-0.038177490234375,
0.004482269287109375,
0.01436614990234375,
0.006855010986328125,
-0.01255035400390625,
-0.00732421875,
0.0104827880859375,
-0.0126495361328125,
-0.006137847900390625,
0.01910400390625,
0.0172119140625,
-0.04638671875,
-0.0172882080078125,
0.0054931640625,
0.007549285888671875,
0.01219940185546875,
0.04522705078125,
0.038421630859375,
-0.0119171142578125,
0.0032138824462890625,
-0.0176849365234375,
0.008331298828125,
0.0166168212890625,
0.044342041015625,
-0.00799560546875,
-0.02630615234375,
0.0034008026123046875,
0.0069732666015625,
0.01104736328125,
0.022308349609375,
0.032196044921875,
0.0221405029296875,
-0.02294921875,
0.031097412109375,
0.0020542144775390625,
0.035430908203125,
0.015655517578125,
-0.020599365234375,
0.0264892578125,
0.0298614501953125,
0.016998291015625,
-0.01009368896484375,
0.0009889602661132812,
-0.005924224853515625,
-0.005664825439453125,
0.01369476318359375,
-0.011810302734375,
-0.0013132095336914062,
0.0195465087890625,
-0.00942230224609375,
0.00957489013671875,
-0.00858306884765625,
-0.037139892578125,
0.0001779794692993164,
-0.01543426513671875,
-0.01505279541015625,
-0.017730712890625,
0.0131683349609375,
-0.039825439453125,
0.0172882080078125,
-0.0222015380859375,
0.0230865478515625,
-0.0012359619140625,
0.00843048095703125,
-0.0138397216796875,
-0.004119873046875,
-0.01020050048828125,
-0.0269622802734375,
0.038055419921875,
0.0080718994140625,
0.023529052734375,
0.0174713134765625,
-0.0261688232421875,
0.00789642333984375,
0.04193115234375,
0.0199127197265625,
0.018463134765625,
-0.0007224082946777344,
-0.0291748046875,
0.00957489013671875,
-0.01031494140625,
0.026214599609375,
0.01318359375,
0.001964569091796875,
-0.0009393692016601562,
-0.0247650146484375,
0.05010986328125,
-0.03265380859375,
-0.0030536651611328125,
0.0195465087890625,
-0.0132904052734375,
0.002323150634765625,
-0.0005865097045898438,
-0.01971435546875,
-0.0107421875,
-0.01233673095703125,
-0.030914306640625,
0.01114654541015625,
0.0224761962890625,
0.032470703125,
0.040252685546875,
-0.006954193115234375,
0.01007080078125,
0.02838134765625,
-0.009674072265625,
0.034820556640625,
-0.0223541259765625,
0.0271453857421875,
0.01311492919921875,
-0.00936126708984375,
0.0024318695068359375,
-0.0167999267578125,
-0.01290130615234375,
-0.01128387451171875,
-0.00331878662109375,
0.0077972412109375,
0.0082244873046875,
-0.0208282470703125,
-0.01393890380859375,
0.0151519775390625,
0.01219940185546875,
-0.014923095703125,
-0.05133056640625,
-0.01690673828125,
-0.001209259033203125,
0.0161285400390625,
-0.0233001708984375,
0.00518798828125,
0.00446319580078125,
-0.035369873046875,
-0.00824737548828125,
0.01496124267578125,
-0.01220703125,
0.0173492431640625,
-0.0099334716796875,
-0.008209228515625,
-0.0017347335815429688,
0.0108795166015625,
-0.01024627685546875,
-0.015716552734375,
0.0004055500030517578,
0.01287841796875,
-0.031402587890625,
0.00521087646484375,
0.0173492431640625,
0.011322021484375,
0.0257415771484375,
-0.01641845703125,
-0.021759033203125,
0.029022216796875,
-0.001369476318359375,
0.00719451904296875,
0.0258636474609375,
-0.0013666152954101562,
-0.0104217529296875,
-0.0218658447265625,
0.0027866363525390625,
-0.0030307769775390625,
-0.008514404296875,
-0.0293121337890625,
-0.017913818359375,
0.0036334991455078125,
0.008056640625,
-0.0037174224853515625,
-0.024383544921875,
0.040771484375,
0.0086669921875,
-0.02679443359375,
-0.0465087890625,
-0.00695037841796875,
0.0267181396484375,
0.001216888427734375,
-0.01432037353515625,
0.005252838134765625,
-0.008758544921875,
-0.0228729248046875,
0.004085540771484375,
0.009674072265625,
0.004726409912109375,
0.035003662109375,
-0.00260162353515625,
-0.01120758056640625,
0.0131378173828125,
-0.00750732421875,
-0.0006070137023925781,
-0.005718231201171875,
-0.004177093505859375,
0.0002720355987548828,
0.01092529296875,
0.00896453857421875,
0.000972747802734375,
0.010467529296875,
0.0296630859375,
0.032562255859375,
-0.035980224609375,
-0.0310211181640625,
-0.01471710205078125,
-0.00213623046875,
0.0083465576171875,
-0.0155487060546875,
0.036346435546875,
-0.02410888671875,
-0.004711151123046875,
0.01529693603515625,
0.011260986328125,
0.0026092529296875,
-0.031097412109375,
0.0238037109375,
-0.02239990234375,
-0.0060882568359375,
-0.0011854171752929688,
0.0047454833984375,
0.0152740478515625,
-0.0177001953125,
0.0157012939453125,
0.007389068603515625,
0.03973388671875,
0.0023517608642578125,
-0.014251708984375,
-0.004810333251953125,
-0.0225372314453125,
-0.015777587890625,
0.008636474609375,
-0.0006618499755859375,
0.000736236572265625,
0.00449371337890625,
-0.01352691650390625,
-0.0104522705078125,
-0.0321044921875,
-0.00862884521484375,
0.019622802734375,
0.0125732421875,
-0.00817108154296875,
0.0022945404052734375,
-0.06292724609375,
0.0030994415283203125,
0.023681640625,
-0.0439453125,
0.01261138916015625,
-0.006000518798828125,
-0.01175689697265625,
0.01324462890625,
-0.0198822021484375,
-0.00464630126953125,
-0.015960693359375,
0.03961181640625,
-0.036041259765625,
-0.01520538330078125,
0.037200927734375,
-0.0003287792205810547,
0.002460479736328125,
-0.00307464599609375,
-0.0005135536193847656,
-0.003192901611328125,
0.03546142578125,
0.0280914306640625,
0.0306549072265625,
0.0098876953125,
0.0005135536193847656,
-0.0012121200561523438,
0.00640106201171875,
-0.05029296875,
-0.03155517578125,
0.0191802978515625,
-0.0005478858947753906,
0.0212249755859375,
-0.003376007080078125,
-0.0088958740234375,
0.014404296875,
0.00800323486328125,
-0.00817108154296875,
-0.009307861328125,
-0.003276824951171875,
-0.00760650634765625,
-0.015594482421875,
-0.0238494873046875,
0.005298614501953125,
0.0030670166015625,
-0.019683837890625,
-0.028961181640625,
0.0238494873046875,
-0.03314208984375,
0.0225372314453125,
-0.0047760009765625,
0.0200958251953125,
-0.033905029296875,
0.0225067138671875,
0.034423828125,
0.00344085693359375,
-0.0231170654296875,
-0.0036907196044921875,
0.037445068359375,
-0.007350921630859375,
0.0195159912109375,
0.035369873046875,
-0.001636505126953125,
0.0037994384765625,
-0.0185546875,
-0.01666259765625,
-0.0025844573974609375,
-0.005523681640625,
-0.032501220703125,
0.006473541259765625,
-0.01317596435546875,
0.023162841796875,
-0.01032257080078125,
-0.015045166015625,
-0.01116943359375,
-0.00257110595703125,
0.027130126953125,
0.002735137939453125,
0.024444580078125,
0.0576171875,
0.0081329345703125,
0.003337860107421875,
-0.013092041015625,
-0.0192718505859375,
0.01238250732421875,
0.00919342041015625,
0.00492095947265625,
-0.0245819091796875,
0.01100921630859375,
-0.01468658447265625,
-0.006717681884765625,
0.036224365234375,
-0.01428985595703125,
0.015899658203125,
-0.0023136138916015625,
0.0025920867919921875,
-0.0022220611572265625,
0.003326416015625,
0.00499725341796875,
0.005428314208984375,
-0.03118896484375,
-0.02313232421875,
-0.01519775390625,
-0.0024127960205078125,
-0.019622802734375,
-0.0270538330078125,
-0.0180206298828125,
0.0304718017578125,
0.0013151168823242188,
0.0159454345703125,
0.01300048828125,
-0.0232696533203125,
-0.017852783203125,
-0.00841522216796875,
-0.026458740234375,
-0.0139312744140625,
0.0047760009765625,
-0.0200347900390625,
0.005157470703125,
-0.0308990478515625,
0.0227203369140625,
0.002964019775390625,
-0.01117706298828125,
0.0133514404296875,
-0.0182647705078125,
0.025482177734375,
-0.0221405029296875,
0.032012939453125,
0.039947509765625,
0.006717681884765625,
-0.026580810546875,
0.0152130126953125,
0.0294189453125,
-0.011993408203125,
-0.033203125,
0.025360107421875,
-0.0128326416015625,
0.032073974609375,
0.002880096435546875,
-0.009002685546875,
0.004268646240234375,
-0.006298065185546875,
0.00872039794921875,
0.01971435546875,
0.018402099609375,
-0.004894256591796875,
0.0276336669921875,
-0.0009489059448242188,
0.0174560546875,
0.0162200927734375,
-0.02783203125,
0.0257110595703125,
-0.006137847900390625,
-0.0164031982421875,
0.0200653076171875,
0.034027099609375,
0.0151824951171875,
-0.03863525390625,
-0.046844482421875,
0.0278167724609375,
-0.022552490234375,
-0.012481689453125,
-0.03179931640625,
-0.02398681640625,
-0.03692626953125,
0.03466796875,
0.0296478271484375,
0.0235443115234375,
-0.01532745361328125,
-0.03253173828125,
0.0102081298828125,
-0.023193359375,
0.00522613525390625,
0.01763916015625,
-0.027923583984375,
0.003406524658203125,
-0.023773193359375,
-0.027252197265625,
0.00447845458984375,
-0.00862884521484375,
0.002452850341796875,
-0.00748443603515625,
0.0174713134765625,
0.01245880126953125,
-0.0025463104248046875,
0.003971099853515625,
0.0212554931640625,
0.044647216796875,
0.01143646240234375,
0.031494140625,
-0.003681182861328125,
0.01274871826171875,
-0.006900787353515625,
0.0244598388671875,
0.00975799560546875,
-0.0194244384765625,
-0.003551483154296875,
-0.0303192138671875,
-0.00720977783203125,
0.01058197021484375,
0.01220703125,
-0.01117706298828125,
0.0090179443359375,
-0.019439697265625,
0.01165008544921875,
0.0157470703125,
-0.0128631591796875,
-0.01605224609375,
0.024261474609375,
0.0009336471557617188,
-0.0271148681640625,
-0.01218414306640625,
-0.0168914794921875,
-0.043243408203125,
0.00406646728515625,
-0.004230499267578125,
-0.0007877349853515625,
-0.0222320556640625,
-0.0207366943359375,
-0.01093292236328125,
0.0159912109375,
0.0284576416015625,
0.00159454345703125,
0.001895904541015625,
0.02557373046875,
0.00021648406982421875,
-0.0007414817810058594,
0.02105712890625,
-0.03759765625,
-0.03656005859375,
-0.006206512451171875,
-0.00165557861328125,
-0.0268707275390625,
-0.0225677490234375,
-0.001857757568359375,
0.0063323974609375,
0.021392822265625,
-0.0243682861328125,
-0.00946044921875,
0.0017261505126953125,
0.01168060302734375,
-0.009368896484375,
-0.01364898681640625,
0.02325439453125,
0.006053924560546875,
-0.0244903564453125,
0.00438690185546875,
0.0269317626953125,
-0.016326904296875,
0.0240478515625,
0.00789642333984375,
0.0296478271484375,
0.01229095458984375,
0.03692626953125,
-0.01129913330078125,
-0.02996826171875,
-0.0215301513671875,
0.014678955078125,
-0.005504608154296875,
-0.02667236328125,
0.058197021484375,
-0.021820068359375,
0.0290374755859375,
-0.0216064453125,
0.007694244384765625,
0.0035839080810546875,
-0.0277252197265625,
0.0046844482421875,
-0.0239105224609375,
-0.007564544677734375,
0.024200439453125,
0.004322052001953125,
-0.0016384124755859375,
-0.03082275390625,
-0.00324249267578125,
0.006557464599609375,
-0.0149383544921875,
0.0037593841552734375,
0.0183563232421875,
0.03466796875,
-0.002166748046875,
0.0007081031799316406,
0.019805908203125,
0.0035877227783203125,
0.0228118896484375,
0.0081634521484375,
-0.00939178466796875,
0.0076904296875,
-0.003856658935546875,
-0.005901336669921875,
-0.003658294677734375,
0.0212860107421875,
-0.0020122528076171875,
0.01345062255859375,
0.0010051727294921875,
0.00011247396469116211,
0.01727294921875,
0.0167236328125,
-0.005077362060546875,
0.005054473876953125,
0.01186370849609375,
0.01324462890625,
0.00534820556640625,
-0.019012451171875,
-0.00798797607421875,
-0.001430511474609375,
-0.01229095458984375,
-0.01235198974609375,
-0.01482391357421875,
-0.00394439697265625,
0.02801513671875,
0.00655364990234375,
0.01373291015625,
-0.006732940673828125,
-0.0106353759765625,
0.039520263671875,
-0.0287933349609375,
-0.01215362548828125,
0.00861358642578125,
-0.035919189453125,
0.000005424022674560547,
0.0017948150634765625,
-0.029449462890625,
-0.00970458984375,
0.016632080078125,
0.0092620849609375,
-0.025726318359375,
0.0199737548828125,
0.0079498291015625,
0.0272216796875,
-0.010040283203125,
-0.0062408447265625,
0.0308837890625,
-0.01375579833984375,
0.037628173828125,
-0.00951385498046875,
-0.0276031494140625,
-0.00664520263671875,
-0.005893707275390625,
-0.016387939453125,
-0.0151214599609375,
-0.0091552734375,
0.044921875,
-0.00197601318359375,
0.00853729248046875,
-0.0268707275390625,
0.0029811859130859375,
-0.00455474853515625,
0.047454833984375,
-0.0186614990234375,
-0.0193939208984375,
0.0084228515625,
0.0179901123046875,
0.0114288330078125,
0.0106201171875,
0.0174407958984375,
-0.0003204345703125,
-0.037384033203125,
-0.01261138916015625,
0.0361328125,
0.004978179931640625,
-0.00905609130859375,
0.0206146240234375,
-0.0125274658203125,
0.0046539306640625,
0.008056640625,
0.004619598388671875,
-0.0266265869140625,
-0.0014390945434570312,
-0.03668212890625,
-0.00039386749267578125,
0.021697998046875,
0.004589080810546875,
0.00525665283203125,
-0.0191802978515625,
0.0211639404296875,
-0.0203094482421875,
0.0157928466796875,
-0.01195526123046875,
-0.01200103759765625,
0.01885986328125,
-0.0015420913696289062,
0.017669677734375,
-0.01335906982421875,
-0.01172637939453125,
-0.0001304149627685547,
-0.01277923583984375,
-0.001377105712890625,
-0.01560211181640625,
0.01116943359375,
0.0283050537109375,
-0.0252685546875,
0.0301666259765625,
-0.020751953125,
-0.0049285888671875,
-0.01322174072265625,
-0.00855255126953125,
0.01050567626953125,
0.0177154541015625,
-0.0243682861328125,
-0.0126800537109375,
0.01015472412109375,
-0.00485992431640625,
0.001964569091796875,
-0.0030879974365234375,
-0.0303497314453125,
0.00934600830078125,
-0.0216522216796875,
-0.0009822845458984375,
0.0272979736328125,
0.0225677490234375,
-0.047119140625,
-0.00914764404296875,
-0.00797271728515625,
-0.01157379150390625,
0.0123291015625,
-0.01953125,
-0.042236328125,
-0.00423431396484375,
0.0178680419921875,
-0.0108184814453125,
-0.019989013671875,
0.009796142578125,
-0.0098114013671875,
-0.007373809814453125,
-0.00833892822265625,
0.0031280517578125,
0.01450347900390625,
0.01342010498046875,
0.0084381103515625,
-0.0027313232421875,
0.0421142578125,
-0.025604248046875,
0.0196075439453125,
-0.007366180419921875,
0.017242431640625,
-0.005382537841796875,
0.036041259765625,
0.01727294921875,
-0.032501220703125,
-0.004970550537109375,
0.005096435546875,
0.0028228759765625,
0.0174102783203125,
0.006679534912109375,
0.005481719970703125,
0.02593994140625,
0.0313720703125,
-0.005191802978515625,
-0.00997161865234375,
0.003284454345703125,
0.044219970703125,
-0.00028514862060546875,
-0.0013837814331054688,
-0.0038299560546875,
-0.0072479248046875,
-0.0284881591796875,
-0.032318115234375,
0.002838134765625,
0.0006718635559082031,
-0.03350830078125,
0.03814697265625,
0.001293182373046875,
0.01320648193359375,
0.0085906982421875,
0.004360198974609375,
-0.0073394775390625,
-0.039337158203125,
0.0208587646484375,
-0.0038166046142578125,
-0.02099609375,
-0.01212310791015625,
0.01551055908203125,
-0.01494598388671875,
0.029937744140625,
0.006420135498046875,
-0.006221771240234375,
0.01629638671875,
0.0494384765625,
0.018035888671875,
0.011566162109375,
-0.007537841796875,
-0.006011962890625,
-0.0022296905517578125,
0.0104522705078125,
0.0005359649658203125,
0.0029392242431640625,
0.04443359375,
-0.04437255859375,
-0.00035834312438964844,
-0.04095458984375,
0.0175018310546875,
-0.0163726806640625,
0.01125335693359375,
-0.0024127960205078125,
-0.01012420654296875,
-0.0215301513671875,
0.0150909423828125,
0.0114288330078125,
-0.032257080078125,
-0.021636962890625,
0.00345611572265625,
-0.0291900634765625,
-0.006259918212890625,
0.01303863525390625,
-0.029449462890625,
0.0010862350463867188,
0.0169525146484375,
-0.03875732421875,
-0.0130615234375,
-0.0218505859375,
-0.0182342529296875,
0.0000972747802734375,
-0.038421630859375,
-0.011260986328125,
0.025421142578125,
-0.006290435791015625,
0.00829315185546875,
-0.0068817138671875,
0.000041961669921875,
0.013885498046875,
0.0247650146484375,
0.0160980224609375,
0.02252197265625,
-0.00263214111328125,
0.023345947265625,
0.00896453857421875,
-0.01678466796875,
-0.0012226104736328125,
0.0031337738037109375,
0.006893157958984375,
-0.031341552734375,
-0.02392578125,
-0.042877197265625,
0.02001953125,
0.00475311279296875,
0.00283050537109375,
-0.0126800537109375,
-0.009674072265625,
-0.01171112060546875,
-0.0241851806640625,
-0.05181884765625,
-0.00848388671875,
0.004337310791015625,
0.0108795166015625,
0.000438690185546875,
0.0458984375,
0.0160675048828125,
-0.014984130859375,
-0.0242767333984375,
0.039337158203125,
0.0022258758544921875,
0.006832122802734375,
-0.010650634765625,
-0.0294189453125,
-0.006626129150390625,
-0.0079193115234375,
-0.01593017578125,
0.007442474365234375,
0.0206146240234375,
0.044464111328125,
0.024658203125,
-0.022857666015625,
0.0029544830322265625,
-0.0245513916015625,
-0.014617919921875,
0.018585205078125,
0.007305145263671875,
-0.0116424560546875,
-0.007747650146484375,
-0.0284576416015625,
-0.0067138671875,
-0.0124053955078125,
0.009246826171875,
0.0293121337890625,
-0.00959014892578125,
-0.01494598388671875,
0.0057830810546875,
0.0200653076171875,
-0.0003113746643066406,
0.014678955078125,
-0.00933837890625,
-0.0085296630859375,
0.01334381103515625,
-0.002643585205078125,
-0.01898193359375,
-0.006702423095703125,
-0.0089874267578125,
0.015899658203125,
0.0079803466796875,
-0.01482391357421875,
-0.0139923095703125,
-0.025634765625,
-0.016082763671875,
0.00373077392578125,
-0.031707763671875,
0.0308074951171875,
-0.005100250244140625,
0.01824951171875,
0.024505615234375,
-0.000017523765563964844,
-0.0036296844482421875,
0.01415252685546875,
-0.00788116455078125,
0.0008668899536132812,
-0.0261688232421875,
-0.00612640380859375,
-0.046630859375,
-0.0263214111328125,
-0.0123291015625,
0.0096282958984375,
0.00583648681640625,
0.0004813671112060547,
0.028656005859375,
0.0078887939453125,
-0.0017414093017578125,
-0.0007810592651367188,
-0.0230865478515625,
-0.0095062255859375,
0.00803375244140625,
0.028228759765625,
0.024200439453125,
0.01085662841796875,
-0.0162200927734375,
-0.0107269287109375,
0.0234375,
0.0153961181640625,
-0.0146636962890625,
0.0189666748046875,
0.00662994384765625,
0.0031223297119140625,
0.0265655517578125,
-0.0243377685546875,
0.00335693359375,
0.016937255859375,
-0.0166168212890625,
-0.00945281982421875,
-0.0418701171875,
0.0052490234375,
-0.0162200927734375,
-0.0017948150634765625,
0.037628173828125,
-0.01334381103515625,
0.0252227783203125,
-0.001232147216796875,
0.033905029296875,
0.00034618377685546875,
0.02410888671875,
-0.005336761474609375,
0.016387939453125,
0.032379150390625,
0.01306915283203125,
0.0019931793212890625,
-0.01456451416015625,
-0.0123748779296875,
0.006015777587890625,
-0.0193634033203125,
0.0172576904296875,
0.0009431838989257812,
-0.0028362274169921875,
0.00807952880859375,
-0.01267242431640625,
-0.035064697265625,
-0.0093841552734375,
-0.0041961669921875,
-0.0076446533203125,
0.030670166015625,
-0.034210205078125,
0.007381439208984375,
-0.01285552978515625,
-0.0174102783203125,
-0.0408935546875,
0.022705078125,
-0.0440673828125,
0.00507354736328125,
0.00452423095703125,
-0.0186767578125,
-0.00540924072265625,
0.00516510009765625,
0.0017690658569335938,
0.0087432861328125,
-0.001819610595703125,
0.037322998046875,
-0.0265655517578125,
0.01383209228515625,
0.0019073486328125,
0.0096588134765625,
-0.0009064674377441406,
-0.022125244140625,
0.03411865234375,
-0.0017976760864257812,
-0.0017862319946289062,
-0.0061798095703125,
0.0193023681640625,
0.02978515625,
0.035980224609375,
-0.021270751953125,
0.0088043212890625,
-0.0005521774291992188,
-0.022613525390625,
-0.00922393798828125,
0.003936767578125,
-0.00928497314453125,
0.0306854248046875,
0.039581298828125,
-0.00746917724609375,
0.01305389404296875,
-0.018341064453125,
-0.0289764404296875,
-0.002979278564453125,
-0.005695343017578125,
0.01364898681640625,
0.05352783203125,
0.01288604736328125,
-0.021026611328125,
-0.0064544677734375,
-0.014923095703125,
0.006580352783203125,
-0.0028553009033203125,
-0.01207733154296875,
0.0192413330078125,
-0.017608642578125,
-0.01507568359375,
-0.0100860595703125,
-0.035858154296875,
0.00107574462890625,
-0.015289306640625,
-0.0300445556640625,
0.003772735595703125,
-0.006114959716796875,
0.01203155517578125,
-0.005207061767578125,
0.0246734619140625,
0.01385498046875,
-0.034027099609375,
0.00577545166015625,
0.0002803802490234375,
-0.0012197494506835938,
-0.0022411346435546875,
-0.042999267578125,
0.01224517822265625,
-0.0261383056640625,
0.003597259521484375,
0.0035228729248046875,
0.005931854248046875,
0.019622802734375,
0.0014238357543945312,
0.0035610198974609375,
0.01245880126953125,
0.043792724609375,
0.00748443603515625,
-0.031768798828125,
-0.024993896484375,
-0.024749755859375,
0.0082855224609375,
-0.049224853515625,
-0.003910064697265625,
0.0081939697265625,
-0.05084228515625,
0.0001175999641418457,
-0.0232391357421875,
0.0011186599731445312,
0.01036834716796875,
-0.00909423828125,
0.00630950927734375,
0.0186309814453125,
-0.0172119140625,
-0.0198822021484375,
-0.00621795654296875,
0.01593017578125,
-0.009735107421875,
0.0014257431030273438,
-0.01219940185546875,
-0.0059051513671875,
-0.01206207275390625,
0.0114288330078125,
0.0235443115234375,
0.037750244140625,
-0.013916015625,
0.0112457275390625,
0.01399993896484375,
0.0020751953125,
-0.0194091796875,
-0.033660888671875,
-0.01486968994140625,
-0.02813720703125,
0.03460693359375,
-0.024627685546875,
0.0278472900390625,
0.006374359130859375,
-0.036865234375,
0.0093536376953125,
0.00905609130859375,
0.007251739501953125,
0.00864410400390625,
-0.0157012939453125,
-0.0201416015625,
0.00933074951171875,
-0.0119171142578125,
0.00887298583984375,
-0.0045013427734375,
0.00783538818359375,
-0.0308074951171875,
0.0203094482421875,
-0.0091094970703125,
0.026702880859375,
0.005908966064453125,
0.002826690673828125,
-0.0251312255859375,
0.0023975372314453125
] |
ours_492
|
Denote by \( \measuredangle \) directed angles modulo \( \pi \).
**Lemma 1:** \( H, Q, O, X \) are concyclic.
**Proof:**
\[
\measuredangle HQX = \measuredangle HQP = \measuredangle HBP = \measuredangle BHP + \measuredangle HPB = \measuredangle BHA + \measuredangle AHP + \measuredangle HPA + \measuredangle APB = \measuredangle HAP + \measuredangle BHA + \measuredangle ACB = \measuredangle HAP + 2 \measuredangle ACB = \measuredangle HAP + \measuredangle AOB = \measuredangle HOA + \measuredangle AOB = \measuredangle HOB = \measuredangle HOX
\]
Thus, \( H, Q, O, X \) are concyclic, as desired.
**Lemma 2:** \( A, H, X \) are collinear.
**Proof:**
\[
\measuredangle XHO = \measuredangle XQO = \measuredangle PQO = \measuredangle PAO = \measuredangle AHO
\]
Thus, \( A, H, X \) are collinear, as desired.
The rest is straightforward. Let \( AH \cap BC = F \) and let \( M \) be the midpoint of \( BC \). Then \( BM = \frac{5}{2} \). Furthermore, \( F \) lies on segment \( BM \) with \( \frac{BF}{FM} = \frac{BX}{XO} = 2 \). Thus \( FM = \frac{5}{6} \).
Now let \( Y \) be the foot of the perpendicular from \( O \) to \( AF \). Then
\[
YF = OM = \sqrt{BO^2 - BM^2} = \sqrt{3^2 - \left(\frac{5}{2}\right)^2} = \frac{\sqrt{11}}{2}
\]
and
\[
AY = \sqrt{AO^2 - OY^2} = \sqrt{AO^2 - FM^2} = \sqrt{3^2 - \left(\frac{5}{6}\right)^2} = \frac{\sqrt{299}}{6}
\]
Then
\[
AF = AY + YF = \frac{\sqrt{299} + 3 \sqrt{11}}{6}
\]
Now let \( A' \) be the reflection of \( A \) over \( O \). Then \( AA' = 6 \). Also, triangle \( ABF \) is similar to triangle \( AA'C \). Thus,
\[
AB \cdot AC = AF \cdot AA' = \sqrt{299} + 3 \sqrt{11}
\]
Thus the answer is \( 29900 + 30 + 11 = 29941 \).
\(\boxed{29941}\)
|
29941
|
{
"competition": "us_comps",
"dataset": "Ours",
"posts": null,
"source": "OMOFall19Solns-2.md"
}
|
Let \( \triangle ABC \) be an acute scalene triangle with orthocenter \( H \) and circumcenter \( O \). Let the line through \( A \) tangent to the circumcircle of triangle \( AHO \) intersect the circumcircle of triangle \( ABC \) at \( A \) and \( P \neq A \). Let the circumcircles of triangles \( AOP \) and \( BHP \) intersect at \( P \) and \( Q \neq P \). Let line \( PQ \) intersect segment \( BO \) at \( X \). Suppose that \( BX = 2 \), \( OX = 1 \), and \( BC = 5 \). Then \( AB \cdot AC = \sqrt{k} + m \sqrt{n} \) for positive integers \( k, m, \) and \( n \), where neither \( k \) nor \( n \) is divisible by the square of any integer greater than 1. Compute \( 100k + 10m + n \).
|
[
"/Mathematics/Geometry/GeneralGeometry/EuclideanGeometry",
"/Mathematics/Geometry/GeneralGeometry/Geometry",
"/Mathematics/Geometry/PlaneGeometry/Circles/Circle",
"/Mathematics/Geometry/PlaneGeometry/Circles/Circle-CircleIntersection",
"/Mathematics/Geometry/PlaneGeometry/Circles/Circumcenter",
"/Mathematics/Geometry/PlaneGeometry/Circles/Concyclic",
"/Mathematics/Geometry/PlaneGeometry/Triangles/TriangleCenters",
"/Mathematics/Geometry/PlaneGeometry/Triangles/TriangleCircles"
] |
Reflect A across O to obtain A' so that ABF ∼ A'A C, turning AB·AC into AF·AA' which can be computed from the geometry.
|
[
-0.0002734661102294922,
-0.03857421875,
0.027740478515625,
0.030364990234375,
-0.0010747909545898438,
-0.01166534423828125,
0.0300445556640625,
0.05035400390625,
-0.00688934326171875,
-0.03240966796875,
-0.0155792236328125,
0.01354217529296875,
-0.01030731201171875,
-0.006649017333984375,
-0.0095367431640625,
-0.0036411285400390625,
0.031494140625,
-0.024169921875,
0.015960693359375,
-0.00470733642578125,
-0.002902984619140625,
-0.01470184326171875,
-0.053375244140625,
-0.010498046875,
-0.0201416015625,
-0.0153656005859375,
-0.01316070556640625,
-0.01348876953125,
-0.039947509765625,
0.0275421142578125,
0.005794525146484375,
-0.0243072509765625,
0.0012559890747070312,
-0.0268707275390625,
0.0021343231201171875,
0.021942138671875,
0.01050567626953125,
-0.005252838134765625,
-0.049835205078125,
-0.04754638671875,
0.0247344970703125,
-0.0008654594421386719,
-0.0216064453125,
0.028656005859375,
0.01346588134765625,
0.004001617431640625,
-0.00030684471130371094,
-0.014007568359375,
-0.00981903076171875,
0.01180267333984375,
0.00586700439453125,
0.01947021484375,
-0.0310516357421875,
-0.0088043212890625,
-0.025360107421875,
-0.038665771484375,
-0.046844482421875,
0.0008039474487304688,
0.01082611083984375,
0.02197265625,
0.00033020973205566406,
0.00876617431640625,
-0.0002677440643310547,
-0.02532958984375,
-0.002475738525390625,
-0.0105133056640625,
-0.0207061767578125,
-0.016845703125,
-0.003612518310546875,
-0.00893402099609375,
0.051544189453125,
-0.014617919921875,
-0.00846099853515625,
0.00441741943359375,
0.024505615234375,
-0.01044464111328125,
-0.0085601806640625,
0.01053619384765625,
-0.0004458427429199219,
0.004375457763671875,
-0.003406524658203125,
-0.017669677734375,
0.015899658203125,
-0.03692626953125,
0.0110626220703125,
0.020111083984375,
-0.0305938720703125,
0.008087158203125,
0.0343017578125,
-0.0101318359375,
0.0078125,
0.030517578125,
-0.042694091796875,
-0.0047607421875,
0.004055023193359375,
0.00890350341796875,
0.005977630615234375,
-0.005496978759765625,
-0.0187835693359375,
0.001865386962890625,
-0.00820159912109375,
-0.00978851318359375,
-0.00348663330078125,
-0.0236968994140625,
0.00872039794921875,
-0.0178375244140625,
0.00012052059173583984,
0.003040313720703125,
-0.005161285400390625,
-0.0007867813110351562,
0.018646240234375,
-0.020355224609375,
0.045501708984375,
0.01111602783203125,
0.017303466796875,
-0.0134124755859375,
0.04052734375,
0.0107269287109375,
0.0077667236328125,
0.020904541015625,
0.003597259521484375,
0.01085662841796875,
0.00911712646484375,
0.0430908203125,
-0.00408172607421875,
-0.0123748779296875,
-0.01001739501953125,
0.003955841064453125,
-0.0219573974609375,
0.0093231201171875,
0.0003209114074707031,
-0.004558563232421875,
-0.0259857177734375,
-0.016754150390625,
-0.0516357421875,
0.011077880859375,
-0.017852783203125,
-0.0146636962890625,
0.004726409912109375,
-0.0189361572265625,
0.01093292236328125,
-0.01541900634765625,
0.01070404052734375,
-0.07623291015625,
0.024169921875,
-0.04827880859375,
0.0022182464599609375,
-0.0025310516357421875,
0.007770538330078125,
0.0080108642578125,
0.005825042724609375,
-0.01091766357421875,
0.01222991943359375,
0.0009169578552246094,
-0.0193023681640625,
-0.01103973388671875,
0.0067291259765625,
0.021759033203125,
0.0188140869140625,
-0.004608154296875,
-0.01168060302734375,
-0.0145721435546875,
0.01222991943359375,
-0.01435089111328125,
-0.01312255859375,
-0.010589599609375,
-0.0099029541015625,
-0.002124786376953125,
-0.0175933837890625,
-0.004428863525390625,
-0.0156707763671875,
0.0112762451171875,
-0.000888824462890625,
-0.01433563232421875,
-0.00028443336486816406,
0.01531219482421875,
-0.020233154296875,
0.004070281982421875,
-0.00882720947265625,
0.03021240234375,
-0.005977630615234375,
-0.03857421875,
-0.01302337646484375,
0.014495849609375,
0.0045928955078125,
0.0031223297119140625,
0.0026149749755859375,
0.00804901123046875,
0.017486572265625,
0.0167236328125,
-0.00423431396484375,
-0.0240478515625,
-0.007534027099609375,
-0.00475311279296875,
0.0203094482421875,
-0.00131988525390625,
-0.0238037109375,
-0.0019435882568359375,
0.021697998046875,
0.008148193359375,
-0.00873565673828125,
-0.0189056396484375,
0.02923583984375,
0.010833740234375,
-0.005672454833984375,
-0.0016155242919921875,
0.0003674030303955078,
-0.004566192626953125,
-0.01419830322265625,
0.008056640625,
0.007518768310546875,
0.01203155517578125,
-0.005706787109375,
-0.01389312744140625,
-0.0092315673828125,
-0.0111083984375,
-0.0262451171875,
0.019561767578125,
-0.0037021636962890625,
0.0142669677734375,
0.005645751953125,
-0.0160064697265625,
0.018829345703125,
-0.0183258056640625,
0.0010547637939453125,
0.0175933837890625,
-0.0028629302978515625,
-0.00859832763671875,
-0.01439666748046875,
0.00757598876953125,
-0.0102386474609375,
0.0086212158203125,
-0.009735107421875,
-0.003665924072265625,
-0.0225830078125,
-0.004543304443359375,
-0.03472900390625,
-0.007381439208984375,
0.005970001220703125,
-0.001247406005859375,
0.032440185546875,
-0.015655517578125,
-0.001399993896484375,
0.012969970703125,
0.014678955078125,
-0.002338409423828125,
0.0091094970703125,
-0.01947021484375,
-0.021484375,
-0.016021728515625,
-0.015472412109375,
0.006504058837890625,
0.01390838623046875,
-0.00928497314453125,
-0.0157470703125,
0.005092620849609375,
-0.004199981689453125,
0.003536224365234375,
-0.0051727294921875,
0.01157379150390625,
-0.0029506683349609375,
-0.01251983642578125,
-0.0017261505126953125,
-0.023468017578125,
0.004039764404296875,
0.0234375,
-0.006946563720703125,
0.0184478759765625,
0.01311492919921875,
-0.0092010498046875,
0.0477294921875,
-0.03057861328125,
0.0113067626953125,
0.014251708984375,
0.009857177734375,
-0.01392364501953125,
-0.01326751708984375,
0.005939483642578125,
0.0090789794921875,
-0.0012693405151367188,
0.01053619384765625,
-0.0202178955078125,
-0.0421142578125,
-0.0014324188232421875,
0.0103302001953125,
-0.005153656005859375,
0.018096923828125,
-0.035186767578125,
0.00579071044921875,
0.032012939453125,
0.0024394989013671875,
0.0172576904296875,
-0.00969696044921875,
-0.0262451171875,
0.054718017578125,
-0.002391815185546875,
-0.0012645721435546875,
0.0008707046508789062,
0.0018558502197265625,
0.006534576416015625,
0.033172607421875,
-0.0194854736328125,
-0.00403594970703125,
0.01287078857421875,
0.03570556640625,
0.00583648681640625,
0.0175323486328125,
0.0032176971435546875,
-0.037628173828125,
0.0081634521484375,
0.003204345703125,
0.0011034011840820312,
-0.017669677734375,
-0.01148223876953125,
-0.04217529296875,
-0.0123443603515625,
-0.01226806640625,
0.00734710693359375,
-0.024017333984375,
0.0195159912109375,
-0.0013065338134765625,
0.027130126953125,
0.0328369140625,
0.00994873046875,
0.0198974609375,
-0.02880859375,
0.015838623046875,
-0.0017690658569335938,
0.034881591796875,
0.0271759033203125,
-0.02081298828125,
-0.0072479248046875,
-0.01143646240234375,
-0.017425537109375,
0.0263519287109375,
0.0000553131103515625,
-0.007328033447265625,
0.024322509765625,
0.0012369155883789062,
-0.0088653564453125,
0.002414703369140625,
0.0159912109375,
0.051300048828125,
-0.06719970703125,
-0.0274810791015625,
0.016448974609375,
-0.0205078125,
0.00041413307189941406,
-0.019317626953125,
-0.0462646484375,
0.024993896484375,
0.0084228515625,
0.0222625732421875,
0.0089111328125,
-0.022003173828125,
-0.021270751953125,
-0.005245208740234375,
0.006694793701171875,
-0.007328033447265625,
-0.0102691650390625,
0.0030078887939453125,
-0.026336669921875,
-0.017425537109375,
0.0234222412109375,
-0.01702880859375,
0.0015230178833007812,
-0.0048675537109375,
0.01184844970703125,
-0.031707763671875,
-0.0105133056640625,
0.00921630859375,
-0.0007867813110351562,
-0.006488800048828125,
-0.003139495849609375,
0.045318603515625,
0.0139312744140625,
0.004974365234375,
0.005290985107421875,
-0.00843048095703125,
-0.01275634765625,
-0.0160064697265625,
-0.0233917236328125,
-0.00737762451171875,
0.01242828369140625,
-0.00914764404296875,
-0.00904083251953125,
-0.00888824462890625,
-0.0310211181640625,
0.016387939453125,
0.003505706787109375,
-0.0116729736328125,
0.00823974609375,
-0.0137786865234375,
-0.00447845458984375,
-0.046234130859375,
0.007633209228515625,
-0.0002429485321044922,
0.003002166748046875,
0.0204010009765625,
-0.0169219970703125,
-0.059661865234375,
-0.012298583984375,
-0.00665283203125,
-0.0245361328125,
0.01529693603515625,
0.005603790283203125,
-0.0299072265625,
0.040374755859375,
-0.006473541259765625,
0.0105438232421875,
-0.01430511474609375,
-0.0072021484375,
0.0021572113037109375,
-0.01261138916015625,
-0.00867462158203125,
0.01390838623046875,
-0.0006885528564453125,
-0.01070404052734375,
0.0300445556640625,
-0.0211944580078125,
0.0086822509765625,
-0.011138916015625,
0.035858154296875,
0.007419586181640625,
0.01983642578125,
0.0109100341796875,
-0.0159454345703125,
0.046478271484375,
-0.0016851425170898438,
-0.02703857421875,
0.031890869140625,
0.00785064697265625,
-0.013031005859375,
0.01219940185546875,
0.0105133056640625,
-0.0029125213623046875,
0.035186767578125,
0.00011068582534790039,
0.00905609130859375,
0.0144805908203125,
-0.004985809326171875,
0.01000213623046875,
-0.01263427734375,
0.01273345947265625,
0.0152587890625,
-0.00821685791015625,
-0.007160186767578125,
-0.016143798828125,
0.0237274169921875,
0.01067352294921875,
-0.00832366943359375,
-0.0137786865234375,
0.0107421875,
-0.0439453125,
0.0213623046875,
0.01409149169921875,
0.048492431640625,
-0.03436279296875,
-0.033203125,
0.06512451171875,
-0.00750732421875,
0.0031719207763671875,
-0.005657196044921875,
0.022064208984375,
-0.0101776123046875,
-0.004077911376953125,
-0.0267181396484375,
0.0109405517578125,
0.012939453125,
-0.019012451171875,
0.01140594482421875,
-0.0224151611328125,
-0.01184844970703125,
-0.015899658203125,
-0.01082611083984375,
0.026763916015625,
0.0261077880859375,
0.002147674560546875,
-0.00029206275939941406,
0.031402587890625,
-0.004734039306640625,
-0.032196044921875,
-0.03424072265625,
-0.020416259765625,
0.00007933378219604492,
0.04107666015625,
0.0235137939453125,
-0.01319122314453125,
0.0091552734375,
-0.0360107421875,
-0.00531005859375,
0.01187896728515625,
-0.01715087890625,
-0.02978515625,
-0.0282135009765625,
-0.0343017578125,
0.019805908203125,
-0.00644683837890625,
-0.0016832351684570312,
-0.01398468017578125,
0.027496337890625,
-0.0279693603515625,
0.00577545166015625,
0.0029087066650390625,
0.028778076171875,
-0.0295257568359375,
0.04095458984375,
0.003093719482421875,
-0.023529052734375,
0.00948333740234375,
0.002674102783203125,
-0.0006151199340820312,
0.0200347900390625,
-0.028839111328125,
0.042327880859375,
0.01727294921875,
0.01157379150390625,
-0.05133056640625,
0.05609130859375,
0.044677734375,
-0.0243377685546875,
0.009368896484375,
-0.00988006591796875,
0.004302978515625,
0.0179595947265625,
0.02239990234375,
-0.01312255859375,
-0.0030651092529296875,
0.03594970703125,
-0.026947021484375,
0.0182342529296875,
0.00992584228515625,
-0.07269287109375,
0.01404571533203125,
-0.0241546630859375,
0.022735595703125,
-0.016357421875,
-0.0203094482421875,
0.00421905517578125,
-0.0028324127197265625,
-0.0142822265625,
0.0131988525390625,
0.004619598388671875,
-0.0202178955078125,
-0.00846099853515625,
0.01270294189453125,
-0.027008056640625,
0.01580810546875,
-0.0227813720703125,
0.0115509033203125,
0.00716400146484375,
0.0018968582153320312,
-0.045684814453125,
0.02740478515625,
-0.04150390625,
-0.01166534423828125,
-0.011383056640625,
0.004978179931640625,
-0.0101470947265625,
0.0197601318359375,
0.0289154052734375,
0.004100799560546875,
0.00635528564453125,
-0.0031147003173828125,
0.0012521743774414062,
-0.030303955078125,
0.012420654296875,
-0.016265869140625,
-0.00452423095703125,
-0.041839599609375,
-0.00791168212890625,
-0.0029659271240234375,
0.0003814697265625,
0.0180206298828125,
0.04876708984375,
-0.040679931640625,
-0.01546478271484375,
0.01026153564453125,
-0.0087432861328125,
-0.02044677734375,
0.0102691650390625,
0.0255889892578125,
-0.016815185546875,
-0.0124664306640625,
-0.00821685791015625,
0.0025081634521484375,
-0.000048279762268066406,
-0.00873565673828125,
0.0008769035339355469,
-0.00237274169921875,
-0.0009169578552246094,
0.01467132568359375,
0.0164337158203125,
0.0012493133544921875,
0.006763458251953125,
-0.0191497802734375,
0.0382080078125,
0.014007568359375,
0.0270843505859375,
0.019287109375,
0.037139892578125,
-0.018341064453125,
-0.0185546875,
0.0159454345703125,
-0.022735595703125,
0.00048089027404785156,
-0.032684326171875,
0.004909515380859375,
0.0210723876953125,
0.01259613037109375,
-0.01230621337890625,
-0.01398468017578125,
-0.0078125,
-0.003753662109375,
0.0127716064453125,
-0.00519561767578125,
-0.0258636474609375,
-0.01282501220703125,
-0.00238800048828125,
-0.002071380615234375,
0.018280029296875,
0.017669677734375,
-0.005462646484375,
0.028533935546875,
0.003917694091796875,
-0.0178985595703125,
-0.00833892822265625,
-0.026885986328125,
0.0282745361328125,
-0.0283966064453125,
-0.028167724609375,
-0.0007176399230957031,
-0.00841522216796875,
-0.0047454833984375,
-0.0167694091796875,
-0.03167724609375,
0.0064239501953125,
0.0175628662109375,
-0.00655364990234375,
-0.0194854736328125,
0.01293182373046875,
0.004077911376953125,
0.020477294921875,
-0.04931640625,
-0.0206451416015625,
0.002277374267578125,
-0.01220703125,
-0.01471710205078125,
-0.002414703369140625,
0.0206146240234375,
0.00702667236328125,
0.0050811767578125,
0.01425933837890625,
-0.0016412734985351562,
0.0128326416015625,
-0.021453857421875,
-0.00496673583984375,
-0.019775390625,
0.02130126953125,
0.0182647705078125,
-0.017425537109375,
-0.0139923095703125,
0.01015472412109375,
0.018463134765625,
-0.0006346702575683594,
0.00042366981506347656,
-0.050750732421875,
-0.047119140625,
0.00902557373046875,
0.0240936279296875,
0.00817108154296875,
-0.0018434524536132812,
-0.0012178421020507812,
-0.0021114349365234375,
-0.013519287109375,
0.019927978515625,
-0.04193115234375,
0.0178985595703125,
0.006561279296875,
-0.0030231475830078125,
0.01309967041015625,
-0.0004703998565673828,
0.0206298828125,
-0.006000518798828125,
-0.00789642333984375,
0.02069091796875,
0.0058746337890625,
0.0018510818481445312,
0.0299072265625,
-0.0191497802734375,
-0.01364898681640625,
0.0200042724609375,
-0.03546142578125,
-0.0122528076171875,
-0.023345947265625,
0.03900146484375,
0.022857666015625,
-0.0018072128295898438,
0.0118408203125,
-0.0231475830078125,
0.0257720947265625,
-0.01131439208984375,
0.0003876686096191406,
-0.027557373046875,
-0.02880859375,
-0.03424072265625,
-0.00010591745376586914,
0.0169677734375,
-0.0291748046875,
0.00014352798461914062,
-0.0239410400390625,
-0.01537322998046875,
-0.0272674560546875,
-0.0028820037841796875,
-0.0245361328125,
-0.00839996337890625,
-0.0050201416015625,
0.02349853515625,
-0.01314544677734375,
0.021881103515625,
-0.004062652587890625,
-0.01421356201171875,
-0.023040771484375,
-0.0240478515625,
0.0270538330078125,
0.025543212890625,
-0.0168609619140625,
0.00046372413635253906,
-0.007434844970703125,
0.00997161865234375,
0.03546142578125,
-0.0150299072265625,
0.026580810546875,
0.0035343170166015625,
-0.00164031982421875,
-0.005771636962890625,
-0.01293182373046875,
-0.048095703125,
-0.01285552978515625,
0.01410675048828125,
0.0294647216796875,
-0.0236968994140625,
0.0000330805778503418,
-0.0091552734375,
-0.0103607177734375,
0.0131378173828125,
-0.01358795166015625,
-0.0149078369140625,
0.0233612060546875,
0.0011091232299804688,
0.0087890625,
0.01096343994140625,
-0.0282440185546875,
-0.05670166015625,
-0.01357269287109375,
0.015106201171875,
-0.01377105712890625,
-0.0217132568359375,
0.0162200927734375,
-0.0067901611328125,
-0.004718780517578125,
-0.00171661376953125,
0.0219879150390625,
0.013214111328125,
-0.0171661376953125,
-0.0041961669921875,
0.003139495849609375,
0.003170013427734375,
-0.0313720703125,
0.00749969482421875,
0.034027099609375,
-0.005603790283203125,
0.00734710693359375,
-0.00640106201171875,
-0.01311492919921875,
-0.0027484893798828125,
-0.042633056640625,
-0.013885498046875,
0.03192138671875,
-0.0032558441162109375,
-0.00913238525390625,
0.0014286041259765625,
-0.03662109375,
0.03179931640625,
-0.0439453125,
-0.0015611648559570312,
-0.0163726806640625,
0.0103912353515625,
0.021636962890625,
-0.01568603515625,
0.020233154296875,
-0.009613037109375,
0.021759033203125,
-0.027069091796875,
-0.01552581787109375,
-0.0323486328125,
-0.0044708251953125,
-0.0176239013671875,
-0.0154876708984375,
-0.0218658447265625,
0.0018682479858398438,
-0.01922607421875,
-0.006229400634765625,
0.0005979537963867188,
0.046478271484375,
0.01070404052734375,
-0.01203155517578125,
0.011077880859375,
-0.01959228515625,
-0.00824737548828125,
0.0322265625,
-0.006931304931640625,
0.006420135498046875,
-0.006839752197265625,
-0.007640838623046875,
-0.019683837890625,
0.004421234130859375,
0.00817108154296875,
0.015228271484375,
0.005046844482421875,
-0.03118896484375,
0.0228118896484375,
-0.0272979736328125,
-0.00519561767578125,
-0.025787353515625,
-0.00829315185546875,
0.0145416259765625,
-0.0144805908203125,
-0.0067596435546875,
-0.0014438629150390625,
-0.0082550048828125,
-0.02166748046875,
-0.01090240478515625,
-0.0183868408203125,
-0.0238494873046875,
0.0212860107421875,
-0.004116058349609375,
0.01007080078125,
-0.00913238525390625,
-0.005458831787109375,
0.042449951171875,
0.0081024169921875,
0.0214996337890625,
0.0323486328125,
0.017120361328125,
-0.01873779296875,
0.0013856887817382812,
0.0290985107421875,
-0.0004608631134033203,
0.029083251953125,
-0.0133514404296875,
-0.0015611648559570312,
-0.038665771484375,
0.0193023681640625,
-0.0189361572265625,
0.019134521484375,
0.004932403564453125,
0.0145111083984375,
0.01506805419921875,
-0.0031032562255859375,
0.0261077880859375,
-0.011962890625,
0.02215576171875,
0.04132080078125,
0.02703857421875,
0.0114288330078125,
0.00591278076171875,
-0.01153564453125,
0.059967041015625,
0.0045013427734375,
0.04498291015625,
-0.0249481201171875,
0.005916595458984375,
0.00911712646484375,
0.034149169921875,
0.045074462890625,
0.01340484619140625,
0.004119873046875,
0.055633544921875,
0.00029087066650390625,
-0.006572723388671875,
-0.0161590576171875,
0.01434326171875,
0.00574493408203125,
-0.0152587890625,
-0.0022754669189453125,
0.02410888671875,
-0.00017905235290527344,
-0.0270233154296875,
0.0012969970703125,
-0.0020313262939453125,
-0.0357666015625,
-0.0198516845703125,
-0.02069091796875,
0.01496124267578125,
0.0032520294189453125,
-0.01534271240234375,
-0.00839996337890625,
0.01139068603515625,
-0.02813720703125,
-0.0100860595703125,
0.00890350341796875,
0.0188446044921875,
-0.0229949951171875,
-0.01137542724609375,
-0.0180511474609375,
-0.0197601318359375,
0.01189422607421875,
0.006237030029296875,
0.025787353515625,
0.01959228515625,
-0.0001780986785888672,
-0.00786590576171875,
0.0242462158203125,
0.000335693359375,
0.006748199462890625,
-0.038543701171875,
-0.004444122314453125,
-0.01041412353515625,
-0.0083465576171875,
0.01403045654296875,
-0.00864410400390625,
-0.0182647705078125,
-0.0002111196517944336,
0.00518035888671875,
-0.031463623046875,
0.005901336669921875,
-0.0011091232299804688,
-0.0123291015625,
0.016571044921875,
0.0032215118408203125,
0.030181884765625,
-0.0399169921875,
-0.0199737548828125,
-0.0287628173828125,
0.0183258056640625,
0.0034694671630859375,
-0.025390625,
0.0136260986328125,
-0.032135009765625,
0.01483154296875,
0.015625,
0.00994110107421875,
-0.0030956268310546875,
-0.0082550048828125,
-0.0134735107421875,
0.01413726806640625,
0.0233917236328125,
0.01812744140625,
-0.0123138427734375,
0.0018663406372070312,
0.0084991455078125,
0.01239776611328125,
0.006961822509765625,
0.004306793212890625,
0.0038928985595703125,
-0.020111083984375,
0.01099395751953125,
0.02032470703125,
-0.01309967041015625,
0.0057220458984375,
0.023651123046875,
0.0167694091796875,
0.01177978515625,
0.0186767578125,
0.0223541259765625,
0.049407958984375,
0.02587890625,
0.0200042724609375,
0.0089569091796875,
0.035736083984375,
-0.01551055908203125,
0.0187835693359375,
-0.041107177734375,
-0.018646240234375,
0.0027713775634765625,
0.039306640625,
0.00916290283203125,
0.0267181396484375,
0.00890350341796875,
-0.045013427734375,
0.017913818359375,
0.02740478515625,
-0.0186614990234375,
-0.02056884765625,
0.021026611328125,
0.02874755859375,
-0.00048089027404785156,
0.05572509765625,
0.000667572021484375,
-0.00904083251953125,
0.005062103271484375,
-0.01305389404296875,
0.0455322265625,
-0.0054168701171875,
0.041595458984375,
0.0186767578125,
-0.0243072509765625,
0.006870269775390625,
-0.0219879150390625,
-0.01373291015625,
-0.0169677734375,
0.0154876708984375,
0.0167236328125,
0.0105133056640625,
-0.0167083740234375,
-0.016876220703125,
0.027496337890625,
0.0058135986328125,
0.010406494140625,
-0.0087738037109375,
0.01861572265625,
-0.0089874267578125,
-0.00588226318359375,
0.01446533203125,
0.03662109375,
-0.0036869049072265625,
0.051116943359375,
-0.035308837890625,
-0.0033626556396484375,
-0.0072479248046875,
-0.036468505859375,
-0.0303497314453125,
-0.031982421875,
0.0275115966796875,
-0.0163726806640625,
-0.01262664794921875,
-0.022064208984375,
-0.002307891845703125,
0.021759033203125,
-0.0250701904296875,
0.01605224609375,
0.006107330322265625,
-0.031036376953125,
0.00580596923828125,
-0.01654052734375,
-0.011138916015625,
-0.0211181640625,
0.0172882080078125,
-0.024993896484375,
-0.0217437744140625,
0.01396942138671875,
0.004116058349609375,
-0.0204315185546875,
-0.00905609130859375,
-0.006420135498046875,
-0.005950927734375,
0.0013475418090820312,
-0.004116058349609375,
0.0016546249389648438,
0.015289306640625,
0.022735595703125,
-0.016357421875,
0.006069183349609375,
-0.0190887451171875,
0.024505615234375,
-0.02215576171875,
-0.00618743896484375,
0.0030994415283203125,
0.01050567626953125,
0.016143798828125,
-0.0350341796875,
-0.00255584716796875,
-0.012176513671875,
0.045928955078125,
-0.01224517822265625,
-0.01435089111328125,
-0.01018524169921875,
-0.00391387939453125,
0.0252227783203125,
-0.049774169921875,
-0.00861358642578125,
-0.00028061866760253906,
-0.0063934326171875,
0.011932373046875,
-0.019989013671875,
-0.00467681884765625,
-0.0265655517578125,
0.011810302734375,
-0.01702880859375,
0.0214691162109375,
-0.005046844482421875,
-0.04034423828125,
0.005615234375,
0.0170440673828125,
-0.024078369140625,
-0.01055145263671875,
-0.0511474609375,
0.016845703125,
-0.010528564453125,
0.014739990234375,
-0.0274200439453125,
-0.002933502197265625,
-0.007274627685546875,
0.0090484619140625,
-0.015899658203125,
0.006389617919921875,
0.041961669921875,
0.025543212890625,
0.0014925003051757812,
0.006988525390625,
0.0321044921875,
0.00708770751953125,
0.02349853515625,
0.0042572021484375,
-0.031097412109375,
-0.02606201171875,
0.0233612060546875,
0.0030536651611328125,
0.01322174072265625,
-0.037384033203125,
0.0238037109375,
0.0106964111328125,
0.025726318359375,
-0.006053924560546875,
-0.01201629638671875,
0.00011402368545532227,
-0.004238128662109375,
0.0203857421875,
-0.001964569091796875,
0.00595855712890625,
-0.006542205810546875,
-0.01192474365234375,
0.043212890625,
-0.0122222900390625,
-0.00507354736328125,
0.00388336181640625,
0.004993438720703125,
-0.040618896484375,
-0.00818634033203125,
0.0058135986328125,
0.018463134765625,
-0.0224609375,
-0.02838134765625,
0.005336761474609375,
0.0186920166015625,
-0.003574371337890625,
-0.00635528564453125,
-0.0146636962890625,
0.005031585693359375,
-0.0027713775634765625,
0.01261138916015625,
-0.0044403076171875,
0.0008845329284667969,
-0.027618408203125,
-0.01250457763671875,
-0.0143890380859375,
-0.0017948150634765625,
0.01131439208984375,
0.00327301025390625,
-0.042327880859375,
0.0008234977722167969,
0.0106048583984375,
0.0303955078125,
-0.01605224609375,
-0.025604248046875,
-0.02313232421875,
0.01256561279296875,
0.032562255859375,
0.01367950439453125,
-0.017852783203125,
-0.0328369140625,
0.0203094482421875,
0.0411376953125,
-0.0084686279296875,
0.00472259521484375,
-0.004550933837890625,
0.04193115234375,
0.0028324127197265625,
0.0167694091796875,
0.01230621337890625,
-0.0028514862060546875,
0.02130126953125,
0.02142333984375,
-0.0018396377563476562,
-0.0014696121215820312,
0.001232147216796875,
-0.0284271240234375,
-0.0240936279296875,
-0.001468658447265625,
-0.0301513671875,
0.0273284912109375,
0.019989013671875,
-0.0092315673828125,
0.00037217140197753906,
-0.0143585205078125,
-0.03338623046875,
0.007747650146484375,
-0.035980224609375,
-0.00954437255859375,
-0.00905609130859375,
-0.00534820556640625,
-0.004150390625,
0.024810791015625,
-0.00203704833984375,
0.015960693359375,
0.0036487579345703125,
-0.0173492431640625,
-0.035430908203125,
-0.0138397216796875,
-0.0156097412109375,
-0.003688812255859375,
-0.0289154052734375,
-0.01641845703125,
-0.006687164306640625,
-0.00284576416015625,
0.0100555419921875,
0.021240234375,
-0.034576416015625,
0.02996826171875,
0.0164642333984375,
-0.005802154541015625,
0.0149993896484375,
-0.01593017578125,
-0.012939453125,
-0.0214080810546875,
-0.0073699951171875,
-0.005825042724609375,
-0.01519012451171875,
-0.018890380859375,
-0.00010818243026733398,
0.032470703125,
0.0027179718017578125,
0.005168914794921875,
-0.0211944580078125,
0.007244110107421875,
-0.0179595947265625,
0.033203125,
0.005802154541015625,
0.0222015380859375,
0.020172119140625,
0.0139312744140625,
0.0021839141845703125,
0.015411376953125,
-0.036468505859375,
-0.034210205078125,
-0.00733184814453125,
0.03509521484375,
-0.0499267578125,
0.035247802734375,
-0.0101776123046875,
0.00257110595703125,
0.0011539459228515625,
-0.02606201171875,
0.019927978515625,
-0.0219268798828125,
-0.0399169921875,
0.005687713623046875,
-0.032318115234375,
0.0274810791015625,
-0.005645751953125,
0.0191497802734375,
-0.0018796920776367188,
0.00044989585876464844,
0.031036376953125,
0.00653839111328125,
0.01477813720703125,
0.007106781005859375,
-0.00519561767578125,
0.0183258056640625,
-0.03472900390625,
0.017578125,
0.0041351318359375,
-0.03759765625,
-0.0012645721435546875,
-0.0103912353515625,
-0.0014944076538085938,
0.05377197265625,
-0.0024318695068359375,
0.0163421630859375,
-0.004512786865234375,
0.0156707763671875,
0.00946807861328125,
0.02825927734375,
0.0231781005859375,
0.002513885498046875,
-0.01322174072265625,
-0.022613525390625,
-0.006649017333984375,
0.00875091552734375,
-0.0120697021484375,
0.01910400390625,
0.04827880859375,
-0.01096343994140625,
-0.0168304443359375,
-0.0159759521484375,
-0.004596710205078125,
0.0364990234375,
0.007904052734375,
0.0139007568359375,
0.01349639892578125,
0.034912109375,
0.00942230224609375,
0.029327392578125,
-0.0029125213623046875,
-0.0171966552734375,
-0.0117034912109375,
0.006317138671875,
0.0238037109375,
-0.01509857177734375,
0.01079559326171875,
-0.00930023193359375,
0.0004322528839111328,
0.003841400146484375,
-0.00876617431640625,
-0.0198822021484375,
0.00286102294921875,
0.01125335693359375,
-0.006649017333984375,
0.0020160675048828125,
0.002880096435546875,
-0.015533447265625,
-0.002651214599609375,
-0.0090179443359375,
0.0270538330078125,
-0.0143585205078125,
0.0010042190551757812,
-0.031280517578125,
-0.01983642578125,
0.0126953125,
0.0007348060607910156,
-0.00597381591796875,
-0.0193328857421875,
0.0008535385131835938,
0.010711669921875,
0.0205535888671875,
0.01412200927734375,
-0.00734710693359375,
-0.0015058517456054688,
-0.021270751953125,
-0.001949310302734375,
-0.001495361328125,
-0.0178680419921875,
-0.0017213821411132812,
-0.01287841796875,
0.024322509765625,
-0.0018310546875,
-0.005279541015625,
0.0151824951171875,
-0.0107269287109375,
0.006114959716796875,
0.005367279052734375,
-0.023223876953125,
-0.00836944580078125,
0.0308837890625,
-0.006153106689453125,
-0.0226593017578125,
0.01206207275390625,
0.0172882080078125,
-0.0149383544921875,
0.00823211669921875,
0.01751708984375,
0.006931304931640625,
0.0655517578125,
-0.0308380126953125,
0.0005826950073242188,
-0.0067901611328125,
0.0333251953125,
0.017669677734375,
0.0163421630859375,
-0.0014085769653320312,
-0.007110595703125,
0.0026836395263671875,
0.0103912353515625,
0.0193939208984375,
0.01348114013671875,
0.0036716461181640625,
-0.022552490234375,
-0.03192138671875,
-0.01024627685546875,
-0.0274658203125,
0.021209716796875,
0.0208740234375,
-0.0286712646484375,
0.00858306884765625,
-0.01181793212890625,
-0.005931854248046875,
0.0164642333984375,
-0.0049591064453125,
-0.0081787109375,
0.0249786376953125,
-0.01039886474609375,
-0.01326751708984375,
-0.0164031982421875,
0.0270843505859375,
0.001300811767578125,
0.0035076141357421875,
0.007198333740234375,
-0.000396728515625,
-0.00885009765625,
0.01457977294921875,
0.0035858154296875,
0.00922393798828125,
0.02325439453125,
0.049835205078125,
-0.0133819580078125,
0.00507354736328125,
-0.005157470703125,
-0.01155853271484375,
-0.018829345703125,
-0.0170745849609375,
-0.004016876220703125,
0.0080108642578125,
-0.003307342529296875,
0.0338134765625,
0.0016164779663085938,
0.01335906982421875,
0.0021514892578125,
0.0009250640869140625,
-0.00530242919921875,
-0.0022029876708984375,
0.006275177001953125,
0.0004584789276123047,
-0.0181427001953125,
-0.007320404052734375,
-0.0491943359375,
-0.001628875732421875,
0.0079803466796875,
-0.048919677734375,
0.003398895263671875,
0.021026611328125,
0.02435302734375,
0.00428009033203125,
0.0121917724609375,
0.00998687744140625,
-0.0246429443359375,
0.0204925537109375,
-0.0135955810546875,
-0.0195465087890625,
0.0194244384765625,
-0.00798797607421875,
0.0155487060546875,
-0.01029205322265625,
0.0188140869140625,
0.0281982421875,
0.01904296875,
0.026123046875,
0.0169677734375,
0.035980224609375,
-0.0266265869140625,
0.0024051666259765625,
-0.01171875,
0.0172119140625,
-0.01338958740234375,
-0.0292510986328125,
0.0011358261108398438,
0.034454345703125,
-0.0109710693359375,
0.0027923583984375,
-0.0036029815673828125,
-0.0150299072265625,
-0.02496337890625,
-0.034454345703125,
-0.004451751708984375,
0.005706787109375,
0.004055023193359375,
-0.013763427734375,
-0.0139007568359375,
0.018951416015625,
-0.0229339599609375,
-0.032501220703125,
0.0019855499267578125,
-0.01383209228515625,
0.00923919677734375,
0.007965087890625,
0.005466461181640625,
0.00818634033203125,
0.047027587890625,
0.004955291748046875,
-0.0080718994140625,
-0.0143585205078125,
-0.028167724609375,
0.0076141357421875,
-0.0064239501953125,
0.024383544921875,
-0.0083465576171875,
0.029693603515625,
-0.029541015625,
0.005950927734375,
0.014892578125,
-0.009307861328125,
0.005428314208984375,
-0.018524169921875,
0.01959228515625,
-0.005908966064453125,
-0.0180206298828125,
0.018310546875,
0.0273895263671875,
-0.020843505859375,
-0.0160675048828125,
-0.01192474365234375,
-0.0091705322265625,
-0.0049896240234375,
-0.00655364990234375,
0.031158447265625,
0.01385498046875,
-0.0164337158203125,
-0.023040771484375,
-0.00760650634765625,
-0.04034423828125,
0.03900146484375,
0.0301055908203125,
0.00603485107421875,
0.0017547607421875,
0.026214599609375,
-0.049713134765625,
-0.018951416015625,
-0.0108795166015625,
-0.0030670166015625,
0.006137847900390625,
-0.0081634521484375,
-0.01074981689453125,
-0.029693603515625,
0.042144775390625,
-0.039703369140625,
0.0199432373046875,
0.0011167526245117188,
0.0198211669921875,
-0.0310211181640625,
0.0082550048828125,
0.03369140625,
0.02093505859375,
-0.0084381103515625,
0.032135009765625,
0.048248291015625,
-0.011627197265625,
0.011810302734375,
0.0018939971923828125,
0.01126861572265625,
0.0318603515625,
-0.00258636474609375,
0.01024627685546875,
0.0299224853515625,
-0.0251007080078125,
0.004985809326171875,
-0.011444091796875,
0.00848388671875,
0.045440673828125,
0.00371551513671875,
-0.045867919921875,
0.01523590087890625,
-0.0105438232421875,
0.0118255615234375,
0.036285400390625,
-0.01070404052734375,
0.00507354736328125,
0.0298004150390625,
0.0176239013671875,
0.044586181640625,
-0.000423431396484375,
0.054443359375,
-0.0010662078857421875,
-0.004550933837890625,
-0.0219879150390625,
0.0029296875,
0.01702880859375,
-0.00815582275390625,
0.01325225830078125,
-0.0130462646484375,
-0.02972412109375,
-0.01995849609375,
0.038787841796875,
-0.017669677734375,
-0.0280609130859375,
-0.03375244140625,
-0.03802490234375,
-0.0008540153503417969,
0.0177154541015625,
-0.0166168212890625,
-0.0014524459838867188,
-0.0086822509765625,
-0.011993408203125,
-0.0031681060791015625,
-0.00873565673828125,
-0.01271820068359375,
0.005859375,
-0.006847381591796875,
0.0024261474609375,
0.0251922607421875,
0.0006108283996582031,
-0.006237030029296875,
-0.02508544921875,
0.0038051605224609375,
0.029571533203125,
0.019622802734375,
-0.01299285888671875,
-0.0266265869140625,
0.037811279296875,
0.007236480712890625,
-0.01454925537109375,
0.01012420654296875,
-0.00750732421875,
0.00795745849609375,
-0.027008056640625,
0.0016460418701171875,
-0.0190582275390625,
0.0139312744140625,
0.0024204254150390625,
0.036590576171875,
0.030487060546875,
-0.0110321044921875,
0.020843505859375,
-0.0008382797241210938,
0.0164337158203125,
0.0013494491577148438,
-0.0004944801330566406,
-0.0025081634521484375,
0.006549835205078125,
-0.004261016845703125,
0.0141754150390625,
-0.00839996337890625,
0.0246124267578125,
-0.0011577606201171875,
0.02142333984375,
-0.008270263671875,
-0.0021419525146484375,
-0.01079559326171875,
0.0281829833984375,
0.00377655029296875,
0.018890380859375,
-0.001384735107421875,
0.02813720703125,
-0.01279449462890625,
0.0069427490234375,
-0.0079345703125,
0.011505126953125,
-0.0036773681640625,
-0.003765106201171875,
-0.024261474609375,
-0.02252197265625,
-0.01560211181640625,
-0.0204010009765625,
0.0018243789672851562,
0.014617919921875,
-0.037841796875,
-0.00942230224609375,
-0.0016832351684570312,
-0.002285003662109375,
-0.006839752197265625,
0.014556884765625,
0.0166473388671875,
-0.0182037353515625,
0.029205322265625,
-0.0310211181640625,
-0.00946044921875,
0.01181793212890625,
-0.012359619140625,
-0.0030059814453125,
0.0160675048828125,
-0.00968170166015625,
0.020782470703125,
0.0236968994140625,
-0.00006389617919921875,
0.0266876220703125,
0.018310546875,
-0.0137786865234375,
-0.00145721435546875,
-0.0245819091796875,
-0.00792694091796875,
0.01220703125,
-0.002918243408203125,
0.004581451416015625,
0.00586700439453125,
0.036834716796875,
0.01107025146484375,
0.000293731689453125,
0.005634307861328125,
0.009490966796875,
-0.018798828125,
0.005451202392578125,
0.0197906494140625,
-0.02606201171875,
0.036407470703125,
-0.016357421875,
0.0006656646728515625,
-0.01155853271484375,
0.006626129150390625,
0.0038814544677734375,
-0.025909423828125,
0.0197601318359375,
-0.001499176025390625,
-0.031402587890625,
-0.02056884765625,
0.0308990478515625,
-0.01165008544921875,
-0.039306640625,
0.00461578369140625,
0.00001901388168334961,
0.0140380859375,
0.0292816162109375,
0.05010986328125,
-0.0026760101318359375,
-0.04315185546875,
-0.0019502639770507812,
0.005474090576171875,
0.02862548828125,
0.0206146240234375,
0.0211944580078125,
-0.02679443359375,
0.0301361083984375,
0.0030918121337890625,
-0.0146331787109375,
0.0026950836181640625,
-0.0187835693359375,
0.0227813720703125,
0.0211334228515625,
-0.03033447265625,
0.0180206298828125,
-0.0207977294921875,
0.007549285888671875,
0.00382232666015625,
-0.048919677734375,
0.009552001953125,
-0.01137542724609375,
-0.0020084381103515625,
0.00551605224609375,
0.0233612060546875,
0.02020263671875,
-0.01910400390625,
-0.040191650390625,
-0.01480865478515625,
-0.01184844970703125,
-0.0037708282470703125,
0.0223388671875,
0.004421234130859375,
0.00766754150390625,
0.0230560302734375,
-0.00684356689453125,
-0.0036830902099609375,
0.01214599609375,
-0.0084686279296875,
0.004581451416015625,
-0.01183319091796875,
-0.0017070770263671875,
-0.01380157470703125,
-0.00928497314453125,
0.0264739990234375,
-0.0254058837890625,
0.01556396484375,
0.0019483566284179688,
-0.03106689453125,
0.018402099609375,
-0.0172119140625,
-0.014190673828125,
0.005706787109375,
0.01132965087890625,
0.0295257568359375,
0.0108489990234375,
0.01041412353515625,
0.029937744140625,
-0.004962921142578125,
-0.01398468017578125,
0.01261138916015625,
0.0185699462890625,
-0.025604248046875,
0.0201263427734375,
-0.01507568359375,
-0.027740478515625,
-0.010345458984375,
0.016571044921875,
0.007190704345703125,
-0.02203369140625,
0.02117919921875,
-0.0389404296875,
-0.0158538818359375,
-0.0011148452758789062,
-0.0189666748046875,
0.0113525390625,
-0.00830078125,
-0.01288604736328125,
0.0215911865234375,
0.03973388671875,
0.0197601318359375,
0.000858306884765625,
-0.005275726318359375,
-0.01122283935546875,
0.0246734619140625,
0.0078887939453125,
-0.0253753662109375,
0.0052032470703125,
0.0131378173828125,
0.00838470458984375,
-0.01317596435546875,
-0.01160430908203125,
-0.01702880859375,
-0.007572174072265625,
0.0168609619140625,
-0.0205230712890625,
-0.0116424560546875,
-0.00685882568359375,
0.018402099609375,
0.020721435546875,
-0.001918792724609375,
-0.033905029296875,
-0.006008148193359375,
0.007381439208984375,
0.008697509765625,
-0.021148681640625,
0.01641845703125,
-0.0010099411010742188,
-0.02130126953125,
0.01708984375,
0.0017366409301757812,
-0.0258941650390625,
0.0284271240234375,
-0.00909423828125,
0.00476837158203125,
-0.0159759521484375,
0.01016998291015625,
-0.025482177734375,
-0.004390716552734375,
-0.007396697998046875,
0.007251739501953125,
-0.0006604194641113281,
-0.05047607421875,
-0.01297760009765625,
0.00788116455078125,
0.0006546974182128906,
-0.038299560546875,
0.03350830078125,
-0.02978515625,
-0.0038700103759765625,
0.00016319751739501953,
-0.042236328125,
-0.00757598876953125,
-0.0278472900390625,
-0.008758544921875,
-0.024932861328125,
-0.0303497314453125,
0.03057861328125,
0.02606201171875,
-0.007694244384765625,
-0.037109375,
-0.0097503662109375,
0.01483917236328125,
-0.02227783203125,
-0.009124755859375,
0.0036602020263671875,
0.0176544189453125,
-0.01105499267578125,
-0.0031833648681640625,
0.004268646240234375,
-0.0125732421875,
0.0303802490234375,
0.0443115234375,
-0.003936767578125,
0.01641845703125,
0.0299224853515625,
0.01079559326171875,
0.0294647216796875,
-0.007022857666015625,
0.007274627685546875,
0.01354217529296875,
0.01715087890625,
-0.001300811767578125,
0.015869140625,
0.0163116455078125,
0.017059326171875,
-0.012542724609375,
-0.004871368408203125,
0.0374755859375,
-0.03546142578125,
-0.0150146484375,
-0.0017518997192382812,
0.01403045654296875,
-0.0184478759765625,
0.003047943115234375,
-0.00899505615234375,
-0.0168914794921875,
0.01012420654296875,
-0.0021266937255859375,
-0.0312347412109375,
-0.01160430908203125,
-0.0018434524536132812,
-0.0008711814880371094,
0.01224517822265625,
-0.025848388671875,
0.00750732421875,
0.025146484375,
0.01561737060546875,
-0.006328582763671875,
0.0095977783203125,
0.00452423095703125,
0.0237579345703125,
-0.01374053955078125,
-0.00469207763671875,
-0.01055908203125,
0.01273345947265625,
0.0243988037109375,
0.01241302490234375,
0.0181427001953125,
0.00737762451171875,
-0.01209259033203125,
0.00873565673828125,
0.0003161430358886719,
-0.005184173583984375,
-0.028106689453125,
0.022613525390625,
-0.00453948974609375,
0.01483917236328125,
-0.0136260986328125,
-0.0014514923095703125,
-0.0016384124755859375,
0.03369140625,
-0.01253509521484375,
0.034149169921875,
0.004329681396484375,
-0.0019893646240234375,
-0.006862640380859375,
0.006000518798828125,
-0.0077056884765625,
-0.0200347900390625,
-0.0114898681640625,
0.01263427734375,
-0.0144195556640625,
0.03289794921875,
-0.0362548828125,
0.0193939208984375,
-0.019561767578125,
0.00220489501953125,
-0.027069091796875,
-0.01219940185546875,
-0.005401611328125,
0.011138916015625,
0.0027370452880859375,
-0.0143890380859375,
-0.01239013671875,
-0.00604248046875,
0.01328277587890625,
-0.0066680908203125,
0.002750396728515625,
-0.0113372802734375,
0.0272216796875,
-0.034332275390625,
0.01386260986328125,
-0.01140594482421875,
-0.0180816650390625,
0.0002334117889404297,
-0.0017652511596679688,
0.00036644935607910156,
-0.00865936279296875,
0.021148681640625,
-0.00986480712890625,
-0.047454833984375,
0.01629638671875,
0.007450103759765625,
-0.006420135498046875,
-0.0055999755859375,
-0.0008502006530761719,
0.0015592575073242188,
0.0219268798828125,
-0.019439697265625,
-0.0204010009765625,
0.030242919921875,
0.00347137451171875,
0.00737762451171875,
0.00472259521484375,
0.0302581787109375,
0.0175018310546875,
0.016815185546875,
0.01105499267578125,
-0.0022907257080078125,
-0.037750244140625,
-0.0183868408203125,
-0.0174407958984375,
-0.00199127197265625,
-0.03021240234375,
-0.0124664306640625,
-0.01467132568359375,
-0.0194854736328125,
0.001667022705078125,
-0.0024871826171875,
-0.0274200439453125,
0.0048675537109375,
0.0243377685546875,
-0.0203399658203125,
0.02215576171875,
0.0148773193359375,
0.004810333251953125,
-0.0223846435546875,
-0.0182342529296875,
-0.0057373046875,
-0.018218994140625,
0.006542205810546875,
0.00885009765625,
-0.039825439453125,
0.0267181396484375,
0.0201263427734375,
0.005657196044921875,
0.0047607421875,
0.037353515625,
-0.001384735107421875,
-0.017181396484375,
0.059814453125,
-0.0008516311645507812,
-0.00458526611328125,
0.0222930908203125,
0.0211639404296875,
-0.01004791259765625,
-0.028167724609375,
-0.003383636474609375,
0.01314544677734375,
0.030548095703125,
-0.00661468505859375,
0.0073089599609375,
-0.0194244384765625,
-0.01593017578125,
-0.0085601806640625,
-0.01751708984375,
-0.020355224609375,
0.01506805419921875,
-0.02581787109375,
0.0311126708984375,
0.007587432861328125,
-0.021942138671875,
0.0273590087890625,
-0.004077911376953125,
-0.0261077880859375,
0.017913818359375,
0.0256195068359375,
-0.0193328857421875,
-0.016387939453125,
-0.0357666015625,
0.0182647705078125,
0.0080413818359375,
-0.0281982421875,
-0.03216552734375,
0.0206451416015625,
0.00888824462890625,
-0.0174102783203125,
-0.0003457069396972656,
-0.0244903564453125,
0.038726806640625,
0.0113525390625,
-0.0028247833251953125,
-0.0121612548828125,
-0.0137481689453125,
0.0248870849609375,
0.008056640625,
-0.0423583984375,
-0.0191650390625,
-0.0184173583984375,
-0.027496337890625,
0.007030487060546875,
0.019805908203125,
0.0063934326171875,
0.05279541015625,
0.0279998779296875,
-0.013275146484375,
-0.034912109375,
0.004520416259765625,
-0.0011892318725585938,
-0.025360107421875,
-0.01013946533203125,
-0.025421142578125,
-0.0002684593200683594,
0.0166015625,
-0.0095367431640625,
0.006946563720703125,
0.00738525390625,
-0.0022258758544921875,
0.005252838134765625,
0.01261138916015625,
-0.01155853271484375,
0.011810302734375,
0.00917816162109375,
0.0071868896484375,
-0.022064208984375,
-0.00046563148498535156,
-0.01320648193359375,
-0.018524169921875,
-0.007396697998046875,
-0.0255889892578125,
-0.0233001708984375,
0.019439697265625,
0.0207977294921875,
-0.01441192626953125,
-0.01007843017578125,
-0.0022983551025390625,
0.01317596435546875,
-0.03680419921875,
-0.004093170166015625,
-0.006092071533203125,
-0.0013132095336914062,
0.04095458984375,
-0.02069091796875,
-0.0200653076171875,
0.0218505859375,
-0.01317596435546875,
-0.017822265625,
-0.0275726318359375,
-0.01277923583984375,
0.001209259033203125,
-0.01323699951171875,
-0.00568389892578125,
0.025238037109375,
0.02490234375,
0.0301971435546875,
-0.0005092620849609375,
-0.0027065277099609375,
0.01513671875,
-0.0021953582763671875,
-0.0012998580932617188,
-0.0057220458984375,
0.0038242340087890625,
0.0233154296875,
0.02392578125,
-0.01314544677734375,
-0.01296234130859375,
0.007808685302734375,
0.0017843246459960938,
0.00023436546325683594,
0.0232086181640625,
-0.0199432373046875,
0.0289459228515625,
-0.005199432373046875,
0.02655029296875,
-0.03765869140625,
0.0367431640625,
0.0103912353515625,
-0.012664794921875,
0.008575439453125,
0.0146331787109375,
0.02423095703125,
-0.0199737548828125,
0.038818359375,
0.04296875,
0.0255279541015625,
0.01184844970703125,
-0.0158538818359375,
-0.0225982666015625,
0.01145172119140625,
0.00047850608825683594,
-0.0308685302734375,
0.00739288330078125,
-0.0008416175842285156,
0.0180511474609375,
-0.00939178466796875,
-0.0132598876953125,
-0.010711669921875,
0.01502227783203125,
0.0031280517578125,
-0.0035076141357421875,
0.024322509765625,
0.018035888671875,
-0.00792694091796875,
0.0313720703125,
0.006946563720703125,
0.046417236328125,
-0.01326751708984375,
-0.0098724365234375,
0.019744873046875,
-0.02874755859375,
0.0194854736328125,
0.04046630859375,
-0.0130767822265625,
0.0154266357421875,
-0.0509033203125,
0.01558685302734375,
0.0240631103515625,
-0.01409149169921875,
0.01290130615234375,
-0.0166778564453125,
-0.01531982421875,
-0.00417327880859375,
-0.0209197998046875,
-0.0146331787109375,
0.0026721954345703125,
0.01012420654296875,
-0.0033206939697265625,
-0.00896453857421875,
0.00774383544921875,
-0.0263824462890625,
-0.017242431640625,
0.0056610107421875,
-0.0018720626831054688,
0.0145416259765625,
-0.0031185150146484375,
0.00223541259765625,
-0.00927734375,
0.003238677978515625,
0.00959014892578125,
-0.04254150390625,
0.02001953125,
-0.00981903076171875,
0.024017333984375,
-0.02008056640625,
0.0120391845703125,
0.0228424072265625,
-0.0039825439453125,
-0.0026721954345703125,
-0.032501220703125,
0.01910400390625,
0.01428985595703125,
-0.009033203125,
0.048614501953125,
0.020233154296875,
-0.0007777214050292969,
0.0029315948486328125,
-0.0258026123046875,
0.00736236572265625,
-0.0157318115234375,
-0.0145263671875,
-0.00238037109375,
0.0035858154296875,
-0.0207977294921875,
0.0029277801513671875,
-0.01001739501953125,
-0.00989532470703125,
-0.02166748046875,
-0.0175628662109375,
0.0226593017578125,
-0.0148773193359375,
0.024993896484375,
-0.0264434814453125,
-0.05096435546875,
0.040191650390625,
-0.007602691650390625,
-0.0175933837890625,
-0.0052337646484375,
-0.04949951171875,
-0.004657745361328125,
0.00385284423828125,
-0.009613037109375,
0.004543304443359375,
0.005756378173828125,
0.0247039794921875,
0.0274505615234375,
0.0047454833984375,
-0.017974853515625,
-0.0164337158203125,
0.024505615234375,
0.04486083984375,
-0.018096923828125,
0.003231048583984375,
0.0272064208984375,
-0.0186920166015625,
0.050933837890625,
-0.0282135009765625,
0.004627227783203125,
-0.015045166015625,
0.0076751708984375,
-0.0176849365234375,
0.031707763671875,
0.001926422119140625,
-0.0157318115234375,
-0.00423431396484375,
-0.01111602783203125,
0.0077056884765625,
0.026214599609375,
-0.0182037353515625,
0.01551055908203125,
0.013519287109375,
0.025970458984375,
0.00506591796875,
-0.015777587890625,
-0.0015707015991210938,
-0.0212249755859375,
-0.0214080810546875,
-0.008270263671875,
-0.00815582275390625,
0.0175933837890625,
-0.00980377197265625,
0.0018224716186523438,
-0.01509857177734375,
-0.01001739501953125,
-0.00229644775390625,
0.01303863525390625,
-0.0193023681640625,
-0.006221771240234375,
0.00046896934509277344,
0.0260009765625,
-0.0015439987182617188,
0.0180206298828125,
-0.01204681396484375,
0.006420135498046875,
0.003849029541015625,
0.0195465087890625,
0.0016613006591796875,
0.00255584716796875,
-0.003208160400390625,
-0.00665283203125,
-0.0267791748046875,
0.0008769035339355469,
0.005321502685546875,
0.01018524169921875,
-0.025726318359375,
-0.0017032623291015625,
-0.004009246826171875,
0.003917694091796875,
0.00791168212890625,
0.0163421630859375,
0.0067138671875,
0.032623291015625,
0.0029392242431640625,
0.043701171875,
0.0278167724609375,
0.0105438232421875,
0.011749267578125,
-0.00019633769989013672,
0.01049041748046875,
0.03216552734375,
0.0330810546875,
-0.037200927734375,
0.0196380615234375,
-0.0016984939575195312,
-0.0025310516357421875,
-0.035186767578125,
-0.0323486328125,
0.006378173828125,
0.006732940673828125,
-0.053863525390625,
0.022491455078125,
0.0008268356323242188,
-0.0041961669921875,
0.007221221923828125,
-0.0170135498046875,
-0.005146026611328125,
0.004070281982421875,
0.005939483642578125,
-0.014129638671875,
-0.014984130859375,
-0.0069580078125,
-0.0021648406982421875,
-0.0015344619750976562,
0.017608642578125,
0.0059814453125,
-0.015625,
0.0445556640625,
-0.0168304443359375,
-0.001361846923828125,
0.008514404296875,
-0.0206146240234375,
0.04083251953125,
0.00047397613525390625,
-0.00498199462890625,
0.0086212158203125,
0.031463623046875,
-0.0341796875,
0.02099609375,
-0.033294677734375,
-0.006591796875,
-0.00574493408203125,
0.003879547119140625,
0.0233154296875,
0.017822265625,
-0.0168609619140625,
-0.0242462158203125,
0.0107421875,
-0.0017957687377929688,
-0.0240936279296875,
0.007427215576171875,
0.003509521484375,
0.018280029296875,
-0.04083251953125,
-0.034088134765625,
-0.0265960693359375,
-0.01255035400390625,
-0.01076507568359375,
0.0009613037109375,
-0.03106689453125,
0.01345062255859375,
-0.03558349609375,
-0.00601959228515625,
-0.01084136962890625,
0.0017862319946289062,
0.0027332305908203125,
-0.00836181640625,
0.041351318359375,
-0.00984954833984375,
0.029693603515625,
0.01047515869140625,
-0.0139007568359375,
-0.0011653900146484375,
0.0160675048828125,
0.03729248046875,
0.0009198188781738281,
-0.0035648345947265625,
0.006206512451171875,
0.03057861328125,
0.03143310546875,
0.0157318115234375,
-0.015960693359375,
-0.0074005126953125,
0.0099334716796875,
0.0038585662841796875,
0.038177490234375,
-0.038848876953125,
0.0236663818359375,
0.01209259033203125,
-0.005908966064453125,
0.044677734375,
0.0077056884765625,
0.002956390380859375,
0.0133819580078125,
-0.0235137939453125,
-0.027801513671875,
0.0003635883331298828,
0.0080718994140625,
0.0023059844970703125,
0.00543212890625,
-0.0012149810791015625,
-0.0027256011962890625,
0.0083160400390625,
-0.0233306884765625,
0.02935791015625,
-0.0070037841796875,
0.004512786865234375,
-0.017578125,
-0.01568603515625,
0.033905029296875,
-0.002185821533203125,
-0.052154541015625,
0.0047760009765625,
-0.01459503173828125,
-0.0024890899658203125,
-0.0021762847900390625,
0.00916290283203125,
-0.0231475830078125,
-0.00433349609375,
0.037078857421875,
0.002597808837890625,
0.004451751708984375,
-0.0166015625,
0.010894775390625,
0.002292633056640625,
-0.002880096435546875,
0.0304718017578125,
-0.0310821533203125,
-0.0174407958984375,
0.0191192626953125,
0.0041656494140625,
0.00753021240234375,
-0.0059967041015625,
-0.0037136077880859375,
-0.01055145263671875,
0.01308441162109375,
0.0228424072265625,
-0.030487060546875,
-0.00312042236328125,
-0.004901885986328125,
0.032012939453125,
0.0318603515625,
-0.00894927978515625,
-0.0112457275390625,
0.056427001953125,
-0.00882720947265625,
0.023590087890625,
-0.0008320808410644531,
-0.00916290283203125,
-0.053314208984375,
-0.022064208984375,
-0.00787353515625,
-0.003574371337890625,
-0.0010385513305664062,
0.0180206298828125,
0.0291595458984375,
0.021820068359375,
-0.03240966796875,
0.009735107421875,
0.0025119781494140625,
0.01387786865234375,
0.029144287109375,
0.0021343231201171875,
-0.017242431640625,
-0.00412750244140625,
-0.005901336669921875,
0.017242431640625,
0.013031005859375,
-0.027557373046875,
0.00542449951171875,
0.0046844482421875,
0.00211334228515625,
-0.0284881591796875,
-0.013427734375,
-0.02587890625,
0.013580322265625,
0.0084686279296875,
-0.025604248046875,
0.0239410400390625,
0.0296173095703125,
-0.0087890625,
0.005344390869140625,
-0.005245208740234375,
-0.0352783203125,
-0.00009959936141967773,
-0.015228271484375,
-0.0137939453125,
-0.0015478134155273438,
-0.046051025390625,
-0.01424407958984375,
-0.044830322265625,
0.00809478759765625,
-0.01340484619140625,
-0.0167388916015625,
0.0064697265625,
-0.020233154296875,
-0.01288604736328125,
-0.0005078315734863281,
0.0180511474609375,
0.0186004638671875,
-0.0133514404296875,
0.0233917236328125,
-0.007282257080078125,
0.0019817352294921875,
-0.0178070068359375,
0.0167083740234375,
-0.018798828125,
0.04180908203125,
0.02520751953125,
-0.0026416778564453125,
0.01558685302734375,
-0.024505615234375,
-0.0239105224609375,
-0.049285888671875,
0.02825927734375,
0.0244598388671875,
-0.04644775390625,
-0.00785064697265625,
0.0189361572265625,
-0.01641845703125,
-0.003879547119140625,
0.006847381591796875,
0.0127410888671875,
-0.00494384765625,
-0.0002257823944091797,
0.0241851806640625,
0.0020599365234375,
0.0169830322265625,
0.006191253662109375,
0.00736236572265625,
0.00429534912109375,
0.0003933906555175781,
-0.0133056640625,
0.031768798828125,
-0.0240478515625,
0.01145172119140625,
-0.027496337890625,
-0.0168304443359375,
0.0108489990234375,
0.0032787322998046875,
0.004764556884765625,
-0.012176513671875,
-0.038482666015625,
-0.0179595947265625,
-0.0168304443359375,
0.0031681060791015625,
0.007015228271484375,
0.0030689239501953125,
-0.01464080810546875,
0.01171875,
0.0285491943359375,
0.0033931732177734375,
-0.01708984375,
0.0333251953125,
-0.004730224609375,
-0.00485992431640625,
0.0019779205322265625,
0.01366424560546875,
-0.007617950439453125
] |
ours_494
|
Let \(\vec{e}_{1}, \ldots, \vec{e}_{k}\) be the standard basis. We see that \( f(\vec{e}_{1}) = \vec{u}_{1}, \ldots, f(\vec{e}_{k}) = \vec{u}_{k} \) are an orthonormal basis. Furthermore, for all \(\vec{v}, i\),
\[
\langle f(\vec{v}), \vec{u}_{i} \rangle = \langle \vec{v}, \vec{e}_{i} \rangle
\]
so if \(\vec{v} = \sum a_{i} \vec{e}_{i}\), then \( f(\vec{v}) = \sum a_{i} \vec{u}_{i} \), thus \( f \) is the linear map taking \(\vec{e}_{i}\) to \(\vec{u}_{i}\) for all \( i \). Thus, \( m(k) \) counts the number of orthonormal bases \((\vec{u}_{1}, \ldots, \vec{u}_{k})\).
First, we need a lemma: Let \(\vec{v}_{1}, \ldots, \vec{v}_{\ell}\) be orthonormal. Then, we can extend this to an orthonormal basis \(\vec{v}_{1}, \ldots, \vec{v}_{k}\).
Proof: Let \( V = (\mathbb{F}_{p})^{k} \) and let \( W = \operatorname{span}(\vec{v}_{1}, \ldots, \vec{v}_{\ell}) \). Let \( U = W^{\perp} \) be the orthogonal complement of \( W \). We will show that there exists \(\vec{u} \in U\), with \(\|\vec{u}\|^{2} = 1\).
Let \( t = k - \ell = \operatorname{dim} U \). If \( t = 1 \), then let \( U = \operatorname{span}(\vec{u}) \). Say \( M \) is the matrix with columns \(\vec{v}_{1}, \ldots, \vec{v}_{k-1}, \vec{u}\), then \( M^{\mathrm{T}} M \) is a diagonal matrix with diagonal entries \( 1, 1, \ldots, 1, \|\vec{u}\|^{2} \), so \(\left\|\frac{\vec{u}}{\operatorname{det} M}\right\|^{2} = 1\) and so \(\vec{v}_{k} = \frac{\vec{u}}{\operatorname{det} M}\) works.
Else, first take an orthogonal basis of \( U \) as follows: Take \(\vec{u}_{1}\) with \(\|\vec{u}_{1}\|^{2} \neq 0\), and replace \( U \) with \( U \cap \operatorname{span}(\vec{u}_{1})^{\perp} \), and repeat on the new \( U \) to get \(\vec{u}_{2}, \ldots, \vec{u}_{t}\). Note in general that after we have generated \(\vec{u}_{1}, \ldots, \vec{u}_{s}\), then \( U^{\perp} \) is currently \(\operatorname{span}(\vec{v}_{1}, \ldots, \vec{v}_{\ell}, \vec{u}_{1}, \ldots, \vec{u}_{s})\). Clearly, the span is contained in \( U^{\perp} \). To show that \( U^{\perp} \) does not intersect \( U \), note that if \(\vec{x} \in U^{\perp} \cap U\), then \(\langle \vec{x}, \vec{v} \rangle = 0\) for all \(\vec{v} \in V\), thus forcing \(\vec{x} = 0\).
Now, we claim that \( U \) must contain an element with nonzero norm. Otherwise, for all \(\vec{u}, \vec{u}^{\prime} \in U\),
\[
\langle \vec{u}, \vec{u}^{\prime} \rangle = \frac{\langle \vec{u} + \vec{u}^{\prime}, \vec{u} + \vec{u}^{\prime} \rangle - \langle \vec{u}, \vec{u} \rangle - \langle \vec{u}^{\prime}, \vec{u}^{\prime} \rangle}{2} = 0
\]
so \( U \in U^{\perp} \), contradiction.
The remainder when \( m(1) + m(2) + m(3) + \cdots + m(p) \) is divided by \( 488 \) is \(\boxed{18}\).
|
18
|
{
"competition": "us_comps",
"dataset": "Ours",
"posts": null,
"source": "OMOFall19Solns-2.md"
}
|
Let \( p = 491 \) be a prime. Let \( S \) be the set of ordered \( k \)-tuples of nonnegative integers that are less than \( p \). We say that a function \( f: S \rightarrow S \) is \( k \)-murine if, for all \( u, v \in S \), \(\langle f(u), f(v)\rangle \equiv \langle u, v\rangle \pmod{p}\), where \(\langle (a_{1}, \ldots, a_{k}), (b_{1}, \ldots, b_{k}) \rangle = a_{1} b_{1} + \cdots + a_{k} b_{k}\) for any \((a_{1}, \ldots, a_{k}), (b_{1}, \ldots, b_{k}) \in S\). Let \( m(k) \) be the number of \( k \)-murine functions. Compute the remainder when \( m(1) + m(2) + m(3) + \cdots + m(p) \) is divided by \( 488 \).
|
[
"/Mathematics/Algebra/FieldTheory/Field",
"/Mathematics/Algebra/FieldTheory/FiniteField",
"/Mathematics/Algebra/LinearAlgebra/Determinants/Determinant",
"/Mathematics/Algebra/LinearAlgebra/Determinants/DeterminantTheorem",
"/Mathematics/Algebra/VectorAlgebra/DotProduct",
"/Mathematics/Algebra/VectorAlgebra/OrthogonalBasis",
"/Mathematics/Algebra/VectorAlgebra/OrthonormalVectors",
"/Mathematics/Algebra/VectorAlgebra/ScalarProduct",
"/Mathematics/DiscreteMathematics/Combinatorics/Enumeration",
"/Mathematics/DiscreteMathematics/Combinatorics/GeneralCombinatorics",
"/Mathematics/DiscreteMathematics/FiniteGroups/GeneralOrthogonalGroup"
] |
A k-murine function must be a linear map sending the standard basis to an orthonormal basis, so m(k) counts orthonormal bases of (F_p)^k.
|
[
0.0000603795051574707,
-0.0106658935546875,
0.0147705078125,
-0.0164947509765625,
0.0005512237548828125,
-0.00836181640625,
0.00554656982421875,
-0.00908660888671875,
0.0102996826171875,
0.032867431640625,
0.01324462890625,
-0.023681640625,
0.0013132095336914062,
0.0278167724609375,
-0.00994873046875,
-0.00732421875,
0.0306549072265625,
-0.0128631591796875,
0.0107574462890625,
-0.0016069412231445312,
-0.0185699462890625,
-0.05352783203125,
-0.01824951171875,
0.050445556640625,
-0.05029296875,
-0.00168609619140625,
-0.0232391357421875,
0.008209228515625,
0.01007843017578125,
0.002155303955078125,
0.006084442138671875,
-0.037628173828125,
0.0123748779296875,
-0.03924560546875,
0.0004968643188476562,
-0.0068511962890625,
0.01047515869140625,
-0.00601959228515625,
-0.044952392578125,
0.00281524658203125,
-0.0277252197265625,
-0.0181121826171875,
0.01351165771484375,
0.0076751708984375,
0.0112457275390625,
-0.01357269287109375,
0.0010728836059570312,
0.0258636474609375,
-0.011474609375,
-0.007579803466796875,
-0.0133514404296875,
0.00972747802734375,
0.018707275390625,
-0.006214141845703125,
-0.003936767578125,
-0.049224853515625,
0.0150604248046875,
0.0025959014892578125,
0.0150146484375,
-0.0113067626953125,
-0.00299835205078125,
-0.00119781494140625,
-0.01561737060546875,
-0.0001367330551147461,
0.0011692047119140625,
-0.011962890625,
0.0150909423828125,
0.0079803466796875,
0.0076904296875,
-0.011199951171875,
0.00957489013671875,
0.0024700164794921875,
-0.00010073184967041016,
0.038665771484375,
0.0296630859375,
-0.01456451416015625,
0.0036468505859375,
0.01337432861328125,
-0.01474761962890625,
-0.0012235641479492188,
0.01397705078125,
0.036590576171875,
0.011444091796875,
0.00739288330078125,
0.00817108154296875,
0.0209808349609375,
-0.0345458984375,
0.0018215179443359375,
-0.007427215576171875,
-0.01206207275390625,
-0.005596160888671875,
0.005733489990234375,
0.03515625,
0.0256805419921875,
0.015869140625,
0.00853729248046875,
-0.005229949951171875,
-0.01296234130859375,
-0.02374267578125,
0.005176544189453125,
0.00244140625,
-0.003009796142578125,
-0.0103912353515625,
-0.01184844970703125,
-0.106689453125,
-0.004283905029296875,
-0.008758544921875,
-0.0032444000244140625,
-0.00855255126953125,
-0.005283355712890625,
0.011688232421875,
0.005828857421875,
-0.0017795562744140625,
0.021148681640625,
0.010772705078125,
0.0140228271484375,
0.00960540771484375,
0.0169677734375,
0.01194000244140625,
-0.044830322265625,
-0.0092620849609375,
-0.003753662109375,
-0.0095367431640625,
0.01540374755859375,
-0.0020809173583984375,
0.0223846435546875,
0.0033969879150390625,
-0.01204681396484375,
-0.006214141845703125,
0.011962890625,
0.006298065185546875,
0.01140594482421875,
-0.0309906005859375,
-0.00403594970703125,
-0.054656982421875,
0.0124969482421875,
-0.020263671875,
-0.02215576171875,
-0.0086669921875,
-0.00847625732421875,
0.005916595458984375,
-0.006969451904296875,
-0.00691986083984375,
-0.005779266357421875,
0.003326416015625,
0.026611328125,
-0.01180267333984375,
-0.039764404296875,
0.0093536376953125,
-0.007762908935546875,
-0.029266357421875,
-0.0089874267578125,
0.023101806640625,
-0.006877899169921875,
-0.0030803680419921875,
0.023162841796875,
0.0024433135986328125,
0.013580322265625,
0.012237548828125,
0.0030670166015625,
0.01065826416015625,
0.0030975341796875,
-0.00481414794921875,
0.01428985595703125,
-0.008575439453125,
0.014007568359375,
-0.01849365234375,
0.00679779052734375,
-0.01000213623046875,
-0.0067596435546875,
0.019073486328125,
0.001979827880859375,
-0.01428985595703125,
-0.013214111328125,
-0.0007219314575195312,
-0.00261688232421875,
0.004146575927734375,
-0.0015153884887695312,
0.00803375244140625,
0.032135009765625,
0.028564453125,
-0.033843994140625,
0.0004229545593261719,
0.007228851318359375,
-0.005588531494140625,
-0.0134735107421875,
-0.0095672607421875,
0.00528717041015625,
0.0149383544921875,
-0.006847381591796875,
-0.0161895751953125,
0.0194854736328125,
-0.0109100341796875,
0.0122833251953125,
-0.022430419921875,
0.00690460205078125,
-0.01439666748046875,
0.01477813720703125,
0.01224517822265625,
0.0210723876953125,
0.006702423095703125,
0.009185791015625,
-0.01385498046875,
0.00920867919921875,
-0.004650115966796875,
-0.0004892349243164062,
0.0172576904296875,
-0.012908935546875,
-0.004436492919921875,
-0.0117034912109375,
0.00572967529296875,
-0.0220489501953125,
-0.00446319580078125,
-0.046234130859375,
0.0017995834350585938,
0.01406097412109375,
-0.0235595703125,
-0.006591796875,
-0.00482177734375,
-0.048126220703125,
-0.0040283203125,
0.002483367919921875,
-0.0031070709228515625,
-0.0195159912109375,
-0.0188751220703125,
-0.0182952880859375,
0.011444091796875,
-0.01551055908203125,
-0.01849365234375,
-0.01532745361328125,
0.00445556640625,
0.0206298828125,
-0.001186370849609375,
0.0039520263671875,
0.0100555419921875,
0.0034008026123046875,
0.02655029296875,
-0.01203155517578125,
0.006595611572265625,
-0.01467132568359375,
0.0523681640625,
-0.0014963150024414062,
-0.00553131103515625,
0.01488494873046875,
-0.02801513671875,
-0.0075531005859375,
-0.003204345703125,
0.00685882568359375,
-0.00469207763671875,
-0.01422119140625,
0.0127410888671875,
-0.0023097991943359375,
-0.01056671142578125,
0.004810333251953125,
0.00870513916015625,
-0.0051116943359375,
0.0021820068359375,
-0.0119476318359375,
-0.0145721435546875,
-0.0240325927734375,
-0.007781982421875,
-0.0357666015625,
0.0008692741394042969,
-0.005664825439453125,
-0.001094818115234375,
-0.00921630859375,
0.006565093994140625,
-0.01441192626953125,
-0.0076141357421875,
-0.0182342529296875,
0.01690673828125,
-0.0303497314453125,
-0.01259613037109375,
0.0022602081298828125,
0.01529693603515625,
-0.0257415771484375,
-0.0024127960205078125,
0.01227569580078125,
0.01519775390625,
-0.01776123046875,
0.01898193359375,
-0.007465362548828125,
0.0178375244140625,
0.00722503662109375,
-0.00386810302734375,
-0.0236663818359375,
-0.002490997314453125,
-0.014556884765625,
-0.0072784423828125,
-0.00693511962890625,
0.0038280487060546875,
-0.00350189208984375,
-0.006046295166015625,
-0.00240325927734375,
0.0390625,
-0.050445556640625,
0.02569580078125,
0.0220947265625,
0.0184478759765625,
-0.0021114349365234375,
0.0208892822265625,
-0.0103302001953125,
-0.008941650390625,
-0.0029277801513671875,
0.0056610107421875,
0.021484375,
0.0014982223510742188,
0.00545501708984375,
-0.019989013671875,
0.0184326171875,
-0.01381683349609375,
0.00034999847412109375,
0.0001404285430908203,
-0.006061553955078125,
-0.0399169921875,
-0.0022182464599609375,
-0.0200347900390625,
-0.0028228759765625,
-0.024566650390625,
-0.0125274658203125,
0.0106964111328125,
-0.017547607421875,
0.00504302978515625,
-0.007747650146484375,
-0.01427459716796875,
0.0009207725524902344,
-0.0029888153076171875,
0.01739501953125,
-0.04156494140625,
-0.00035119056701660156,
-0.039947509765625,
-0.0035686492919921875,
-0.01253509521484375,
-0.016693115234375,
-0.00881195068359375,
0.0238800048828125,
-0.0115814208984375,
0.0023479461669921875,
0.02618408203125,
0.000988006591796875,
-0.01047515869140625,
-0.01297760009765625,
0.02789306640625,
0.01873779296875,
-0.014617919921875,
0.01007843017578125,
0.03472900390625,
-0.0080108642578125,
0.002719879150390625,
-0.0055999755859375,
0.015594482421875,
-0.0004420280456542969,
-0.0136566162109375,
0.0056915283203125,
-0.026123046875,
0.004489898681640625,
0.0025310516357421875,
0.00012683868408203125,
-0.058502197265625,
-0.0079193115234375,
-0.002777099609375,
0.0070953369140625,
-0.004703521728515625,
0.0099029541015625,
0.01348876953125,
0.004116058349609375,
-0.0206451416015625,
0.002685546875,
-0.06439208984375,
0.01125335693359375,
-0.02459716796875,
-0.01605224609375,
-0.01378631591796875,
0.01248931884765625,
-0.0200653076171875,
0.005035400390625,
0.004764556884765625,
-0.0285186767578125,
0.011871337890625,
-0.00498199462890625,
0.0162811279296875,
0.03955078125,
-0.00809478759765625,
0.01197052001953125,
0.016326904296875,
-0.0023899078369140625,
-0.004375457763671875,
-0.043975830078125,
-0.05535888671875,
0.0144805908203125,
-0.01413726806640625,
-0.0013074874877929688,
-0.00787353515625,
0.0272064208984375,
0.00506591796875,
-0.028564453125,
0.0138702392578125,
0.010589599609375,
0.035980224609375,
-0.0269622802734375,
-0.01554107666015625,
0.004520416259765625,
-0.017486572265625,
-0.01537322998046875,
0.001956939697265625,
0.0026149749755859375,
0.0006031990051269531,
-0.00623321533203125,
0.01129913330078125,
0.02294921875,
0.023651123046875,
0.009552001953125,
-0.0166015625,
-0.008087158203125,
0.03515625,
-0.01446533203125,
0.022125244140625,
-0.00904083251953125,
-0.01137542724609375,
0.0124359130859375,
-0.023529052734375,
-0.01555633544921875,
0.01033782958984375,
-0.0005364418029785156,
0.00014638900756835938,
0.0291595458984375,
-0.051055908203125,
0.01776123046875,
-0.0081939697265625,
0.0122528076171875,
0.0072479248046875,
-0.009063720703125,
0.01312255859375,
0.0166473388671875,
-0.0022296905517578125,
0.006259918212890625,
0.0272674560546875,
-0.015594482421875,
-0.004302978515625,
0.0198822021484375,
-0.0205841064453125,
-0.0133056640625,
-0.01375579833984375,
-0.005290985107421875,
-0.01364898681640625,
-0.0203704833984375,
0.0278778076171875,
0.00664520263671875,
0.00823211669921875,
-0.0162200927734375,
-0.022552490234375,
-0.019500732421875,
-0.0019073486328125,
0.01953125,
-0.0026912689208984375,
0.00370025634765625,
0.01242828369140625,
0.01404571533203125,
-0.0000795125961303711,
0.0028629302978515625,
0.0164947509765625,
-0.022369384765625,
0.00437164306640625,
0.0114288330078125,
-0.03436279296875,
-0.013946533203125,
0.01407623291015625,
-0.00873565673828125,
0.0300140380859375,
-0.006099700927734375,
-0.0196990966796875,
-0.0252227783203125,
0.00608062744140625,
-0.0087127685546875,
-0.043853759765625,
0.00582122802734375,
0.01103973388671875,
-0.0087127685546875,
-0.016632080078125,
-0.0074615478515625,
0.029571533203125,
0.0090484619140625,
0.0013837814331054688,
0.0528564453125,
-0.0185089111328125,
0.01157379150390625,
0.0189056396484375,
0.006656646728515625,
-0.006256103515625,
-0.002918243408203125,
0.004940032958984375,
0.0257720947265625,
-0.0162506103515625,
0.004474639892578125,
-0.01132965087890625,
-0.0165252685546875,
-0.0193328857421875,
-0.0205535888671875,
-0.022674560546875,
0.01837158203125,
0.002880096435546875,
-0.0088043212890625,
0.010711669921875,
0.0516357421875,
0.011016845703125,
0.00986480712890625,
0.041839599609375,
-0.019927978515625,
-0.005741119384765625,
-0.01561737060546875,
0.00879669189453125,
-0.00872039794921875,
0.00868988037109375,
-0.0252532958984375,
0.01323699951171875,
0.028076171875,
-0.02734375,
-0.0211029052734375,
0.00254058837890625,
-0.0021457672119140625,
-0.0192718505859375,
-0.00446319580078125,
0.056610107421875,
-0.0080413818359375,
0.02044677734375,
0.025726318359375,
-0.003864288330078125,
-0.0007476806640625,
-0.023651123046875,
-0.0124053955078125,
0.0264129638671875,
-0.04779052734375,
-0.0083160400390625,
-0.01427459716796875,
-0.036407470703125,
0.0022640228271484375,
0.0259552001953125,
-0.01068878173828125,
0.00424957275390625,
0.0025196075439453125,
0.0041046142578125,
0.00931549072265625,
0.0177001953125,
-0.005184173583984375,
0.0014524459838867188,
0.007511138916015625,
-0.00620269775390625,
0.034393310546875,
-0.019073486328125,
0.00946044921875,
-0.01195526123046875,
0.0031890869140625,
-0.0169219970703125,
0.0007109642028808594,
-0.03509521484375,
0.007781982421875,
0.0023593902587890625,
-0.025604248046875,
-0.021240234375,
0.002277374267578125,
0.0014019012451171875,
-0.0028209686279296875,
0.024505615234375,
-0.01354217529296875,
0.0226898193359375,
-0.028594970703125,
-0.0007390975952148438,
0.01538848876953125,
0.007686614990234375,
-0.044189453125,
0.01099395751953125,
0.01015472412109375,
-0.017822265625,
-0.0292205810546875,
-0.0171051025390625,
-0.035736083984375,
0.003009796142578125,
-0.028839111328125,
-0.0016889572143554688,
0.0025348663330078125,
0.01873779296875,
0.0160675048828125,
-0.0036468505859375,
-0.03338623046875,
0.0202178955078125,
0.00833892822265625,
0.0440673828125,
0.00011152029037475586,
0.035736083984375,
0.00316619873046875,
0.006439208984375,
0.0311279296875,
-0.0027713775634765625,
0.00574493408203125,
0.0249786376953125,
-0.01026153564453125,
0.019622802734375,
-0.0128326416015625,
-0.0095672607421875,
-0.0259246826171875,
0.023681640625,
0.0008783340454101562,
-0.0222625732421875,
-0.00136566162109375,
-0.0247650146484375,
-0.0206146240234375,
0.036407470703125,
0.004154205322265625,
-0.0311431884765625,
0.00951385498046875,
0.01751708984375,
-0.005023956298828125,
0.02001953125,
0.0116729736328125,
0.0086669921875,
-0.00383758544921875,
0.0039043426513671875,
-0.006500244140625,
-0.007686614990234375,
-0.005428314208984375,
0.0005059242248535156,
0.01354217529296875,
0.0119476318359375,
0.0248565673828125,
0.00409698486328125,
-0.0215911865234375,
0.0252532958984375,
0.003513336181640625,
0.01360321044921875,
0.01611328125,
-0.00797271728515625,
0.0007996559143066406,
0.0170440673828125,
-0.0030612945556640625,
-0.016998291015625,
0.01541900634765625,
-0.010467529296875,
0.0194549560546875,
-0.004863739013671875,
-0.00399017333984375,
0.002521514892578125,
0.035064697265625,
-0.002887725830078125,
-0.040283203125,
-0.0025882720947265625,
0.01200103759765625,
-0.00821685791015625,
0.0088348388671875,
-0.01983642578125,
0.0227203369140625,
-0.03326416015625,
-0.037841796875,
-0.0008754730224609375,
0.02728271484375,
-0.0101165771484375,
0.00710296630859375,
0.0183563232421875,
0.0029811859130859375,
0.035797119140625,
0.0124053955078125,
0.01003265380859375,
-0.0013418197631835938,
0.01081085205078125,
-0.045654296875,
-0.0308074951171875,
0.005077362060546875,
-0.04864501953125,
-0.0015459060668945312,
0.045562744140625,
-0.06072998046875,
-0.0220184326171875,
-0.06439208984375,
0.0001875162124633789,
0.00572967529296875,
0.0171356201171875,
-0.022308349609375,
0.0157928466796875,
-0.002971649169921875,
-0.020538330078125,
0.0121002197265625,
-0.00421142578125,
0.0040435791015625,
0.030853271484375,
-0.00921630859375,
-0.017578125,
-0.003490447998046875,
-0.02740478515625,
0.004024505615234375,
0.026123046875,
0.0037670135498046875,
-0.00965118408203125,
-0.002399444580078125,
-0.01032257080078125,
0.02203369140625,
0.0085906982421875,
-0.0282745361328125,
-0.0291900634765625,
0.005779266357421875,
-0.0048370361328125,
0.00943756103515625,
-0.04638671875,
-0.0185699462890625,
0.0028533935546875,
0.00783538818359375,
-0.0202789306640625,
-0.0198211669921875,
-0.00004971027374267578,
0.0159912109375,
-0.0200347900390625,
-0.01190185546875,
-0.0080413818359375,
0.01401519775390625,
0.0253753662109375,
-0.0001361370086669922,
-0.0159912109375,
0.0206451416015625,
0.0172119140625,
0.0225982666015625,
0.003765106201171875,
0.002132415771484375,
-0.0215911865234375,
0.0182647705078125,
-0.06573486328125,
0.0011043548583984375,
-0.0020751953125,
-0.0029773712158203125,
0.01024627685546875,
-0.0147705078125,
-0.00604248046875,
-0.006938934326171875,
-0.006744384765625,
-0.02899169921875,
0.0223846435546875,
0.005645751953125,
-0.034423828125,
-0.01154327392578125,
0.006805419921875,
-0.017669677734375,
0.0231781005859375,
-0.00640106201171875,
0.0439453125,
-0.0033721923828125,
0.01325225830078125,
0.002140045166015625,
0.02001953125,
-0.00226593017578125,
0.011444091796875,
-0.01235198974609375,
-0.0230712890625,
-0.013580322265625,
0.0170745849609375,
0.0222015380859375,
-0.01221466064453125,
-0.0199737548828125,
-0.01605224609375,
0.0010280609130859375,
0.0499267578125,
-0.0260009765625,
-0.0012350082397460938,
-0.02490234375,
-0.0256805419921875,
0.006015777587890625,
-0.002044677734375,
-0.00579071044921875,
-0.009552001953125,
0.0009369850158691406,
-0.006534576416015625,
-0.0097503662109375,
-0.0333251953125,
0.0290069580078125,
-0.01316070556640625,
0.027130126953125,
-0.0036411285400390625,
-0.0258026123046875,
0.025909423828125,
-0.001049041748046875,
-0.05035400390625,
0.00933837890625,
0.0229339599609375,
-0.00843048095703125,
-0.0002243518829345703,
0.002735137939453125,
-0.01346588134765625,
0.0028934478759765625,
-0.04022216796875,
0.0078277587890625,
-0.0175018310546875,
-0.04656982421875,
0.0010328292846679688,
0.005062103271484375,
0.01922607421875,
0.0140838623046875,
0.016693115234375,
-0.020599365234375,
0.008758544921875,
-0.0027866363525390625,
0.0080413818359375,
-0.018218994140625,
0.0145111083984375,
0.0457763671875,
0.007659912109375,
-0.0175018310546875,
-0.01031494140625,
0.03228759765625,
-0.0011949539184570312,
0.0111541748046875,
0.006618499755859375,
-0.01136016845703125,
0.0016651153564453125,
0.00640869140625,
-0.0035953521728515625,
-0.007568359375,
-0.01087188720703125,
-0.0028667449951171875,
0.023681640625,
-0.01525115966796875,
0.0052337646484375,
0.033111572265625,
0.01079559326171875,
0.039642333984375,
-0.0167388916015625,
0.0286102294921875,
0.00016450881958007812,
0.00865936279296875,
-0.014373779296875,
0.0089263916015625,
0.017913818359375,
-0.03851318359375,
-0.013458251953125,
0.036041259765625,
-0.01540374755859375,
0.0185699462890625,
0.0212554931640625,
0.034149169921875,
0.0033435821533203125,
-0.02691650390625,
-0.00946044921875,
0.0045166015625,
-0.0002491474151611328,
0.01171112060546875,
-0.01163482666015625,
0.047515869140625,
0.01482391357421875,
-0.006195068359375,
-0.01244354248046875,
0.01129150390625,
0.0087127685546875,
0.024169921875,
0.026031494140625,
-0.0211639404296875,
-0.004741668701171875,
-0.027069091796875,
-0.0325927734375,
-0.009857177734375,
-0.050872802734375,
0.013916015625,
0.02996826171875,
0.0166168212890625,
-0.036895751953125,
-0.017913818359375,
0.006267547607421875,
-0.03424072265625,
0.015960693359375,
-0.019866943359375,
-0.00952911376953125,
0.016387939453125,
0.0093841552734375,
-0.0129852294921875,
-0.0390625,
-0.00032830238342285156,
0.02313232421875,
0.0038509368896484375,
0.0179290771484375,
0.0266876220703125,
0.0210723876953125,
-0.01611328125,
0.00888824462890625,
0.01517486572265625,
0.0167694091796875,
0.03369140625,
0.00933074951171875,
-0.054168701171875,
-0.00997161865234375,
0.01227569580078125,
-0.048980712890625,
0.028228759765625,
0.0105133056640625,
-0.0233154296875,
-0.01459503173828125,
-0.0113525390625,
0.02911376953125,
-0.01983642578125,
-0.025726318359375,
-0.038543701171875,
0.00466156005859375,
0.01543426513671875,
-0.0088653564453125,
-0.00864410400390625,
0.0000388026237487793,
-0.0372314453125,
0.0129547119140625,
0.024627685546875,
0.00878143310546875,
0.013519287109375,
0.00949859619140625,
-0.016021728515625,
-0.048095703125,
0.029205322265625,
-0.023468017578125,
0.0020389556884765625,
0.0098419189453125,
-0.0242767333984375,
0.024993896484375,
0.005550384521484375,
-0.045013427734375,
-0.0030994415283203125,
0.016204833984375,
0.0046234130859375,
0.027008056640625,
0.00704193115234375,
0.006908416748046875,
-0.01030731201171875,
0.0171966552734375,
-0.0138702392578125,
0.0152130126953125,
-0.006397247314453125,
-0.00616455078125,
-0.0244140625,
-0.0286865234375,
-0.01122283935546875,
-0.0042877197265625,
0.017913818359375,
0.004322052001953125,
0.0084381103515625,
-0.0198211669921875,
0.031524658203125,
-0.00817108154296875,
-0.0305633544921875,
0.0040283203125,
-0.0130157470703125,
-0.01043701171875,
-0.003997802734375,
0.005718231201171875,
0.010162353515625,
0.0180206298828125,
-0.0074462890625,
-0.0064697265625,
0.0283660888671875,
-0.038421630859375,
-0.0229949951171875,
-0.011688232421875,
0.00185394287109375,
-0.01146697998046875,
-0.01611328125,
0.00921630859375,
-0.028076171875,
-0.006561279296875,
-0.00824737548828125,
-0.007598876953125,
-0.02313232421875,
-0.045318603515625,
-0.00791168212890625,
-0.046234130859375,
0.0099334716796875,
-0.00891876220703125,
0.054534912109375,
0.038116455078125,
0.0290679931640625,
-0.020355224609375,
0.00855255126953125,
-0.005580902099609375,
-0.0259246826171875,
-0.0022716522216796875,
-0.043731689453125,
-0.00982666015625,
0.005359649658203125,
-0.0009984970092773438,
0.01027679443359375,
0.003292083740234375,
0.034027099609375,
-0.0186004638671875,
0.00458526611328125,
-0.004810333251953125,
-0.0242767333984375,
-0.0265960693359375,
0.00942230224609375,
0.0027980804443359375,
-0.025482177734375,
0.007415771484375,
0.00952911376953125,
-0.053741455078125,
0.04248046875,
-0.02301025390625,
0.01251220703125,
0.027618408203125,
0.044464111328125,
-0.0007791519165039062,
0.0159149169921875,
-0.002960205078125,
-0.006313323974609375,
-0.00301361083984375,
0.006542205810546875,
0.00502777099609375,
0.0208740234375,
0.050201416015625,
-0.0201873779296875,
0.041534423828125,
0.0033283233642578125,
0.0209503173828125,
0.02203369140625,
-0.00528717041015625,
-0.00829315185546875,
-0.0014905929565429688,
-0.0192413330078125,
0.00640106201171875,
0.03985595703125,
0.022247314453125,
-0.002239227294921875,
-0.06201171875,
-0.015869140625,
-0.0129241943359375,
-0.0090789794921875,
-0.01953125,
-0.0389404296875,
-0.015869140625,
-0.02410888671875,
-0.01824951171875,
0.022796630859375,
0.02691650390625,
-0.0203704833984375,
-0.0037441253662109375,
-0.0560302734375,
-0.03704833984375,
-0.00893402099609375,
0.000225067138671875,
0.00954437255859375,
-0.0055084228515625,
-0.026336669921875,
0.0259857177734375,
-0.01062774658203125,
-0.0171661376953125,
-0.016845703125,
0.01837158203125,
-0.00518035888671875,
-0.02880859375,
0.01085662841796875,
0.01459503173828125,
-0.006866455078125,
-0.05657958984375,
-0.01145172119140625,
-0.0028591156005859375,
0.0074615478515625,
-0.0145416259765625,
0.015625,
-0.000040650367736816406,
0.0066375732421875,
-0.0038604736328125,
0.0189361572265625,
0.0195465087890625,
0.001064300537109375,
0.02587890625,
-0.0084381103515625,
-0.01751708984375,
0.0208587646484375,
0.00606536865234375,
0.00882720947265625,
-0.032440185546875,
0.0205535888671875,
-0.046875,
0.037261962890625,
-0.0252227783203125,
0.0259857177734375,
-0.01125335693359375,
-0.032562255859375,
0.00897216796875,
0.0005035400390625,
0.0215911865234375,
-0.01416778564453125,
0.0157928466796875,
-0.0091705322265625,
0.005115509033203125,
0.01248931884765625,
-0.059600830078125,
0.003509521484375,
-0.01486968994140625,
0.045135498046875,
-0.01788330078125,
-0.0025119781494140625,
0.0000483393669128418,
-0.0019254684448242188,
-0.0156097412109375,
-0.0123443603515625,
-0.0238800048828125,
-0.0037384033203125,
-0.006214141845703125,
0.042449951171875,
0.02008056640625,
0.00542449951171875,
-0.017547607421875,
-0.019561767578125,
-0.0151824951171875,
0.005146026611328125,
0.00015687942504882812,
0.0196685791015625,
0.0251617431640625,
0.0022735595703125,
0.0084991455078125,
-0.0190277099609375,
-0.0172119140625,
0.0284881591796875,
0.0029144287109375,
0.034088134765625,
0.01214599609375,
-0.007080078125,
-0.01071929931640625,
0.00396728515625,
-0.047637939453125,
-0.0194244384765625,
-0.0130157470703125,
-0.01329803466796875,
0.028472900390625,
0.038543701171875,
-0.0005474090576171875,
-0.01396942138671875,
-0.004138946533203125,
0.0184326171875,
-0.034210205078125,
-0.006927490234375,
-0.0170745849609375,
-0.0023345947265625,
-0.0172271728515625,
0.00876617431640625,
0.0238494873046875,
-0.019073486328125,
0.0183258056640625,
-0.0107574462890625,
-0.01073455810546875,
-0.0199432373046875,
0.004802703857421875,
-0.01268768310546875,
0.008636474609375,
-0.02105712890625,
-0.04278564453125,
-0.0119781494140625,
0.004688262939453125,
0.0181427001953125,
0.0311279296875,
0.01708984375,
0.02294921875,
-0.0234527587890625,
-0.018310546875,
0.0128326416015625,
-0.02789306640625,
0.00786590576171875,
-0.01468658447265625,
0.0029201507568359375,
0.00722503662109375,
-0.0287933349609375,
0.0097808837890625,
0.0159912109375,
0.01213836669921875,
-0.0046234130859375,
-0.01270294189453125,
0.004756927490234375,
-0.03521728515625,
-0.0171051025390625,
0.01151275634765625,
0.029083251953125,
0.002994537353515625,
-0.00841522216796875,
-0.0213470458984375,
-0.0261688232421875,
-0.00484466552734375,
0.01885986328125,
0.02105712890625,
-0.005191802978515625,
-0.0021686553955078125,
-0.038482666015625,
-0.0259552001953125,
-0.01453399658203125,
-0.0015211105346679688,
0.02081298828125,
0.03662109375,
0.007251739501953125,
-0.005584716796875,
-0.015838623046875,
0.01172637939453125,
0.00034546852111816406,
-0.0126800537109375,
0.01020050048828125,
-0.030364990234375,
0.01180267333984375,
-0.001003265380859375,
-0.018524169921875,
-0.022491455078125,
-0.04754638671875,
0.029144287109375,
-0.0184478759765625,
0.01554107666015625,
-0.0194549560546875,
-0.011383056640625,
0.01346588134765625,
-0.022918701171875,
0.005092620849609375,
0.01461029052734375,
0.01214599609375,
-0.00365447998046875,
0.01605224609375,
-0.0147247314453125,
-0.0111541748046875,
-0.015869140625,
-0.0302886962890625,
0.00879669189453125,
-0.03179931640625,
0.007720947265625,
0.00795745849609375,
0.0108795166015625,
-0.016326904296875,
-0.01258087158203125,
-0.01708984375,
0.0207977294921875,
0.0114288330078125,
-0.003551483154296875,
0.021820068359375,
-0.0092010498046875,
-0.04229736328125,
-0.0235137939453125,
0.02947998046875,
0.007843017578125,
-0.01320648193359375,
0.01515960693359375,
0.00635528564453125,
-0.0007572174072265625,
0.00830841064453125,
-0.015045166015625,
-0.03515625,
-0.021820068359375,
-0.0004584789276123047,
0.03302001953125,
0.0308837890625,
-0.03564453125,
0.03228759765625,
0.015167236328125,
-0.0024280548095703125,
0.0222015380859375,
-0.00716400146484375,
-0.0173492431640625,
-0.01336669921875,
-0.002307891845703125,
-0.013092041015625,
0.01023101806640625,
0.00894927978515625,
-0.042266845703125,
0.026092529296875,
-0.0163726806640625,
-0.0196380615234375,
0.0190887451171875,
-0.0204620361328125,
-0.007244110107421875,
0.008544921875,
-0.028411865234375,
0.00832366943359375,
-0.047637939453125,
0.0043792724609375,
-0.03271484375,
-0.026397705078125,
-0.005367279052734375,
0.0147552490234375,
-0.022430419921875,
0.04937744140625,
-0.0005655288696289062,
0.01354217529296875,
-0.018096923828125,
0.00467681884765625,
-0.02117919921875,
-0.0133514404296875,
-0.02642822265625,
-0.02374267578125,
0.01515960693359375,
0.0251007080078125,
-0.0047607421875,
0.0242919921875,
0.0225067138671875,
-0.046661376953125,
-0.03863525390625,
-0.01184844970703125,
0.0171051025390625,
0.01166534423828125,
0.0035247802734375,
-0.0016241073608398438,
-0.0022144317626953125,
-0.0071868896484375,
0.00370025634765625,
0.01336669921875,
-0.02740478515625,
-0.0024890899658203125,
0.0148468017578125,
0.038238525390625,
0.00936126708984375,
0.038848876953125,
-0.0139312744140625,
-0.023040771484375,
0.01165008544921875,
-0.0012950897216796875,
-0.007038116455078125,
0.004039764404296875,
0.0243377685546875,
0.0034046173095703125,
-0.01497650146484375,
-0.0199737548828125,
-0.024566650390625,
0.030426025390625,
0.0184326171875,
0.00025343894958496094,
0.0182647705078125,
0.00336456298828125,
-0.0206298828125,
0.0251312255859375,
-0.041046142578125,
-0.008880615234375,
-0.0022430419921875,
0.036956787109375,
-0.0132293701171875,
0.0196533203125,
-0.0004572868347167969,
0.01280975341796875,
0.00020051002502441406,
0.0121612548828125,
-0.0253143310546875,
-0.0127105712890625,
0.0172271728515625,
0.020263671875,
-0.052215576171875,
-0.0005059242248535156,
-0.0108184814453125,
0.01316070556640625,
0.0186767578125,
0.033477783203125,
-0.01061248779296875,
-0.0300140380859375,
-0.011444091796875,
0.018463134765625,
0.0019388198852539062,
-0.01548004150390625,
-0.00455474853515625,
0.01088714599609375,
-0.051849365234375,
0.039581298828125,
0.033477783203125,
-0.0310821533203125,
0.01284027099609375,
0.00879669189453125,
0.01293182373046875,
0.039306640625,
-0.0003540515899658203,
-0.01262664794921875,
0.0016889572143554688,
0.01538848876953125,
0.0277099609375,
-0.0125732421875,
-0.00788116455078125,
0.00467681884765625,
-0.00452423095703125,
-0.051605224609375,
-0.00435638427734375,
0.037506103515625,
0.018829345703125,
-0.002376556396484375,
0.0226593017578125,
-0.01306915283203125,
0.01181793212890625,
0.0210418701171875,
-0.012054443359375,
0.02001953125,
-0.00605010986328125,
-0.0355224609375,
-0.00583648681640625,
0.0006780624389648438,
-0.017242431640625,
-0.013763427734375,
-0.015380859375,
-0.035980224609375,
-0.005435943603515625,
-0.01151275634765625,
-0.00030112266540527344,
0.011932373046875,
0.027984619140625,
-0.006000518798828125,
-0.004848480224609375,
0.0131988525390625,
-0.0011882781982421875,
-0.005878448486328125,
-0.0008120536804199219,
-0.0025463104248046875,
0.006725311279296875,
0.0026264190673828125,
0.0020847320556640625,
-0.010040283203125,
-0.0279083251953125,
0.0066375732421875,
0.0408935546875,
0.018798828125,
-0.01450347900390625,
0.00799560546875,
0.01367950439453125,
-0.02093505859375,
-0.0106964111328125,
-0.01401519775390625,
0.0293426513671875,
-0.002811431884765625,
0.0033721923828125,
0.058502197265625,
0.01497650146484375,
-0.034881591796875,
0.01580810546875,
-0.0064849853515625,
-0.00943756103515625,
0.0004811286926269531,
-0.0082550048828125,
0.055633544921875,
0.01275634765625,
0.034912109375,
-0.0296173095703125,
0.01490020751953125,
0.007747650146484375,
0.022064208984375,
0.01483917236328125,
0.017181396484375,
-0.005908966064453125,
0.0122528076171875,
-0.00022411346435546875,
-0.0120086669921875,
0.006778717041015625,
0.0059661865234375,
0.004482269287109375,
-0.0099945068359375,
0.026885986328125,
-0.0038318634033203125,
0.030181884765625,
0.0056915283203125,
0.0038814544677734375,
0.0163726806640625,
0.006805419921875,
0.00414276123046875,
0.004489898681640625,
0.0005888938903808594,
-0.00165557861328125,
0.0243682861328125,
-0.019256591796875,
0.0216217041015625,
-0.00342559814453125,
-0.01425933837890625,
-0.00743865966796875,
0.017578125,
0.0216217041015625,
-0.0020427703857421875,
-0.0191650390625,
0.016998291015625,
-0.0298004150390625,
0.0171356201171875,
-0.020660400390625,
-0.0072784423828125,
0.0012674331665039062,
0.0113067626953125,
0.032562255859375,
0.01727294921875,
-0.03900146484375,
0.01529693603515625,
0.0228271484375,
-0.0086212158203125,
-0.007610321044921875,
0.021148681640625,
-0.00771331787109375,
0.01479339599609375,
-0.010589599609375,
-0.027618408203125,
0.0270538330078125,
0.00003618001937866211,
0.0121002197265625,
-0.0002167224884033203,
0.0006546974182128906,
-0.0194549560546875,
-0.0038299560546875,
-0.00626373291015625,
-0.005985260009765625,
-0.021728515625,
-0.00787353515625,
0.003631591796875,
0.0028743743896484375,
-0.01593017578125,
0.0012302398681640625,
0.00569915771484375,
-0.0179901123046875,
0.031494140625,
0.00025844573974609375,
0.0063018798828125,
-0.044708251953125,
-0.0019378662109375,
0.005390167236328125,
0.01345062255859375,
-0.00589752197265625,
-0.00891876220703125,
0.0015764236450195312,
-0.03436279296875,
-0.0281524658203125,
-0.028350830078125,
-0.0012502670288085938,
-0.0038127899169921875,
0.021820068359375,
-0.0163726806640625,
0.00038552284240722656,
-0.0004513263702392578,
0.00026035308837890625,
0.0032787322998046875,
-0.01067352294921875,
0.003841400146484375,
-0.0236663818359375,
-0.009033203125,
-0.0150146484375,
0.022674560546875,
0.011566162109375,
0.009613037109375,
-0.002864837646484375,
-0.002101898193359375,
0.01143646240234375,
0.01152801513671875,
0.01947021484375,
0.004703521728515625,
-0.0242919921875,
0.00540924072265625,
0.0290374755859375,
0.0023822784423828125,
-0.0013742446899414062,
0.02557373046875,
0.0293731689453125,
-0.03082275390625,
0.02142333984375,
0.006351470947265625,
-0.0046539306640625,
0.0135498046875,
0.012298583984375,
-0.0168304443359375,
0.00013005733489990234,
0.0292816162109375,
0.0024127960205078125,
0.0303192138671875,
-0.018585205078125,
0.023529052734375,
-0.0022106170654296875,
-0.0023097991943359375,
0.015655517578125,
0.00919342041015625,
0.006816864013671875,
-0.01088714599609375,
0.005641937255859375,
0.0059051513671875,
-0.006076812744140625,
-0.01751708984375,
0.0166015625,
-0.0163421630859375,
-0.004909515380859375,
0.0150146484375,
-0.0304107666015625,
-0.0105438232421875,
-0.032073974609375,
0.038726806640625,
-0.0213165283203125,
-0.0075225830078125,
0.0009160041809082031,
0.01898193359375,
0.0122833251953125,
0.024261474609375,
0.0159454345703125,
0.0033969879150390625,
-0.0191650390625,
-0.0277252197265625,
0.03350830078125,
-0.001251220703125,
0.03948974609375,
0.01132965087890625,
0.0192108154296875,
-0.0080108642578125,
-0.00803375244140625,
0.0005087852478027344,
0.01270294189453125,
-0.016021728515625,
0.0032215118408203125,
0.0269927978515625,
-0.038970947265625,
-0.0243377685546875,
-0.0167388916015625,
-0.01392364501953125,
-0.01435089111328125,
0.018402099609375,
-0.019195556640625,
0.01291656494140625,
0.0313720703125,
0.0102996826171875,
0.00867462158203125,
0.0224456787109375,
-0.0175018310546875,
-0.002593994140625,
-0.004241943359375,
0.01806640625,
0.04937744140625,
-0.0154571533203125,
0.0111541748046875,
0.006011962890625,
-0.0113677978515625,
-0.01010894775390625,
-0.004398345947265625,
0.004604339599609375,
-0.0146484375,
0.0034999847412109375,
0.0277862548828125,
0.0009393692016601562,
-0.008331298828125,
0.048248291015625,
-0.007411956787109375,
0.01381683349609375,
0.037750244140625,
0.016448974609375,
0.01192474365234375,
-0.00023686885833740234,
0.0277252197265625,
0.04705810546875,
-0.0276336669921875,
0.0204315185546875,
0.003986358642578125,
0.002941131591796875,
-0.0034046173095703125,
-0.0008687973022460938,
-0.028045654296875,
0.0136871337890625,
-0.01219940185546875,
0.0090179443359375,
-0.00033783912658691406,
-0.0004742145538330078,
-0.0198211669921875,
-0.00247955322265625,
-0.027587890625,
-0.04364013671875,
0.01470184326171875,
-0.01544189453125,
0.03125,
0.01348114013671875,
0.01313018798828125,
0.00836181640625,
0.01641845703125,
-0.02032470703125,
-0.013031005859375,
0.0267333984375,
0.0014934539794921875,
0.01273345947265625,
0.0312042236328125,
-0.017333984375,
-0.01119232177734375,
-0.0099945068359375,
-0.00214385986328125,
0.0145721435546875,
0.01540374755859375,
0.01413726806640625,
-0.004398345947265625,
0.00655364990234375,
-0.0196533203125,
-0.00408172607421875,
0.0213470458984375,
0.0096893310546875,
-0.062164306640625,
0.01212310791015625,
-0.0125885009765625,
-0.02447509765625,
0.00765228271484375,
0.0277252197265625,
-0.019195556640625,
0.01253509521484375,
0.004833221435546875,
-0.022796630859375,
0.002246856689453125,
0.0182037353515625,
0.01053619384765625,
-0.00885009765625,
0.00469970703125,
-0.02276611328125,
-0.0264129638671875,
0.01288604736328125,
0.0279388427734375,
-0.0018110275268554688,
0.0193634033203125,
0.0079498291015625,
0.055084228515625,
0.002445220947265625,
0.0004711151123046875,
-0.0012989044189453125,
0.0213623046875,
0.01393890380859375,
0.01280975341796875,
0.0026092529296875,
0.004627227783203125,
0.02593994140625,
-0.0208892822265625,
0.0152587890625,
-0.00560760498046875,
-0.017333984375,
0.024139404296875,
0.01690673828125,
-0.046478271484375,
0.0205535888671875,
-0.053680419921875,
0.0274658203125,
0.0016603469848632812,
-0.01256561279296875,
-0.037261962890625,
-0.020538330078125,
-0.0068359375,
-0.0236053466796875,
0.01384735107421875,
0.007755279541015625,
-0.004734039306640625,
-0.0277557373046875,
0.011627197265625,
-0.0029239654541015625,
0.00521087646484375,
-0.0257110595703125,
0.0002791881561279297,
0.0081024169921875,
0.01519012451171875,
0.00701141357421875,
-0.0021991729736328125,
0.022125244140625,
0.01690673828125,
0.0242156982421875,
0.003936767578125,
0.0175933837890625,
-0.01483917236328125,
0.00015151500701904297,
0.002338409423828125,
-0.0230865478515625,
-0.006893157958984375,
0.005401611328125,
-0.02313232421875,
-0.0010662078857421875,
0.029022216796875,
-0.0142974853515625,
-0.0043792724609375,
0.013153076171875,
-0.0184326171875,
0.010589599609375,
0.01129913330078125,
0.008453369140625,
0.038604736328125,
-0.01458740234375,
0.0008687973022460938,
-0.0294952392578125,
-0.0217742919921875,
0.0006012916564941406,
0.0027980804443359375,
-0.0328369140625,
-0.01262664794921875,
0.0240631103515625,
-0.02996826171875,
-0.0204925537109375,
-0.0228118896484375,
0.00848388671875,
-0.00720977783203125,
0.0325927734375,
-0.006572723388671875,
-0.007755279541015625,
-0.0024166107177734375,
0.03045654296875,
-0.003936767578125,
-0.0136871337890625,
0.000469207763671875,
-0.006122589111328125,
0.01404571533203125,
-0.016815185546875,
0.0241851806640625,
0.00856781005859375,
-0.0200042724609375,
0.01352691650390625,
-0.0162200927734375,
0.008056640625,
-0.003936767578125,
-0.0086212158203125,
-0.0033397674560546875,
0.0030689239501953125,
0.0024127960205078125,
-0.017333984375,
0.002044677734375,
0.00107574462890625,
0.00775909423828125,
0.0177459716796875,
-0.003604888916015625,
0.0034503936767578125,
-0.0119171142578125,
0.00989532470703125,
0.017547607421875,
0.01971435546875,
0.004154205322265625,
0.031097412109375,
0.022735595703125,
0.01195526123046875,
-0.00394439697265625,
-0.01715087890625,
-0.0036602020263671875,
-0.0007028579711914062,
-0.0030689239501953125,
0.0117034912109375,
0.012908935546875,
0.010345458984375,
-0.0190887451171875,
-0.017181396484375,
0.002765655517578125,
-0.00482177734375,
-0.0390625,
-0.02410888671875,
0.0176239013671875,
0.005153656005859375,
0.01474761962890625,
-0.00800323486328125,
0.0048980712890625,
0.00830841064453125,
-0.0062103271484375,
-0.01470184326171875,
0.01155853271484375,
0.006488800048828125,
0.032440185546875,
0.0003437995910644531,
-0.0169219970703125,
0.03814697265625,
0.0007734298706054688,
0.01132965087890625,
-0.00870513916015625,
0.0028972625732421875,
-0.018157958984375,
-0.00507354736328125,
-0.007526397705078125,
0.004405975341796875,
-0.005519866943359375,
-0.0231781005859375,
0.033172607421875,
-0.0005540847778320312,
-0.00952911376953125,
-0.0021724700927734375,
0.021331787109375,
-0.009796142578125,
0.01096343994140625,
-0.0162353515625,
0.01248931884765625,
0.01425933837890625,
-0.0033416748046875,
-0.01512908935546875,
-0.0184783935546875,
0.0093231201171875,
-0.00524139404296875,
0.033905029296875,
-0.002864837646484375,
0.03955078125,
-0.00494384765625,
-0.045867919921875,
-0.00016570091247558594,
-0.0390625,
-0.0012111663818359375,
0.0022220611572265625,
0.0229034423828125,
0.00147247314453125,
-0.004802703857421875,
0.013641357421875,
-0.0116729736328125,
0.017425537109375,
0.0284881591796875,
0.0004324913024902344,
-0.0291290283203125,
0.018310546875,
0.0028743743896484375,
-0.0101318359375,
-0.0035495758056640625,
0.0138092041015625,
0.02056884765625,
-0.0113372802734375,
0.00921630859375,
0.0408935546875,
0.018646240234375,
0.01198577880859375,
-0.006317138671875,
0.0184783935546875,
-0.00913238525390625,
0.058349609375,
0.004932403564453125,
0.0194091796875,
-0.0247344970703125,
0.0024318695068359375,
0.020965576171875,
0.0038928985595703125,
0.0091552734375,
-0.0023651123046875,
0.0100860595703125,
0.0163726806640625,
-0.0167694091796875,
-0.0171966552734375,
0.0005931854248046875,
0.005496978759765625,
-0.0127716064453125,
0.036834716796875,
-0.01544189453125,
0.052154541015625,
-0.022003173828125,
0.01215362548828125,
0.022216796875,
0.01445770263671875,
0.003910064697265625,
-0.01203155517578125,
-0.05047607421875,
-0.0330810546875,
-0.01479339599609375,
0.00909423828125,
-0.0206756591796875,
0.0101470947265625,
0.01837158203125,
0.0134429931640625,
-0.024169921875,
0.0084381103515625,
0.018310546875,
0.00933837890625,
0.0017375946044921875,
-0.010040283203125,
0.00278472900390625,
0.0261993408203125,
0.0004911422729492188,
0.0048828125,
0.00604248046875,
0.020172119140625,
0.003993988037109375,
0.0053863525390625,
-0.035400390625,
-0.00266265869140625,
-0.00836944580078125,
0.02276611328125,
-0.00106048583984375,
0.01033782958984375,
-0.01378631591796875,
-0.0186920166015625,
0.023895263671875,
0.00323486328125,
0.0013723373413085938,
-0.0117340087890625,
0.00830841064453125,
-0.018463134765625,
0.002105712890625,
-0.054840087890625,
0.01611328125,
-0.030853271484375,
-0.031768798828125,
-0.00585174560546875,
0.03216552734375,
0.044219970703125,
0.02349853515625,
0.0037441253662109375,
0.01137542724609375,
0.0110015869140625,
-0.00843048095703125,
-0.01229095458984375,
-0.015625,
-0.05645751953125,
-0.0013408660888671875,
0.003963470458984375,
0.0265655517578125,
-0.036865234375,
-0.054962158203125,
-0.0283966064453125,
-0.00998687744140625,
-0.0438232421875,
-0.0037746429443359375,
0.017913818359375,
0.01308441162109375,
-0.0112152099609375,
-0.0100250244140625,
0.03826904296875,
-0.0014848709106445312,
0.00769805908203125,
-0.0161285400390625,
-0.0209808349609375,
-0.0308074951171875,
0.0158538818359375,
0.0026874542236328125,
-0.035858154296875,
0.01409149169921875,
-0.0135498046875,
0.0039215087890625,
0.025146484375,
-0.0006265640258789062,
-0.0244140625,
0.00275421142578125,
0.02667236328125,
-0.0203399658203125,
0.0102691650390625,
0.0295562744140625,
-0.007568359375,
-0.006603240966796875,
-0.006320953369140625,
0.006038665771484375,
0.005847930908203125,
0.0367431640625,
0.0022258758544921875,
-0.002910614013671875,
0.008148193359375,
0.02484130859375,
0.01114654541015625,
-0.005706787109375,
-0.004638671875,
0.01529693603515625,
-0.0020427703857421875,
-0.0167388916015625,
-0.03173828125,
-0.039215087890625,
0.01324462890625,
-0.0428466796875,
0.019317626953125,
-0.0204925537109375,
0.028717041015625,
0.004528045654296875,
-0.001251220703125,
0.00437164306640625,
-0.0195465087890625,
0.006710052490234375,
0.0158843994140625,
-0.011566162109375,
-0.013519287109375,
-0.0195770263671875,
0.015594482421875,
0.020050048828125,
-0.01358795166015625,
0.01605224609375,
0.0017213821411132812,
0.017364501953125,
-0.003814697265625,
-0.0186614990234375,
-0.007244110107421875,
0.007476806640625,
-0.002780914306640625,
0.014068603515625,
-0.002902984619140625,
-0.03228759765625,
0.00310516357421875,
-0.0096588134765625,
-0.01058197021484375,
-0.004093170166015625,
0.007061004638671875,
0.01116180419921875,
0.03704833984375,
0.02435302734375,
0.00617218017578125,
0.00418853759765625,
0.007511138916015625,
0.00762176513671875,
-0.007061004638671875,
0.04913330078125,
-0.0081024169921875,
0.0001283884048461914,
0.032867431640625,
0.0291290283203125,
0.016693115234375,
0.003448486328125,
-0.009429931640625,
0.0171966552734375,
0.037261962890625,
-0.017913818359375,
-0.0258941650390625,
0.0233612060546875,
-0.031097412109375,
-0.005146026611328125,
-0.0040283203125,
-0.0309295654296875,
-0.0254669189453125,
0.01447296142578125,
-0.005702972412109375,
-0.031768798828125,
0.040740966796875,
0.0035800933837890625,
-0.01458740234375,
-0.06158447265625,
0.00897216796875,
0.041961669921875,
-0.0198974609375,
-0.020599365234375,
-0.00299835205078125,
-0.001506805419921875,
0.0248870849609375,
-0.0081787109375,
-0.0226287841796875,
0.0008697509765625,
0.0034275054931640625,
-0.0240478515625,
0.0261688232421875,
0.026611328125,
0.025787353515625,
-0.005245208740234375,
-0.01398468017578125,
0.0033016204833984375,
-0.035675048828125,
-0.0298309326171875,
-0.0209503173828125,
0.0010280609130859375,
-0.0325927734375,
0.006977081298828125,
-0.0016679763793945312,
-0.0100250244140625,
-0.03424072265625,
-0.0260467529296875,
0.0206451416015625,
0.00432586669921875,
-0.036529541015625,
0.021240234375,
-0.0182037353515625,
0.028594970703125,
0.01384735107421875,
0.012664794921875,
-0.0120697021484375,
0.044830322265625,
0.035919189453125,
0.0311126708984375,
0.0008821487426757812,
0.027679443359375,
0.01021575927734375,
-0.00943756103515625,
0.0015878677368164062,
0.00432586669921875,
-0.0026302337646484375,
-0.0196075439453125,
-0.01105499267578125,
0.00018322467803955078,
-0.02972412109375,
-0.0095367431640625,
-0.0262603759765625,
0.0157928466796875,
-0.0162506103515625,
0.01287078857421875,
-0.01039886474609375,
-0.0018901824951171875,
0.01303863525390625,
0.0005998611450195312,
-0.01204681396484375,
0.000823974609375,
0.0082550048828125,
0.0286712646484375,
0.01148223876953125,
0.016571044921875,
-0.0005660057067871094,
-0.0146942138671875,
0.01354217529296875,
-0.01548004150390625,
0.0096282958984375,
0.0099945068359375,
-0.0021457672119140625,
0.04095458984375,
0.0173492431640625,
-0.0252227783203125,
-0.0110626220703125,
-0.0243988037109375,
-0.018707275390625,
-0.008331298828125,
-0.01129913330078125,
-0.00453948974609375,
-0.0282745361328125,
0.03350830078125,
-0.0277557373046875,
-0.022857666015625,
-0.02508544921875,
-0.00539398193359375,
0.019439697265625,
-0.0190277099609375,
-0.0056610107421875,
0.0121917724609375,
0.0189971923828125,
0.01406097412109375,
0.0239410400390625,
0.00534820556640625,
0.0360107421875,
0.0242156982421875,
-0.0211334228515625,
-0.0216064453125,
-0.0005393028259277344,
-0.01303863525390625,
0.005970001220703125,
0.000640869140625,
0.006488800048828125,
-0.008758544921875,
-0.006954193115234375,
0.01371002197265625,
-0.0092620849609375,
0.00777435302734375,
-0.01380157470703125,
-0.0107269287109375,
0.00336456298828125,
-0.0087127685546875,
-0.005855560302734375,
0.00408935546875,
0.043426513671875,
-0.0308074951171875,
0.01241302490234375,
0.0228729248046875,
-0.0282440185546875,
-0.018585205078125,
-0.0367431640625,
0.0013227462768554688,
0.004680633544921875,
0.017425537109375,
-0.006999969482421875,
-0.01169586181640625,
-0.01378631591796875,
0.00247955322265625,
0.003780364990234375,
0.01100921630859375,
0.00428009033203125,
-0.0008835792541503906,
0.0005745887756347656,
0.0254058837890625,
-0.0083160400390625,
0.011016845703125,
0.003940582275390625,
0.0294647216796875,
0.0089569091796875,
0.0025310516357421875,
0.0027561187744140625,
0.00685882568359375,
0.01248931884765625,
-0.0132904052734375,
-0.00344085693359375,
0.0007867813110351562,
0.0216217041015625,
-0.007843017578125,
0.01012420654296875,
0.01546478271484375,
-0.006916046142578125,
0.006053924560546875,
-0.021697998046875,
-0.01470947265625,
0.00884246826171875,
0.01322174072265625,
0.0134429931640625,
-0.028289794921875,
0.00452423095703125,
-0.00524139404296875,
-0.0016298294067382812,
-0.03509521484375,
0.00667572021484375,
0.06231689453125,
-0.0230255126953125,
0.0283966064453125,
0.0026092529296875,
-0.05206298828125,
-0.0181884765625,
-0.040618896484375,
0.021759033203125,
0.0450439453125,
-0.0101165771484375,
0.0011606216430664062,
0.00011438131332397461,
0.01007080078125,
0.0073394775390625,
-0.007965087890625,
0.0275726318359375,
-0.00803375244140625,
-0.000995635986328125,
0.000052928924560546875,
0.0019969940185546875,
-0.026885986328125,
-0.0264739990234375,
0.007755279541015625,
-0.00372314453125,
-0.015838623046875,
0.0158233642578125,
0.007709503173828125,
0.01039886474609375,
0.0261993408203125,
-0.00676727294921875,
0.0017042160034179688,
0.0171661376953125,
-0.00934600830078125,
-0.003604888916015625,
-0.011016845703125,
-0.0186309814453125,
-0.041473388671875,
-0.038818359375,
0.0255889892578125,
-0.00733184814453125,
0.0042877197265625,
0.02581787109375,
0.02734375,
0.003971099853515625,
-0.00750732421875,
-0.025238037109375,
-0.0034923553466796875,
0.0272064208984375,
-0.002361297607421875,
0.0240325927734375,
0.0252227783203125,
0.0115966796875,
0.029205322265625,
0.0019588470458984375,
0.00829315185546875,
-0.00919342041015625,
0.033172607421875,
-0.0137786865234375,
0.017486572265625,
-0.0294952392578125,
-0.0167694091796875,
0.00997161865234375,
0.0022487640380859375,
0.00992584228515625,
-0.005100250244140625,
-0.02838134765625,
0.03448486328125,
-0.0226898193359375,
-0.05084228515625,
-0.0034160614013671875,
-0.006298065185546875,
0.0072021484375,
0.0035152435302734375,
-0.0066375732421875,
-0.03985595703125,
0.035308837890625,
-0.005634307861328125,
0.01806640625,
-0.0157928466796875,
0.0034732818603515625,
-0.009063720703125,
-0.00859832763671875,
0.0168304443359375,
-0.048828125,
0.02752685546875,
-0.033111572265625,
0.0234375,
0.0251007080078125,
-0.00017833709716796875,
0.01535797119140625,
-0.020416259765625,
-0.004611968994140625,
0.014617919921875,
-0.0217437744140625,
-0.01032257080078125,
0.014007568359375,
-0.0029144287109375,
0.0109100341796875,
-0.003948211669921875,
0.026580810546875,
-0.0282745361328125,
-0.01287841796875,
-0.0287628173828125,
-0.0037670135498046875,
0.0279998779296875,
-0.01385498046875,
0.0180816650390625,
-0.019744873046875,
-0.0099029541015625,
0.01119232177734375,
-0.0025177001953125,
0.00042438507080078125,
0.0116119384765625,
-0.02227783203125,
-0.00850677490234375,
-0.0009794235229492188,
-0.01490020751953125,
0.006259918212890625,
-0.028411865234375,
0.0226593017578125,
-0.0038356781005859375,
-0.02105712890625,
-0.0012302398681640625,
-0.00946807861328125,
0.007274627685546875,
-0.012420654296875,
-0.024200439453125,
-0.00466156005859375,
-0.01007080078125,
0.02392578125,
0.0242767333984375,
0.005619049072265625,
0.037445068359375,
-0.0230560302734375,
0.0276947021484375,
0.058380126953125,
-0.008941650390625,
-0.0281982421875,
0.009368896484375,
-0.01088714599609375,
0.0194549560546875,
-0.014678955078125,
0.014892578125,
0.00888824462890625,
0.00933837890625,
0.00579071044921875,
0.009124755859375,
-0.029083251953125,
0.0229644775390625,
0.0228424072265625,
-0.0236053466796875,
-0.0029621124267578125,
-0.01258087158203125,
-0.00925445556640625,
0.004150390625,
-0.01446533203125,
0.0062255859375,
-0.024505615234375,
-0.00197601318359375,
0.01235198974609375,
0.0159454345703125,
0.045379638671875,
-0.000980377197265625,
-0.0372314453125,
-0.010498046875,
0.05499267578125,
-0.0218658447265625,
-0.01788330078125,
-0.02130126953125,
0.00433349609375,
0.0054779052734375,
0.0273284912109375,
-0.0016717910766601562,
0.01479339599609375,
0.017486572265625,
0.01262664794921875,
0.0086212158203125,
-0.0182952880859375,
-0.0250396728515625,
-0.045074462890625,
0.020904541015625,
0.024658203125,
-0.0399169921875,
0.01025390625,
0.00823974609375,
-0.01041412353515625,
0.025238037109375,
-0.041534423828125,
-0.020660400390625,
-0.01560211181640625,
0.017181396484375,
0.002994537353515625,
-0.02703857421875,
0.031280517578125,
-0.0227203369140625,
-0.029022216796875,
0.02752685546875,
0.0185546875,
0.0007190704345703125,
-0.014617919921875,
-0.000797271728515625,
-0.0127105712890625,
0.0209808349609375,
0.05584716796875,
-0.01739501953125,
-0.0006060600280761719,
-0.008056640625,
0.006740570068359375,
0.002391815185546875,
-0.006710052490234375,
-0.020233154296875,
-0.00778961181640625,
-0.0103607177734375,
0.0017070770263671875,
-0.0306243896484375,
-0.01824951171875,
0.055999755859375,
0.006572723388671875,
-0.00780487060546875,
-0.02642822265625,
-0.045074462890625,
0.00627899169921875,
-0.02777099609375,
0.028350830078125,
0.024871826171875,
-0.004638671875,
0.006923675537109375,
-0.0069732666015625,
-0.0225982666015625,
0.0195159912109375,
0.00864410400390625,
0.016387939453125,
0.0018148422241210938,
-0.048828125,
-0.01143646240234375,
0.012237548828125,
0.0276641845703125,
0.00838470458984375,
0.0014743804931640625,
-0.011444091796875,
0.0020160675048828125,
-0.02301025390625,
0.00997161865234375,
-0.0198211669921875,
-0.005069732666015625,
0.0088348388671875,
0.0155181884765625,
-0.00838470458984375,
0.0156402587890625,
-0.00024235248565673828,
-0.01282501220703125,
0.014984130859375,
0.01543426513671875,
0.03021240234375,
0.004550933837890625,
-0.05816650390625,
0.0220794677734375,
0.0198516845703125,
0.025909423828125,
-0.0210113525390625,
0.01268768310546875,
-0.028350830078125,
0.01216888427734375,
0.01305389404296875,
-0.0133056640625,
0.0075225830078125,
-0.02569580078125,
-0.0267333984375,
0.0115814208984375,
0.0011816024780273438,
0.047698974609375,
0.019683837890625,
0.0135345458984375,
0.00733184814453125,
-0.0292816162109375,
0.04254150390625,
-0.0263671875,
-0.02117919921875,
-0.005550384521484375,
-0.00811004638671875,
-0.006763458251953125,
-0.0040435791015625,
0.0032711029052734375,
0.0013275146484375,
-0.00945281982421875,
0.004962921142578125,
-0.0160064697265625,
0.0145416259765625,
-0.0146026611328125,
0.0163726806640625,
-0.0006647109985351562,
0.0014791488647460938,
0.0208892822265625,
0.0162200927734375,
0.004367828369140625,
0.0003876686096191406,
-0.0014438629150390625,
0.0297088623046875,
-0.01531219482421875,
-0.003879547119140625,
0.00811004638671875,
0.0179290771484375,
0.0203399658203125,
-0.0295867919921875,
-0.0148468017578125,
-0.0202789306640625,
-0.0364990234375,
0.0036296844482421875,
0.01861572265625,
-0.0011205673217773438,
-0.00467681884765625,
0.003875732421875,
0.0217742919921875,
0.057342529296875
] |
ours_495
|
Solution.
Lemma 1: If a complex expression \(E\) has complexity \(e\) and evaluates to a complex set \(C\) that has complexity \(c\), then \(e \geq c\) and \(e \equiv c \pmod{2}\); furthermore, if \(e=c\), then \(E=C\).
Let \(C_{k}=\frac{\binom{2k}{k}}{k+1}\) be the \(k\)-th Catalan number for \(k \geq 0\).
Lemma 2: For all positive integers \(i\), there are exactly \(C_{i-1}\) complex sets of complexity \(i\).
Now define a function \(f\) from nonnegative integers to integers recursively by \(f(0)=1\) and, for \(x>0\), \(f(x)=\sum C_{a} f(b) f(c)\), where the sum is over all ordered triples \((a, b, c)\) of nonnegative integers such that \(a+b+c=x-1\).
Lemma 3: For any nonnegative integer \(n\), the following is true: for any positive integer \(k\) and for any complex set \(C\) of complexity \(k\), the number of complex expressions of complexity \(k+2n\) that evaluate to \(C\) is \(f(n)\).
Proof: Proceed by strong induction on \(n\).
For \(n=0\), any complex expression of complexity \(k\) that evaluates to \(C\) must be \(C\) by Lemma 1; also, \(C\) is such a complex expression. Thus, there is exactly \(1=f(0)\) such complex expression, as desired.
For \(n>0\), any complex expression \(E\) of complexity \(k+2n\) that evaluates to \(C\) is such that \(E \neq C\) (since the complexity of the complex expression \(C\) is \(k\), and \(k \neq k+2n\) as \(n>0\)), so \(E=(E_{1}, E_{2})\) for some complex expressions \(E_{1}\) and \(E_{2}\) such that, for some complex set \(C^{\prime}, E_{1}\) evaluates to \([C^{\prime}, C]\), and \(E_{2}\) evaluates to \(C^{\prime}\). The complexity of \(C^{\prime}\) is \(a+1\) for some nonnegative integer \(a\). Then the complexity of \([C^{\prime}, C]\) is \(a+1+k\). Then, by Lemma 1, the complexity of \(E_{1}\) is \(a+1+k+2b\) and the complexity of \(E_{2}\) is \(a+1+2c\) for some nonnegative integers \(b\) and \(c\). Then the complexity of \(E\) is \((a+1+k+2b)+(a+1+2c)=k+2(a+b+c+1)\); then \(k+2(a+b+c+1)=k+2n\), so \(a+b+c=n-1\).
Now, for any ordered triple \((a, b, c)\) of nonnegative integers such that \(a+b+c=n-1\), there are \(C_{a}\) complex sets \(C^{\prime}\) of complexity \(a+1\). Then once \(C^{\prime}\) is chosen, as \(b, c<n\), by the strong inductive hypothesis there are \(f(b)\) complex expressions \(E_{1}\) of complexity \(a+1+k+2b\) that evaluate to \([C^{\prime}, C]\), and there are \(f(c)\) complex expressions \(E_{2}\) of complexity \(a+1+2c\) that evaluate to \(C^{\prime}\). This yields \(C_{a} f(b) f(c)\) complex expressions \(E=(E_{1}, E_{2})\) of complexity \(k+2n\) that evaluate to \(C\), for this case of what \((a, b, c)\) is.
Now if we sum over all cases to get \(\sum C_{a} f(b) f(c)\) complex expressions (where the sum is over all ordered triples \((a, b, c)\) of nonnegative integers such that \(a+b+c=n-1\)), then we count only complex expressions of complexity \(k+2n\) that evaluate to \(C\), we count all such complex expressions, and we don't count any such complex expression more than once. Thus there are exactly \(\sum C_{a} f(b) f(c)\) complex expressions of complexity \(k+2n\) that evaluate to \(C\); by the definition of \(f\), there are thus exactly \(f(n)\) complex expressions of complexity \(k+2n\) that evaluate to \(C\), as desired.
Thus Lemma 3 is true.
Now, for all positive integers \(i\), \(a_{i}=0\) if \(i\) is even and \(a_{i}=f\left(\frac{i-1}{2}\right)\) if \(i\) is odd. Let \(y=x^{2}\); then \(y>0\) and \(f(0)+f(1) y+f(2) y^{2}+\cdots=\frac{7}{4}\). Now the sequence \(f(0), f(1), f(2), \ldots\) is sequence A127632 in the OEIS, so by a result listed at we know that \(f(0)+f(1) y+f(2) y^{2}+\cdots=\frac{2}{1+\sqrt{2 \sqrt{1-4 y}-1}}\). Thus \(\frac{2}{1+\sqrt{2 \sqrt{1-4 y}-1}}=\frac{7}{4}\), so \(y=\frac{444}{2401}\), so \(x=\sqrt{y}=\frac{2 \sqrt{111}}{49}\), so the answer is \(2 \cdot 100+111 \cdot 10+49=1359\).
\(\boxed{1359}\)
|
1359
|
{
"competition": "us_comps",
"dataset": "Ours",
"posts": null,
"source": "OMOFall19Solns-3.md"
}
|
A complex set, along with its complexity, is defined recursively as follows:
- The set \(\mathbb{C}\) of complex numbers is a complex set with complexity \(1\).
- Given two complex sets \(C_{1}, C_{2}\) with complexity \(c_{1}, c_{2}\) respectively, the set of all functions \(f : C_{1} \rightarrow C_{2}\) is a complex set denoted \([C_{1}, C_{2}]\) with complexity \(c_{1}+c_{2}\).
A complex expression, along with its evaluation and its complexity, is defined recursively as follows:
- A single complex set \(C\) with complexity \(c\) is a complex expression with complexity \(c\) that evaluates to itself.
- Given two complex expressions \(E_{1}, E_{2}\) with complexity \(e_{1}, e_{2}\) that evaluate to \(C_{1}\) and \(C_{2}\) respectively, if \(C_{1}=[C_{2}, C]\) for some complex set \(C\), then \((E_{1}, E_{2})\) is a complex expression with complexity \(e_{1}+e_{2}\) that evaluates to \(C\).
For a positive integer \(n\), let \(a_{n}\) be the number of complex expressions with complexity \(n\) that evaluate to \(\mathbb{C}\). Let \(x\) be a positive real number. Suppose that
\[
a_{1}+a_{2} x+a_{3} x^{2}+\cdots=\frac{7}{4}
\]
Then \(x=\frac{k \sqrt{m}}{n}\), where \(k, m\), and \(n\) are positive integers such that \(m\) is not divisible by the square of any integer greater than \(1\), and \(k\) and \(n\) are relatively prime. Compute \(100 k+10 m+n\).
|
[
"/Mathematics/Algebra/NumberTheory/GeneratingFunctions/GeneratingFunction",
"/Mathematics/Algebra/NumberTheory/Sequences/IntegerSequence",
"/Mathematics/Algebra/NumberTheory/Sequences/Sequence",
"/Mathematics/Algebra/NumberTheory/SpecialNumbers",
"/Mathematics/DiscreteMathematics/Combinatorics/BinomialCoefficients",
"/Mathematics/DiscreteMathematics/Combinatorics/CombinatorialIdentities",
"/Mathematics/DiscreteMathematics/Combinatorics/Enumeration",
"/Mathematics/DiscreteMathematics/Combinatorics/GeneralCombinatorics",
"/Mathematics/DiscreteMathematics/GeneralDiscreteMathematics/ConcreteMath",
"/Mathematics/DiscreteMathematics/GeneralDiscreteMathematics/ConcreteMathematics",
"/Mathematics/DiscreteMathematics/GeneralDiscreteMathematics/DiscreteMath",
"/Mathematics/DiscreteMathematics/GeneralDiscreteMathematics/DiscreteMathematics",
"/Mathematics/DiscreteMathematics/RecurrenceEquations/CatalanNumber",
"/Mathematics/DiscreteMathematics/RecurrenceEquations/RecurrenceRelation",
"/Mathematics/DiscreteMathematics/RecurrenceEquations/RecursiveSequence"
] |
Model the expression count with a Catalan‑based recurrence and use its known generating function to determine the series sum and solve for x.
|
[
-0.00002002716064453125,
0.0101776123046875,
0.0282135009765625,
0.0254669189453125,
0.0002865791320800781,
0.00279998779296875,
-0.0095977783203125,
0.0006098747253417969,
0.00036263465881347656,
-0.019073486328125,
0.02783203125,
-0.044097900390625,
-0.0021343231201171875,
0.047882080078125,
-0.006496429443359375,
-0.0236053466796875,
0.01556396484375,
-0.00677490234375,
0.008575439453125,
-0.004337310791015625,
-0.00984954833984375,
0.007232666015625,
-0.058135986328125,
0.038818359375,
-0.051483154296875,
-0.00970458984375,
-0.020111083984375,
-0.035858154296875,
0.01305389404296875,
0.01383209228515625,
0.0225067138671875,
-0.039398193359375,
0.0055694580078125,
-0.035125732421875,
-0.0029163360595703125,
-0.01369476318359375,
0.0013475418090820312,
-0.00235748291015625,
-0.01486968994140625,
-0.00965118408203125,
0.00377655029296875,
0.00960540771484375,
-0.0010328292846679688,
0.0201416015625,
0.02508544921875,
0.0069732666015625,
0.0016660690307617188,
-0.0007028579711914062,
-0.01125335693359375,
0.0120697021484375,
-0.00908660888671875,
0.0145416259765625,
0.0160369873046875,
-0.01373291015625,
-0.0276947021484375,
-0.027862548828125,
-0.0107879638671875,
-0.0009527206420898438,
-0.0206146240234375,
0.007518768310546875,
0.0027713775634765625,
0.02044677734375,
-0.0249786376953125,
-0.00917816162109375,
-0.004886627197265625,
-0.0006375312805175781,
0.021575927734375,
-0.0128936767578125,
0.00513458251953125,
0.01003265380859375,
0.01462554931640625,
-0.01557159423828125,
0.0004665851593017578,
0.036224365234375,
-0.004459381103515625,
0.0004703998565673828,
-0.00597381591796875,
0.020355224609375,
0.01361846923828125,
-0.0134429931640625,
-0.011444091796875,
0.00844573974609375,
0.01203155517578125,
-0.0391845703125,
-0.0015478134155273438,
-0.0168304443359375,
-0.0194091796875,
0.005855560302734375,
0.038665771484375,
-0.0257415771484375,
0.005664825439453125,
0.0250244140625,
0.0176544189453125,
-0.0286712646484375,
0.0005779266357421875,
0.0060577392578125,
0.00843048095703125,
-0.002925872802734375,
-0.028594970703125,
0.0030231475830078125,
-0.011688232421875,
-0.0014390945434570312,
0.00511932373046875,
0.001720428466796875,
-0.0947265625,
-0.03240966796875,
0.0038585662841796875,
0.024322509765625,
0.005096435546875,
0.009033203125,
0.0014314651489257812,
0.0002002716064453125,
0.006988525390625,
0.004962921142578125,
-0.01428985595703125,
-0.009429931640625,
0.02056884765625,
0.0213775634765625,
-0.0215911865234375,
-0.0261993408203125,
0.0029964447021484375,
-0.007080078125,
-0.00435638427734375,
-0.0031871795654296875,
-0.006622314453125,
0.016357421875,
0.0016679763793945312,
-0.0191497802734375,
-0.01354217529296875,
0.021087646484375,
0.005046844482421875,
-0.0279083251953125,
-0.01910400390625,
-0.0330810546875,
-0.0926513671875,
0.0008816719055175781,
-0.02716064453125,
-0.0330810546875,
-0.0183868408203125,
-0.010772705078125,
-0.0030651092529296875,
-0.01183319091796875,
0.0102386474609375,
-0.0007023811340332031,
-0.0003707408905029297,
0.0037441253662109375,
0.01372528076171875,
-0.0223846435546875,
-0.0008177757263183594,
-0.01323699951171875,
0.0176239013671875,
-0.0035877227783203125,
0.0233306884765625,
0.00363922119140625,
-0.0017251968383789062,
0.0016717910766601562,
0.0230255126953125,
0.01280975341796875,
-0.01020050048828125,
0.0150146484375,
0.01026153564453125,
-0.01415252685546875,
0.035369873046875,
0.0151519775390625,
0.0008983612060546875,
-0.00890350341796875,
-0.01114654541015625,
0.0123138427734375,
0.0037708282470703125,
0.004283905029296875,
-0.01238250732421875,
-0.0015554428100585938,
-0.00389862060546875,
-0.0128326416015625,
0.016998291015625,
0.0078887939453125,
-0.03216552734375,
0.003429412841796875,
0.006206512451171875,
0.01241302490234375,
0.006099700927734375,
-0.033935546875,
-0.0090484619140625,
0.003997802734375,
-0.0092315673828125,
-0.005374908447265625,
0.00017499923706054688,
0.004039764404296875,
0.02484130859375,
0.001712799072265625,
0.00836944580078125,
-0.0191650390625,
-0.02496337890625,
0.006072998046875,
-0.03155517578125,
0.0016613006591796875,
0.01251983642578125,
0.01068878173828125,
0.037109375,
0.0014495849609375,
0.013153076171875,
0.003570556640625,
-0.0107879638671875,
0.019256591796875,
0.01763916015625,
-0.004573822021484375,
-0.01531219482421875,
-0.0087738037109375,
0.00016176700592041016,
0.00991058349609375,
0.026214599609375,
0.002895355224609375,
-0.0156707763671875,
-0.045196533203125,
-0.00746917724609375,
0.002651214599609375,
-0.00402069091796875,
0.00653839111328125,
0.007080078125,
-0.0091705322265625,
0.0100555419921875,
0.01435089111328125,
0.0035915374755859375,
-0.0272216796875,
-0.0029163360595703125,
-0.0006623268127441406,
-0.009918212890625,
0.004108428955078125,
0.0112762451171875,
0.021087646484375,
0.0266571044921875,
0.0193023681640625,
-0.03155517578125,
-0.01132965087890625,
0.0010290145874023438,
0.007694244384765625,
-0.02423095703125,
-0.021087646484375,
0.02130126953125,
-0.0228271484375,
-0.012115478515625,
-0.0023822784423828125,
0.034332275390625,
0.019622802734375,
0.002227783203125,
-0.0159149169921875,
-0.01024627685546875,
-0.0016317367553710938,
0.03387451171875,
-0.0061187744140625,
-0.01493072509765625,
0.00339508056640625,
-0.010040283203125,
-0.005550384521484375,
-0.0224151611328125,
0.005645751953125,
0.006076812744140625,
-0.0164947509765625,
-0.0174713134765625,
0.01305389404296875,
-0.0017347335815429688,
0.0033092498779296875,
-0.00582122802734375,
-0.013427734375,
-0.00484466552734375,
0.00823211669921875,
-0.02447509765625,
-0.00616455078125,
0.0137786865234375,
-0.00870513916015625,
0.046539306640625,
-0.0183258056640625,
-0.0013074874877929688,
0.012451171875,
-0.00933074951171875,
-0.01435089111328125,
-0.0177001953125,
0.0146331787109375,
0.016632080078125,
-0.0023555755615234375,
0.0078582763671875,
-0.00254058837890625,
-0.023101806640625,
0.00496673583984375,
-0.0128631591796875,
0.000797271728515625,
0.0226287841796875,
-0.0296478271484375,
-0.00640106201171875,
0.00699615478515625,
-0.0011138916015625,
-0.0060882568359375,
-0.01232147216796875,
0.0035114288330078125,
0.039947509765625,
-0.031341552734375,
0.0019893646240234375,
-0.0096588134765625,
0.0004992485046386719,
-0.01947021484375,
0.049591064453125,
0.0107421875,
-0.002231597900390625,
-0.01158905029296875,
0.039886474609375,
0.00385284423828125,
-0.0013990402221679688,
0.00444793701171875,
-0.054962158203125,
0.01143646240234375,
0.0311279296875,
0.01483154296875,
-0.01108551025390625,
0.000007450580596923828,
-0.045379638671875,
-0.029449462890625,
0.008087158203125,
-0.00026416778564453125,
-0.01090240478515625,
0.020843505859375,
-0.01154327392578125,
0.022979736328125,
-0.019073486328125,
0.005908966064453125,
-0.032562255859375,
-0.0213623046875,
0.01141357421875,
0.0090179443359375,
-0.0396728515625,
0.005283355712890625,
-0.04351806640625,
0.00525665283203125,
-0.0023670196533203125,
-0.024139404296875,
0.0005578994750976562,
0.00749969482421875,
-0.00067901611328125,
0.003223419189453125,
-0.017608642578125,
0.005069732666015625,
0.0035877227783203125,
0.0015745162963867188,
-0.0030460357666015625,
-0.01788330078125,
-0.021148681640625,
0.0254974365234375,
-0.004604339599609375,
-0.0052337646484375,
-0.00777435302734375,
0.002353668212890625,
0.00347137451171875,
0.01023101806640625,
-0.0191650390625,
0.0189971923828125,
-0.032928466796875,
0.020965576171875,
0.01058197021484375,
0.002681732177734375,
-0.002132415771484375,
0.019775390625,
-0.0020427703857421875,
-0.0261993408203125,
-0.0157470703125,
0.00316619873046875,
-0.002315521240234375,
-0.0076141357421875,
-0.022735595703125,
0.01543426513671875,
-0.0615234375,
0.0015935897827148438,
-0.027191162109375,
-0.004642486572265625,
0.0023365020751953125,
0.0110321044921875,
0.0257110595703125,
-0.02886962890625,
0.0245208740234375,
0.0018835067749023438,
0.0132293701171875,
0.01499176025390625,
-0.0251617431640625,
0.0306243896484375,
0.006076812744140625,
0.0246124267578125,
-0.0061798095703125,
-0.01088714599609375,
0.0104522705078125,
-0.0654296875,
-0.03204345703125,
0.003299713134765625,
-0.007633209228515625,
0.005123138427734375,
0.00688934326171875,
0.0121307373046875,
-0.046966552734375,
-0.034820556640625,
-0.00798797607421875,
0.023345947265625,
-0.0033969879150390625,
-0.00316619873046875,
-0.0242156982421875,
-0.01202392578125,
-0.020904541015625,
-0.0199737548828125,
-0.0258636474609375,
-0.0175323486328125,
-0.000058770179748535156,
-0.0270538330078125,
-0.0203094482421875,
0.0107879638671875,
-0.034942626953125,
0.016357421875,
0.01097869873046875,
0.0076141357421875,
-0.01885986328125,
-0.0222320556640625,
0.0065460205078125,
-0.018341064453125,
0.020538330078125,
-0.0076141357421875,
0.00327301025390625,
-0.018646240234375,
0.0120391845703125,
0.02252197265625,
-0.0032253265380859375,
0.022979736328125,
0.0023059844970703125,
0.0294036865234375,
-0.0262908935546875,
-0.0220947265625,
-0.019073486328125,
-0.0069427490234375,
0.01546478271484375,
0.00591278076171875,
0.007213592529296875,
-0.0254974365234375,
0.030120849609375,
0.00830841064453125,
-0.006237030029296875,
0.0191192626953125,
-0.0127716064453125,
-0.01091766357421875,
-0.00785064697265625,
0.004001617431640625,
-0.023162841796875,
-0.0007529258728027344,
0.0233612060546875,
-0.0035552978515625,
0.004627227783203125,
0.03594970703125,
0.0137176513671875,
-0.0163726806640625,
-0.0214080810546875,
-0.01023101806640625,
-0.00112152099609375,
0.043853759765625,
0.02398681640625,
-0.01123809814453125,
-0.0113983154296875,
-0.035736083984375,
0.0145263671875,
-0.00501251220703125,
0.00555419921875,
-0.004291534423828125,
-0.001556396484375,
-0.0008902549743652344,
0.0113525390625,
0.023468017578125,
-0.035400390625,
0.016937255859375,
0.002834320068359375,
-0.0260162353515625,
-0.0100250244140625,
-0.0222625732421875,
-0.034271240234375,
0.0296173095703125,
0.0313720703125,
0.0212554931640625,
-0.01232147216796875,
-0.005977630615234375,
0.0258941650390625,
0.0303955078125,
-0.0092315673828125,
-0.0028362274169921875,
-0.0213470458984375,
0.015472412109375,
0.0202484130859375,
0.0244140625,
-0.0276641845703125,
-0.0335693359375,
0.0214996337890625,
0.050689697265625,
-0.0164947509765625,
-0.024688720703125,
-0.006267547607421875,
-0.01018524169921875,
-0.00449371337890625,
0.017333984375,
0.006931304931640625,
0.0025272369384765625,
0.01113128662109375,
-0.0304718017578125,
0.01415252685546875,
0.01059722900390625,
0.0250244140625,
-0.0033721923828125,
0.032958984375,
-0.00429534912109375,
0.005748748779296875,
0.020599365234375,
0.033233642578125,
-0.0015316009521484375,
-0.01259613037109375,
-0.02288818359375,
0.0292205810546875,
0.004894256591796875,
0.0198211669921875,
-0.01059722900390625,
-0.0016164779663085938,
-0.01352691650390625,
-0.0212249755859375,
0.034912109375,
0.0141754150390625,
-0.01213836669921875,
0.0233001708984375,
0.03948974609375,
0.00588226318359375,
0.0016012191772460938,
-0.0127105712890625,
-0.014434814453125,
-0.0206146240234375,
-0.043243408203125,
-0.01479339599609375,
-0.00952911376953125,
-0.02313232421875,
0.029541015625,
0.0167999267578125,
-0.00344085693359375,
0.00922393798828125,
0.00856781005859375,
-0.0081634521484375,
0.0020771026611328125,
-0.0099334716796875,
-0.0121612548828125,
-0.027801513671875,
-0.0037593841552734375,
-0.00782012939453125,
0.03717041015625,
-0.0271453857421875,
0.01824951171875,
0.025787353515625,
0.0229339599609375,
0.007526397705078125,
-0.0023555755615234375,
-0.0295867919921875,
0.00847625732421875,
0.0193023681640625,
0.004970550537109375,
-0.0174102783203125,
0.0197601318359375,
0.04705810546875,
0.007053375244140625,
0.01418304443359375,
0.0181427001953125,
0.0038585662841796875,
-0.01474761962890625,
0.0181884765625,
-0.01372528076171875,
0.00672149658203125,
-0.0231781005859375,
0.0078277587890625,
-0.0004839897155761719,
0.0003371238708496094,
0.00177001953125,
0.0170745849609375,
-0.0215606689453125,
-0.0182342529296875,
0.02667236328125,
-0.003582000732421875,
-0.0355224609375,
0.0302734375,
0.0057525634765625,
-0.0288543701171875,
-0.01189422607421875,
0.0004265308380126953,
-0.006816864013671875,
0.030303955078125,
-0.00342559814453125,
0.01473236083984375,
0.00475311279296875,
-0.00472259521484375,
0.0246124267578125,
-0.01302337646484375,
0.0005083084106445312,
0.010162353515625,
-0.0142059326171875,
0.024993896484375,
0.003940582275390625,
-0.021148681640625,
-0.03192138671875,
0.03045654296875,
-0.0201873779296875,
0.007495880126953125,
0.034942626953125,
-0.0406494140625,
-0.0038242340087890625,
-0.007213592529296875,
0.008392333984375,
0.0058135986328125,
0.0177764892578125,
0.04345703125,
-0.001972198486328125,
-0.0254364013671875,
0.030792236328125,
0.011383056640625,
-0.011505126953125,
-0.00726318359375,
-0.0081634521484375,
0.05523681640625,
-0.012542724609375,
-0.00809478759765625,
0.0181732177734375,
-0.00469970703125,
-0.0175933837890625,
0.0112762451171875,
0.026702880859375,
0.0333251953125,
-0.0225372314453125,
0.01690673828125,
0.003875732421875,
-0.01250457763671875,
-0.0095672607421875,
-0.012664794921875,
0.00882720947265625,
0.010955810546875,
-0.0024433135986328125,
-0.0131988525390625,
0.016571044921875,
-0.01324462890625,
0.00539398193359375,
0.02703857421875,
0.006561279296875,
0.01678466796875,
-0.0309295654296875,
-0.012908935546875,
-0.01125335693359375,
-0.009613037109375,
-0.023162841796875,
-0.007358551025390625,
-0.007396697998046875,
-0.03955078125,
-0.00754547119140625,
0.0009479522705078125,
0.0273590087890625,
-0.00579833984375,
-0.00519561767578125,
0.00640106201171875,
-0.007228851318359375,
0.008941650390625,
-0.0007462501525878906,
-0.0022563934326171875,
-0.01074981689453125,
0.00815582275390625,
-0.0115203857421875,
-0.0182342529296875,
-0.0037174224853515625,
-0.0193328857421875,
-0.02593994140625,
0.02069091796875,
-0.0482177734375,
0.01983642578125,
-0.0018835067749023438,
0.0244598388671875,
-0.0168914794921875,
0.01012420654296875,
-0.0025482177734375,
0.00521087646484375,
-0.00034928321838378906,
-0.0196685791015625,
0.0273284912109375,
0.03521728515625,
0.00595855712890625,
0.020721435546875,
0.0038356781005859375,
0.045989990234375,
-0.003215789794921875,
0.007625579833984375,
-0.01540374755859375,
0.005428314208984375,
-0.0026645660400390625,
-0.00878143310546875,
0.004322052001953125,
-0.00879669189453125,
0.0171661376953125,
0.004970550537109375,
0.028167724609375,
0.007965087890625,
-0.0104522705078125,
-0.004428863525390625,
-0.03411865234375,
0.019927978515625,
-0.0174713134765625,
0.0174102783203125,
-0.0200042724609375,
0.0114288330078125,
-0.02667236328125,
0.0038089752197265625,
-0.00030350685119628906,
-0.0236968994140625,
0.03472900390625,
-0.035491943359375,
0.0193939208984375,
-0.0173492431640625,
-0.0019664764404296875,
-0.020355224609375,
-0.0047760009765625,
0.0108642578125,
0.006011962890625,
0.029388427734375,
0.0226593017578125,
-0.01337432861328125,
-0.01175689697265625,
-0.0149078369140625,
-0.0118408203125,
0.00913238525390625,
0.01216888427734375,
-0.0239105224609375,
-0.040985107421875,
-0.0251617431640625,
0.006679534912109375,
-0.017120361328125,
-0.0214080810546875,
0.01024627685546875,
-0.03179931640625,
-0.006137847900390625,
-0.01934814453125,
0.01457977294921875,
-0.0020923614501953125,
0.0121002197265625,
-0.0062408447265625,
0.03466796875,
-0.004146575927734375,
0.0121307373046875,
0.0134429931640625,
0.01004791259765625,
-0.006359100341796875,
-0.02093505859375,
0.0132293701171875,
0.00923919677734375,
0.0092010498046875,
0.0261383056640625,
0.006916046142578125,
0.00374603271484375,
-0.059539794921875,
-0.00531005859375,
-0.004970550537109375,
0.0141448974609375,
-0.02734375,
0.005512237548828125,
0.0076904296875,
-0.049285888671875,
0.0222625732421875,
0.004177093505859375,
-0.0111541748046875,
0.0117034912109375,
0.00988006591796875,
-0.016143798828125,
0.00098419189453125,
-0.0218963623046875,
0.0246734619140625,
-0.006900787353515625,
-0.02093505859375,
-0.02294921875,
0.00992584228515625,
0.04052734375,
-0.000629425048828125,
-0.044921875,
-0.00588226318359375,
0.04278564453125,
-0.018280029296875,
0.006008148193359375,
0.029693603515625,
0.005130767822265625,
0.0014657974243164062,
-0.033477783203125,
0.02349853515625,
0.00860595703125,
-0.00899505615234375,
-0.0012493133544921875,
0.01233673095703125,
0.0268402099609375,
0.00008881092071533203,
0.0087432861328125,
0.00807952880859375,
-0.006870269775390625,
-0.02093505859375,
-0.0079193115234375,
-0.0133819580078125,
0.005367279052734375,
-0.0236358642578125,
0.010009765625,
0.004993438720703125,
-0.01171112060546875,
-0.0193328857421875,
-0.0135955810546875,
0.0157928466796875,
0.034210205078125,
0.004657745361328125,
-0.00537872314453125,
0.0367431640625,
-0.017578125,
-0.00804901123046875,
-0.0225677490234375,
-0.01189422607421875,
-0.0006809234619140625,
-0.01483917236328125,
-0.01209259033203125,
0.030181884765625,
0.00817108154296875,
0.01026153564453125,
-0.01450347900390625,
-0.00714111328125,
-0.01532745361328125,
-0.00684356689453125,
-0.01027679443359375,
0.00505828857421875,
0.01058197021484375,
0.0217437744140625,
0.0285491943359375,
-0.01007080078125,
-0.01285552978515625,
-0.010009765625,
-0.034149169921875,
0.01123046875,
-0.020721435546875,
0.01137542724609375,
-0.02276611328125,
0.0181732177734375,
0.02569580078125,
0.002105712890625,
-0.004161834716796875,
0.025390625,
-0.002498626708984375,
-0.010101318359375,
0.032501220703125,
0.020843505859375,
0.0001087188720703125,
0.005046844482421875,
0.01029205322265625,
0.01520538330078125,
-0.0034732818603515625,
-0.01216888427734375,
-0.01433563232421875,
0.001972198486328125,
0.01177215576171875,
-0.0015687942504882812,
-0.00220489501953125,
0.04547119140625,
0.0111846923828125,
-0.0171356201171875,
-0.0007305145263671875,
-0.0266265869140625,
-0.00939178466796875,
-0.015655517578125,
-0.0137786865234375,
0.0133209228515625,
-0.01540374755859375,
-0.026702880859375,
0.0312042236328125,
-0.004154205322265625,
0.009613037109375,
-0.042205810546875,
0.03155517578125,
-0.00311279296875,
0.01605224609375,
-0.0189361572265625,
0.00267791748046875,
-0.00846099853515625,
0.0063934326171875,
0.004634857177734375,
0.02008056640625,
-0.0226593017578125,
-0.032257080078125,
-0.0206451416015625,
-0.0276947021484375,
0.0125885009765625,
0.005504608154296875,
-0.0236968994140625,
0.01018524169921875,
-0.037872314453125,
-0.0036830902099609375,
-0.004955291748046875,
0.01045989990234375,
-0.0209808349609375,
0.033966064453125,
0.01020050048828125,
-0.02960205078125,
-0.0279541015625,
-0.0143280029296875,
-0.0253753662109375,
-0.0009102821350097656,
-0.00029850006103515625,
0.00569915771484375,
-0.0014772415161132812,
-0.0134124755859375,
-0.0167388916015625,
-0.0114593505859375,
-0.0026397705078125,
-0.01187896728515625,
0.048797607421875,
-0.03045654296875,
-0.0013904571533203125,
-0.01050567626953125,
0.02642822265625,
-0.0266876220703125,
0.00582122802734375,
-0.006992340087890625,
0.0026397705078125,
-0.01311492919921875,
0.01013946533203125,
0.0012788772583007812,
-0.008056640625,
-0.015716552734375,
0.0230712890625,
0.0307769775390625,
-0.0010480880737304688,
-0.0251617431640625,
-0.016448974609375,
-0.023040771484375,
0.0301055908203125,
-0.035491943359375,
0.027587890625,
-0.01294708251953125,
0.020050048828125,
-0.02105712890625,
-0.007663726806640625,
-0.0190582275390625,
-0.0295867919921875,
0.006618499755859375,
0.01116943359375,
-0.01210784912109375,
0.030242919921875,
0.0078582763671875,
0.05963134765625,
0.018646240234375,
-0.019317626953125,
0.023193359375,
-0.008697509765625,
-0.052581787109375,
-0.031402587890625,
0.00832366943359375,
-0.00231170654296875,
-0.016357421875,
0.035736083984375,
-0.0158843994140625,
-0.006809234619140625,
0.0171356201171875,
-0.024444580078125,
-0.0018062591552734375,
-0.0287933349609375,
-0.01178741455078125,
-0.006931304931640625,
-0.0244598388671875,
-0.0279693603515625,
-0.005840301513671875,
-0.01406097412109375,
0.034393310546875,
-0.0029392242431640625,
-0.0206298828125,
0.00867462158203125,
0.005283355712890625,
-0.0186767578125,
-0.0020923614501953125,
-0.0240936279296875,
-0.0022678375244140625,
-0.007282257080078125,
0.007114410400390625,
0.00270843505859375,
-0.0110626220703125,
0.0153961181640625,
-0.0215911865234375,
0.005062103271484375,
0.0042724609375,
-0.0223846435546875,
-0.016387939453125,
-0.0008740425109863281,
0.007083892822265625,
-0.0034332275390625,
0.02862548828125,
-0.0222930908203125,
-0.03955078125,
0.05194091796875,
0.0013370513916015625,
0.052032470703125,
-0.018096923828125,
-0.0008606910705566406,
0.0106048583984375,
-0.0111541748046875,
0.0023899078369140625,
-0.0165252685546875,
-0.007144927978515625,
0.011505126953125,
0.0027484893798828125,
0.003116607666015625,
0.03912353515625,
0.028717041015625,
-0.0007891654968261719,
0.00012814998626708984,
0.0150146484375,
-0.01232147216796875,
0.00865936279296875,
-0.007015228271484375,
-0.0117645263671875,
-0.013824462890625,
-0.0281829833984375,
-0.00011283159255981445,
-0.026947021484375,
-0.0083770751953125,
-0.02691650390625,
-0.01142120361328125,
0.01364898681640625,
0.0272979736328125,
-0.030364990234375,
-0.05841064453125,
0.01666259765625,
-0.01197052001953125,
-0.0310211181640625,
0.00858306884765625,
0.039581298828125,
0.01119232177734375,
-0.01042938232421875,
-0.0014705657958984375,
0.022125244140625,
-0.00589752197265625,
-0.0017175674438476562,
-0.04351806640625,
-0.01143646240234375,
0.0022487640380859375,
0.0179901123046875,
0.012664794921875,
-0.0186004638671875,
-0.005245208740234375,
0.01332855224609375,
-0.0257415771484375,
-0.02667236328125,
-0.00844573974609375,
-0.004398345947265625,
-0.001018524169921875,
-0.01113128662109375,
0.0175018310546875,
0.00536346435546875,
0.00628662109375,
-0.0169219970703125,
0.00408935546875,
-0.0018663406372070312,
0.0235748291015625,
0.013641357421875,
0.004940032958984375,
0.03643798828125,
0.01207733154296875,
0.017364501953125,
-0.0305938720703125,
-0.0175323486328125,
-0.0236053466796875,
-0.0038318634033203125,
-0.02349853515625,
-0.035614013671875,
0.001415252685546875,
-0.0002472400665283203,
0.033660888671875,
-0.03057861328125,
-0.0085601806640625,
-0.01922607421875,
-0.0247650146484375,
0.00370025634765625,
-0.011962890625,
0.00930023193359375,
-0.02801513671875,
0.0179901123046875,
-0.005062103271484375,
0.0229644775390625,
-0.02630615234375,
-0.0243682861328125,
-0.0178985595703125,
0.0295562744140625,
0.00728607177734375,
-0.0128936767578125,
0.0171356201171875,
0.0197296142578125,
0.023590087890625,
0.0066375732421875,
0.008026123046875,
0.0011358261108398438,
-0.00136566162109375,
-0.005931854248046875,
-0.0300750732421875,
0.04656982421875,
-0.0026912689208984375,
0.043731689453125,
0.005443572998046875,
0.034149169921875,
0.037872314453125,
-0.01018524169921875,
0.00839996337890625,
0.01409912109375,
-0.0052947998046875,
0.0008077621459960938,
0.038970947265625,
0.01168060302734375,
0.00485992431640625,
0.0014286041259765625,
0.029693603515625,
-0.0069122314453125,
-0.00626373291015625,
0.01593017578125,
-0.01030731201171875,
-0.0233612060546875,
-0.01219940185546875,
0.01326751708984375,
-0.0302734375,
0.008026123046875,
0.0228271484375,
0.017425537109375,
0.0229339599609375,
-0.01007843017578125,
-0.005584716796875,
0.00807952880859375,
0.0018396377563476562,
-0.0230255126953125,
0.04583740234375,
-0.007110595703125,
0.0307159423828125,
0.028228759765625,
0.0012874603271484375,
-0.0086669921875,
-0.0013208389282226562,
-0.004703521728515625,
0.0017824172973632812,
0.0167388916015625,
-0.00850677490234375,
-0.00402069091796875,
0.00545501708984375,
-0.01441192626953125,
0.0059051513671875,
0.0180206298828125,
0.0021686553955078125,
0.0018186569213867188,
-0.01430511474609375,
0.0267181396484375,
0.0288238525390625,
0.006168365478515625,
0.0199432373046875,
0.0018110275268554688,
0.00464630126953125,
-0.00638580322265625,
0.0016813278198242188,
-0.01514434814453125,
-0.004802703857421875,
0.006359100341796875,
-0.0107269287109375,
-0.01007080078125,
-0.0178375244140625,
-0.034637451171875,
0.0263214111328125,
-0.00527191162109375,
0.0180816650390625,
0.0013952255249023438,
0.0074462890625,
-0.06500244140625,
0.030364990234375,
-0.013885498046875,
-0.01194000244140625,
-0.01239013671875,
-0.0171051025390625,
0.017242431640625,
0.0428466796875,
0.0231170654296875,
-0.037841796875,
-0.00939178466796875,
-0.003681182861328125,
-0.05853271484375,
-0.00049591064453125,
-0.002803802490234375,
-0.0151824951171875,
-0.0168304443359375,
-0.01120758056640625,
-0.00540924072265625,
0.029815673828125,
-0.012420654296875,
0.04290771484375,
0.03070068359375,
0.009674072265625,
-0.0223541259765625,
-0.003803253173828125,
0.01007843017578125,
0.00638580322265625,
-0.0230865478515625,
-0.0295257568359375,
-0.0242462158203125,
0.0000680088996887207,
-0.0222320556640625,
-0.01678466796875,
-0.035400390625,
-0.0167694091796875,
0.0228118896484375,
0.01800537109375,
-0.0015211105346679688,
0.03985595703125,
0.00551605224609375,
-0.0206451416015625,
-0.0284423828125,
0.0143585205078125,
0.009429931640625,
-0.041229248046875,
0.03985595703125,
0.006649017333984375,
-0.0110931396484375,
-0.0122528076171875,
-0.021087646484375,
-0.039947509765625,
0.0081787109375,
0.0266876220703125,
0.0084381103515625,
-0.000034332275390625,
0.007343292236328125,
0.0218048095703125,
-0.037017822265625,
0.06903076171875,
0.0012760162353515625,
0.00742340087890625,
0.032806396484375,
-0.00966644287109375,
-0.0086669921875,
0.01291656494140625,
-0.0308837890625,
-0.001346588134765625,
-0.035247802734375,
0.0584716796875,
-0.0113525390625,
0.005977630615234375,
0.006336212158203125,
0.0009965896606445312,
-0.0172271728515625,
0.0037899017333984375,
-0.007137298583984375,
-0.0255584716796875,
-0.04571533203125,
0.0458984375,
-0.01105499267578125,
0.0303192138671875,
0.0034999847412109375,
0.0165557861328125,
-0.025970458984375,
-0.0015964508056640625,
-0.0137176513671875,
-0.01462554931640625,
-0.0004305839538574219,
-0.004573822021484375,
-0.0206756591796875,
-0.015960693359375,
-0.017242431640625,
-0.002727508544921875,
-0.0188140869140625,
-0.049407958984375,
0.0011873245239257812,
-0.0030117034912109375,
0.0113372802734375,
0.026580810546875,
-0.0242919921875,
-0.0243377685546875,
0.0177764892578125,
-0.0063629150390625,
-0.005107879638671875,
0.00856781005859375,
-0.01114654541015625,
0.05377197265625,
-0.011566162109375,
-0.00884246826171875,
-0.0122222900390625,
0.0184783935546875,
-0.00017976760864257812,
0.03924560546875,
0.006099700927734375,
-0.01047515869140625,
-0.01229095458984375,
-0.04913330078125,
-0.0206756591796875,
0.058868408203125,
-0.031829833984375,
0.0018529891967773438,
-0.0017652511596679688,
0.00882720947265625,
-0.036712646484375,
0.032257080078125,
0.0394287109375,
-0.0032596588134765625,
0.011962890625,
0.0195770263671875,
-0.0078887939453125,
-0.006877899169921875,
0.0187225341796875,
-0.01953125,
-0.005474090576171875,
0.00251007080078125,
0.0160369873046875,
-0.00975799560546875,
-0.00006133317947387695,
0.00048470497131347656,
0.017913818359375,
-0.0083465576171875,
0.019989013671875,
0.0478515625,
-0.00011366605758666992,
0.0306854248046875,
0.033660888671875,
0.0147247314453125,
-0.01971435546875,
-0.0000795125961303711,
-0.0316162109375,
0.0113983154296875,
0.0197906494140625,
0.041473388671875,
-0.00858306884765625,
0.006961822509765625,
0.0164031982421875,
0.01154327392578125,
-0.02813720703125,
0.00298309326171875,
-0.04180908203125,
-0.025909423828125,
0.006198883056640625,
0.0117034912109375,
-0.0025272369384765625,
0.005649566650390625,
-0.011077880859375,
0.044097900390625,
-0.0008053779602050781,
-0.005947113037109375,
0.01296234130859375,
-0.041229248046875,
0.0183868408203125,
0.02490234375,
-0.016815185546875,
-0.017913818359375,
-0.00876617431640625,
0.00472259521484375,
-0.049407958984375,
0.036834716796875,
0.01702880859375,
-0.03369140625,
-0.010467529296875,
0.0196380615234375,
-0.00965118408203125,
-0.014495849609375,
-0.0234527587890625,
-0.01268768310546875,
-0.0162353515625,
0.0499267578125,
0.0274200439453125,
0.0087432861328125,
0.032073974609375,
-0.0230712890625,
0.00894927978515625,
-0.0244293212890625,
0.0177001953125,
0.018096923828125,
-0.01241302490234375,
0.0079498291015625,
-0.0144805908203125,
0.01015472412109375,
-0.022125244140625,
-0.0214996337890625,
-0.0233612060546875,
-0.04974365234375,
-0.007694244384765625,
-0.010833740234375,
-0.00954437255859375,
0.044097900390625,
-0.007320404052734375,
-0.008026123046875,
0.0084075927734375,
-0.035980224609375,
-0.0140228271484375,
-0.049591064453125,
0.035430908203125,
0.00789642333984375,
-0.01030731201171875,
0.031585693359375,
0.0238800048828125,
-0.031280517578125,
0.035430908203125,
0.0164337158203125,
-0.0161590576171875,
-0.0123138427734375,
-0.007305145263671875,
0.01126861572265625,
0.004993438720703125,
0.0086669921875,
0.01104736328125,
0.0108184814453125,
0.04779052734375,
0.007476806640625,
-0.0160064697265625,
-0.00731658935546875,
0.027496337890625,
0.006038665771484375,
-0.0158538818359375,
-0.0033588409423828125,
-0.0065460205078125,
0.00916290283203125,
-0.0289154052734375,
-0.0021572113037109375,
-0.02264404296875,
-0.0406494140625,
0.007411956787109375,
-0.0017576217651367188,
-0.01641845703125,
0.0246124267578125,
0.0231475830078125,
0.0175323486328125,
0.03875732421875,
0.043304443359375,
-0.0044403076171875,
0.0036907196044921875,
0.010162353515625,
-0.0240020751953125,
0.006748199462890625,
-0.0020122528076171875,
-0.0292205810546875,
0.0022411346435546875,
0.003711700439453125,
-0.0266571044921875,
-0.003986358642578125,
-0.038055419921875,
-0.0015087127685546875,
-0.00275421142578125,
0.0145721435546875,
0.005825042724609375,
0.016815185546875,
0.022918701171875,
-0.0010280609130859375,
0.00220489501953125,
0.011688232421875,
-0.01302337646484375,
-0.03607177734375,
0.026092529296875,
0.00988006591796875,
0.020538330078125,
0.00778961181640625,
-0.0237884521484375,
-0.004581451416015625,
-0.0238494873046875,
0.00371551513671875,
0.007259368896484375,
0.0015439987182617188,
0.0029544830322265625,
0.01396942138671875,
0.0041046142578125,
-0.003414154052734375,
-0.007472991943359375,
-0.02252197265625,
0.00160980224609375,
-0.003246307373046875,
0.037445068359375,
0.0289459228515625,
-0.040313720703125,
-0.007320404052734375,
0.023895263671875,
0.0264892578125,
0.0015516281127929688,
-0.0287017822265625,
-0.010040283203125,
-0.01372528076171875,
0.01090240478515625,
-0.043060302734375,
-0.0223388671875,
0.0286865234375,
-0.0277099609375,
-0.01158905029296875,
-0.035400390625,
0.0196685791015625,
-0.0037136077880859375,
0.03179931640625,
-0.0035495758056640625,
-0.0170440673828125,
-0.00070953369140625,
-0.001312255859375,
-0.01617431640625,
-0.029052734375,
-0.0029048919677734375,
-0.035186767578125,
-0.0103912353515625,
0.0005674362182617188,
-0.021453857421875,
0.042938232421875,
0.0182037353515625,
-0.03564453125,
0.004940032958984375,
-0.0066070556640625,
0.00588226318359375,
0.027557373046875,
-0.007663726806640625,
-0.007610321044921875,
-0.01541900634765625,
0.040802001953125,
0.01158905029296875,
-0.012908935546875,
-0.01091766357421875,
-0.0096282958984375,
-0.020050048828125,
-0.022857666015625,
-0.0208587646484375,
0.0035152435302734375,
0.033599853515625,
-0.04290771484375,
-0.0022296905517578125,
-0.03106689453125,
-0.0121307373046875,
-0.00039649009704589844,
0.00974273681640625,
-0.0064697265625,
-0.004547119140625,
-0.006866455078125,
0.01922607421875,
0.00019872188568115234,
-0.046234130859375,
0.011474609375,
0.0046234130859375,
0.007793426513671875,
0.0010166168212890625,
0.00030303001403808594,
-0.01486968994140625,
-0.006618499755859375,
0.01450347900390625,
0.005435943603515625,
-0.0034389495849609375,
-0.001216888427734375,
0.01468658447265625,
0.0130462646484375,
0.0382080078125,
-0.0262603759765625,
-0.03399658203125,
-0.001922607421875,
0.03326416015625,
-0.013763427734375,
-0.003143310546875,
0.0160064697265625,
0.0182037353515625,
0.046539306640625,
0.0166778564453125,
0.0230865478515625,
-0.00403594970703125,
-0.0272979736328125,
0.0071563720703125,
-0.00878143310546875,
-0.007785797119140625,
0.02239990234375,
0.01104736328125,
0.00274658203125,
-0.035003662109375,
0.010589599609375,
-0.0069122314453125,
0.01232147216796875,
0.01654052734375,
-0.043060302734375,
0.003299713134765625,
-0.01439666748046875,
0.035614013671875,
0.037445068359375,
-0.02532958984375,
-0.0024929046630859375,
-0.0130157470703125,
-0.0230712890625,
0.0043792724609375,
-0.00803375244140625,
0.0137939453125,
0.0126953125,
-0.0026187896728515625,
0.03240966796875,
-0.0262451171875,
-0.0011854171752929688,
-0.028961181640625,
0.02984619140625,
0.003070831298828125,
0.0197296142578125,
-0.0014677047729492188,
0.01055908203125,
0.057525634765625,
-0.0188446044921875,
-0.025634765625,
0.0027828216552734375,
-0.01328277587890625,
-0.0284423828125,
0.002033233642578125,
-0.01495361328125,
0.00027060508728027344,
0.0220794677734375,
-0.044403076171875,
0.044647216796875,
0.0226593017578125,
0.024322509765625,
-0.017333984375,
0.00818634033203125,
-0.0009021759033203125,
0.0032176971435546875,
0.004352569580078125,
0.01708984375,
-0.0150909423828125,
0.00522613525390625,
-0.0088348388671875,
0.00577545166015625,
-0.00930023193359375,
0.00820159912109375,
-0.00975799560546875,
0.01410675048828125,
0.0253143310546875,
0.01534271240234375,
0.006458282470703125,
-0.007694244384765625,
0.0239105224609375,
0.0155181884765625,
0.004055023193359375,
-0.0296173095703125,
-0.00714111328125,
0.0276031494140625,
0.015228271484375,
0.0117034912109375,
0.043182373046875,
-0.01398468017578125,
-0.01666259765625,
0.00945281982421875,
-0.018402099609375,
-0.01214599609375,
0.0083160400390625,
-0.03173828125,
0.0037899017333984375,
-0.01097869873046875,
0.01556396484375,
-0.008575439453125,
-0.0112152099609375,
-0.0135498046875,
-0.0296173095703125,
-0.01537322998046875,
-0.0290679931640625,
-0.011077880859375,
-0.00908660888671875,
-0.0252838134765625,
0.01012420654296875,
-0.01480865478515625,
0.01288604736328125,
0.01221466064453125,
0.0161590576171875,
0.0406494140625,
-0.0214385986328125,
0.008514404296875,
-0.0042877197265625,
-0.0144500732421875,
0.016021728515625,
-0.0115509033203125,
-0.0009150505065917969,
-0.0085296630859375,
0.005596160888671875,
-0.00124359130859375,
0.01348876953125,
0.01001739501953125,
0.002223968505859375,
0.0187225341796875,
0.007625579833984375,
-0.051025390625,
0.00193023681640625,
-0.01412200927734375,
-0.0255889892578125,
0.012664794921875,
0.059783935546875,
-0.0224456787109375,
-0.01434326171875,
-0.0076141357421875,
-0.0255889892578125,
0.016357421875,
-0.01739501953125,
0.0234222412109375,
-0.03607177734375,
0.0015134811401367188,
-0.00423431396484375,
-0.025390625,
-0.0022182464599609375,
0.034210205078125,
0.0125885009765625,
0.0275115966796875,
0.03302001953125,
0.02777099609375,
0.01543426513671875,
-0.024810791015625,
0.0183258056640625,
0.0201416015625,
0.04193115234375,
0.002155303955078125,
0.01177215576171875,
0.01007843017578125,
0.021881103515625,
0.004131317138671875,
0.00101470947265625,
-0.01226043701171875,
-0.0040435791015625,
0.01374053955078125,
0.0031280517578125,
-0.0250701904296875,
0.02227783203125,
-0.03375244140625,
0.0213623046875,
0.0280303955078125,
0.0015048980712890625,
-0.0164642333984375,
0.0133209228515625,
-0.034912109375,
-0.00499725341796875,
0.036163330078125,
0.0034847259521484375,
0.005619049072265625,
-0.0297088623046875,
0.01351165771484375,
-0.00540924072265625,
-0.0155181884765625,
-0.03759765625,
0.0223541259765625,
-0.033966064453125,
0.045135498046875,
-0.0210113525390625,
-0.0227813720703125,
0.0127716064453125,
0.00588226318359375,
0.025848388671875,
0.006015777587890625,
-0.0268096923828125,
0.01381683349609375,
0.0002796649932861328,
0.001773834228515625,
-0.0174407958984375,
-0.0296173095703125,
0.005939483642578125,
0.004329681396484375,
-0.01154327392578125,
0.0019168853759765625,
-0.0129241943359375,
-0.00695037841796875,
0.0124359130859375,
-0.0199127197265625,
0.002895355224609375,
-0.00363922119140625,
-0.036773681640625,
0.02783203125,
-0.02532958984375,
0.011627197265625,
-0.00013124942779541016,
-0.0107269287109375,
-0.0262451171875,
-0.03070068359375,
-0.025299072265625,
-0.02362060546875,
0.01020050048828125,
0.0115814208984375,
-0.0146636962890625,
0.00614166259765625,
0.00121307373046875,
-0.020111083984375,
0.01113128662109375,
0.010894775390625,
-0.022674560546875,
-0.01018524169921875,
-0.0253448486328125,
0.0114898681640625,
0.012939453125,
0.01180267333984375,
-0.002811431884765625,
0.02716064453125,
-0.00974273681640625,
0.0421142578125,
0.00424957275390625,
-0.01727294921875,
0.029571533203125,
0.004055023193359375,
0.0130157470703125,
0.039581298828125,
-0.011444091796875,
-0.0003795623779296875,
0.01044464111328125,
0.004238128662109375,
-0.015045166015625,
-0.0271759033203125,
-0.0082855224609375,
-0.0053558349609375,
0.0013608932495117188,
0.035614013671875,
0.0147705078125,
0.012451171875,
-0.006008148193359375,
-0.004787445068359375,
-0.042266845703125,
0.044158935546875,
0.0091094970703125,
0.00527191162109375,
-0.00811004638671875,
0.0284271240234375,
0.0014009475708007812,
0.009307861328125,
-0.004322052001953125,
-0.01544189453125,
-0.0022296905517578125,
-0.0116424560546875,
-0.002590179443359375,
-0.01253509521484375,
0.00460052490234375,
0.00013172626495361328,
0.01947021484375,
-0.0240631103515625,
-0.0298309326171875,
0.004810333251953125,
0.0218505859375,
-0.005443572998046875,
0.00884246826171875,
-0.0000623464584350586,
0.003665924072265625,
-0.0153350830078125,
-0.0088958740234375,
0.0249176025390625,
-0.0089111328125,
-0.006938934326171875,
0.01068878173828125,
-0.0028228759765625,
0.013336181640625,
0.0202484130859375,
0.01451873779296875,
-0.038787841796875,
-0.0307464599609375,
0.0015707015991210938,
-0.0004782676696777344,
-0.024871826171875,
-0.0225677490234375,
-0.006298065185546875,
-0.0097503662109375,
-0.00782012939453125,
0.004425048828125,
-0.031585693359375,
0.02703857421875,
0.03497314453125,
-0.0028858184814453125,
0.0187225341796875,
0.00293731689453125,
-0.005596160888671875,
-0.01462554931640625,
-0.0006308555603027344,
-0.0133056640625,
-0.035491943359375,
-0.0010089874267578125,
0.028289794921875,
0.0088348388671875,
-0.005596160888671875,
-0.0037746429443359375,
0.00411224365234375,
0.00574493408203125,
0.041229248046875,
-0.01065826416015625,
-0.00876617431640625,
-0.00785064697265625,
0.0288238525390625,
0.010650634765625,
-0.0069122314453125,
-0.0217742919921875,
-0.00800323486328125,
0.0212249755859375,
-0.003559112548828125,
0.01800537109375,
0.005084991455078125,
-0.00792694091796875,
0.01210784912109375,
-0.0030231475830078125,
-0.05706787109375,
-0.008514404296875,
0.040863037109375,
-0.0218048095703125,
-0.002368927001953125,
0.0108642578125,
0.0193023681640625,
0.03179931640625,
-0.021026611328125,
0.0296630859375,
-0.007740020751953125,
0.019989013671875,
0.014617919921875,
0.0220489501953125,
0.0137786865234375,
0.0013637542724609375,
-0.0098724365234375,
-0.0010623931884765625,
0.006313323974609375,
-0.025146484375,
-0.049102783203125,
0.0233306884765625,
-0.0012903213500976562,
-0.0015459060668945312,
-0.00031256675720214844,
0.02947998046875,
-0.0195770263671875,
-0.0012683868408203125,
-0.021331787109375,
0.01139068603515625,
0.01374053955078125,
-0.02581787109375,
0.04315185546875,
-0.0162200927734375,
0.00868988037109375,
0.0051116943359375,
-0.034332275390625,
-0.01611328125,
0.00024366378784179688,
0.02044677734375,
0.0094146728515625,
-0.037261962890625,
-0.059722900390625,
-0.0007486343383789062,
-0.029296875,
0.0046539306640625,
0.01120758056640625,
-0.004306793212890625,
0.0233612060546875,
0.0009369850158691406,
-0.03424072265625,
0.00299072265625,
-0.00812530517578125,
0.00991058349609375,
0.018829345703125,
0.018463134765625,
0.0017518997192382812,
-0.0260467529296875,
-0.0023822784423828125,
-0.029144287109375,
0.0274200439453125,
0.0118865966796875,
-0.001987457275390625,
-0.0118865966796875,
-0.01073455810546875,
-0.004711151123046875,
-0.006031036376953125,
-0.029815673828125,
-0.0298919677734375,
-0.001583099365234375,
-0.007526397705078125,
-0.0034465789794921875,
0.03375244140625,
-0.0169525146484375,
-0.00006687641143798828,
-0.00653076171875,
-0.035400390625,
-0.0274200439453125,
0.016448974609375,
0.028717041015625,
0.00984954833984375,
0.0003294944763183594,
0.037353515625,
0.024566650390625,
-0.0031261444091796875,
-0.005794525146484375,
-0.0011186599731445312,
-0.01279449462890625,
-0.03265380859375,
0.00910186767578125,
0.02947998046875,
-0.0176544189453125,
-0.01922607421875,
-0.035675048828125,
-0.00838470458984375,
0.01078033447265625,
0.0380859375,
0.00510406494140625,
0.0022296905517578125,
-0.0162811279296875,
-0.005977630615234375,
-0.003631591796875,
-0.00980377197265625,
-0.02984619140625,
-0.0155029296875,
-0.0345458984375,
-0.01387786865234375,
-0.016998291015625,
0.0111846923828125,
0.00370025634765625,
0.0010814666748046875,
0.0003695487976074219,
0.004299163818359375,
0.0233154296875,
0.010528564453125,
-0.036865234375,
-0.0038204193115234375,
0.0172882080078125,
0.0126190185546875,
0.0103912353515625,
0.006565093994140625,
0.006626129150390625,
-0.005016326904296875,
-0.0021190643310546875,
-0.0030117034912109375,
0.0168914794921875,
0.0201568603515625,
-0.004276275634765625,
-0.0225677490234375,
-0.0078125,
-0.0298614501953125,
0.005950927734375,
0.00208282470703125,
-0.0176544189453125,
0.0179290771484375,
-0.033477783203125,
0.008544921875,
-0.01412200927734375,
-0.0096588134765625,
0.039794921875,
-0.0220794677734375,
0.010345458984375,
-0.00972747802734375,
0.009796142578125,
-0.0166473388671875,
-0.01342010498046875,
-0.006000518798828125,
-0.007625579833984375,
-0.0018682479858398438,
-0.004489898681640625,
-0.002452850341796875,
0.0039520263671875,
-0.006076812744140625,
-0.0159759521484375,
0.0038204193115234375,
-0.0193023681640625,
0.0183258056640625,
0.0416259765625,
0.026214599609375,
0.005706787109375,
-0.01447296142578125,
-0.003131866455078125,
0.0025081634521484375,
-0.01116943359375,
0.0106048583984375,
-0.01105499267578125,
-0.0124053955078125,
0.0169525146484375,
-0.013275146484375,
-0.00833892822265625,
0.013946533203125,
0.00603485107421875,
0.015594482421875,
0.00998687744140625,
-0.005229949951171875,
-0.013092041015625,
-0.006267547607421875,
-0.011138916015625,
-0.011566162109375,
-0.006397247314453125,
0.03985595703125,
-0.00933074951171875,
0.0006113052368164062,
0.007266998291015625,
0.00313568115234375,
-0.0005288124084472656,
0.00887298583984375,
0.0026645660400390625,
-0.0236358642578125,
0.02685546875,
-0.009246826171875,
-0.0265045166015625,
0.0154266357421875,
0.006198883056640625,
0.0246429443359375,
0.00855255126953125,
-0.006855010986328125,
0.0173187255859375,
0.0018768310546875,
0.0159912109375,
0.011810302734375,
0.0193634033203125,
-0.02276611328125,
0.025604248046875,
-0.0479736328125,
-0.004688262939453125,
0.035125732421875,
0.0162200927734375,
0.0233917236328125,
-0.024627685546875,
-0.0270538330078125,
-0.0197906494140625,
-0.000919342041015625,
-0.050567626953125,
-0.0205841064453125,
-0.0006008148193359375,
0.00841522216796875,
0.0036640167236328125,
-0.0049896240234375,
-0.0157012939453125,
-0.02587890625,
-0.00582122802734375,
0.0028667449951171875,
-0.0292510986328125,
-0.021484375,
0.005886077880859375,
0.00434112548828125,
-0.0022068023681640625,
0.028839111328125,
0.0272674560546875,
0.004150390625,
-0.0177764892578125,
-0.00914764404296875,
0.01033782958984375,
-0.002742767333984375,
-0.01995849609375,
0.027557373046875,
-0.0111083984375,
0.010345458984375,
0.007564544677734375,
-0.002399444580078125,
-0.053466796875,
0.0272369384765625,
0.001392364501953125,
0.0142059326171875,
-0.008514404296875,
0.0162506103515625,
0.0200042724609375,
-0.0022125244140625,
0.0007619857788085938,
-0.01434326171875,
0.0274810791015625,
-0.00420379638671875,
0.00247955322265625,
0.0014247894287109375,
-0.0018024444580078125,
0.0028553009033203125,
-0.010772705078125,
-0.002567291259765625,
-0.0160675048828125,
0.03106689453125,
0.01041412353515625,
-0.0015668869018554688,
-0.0169830322265625,
0.0130615234375,
0.0019550323486328125,
-0.0019989013671875,
0.0027103424072265625,
-0.02752685546875,
-0.0206298828125,
0.01192474365234375,
0.00904083251953125,
0.012786865234375,
-0.0033321380615234375,
0.00868988037109375,
0.0246734619140625,
-0.0143585205078125,
0.0386962890625,
0.016082763671875,
0.0445556640625,
0.017242431640625,
-0.01161956787109375,
-0.02301025390625,
0.0104217529296875,
0.003406524658203125,
0.0030040740966796875,
-0.033660888671875,
0.0088348388671875,
-0.01177978515625,
-0.0200347900390625,
-0.01407623291015625,
-0.024139404296875,
0.009002685546875,
0.005268096923828125,
0.0120391845703125,
0.010894775390625,
0.0015459060668945312,
0.0006418228149414062,
0.03076171875,
0.0055999755859375,
-0.022735595703125,
0.0232086181640625,
-0.0029697418212890625,
-0.011749267578125,
0.005645751953125,
0.021240234375,
-0.036468505859375,
0.0187835693359375,
0.00701904296875,
0.005321502685546875,
-0.0064239501953125,
0.0121917724609375,
-0.001964569091796875,
0.00112152099609375,
0.030609130859375,
-0.0011196136474609375,
0.007701873779296875,
-0.0005121231079101562,
-0.00659942626953125,
-0.0179901123046875,
0.0037059783935546875,
0.0119781494140625,
-0.01010894775390625,
-0.022125244140625,
0.018096923828125,
-0.0009765625,
-0.00542449951171875,
-0.0009665489196777344,
0.016082763671875,
-0.01275634765625,
-0.0184326171875,
-0.029510498046875,
-0.005496978759765625,
0.0149078369140625,
-0.0323486328125,
0.03009033203125,
-0.00894927978515625,
0.0091400146484375,
-0.0015821456909179688,
0.01218414306640625,
-0.0006704330444335938,
0.0091094970703125,
0.00928497314453125,
0.0109405517578125,
-0.0147552490234375,
-0.006801605224609375,
0.004894256591796875,
0.0073089599609375,
0.022369384765625,
-0.00577545166015625,
0.01277923583984375,
-0.019134521484375,
-0.004425048828125,
0.029510498046875,
0.004711151123046875,
0.0133514404296875,
0.0193634033203125,
0.002155303955078125,
-0.003055572509765625,
0.0022106170654296875,
0.029510498046875,
0.0066070556640625,
-0.0036144256591796875,
0.02154541015625,
0.01540374755859375,
0.0191650390625,
0.0023956298828125,
-0.0010690689086914062,
-0.0034999847412109375,
-0.0275421142578125,
0.0281524658203125,
0.0162811279296875,
-0.01580810546875,
0.02996826171875,
-0.029754638671875,
0.00458526611328125,
-0.01009368896484375,
-0.024871826171875,
0.01343536376953125,
-0.0300140380859375,
-0.0179901123046875,
-0.034912109375,
-0.040557861328125,
-0.0218963623046875,
0.01282501220703125,
0.01251983642578125,
0.01024627685546875,
0.01305389404296875,
-0.00433349609375,
0.031707763671875,
-0.00104522705078125,
-0.025146484375,
-0.019012451171875,
-0.0234375,
0.0127410888671875,
-0.0203857421875,
-0.01123809814453125,
0.0133209228515625,
-0.0264892578125,
0.00804901123046875,
0.0169219970703125,
0.00855255126953125,
-0.040252685546875,
0.01018524169921875,
-0.0009446144104003906,
-0.003917694091796875,
-0.01328277587890625,
0.012664794921875,
0.0278167724609375,
0.00913238525390625,
-0.01044464111328125,
-0.01401519775390625,
0.027679443359375,
-0.004421234130859375,
0.00798797607421875,
-0.0120391845703125,
0.00621795654296875,
0.012420654296875,
0.03271484375,
0.004611968994140625,
0.01378631591796875,
0.0035247802734375,
0.015533447265625,
0.0015192031860351562,
0.038848876953125,
-0.008636474609375,
-0.018829345703125,
-0.0093841552734375,
0.02117919921875,
-0.0116424560546875,
-0.01457977294921875,
-0.01177978515625,
0.03875732421875,
-0.0007719993591308594,
0.0021762847900390625,
0.0250701904296875,
0.014556884765625,
0.0137939453125,
-0.0234375,
0.00579833984375,
-0.0219879150390625,
-0.0166168212890625,
-0.0002684593200683594,
-0.00946044921875,
-0.050872802734375,
-0.0173492431640625,
0.0036258697509765625,
0.044647216796875,
-0.0066070556640625,
-0.036224365234375,
-0.001201629638671875,
0.0185089111328125,
-0.00714111328125,
-0.0018396377563476562,
-0.00899505615234375,
-0.02740478515625,
-0.0044403076171875,
0.02288818359375,
-0.0180511474609375,
-0.00830078125,
-0.007328033447265625,
-0.0200653076171875,
0.002162933349609375,
0.0228271484375,
0.0005130767822265625,
0.0142822265625,
-0.01181793212890625,
0.0212249755859375,
-0.00485992431640625,
0.0309906005859375,
0.01216888427734375,
-0.01885986328125,
-0.01641845703125,
-0.0220184326171875,
-0.008331298828125,
-0.005901336669921875,
-0.01239013671875,
0.0126800537109375,
-0.040283203125,
0.004932403564453125,
-0.00627899169921875,
-0.02569580078125,
-0.02642822265625,
-0.019378662109375,
-0.018402099609375,
-0.00844573974609375,
-0.0097198486328125,
-0.00926971435546875,
0.004825592041015625,
0.019775390625,
-0.005825042724609375,
-0.0244293212890625,
0.05267333984375,
-0.0005483627319335938,
0.0214080810546875,
0.03900146484375,
-0.01318359375,
0.0027713775634765625,
-0.0299072265625,
0.023223876953125,
0.0247802734375,
-0.035675048828125,
0.036376953125,
0.0015048980712890625,
0.0309906005859375,
0.043426513671875,
-0.00962066650390625,
-0.006275177001953125,
-0.01058197021484375,
-0.0108184814453125,
0.020111083984375,
-0.00841522216796875,
-0.00024080276489257812,
0.0089263916015625,
-0.0006198883056640625,
0.02911376953125,
-0.0141448974609375,
-0.032135009765625,
0.0178680419921875,
0.0034008026123046875,
0.0193023681640625,
0.00902557373046875,
0.00899505615234375,
0.00621795654296875,
0.04840087890625,
-0.01168060302734375,
0.000331878662109375,
-0.0224609375,
0.006275177001953125,
0.0110015869140625,
-0.0034503936767578125,
0.00295257568359375,
-0.00860595703125,
-0.00469970703125,
0.037200927734375,
0.00853729248046875,
-0.0217132568359375,
0.0016536712646484375,
-0.01259613037109375,
-0.01291656494140625,
-0.002288818359375,
-0.00936126708984375,
-0.0261383056640625,
-0.0231170654296875,
0.018096923828125,
-0.0195465087890625,
0.0032958984375,
-0.0074462890625,
0.0025310516357421875,
-0.033294677734375,
0.0076904296875,
0.01387786865234375,
-0.006595611572265625,
-0.0102081298828125,
0.0139312744140625,
-0.0094146728515625,
0.0171661376953125,
-0.005039215087890625,
-0.030517578125,
-0.0022792816162109375,
0.01174163818359375,
-0.025848388671875,
-0.0042572021484375,
0.0273284912109375,
-0.021759033203125,
0.005092620849609375,
0.0039825439453125,
-0.0020580291748046875,
0.04656982421875,
0.01126861572265625,
0.01241302490234375,
0.01337432861328125,
-0.03619384765625,
0.030517578125,
0.0189056396484375,
0.01337432861328125,
0.0007205009460449219,
0.0242919921875,
0.031097412109375,
-0.0230865478515625,
0.005939483642578125,
0.01361083984375,
-0.0170135498046875,
-0.01364898681640625,
-0.0235595703125,
0.0015668869018554688,
0.042144775390625,
0.005641937255859375,
-0.04071044921875,
-0.03857421875,
-0.01493072509765625,
0.0266571044921875,
0.0008740425109863281,
0.004795074462890625,
0.0201568603515625,
0.006900787353515625,
-0.01319122314453125,
-0.01336669921875,
-0.0301666259765625,
-0.0237274169921875,
-0.0042877197265625,
-0.00963592529296875,
-0.017242431640625,
0.006622314453125,
0.0007529258728027344,
0.024383544921875,
-0.00458526611328125,
0.0233001708984375,
-0.0206146240234375,
-0.025238037109375,
-0.005580902099609375,
0.0036563873291015625,
0.0139312744140625,
-0.03045654296875,
-0.056640625,
-0.013458251953125,
-0.003070831298828125,
-0.037994384765625,
0.01499176025390625,
0.0006265640258789062,
-0.017364501953125,
0.00864410400390625,
-0.006359100341796875,
0.03076171875,
0.00611114501953125,
-0.00930023193359375,
-0.0223236083984375,
-0.01934814453125,
0.00824737548828125,
-0.00969696044921875,
-0.02313232421875,
-0.00997161865234375,
-0.0012645721435546875,
-0.0017910003662109375,
-0.002506256103515625,
-0.02081298828125,
0.00113677978515625,
-0.00962066650390625,
-0.0293731689453125,
0.006664276123046875,
0.01788330078125,
-0.0118560791015625,
0.0137939453125,
-0.003078460693359375,
-0.0174713134765625,
0.0014791488647460938,
-0.019744873046875,
-0.010955810546875,
0.0008378028869628906,
0.0298309326171875,
0.0242767333984375,
-0.01293182373046875,
0.008148193359375,
0.018829345703125,
-0.003948211669921875,
0.0057220458984375,
-0.0255279541015625,
-0.050567626953125,
0.0171966552734375,
-0.004085540771484375,
0.015869140625,
0.00225830078125,
-0.0261077880859375,
-0.01345062255859375,
-0.017913818359375,
0.052642822265625,
0.02032470703125,
0.0183868408203125,
0.0218658447265625,
-0.00797271728515625,
0.002513885498046875,
0.00458526611328125,
0.01049041748046875,
-0.0479736328125,
-0.0127410888671875,
-0.01433563232421875,
-0.0190887451171875,
-0.0027484893798828125,
0.0180816650390625,
-0.0187835693359375,
0.0045623779296875,
-0.024078369140625,
0.0241241455078125,
0.0604248046875
] |
ours_496
|
Clearly, \( f \) is equivalent to multiplying the matrix \(\left[\begin{array}{c}x_{1} \\ x_{2} \\ \vdots \\ x_{2020}\end{array}\right]\) by \( M+cI \), where
\[
M=\left[\begin{array}{cccccc}0 & 0 & \ldots & 0 & a_{1} & b_{1} \\ 0 & 0 & \ldots & 0 & a_{2} & b_{2} \\ 1 & 0 & \ldots & 0 & a_{3} & b_{3} \\ 0 & 1 & \ldots & 0 & a_{4} & b_{4} \\ \vdots & \vdots & \ddots & \vdots & \vdots & \vdots \\ 0 & 0 & \ldots & 1 & a_{2020} & b_{2020}\end{array}\right]
\]
If solutions exist for some \( m \), then the minimal polynomial of \( M \) must have degree at most \( m \).
The main observation is that, for \( 1 \leq i \leq 1009 \), the matrix \( M^{i} \) has its first 2018 columns equal to the last 2018 columns of \( M^{i-1} \). This implies that \( M^{0}, M^{1}, \ldots, M^{1009} \) are linearly independent, because the first column of each such \( M^{i} \) consists of all 0s and a single 1 in the \( 2i+1 \)-th position, so no linear combination of them can sum to zero. From this, it follows that \( m \geq 1010 \).
Next, we'll show that solutions exist for \( m=1010 \) and find all of them. For each \( 1 \leq i \leq 1009 \), \( M^{i} \) has all 0 entries in the even positions of the first column and the odd positions of the second column. Therefore, for a linear dependence between \( M^{0}, M^{1}, \ldots, M^{1010} \) to exist, \( M^{1010} \) must also have all 0 entries in the even positions of the first column and all odd positions of the second column, so \( a_{2}=a_{4}=\cdots=a_{2020}=0 \) and \( b_{1}=b_{3}=\cdots=b_{2019}=0 \). Similarly, each \( M^{i} \) for \( 1 \leq i \leq 1009 \) has the property that the \( 2j+1 \)-th position of the first column and the \( 2j+2 \)-th position of the second column are equal, so \( M^{1010} \) must also have this property, meaning that \( a_{2j+1}=b_{2j+2}=c_{j} \) for some constants \( c_{j} \).
Then it's not hard to verify that \( M \) is the square of the \( 2020 \times 2020 \) matrix
\[
N=\left[\begin{array}{cccccc}0 & 0 & \ldots & 0 & 0 & c_{0} \\ 1 & 0 & \ldots & 0 & 0 & 0 \\ 0 & 1 & \ldots & 0 & 0 & c_{1} \\ 0 & 0 & \ddots & 0 & 0 & 0 \\ \vdots & \vdots & & \ddots & \vdots & \vdots \\ 0 & 0 & \ldots & \ldots & 1 & 0\end{array}\right]
\]
Since the minimal polynomial of \( N \) has degree \(\leq 2020\), it follows \( N \)'s minimal polynomial has degree exactly 2020 as we wanted. Furthermore, the first 2019 columns of \( N^{i} \) are the last 2019 columns of \( N^{i-1} \), so it follows that \( N^{i} \)'s first column for \( 0 \leq i \leq 2019 \) is just all 0s along with a 1 on the \( 2i+1 \)-th position, while \( N^{2020} \)'s first column alternates between the \( c_{i} \)s and 0s. Then it's clear that the minimal polynomial of \( N \) must be \( N^{2020}-c_{1009} N^{2018}-\cdots-c_{0} \), so the minimal polynomial of \( M \) is \( M^{1010}-c_{1009} M^{1009}-\cdots-c_{0} \). Since we want \( M \)'s minimal polynomial to be \((M+c)^{1010}\) for some residue \( c \) modulo 2020, for each \( c \) we just expand \((M+c)^{1010}\) and set the \( c_{i} \) to be the appropriate values, and we are done; clearly this shows \( m=1010 \) and \( n=2020 \), so the answer is \( 100 \cdot 1010+2020=103020 \).
\(\boxed{103020}\)
|
103020
|
{
"competition": "us_comps",
"dataset": "Ours",
"posts": null,
"source": "OMOFall19Solns-3.md"
}
|
Let \( S \) be the set of integers modulo 2020. Suppose that \( a_{1}, a_{2}, \ldots, a_{2020}, b_{1}, b_{2}, \ldots, b_{2020}, c \) are arbitrary elements of \( S \). For any \( x_{1}, x_{2}, \ldots, x_{2020} \in S \), define \( f\left(x_{1}, x_{2}, \ldots, x_{2020}\right) \) to be the 2020-tuple whose \( i \)-th coordinate is \( x_{i-2}+a_{i} x_{2019}+b_{i} x_{2020}+c x_{i} \), where we set \( x_{-1}=x_{0}=0 \). Let \( m \) be the smallest positive integer such that, for some values of \( a_{1}, a_{2}, \ldots, a_{2020}, b_{1}, b_{2}, \ldots, b_{2020}, c \), we have, for all \( x_{1}, x_{2}, \ldots, x_{2020} \in S \), that \( f^{m}\left(x_{1}, x_{2}, \ldots, x_{2020}\right)=(0,0, \ldots, 0) \). For this value of \( m \), there are exactly \( n \) choices of the tuple \( \left(a_{1}, a_{2}, \ldots, a_{2020}, b_{1}, b_{2}, \ldots, b_{2020}, c\right) \) such that, for all \( x_{1}, x_{2}, \ldots, x_{2020} \in S, f^{m}\left(x_{1}, x_{2}, \ldots, x_{2020}\right)=(0,0, \ldots, 0) \). Compute \( 100m+n \).
|
[
"/Mathematics/Algebra/LinearAlgebra/LinearIndependence/LinearlyIndependent",
"/Mathematics/Algebra/LinearAlgebra/Matrices/IntegerMatrices",
"/Mathematics/Algebra/LinearAlgebra/Matrices/MatrixOperations",
"/Mathematics/Algebra/Polynomials/MatrixPolynomial",
"/Mathematics/Algebra/Polynomials/Polynomial",
"/Mathematics/DiscreteMathematics/RecurrenceEquations/LinearRecurrenceEquation",
"/Mathematics/DiscreteMathematics/RecurrenceEquations/RecurrenceEquation",
"/Mathematics/DiscreteMathematics/RecurrenceEquations/RecurrenceRelation",
"/Mathematics/NumberTheory/Congruences/Congruence",
"/Mathematics/NumberTheory/Congruences/Mod",
"/Mathematics/NumberTheory/Congruences/ModularArithmetic",
"/Mathematics/NumberTheory/Congruences/Modulus",
"/Mathematics/NumberTheory/GeneralNumberTheory/ElementaryNumberTheory",
"/Mathematics/NumberTheory/GeneralNumberTheory/NumberTheory"
] |
Model the iteration as a matrix transformation and bound the smallest m by the degree of the matrix's minimal polynomial, using column patterns in powers to force a power of a linear factor.
|
[
-0.00015163421630859375,
-0.0063323974609375,
0.038665771484375,
0.01898193359375,
-0.0006785392761230469,
0.041046142578125,
0.0015010833740234375,
-0.04254150390625,
0.0126190185546875,
0.030059814453125,
0.049285888671875,
-0.05029296875,
-0.0008611679077148438,
0.031219482421875,
-0.03173828125,
-0.006195068359375,
0.01126861572265625,
0.0033130645751953125,
-0.01317596435546875,
-0.006053924560546875,
-0.01373291015625,
0.006275177001953125,
-0.01274871826171875,
0.045074462890625,
-0.0272064208984375,
-0.0221405029296875,
-0.0282135009765625,
0.042144775390625,
-0.01227569580078125,
-0.0180206298828125,
0.00872039794921875,
-0.0274658203125,
0.0142974853515625,
-0.02569580078125,
0.0013780593872070312,
-0.020111083984375,
-0.01279449462890625,
-0.0011930465698242188,
-0.0095062255859375,
-0.025787353515625,
-0.003082275390625,
0.0097198486328125,
-0.008087158203125,
0.0255126953125,
-0.015411376953125,
-0.00891876220703125,
-0.0002002716064453125,
0.006320953369140625,
-0.0014667510986328125,
0.0093231201171875,
-0.006122589111328125,
0.01099395751953125,
-0.01416015625,
-0.01448822021484375,
-0.044403076171875,
-0.033905029296875,
0.00467681884765625,
0.0016832351684570312,
0.039886474609375,
-0.0178070068359375,
-0.0013666152954101562,
-0.0139923095703125,
-0.021240234375,
-0.0128631591796875,
0.0018062591552734375,
-0.00945281982421875,
0.034271240234375,
0.01110076904296875,
-0.0017957687377929688,
-0.00801849365234375,
0.05914306640625,
-0.02825927734375,
-0.0172119140625,
0.06280517578125,
0.0303802490234375,
-0.0183563232421875,
-0.0035572052001953125,
0.03436279296875,
0.0095062255859375,
-0.0006933212280273438,
0.0006074905395507812,
0.0235595703125,
0.026031494140625,
-0.00350189208984375,
0.0145416259765625,
-0.0025787353515625,
-0.0274505615234375,
-0.0006146430969238281,
0.039764404296875,
0.007190704345703125,
0.0013875961303710938,
-0.0147705078125,
-0.007415771484375,
0.020233154296875,
0.0036945343017578125,
0.014434814453125,
0.0201873779296875,
-0.00983428955078125,
-0.020355224609375,
-0.0086669921875,
-0.006866455078125,
-0.00887298583984375,
0.007904052734375,
-0.0072784423828125,
-0.059967041015625,
-0.015716552734375,
-0.0113067626953125,
0.0189666748046875,
-0.0189208984375,
0.003246307373046875,
0.01329803466796875,
0.001941680908203125,
0.0198974609375,
0.0028018951416015625,
0.005214691162109375,
-0.00084686279296875,
0.01457977294921875,
0.0016832351684570312,
0.005523681640625,
-0.02374267578125,
-0.00945281982421875,
0.0038509368896484375,
-0.002899169921875,
0.0270538330078125,
0.01538848876953125,
-0.03228759765625,
-0.005352020263671875,
-0.02740478515625,
-0.01143646240234375,
0.01544952392578125,
-0.000008463859558105469,
0.0102081298828125,
-0.0005383491516113281,
-0.043853759765625,
-0.0670166015625,
0.021209716796875,
-0.0221710205078125,
-0.014251708984375,
-0.0045623779296875,
-0.004283905029296875,
0.003215789794921875,
-0.00954437255859375,
-0.0038471221923828125,
-0.021820068359375,
-0.0004286766052246094,
-0.01450347900390625,
-0.003635406494140625,
-0.03546142578125,
0.0028285980224609375,
-0.00983428955078125,
-0.00482940673828125,
0.0125732421875,
0.04132080078125,
0.01473236083984375,
-0.02581787109375,
0.01427459716796875,
0.0049591064453125,
0.003200531005859375,
0.0037593841552734375,
0.0101165771484375,
0.024810791015625,
0.0015497207641601562,
-0.0174560546875,
0.03717041015625,
0.00696563720703125,
0.00016677379608154297,
0.007053375244140625,
-0.0104217529296875,
-0.0032558441162109375,
-0.017120361328125,
0.0018205642700195312,
-0.0010499954223632812,
-0.0015707015991210938,
-0.01947021484375,
0.007419586181640625,
-0.00820159912109375,
-0.0160980224609375,
0.0022029876708984375,
-0.007389068603515625,
0.0090789794921875,
0.0198211669921875,
-0.048004150390625,
-0.0133819580078125,
-0.002887725830078125,
-0.00765228271484375,
-0.01934814453125,
-0.0136566162109375,
0.0032863616943359375,
0.0217132568359375,
0.0082550048828125,
-0.0087127685546875,
0.0016794204711914062,
0.004390716552734375,
0.0024929046630859375,
-0.0228271484375,
0.00844573974609375,
-0.003849029541015625,
0.037261962890625,
0.032379150390625,
0.021148681640625,
0.004589080810546875,
0.0193023681640625,
0.005550384521484375,
0.01079559326171875,
-0.0069427490234375,
-0.005725860595703125,
0.019012451171875,
-0.0227203369140625,
-0.0076751708984375,
-0.007415771484375,
0.01776123046875,
-0.03179931640625,
-0.01161956787109375,
-0.03253173828125,
-0.004886627197265625,
0.012237548828125,
-0.0185089111328125,
-0.0009641647338867188,
0.0105743408203125,
-0.01343536376953125,
0.0013742446899414062,
0.00464630126953125,
0.0111846923828125,
-0.018798828125,
-0.01983642578125,
-0.0132293701171875,
-0.00160980224609375,
-0.0084991455078125,
-0.00414276123046875,
0.019500732421875,
0.032257080078125,
0.0282135009765625,
-0.0137939453125,
0.00841522216796875,
0.0121612548828125,
0.00983428955078125,
0.0355224609375,
-0.01258087158203125,
0.019378662109375,
-0.034210205078125,
0.000949859619140625,
-0.0186309814453125,
-0.00794219970703125,
0.004779815673828125,
-0.0175933837890625,
0.00713348388671875,
0.00817108154296875,
0.006649017333984375,
-0.0038738250732421875,
-0.016815185546875,
-0.0207977294921875,
0.018035888671875,
-0.00795745849609375,
0.0218048095703125,
-0.0028285980224609375,
-0.01049041748046875,
0.0022602081298828125,
-0.04541015625,
-0.0264892578125,
0.01218414306640625,
0.0028781890869140625,
-0.01137542724609375,
0.002368927001953125,
-0.00039076805114746094,
-0.0147552490234375,
-0.00145721435546875,
0.0022430419921875,
0.0036754608154296875,
0.0203704833984375,
-0.002063751220703125,
0.031005859375,
-0.007358551025390625,
-0.01739501953125,
0.0013628005981445312,
0.0301361083984375,
-0.0301513671875,
-0.0121917724609375,
-0.01180267333984375,
0.0003857612609863281,
0.0046844482421875,
0.026763916015625,
0.0005970001220703125,
-0.0089111328125,
-0.0026302337646484375,
0.007457733154296875,
0.00274658203125,
-0.0192108154296875,
0.0003936290740966797,
-0.0234375,
0.0019130706787109375,
-0.00018918514251708984,
-0.031219482421875,
-0.01116180419921875,
0.0028133392333984375,
0.073486328125,
-0.026824951171875,
0.00606536865234375,
0.0301513671875,
0.01045989990234375,
-0.01308441162109375,
0.0380859375,
0.00572967529296875,
-0.02044677734375,
0.01424407958984375,
0.014678955078125,
-0.01531219482421875,
-0.0045928955078125,
-0.01149749755859375,
-0.0489501953125,
-0.002178192138671875,
0.01471710205078125,
-0.0016613006591796875,
-0.00762176513671875,
-0.006885528564453125,
-0.038330078125,
-0.041107177734375,
-0.0001939535140991211,
0.007221221923828125,
-0.01214599609375,
0.0209197998046875,
0.018707275390625,
0.0295562744140625,
-0.0025424957275390625,
0.0038623809814453125,
-0.02935791015625,
-0.01800537109375,
0.0013685226440429688,
-0.003536224365234375,
-0.04058837890625,
0.0167999267578125,
-0.036041259765625,
0.00441741943359375,
-0.003864288330078125,
-0.01097869873046875,
-0.0136566162109375,
0.00489044189453125,
0.0017499923706054688,
0.021392822265625,
-0.0016679763793945312,
-0.0148468017578125,
0.00649261474609375,
-0.00893402099609375,
0.0181121826171875,
-0.0345458984375,
-0.01312255859375,
-0.0015935897827148438,
-0.004596710205078125,
0.0014543533325195312,
0.0083770751953125,
-0.02923583984375,
0.0401611328125,
0.0194854736328125,
-0.01488494873046875,
-0.007022857666015625,
-0.004238128662109375,
0.00675201416015625,
0.0020961761474609375,
0.0030002593994140625,
-0.00882720947265625,
0.0207977294921875,
-0.0002701282501220703,
-0.0014753341674804688,
-0.012725830078125,
0.0039215087890625,
-0.00344085693359375,
-0.0018091201782226562,
-0.0243377685546875,
0.0236358642578125,
-0.049530029296875,
0.0041961669921875,
-0.00814056396484375,
-0.00385284423828125,
0.00914764404296875,
-0.021881103515625,
-0.0083770751953125,
-0.02001953125,
0.005428314208984375,
0.007427215576171875,
0.0130157470703125,
-0.018402099609375,
0.00428009033203125,
0.056640625,
-0.00846099853515625,
0.0175018310546875,
-0.0137786865234375,
-0.01328277587890625,
-0.014373779296875,
-0.04473876953125,
-0.028839111328125,
0.01215362548828125,
-0.0208282470703125,
-0.00914764404296875,
-0.027252197265625,
0.004116058349609375,
-0.031585693359375,
-0.006717681884765625,
-0.00959014892578125,
0.0113067626953125,
0.0094451904296875,
-0.017913818359375,
-0.0131988525390625,
0.01010894775390625,
-0.022674560546875,
-0.007904052734375,
-0.002880096435546875,
0.01003265380859375,
-0.0155792236328125,
-0.004070281982421875,
-0.0235595703125,
0.007022857666015625,
0.0010547637939453125,
-0.0032672882080078125,
0.011810302734375,
-0.007747650146484375,
0.04736328125,
0.001537322998046875,
-0.0099334716796875,
-0.042755126953125,
-0.0217742919921875,
0.006534576416015625,
-0.00820159912109375,
-0.037322998046875,
0.044677734375,
-0.01146697998046875,
0.0067291259765625,
0.0302581787109375,
-0.0167388916015625,
0.0229034423828125,
0.0027408599853515625,
0.0156097412109375,
-0.004756927490234375,
-0.04754638671875,
0.0101165771484375,
0.0240325927734375,
0.002986907958984375,
0.0004742145538330078,
0.042633056640625,
0.01103973388671875,
-0.0079193115234375,
0.032257080078125,
-0.0035877227783203125,
-0.00783538818359375,
0.0079498291015625,
0.007129669189453125,
-0.0217742919921875,
-0.00911712646484375,
-0.0035762786865234375,
0.00794219970703125,
-0.034210205078125,
-0.013397216796875,
-0.02496337890625,
0.01251983642578125,
-0.0082855224609375,
0.016845703125,
0.0056304931640625,
0.01824951171875,
0.002521514892578125,
0.0165252685546875,
-0.007419586181640625,
-0.0328369140625,
0.024810791015625,
-0.019805908203125,
-0.021453857421875,
0.0203704833984375,
-0.05352783203125,
0.0023956298828125,
-0.00847625732421875,
0.002246856689453125,
0.0271759033203125,
0.01253509521484375,
-0.001556396484375,
-0.022247314453125,
-0.00685882568359375,
-0.01861572265625,
-0.02984619140625,
0.0242156982421875,
0.032501220703125,
0.01169586181640625,
-0.032745361328125,
-0.02667236328125,
0.01180267333984375,
0.007205963134765625,
-0.01377105712890625,
0.005489349365234375,
-0.013397216796875,
0.0180511474609375,
0.037353515625,
0.0150604248046875,
0.01076507568359375,
0.01261138916015625,
0.01267242431640625,
0.03009033203125,
-0.0272064208984375,
-0.01175689697265625,
-0.02264404296875,
0.0034942626953125,
0.0164794921875,
0.00807952880859375,
-0.0230560302734375,
0.0231781005859375,
0.01629638671875,
-0.0260162353515625,
-0.0093536376953125,
0.027740478515625,
0.0150604248046875,
0.01044464111328125,
0.0113983154296875,
-0.040863037109375,
-0.01258087158203125,
-0.01302337646484375,
-0.00991058349609375,
0.00977325439453125,
-0.00650787353515625,
-0.01291656494140625,
0.0357666015625,
0.01035308837890625,
0.0209808349609375,
0.00922393798828125,
0.006748199462890625,
-0.002208709716796875,
-0.0229034423828125,
0.0079803466796875,
0.03338623046875,
-0.0090484619140625,
-0.0010013580322265625,
0.0285186767578125,
0.017486572265625,
0.0257720947265625,
0.00553131103515625,
-0.01360321044921875,
-0.029571533203125,
-0.04876708984375,
-0.0064849853515625,
0.0002627372741699219,
-0.0292510986328125,
0.009765625,
-0.01165771484375,
-0.024932861328125,
0.0180816650390625,
0.0225830078125,
0.001781463623046875,
0.01409149169921875,
-0.0175933837890625,
-0.04144287109375,
0.0075836181640625,
-0.007259368896484375,
-0.01177215576171875,
0.024322509765625,
0.00487518310546875,
0.04095458984375,
-0.004383087158203125,
0.0051727294921875,
-0.035797119140625,
0.00890350341796875,
-0.02789306640625,
-0.0262908935546875,
0.0018482208251953125,
-0.0193023681640625,
-0.003139495849609375,
0.0006308555603027344,
0.0291900634765625,
0.00919342041015625,
0.0445556640625,
0.01059722900390625,
0.0236968994140625,
-0.0433349609375,
0.01227569580078125,
0.0015211105346679688,
0.010650634765625,
-0.043701171875,
-0.005115509033203125,
-0.0014972686767578125,
-0.0142974853515625,
0.0217132568359375,
0.00658416748046875,
-0.006580352783203125,
-0.01617431640625,
-0.00016736984252929688,
0.0018472671508789062,
0.0015668869018554688,
0.00945281982421875,
0.050323486328125,
-0.01549530029296875,
0.0233306884765625,
0.02630615234375,
-0.0035228729248046875,
0.007518768310546875,
0.0017995834350585938,
-0.00847625732421875,
-0.0137939453125,
-0.02410888671875,
-0.00485992431640625,
-0.01010894775390625,
0.0159759521484375,
0.00614166259765625,
-0.0111541748046875,
0.041595458984375,
0.0096435546875,
0.0111083984375,
-0.0183868408203125,
0.03582763671875,
-0.003139495849609375,
-0.042877197265625,
0.01053619384765625,
-0.016357421875,
-0.01849365234375,
-0.01555633544921875,
0.019744873046875,
-0.01117706298828125,
0.023468017578125,
0.01788330078125,
0.006137847900390625,
0.0114593505859375,
0.00453948974609375,
0.01262664794921875,
0.0016431808471679688,
0.00801849365234375,
-0.020751953125,
0.0251312255859375,
0.00027179718017578125,
-0.0240325927734375,
0.008880615234375,
-0.005207061767578125,
0.0208892822265625,
-0.006999969482421875,
0.01081085205078125,
-0.0019311904907226562,
-0.0297698974609375,
0.0287322998046875,
0.009124755859375,
-0.0166778564453125,
0.0143585205078125,
0.016815185546875,
0.0035648345947265625,
-0.0031299591064453125,
0.017852783203125,
-0.005527496337890625,
0.00704193115234375,
-0.0068511962890625,
-0.0106964111328125,
0.01082611083984375,
0.01139068603515625,
-0.006107330322265625,
-0.03948974609375,
-0.0095672607421875,
0.0138702392578125,
0.0124664306640625,
-0.0145111083984375,
-0.045562744140625,
0.01204681396484375,
-0.0140380859375,
-0.0283660888671875,
-0.0234222412109375,
0.0264739990234375,
-0.00015723705291748047,
0.01190948486328125,
0.0078887939453125,
0.003955841064453125,
0.01064300537109375,
-0.0196533203125,
0.040771484375,
-0.0400390625,
-0.007724761962890625,
-0.03662109375,
-0.027862548828125,
0.00859832763671875,
-0.0040740966796875,
-0.002750396728515625,
0.046417236328125,
-0.0267333984375,
0.015045166015625,
-0.017181396484375,
-0.00807952880859375,
-0.01290130615234375,
0.0179290771484375,
-0.0016193389892578125,
0.00628662109375,
-0.004665374755859375,
0.0226287841796875,
0.00811004638671875,
0.0205230712890625,
0.02252197265625,
0.0217132568359375,
-0.0041656494140625,
0.01690673828125,
0.0118408203125,
-0.020355224609375,
0.001995086669921875,
-0.004852294921875,
-0.019775390625,
0.0028514862060546875,
0.0160064697265625,
-0.0241546630859375,
0.005279541015625,
0.0016527175903320312,
-0.01806640625,
0.00501251220703125,
-0.01177215576171875,
-0.01253509521484375,
0.004444122314453125,
-0.01165008544921875,
-0.031890869140625,
0.0293121337890625,
0.01129150390625,
-0.01739501953125,
-0.05194091796875,
0.0017681121826171875,
-0.007007598876953125,
-0.0384521484375,
0.0236358642578125,
-0.040924072265625,
0.012939453125,
-0.0167999267578125,
-0.0173492431640625,
-0.0267333984375,
-0.0007834434509277344,
0.0262603759765625,
0.04559326171875,
-0.012847900390625,
0.01018524169921875,
-0.0167694091796875,
0.00450897216796875,
-0.0174407958984375,
-0.01123809814453125,
0.004840850830078125,
0.01245880126953125,
-0.006694793701171875,
-0.02801513671875,
-0.0045623779296875,
-0.0221405029296875,
0.004459381103515625,
-0.01629638671875,
0.01043701171875,
-0.01444244384765625,
-0.03363037109375,
-0.035797119140625,
0.039886474609375,
-0.0204620361328125,
-0.00791168212890625,
-0.0187530517578125,
0.051727294921875,
0.0082550048828125,
0.0234375,
-0.0245208740234375,
-0.00832366943359375,
0.00357818603515625,
-0.003940582275390625,
-0.007389068603515625,
0.0013017654418945312,
0.038848876953125,
0.044464111328125,
0.0033359527587890625,
0.0266265869140625,
-0.040924072265625,
-0.0416259765625,
-0.0206756591796875,
0.0226898193359375,
-0.024993896484375,
-0.005382537841796875,
0.0006618499755859375,
-0.04522705078125,
-0.0015811920166015625,
-0.0128936767578125,
0.01357269287109375,
0.001617431640625,
-0.00020694732666015625,
-0.0310821533203125,
-0.013824462890625,
-0.042236328125,
0.03887939453125,
-0.0506591796875,
0.01009368896484375,
-0.004184722900390625,
-0.0096282958984375,
0.01165771484375,
-0.007381439208984375,
-0.04351806640625,
0.01386260986328125,
0.018310546875,
-0.009735107421875,
0.034393310546875,
-0.008514404296875,
-0.00287628173828125,
0.004566192626953125,
-0.0277557373046875,
-0.0133056640625,
-0.00335693359375,
-0.0169219970703125,
0.034637451171875,
0.00597381591796875,
0.005390167236328125,
-0.005619049072265625,
0.0298614501953125,
-0.000614166259765625,
-0.020477294921875,
0.0018978118896484375,
0.01094818115234375,
-0.02532958984375,
-0.0302581787109375,
0.00811004638671875,
0.0080718994140625,
-0.0221099853515625,
-0.0103302001953125,
0.01690673828125,
0.0018587112426757812,
-0.005290985107421875,
0.0030059814453125,
0.0010347366333007812,
-0.0430908203125,
0.02752685546875,
0.00016641616821289062,
-0.006038665771484375,
0.0174102783203125,
-0.013427734375,
-0.0036773681640625,
-0.025390625,
-0.00872802734375,
0.0234222412109375,
-0.005092620849609375,
0.01299285888671875,
-0.012969970703125,
0.008148193359375,
0.021697998046875,
0.00908660888671875,
-0.01275634765625,
-0.0004870891571044922,
-0.0014333724975585938,
0.0450439453125,
0.0179595947265625,
0.004283905029296875,
-0.0019855499267578125,
0.00989532470703125,
-0.00240325927734375,
0.009552001953125,
0.005199432373046875,
0.005321502685546875,
-0.0027923583984375,
0.00945281982421875,
0.0116424560546875,
0.0116119384765625,
0.0196990966796875,
-0.007190704345703125,
0.0270233154296875,
-0.0003561973571777344,
0.0153045654296875,
-0.026123046875,
0.006694793701171875,
0.055755615234375,
0.004241943359375,
-0.044830322265625,
-0.0025272369384765625,
0.0284576416015625,
-0.035858154296875,
0.01090240478515625,
-0.0034942626953125,
0.007061004638671875,
0.0280914306640625,
0.0189361572265625,
0.003910064697265625,
-0.038299560546875,
-0.004795074462890625,
-0.035736083984375,
0.0027904510498046875,
-0.025054931640625,
-0.0103302001953125,
0.0153350830078125,
-0.00931549072265625,
0.0018892288208007812,
0.028900146484375,
-0.019012451171875,
0.006893157958984375,
-0.0015993118286132812,
0.0150909423828125,
0.0158843994140625,
0.003337860107421875,
0.006092071533203125,
-0.01102447509765625,
0.003955841064453125,
0.0028133392333984375,
0.022918701171875,
0.009613037109375,
-0.033355712890625,
-0.01064300537109375,
-0.002796173095703125,
0.00397491455078125,
-0.00737762451171875,
0.00113677978515625,
0.00678253173828125,
-0.00640869140625,
-0.005153656005859375,
0.028472900390625,
-0.0008554458618164062,
0.052978515625,
-0.0146636962890625,
0.0186309814453125,
0.02154541015625,
-0.02886962890625,
-0.01035308837890625,
-0.0021915435791015625,
-0.048248291015625,
-0.0079498291015625,
0.00215911865234375,
-0.01739501953125,
0.0030364990234375,
-0.00955963134765625,
-0.023040771484375,
-0.01392364501953125,
-0.0249176025390625,
0.005462646484375,
-0.00830841064453125,
-0.01247406005859375,
0.009185791015625,
0.01551055908203125,
0.021331787109375,
-0.0131378173828125,
-0.0258636474609375,
-0.013885498046875,
0.03094482421875,
0.009307861328125,
0.0107269287109375,
0.0091400146484375,
-0.00597381591796875,
0.01267242431640625,
-0.023681640625,
0.007610321044921875,
0.00701904296875,
0.0179443359375,
0.00909423828125,
-0.042877197265625,
0.0087432861328125,
0.002197265625,
0.021331787109375,
-0.0018596649169921875,
0.00333404541015625,
-0.004985809326171875,
0.0032711029052734375,
-0.0121612548828125,
-0.00640869140625,
-0.0194091796875,
-0.0019683837890625,
-0.027740478515625,
-0.0088958740234375,
0.01336669921875,
0.0301513671875,
0.0251617431640625,
-0.0035858154296875,
0.005664825439453125,
-0.0011510848999023438,
-0.0174560546875,
-0.0260009765625,
-0.03521728515625,
-0.01000213623046875,
0.00769805908203125,
0.036376953125,
0.0009946823120117188,
-0.03369140625,
-0.00965118408203125,
-0.02471923828125,
-0.009307861328125,
-0.020172119140625,
-0.01233673095703125,
0.0136871337890625,
-0.029693603515625,
0.0164031982421875,
0.0010976791381835938,
0.0277557373046875,
-0.0026187896728515625,
0.0153350830078125,
0.0202789306640625,
0.01446533203125,
-0.024627685546875,
-0.0224609375,
-0.0215301513671875,
-0.0379638671875,
-0.006481170654296875,
-0.0012969970703125,
-0.01432037353515625,
-0.00928497314453125,
0.01238250732421875,
0.01059722900390625,
-0.025299072265625,
-0.007244110107421875,
-0.02471923828125,
-0.031951904296875,
-0.0057373046875,
0.05194091796875,
0.0140228271484375,
-0.005939483642578125,
0.030487060546875,
0.003631591796875,
-0.02081298828125,
0.039581298828125,
0.006824493408203125,
0.040191650390625,
-0.001556396484375,
0.004055023193359375,
-0.001575469970703125,
0.0004405975341796875,
-0.0157928466796875,
0.0013093948364257812,
-0.0237579345703125,
-0.01031494140625,
0.00994110107421875,
0.0095672607421875,
0.0015048980712890625,
-0.0124664306640625,
-0.0012836456298828125,
-0.0016641616821289062,
-0.0052490234375,
0.0200958251953125,
-0.039276123046875,
-0.0006031990051269531,
-0.0157012939453125,
-0.004962921142578125,
-0.006084442138671875,
-0.00986480712890625,
0.00861358642578125,
-0.0020008087158203125,
-0.05419921875,
-0.0107574462890625,
0.034423828125,
0.034698486328125,
-0.0245513916015625,
-0.02764892578125,
-0.0288543701171875,
0.0214080810546875,
-0.021514892578125,
0.0118408203125,
0.04754638671875,
0.0024776458740234375,
0.00044226646423339844,
-0.02752685546875,
-0.002166748046875,
-0.035064697265625,
-0.00640106201171875,
-0.024169921875,
0.00008165836334228516,
-0.033599853515625,
0.01439666748046875,
-0.0014829635620117188,
-0.00045990943908691406,
0.006053924560546875,
0.0029811859130859375,
0.021820068359375,
-0.004940032958984375,
-0.017791748046875,
0.01061248779296875,
-0.001247406005859375,
0.0072784423828125,
-0.0321044921875,
-0.00373077392578125,
0.0248565673828125,
0.02783203125,
-0.00560760498046875,
0.036041259765625,
0.0169525146484375,
0.02587890625,
-0.0347900390625,
0.0268402099609375,
0.0107421875,
0.0276641845703125,
-0.0113677978515625,
-0.03533935546875,
-0.031829833984375,
0.0100555419921875,
-0.0103759765625,
-0.0038471221923828125,
-0.001560211181640625,
-0.02081298828125,
0.0257415771484375,
-0.03594970703125,
0.00876617431640625,
0.001285552978515625,
-0.033905029296875,
0.03985595703125,
-0.0001285076141357422,
0.00931549072265625,
-0.006755828857421875,
0.007259368896484375,
-0.00946044921875,
-0.022552490234375,
0.0167694091796875,
-0.042724609375,
-0.0003285408020019531,
0.027740478515625,
-0.0022144317626953125,
-0.0119171142578125,
-0.0123443603515625,
-0.00450897216796875,
-0.0143890380859375,
-0.0212249755859375,
-0.0126800537109375,
0.005077362060546875,
-0.0028705596923828125,
0.00693511962890625,
-0.0011348724365234375,
0.01534271240234375,
-0.004138946533203125,
0.0188140869140625,
0.00890350341796875,
0.005645751953125,
0.0260009765625,
-0.009002685546875,
-0.0078582763671875,
0.0208892822265625,
0.005161285400390625,
-0.01297760009765625,
0.004077911376953125,
-0.0253143310546875,
-0.0014410018920898438,
-0.0177001953125,
0.01499176025390625,
-0.012939453125,
0.0025730133056640625,
-0.0033473968505859375,
0.00479888916015625,
-0.006992340087890625,
-0.036956787109375,
-0.0250244140625,
-0.01074981689453125,
0.018707275390625,
0.0440673828125,
-0.0031681060791015625,
0.004756927490234375,
0.0005764961242675781,
0.03271484375,
-0.035125732421875,
-0.0029010772705078125,
0.004276275634765625,
0.00789642333984375,
-0.023406982421875,
0.011138916015625,
0.00710296630859375,
-0.032989501953125,
-0.00885009765625,
-0.007274627685546875,
-0.01123046875,
0.0255584716796875,
0.023040771484375,
-0.012481689453125,
0.0218963623046875,
-0.01739501953125,
0.00785064697265625,
0.01042938232421875,
-0.028076171875,
0.004543304443359375,
0.005558013916015625,
-0.00234222412109375,
0.00838470458984375,
0.0124359130859375,
0.004634857177734375,
0.03253173828125,
-0.0022029876708984375,
0.0018091201782226562,
-0.022613525390625,
-0.004695892333984375,
-0.0222320556640625,
-0.00726318359375,
0.009735107421875,
-0.006275177001953125,
0.00785064697265625,
-0.0200347900390625,
0.025146484375,
0.0219268798828125,
-0.056976318359375,
-0.005741119384765625,
0.00988006591796875,
0.0252838134765625,
-0.050201416015625,
-0.01348876953125,
-0.003902435302734375,
-0.0083160400390625,
0.0143890380859375,
0.01470947265625,
-0.01520538330078125,
-0.01025390625,
0.00794219970703125,
-0.0157318115234375,
-0.032501220703125,
-0.00894927978515625,
-0.02459716796875,
0.0277862548828125,
0.0141754150390625,
-0.005084991455078125,
-0.003314971923828125,
-0.0027141571044921875,
-0.00688934326171875,
0.005157470703125,
-0.00006347894668579102,
0.0019397735595703125,
0.01107025146484375,
0.014984130859375,
0.006687164306640625,
0.01837158203125,
-0.023223876953125,
0.008148193359375,
-0.00028061866760253906,
0.012603759765625,
-0.0001558065414428711,
-0.0136871337890625,
-0.0037746429443359375,
0.032501220703125,
-0.00508880615234375,
-0.03472900390625,
0.0161895751953125,
0.006298065185546875,
-0.0036144256591796875,
0.037017822265625,
-0.0158233642578125,
-0.004474639892578125,
0.00533294677734375,
-0.0191802978515625,
-0.01020050048828125,
-0.038360595703125,
0.003993988037109375,
-0.007049560546875,
0.031402587890625,
-0.005680084228515625,
-0.00836181640625,
-0.0207061767578125,
0.037841796875,
0.0086212158203125,
-0.0205535888671875,
0.0099945068359375,
0.008270263671875,
-0.02166748046875,
-0.024932861328125,
0.0237274169921875,
0.01099395751953125,
-0.00893402099609375,
0.0006732940673828125,
-0.01128387451171875,
-0.0151214599609375,
-0.004657745361328125,
-0.0311279296875,
-0.00015783309936523438,
-0.02056884765625,
0.034881591796875,
-0.031097412109375,
0.023712158203125,
-0.01849365234375,
0.0267181396484375,
0.0204925537109375,
0.00833892822265625,
0.04351806640625,
-0.0211639404296875,
-0.01105499267578125,
0.027130126953125,
0.00571441650390625,
0.0264739990234375,
0.00812530517578125,
0.0280303955078125,
-0.0013246536254882812,
0.0004019737243652344,
-0.0102386474609375,
-0.029754638671875,
0.00702667236328125,
0.01251220703125,
0.0037403106689453125,
0.0024261474609375,
-0.0298004150390625,
0.040283203125,
-0.0252532958984375,
-0.032257080078125,
-0.03326416015625,
0.00577545166015625,
0.00603485107421875,
0.01140594482421875,
-0.010406494140625,
0.012969970703125,
0.015289306640625,
0.006465911865234375,
-0.0027751922607421875,
0.042388916015625,
-0.0119171142578125,
-0.005802154541015625,
-0.023193359375,
-0.01512908935546875,
0.024078369140625,
0.0159759521484375,
-0.01265716552734375,
0.0396728515625,
0.017608642578125,
-0.0087890625,
-0.026702880859375,
-0.03033447265625,
-0.0115203857421875,
0.006961822509765625,
-0.002346038818359375,
0.005039215087890625,
-0.010345458984375,
-0.001346588134765625,
-0.025482177734375,
0.00803375244140625,
0.007411956787109375,
0.0108489990234375,
0.00762939453125,
0.025146484375,
-0.00148773193359375,
0.03118896484375,
-0.0003819465637207031,
-0.0098419189453125,
0.02215576171875,
-0.006595611572265625,
0.002513885498046875,
0.02020263671875,
0.0242156982421875,
0.0030002593994140625,
0.01328277587890625,
0.00852203369140625,
-0.01019287109375,
-0.01361846923828125,
-0.0012311935424804688,
-0.00506591796875,
0.030517578125,
-0.003696441650390625,
-0.003780364990234375,
0.0018224716186523438,
-0.050323486328125,
-0.0203857421875,
-0.01374053955078125,
0.0225677490234375,
-0.0222930908203125,
-0.0167999267578125,
0.01294708251953125,
0.0172882080078125,
-0.0428466796875,
-0.0006880760192871094,
-0.0166473388671875,
-0.031585693359375,
-0.0021572113037109375,
0.0039825439453125,
-0.0452880859375,
0.01605224609375,
-0.0111846923828125,
0.01287078857421875,
0.0308837890625,
0.024993896484375,
0.0196380615234375,
-0.01393890380859375,
-0.0216522216796875,
0.01270294189453125,
-0.0167236328125,
-0.0194244384765625,
0.0035305023193359375,
0.024658203125,
-0.037109375,
-0.013946533203125,
-0.00858306884765625,
-0.0004820823669433594,
-0.0037631988525390625,
0.021331787109375,
0.005237579345703125,
0.0328369140625,
-0.015289306640625,
-0.0030803680419921875,
0.0048065185546875,
0.0012407302856445312,
0.0171356201171875,
-0.00791168212890625,
0.00699615478515625,
-0.03985595703125,
0.010406494140625,
-0.0307159423828125,
0.014556884765625,
0.01519775390625,
-0.035675048828125,
0.01390838623046875,
-0.003437042236328125,
-0.0262908935546875,
-0.01512908935546875,
0.00862884521484375,
-0.0168304443359375,
-0.0180511474609375,
0.0289306640625,
-0.030975341796875,
0.0032367706298828125,
-0.002185821533203125,
-0.00579833984375,
-0.003238677978515625,
-0.0171356201171875,
-0.0206451416015625,
-0.01500701904296875,
-0.017364501953125,
0.01438140869140625,
0.0181884765625,
0.0087127685546875,
0.0153350830078125,
0.001949310302734375,
-0.01538848876953125,
0.03875732421875,
-0.007564544677734375,
-0.01377105712890625,
-0.025115966796875,
0.0188446044921875,
-0.0111846923828125,
0.00638580322265625,
0.007061004638671875,
-0.019073486328125,
0.0131378173828125,
0.00853729248046875,
0.004199981689453125,
-0.0126190185546875,
0.007625579833984375,
0.01708984375,
-0.00959014892578125,
0.03179931640625,
-0.0079803466796875,
0.02056884765625,
0.0110931396484375,
-0.0211944580078125,
0.0010509490966796875,
0.0218353271484375,
-0.05694580078125,
0.0032291412353515625,
-0.016571044921875,
0.01282501220703125,
-0.0269927978515625,
0.00228118896484375,
0.0257415771484375,
0.0222015380859375,
0.00791168212890625,
-0.01153564453125,
0.00711822509765625,
-0.015594482421875,
0.01110076904296875,
0.01120758056640625,
-0.013916015625,
-0.0078887939453125,
-0.0254974365234375,
0.0018415451049804688,
-0.0237274169921875,
-0.0455322265625,
0.002033233642578125,
-0.0065155029296875,
-0.0361328125,
0.0162200927734375,
0.01102447509765625,
0.0185394287109375,
-0.001972198486328125,
0.00714111328125,
-0.033935546875,
0.00811004638671875,
0.018646240234375,
0.00946044921875,
-0.01393890380859375,
0.004611968994140625,
0.019744873046875,
-0.03204345703125,
-0.01247406005859375,
-0.01134490966796875,
-0.0195159912109375,
-0.007080078125,
0.00958251953125,
0.043792724609375,
0.01512908935546875,
0.00618743896484375,
0.023468017578125,
0.0022335052490234375,
-0.0292510986328125,
-0.030670166015625,
0.0308990478515625,
-0.01010894775390625,
0.003200531005859375,
0.01708984375,
0.0001208186149597168,
0.0105438232421875,
0.032806396484375,
0.01251983642578125,
-0.0265350341796875,
-0.01296234130859375,
-0.007198333740234375,
0.00525665283203125,
0.02349853515625,
-0.020294189453125,
-0.006259918212890625,
0.044525146484375,
-0.021636962890625,
0.0243682861328125,
-0.0157012939453125,
-0.004367828369140625,
-0.0081939697265625,
-0.0007281303405761719,
0.0312347412109375,
-0.0300750732421875,
-0.0127716064453125,
0.0016765594482421875,
-0.0101165771484375,
-0.0124969482421875,
0.0004096031188964844,
-0.01512908935546875,
-0.004547119140625,
0.0124969482421875,
0.0140380859375,
0.023712158203125,
0.01445770263671875,
0.00510406494140625,
-0.003688812255859375,
0.007320404052734375,
-0.016693115234375,
0.021728515625,
0.007015228271484375,
0.0007910728454589844,
-0.0256195068359375,
0.0310516357421875,
-0.01430511474609375,
-0.0029296875,
-0.0033130645751953125,
0.00958251953125,
-0.0031452178955078125,
-0.0090484619140625,
-0.0396728515625,
0.03240966796875,
-0.01079559326171875,
-0.052703857421875,
-0.00940704345703125,
-0.009918212890625,
-0.030120849609375,
-0.0045318603515625,
-0.0023651123046875,
0.006137847900390625,
-0.000457763671875,
-0.0204010009765625,
0.00873565673828125,
0.02020263671875,
-0.007770538330078125,
0.02349853515625,
-0.0289764404296875,
-0.007293701171875,
0.0045318603515625,
0.01214599609375,
-0.003993988037109375,
0.00012290477752685547,
0.0274658203125,
0.017608642578125,
-0.01219940185546875,
0.04693603515625,
0.00948333740234375,
0.018798828125,
0.003002166748046875,
0.006610870361328125,
-0.00921630859375,
-0.005168914794921875,
0.0287322998046875,
-0.033050537109375,
0.0083160400390625,
0.002758026123046875,
0.015350341796875,
0.00033783912658691406,
-0.02020263671875,
0.049591064453125,
0.003208160400390625,
0.01230621337890625,
-0.029022216796875,
-0.01013946533203125,
-0.0008668899536132812,
0.017486572265625,
0.017547607421875,
0.02215576171875,
-0.06268310546875,
0.01190185546875,
-0.004863739013671875,
-0.0018510818481445312,
-0.00714874267578125,
-0.0212554931640625,
-0.00634765625,
0.01336669921875,
0.01806640625,
-0.0011892318725585938,
-0.01538848876953125,
0.027740478515625,
0.0113677978515625,
-0.003292083740234375,
0.0142974853515625,
-0.0157623291015625,
0.00955963134765625,
0.0026302337646484375,
-0.00727081298828125,
0.00021159648895263672,
0.00392913818359375,
-0.006732940673828125,
0.01284027099609375,
0.00977325439453125,
0.01025390625,
-0.0226593017578125,
0.00315093994140625,
-0.004245758056640625,
0.0212249755859375,
-0.01282501220703125,
0.0012302398681640625,
0.016021728515625,
-0.0046234130859375,
-0.0118408203125,
-0.01776123046875,
0.0004954338073730469,
-0.00811004638671875,
0.0506591796875,
0.022674560546875,
0.03118896484375,
0.0204315185546875,
-0.03411865234375,
-0.01107025146484375,
-0.031097412109375,
0.0044708251953125,
-0.00231170654296875,
0.0111846923828125,
0.0156707763671875,
0.0341796875,
-0.020477294921875,
0.01025390625,
0.0104217529296875,
-0.01224517822265625,
-0.00888824462890625,
-0.028106689453125,
-0.01214599609375,
-0.01226043701171875,
-0.01039886474609375,
0.046417236328125,
-0.0009579658508300781,
0.0271148681640625,
0.0360107421875,
0.00506591796875,
-0.016082763671875,
-0.0115203857421875,
0.036041259765625,
0.0008153915405273438,
0.0045013427734375,
-0.002864837646484375,
-0.0165863037109375,
-0.0134429931640625,
0.0236358642578125,
-0.00637054443359375,
-0.03900146484375,
0.039825439453125,
-0.0029125213623046875,
-0.002849578857421875,
-0.005767822265625,
0.0122222900390625,
-0.0015478134155273438,
-0.002208709716796875,
-0.0330810546875,
-0.0231781005859375,
0.0010595321655273438,
-0.0565185546875,
-0.01045989990234375,
-0.0291290283203125,
0.0005407333374023438,
0.038421630859375,
-0.006526947021484375,
-0.0241546630859375,
0.0098876953125,
0.017425537109375,
0.0186309814453125,
-0.01071929931640625,
0.01117706298828125,
-0.0214385986328125,
-0.00937652587890625,
-0.0008063316345214844,
0.007678985595703125,
0.026611328125,
0.009490966796875,
0.0189971923828125,
0.032073974609375,
-0.0223236083984375,
-0.047393798828125,
0.0369873046875,
0.0178375244140625,
-0.00949859619140625,
-0.040618896484375,
0.0250091552734375,
-0.036102294921875,
-0.02227783203125,
0.0099639892578125,
0.032440185546875,
-0.024658203125,
-0.0120849609375,
0.0177459716796875,
-0.00771331787109375,
-0.0027828216552734375,
-0.01140594482421875,
-0.0216522216796875,
-0.03192138671875,
0.0030231475830078125,
-0.00664520263671875,
0.00858306884765625,
-0.005413055419921875,
0.00498199462890625,
0.00011944770812988281,
0.006084442138671875,
0.004791259765625,
0.060943603515625,
-0.021514892578125,
-0.0066986083984375,
0.00899505615234375,
0.032318115234375,
0.014007568359375,
0.01546478271484375,
-0.0250091552734375,
0.00048351287841796875,
0.018402099609375,
0.004451751708984375,
-0.01158905029296875,
0.00010025501251220703,
-0.026153564453125,
0.0116729736328125,
0.005565643310546875,
-0.048248291015625,
0.0281219482421875,
-0.0269317626953125,
0.005828857421875,
0.03448486328125,
-0.00457000732421875,
-0.0274658203125,
0.012786865234375,
-0.005184173583984375,
-0.0203704833984375,
0.0294036865234375,
-0.0018177032470703125,
-0.00859832763671875,
-0.0543212890625,
0.030426025390625,
-0.0138092041015625,
0.00670623779296875,
-0.0042266845703125,
-0.0121917724609375,
-0.02294921875,
0.0167999267578125,
-0.008331298828125,
0.01261138916015625,
0.0018720626831054688,
-0.0182647705078125,
0.03204345703125,
-0.006008148193359375,
-0.007015228271484375,
0.01654052734375,
-0.0147552490234375,
0.0169830322265625,
-0.00775909423828125,
-0.0246124267578125,
-0.00658416748046875,
0.03033447265625,
0.0096435546875,
0.01157379150390625,
-0.00421142578125,
-0.0117950439453125,
-0.0330810546875,
-0.0134735107421875,
0.0074920654296875,
-0.0017614364624023438,
0.007312774658203125,
-0.007312774658203125,
-0.0440673828125,
0.018646240234375,
-0.0028324127197265625,
-0.023773193359375,
-0.000797271728515625,
-0.0015583038330078125,
-0.03387451171875,
-0.018798828125,
-0.005123138427734375,
0.004756927490234375,
-0.0234832763671875,
-0.00262451171875,
0.0088043212890625,
-0.007843017578125,
0.00978851318359375,
0.00763702392578125,
0.006069183349609375,
-0.0439453125,
-0.018280029296875,
0.0196075439453125,
0.009033203125,
0.021453857421875,
-0.0003871917724609375,
-0.00458526611328125,
-0.021026611328125,
0.0228729248046875,
-0.00955963134765625,
-0.00905609130859375,
-0.0014200210571289062,
-0.004791259765625,
0.01200103759765625,
0.03515625,
0.0158843994140625,
0.0027523040771484375,
0.0037994384765625,
0.007068634033203125,
0.0130462646484375,
-0.01507568359375,
-0.00743865966796875,
-0.037445068359375,
-0.00836181640625,
-0.0016050338745117188,
0.00988006591796875,
-0.00970458984375,
0.0113983154296875,
0.0178680419921875,
0.0202178955078125,
0.00228118896484375,
-0.0005145072937011719,
-0.00811004638671875,
0.01348876953125,
-0.0235137939453125,
-0.0110931396484375,
0.0236053466796875,
-0.0087738037109375,
-0.005153656005859375,
0.01532745361328125,
0.0266571044921875,
-0.004856109619140625,
0.004535675048828125,
-0.00147247314453125,
-0.01323699951171875,
-0.00115966796875,
-0.0156097412109375,
-0.01702880859375,
0.0185394287109375,
0.007049560546875,
-0.0114593505859375,
-0.0245513916015625,
-0.0071868896484375,
0.029052734375,
0.0033111572265625,
0.00859832763671875,
0.00429534912109375,
-0.01119232177734375,
0.0177764892578125,
-0.0182952880859375,
-0.021820068359375,
0.0218353271484375,
0.005584716796875,
0.01230621337890625,
-0.035736083984375,
-0.03936767578125,
0.006984710693359375,
0.004604339599609375,
-0.007328033447265625,
-0.00815582275390625,
-0.0032806396484375,
0.0157012939453125,
-0.02288818359375,
0.033416748046875,
-0.0209503173828125,
0.0193634033203125,
0.010650634765625,
-0.0347900390625,
-0.018951416015625,
-0.00211334228515625,
0.0056304931640625,
-0.0190277099609375,
0.040435791015625,
-0.023406982421875,
-0.0010137557983398438,
0.0018787384033203125,
-0.0132904052734375,
0.0219573974609375,
0.0360107421875,
-0.005008697509765625,
-0.018829345703125,
-0.016845703125,
0.033416748046875,
-0.007541656494140625,
-0.021636962890625,
-0.00489044189453125,
-0.00804901123046875,
0.011962890625,
-0.0284881591796875,
-0.00594329833984375,
-0.0159149169921875,
0.029571533203125,
0.044097900390625,
-0.006610870361328125,
-0.017364501953125,
0.00859832763671875,
0.00872039794921875,
0.0160675048828125,
0.00455474853515625,
-0.025909423828125,
0.01189422607421875,
0.0189666748046875,
-0.0117645263671875,
0.028594970703125,
0.00864410400390625,
0.0203857421875,
0.0015592575073242188,
0.007701873779296875,
0.0099639892578125,
0.053985595703125,
0.004665374755859375,
-0.00457763671875,
0.000015437602996826172,
-0.0032253265380859375,
0.03277587890625,
0.01446533203125,
-0.00627899169921875,
0.006359100341796875,
-0.01708984375,
0.0198974609375,
-0.01169586181640625,
0.01381683349609375,
0.02105712890625,
-0.0006604194641113281,
-0.02215576171875,
0.005352020263671875,
-0.019012451171875,
0.01763916015625,
-0.0190582275390625,
-0.022491455078125,
0.0183868408203125,
-0.0029926300048828125,
-0.027557373046875,
-0.0201416015625,
-0.0169830322265625,
-0.0091552734375,
-0.0293731689453125,
0.0343017578125,
-0.0004057884216308594,
0.0396728515625,
-0.020294189453125,
0.0065765380859375,
-0.007061004638671875,
-0.0115814208984375,
0.028594970703125,
0.0261383056640625,
0.01082611083984375,
0.0338134765625,
-0.01371002197265625,
-0.0023746490478515625,
-0.031890869140625,
-0.00775909423828125,
0.015472412109375,
0.0275726318359375,
-0.0172576904296875,
-0.00656890869140625,
-0.0172882080078125,
-0.0133056640625,
0.01629638671875,
0.029296875,
0.0002942085266113281,
-0.0007982254028320312,
-0.00013720989227294922,
-0.0011539459228515625,
0.0170745849609375,
-0.0193328857421875,
0.00308990478515625,
-0.00408172607421875,
0.0290069580078125,
-0.0161590576171875,
-0.0157470703125,
-0.0335693359375,
0.00946807861328125,
0.01018524169921875,
-0.0279541015625,
-0.032684326171875,
-0.014617919921875,
0.0154876708984375,
0.028533935546875,
-0.01165771484375,
-0.01171875,
0.0197906494140625,
-0.01111602783203125,
-0.043792724609375,
-0.04107666015625,
-0.01338958740234375,
-0.01910400390625,
-0.004810333251953125,
0.0052947998046875,
-0.040069580078125,
-0.0241241455078125,
-0.01512908935546875,
-0.005146026611328125,
-0.007488250732421875,
0.006561279296875,
0.033355712890625,
0.0211639404296875,
-0.0265960693359375,
0.0177001953125,
0.04498291015625,
0.0208282470703125,
-0.00772857666015625,
-0.0199737548828125,
-0.016693115234375,
-0.0130462646484375,
-0.00519561767578125,
0.00325775146484375,
-0.034454345703125,
0.03857421875,
-0.00902557373046875,
-0.0084381103515625,
0.016571044921875,
0.0299224853515625,
-0.0404052734375,
0.0220489501953125,
0.004261016845703125,
-0.0160369873046875,
0.002193450927734375,
0.0027065277099609375,
-0.001861572265625,
-0.0010175704956054688,
-0.004772186279296875,
0.00701141357421875,
0.0226287841796875,
0.040374755859375,
-0.006618499755859375,
0.0180206298828125,
-0.0163726806640625,
-0.00873565673828125,
0.033447265625,
0.0195770263671875,
-0.00970458984375,
-0.00789642333984375,
-0.063720703125,
0.00562286376953125,
-0.0131683349609375,
-0.022247314453125,
0.02093505859375,
-0.032958984375,
0.00550079345703125,
-0.00757598876953125,
0.02874755859375,
-0.01666259765625,
-0.004100799560546875,
-0.0179901123046875,
-0.0227813720703125,
-0.01311492919921875,
0.026885986328125,
0.021209716796875,
-0.0009059906005859375,
-0.0196380615234375,
0.0010004043579101562,
-0.0147247314453125,
-0.0270843505859375,
0.043304443359375,
0.04437255859375,
0.0198516845703125,
-0.0163116455078125,
-0.00943756103515625,
0.0107574462890625,
0.0023250579833984375,
-0.01194000244140625,
0.01666259765625,
-0.004116058349609375,
0.0006885528564453125,
-0.0017557144165039062,
-0.0152435302734375,
-0.02557373046875,
0.0179443359375,
0.004299163818359375,
-0.022003173828125,
0.0078125,
0.0157470703125,
0.0279388427734375,
0.0173797607421875,
0.0126495361328125,
-0.0205535888671875,
0.0017757415771484375,
0.02667236328125,
0.01447296142578125,
-0.0180816650390625,
0.04486083984375,
-0.0133209228515625,
0.0267791748046875,
0.00501251220703125,
0.0060272216796875,
-0.02178955078125,
0.017059326171875,
-0.033447265625,
-0.03192138671875,
0.008941650390625,
-0.022918701171875,
-0.0032978057861328125,
-0.0160064697265625,
0.0037689208984375,
-0.01763916015625,
0.01447296142578125,
-0.0225830078125,
-0.025146484375,
0.009185791015625,
0.0102386474609375,
-0.003360748291015625,
-0.03778076171875,
0.0085296630859375,
0.019805908203125,
0.007289886474609375,
0.0141143798828125,
-0.0226898193359375,
-0.0257568359375,
-0.01174163818359375,
0.0087432861328125,
-0.01837158203125,
-0.0010099411010742188,
0.002285003662109375,
-0.006866455078125,
0.0008459091186523438,
-0.008209228515625,
-0.02044677734375,
0.020965576171875,
0.0197906494140625,
0.02960205078125,
-0.040191650390625,
-0.003360748291015625,
0.0016841888427734375,
0.0011777877807617188,
-0.0254669189453125,
-0.01043701171875,
0.017425537109375,
-0.0220184326171875,
-0.017669677734375,
-0.01398468017578125,
-0.01396942138671875,
-0.01641845703125,
0.0062408447265625,
0.03582763671875,
-0.0145416259765625,
0.0237579345703125,
0.0122833251953125,
0.01812744140625,
-0.026092529296875,
0.0211639404296875,
-0.01471710205078125,
0.03387451171875,
0.0058746337890625,
-0.00905609130859375,
0.0214080810546875,
-0.020965576171875,
0.00679779052734375,
-0.002864837646484375,
0.0296173095703125,
-0.0067901611328125,
-0.0019407272338867188,
-0.0000794529914855957,
0.00493621826171875,
0.005992889404296875,
-0.02984619140625,
-0.004375457763671875,
-0.00673675537109375,
0.0262298583984375,
0.015838623046875,
-0.0238494873046875,
0.0302581787109375,
0.0239410400390625,
-0.0205841064453125,
0.013397216796875,
0.00797271728515625,
0.0201568603515625,
-0.0018434524536132812,
0.014801025390625,
0.0205841064453125,
0.0016641616821289062,
-0.00424957275390625,
-0.006969451904296875,
0.026763916015625,
-0.00638580322265625,
0.01514434814453125,
0.037841796875,
0.0085601806640625,
-0.0207366943359375,
-0.023773193359375,
-0.0007886886596679688,
0.0159454345703125,
0.0154266357421875,
-0.01114654541015625,
-0.0228118896484375,
-0.0206756591796875,
-0.0031871795654296875,
-0.016021728515625,
-0.0310211181640625,
0.0070037841796875,
0.021484375,
0.00904083251953125,
-0.03167724609375,
0.001438140869140625,
-0.01331329345703125,
0.002777099609375,
0.0018672943115234375,
-0.0147247314453125,
0.0202484130859375,
0.0192718505859375,
0.0296783447265625,
-0.0018253326416015625,
0.01218414306640625,
-0.004726409912109375,
-0.05743408203125,
0.0269317626953125,
0.0121307373046875,
-0.00577545166015625,
0.0004374980926513672,
0.01113128662109375,
0.031219482421875,
-0.0113677978515625,
0.034149169921875,
-0.0060577392578125,
0.052337646484375,
0.019195556640625,
0.0064849853515625,
-0.0261383056640625,
0.014892578125,
0.01447296142578125,
-0.01348114013671875,
0.0021915435791015625,
0.007076263427734375,
-0.0008058547973632812,
-0.03485107421875,
0.0160980224609375,
0.007904052734375,
-0.0151824951171875,
-0.007904052734375,
-0.0220489501953125,
-0.00620269775390625,
-0.003963470458984375,
-0.0191802978515625,
0.01508331298828125,
-0.031280517578125,
0.0152435302734375,
-0.039886474609375,
-0.01202392578125,
-0.0200042724609375,
-0.0150604248046875,
0.0233917236328125,
0.0157012939453125,
0.01233673095703125,
0.0013933181762695312,
0.0257568359375,
-0.0022525787353515625,
0.00872039794921875,
-0.0203704833984375,
-0.0040740966796875,
-0.00682830810546875,
0.023773193359375,
-0.01100921630859375,
0.004314422607421875,
0.0021953582763671875,
0.0224456787109375,
0.00555419921875,
0.01544189453125,
0.000024199485778808594,
-0.0014562606811523438,
0.047027587890625,
-0.004566192626953125,
0.0203857421875,
-0.057586669921875,
0.01352691650390625,
-0.01406097412109375,
0.0034637451171875,
-0.0223388671875,
-0.014678955078125,
0.017059326171875,
-0.0173187255859375,
0.00942230224609375,
-0.0282135009765625,
-0.00733184814453125,
-0.036773681640625,
-0.02301025390625,
0.02252197265625,
0.0168914794921875,
-0.0126800537109375,
-0.01195526123046875,
-0.01282501220703125,
0.00806427001953125,
0.0258636474609375,
-0.0038928985595703125,
0.0308380126953125,
0.01078033447265625,
0.0244140625,
0.01491546630859375,
0.010345458984375,
-0.012542724609375,
0.009735107421875,
0.01666259765625,
-0.01922607421875,
-0.0203857421875,
-0.01004791259765625,
0.00786590576171875,
0.0010013580322265625,
0.0063629150390625,
0.0012607574462890625,
0.006221771240234375,
0.0136871337890625,
0.01605224609375,
0.0246734619140625,
0.0008840560913085938,
-0.002071380615234375,
-0.00803375244140625,
-0.0299835205078125,
0.02734375,
-0.0017404556274414062,
0.004131317138671875,
-0.014007568359375,
0.0272674560546875,
-0.02593994140625,
0.0016450881958007812,
-0.04937744140625,
0.01192474365234375,
0.0222015380859375,
0.017547607421875,
-0.0025653839111328125,
0.0341796875,
-0.001842498779296875,
-0.006378173828125,
0.0111846923828125,
0.0260162353515625,
0.002964019775390625,
-0.007720947265625,
-0.0034580230712890625,
0.00418853759765625,
-0.038665771484375,
-0.036773681640625,
0.004032135009765625,
-0.0006766319274902344,
0.018768310546875,
-0.005985260009765625,
-0.0152130126953125,
-0.0009288787841796875,
0.0089263916015625,
-0.0182037353515625,
0.02435302734375,
-0.01513671875,
0.046234130859375,
0.0054473876953125,
-0.0345458984375,
-0.038482666015625,
0.0093536376953125,
0.019256591796875,
0.0272979736328125,
-0.00734710693359375,
0.00888824462890625,
-0.0267791748046875,
0.01087188720703125,
0.042755126953125,
0.0096435546875,
0.0047607421875,
-0.031585693359375,
0.0214996337890625,
0.03326416015625,
-0.0267791748046875,
0.01519775390625,
0.002552032470703125,
-0.002216339111328125,
-0.00879669189453125,
-0.0016622543334960938,
0.004425048828125,
-0.0164642333984375,
-0.00290679931640625,
-0.02496337890625,
-0.01174163818359375,
0.0058135986328125,
0.044525146484375,
-0.013702392578125,
-0.018096923828125,
-0.0249481201171875,
-0.010009765625,
-0.00107574462890625,
-0.005367279052734375,
0.0310821533203125,
-0.0300445556640625,
0.005126953125,
-0.0268402099609375,
-0.015838623046875,
0.01519775390625,
-0.0233306884765625,
-0.0047454833984375,
0.00131988525390625,
-0.02886962890625,
-0.010498046875,
-0.0267791748046875,
0.007328033447265625,
0.0242156982421875,
-0.026153564453125,
-0.01300048828125,
-0.00592803955078125,
0.0232696533203125,
0.0009832382202148438,
-0.007602691650390625,
-0.01103973388671875,
-0.02252197265625,
0.026275634765625,
0.026519775390625,
-0.01549530029296875,
0.0426025390625,
0.01739501953125,
0.05218505859375,
0.039306640625,
-0.01947021484375,
0.0073089599609375,
0.006866455078125,
0.00872039794921875,
0.01934814453125,
-0.0290069580078125,
0.006687164306640625,
0.00018715858459472656,
0.02728271484375,
0.041229248046875,
0.004764556884765625,
-0.01320648193359375,
0.04339599609375,
0.01560211181640625,
0.0172271728515625,
-0.0061187744140625,
-0.00701141357421875,
0.032135009765625,
0.03363037109375,
0.03631591796875,
0.0135498046875,
0.007587432861328125,
-0.006816864013671875,
-0.0141754150390625,
-0.0163726806640625,
0.01248931884765625,
0.007495880126953125,
-0.018829345703125,
0.0281219482421875,
0.0230865478515625,
-0.01476287841796875,
0.0032405853271484375,
0.0008535385131835938,
0.01096343994140625,
-0.0005693435668945312,
0.0010385513305664062,
-0.00420379638671875,
-0.0029544830322265625,
0.02783203125,
-0.0149383544921875,
0.0014705657958984375,
0.0224456787109375,
-0.01189422607421875,
-0.031219482421875,
0.007633209228515625,
0.041595458984375,
-0.0186767578125,
-0.0125885009765625,
0.006206512451171875,
0.003032684326171875,
0.033172607421875,
-0.0304107666015625,
-0.010589599609375,
-0.004791259765625,
0.0249481201171875,
-0.0079803466796875,
-0.0216522216796875,
0.005764007568359375,
0.00164031982421875,
0.007411956787109375,
0.03363037109375,
0.0092315673828125,
-0.00757598876953125,
0.0146484375,
-0.0175933837890625,
0.013885498046875,
-0.01094818115234375,
0.040740966796875,
-0.03546142578125,
-0.00246429443359375,
-0.031646728515625,
0.03802490234375,
-0.004238128662109375,
-0.0229644775390625,
0.023345947265625,
-0.048309326171875,
-0.0141143798828125,
-0.0292816162109375,
-0.02252197265625,
-0.004535675048828125,
0.04644775390625,
-0.00719451904296875,
-0.03057861328125,
-0.04046630859375,
-0.03857421875,
0.0399169921875,
-0.029815673828125,
-0.009307861328125,
0.02081298828125,
0.0123291015625,
0.006496429443359375,
-0.010711669921875,
-0.0455322265625,
-0.0245361328125,
0.02581787109375,
-0.01416778564453125,
0.0092620849609375,
0.0258636474609375,
-0.00250244140625,
0.0072479248046875,
0.0042724609375,
-0.004791259765625,
0.0038852691650390625,
-0.005489349365234375,
-0.01277923583984375,
-0.0006680488586425781,
0.0016508102416992188,
-0.04046630859375,
-0.025390625,
-0.0220794677734375,
0.007244110107421875,
0.0027217864990234375,
-0.0106201171875,
0.004486083984375,
-0.01541900634765625,
-0.004058837890625,
-0.002437591552734375,
0.0165557861328125,
0.0135040283203125,
-0.026580810546875,
0.0003578662872314453,
-0.0264434814453125,
0.05108642578125,
-0.0299835205078125,
0.0019283294677734375,
-0.036346435546875,
-0.04107666015625,
0.004749298095703125,
-0.02325439453125,
-0.0158843994140625,
-0.0121917724609375,
-0.0294342041015625,
-0.0202178955078125,
0.0032196044921875,
0.0024738311767578125,
-0.0195770263671875,
0.00030350685119628906,
0.01511383056640625,
-0.04730224609375,
-0.000949859619140625,
-0.002780914306640625,
-0.0247039794921875,
0.0208740234375,
-0.01502227783203125,
0.0149993896484375,
0.01087188720703125,
0.035125732421875,
0.01323699951171875,
0.00907135009765625,
-0.0080718994140625,
-0.02496337890625,
-0.0100250244140625,
-0.0007810592651367188,
0.0192718505859375,
0.014007568359375,
-0.0029773712158203125,
0.0012836456298828125,
0.03106689453125,
0.01395416259765625,
-0.0006060600280761719,
0.030792236328125,
0.0194091796875,
0.0303497314453125,
0.00751495361328125,
-0.01446533203125,
0.0269317626953125,
0.007602691650390625,
-0.0137939453125,
0.008331298828125,
-0.007678985595703125,
-0.023284912109375,
-0.0043487548828125,
0.031219482421875,
-0.0204620361328125,
0.004077911376953125,
-0.015655517578125,
0.00551605224609375,
0.00728607177734375
] |
ours_497
|
Let \( O \) be the circumcenter of \( \triangle ABC \). Key Claim: \( V = O \) and \( (U, AO \cap BC; B, C) = -1 \).
Proof of Key Claim: Perform a \(\sqrt{bc}\)-inversion. Denote the image of any point \( K \) by \( K' \). Note that \( AB \neq AC \) and \( \angle BAC \neq 90^\circ \). Let \( \ell \) be the perpendicular bisector of \( BC \), and let \( m \) be the line through \( A \) parallel to \( BC \). Now \( W' = m \cap (ABC) \). The image of \( (AXY) \) becomes the perpendicular bisector of \( AW' \), which is \( \ell \). Thus \( X' = AB \cap \ell \) and \( Y' = AC \cap \ell \). Now \( X_1' \) is the foot of the perpendicular from \( X' \) to \( AC \), and \( X_2' \) is the foot of the perpendicular from \( X_1' \) to \( AB \). Similarly, \( Y_1' \) is the foot of the perpendicular from \( Y' \) to \( AB \), and \( Y_2' \) is the foot of the perpendicular from \( Y_1' \) to \( AC \). Now \( Z' = (AX'Y') \cap m \). Also, note that \( P = (AX_1X_2) \cap (AY_1Y_2) \). Then \( P' = X_1'X_2' \cap Y_1'Y_2' \).
Let \( S = AO \cap BC \), and let \( T \) be on \( BC \) such that \( (T, S; B, C) = -1 \). We want \( V = O \) and \( U = T \); i.e., we want \( Z, P, O, T \) collinear. Thus we need \( A, Z', P', O', T' \) concyclic.
Let \( R = X'X_1' \cap Y'Y_1' \). Let \( M \) be the midpoint of \( BC \). Let \( R_1 \) be the reflection of \( R \) over \( M \). Let \( \gamma \) be the circle with diameter \( AR_1 \). I claim that \( A, Z', P', O', T' \) all lie on \( \gamma \).
Note that \( R \) is the orthocenter of \( \triangle AX'Y' \). Also, note that \( Z' \) is the intersection of the \( A \)-altitude and the circumcircle of \( \triangle AX'Y' \). Then \( R \) and \( Z' \) are reflections of one another over \( \ell \); then \( Z'R_1 \) is parallel to \( \ell \), so \( Z'R_1 \perp BC \). Also, \( R, A, Z' \) all lie on \( m \). Thus \( AZ' \| BC \). Thus \( AZ' \perp Z'R_1 \), so \( Z' \) lies on \( \gamma \).
Note that quadrilaterals \( CMX'X_1' \) and \( BMY'Y_1' \) are cyclic. Thus \( M, X_1', Y_1' \) are collinear. Note that \( RX_1'P'Y_1' \) is a parallelogram. Then the midpoints of \( RP' \) and \( RR_1 \) both lie on line \( X_1'Y_1' \). Thus lines \( P'R_1 \) and \( X_1'Y_1' \) are parallel or coincide. Also, \( P' \) is the orthocenter of \( \triangle AX_1'Y_1' \), so \( AP' \perp X_1'Y_1' \). Thus \( AP' \perp P'R_1 \), so \( P' \) lies on \( \gamma \).
Note that \( O' \) is the reflection of \( A \) over \( BC \). Let \( n \) be the reflection of \( m \) over \( BC \). Now \( AO' \) is perpendicular to \( BC \), while \( O' \) and \( R_1 \) both lie on \( n \), which is parallel to \( BC \). Then \( O' \) lies on \( \gamma \).
Let \( H \) be the orthocenter of \( \triangle ABC \). Consider complete quadrilateral \( ABCMX'Y' \). Then \( H \), which is the orthocenter of \( \triangle ABC \), \( M \), which is the orthocenter of \( \triangle X'MB \), and \( R \), which is the orthocenter of \( \triangle AX'Y' \), all lie on the Steiner line of this complete quadrilateral. Thus \( H, M, R \) are collinear.
Now, in \( \triangle ABC \), the \( A \)-altitude intersects \( (ABC) \) at \( S' \). Now \( T' \) lies on \( (ABC) \) such that \( (T', S'; B, C) = -1 \). Let \( A_1 \) be the antipode of \( A \) on \( (ABC) \). Now \( S' \neq A_1 \). Now \( S'A_1 \perp AS' \perp BC, S'A_1 \| BC \), so \( S'A_1 \cap BC = \infty \). Let \( L = T'A_1 \cap BC \). Then, projecting through \( A_1, -1 = (T', S'; B, C) = (L, \infty; B, C) \), so \( L \) is the midpoint of \( BC \). Thus \( L = M \). Thus \( T', A_1, M \) are collinear. It is well-known that \( M \) is the midpoint of \( HA_1 \). Thus \( T', A_1, H, M \) are collinear.
Now, as \( H \neq M \), we have that \( T', A_1, R \) all lie on line \( HM \). Note that \( A \) does not lie on line \( HM \), so \( T' \neq A \). Note that \( T' \neq A_1 \). If \( T' = R \), then \( T' \) lies on \( \gamma \). Otherwise, \( \measuredangle AT'R = \measuredangle AT'A_1 = 90^\circ \), so \( T' \) lies on \( \gamma \). Thus, in either case, \( T' \) lies on \( \gamma \).
Thus, \( A, Z', P', O', T' \) are concyclic. Thus \( Z, P, O, T \) are collinear. Thus the Key Claim is true.
Now \(\frac{BU}{CU} = \frac{BC}{CU} + 1 = x + 1\). Then \((U, S; B, C) = -1\); then \( S \) lies on segment \( BC \), as \( U \) lies on ray \( BC \) beyond \( C \). Then \(\frac{[ABO]}{[ACO]} = \frac{BS}{CS} = \frac{BU}{CU} = x + 1\). Now let \( M_B \) and \( M_C \) be the midpoints of \( AC \) and \( AB \), respectively. Then \([ABO] = \frac{AB \cdot OM_C}{2}\) and \([ACO] = \frac{AC \cdot OM_B}{2}\). Thus \(\frac{(x+1)OM_C}{3OM_B} = \frac{[ABO]}{[ACO]} = x + 1\). Thus \( OM_C = 3OM_B \), so \( OM_C^2 = 9OM_B^2 \). Now \( OM_C^2 = x^2 - \left(\frac{x+1}{2}\right)^2 \) and \( OM_B^2 = x^2 - \frac{9}{4} \). Thus \( x^2 - \left(\frac{x+1}{2}\right)^2 = 9\left(x^2 - \frac{9}{4}\right) \). Thus \( 3x^2 - 2x - 1 = 36x^2 - 81 \), so \( 33x^2 + 2x - 80 = 0 \). Thus, as \( x > 0 \), we get \( x = \frac{\sqrt{2641} - 1}{33} \), so the answer is \( 2641 \cdot 100 + 1 \cdot 10 + 33 = 264143 \).
\(\boxed{264143}\)
|
264143
|
{
"competition": "us_comps",
"dataset": "Ours",
"posts": null,
"source": "OMOFall19Solns-3.md"
}
|
Let \( \triangle ABC \) be a triangle. The line through \( A \) tangent to the circumcircle of \( \triangle ABC \) intersects line \( BC \) at point \( W \). Points \( X, Y \neq A \) lie on lines \( AC \) and \( AB \), respectively, such that \( WA = WX = WY \). Point \( X_1 \) lies on line \( AB \) such that \( \angle AXX_1 = 90^\circ \), and point \( X_2 \) lies on line \( AC \) such that \( \angle AX_1X_2 = 90^\circ \). Point \( Y_1 \) lies on line \( AC \) such that \( \angle AYY_1 = 90^\circ \), and point \( Y_2 \) lies on line \( AB \) such that \( \angle AY_1Y_2 = 90^\circ \). Let lines \( AW \) and \( XY \) intersect at point \( Z \), and let point \( P \) be the foot of the perpendicular from \( A \) to line \( X_2Y_2 \). Let line \( ZP \) intersect line \( BC \) at \( U \) and the perpendicular bisector of segment \( BC \) at \( V \). Suppose that \( C \) lies between \( B \) and \( U \). Let \( x \) be a positive real number. Suppose that \( AB = x+1 \), \( AC = 3 \), \( AV = x \), and \( \frac{BC}{CU} = x \). Then \( x = \frac{\sqrt{k}-m}{n} \) for positive integers \( k, m, \) and \( n \) such that \( k \) is not divisible by the square of any integer greater than 1. Compute \( 100k + 10m + n \).
|
[
"/Mathematics/Geometry/GeneralGeometry/EuclideanGeometry",
"/Mathematics/Geometry/GeneralGeometry/Geometry",
"/Mathematics/Geometry/GeometricConstruction/PerpendicularBisector",
"/Mathematics/Geometry/InversiveGeometry/Inversion",
"/Mathematics/Geometry/PlaneGeometry/Circles",
"/Mathematics/Geometry/PlaneGeometry/Triangles"
] |
Apply a √bc inversion to transform the figure so V becomes the circumcenter and A, Z', P', O', T' lie on one circle, giving a harmonic division.
|
[
-0.0002789497375488281,
-0.006443023681640625,
0.0204620361328125,
0.01155853271484375,
-0.0010747909545898438,
0.013336181640625,
0.01108551025390625,
0.0249176025390625,
-0.014556884765625,
-0.03277587890625,
0.0047149658203125,
0.0156707763671875,
-0.0107269287109375,
-0.00182342529296875,
0.0054473876953125,
-0.0094451904296875,
0.01210784912109375,
-0.015716552734375,
0.0179595947265625,
-0.001148223876953125,
-0.00208282470703125,
-0.04248046875,
-0.0540771484375,
-0.0167999267578125,
-0.01503753662109375,
0.01434326171875,
-0.00719451904296875,
0.0135650634765625,
0.00850677490234375,
0.03802490234375,
-0.00310516357421875,
-0.006191253662109375,
0.004119873046875,
-0.0284881591796875,
0.0022563934326171875,
0.0167999267578125,
-0.015472412109375,
-0.0032291412353515625,
-0.04901123046875,
-0.0252685546875,
0.01031494140625,
0.018768310546875,
-0.01253509521484375,
0.0166473388671875,
0.0263214111328125,
0.003665924072265625,
-0.0018482208251953125,
0.0229949951171875,
-0.0024242401123046875,
0.015869140625,
0.005664825439453125,
0.0158233642578125,
-0.0301971435546875,
-0.01593017578125,
-0.02996826171875,
-0.046417236328125,
-0.032196044921875,
-0.00591278076171875,
-0.0104217529296875,
0.020782470703125,
0.0019474029541015625,
-0.0007700920104980469,
0.005054473876953125,
-0.0212249755859375,
0.0002875328063964844,
-0.006977081298828125,
-0.006916046142578125,
-0.0217437744140625,
0.004833221435546875,
-0.00278472900390625,
0.0305328369140625,
-0.01537322998046875,
0.006328582763671875,
0.031646728515625,
0.01230621337890625,
-0.001667022705078125,
-0.00921630859375,
0.00734710693359375,
0.0150299072265625,
0.00494384765625,
0.002620697021484375,
0.0028667449951171875,
0.0038089752197265625,
-0.0560302734375,
0.0021457672119140625,
-0.008575439453125,
-0.04852294921875,
0.01503753662109375,
0.044891357421875,
-0.0361328125,
-0.004486083984375,
0.0018739700317382812,
-0.0240020751953125,
-0.014678955078125,
0.01178741455078125,
0.00971221923828125,
0.0236053466796875,
0.002384185791015625,
-0.0231475830078125,
-0.0022068023681640625,
-0.01904296875,
-0.0006108283996582031,
-0.004932403564453125,
-0.01352691650390625,
-0.01611328125,
-0.010162353515625,
-0.016265869140625,
0.00787353515625,
0.002414703369140625,
0.0002269744873046875,
0.0005431175231933594,
-0.0188751220703125,
0.034912109375,
-0.004825592041015625,
0.0160675048828125,
-0.004779815673828125,
0.02337646484375,
0.0257415771484375,
-0.014404296875,
0.0218048095703125,
-0.005336761474609375,
0.0126190185546875,
-0.0021610260009765625,
0.0286865234375,
0.007190704345703125,
-0.0140533447265625,
0.004619598388671875,
-0.01038360595703125,
-0.034088134765625,
-0.007740020751953125,
-0.006389617919921875,
0.00579071044921875,
-0.05206298828125,
-0.00909423828125,
-0.05645751953125,
0.01079559326171875,
-0.0016584396362304688,
-0.005252838134765625,
-0.0111236572265625,
-0.01345062255859375,
-0.0016374588012695312,
-0.006305694580078125,
0.004791259765625,
-0.06280517578125,
0.01142120361328125,
-0.05670166015625,
0.01108551025390625,
-0.0019044876098632812,
-0.00566864013671875,
0.010955810546875,
-0.00275421142578125,
-0.0046234130859375,
0.00909423828125,
-0.006481170654296875,
-0.005950927734375,
-0.0009183883666992188,
0.00615692138671875,
0.01387786865234375,
0.0268402099609375,
-0.0007405281066894531,
-0.00601959228515625,
-0.016021728515625,
-0.0010156631469726562,
-0.017364501953125,
-0.0139617919921875,
-0.0126190185546875,
-0.0148162841796875,
-0.0095977783203125,
-0.0229034423828125,
-0.01464080810546875,
-0.004329681396484375,
0.0151214599609375,
-0.002788543701171875,
-0.0115203857421875,
-0.0077667236328125,
0.0082244873046875,
-0.01849365234375,
0.0036602020263671875,
-0.0217132568359375,
0.0216522216796875,
0.0027751922607421875,
-0.0192413330078125,
0.0025787353515625,
0.011810302734375,
0.0110626220703125,
0.0119781494140625,
0.004669189453125,
0.007221221923828125,
0.0101776123046875,
0.0086517333984375,
-0.01393890380859375,
-0.0163726806640625,
-0.0137786865234375,
-0.00954437255859375,
-0.0018444061279296875,
-0.01355743408203125,
-0.04132080078125,
0.004962921142578125,
-0.00396728515625,
0.020721435546875,
-0.0008082389831542969,
-0.01522064208984375,
0.01197052001953125,
0.00926971435546875,
-0.014404296875,
0.0029201507568359375,
0.01509857177734375,
-0.014739990234375,
-0.0156402587890625,
0.0223388671875,
-0.0013217926025390625,
0.014312744140625,
-0.01006317138671875,
-0.02081298828125,
-0.015838623046875,
0.0023555755615234375,
-0.026031494140625,
0.01465606689453125,
-0.00461578369140625,
0.005096435546875,
0.01666259765625,
0.003307342529296875,
0.01096343994140625,
-0.0171051025390625,
-0.0072784423828125,
0.027130126953125,
-0.0133056640625,
-0.029693603515625,
0.0146942138671875,
0.004581451416015625,
-0.00583648681640625,
-0.0004305839538574219,
-0.018707275390625,
-0.0003275871276855469,
-0.007518768310546875,
0.00560760498046875,
-0.024444580078125,
-0.0007071495056152344,
0.0025634765625,
-0.0015745162963867188,
0.0249481201171875,
-0.0115814208984375,
0.0111236572265625,
0.012908935546875,
0.024261474609375,
-0.0109710693359375,
0.01079559326171875,
-0.021240234375,
0.010986328125,
0.0010166168212890625,
-0.01788330078125,
0.0158843994140625,
0.006381988525390625,
-0.02020263671875,
-0.0211639404296875,
0.00733184814453125,
0.002490997314453125,
-0.015380859375,
-0.01343536376953125,
0.006145477294921875,
-0.0063934326171875,
0.0057525634765625,
-0.005893707275390625,
-0.02294921875,
-0.01493072509765625,
0.039276123046875,
0.012115478515625,
-0.00751495361328125,
0.01354217529296875,
-0.0011034011840820312,
0.050872802734375,
-0.01052093505859375,
0.003147125244140625,
0.01363372802734375,
0.00146484375,
-0.0126953125,
-0.004764556884765625,
0.020599365234375,
0.001712799072265625,
0.0174713134765625,
0.00568389892578125,
-0.03387451171875,
-0.0239715576171875,
0.0039005279541015625,
-0.003971099853515625,
-0.0264739990234375,
0.01105499267578125,
-0.03826904296875,
0.004726409912109375,
0.0162506103515625,
-0.00223541259765625,
-0.0226287841796875,
-0.015655517578125,
-0.0187835693359375,
0.06378173828125,
-0.003208160400390625,
0.0013952255249023438,
0.0219268798828125,
0.007015228271484375,
0.009765625,
0.04571533203125,
-0.024322509765625,
0.0172576904296875,
0.0149993896484375,
0.044677734375,
0.0302886962890625,
0.00786590576171875,
0.01318359375,
-0.0265960693359375,
0.0226898193359375,
0.00954437255859375,
-0.0046234130859375,
-0.0132598876953125,
-0.00617218017578125,
-0.047760009765625,
-0.02044677734375,
-0.002361297607421875,
0.007904052734375,
-0.0156402587890625,
0.036102294921875,
0.01207733154296875,
0.02056884765625,
0.053680419921875,
0.01134490966796875,
0.0457763671875,
-0.02252197265625,
-0.0006437301635742188,
0.020599365234375,
0.0239715576171875,
0.02801513671875,
-0.01323699951171875,
0.01507568359375,
0.00849151611328125,
-0.00009047985076904297,
0.026092529296875,
0.0017881393432617188,
0.0033321380615234375,
0.00949859619140625,
-0.005096435546875,
-0.007404327392578125,
0.01708984375,
0.012420654296875,
0.01175689697265625,
-0.062103271484375,
-0.0181427001953125,
0.011260986328125,
-0.0180816650390625,
-0.003902435302734375,
-0.00994110107421875,
-0.0235595703125,
0.0205535888671875,
0.01520538330078125,
0.0019397735595703125,
0.0005788803100585938,
-0.0083770751953125,
-0.0010957717895507812,
-0.0118408203125,
0.023651123046875,
-0.006069183349609375,
0.0164794921875,
0.0166015625,
-0.03729248046875,
-0.00403594970703125,
0.01499176025390625,
-0.01265716552734375,
-0.00919342041015625,
-0.0161590576171875,
0.01355743408203125,
-0.05767822265625,
0.003814697265625,
-0.014984130859375,
-0.0033721923828125,
0.001514434814453125,
0.007747650146484375,
0.044677734375,
0.0227508544921875,
0.002017974853515625,
0.010589599609375,
-0.006961822509765625,
0.00196075439453125,
0.003276824951171875,
-0.02679443359375,
0.0007510185241699219,
0.028594970703125,
-0.020477294921875,
-0.006603240966796875,
0.00733184814453125,
-0.025970458984375,
0.004062652587890625,
0.007472991943359375,
0.0046844482421875,
0.004444122314453125,
-0.0008482933044433594,
-0.00017571449279785156,
-0.038848876953125,
-0.0005559921264648438,
-0.005645751953125,
0.0065765380859375,
0.0234527587890625,
-0.0173492431640625,
-0.0394287109375,
-0.01062774658203125,
-0.01181793212890625,
-0.00809478759765625,
0.0225677490234375,
-0.003215789794921875,
-0.0196075439453125,
0.0202178955078125,
0.005153656005859375,
0.0014820098876953125,
0.011199951171875,
-0.0279541015625,
-0.0158843994140625,
-0.01424407958984375,
-0.00519561767578125,
0.00342559814453125,
0.00023066997528076172,
0.0005731582641601562,
0.019500732421875,
-0.0261077880859375,
0.0241851806640625,
-0.0224456787109375,
0.0226898193359375,
-0.0182952880859375,
0.032318115234375,
0.0219268798828125,
-0.00981903076171875,
0.0276031494140625,
-0.006702423095703125,
-0.035003662109375,
0.02557373046875,
-0.00091552734375,
-0.0006895065307617188,
-0.006458282470703125,
-0.005001068115234375,
-0.01312255859375,
0.0192413330078125,
0.0008025169372558594,
0.01444244384765625,
0.0243988037109375,
-0.0174102783203125,
-0.0035400390625,
-0.0062103271484375,
0.01509857177734375,
0.006893157958984375,
-0.003887176513671875,
0.006195068359375,
0.0030879974365234375,
0.0107269287109375,
0.0189971923828125,
0.00405120849609375,
-0.004131317138671875,
0.0059051513671875,
-0.039276123046875,
-0.01045989990234375,
0.0205078125,
0.0428466796875,
-0.035064697265625,
-0.0188751220703125,
0.04534912109375,
-0.02789306640625,
-0.0196380615234375,
-0.0070037841796875,
-0.0015573501586914062,
-0.01224517822265625,
-0.0094757080078125,
-0.004596710205078125,
0.02001953125,
-0.00016880035400390625,
-0.0218963623046875,
0.003490447998046875,
-0.030364990234375,
-0.026123046875,
-0.025146484375,
-0.0364990234375,
0.0274810791015625,
0.0156097412109375,
0.0183868408203125,
-0.003963470458984375,
0.03619384765625,
0.01535797119140625,
-0.032196044921875,
-0.01873779296875,
0.00557708740234375,
0.005184173583984375,
0.03155517578125,
0.0347900390625,
-0.0003662109375,
-0.02716064453125,
-0.02899169921875,
0.0218658447265625,
0.0258331298828125,
-0.0223236083984375,
-0.0216827392578125,
-0.046417236328125,
-0.025054931640625,
0.0195159912109375,
-0.00038743019104003906,
0.00356292724609375,
-0.00018990039825439453,
0.022003173828125,
-0.0112457275390625,
0.0162353515625,
0.01824951171875,
0.00492095947265625,
-0.041595458984375,
0.03375244140625,
0.0015630722045898438,
-0.0008525848388671875,
0.012420654296875,
0.0231475830078125,
0.01302337646484375,
0.015716552734375,
-0.034576416015625,
0.03900146484375,
0.019866943359375,
-0.00888824462890625,
-0.025054931640625,
0.0136566162109375,
0.060882568359375,
-0.0122833251953125,
0.037384033203125,
0.00217437744140625,
-0.0091400146484375,
0.0250701904296875,
0.0134735107421875,
0.00902557373046875,
-0.0014295578002929688,
0.0228271484375,
0.0004372596740722656,
-0.01110076904296875,
-0.0166015625,
-0.043609619140625,
0.033050537109375,
-0.015167236328125,
0.0114288330078125,
-0.0126800537109375,
-0.023101806640625,
0.0035037994384765625,
-0.0043487548828125,
-0.031768798828125,
-0.00428009033203125,
-0.0116424560546875,
-0.033416748046875,
-0.002346038818359375,
-0.00043201446533203125,
-0.0178985595703125,
0.01497650146484375,
-0.00231170654296875,
0.0113067626953125,
0.0018396377563476562,
0.0161285400390625,
-0.001995086669921875,
0.0233917236328125,
-0.05682373046875,
0.0009493827819824219,
-0.0229949951171875,
-0.007537841796875,
0.00731658935546875,
0.0372314453125,
0.035980224609375,
0.0086212158203125,
0.032501220703125,
-0.01538848876953125,
0.00489044189453125,
0.003429412841796875,
0.04168701171875,
-0.030517578125,
-0.0220947265625,
-0.04156494140625,
-0.00370025634765625,
-0.022491455078125,
-0.015106201171875,
0.00734710693359375,
0.047698974609375,
-0.0169830322265625,
-0.010589599609375,
0.009857177734375,
-0.01520538330078125,
-0.007965087890625,
0.036529541015625,
0.05926513671875,
-0.0202789306640625,
-0.0209197998046875,
0.002361297607421875,
-0.0074920654296875,
-0.0019588470458984375,
-0.0097503662109375,
0.0008945465087890625,
-0.027618408203125,
0.0015954971313476562,
0.042144775390625,
0.033050537109375,
-0.0174102783203125,
0.005615234375,
-0.02374267578125,
0.03314208984375,
-0.0108642578125,
0.021331787109375,
0.01611328125,
0.0147857666015625,
-0.0033664703369140625,
-0.006256103515625,
0.004947662353515625,
-0.048004150390625,
0.0222015380859375,
-0.055389404296875,
0.0312347412109375,
0.01494598388671875,
0.0079498291015625,
0.0054779052734375,
-0.0030364990234375,
-0.01285552978515625,
0.009307861328125,
0.00614166259765625,
0.00836181640625,
-0.0177764892578125,
0.0026454925537109375,
-0.00717926025390625,
0.007610321044921875,
0.0017852783203125,
0.001537322998046875,
0.00800323486328125,
0.03997802734375,
-0.003948211669921875,
0.00481414794921875,
0.0100555419921875,
-0.004573822021484375,
0.01010894775390625,
-0.0360107421875,
-0.012603759765625,
-0.0259857177734375,
-0.002887725830078125,
0.01165008544921875,
-0.035491943359375,
-0.0050048828125,
0.00835418701171875,
0.0214080810546875,
-0.00824737548828125,
-0.02203369140625,
0.021331787109375,
0.0106964111328125,
0.02325439453125,
-0.04266357421875,
-0.0120697021484375,
-0.004947662353515625,
0.006702423095703125,
-0.025054931640625,
-0.0185699462890625,
0.014892578125,
-0.0009984970092773438,
-0.0101165771484375,
0.0015468597412109375,
0.022216796875,
0.016754150390625,
0.0074005126953125,
-0.022491455078125,
-0.03485107421875,
0.03564453125,
0.020751953125,
0.0116424560546875,
-0.0015573501586914062,
-0.0007290840148925781,
-0.00708770751953125,
0.0176544189453125,
0.00676727294921875,
-0.043548583984375,
-0.014892578125,
0.00701141357421875,
0.0474853515625,
-0.008331298828125,
0.00383758544921875,
0.005889892578125,
0.00292205810546875,
-0.00904083251953125,
0.0198211669921875,
-0.02935791015625,
0.03936767578125,
0.0106201171875,
-0.0170135498046875,
0.02972412109375,
0.01385498046875,
0.0192108154296875,
-0.00909423828125,
-0.0006823539733886719,
0.0285797119140625,
0.0184173583984375,
-0.011932373046875,
0.01922607421875,
-0.0187225341796875,
-0.013885498046875,
0.030426025390625,
-0.043914794921875,
0.01151275634765625,
-0.01236724853515625,
0.035430908203125,
0.0279541015625,
0.016693115234375,
-0.00739288330078125,
-0.0189361572265625,
0.016998291015625,
-0.01593017578125,
0.004512786865234375,
-0.023712158203125,
-0.01386260986328125,
-0.00910186767578125,
-0.0003421306610107422,
0.03253173828125,
-0.06793212890625,
-0.01378631591796875,
-0.048095703125,
-0.012786865234375,
-0.014251708984375,
0.0086822509765625,
-0.01708984375,
-0.0259857177734375,
-0.0104217529296875,
-0.005847930908203125,
-0.012115478515625,
0.0214996337890625,
0.02020263671875,
-0.0104522705078125,
-0.0108184814453125,
-0.02960205078125,
0.0293731689453125,
0.01020050048828125,
-0.0204620361328125,
-0.01081085205078125,
0.0084228515625,
0.0203857421875,
0.0036602020263671875,
-0.00833892822265625,
0.033782958984375,
0.004669189453125,
0.0032520294189453125,
-0.003185272216796875,
0.00131988525390625,
-0.057708740234375,
0.005519866943359375,
0.00423431396484375,
0.05999755859375,
-0.015960693359375,
0.005229949951171875,
-0.006046295166015625,
-0.008056640625,
0.0012788772583007812,
0.004886627197265625,
-0.0221405029296875,
0.0272216796875,
0.01515960693359375,
0.0140838623046875,
0.0007443428039550781,
-0.022430419921875,
0.004116058349609375,
-0.01000213623046875,
-0.000037610530853271484,
-0.0155792236328125,
-0.008209228515625,
0.004180908203125,
0.0133056640625,
-0.02655029296875,
0.00897216796875,
0.0191802978515625,
0.007656097412109375,
-0.00217437744140625,
-0.0004563331604003906,
-0.0283966064453125,
-0.0004987716674804688,
-0.025634765625,
0.010955810546875,
0.02813720703125,
0.0005002021789550781,
-0.004901885986328125,
-0.0306243896484375,
0.0082244873046875,
0.0153045654296875,
-0.023223876953125,
-0.006580352783203125,
0.033355712890625,
-0.005901336669921875,
0.0029048919677734375,
-0.0018033981323242188,
-0.01751708984375,
0.037994384765625,
-0.036529541015625,
0.0030345916748046875,
-0.0172882080078125,
-0.001003265380859375,
0.018524169921875,
-0.01105499267578125,
0.01275634765625,
0.00917816162109375,
0.00859832763671875,
-0.0055999755859375,
-0.01898193359375,
-0.022186279296875,
0.0002968311309814453,
-0.0025348663330078125,
-0.01220703125,
-0.0179290771484375,
0.00850677490234375,
-0.005306243896484375,
-0.0012235641479492188,
-0.01593017578125,
0.04644775390625,
0.00592041015625,
0.01934814453125,
-0.004581451416015625,
-0.01042938232421875,
-0.006565093994140625,
-0.0149383544921875,
-0.0012035369873046875,
0.0096435546875,
0.0064697265625,
-0.0294036865234375,
-0.0302734375,
0.0129241943359375,
-0.01396942138671875,
0.01788330078125,
-0.00855255126953125,
-0.041900634765625,
-0.00036716461181640625,
-0.006381988525390625,
-0.00836944580078125,
-0.0264129638671875,
-0.001873016357421875,
-0.01399993896484375,
0.0018548965454101562,
0.01580810546875,
0.00044608116149902344,
-0.004543304443359375,
-0.031341552734375,
-0.0308990478515625,
-0.0304412841796875,
-0.0177001953125,
0.0323486328125,
-0.0243988037109375,
-0.007171630859375,
-0.0260772705078125,
-0.0110626220703125,
0.006450653076171875,
-0.01166534423828125,
0.006160736083984375,
-0.0004858970642089844,
0.004016876220703125,
-0.03387451171875,
-0.0298309326171875,
0.030303955078125,
0.0193939208984375,
0.00937652587890625,
-0.019561767578125,
0.009918212890625,
-0.0224609375,
0.01010894775390625,
-0.0118255615234375,
0.0018215179443359375,
0.008697509765625,
0.0160675048828125,
0.0169219970703125,
0.01593017578125,
0.0084686279296875,
-0.0010890960693359375,
0.00305938720703125,
0.038177490234375,
0.022705078125,
0.007160186767578125,
-0.004917144775390625,
-0.024078369140625,
0.0504150390625,
-0.0094757080078125,
0.0105438232421875,
-0.0286102294921875,
-0.005924224853515625,
-0.00030994415283203125,
0.041839599609375,
0.017852783203125,
0.007190704345703125,
0.0160675048828125,
0.06219482421875,
0.01413726806640625,
0.0152740478515625,
-0.018890380859375,
0.0112762451171875,
-0.02911376953125,
0.008819580078125,
-0.0022907257080078125,
0.004352569580078125,
0.02093505859375,
0.002185821533203125,
-0.0030803680419921875,
0.01517486572265625,
-0.043060302734375,
-0.0004417896270751953,
-0.0399169921875,
0.036407470703125,
0.0206756591796875,
-0.01708984375,
-0.02069091796875,
0.0160369873046875,
-0.039398193359375,
0.01020050048828125,
-0.0228729248046875,
0.0276336669921875,
-0.0079803466796875,
-0.0183258056640625,
-0.0201263427734375,
0.010498046875,
-0.019927978515625,
0.01172637939453125,
0.044158935546875,
0.0017633438110351562,
0.0027751922607421875,
-0.0007753372192382812,
0.02569580078125,
-0.0159912109375,
-0.0014553070068359375,
-0.03155517578125,
-0.00482940673828125,
-0.01812744140625,
0.0245819091796875,
-0.01503753662109375,
0.0010042190551757812,
-0.0102996826171875,
0.0017185211181640625,
-0.0001518726348876953,
-0.0279998779296875,
0.01788330078125,
0.0051116943359375,
-0.0155792236328125,
0.005512237548828125,
-0.0251922607421875,
0.030029296875,
-0.0159149169921875,
-0.012603759765625,
-0.02642822265625,
-0.0035266876220703125,
-0.0206756591796875,
-0.01213836669921875,
0.0164794921875,
-0.0172576904296875,
0.0078582763671875,
0.0172271728515625,
0.0090179443359375,
0.00849151611328125,
-0.00365447998046875,
0.006805419921875,
0.0184173583984375,
0.0111083984375,
0.01239776611328125,
-0.0027923583984375,
0.00334930419921875,
-0.003429412841796875,
0.0291290283203125,
0.00736236572265625,
0.0018072128295898438,
-0.0189666748046875,
-0.0177459716796875,
0.0222320556640625,
0.004741668701171875,
0.0031909942626953125,
0.02655029296875,
0.030548095703125,
0.0122528076171875,
0.004695892333984375,
-0.005706787109375,
-0.002101898193359375,
0.0113372802734375,
0.032257080078125,
-0.009490966796875,
0.01035308837890625,
0.01274871826171875,
-0.00044655799865722656,
-0.01702880859375,
-0.026519775390625,
0.0036163330078125,
-0.005481719970703125,
0.01739501953125,
0.0231170654296875,
0.0211181640625,
0.0020656585693359375,
-0.04302978515625,
0.0032062530517578125,
0.0016069412231445312,
0.0010404586791992188,
0.0002263784408569336,
0.0161285400390625,
0.028839111328125,
0.00133514404296875,
0.07000732421875,
-0.00444793701171875,
0.01248931884765625,
0.004230499267578125,
-0.0009093284606933594,
0.0290069580078125,
0.00269317626953125,
0.0230560302734375,
0.0136871337890625,
-0.031829833984375,
-0.0073699951171875,
-0.044708251953125,
-0.020233154296875,
-0.01558685302734375,
0.038818359375,
0.0080413818359375,
-0.00907135009765625,
-0.016937255859375,
-0.0254364013671875,
0.007480621337890625,
-0.005771636962890625,
0.002590179443359375,
-0.0209808349609375,
0.0117950439453125,
-0.00009149312973022461,
0.02813720703125,
-0.0225677490234375,
0.01509857177734375,
0.01224517822265625,
0.007709503173828125,
-0.041748046875,
0.0184783935546875,
-0.00001913309097290039,
-0.012786865234375,
-0.03179931640625,
-0.0546875,
0.0307159423828125,
-0.0148468017578125,
-0.019805908203125,
-0.0210418701171875,
0.0155792236328125,
0.01024627685546875,
-0.02825927734375,
0.0064239501953125,
-0.03155517578125,
-0.0299835205078125,
0.005626678466796875,
-0.001819610595703125,
-0.01800537109375,
-0.0214080810546875,
0.03253173828125,
0.0175323486328125,
-0.012725830078125,
0.026580810546875,
-0.01155853271484375,
-0.0305023193359375,
-0.037872314453125,
-0.00995635986328125,
0.0025634765625,
-0.01403045654296875,
-0.00836181640625,
0.0163116455078125,
0.018798828125,
0.0018434524536132812,
-0.0033740997314453125,
-0.0051116943359375,
-0.010650634765625,
0.0304718017578125,
-0.01763916015625,
-0.00916290283203125,
-0.00803375244140625,
0.00864410400390625,
0.0174407958984375,
-0.025726318359375,
-0.00865936279296875,
-0.0213165283203125,
0.01375579833984375,
-0.0270233154296875,
-0.01039886474609375,
0.00482177734375,
0.0024280548095703125,
0.02398681640625,
-0.049041748046875,
-0.009918212890625,
-0.0147857666015625,
-0.0120849609375,
0.01335906982421875,
-0.01113128662109375,
-0.005523681640625,
-0.0027027130126953125,
0.00939178466796875,
-0.0055694580078125,
0.01039886474609375,
-0.00850677490234375,
-0.050994873046875,
0.0198822021484375,
0.014373779296875,
0.0185699462890625,
-0.01497650146484375,
-0.0285186767578125,
0.004634857177734375,
0.006496429443359375,
0.00588226318359375,
-0.00528717041015625,
0.01332855224609375,
-0.005664825439453125,
0.01326751708984375,
-0.00868988037109375,
0.005290985107421875,
0.018798828125,
0.0267486572265625,
0.013336181640625,
0.0252532958984375,
0.03192138671875,
0.050384521484375,
-0.0023097991943359375,
0.0034351348876953125,
-0.038116455078125,
0.0013017654418945312,
0.0335693359375,
-0.0037288665771484375,
0.00440216064453125,
-0.013336181640625,
0.0092620849609375,
0.018798828125,
0.0172271728515625,
-0.002056121826171875,
0.006641387939453125,
-0.02655029296875,
-0.006931304931640625,
-0.01125335693359375,
-0.0175323486328125,
0.0246734619140625,
-0.0010089874267578125,
0.00185394287109375,
0.0198211669921875,
0.006603240966796875,
-0.0132598876953125,
-0.00038433074951171875,
-0.0023670196533203125,
-0.0526123046875,
0.001316070556640625,
-0.0161590576171875,
0.01342010498046875,
-0.01538848876953125,
-0.042755126953125,
-0.00008749961853027344,
0.0205230712890625,
0.0234222412109375,
-0.0019054412841796875,
0.0010175704956054688,
-0.00879669189453125,
-0.0032196044921875,
-0.00545501708984375,
0.0019159317016601562,
0.01273345947265625,
-0.034393310546875,
-0.01227569580078125,
-0.0011739730834960938,
-0.0015964508056640625,
0.020477294921875,
0.0251007080078125,
-0.0307159423828125,
-0.006313323974609375,
0.004100799560546875,
0.013641357421875,
0.01340484619140625,
-0.0036163330078125,
-0.03619384765625,
-0.00048351287841796875,
0.04083251953125,
-0.0005078315734863281,
-0.0101318359375,
-0.022369384765625,
0.0114288330078125,
0.00417327880859375,
-0.0111541748046875,
0.0122222900390625,
-0.0234832763671875,
0.01377105712890625,
-0.0163726806640625,
0.041107177734375,
0.017578125,
-0.0034084320068359375,
0.01015472412109375,
0.004734039306640625,
0.0033721923828125,
0.006992340087890625,
0.03082275390625,
-0.037567138671875,
0.0019512176513671875,
0.009002685546875,
-0.0543212890625,
0.0129547119140625,
0.0222320556640625,
-0.0025310516357421875,
-0.00397491455078125,
-0.01523590087890625,
-0.007534027099609375,
0.0162506103515625,
-0.0233001708984375,
-0.01146697998046875,
0.0009093284606933594,
0.004787445068359375,
-0.0312347412109375,
0.00490570068359375,
0.00592803955078125,
0.0369873046875,
-0.0196685791015625,
-0.0361328125,
-0.02032470703125,
-0.004573822021484375,
-0.0025272369384765625,
-0.01015472412109375,
-0.021484375,
-0.0152130126953125,
0.020751953125,
-0.004680633544921875,
0.01094818115234375,
0.02459716796875,
0.007335662841796875,
0.03570556640625,
-0.00502777099609375,
-0.0158843994140625,
0.0128936767578125,
-0.006351470947265625,
0.01104736328125,
-0.01245880126953125,
0.0089569091796875,
0.0055694580078125,
-0.018707275390625,
0.003269195556640625,
0.01214599609375,
0.034088134765625,
-0.00815582275390625,
-0.006778717041015625,
-0.035186767578125,
-0.0021533966064453125,
0.0011310577392578125,
0.058074951171875,
0.00328826904296875,
0.0382080078125,
0.0296630859375,
0.0391845703125,
-0.029022216796875,
0.01107025146484375,
-0.0143585205078125,
-0.006900787353515625,
-0.007183074951171875,
0.0386962890625,
-0.0258636474609375,
0.0360107421875,
-0.006809234619140625,
0.0014886856079101562,
-0.01416778564453125,
-0.0238189697265625,
0.037261962890625,
-0.0260009765625,
-0.039459228515625,
0.0019130706787109375,
-0.043121337890625,
0.020660400390625,
0.0023040771484375,
0.05706787109375,
-0.014556884765625,
-0.027801513671875,
-0.0159912109375,
0.0009407997131347656,
-0.01074981689453125,
0.019561767578125,
0.002536773681640625,
-0.0025653839111328125,
-0.0025234222412109375,
0.0007429122924804688,
-0.005504608154296875,
-0.025482177734375,
0.01568603515625,
-0.005435943603515625,
0.00289154052734375,
0.0465087890625,
0.01435089111328125,
-0.002437591552734375,
0.015533447265625,
0.0233306884765625,
-0.006809234619140625,
0.0062255859375,
0.0173187255859375,
0.00807952880859375,
-0.020172119140625,
-0.037689208984375,
-0.0039825439453125,
0.006679534912109375,
-0.0014410018920898438,
-0.011962890625,
0.046142578125,
-0.005901336669921875,
-0.03118896484375,
-0.0279693603515625,
-0.01922607421875,
0.040618896484375,
0.0374755859375,
-0.007411956787109375,
0.0287628173828125,
0.03973388671875,
-0.00543212890625,
0.03753662109375,
-0.009765625,
0.007068634033203125,
-0.031036376953125,
0.033294677734375,
0.025543212890625,
-0.0108489990234375,
-0.007808685302734375,
-0.02532958984375,
0.00763702392578125,
0.0035991668701171875,
0.001964569091796875,
-0.0396728515625,
-0.0010728836059570312,
0.0027256011962890625,
0.02020263671875,
-0.004608154296875,
0.0273895263671875,
-0.0097198486328125,
0.005428314208984375,
0.00777435302734375,
0.02166748046875,
0.0206146240234375,
0.0156707763671875,
-0.012603759765625,
0.0149383544921875,
-0.003467559814453125,
0.0340576171875,
0.019287109375,
-0.029144287109375,
-0.0271759033203125,
-0.007503509521484375,
0.0126190185546875,
-0.00313568115234375,
-0.01480865478515625,
-0.040252685546875,
-0.03997802734375,
0.00867462158203125,
-0.0106964111328125,
-0.00493621826171875,
0.03167724609375,
0.00020396709442138672,
0.02410888671875,
0.0243377685546875,
0.01513671875,
-0.002288818359375,
-0.02392578125,
0.003513336181640625,
0.01165771484375,
-0.018035888671875,
0.005756378173828125,
0.0243682861328125,
-0.003055572509765625,
-0.05645751953125,
0.002986907958984375,
-0.0112457275390625,
-0.0149993896484375,
0.0350341796875,
0.0094757080078125,
0.000028014183044433594,
0.04058837890625,
-0.034698486328125,
0.0179290771484375,
-0.00807952880859375,
0.0285491943359375,
0.01290130615234375,
0.008819580078125,
0.0006995201110839844,
-0.0076904296875,
0.002140045166015625,
0.0022640228271484375,
0.03302001953125,
0.012420654296875,
-0.01983642578125,
-0.027130126953125,
-0.035736083984375,
-0.02386474609375,
-0.00994110107421875,
-0.002685546875,
0.00475311279296875,
-0.033935546875,
-0.005035400390625,
-0.0021343231201171875,
-0.00922393798828125,
0.00522613525390625,
0.00519561767578125,
0.006252288818359375,
0.0064697265625,
0.005809783935546875,
-0.0015773773193359375,
-0.045745849609375,
0.0298919677734375,
0.0170135498046875,
-0.00344085693359375,
-0.01529693603515625,
0.004581451416015625,
0.00208282470703125,
0.0225830078125,
-0.0015344619750976562,
0.01230621337890625,
-0.00347900390625,
0.0222320556640625,
0.01039886474609375,
0.0112152099609375,
0.0166778564453125,
-0.0192413330078125,
0.002773284912109375,
0.01519775390625,
0.00046515464782714844,
-0.0005764961242675781,
0.009490966796875,
0.020355224609375,
0.0102691650390625,
0.005718231201171875,
-0.01177978515625,
0.0103759765625,
0.0021915435791015625,
-0.00927734375,
0.00550079345703125,
-0.0153350830078125,
-0.00504302978515625,
-0.0117034912109375,
-0.0286407470703125,
0.006317138671875,
0.0061798095703125,
-0.044525146484375,
-0.0016965866088867188,
0.01459503173828125,
0.037078857421875,
-0.0192108154296875,
0.007598876953125,
0.014678955078125,
-0.0042266845703125,
0.01251983642578125,
-0.003170013427734375,
-0.0270843505859375,
0.0014944076538085938,
0.0021381378173828125,
-0.004878997802734375,
-0.005825042724609375,
-0.007701873779296875,
0.0229644775390625,
0.0032405853271484375,
0.004238128662109375,
0.0307769775390625,
0.041412353515625,
0.0013589859008789062,
-0.033721923828125,
0.0234832763671875,
0.0210418701171875,
-0.0252532958984375,
-0.0250396728515625,
-0.0021915435791015625,
-0.0008525848388671875,
0.0045166015625,
-0.0115966796875,
-0.0103912353515625,
0.007080078125,
-0.016204833984375,
-0.00667572021484375,
0.0008549690246582031,
0.01221466064453125,
0.00787353515625,
-0.0270538330078125,
0.00965118408203125,
0.015594482421875,
-0.03179931640625,
-0.043975830078125,
0.0045013427734375,
-0.00012111663818359375,
0.043182373046875,
-0.0251312255859375,
0.00403594970703125,
0.025390625,
0.0394287109375,
0.0189361572265625,
-0.0034809112548828125,
-0.0289306640625,
-0.01116943359375,
0.000545501708984375,
0.0127716064453125,
0.029296875,
-0.02734375,
0.0309600830078125,
0.0010395050048828125,
0.019195556640625,
-0.007129669189453125,
-0.00920867919921875,
-0.0005822181701660156,
-0.0113677978515625,
-0.01367950439453125,
0.0088653564453125,
-0.02716064453125,
0.0009360313415527344,
0.0111236572265625,
-0.0008134841918945312,
-0.0258026123046875,
0.001964569091796875,
-0.0279693603515625,
0.0279388427734375,
-0.02508544921875,
0.0301971435546875,
0.0057220458984375,
-0.0207977294921875,
-0.00078582763671875,
-0.0072021484375,
-0.0239410400390625,
0.03765869140625,
-0.0007891654968261719,
0.016845703125,
-0.0029735565185546875,
0.0083160400390625,
-0.03564453125,
-0.028839111328125,
-0.007518768310546875,
0.029541015625,
0.0004067420959472656,
-0.0065765380859375,
-0.00699615478515625,
-0.00727081298828125,
0.0216827392578125,
-0.01812744140625,
0.0016965866088867188,
-0.0025787353515625,
0.005825042724609375,
-0.009490966796875,
-0.014312744140625,
0.0350341796875,
0.00321197509765625,
0.0010461807250976562,
0.02978515625,
0.018280029296875,
-0.0097198486328125,
-0.012176513671875,
-0.0160369873046875,
0.0007567405700683594,
0.03228759765625,
0.0029850006103515625,
-0.00360870361328125,
0.034454345703125,
-0.00510406494140625,
-0.0281219482421875,
-0.01171875,
-0.0135955810546875,
0.0214385986328125,
0.002826690673828125,
0.0019140243530273438,
0.03570556640625,
-0.0215606689453125,
0.0023708343505859375,
0.0237884521484375,
-0.018646240234375,
0.0206146240234375,
0.003986358642578125,
0.01511383056640625,
0.038330078125,
-0.0169830322265625,
0.050537109375,
0.0106048583984375,
-0.015899658203125,
-0.001750946044921875,
-0.00278472900390625,
-0.0083465576171875,
0.006305694580078125,
0.0278472900390625,
0.002033233642578125,
-0.037261962890625,
0.00820159912109375,
0.03192138671875,
-0.01306915283203125,
-0.01898193359375,
-0.046844482421875,
-0.027923583984375,
0.002071380615234375,
-0.002574920654296875,
0.0009622573852539062,
-0.0200958251953125,
-0.0075836181640625,
-0.01087188720703125,
-0.020782470703125,
-0.0277252197265625,
-0.00417327880859375,
0.0286865234375,
0.005764007568359375,
-0.0087890625,
0.0304718017578125,
0.005352020263671875,
-0.00424957275390625,
-0.01020050048828125,
-0.0190582275390625,
0.037628173828125,
0.03631591796875,
0.00884246826171875,
-0.011077880859375,
0.02532958984375,
-0.0218353271484375,
-0.0090179443359375,
0.006870269775390625,
0.0192108154296875,
-0.0031795501708984375,
-0.003326416015625,
-0.004878997802734375,
-0.004642486572265625,
0.031280517578125,
-0.0272064208984375,
0.0281219482421875,
0.0382080078125,
-0.00582122802734375,
0.0169219970703125,
-0.01482391357421875,
0.0201263427734375,
-0.038970947265625,
-0.0037403106689453125,
0.023162841796875,
-0.005336761474609375,
-0.0030670166015625,
0.00435638427734375,
-0.01934814453125,
-0.002532958984375,
-0.00887298583984375,
0.0251312255859375,
-0.015472412109375,
0.0004601478576660156,
0.00605010986328125,
0.0031223297119140625,
0.0196685791015625,
0.023956298828125,
0.0257568359375,
0.01192474365234375,
-0.02197265625,
-0.01152801513671875,
0.01605224609375,
0.01432037353515625,
-0.01413726806640625,
0.00099945068359375,
-0.034210205078125,
-0.00841522216796875,
0.005153656005859375,
-0.00910186767578125,
0.0022487640380859375,
0.012939453125,
-0.0206146240234375,
-0.033905029296875,
-0.0258636474609375,
0.0015764236450195312,
-0.0313720703125,
0.0074615478515625,
0.007091522216796875,
-0.0073089599609375,
0.032928466796875,
-0.0018205642700195312,
-0.011993408203125,
-0.0015506744384765625,
-0.0021953582763671875,
-0.01458740234375,
-0.014678955078125,
-0.037078857421875,
0.0028781890869140625,
0.007045745849609375,
0.02459716796875,
-0.01419830322265625,
-0.01125335693359375,
-0.008392333984375,
0.032073974609375,
-0.0162353515625,
-0.006317138671875,
0.010345458984375,
-0.00180816650390625,
0.033416748046875,
-0.0169677734375,
0.011749267578125,
-0.00908660888671875,
-0.01280975341796875,
0.0133514404296875,
0.007526397705078125,
-0.00984954833984375,
-0.021026611328125,
0.006683349609375,
-0.0190887451171875,
0.0151519775390625,
0.0084381103515625,
-0.027252197265625,
-0.01141357421875,
-0.009613037109375,
-0.0100250244140625,
-0.0207672119140625,
0.01047515869140625,
0.0104522705078125,
-0.03399658203125,
0.0165557861328125,
-0.01003265380859375,
-0.00609588623046875,
-0.03204345703125,
-0.0033130645751953125,
-0.00988006591796875,
0.01314544677734375,
0.0233154296875,
0.050537109375,
0.01177215576171875,
-0.041168212890625,
0.038543701171875,
0.00359344482421875,
0.0310821533203125,
0.0160675048828125,
-0.00959014892578125,
-0.01421356201171875,
0.0029926300048828125,
-0.0022144317626953125,
-0.0103607177734375,
0.0091552734375,
-0.020904541015625,
0.0178985595703125,
0.01461029052734375,
-0.032928466796875,
0.0263519287109375,
-0.03582763671875,
-0.0018396377563476562,
0.031585693359375,
-0.02020263671875,
-0.0298004150390625,
0.0005545616149902344,
-0.039215087890625,
0.005245208740234375,
0.01277923583984375,
0.020782470703125,
-0.01123046875,
-0.0167388916015625,
-0.0080413818359375,
-0.01062774658203125,
-0.0157012939453125,
0.0239105224609375,
-0.007534027099609375,
0.004852294921875,
0.0027141571044921875,
-0.00936126708984375,
-0.01324462890625,
-0.0005540847778320312,
0.005626678466796875,
-0.0216522216796875,
-0.0266265869140625,
-0.0031585693359375,
-0.0240325927734375,
-0.012054443359375,
0.01520538330078125,
0.00626373291015625,
0.0124359130859375,
0.00907135009765625,
0.00722503662109375,
0.034332275390625,
-0.01227569580078125,
0.0162506103515625,
0.0000286102294921875,
-0.0086517333984375,
0.040557861328125,
0.018951416015625,
0.01605224609375,
0.019439697265625,
-0.006114959716796875,
-0.033172607421875,
0.0015163421630859375,
0.00350189208984375,
-0.031890869140625,
0.02813720703125,
0.024566650390625,
-0.0220184326171875,
-0.0125885009765625,
0.01229095458984375,
-0.01373291015625,
0.0026950836181640625,
0.05078125,
-0.03533935546875,
-0.0022525787353515625,
-0.0060272216796875,
0.00518798828125,
-0.02044677734375,
0.002368927001953125,
0.02362060546875,
0.022430419921875,
0.01206207275390625,
0.0218353271484375,
0.01128387451171875,
0.0305023193359375,
0.005523681640625,
0.01336669921875,
0.00952911376953125,
-0.0256195068359375,
0.0184173583984375,
-0.0061187744140625,
0.00708770751953125,
-0.00506591796875,
-0.00820159912109375,
-0.0237274169921875,
-0.004550933837890625,
-0.0182342529296875,
-0.03289794921875,
-0.00812530517578125,
-0.013397216796875,
-0.018035888671875,
0.003513336181640625,
0.005859375,
-0.02435302734375,
-0.0162811279296875,
0.0010843276977539062,
-0.017791748046875,
0.002178192138671875,
0.030609130859375,
0.0020904541015625,
-0.018829345703125,
0.0210418701171875,
-0.01116180419921875,
-0.01439666748046875,
0.0233917236328125,
-0.008636474609375,
-0.0184478759765625,
-0.0163116455078125,
-0.006473541259765625,
-0.0235595703125,
-0.0062713623046875,
0.0074920654296875,
-0.0164794921875,
0.014404296875,
-0.025909423828125,
-0.00934600830078125,
0.0055999755859375,
-0.0024127960205078125,
-0.038818359375,
0.019561767578125,
-0.004486083984375,
-0.01010894775390625,
-0.0244293212890625,
-0.02825927734375,
-0.0014410018920898438,
-0.038909912109375,
0.00728607177734375,
-0.01654052734375,
-0.0083770751953125,
0.0163726806640625,
0.023223876953125,
0.0029392242431640625,
-0.02435302734375,
-0.03271484375,
0.012359619140625,
0.0172271728515625,
-0.0218353271484375,
-0.033172607421875,
0.01153564453125,
-0.029083251953125,
0.0170440673828125,
0.01308441162109375,
-0.023895263671875,
0.031646728515625,
0.02459716796875,
-0.0275115966796875,
-0.0072021484375,
0.0223388671875,
-0.008941650390625,
0.0177001953125,
0.0057830810546875,
0.0026397705078125,
0.00269317626953125,
-0.00030803680419921875,
-0.01153564453125,
0.01305389404296875,
0.0032444000244140625,
0.0191802978515625,
-0.025604248046875,
0.027252197265625,
0.030609130859375,
-0.00930023193359375,
-0.0013275146484375,
0.02032470703125,
0.0007224082946777344,
0.00482177734375,
-0.0133819580078125,
0.010467529296875,
-0.00827789306640625,
0.00307464599609375,
-0.0204010009765625,
-0.0211639404296875,
0.00926971435546875,
0.004398345947265625,
-0.00305938720703125,
0.018402099609375,
-0.005008697509765625,
0.01100921630859375,
0.0232391357421875,
0.01483917236328125,
-0.01409149169921875,
0.00400543212890625,
0.0014867782592773438,
0.01342010498046875,
-0.01239776611328125,
-0.018402099609375,
0.0039520263671875,
0.03887939453125,
0.044891357421875,
0.01824951171875,
0.015777587890625,
0.00403594970703125,
-0.0160980224609375,
0.00611114501953125,
0.0235595703125,
-0.0025424957275390625,
-0.019744873046875,
0.019927978515625,
-0.013641357421875,
-0.00038433074951171875,
-0.005641937255859375,
-0.003192901611328125,
0.00705718994140625,
0.0157623291015625,
-0.02349853515625,
0.03204345703125,
0.0142822265625,
-0.00310516357421875,
0.01251983642578125,
0.0010623931884765625,
-0.03338623046875,
-0.01087188720703125,
-0.0226593017578125,
-0.006290435791015625,
-0.019989013671875,
0.059722900390625,
-0.0073699951171875,
0.025115966796875,
-0.01471710205078125,
-0.0113677978515625,
-0.0288543701171875,
-0.032989501953125,
0.0306549072265625,
0.0038127899169921875,
-0.010833740234375,
0.0085601806640625,
0.00533294677734375,
0.004047393798828125,
0.01776123046875,
0.013763427734375,
0.008697509765625,
-0.0116119384765625,
0.032073974609375,
-0.0303955078125,
0.01261138916015625,
-0.0241851806640625,
-0.008148193359375,
0.010955810546875,
0.013763427734375,
-0.00022900104522705078,
-0.0274200439453125,
0.0017099380493164062,
-0.002994537353515625,
-0.037811279296875,
-0.0017156600952148438,
-0.004726409912109375,
-0.0012254714965820312,
0.0204620361328125,
-0.034515380859375,
-0.0082550048828125,
0.00630950927734375,
-0.029083251953125,
-0.0022182464599609375,
0.006023406982421875,
0.0195159912109375,
0.0196990966796875,
0.01374053955078125,
-0.00475311279296875,
0.00888824462890625,
0.009613037109375,
-0.002410888671875,
0.005481719970703125,
-0.04327392578125,
-0.004425048828125,
-0.006679534912109375,
0.020782470703125,
0.007564544677734375,
-0.004779815673828125,
0.00850677490234375,
-0.01525115966796875,
-0.014312744140625,
0.0171051025390625,
-0.00016939640045166016,
0.003307342529296875,
0.01236724853515625,
-0.032684326171875,
0.01611328125,
0.02813720703125,
-0.0008339881896972656,
-0.0308837890625,
-0.01029205322265625,
-0.0037288665771484375,
-0.007213592529296875,
-0.0023136138916015625,
-0.01178741455078125,
-0.0185089111328125,
0.0236663818359375,
0.0158233642578125,
0.0032367706298828125,
0.0013074874877929688,
0.0241241455078125,
-0.005840301513671875,
-0.00798797607421875,
0.05218505859375,
-0.012359619140625,
0.0097198486328125,
0.0014429092407226562,
0.02099609375,
-0.0249481201171875,
0.003437042236328125,
-0.01332855224609375,
0.004852294921875,
0.0247344970703125,
-0.007007598876953125,
0.01357269287109375,
-0.00867462158203125,
-0.004261016845703125,
-0.0185546875,
0.01125335693359375,
-0.01247406005859375,
0.018341064453125,
-0.03564453125,
-0.00811004638671875,
-0.028076171875,
0.00011152029037475586,
0.032623291015625,
-0.0149993896484375,
-0.037322998046875,
0.0146484375,
0.004245758056640625,
-0.02874755859375,
-0.0221405029296875,
0.0076141357421875,
-0.0027561187744140625,
0.0248870849609375,
-0.0257415771484375,
-0.0223541259765625,
0.0174407958984375,
0.006374359130859375,
-0.00591278076171875,
-0.02777099609375,
-0.00921630859375,
0.0236663818359375,
0.00521087646484375,
-0.007659912109375,
0.0027065277099609375,
-0.00174713134765625,
0.007320404052734375,
0.0012035369873046875,
-0.01168060302734375,
0.0009431838989257812,
-0.02093505859375,
-0.007678985595703125,
0.0204010009765625,
0.01153564453125,
0.00266265869140625,
0.049774169921875,
0.024383544921875,
-0.0274658203125,
-0.005741119384765625,
0.0174713134765625,
0.028045654296875,
-0.00762176513671875,
0.0004322528839111328,
0.0010023117065429688,
0.011260986328125,
0.00957489013671875,
0.004886627197265625,
0.0166168212890625,
0.0099945068359375,
-0.0007104873657226562,
0.04302978515625,
0.021209716796875,
0.00969696044921875,
-0.0015125274658203125,
-0.0001882314682006836,
0.00286865234375,
-0.0134124755859375,
-0.004878997802734375,
-0.004367828369140625,
0.01427459716796875,
0.00342559814453125,
0.0021648406982421875,
-0.018463134765625,
0.013031005859375,
0.0151519775390625,
-0.00551605224609375,
-0.01407623291015625,
0.0047760009765625,
0.047210693359375,
-0.0355224609375,
0.0118865966796875,
0.0183563232421875,
0.01232147216796875,
0.052001953125,
-0.03582763671875,
-0.0179595947265625,
0.023284912109375,
-0.0026226043701171875,
-0.0070648193359375,
-0.0203399658203125,
-0.024688720703125,
-0.01641845703125,
-0.00569915771484375,
0.0055999755859375,
0.0016183853149414062,
0.0252685546875,
0.0303192138671875,
0.0021514892578125,
-0.0308990478515625,
0.01285552978515625,
0.0005960464477539062,
0.0220794677734375,
-0.0142364501953125,
-0.005672454833984375,
0.000682830810546875,
0.030426025390625,
-0.0302734375,
-0.037322998046875,
-0.005889892578125,
-0.0031719207763671875,
-0.01302337646484375,
0.02667236328125,
-0.0220489501953125,
0.0223846435546875,
0.016845703125,
0.005977630615234375,
-0.026611328125,
0.057830810546875,
0.005084991455078125,
-0.0256805419921875,
-0.002567291259765625,
0.01018524169921875,
0.015228271484375,
-0.0194854736328125,
0.0104827880859375,
0.01384735107421875,
0.016876220703125,
0.0024089813232421875,
-0.0222015380859375,
-0.014251708984375,
-0.0299072265625,
0.004413604736328125,
-0.033599853515625,
0.004825592041015625,
0.0041046142578125,
-0.00007039308547973633,
-0.027008056640625,
0.00392913818359375,
-0.01812744140625,
0.007419586181640625,
0.01549530029296875,
0.025543212890625,
0.01418304443359375,
0.0283966064453125,
0.00034999847412109375,
-0.00551605224609375,
0.006244659423828125,
0.01544952392578125,
-0.033355712890625,
-0.01499176025390625,
0.0262298583984375,
0.0028133392333984375,
0.0148468017578125,
0.0303497314453125,
-0.0226287841796875,
-0.0021152496337890625,
-0.041015625,
0.00229644775390625,
0.0253753662109375,
0.0159454345703125,
0.0211029052734375,
-0.0272979736328125,
-0.0225830078125,
-0.00860595703125,
-0.0408935546875,
-0.0106353759765625,
0.00490570068359375,
-0.0076141357421875,
0.00989532470703125,
0.0016193389892578125,
0.002239227294921875,
-0.01739501953125,
-0.0321044921875,
0.001239776611328125,
0.018218994140625,
0.0132904052734375,
-0.0036602020263671875,
0.00888824462890625,
-0.0084381103515625,
-0.00614166259765625,
0.004486083984375,
-0.036407470703125,
0.0097198486328125,
0.006084442138671875,
0.031494140625,
-0.036102294921875,
0.0018215179443359375,
0.011627197265625,
-0.02667236328125,
0.0126495361328125,
0.0011491775512695312,
0.03240966796875,
0.03082275390625,
-0.0277862548828125,
0.01129150390625,
0.0085906982421875,
0.0133819580078125,
-0.01326751708984375,
-0.0096588134765625,
0.007843017578125,
-0.00016355514526367188,
-0.005840301513671875,
-0.0026302337646484375,
0.01169586181640625,
-0.024322509765625,
-0.00907135009765625,
-0.01031494140625,
0.000278472900390625,
-0.01003265380859375,
-0.030517578125,
0.030731201171875,
-0.0090179443359375,
-0.0054168701171875,
0.014923095703125,
-0.0160675048828125,
0.0251922607421875,
0.0204620361328125,
0.01110076904296875,
-0.0036602020263671875,
-0.0152740478515625,
-0.0066070556640625,
0.0003151893615722656,
-0.0199127197265625,
0.0298919677734375,
-0.00543212890625,
0.0187530517578125,
0.00922393798828125,
-0.0144195556640625,
-0.0016946792602539062,
-0.01555633544921875,
-0.001552581787109375,
0.022369384765625,
-0.0166778564453125,
-0.0194549560546875,
0.0149078369140625,
-0.0249481201171875,
0.0220947265625,
-0.0482177734375,
-0.01412200927734375,
-0.0220184326171875,
0.02349853515625,
-0.050689697265625,
0.042205810546875,
-0.0005459785461425781,
-0.033294677734375,
0.007167816162109375,
0.0234222412109375,
0.00882720947265625,
0.01241302490234375,
-0.027618408203125,
0.0169677734375,
0.003025054931640625,
0.01629638671875,
-0.004146575927734375,
-0.0268096923828125,
-0.00675201416015625,
-0.02276611328125,
-0.03204345703125,
-0.012939453125,
-0.007099151611328125,
0.01556396484375,
-0.0272369384765625,
-0.00365447998046875,
0.00687408447265625,
-0.00498199462890625,
-0.015869140625,
0.01467132568359375,
-0.0191192626953125,
-0.00952911376953125,
0.03729248046875,
0.045654296875,
-0.013427734375,
-0.002841949462890625,
-0.01190948486328125,
0.032012939453125,
-0.0166778564453125,
0.03594970703125,
0.0179290771484375,
0.0150909423828125,
0.0015878677368164062,
-0.01007843017578125,
-0.0267791748046875,
-0.021087646484375,
0.018463134765625,
0.004245758056640625,
-0.0241241455078125,
0.0008068084716796875,
0.021209716796875,
0.0039825439453125,
0.024749755859375,
0.0038089752197265625,
0.0172882080078125,
0.00707244873046875,
0.00424957275390625,
0.0272369384765625,
0.01439666748046875,
0.00830078125,
0.01800537109375,
0.03314208984375,
0.0097808837890625,
0.0123443603515625,
0.02703857421875,
-0.04132080078125,
-0.0247650146484375,
-0.0032596588134765625,
-0.0049591064453125,
-0.023468017578125,
-0.01580810546875,
0.014190673828125,
0.0185089111328125,
-0.0411376953125,
0.0310211181640625,
-0.0006237030029296875,
-0.0174560546875,
-0.0277862548828125,
-0.0229034423828125,
0.003360748291015625,
0.0218505859375,
0.00505828857421875,
-0.0298004150390625,
-0.0264129638671875,
-0.00954437255859375,
0.01369476318359375,
0.00146484375,
-0.0108184814453125,
-0.006267547607421875,
-0.01200103759765625,
0.0157318115234375,
-0.01111602783203125,
-0.0087432861328125,
0.01491546630859375,
-0.0280609130859375,
0.04217529296875,
-0.013275146484375,
-0.0063629150390625,
0.015411376953125,
0.01035308837890625,
-0.038818359375,
0.032806396484375,
-0.031890869140625,
-0.0096282958984375,
0.0030994415283203125,
0.0042572021484375,
0.01166534423828125,
0.005809783935546875,
-0.004718780517578125,
-0.0015211105346679688,
0.002605438232421875,
-0.0027008056640625,
-0.02410888671875,
0.025238037109375,
-0.0267791748046875,
0.0259857177734375,
-0.04290771484375,
-0.0098724365234375,
-0.022796630859375,
-0.005725860595703125,
-0.0310516357421875,
-0.0018796920776367188,
0.00011545419692993164,
0.0163726806640625,
-0.047698974609375,
0.0008382797241210938,
-0.0106048583984375,
0.0179290771484375,
0.01535797119140625,
-0.001461029052734375,
0.05255126953125,
0.01224517822265625,
0.050018310546875,
0.021881103515625,
-0.028533935546875,
-0.0035839080810546875,
-0.00542449951171875,
0.02484130859375,
0.0093536376953125,
-0.0002543926239013672,
-0.0011167526245117188,
-0.0087127685546875,
0.019439697265625,
0.03076171875,
-0.018157958984375,
0.0050811767578125,
0.0101470947265625,
0.0037250518798828125,
0.03271484375,
-0.042510986328125,
0.004352569580078125,
0.008270263671875,
0.024871826171875,
0.02960205078125,
-0.0080718994140625,
-0.01424407958984375,
-0.00345611572265625,
-0.0047149658203125,
-0.0292510986328125,
0.01519012451171875,
0.00408172607421875,
0.0035305023193359375,
0.036376953125,
0.0008749961853027344,
-0.0048980712890625,
-0.0216522216796875,
-0.0086822509765625,
0.0291290283203125,
-0.0008630752563476562,
0.032623291015625,
-0.0029468536376953125,
-0.031829833984375,
0.0244598388671875,
0.0026493072509765625,
-0.036865234375,
0.0007023811340332031,
-0.031219482421875,
0.00923919677734375,
0.01227569580078125,
-0.01256561279296875,
-0.02459716796875,
-0.0128326416015625,
0.03814697265625,
-0.0093231201171875,
0.01126861572265625,
0.0024204254150390625,
0.019866943359375,
0.01064300537109375,
0.031524658203125,
0.01187896728515625,
-0.01111602783203125,
-0.019287109375,
0.0194091796875,
0.0005822181701660156,
0.00789642333984375,
0.005802154541015625,
-0.009979248046875,
-0.0318603515625,
0.0203704833984375,
0.020965576171875,
0.0052032470703125,
0.0261688232421875,
-0.01044464111328125,
0.0360107421875,
0.0252227783203125,
0.0216064453125,
0.019012451171875,
0.04248046875,
-0.01108551025390625,
0.01476287841796875,
-0.0188140869140625,
-0.0004911422729492188,
-0.059295654296875,
-0.01044464111328125,
-0.005535125732421875,
0.0275421142578125,
0.0438232421875,
-0.02496337890625,
0.040496826171875,
0.02459716796875,
-0.0074462890625,
0.03192138671875,
0.0170440673828125,
0.00688934326171875,
0.038848876953125,
-0.00304412841796875,
-0.00782012939453125,
-0.029632568359375,
-0.016448974609375,
-0.0023212432861328125,
-0.003826141357421875,
-0.0192718505859375,
0.02447509765625,
-0.006015777587890625,
-0.02130126953125,
-0.0142364501953125,
-0.042083740234375,
-0.0263824462890625,
0.007778167724609375,
-0.01605224609375,
-0.0085601806640625,
0.0281982421875,
0.005512237548828125,
0.00888824462890625,
0.007625579833984375,
-0.03173828125,
-0.0269317626953125,
0.002063751220703125,
-0.021392822265625,
-0.00855255126953125,
0.003986358642578125,
-0.0626220703125,
-0.0152740478515625,
-0.02349853515625,
0.0240325927734375,
-0.0207366943359375,
-0.0087432861328125,
0.0193634033203125,
-0.027923583984375,
0.01116943359375,
-0.005889892578125,
0.034942626953125,
0.0282440185546875,
-0.0275421142578125,
-0.00046563148498535156,
-0.0233154296875,
-0.01099395751953125,
-0.00957489013671875,
-0.004253387451171875,
-0.0268402099609375,
-0.00937652587890625,
-0.0072174072265625,
0.0197601318359375,
0.0258636474609375,
-0.005275726318359375,
-0.0225372314453125,
-0.0189056396484375,
0.00959014892578125,
0.0458984375,
-0.0005331039428710938,
-0.0175018310546875,
0.02032470703125,
-0.03387451171875,
0.00536346435546875,
-0.018585205078125,
0.031280517578125,
0.00901031494140625,
0.0203094482421875,
0.0007448196411132812,
0.01004791259765625,
0.004550933837890625,
0.0019426345825195312,
0.0301361083984375,
0.00531005859375,
-0.02301025390625,
-0.037872314453125,
0.006320953369140625,
-0.0019855499267578125,
0.01180267333984375,
0.0020599365234375,
-0.025482177734375,
0.0184173583984375,
-0.02105712890625,
-0.0019044876098632812,
0.0064239501953125,
-0.027313232421875,
-0.0127410888671875,
0.0087127685546875,
0.0176239013671875,
0.00812530517578125,
-0.008392333984375,
-0.0186767578125,
0.00821685791015625,
0.01560211181640625,
-0.016510009765625,
-0.00997161865234375,
-0.018310546875,
-0.004848480224609375,
-0.00284576416015625,
-0.0012006759643554688,
-0.00547027587890625,
0.008026123046875
] |
ours_498
|
Let \( I_{n} \) be the set of all \( n \)-transpositions.
Definition. Fix some subset \( T \subseteq I_{n} \). We say that a multilinear function \( f:\left(\mathbb{F}_{q}^{n}\right)^{n} \rightarrow \mathbb{F}_{q} \) is \( T \)-good if
\[ f\left(x_{1}, \ldots, x_{n}\right)=-f\left(x_{\sigma(1)}, \ldots, x_{\sigma(n)}\right) \]
for all \(\sigma \in T\) and \(\left(x_{1}, \ldots, x_{n}\right) \in\left(\mathbb{F}_{q}^{n}\right)^{n}\).
Definition. Fix some subset \( T \subseteq I_{n} \). For any \(\left(x_{1}, \ldots, x_{n}\right) \in\left(\mathbb{F}_{q}^{n}\right)^{n}\), let \( g_{T}\left(x_{1}, \ldots, x_{n}\right) \) denote the number of different values \( f\left(x_{1}, \ldots, x_{n}\right) \) takes over all \( T \)-good functions \( f \).
Definition. Fix some subset \( T \subseteq I_{n} \). Let \( G_{T} \) be the graph with vertex set \([n]=\{1,2, \ldots, n\}\) and edge \(\{a, b\}\) if and only if the transposition \((a, b)\) is in \( T \). Let \( C_{1} \sqcup \cdots \sqcup C_{r} \) be the partition of the vertex set into connected components of \( G_{T} \). Call a matrix \(\left(x_{1}, \ldots, x_{n}\right) \in\left(\mathbb{F}_{q}^{n}\right)^{n} T\)-invertible if the sets \(\left\{x_{i}\right\}_{i \in C_{k}}\) are each a set of linearly independent vectors.
Definition. Let \(\varepsilon(q, T)\) be the expected value of \( g_{T}\left(x_{1}, \ldots, x_{n}\right) \) if \(\left(x_{1}, \ldots, x_{n}\right) \in\left(\mathbb{F}_{q}^{n}\right)^{n}\) is chosen uniformly at random. Also define
\[ \kappa(T)=-\lim _{q \rightarrow \infty} \log _{q}\left(-\ln \left(\frac{\varepsilon(q, T)-1}{q-1}\right)\right). \]
We have the following lemma.
Lemma. Let \( f \) be a \( T \)-good function for some \( T \subseteq I_{n} \). Let \( C_{1} \sqcup \cdots \sqcup C_{r} \) be the connected components of \( G_{T} \). Then, if \( a, b \in C_{k} \), then
\[ f\left(x_{1}, \ldots, x_{n}\right)=-f\left(x_{\sigma(1)}, \ldots, x_{\sigma(n)}\right) \]
where \(\sigma\) is the transposition swapping \( a \) and \( b \).
Sketch. Let \(\bar{T}\) be the set of transpositions \(\sigma\) such that
\[ f\left(x_{1}, \ldots, x_{n}\right)=-f\left(x_{\sigma(1)}, \ldots, x_{\sigma(n)}\right) \]
for all \(\left(x_{1}, \ldots, x_{n}\right) \in\left(\mathbb{F}_{q}^{n}\right)^{n}\). It suffices to show that if \((a, b),(b, c) \in \bar{T}\), then \((a, c) \in \bar{T}\). This follows since \((a, b) \circ(b, c) \circ(a, b)=(a, c)\) and \((-1)^{3}=-1\).
We have the following key linear algebra claim.
Claim (Main Linear Algebra Step). Fix some set \( T \subseteq I_{n} \). Then \( g_{T}\left(x_{1}, \ldots, x_{n}\right)=q \) if \(\left(x_{1}, \ldots, x_{n}\right)\) is \( T \)-invertible, and \( g_{T}\left(x_{1}, \ldots, x_{n}\right)=1 \) otherwise.
Proof. First suppose that \( X=\left(x_{1}, \ldots, x_{n}\right) \) is not \( T \)-invertible. As above, let \( C_{1} \sqcup \cdots \sqcup C_{r} \) be the partition of the vertex set into connected components of \( G_{T} \). Then, there is some \( 1 \leq k \leq r \) such that the set of vectors \(\left\{x_{i}\right\}_{i \in C_{k}}\) is linearly dependent. So
\[ x_{j}+\sum_{\substack{i \in C_{k} \\ i \neq j}} \alpha_{i} x_{i}=0 \]
for some \( j \in C_{k} \) and scalars \(\alpha_{i} \in \mathbb{F}_{q}\).
Note that if \( x_{a}=x_{b} \) for \( a, b \in C_{k} \) and \( a \neq b \), then \( f\left(x_{1}, \ldots, x_{n}\right)=0 \) (this is due to the lemma). Thus, \( f\left(x_{1}, \ldots, x_{n}\right) \) is unchanged if we replace \( x_{j} \) with \( x_{j}+\sum_{\substack{i \in C_{k} \\ i \neq j}} \alpha_{i} x_{i} \), or \( 0 \). But \( f\left(x_{1}, \ldots, x_{j-1}, 0, x_{j+1}, \ldots, x_{n}\right)=0 \) by multilinearity, so we have \( f(X)=0 \). Thus, if \( X \) is not \( T \)-invertible, then \( f(X)=0 \), so \( g_{T}(X)=1 \).
Now, suppose that \( X=\left(x_{1}, \ldots, x_{n}\right) \) is \( T \)-invertible. We'll construct a \( T \)-good function \( f \) such that \( f(X) \neq 0 \). By scaling this function, we see that \( h(X) \) can take any value in \(\mathbb{F}_{q}\) for \( T \)-good functions \( h \), so \( g(X)=q \).
Extend each set \(\left\{x_{i}\right\}_{i \in C_{k}}\) to a basis \( D_{k}=\left\{z_{i}^{(k)}\right\}_{i \in[n]} \) of \(\mathbb{F}_{q}^{n}\). In particular, we have \( z_{i}^{(k)}=x_{i} \) if \( i \in C_{k} \). Now, for any \(\left(y_{1}, \ldots, y_{n}\right) \in\left(\mathbb{F}_{q}^{n}\right)^{n}\), set
\[ f\left(y_{1}, \ldots, y_{n}\right)=\prod_{k=1}^{r} \operatorname{det}\left(w_{1}^{(k)}, \ldots, w_{n}^{(k)}\right) \]
where \( w_{i}^{(k)}=y_{i} \) if \( i \in C_{k} \), and \( w_{i}^{(k)}=z_{i}^{(k)} \) otherwise. It is easy to check that this function is \( T \)-good, and that \( f\left(x_{1}, \ldots, x_{n}\right) \neq 0 \), so we're done. This proves the Main Linear Algebra Step.
We have the following well-known counting step.
Claim (Counting \( T \)-Invertible Matrices). Let \( T \subseteq[n] \), and let \( C_{1} \sqcup \cdots \sqcup C_{r} \) be the connected components of \( G_{T} \). Then,
\[ \frac{\varepsilon(q, T)-1}{q-1}=\prod_{k=1}^{r}\left(1-q^{-n}\right)\left(1-q^{-n+1}\right) \cdots\left(1-q^{-n+\left|C_{k}\right|-1}\right). \]
Proof. By the previous claim, \(\frac{\varepsilon(q, T)-1}{q-1}\) is simply the probability that a randomly chosen element of \(\left(\mathbb{F}_{q}^{n}\right)^{n}\) is \( T \)-good.
Let's count the number of ordered lists of \( m \) vectors in \(\mathbb{F}_{q}^{n}\) that are linearly independent. We have \( q^{n}-1 \) choices for the first vector, \( q^{n}-q \) for the second, \( q^{n}-q^{2} \) for the third, and so on. Thus the number of lists is
\[ \left(q^{n}-1\right) \cdot\left(q^{n}-q\right) \cdots\left(q^{n}-q^{n-m+1}\right). \]
Now, the number of \( T \)-good matrices is just the product of the above quantity where \( m \) ranges over all the \(\left|C_{k}\right|\), since we just have to choose the vectors such that the sets \(\left\{x_{i}\right\}_{i \in C_{k}}\) are sets of linearly independent vectors. Thus, the number of \( T \)-good matrices is
\[ \prod_{k=1}^{r}\left(q^{n}-1\right) \cdot\left(q^{n}-q\right) \cdots\left(q^{n}-q^{n-\left|C_{k}\right|+1}\right). \]
The result follows since the number of total matrices is \( q^{n^{2}}=q^{n\left|C_{1}\right|} \cdots q^{n\left|C_{k}\right|} \). This proves the Claim.
We'll now evaluate the limit.
Claim (Evaluating the Limit). Let \( T \subseteq I_{n} \), and let \( C_{1} \sqcup \cdots \sqcup C_{r} \) be the connected components of \( G_{T} \). Let \(\gamma\) be the size of the largest connected components. Then, \(\kappa(T)=n+1-\gamma\).
Proof. Note that
\[ -\ln \left[\left(\left(1-q^{-n}\right)\left(1-q^{-n+1}\right) \cdots\left(1-q^{-n+\left|C_{k}\right|-1}\right)\right]=q^{-n+\left|C_{k}\right|-1}+O\left(q^{-n+\left|C_{k}\right|-2}\right)\right. \]
Now, suppose that \(\ell\) of \( C_{1}, \ldots, C_{r} \) are all the "largest connected component", so they all have size \(\gamma\). Then, we see that
\[ -\ln \left[\prod_{k=1}^{r}\left(1-q^{-n}\right)\left(1-q^{-n+1}\right) \cdots\left(1-q^{-n+\left|C_{k}\right|-1}\right)\right]=\ell \cdot q^{-n+\gamma-1}+O\left(q^{-n+\gamma-2}\right). \]
The result then follows by taking \(\log _{q}\) and noting that \(\log _{q} \ell \rightarrow 0\) as \( q \rightarrow \infty \). This proves the Claim.
We see that \(\pi(n)=n+1-\mathbb{E} \gamma\), where \(\mathbb{E} \gamma\) is the expected size of the largest connected components over all labeled graphs on \( n \) vertices and four edges. Let \( g_{\gamma} \) be the number of graphs with four edges and largest connected components size \(\gamma\).
Here is a list of all non-isomorphic graphs on four vertices (we're ignoring lone vertices), and the number of labeled graphs on \( n \) vertices corresponding to each isomorphism class.
From here, we calculate
\[
\begin{aligned}
& g_{2}=105\binom{n}{8}, \\
& g_{3}=315\binom{n}{7}+90\binom{n}{6}+10\binom{n}{5}, \\
& g_{4}=240\binom{n}{6}+15\binom{n}{4}, \\
& g_{5}=125\binom{n}{5},
\end{aligned}
\]
yielding a final answer of
\[
\pi(n)=n+1-\frac{210\binom{n}{8}+945\binom{n}{7}+1230\binom{n}{6}+655\binom{n}{5}+60\binom{n}{4}}{\binom{n}{2}}.
\]
A calculation yields \(\frac{p(-3)}{q(-3)}=197\).
\(\boxed{197}\)
|
197
|
{
"competition": "us_comps",
"dataset": "Ours",
"posts": null,
"source": "OMOFall19Solns-3.md"
}
|
For a positive integer \( n \), we say an \( n \)-transposition is a bijection \(\sigma:\{1,2, \ldots, n\} \rightarrow\{1,2, \ldots, n\}\) such that there exist exactly two elements \( i \) of \(\{1,2, \ldots, n\}\) such that \(\sigma(i) \neq i\).
Fix some four pairwise distinct \( n \)-transpositions \(\sigma_{1}, \sigma_{2}, \sigma_{3}, \sigma_{4}\). Let \( q \) be any prime, and let \(\mathbb{F}_{q}\) be the integers modulo \( q \). Consider all functions \( f:\left(\mathbb{F}_{q}^{n}\right)^{n} \rightarrow \mathbb{F}_{q} \) that satisfy, for all integers \( i \) with \( 1 \leq i \leq n \) and all \( x_{1}, \ldots x_{i-1}, x_{i+1}, \ldots, x_{n}, y, z \in \mathbb{F}_{q}^{n} \),
\[ f\left(x_{1}, \ldots, x_{i-1}, y, x_{i+1}, \ldots, x_{n}\right)+f\left(x_{1}, \ldots, x_{i-1}, z, x_{i+1}, \ldots, x_{n}\right)=f\left(x_{1}, \ldots, x_{i-1}, y+z, x_{i+1}, \ldots, x_{n}\right), \]
and that satisfy, for all \( x_{1}, \ldots, x_{n} \in \mathbb{F}_{q}^{n} \) and all \(\sigma \in\left\{\sigma_{1}, \sigma_{2}, \sigma_{3}, \sigma_{4}\right\}\),
\[ f\left(x_{1}, \ldots, x_{n}\right)=-f\left(x_{\sigma(1)}, \ldots, x_{\sigma(n)}\right). \]
(Note that the equalities in the previous sentence are in \(\mathbb{F}_{q}\). Note that, for any \( a_{1}, \ldots, a_{n}, b_{1}, \ldots, b_{n} \in \mathbb{F}_{q} \), we have \(\left(a_{1}, \ldots, a_{n}\right)+\left(b_{1}, \ldots, b_{n}\right)=\left(a_{1}+b_{1}, \ldots, a_{n}+b_{n}\right)\), where \( a_{1}+b_{1}, \ldots, a_{n}+b_{n} \in \mathbb{F}_{q} \).)
For a given tuple \(\left(x_{1}, \ldots, x_{n}\right) \in\left(\mathbb{F}_{q}^{n}\right)^{n}\), let \( g\left(x_{1}, \ldots, x_{n}\right) \) be the number of different values of \( f\left(x_{1}, \ldots, x_{n}\right) \) over all possible functions \( f \) satisfying the above conditions.
Pick \(\left(x_{1}, \ldots, x_{n}\right) \in\left(\mathbb{F}_{q}^{n}\right)^{n}\) uniformly at random, and let \(\varepsilon\left(q, \sigma_{1}, \sigma_{2}, \sigma_{3}, \sigma_{4}\right)\) be the expected value of \( g\left(x_{1}, \ldots, x_{n}\right) \). Finally, let
\[ \kappa\left(\sigma_{1}, \sigma_{2}, \sigma_{3}, \sigma_{4}\right)=-\lim _{q \rightarrow \infty} \log _{q}\left(-\ln \left(\frac{\varepsilon\left(q, \sigma_{1}, \sigma_{2}, \sigma_{3}, \sigma_{4}\right)-1}{q-1}\right)\right). \]
Pick four pairwise distinct \( n \)-transpositions \(\sigma_{1}, \sigma_{2}, \sigma_{3}, \sigma_{4}\) uniformly at random from the set of all \( n \) transpositions. Let \(\pi(n)\) denote the expected value of \(\kappa\left(\sigma_{1}, \ldots, \sigma_{4}\right)\). Suppose that \( p(x) \) and \( q(x) \) are polynomials with real coefficients such that \( q(-3) \neq 0 \) and such that \(\pi(n)=\frac{p(n)}{q(n)}\) for infinitely many positive integers \( n \). Compute \(\frac{p(-3)}{q(-3)}\).
|
[
"/Mathematics/Algebra/LinearAlgebra/Determinants/Determinant",
"/Mathematics/Algebra/LinearAlgebra/LinearIndependence/LinearlyIndependent",
"/Mathematics/Algebra/LinearAlgebra/LinearIndependence/VectorBasis",
"/Mathematics/Algebra/LinearAlgebra/Matrices/MatrixProperties",
"/Mathematics/DiscreteMathematics/Combinatorics/BinomialCoefficients",
"/Mathematics/DiscreteMathematics/Combinatorics/Enumeration",
"/Mathematics/DiscreteMathematics/Combinatorics/GeneralCombinatorics",
"/Mathematics/DiscreteMathematics/GraphTheory/LabeledGraphs",
"/Mathematics/DiscreteMathematics/GraphTheory/SimpleGraphs"
] |
Translate the antisymmetry conditions into a graph whose connected components dictate that f is nonzero only when the vectors in each component are linearly independent.
|
[
0.000056684017181396484,
0.0192108154296875,
0.033447265625,
-0.00643157958984375,
0.0002734661102294922,
-0.00572967529296875,
0.03460693359375,
0.005901336669921875,
0.0163421630859375,
0.007049560546875,
0.005847930908203125,
-0.015228271484375,
0.0022716522216796875,
0.01200103759765625,
-0.0238800048828125,
-0.004535675048828125,
0.01424407958984375,
0.0213775634765625,
-0.004100799560546875,
-0.0068817138671875,
-0.006443023681640625,
-0.006511688232421875,
-0.03204345703125,
0.062408447265625,
-0.076416015625,
-0.0096435546875,
-0.0185089111328125,
0.0030384063720703125,
-0.01548004150390625,
0.04119873046875,
-0.010528564453125,
-0.0232391357421875,
0.01361083984375,
0.0153961181640625,
-0.001255035400390625,
-0.00899505615234375,
-0.01094818115234375,
0.0000750422477722168,
-0.032928466796875,
-0.042449951171875,
-0.0046234130859375,
0.0298309326171875,
0.018646240234375,
0.020538330078125,
0.044830322265625,
0.011993408203125,
0.0113983154296875,
-0.0108489990234375,
-0.0233612060546875,
0.0029315948486328125,
-0.00527191162109375,
0.0160064697265625,
-0.0191802978515625,
-0.0226898193359375,
-0.0220184326171875,
-0.0914306640625,
-0.00887298583984375,
-0.003498077392578125,
0.0011959075927734375,
0.01030731201171875,
-0.0003008842468261719,
0.0021114349365234375,
-0.0009002685546875,
-0.0086517333984375,
-0.004772186279296875,
0.0012388229370117188,
0.0242919921875,
-0.01511383056640625,
0.01554107666015625,
-0.0010290145874023438,
0.0154876708984375,
-0.00989532470703125,
0.011474609375,
0.046875,
0.0272979736328125,
-0.0047607421875,
-0.006160736083984375,
0.017974853515625,
0.0169677734375,
0.005695343017578125,
-0.00901031494140625,
0.018768310546875,
0.004428863525390625,
-0.036956787109375,
0.0179901123046875,
0.0284423828125,
-0.00878143310546875,
-0.01500701904296875,
0.04168701171875,
-0.002689361572265625,
0.0011882781982421875,
0.02093505859375,
0.01009368896484375,
0.01108551025390625,
0.0098876953125,
-0.004543304443359375,
0.0029850006103515625,
-0.005565643310546875,
-0.02630615234375,
0.01018524169921875,
-0.00896453857421875,
-0.0053558349609375,
0.030059814453125,
0.01342010498046875,
-0.048797607421875,
-0.038665771484375,
-0.0116729736328125,
-0.0035247802734375,
0.00797271728515625,
0.00806427001953125,
0.00872039794921875,
-0.0203857421875,
0.033355712890625,
0.019195556640625,
0.006622314453125,
0.005435943603515625,
0.01355743408203125,
0.01465606689453125,
0.0099029541015625,
-0.025238037109375,
0.0021762847900390625,
0.0112152099609375,
0.0038738250732421875,
0.025634765625,
-0.006298065185546875,
-0.001033782958984375,
-0.004940032958984375,
-0.003871917724609375,
0.00012803077697753906,
0.0009965896606445312,
-0.032196044921875,
-0.004741668701171875,
0.006824493408203125,
-0.027679443359375,
-0.0284271240234375,
0.018585205078125,
-0.0201568603515625,
-0.0004329681396484375,
0.00968170166015625,
-0.002758026123046875,
0.0027828216552734375,
-0.017181396484375,
0.0085601806640625,
-0.03546142578125,
-0.0031223297119140625,
0.0105438232421875,
0.00307464599609375,
-0.0178375244140625,
0.00818634033203125,
-0.00579833984375,
0.0157012939453125,
0.0069732666015625,
0.021514892578125,
-0.0013332366943359375,
-0.0010290145874023438,
0.00151824951171875,
0.0125732421875,
0.01605224609375,
0.006580352783203125,
0.010223388671875,
-0.00142669677734375,
-0.0020313262939453125,
0.0232391357421875,
0.01800537109375,
0.0191497802734375,
0.0177001953125,
0.01041412353515625,
0.0198974609375,
-0.006927490234375,
-0.0006299018859863281,
0.00335693359375,
-0.0227203369140625,
0.0003540515899658203,
-0.0012826919555664062,
-0.005458831787109375,
0.0007348060607910156,
-0.021697998046875,
0.01068115234375,
0.0005202293395996094,
0.0111083984375,
0.008148193359375,
-0.03570556640625,
0.038848876953125,
0.00754547119140625,
0.0087432861328125,
-0.00982666015625,
-0.0212860107421875,
0.02264404296875,
0.01800537109375,
0.004192352294921875,
0.008636474609375,
0.0260162353515625,
-0.0154571533203125,
0.01174163818359375,
-0.001979827880859375,
-0.00013434886932373047,
-0.0223236083984375,
0.03173828125,
0.00664520263671875,
0.0233154296875,
-0.0030364990234375,
0.01360321044921875,
-0.0098724365234375,
-0.0164947509765625,
-0.005466461181640625,
-0.01318359375,
0.01042938232421875,
-0.00762939453125,
0.003566741943359375,
-0.00896453857421875,
0.00945281982421875,
-0.01122283935546875,
-0.0106964111328125,
-0.03485107421875,
-0.0069580078125,
0.00969696044921875,
-0.01947021484375,
-0.01456451416015625,
0.004657745361328125,
-0.0528564453125,
-0.0043792724609375,
0.01264190673828125,
0.00001704692840576172,
-0.003871917724609375,
-0.0014333724975585938,
0.001007080078125,
0.0031414031982421875,
0.004322052001953125,
-0.00348663330078125,
0.0150604248046875,
0.005451202392578125,
0.0181884765625,
-0.0184173583984375,
0.0013303756713867188,
-0.0212860107421875,
-0.0032444000244140625,
-0.0181121826171875,
-0.01702880859375,
0.0125885009765625,
-0.018524169921875,
0.034820556640625,
-0.015594482421875,
0.002410888671875,
0.006389617919921875,
0.006866455078125,
-0.0130462646484375,
0.010986328125,
0.0073699951171875,
0.006927490234375,
-0.0225372314453125,
-0.0280303955078125,
0.017120361328125,
0.0033435821533203125,
0.006671905517578125,
0.022125244140625,
0.00897216796875,
0.00247955322265625,
0.0028896331787109375,
-0.0186920166015625,
-0.00864410400390625,
-0.0088043212890625,
-0.023712158203125,
0.0064697265625,
-0.003299713134765625,
-0.0178070068359375,
-0.007801055908203125,
0.033782958984375,
-0.006473541259765625,
0.033538818359375,
0.00698089599609375,
0.0125579833984375,
-0.006175994873046875,
-0.0008959770202636719,
0.0071868896484375,
-0.0135498046875,
-0.00013363361358642578,
0.0023479461669921875,
0.0185546875,
0.0021419525146484375,
0.0009074211120605469,
0.00299835205078125,
-0.01001739501953125,
-0.0377197265625,
0.01525115966796875,
-0.01013946533203125,
-0.005039215087890625,
0.027862548828125,
-0.0098419189453125,
-0.0130767822265625,
0.013397216796875,
-0.009796142578125,
-0.0017299652099609375,
-0.01033782958984375,
-0.01241302490234375,
0.048797607421875,
-0.01154327392578125,
0.005954742431640625,
0.011138916015625,
0.01678466796875,
-0.0008792877197265625,
0.0228118896484375,
0.0112762451171875,
-0.005519866943359375,
0.0217437744140625,
0.0180206298828125,
-0.00322723388671875,
0.007030487060546875,
-0.003643035888671875,
-0.023834228515625,
0.00021278858184814453,
-0.009796142578125,
0.0020847320556640625,
0.0020923614501953125,
0.0063018798828125,
-0.01453399658203125,
-0.00563812255859375,
0.00018143653869628906,
0.0021514892578125,
-0.03656005859375,
-0.013397216796875,
0.0084686279296875,
-0.0100250244140625,
-0.0443115234375,
0.0089569091796875,
0.016448974609375,
-0.005985260009765625,
-0.00910186767578125,
0.009429931640625,
-0.06048583984375,
-0.004390716552734375,
-0.044464111328125,
0.0151824951171875,
-0.01480865478515625,
0.01216888427734375,
-0.0204010009765625,
0.01383209228515625,
-0.01293182373046875,
-0.00470733642578125,
-0.0095062255859375,
-0.0038909912109375,
0.020294189453125,
-0.002216339111328125,
0.0472412109375,
-0.066162109375,
-0.007419586181640625,
0.00791168212890625,
-0.029022216796875,
-0.0003681182861328125,
-0.0010538101196289062,
-0.0159912109375,
-0.00878143310546875,
0.0033626556396484375,
0.0227508544921875,
0.009735107421875,
-0.029327392578125,
0.00565338134765625,
0.00925445556640625,
-0.0020618438720703125,
0.0188751220703125,
-0.011932373046875,
-0.004688262939453125,
-0.006923675537109375,
-0.008697509765625,
-0.015106201171875,
0.007781982421875,
0.006496429443359375,
-0.00823974609375,
0.0030841827392578125,
-0.05340576171875,
0.00690460205078125,
-0.00949859619140625,
0.027099609375,
-0.0009403228759765625,
-0.0311126708984375,
-0.008636474609375,
0.0037994384765625,
0.02178955078125,
-0.01340484619140625,
0.0020751953125,
0.0262603759765625,
-0.005954742431640625,
0.0826416015625,
-0.0107421875,
0.030548095703125,
-0.01666259765625,
-0.0035953521728515625,
0.00934600830078125,
-0.047027587890625,
-0.054443359375,
0.016754150390625,
-0.01265716552734375,
-0.0016717910766601562,
0.00531005859375,
0.027374267578125,
-0.0194854736328125,
-0.0306243896484375,
0.0027256011962890625,
0.0570068359375,
0.041046142578125,
-0.0281982421875,
-0.008392333984375,
0.0056610107421875,
0.006305694580078125,
-0.0027751922607421875,
-0.0153961181640625,
-0.0131988525390625,
0.0029087066650390625,
-0.018341064453125,
-0.0181884765625,
0.0233917236328125,
-0.018402099609375,
0.0261383056640625,
-0.0032787322998046875,
0.0102691650390625,
-0.01264190673828125,
-0.0174713134765625,
0.020233154296875,
0.00452423095703125,
-0.0257568359375,
0.01346588134765625,
-0.05291748046875,
-0.033538818359375,
0.0019369125366210938,
-0.0004754066467285156,
0.0085296630859375,
0.02484130859375,
-0.004467010498046875,
0.0268096923828125,
-0.044830322265625,
-0.018798828125,
-0.0034236907958984375,
-0.0236358642578125,
0.01666259765625,
0.026153564453125,
0.01184844970703125,
0.06103515625,
0.028656005859375,
-0.01259613037109375,
-0.00746917724609375,
0.020294189453125,
-0.0189361572265625,
-0.0014858245849609375,
0.00341796875,
0.00489044189453125,
-0.019805908203125,
-0.0033702850341796875,
0.01012420654296875,
0.004077911376953125,
-0.0012340545654296875,
-0.0068359375,
-0.025970458984375,
-0.039031982421875,
0.01513671875,
0.00852203369140625,
0.0023326873779296875,
0.03118896484375,
-0.00115203857421875,
-0.0220489501953125,
-0.0033931732177734375,
-0.01287078857421875,
0.01043701171875,
-0.024261474609375,
0.0280303955078125,
0.0160980224609375,
-0.032684326171875,
0.0295562744140625,
-0.002788543701171875,
0.008636474609375,
-0.003612518310546875,
0.00894927978515625,
-0.0307159423828125,
-0.02996826171875,
0.018310546875,
0.01947021484375,
-0.03790283203125,
0.051422119140625,
0.0187530517578125,
0.0205535888671875,
-0.0162353515625,
-0.0301361083984375,
0.0237579345703125,
-0.012542724609375,
-0.0231781005859375,
0.0275115966796875,
0.0102996826171875,
-0.0006122589111328125,
-0.0029296875,
0.02911376953125,
-0.0142974853515625,
-0.0170745849609375,
0.01953125,
0.035614013671875,
-0.028045654296875,
-0.0197906494140625,
0.0021686553955078125,
-0.03460693359375,
0.01528167724609375,
-0.017486572265625,
-0.01505279541015625,
0.007904052734375,
-0.0009226799011230469,
-0.0151519775390625,
0.01229095458984375,
0.039947509765625,
0.030609130859375,
-0.005115509033203125,
0.01261138916015625,
0.02264404296875,
-0.0116119384765625,
0.0231781005859375,
0.03045654296875,
0.011444091796875,
0.02008056640625,
-0.01105499267578125,
0.042022705078125,
-0.0023441314697265625,
0.0175018310546875,
-0.01079559326171875,
-0.0242462158203125,
0.0025157928466796875,
-0.0321044921875,
0.01143646240234375,
0.046417236328125,
0.0018129348754882812,
-0.00637054443359375,
0.0384521484375,
0.0303955078125,
0.00823974609375,
-0.0213165283203125,
0.00714111328125,
-0.007740020751953125,
-0.0298614501953125,
0.00873565673828125,
-0.017608642578125,
-0.043975830078125,
-0.003963470458984375,
0.025146484375,
-0.0130462646484375,
0.035614013671875,
0.0203704833984375,
0.015716552734375,
0.005657196044921875,
0.0031890869140625,
-0.01605224609375,
-0.0024852752685546875,
0.0092926025390625,
-0.021881103515625,
-0.0104827880859375,
-0.03363037109375,
0.026092529296875,
-0.0007977485656738281,
0.00279998779296875,
-0.0230712890625,
0.0171051025390625,
-0.002758026123046875,
-0.007617950439453125,
0.009307861328125,
0.02093505859375,
-0.01398468017578125,
-0.005401611328125,
0.025390625,
0.007228851318359375,
0.0013790130615234375,
0.029266357421875,
0.00634765625,
-0.005218505859375,
0.015411376953125,
-0.0023555755615234375,
0.042083740234375,
-0.0279693603515625,
0.008026123046875,
0.0020084381103515625,
-0.003627777099609375,
-0.01036834716796875,
0.0401611328125,
-0.037689208984375,
0.001255035400390625,
-0.0089874267578125,
-0.004119873046875,
-0.048370361328125,
0.01003265380859375,
0.031829833984375,
0.024505615234375,
0.014129638671875,
0.01079559326171875,
0.00020551681518554688,
0.0156402587890625,
0.00939178466796875,
-0.0002765655517578125,
-0.006320953369140625,
-0.0016775131225585938,
0.0211334228515625,
0.00701904296875,
0.022979736328125,
0.002910614013671875,
-0.020538330078125,
0.0028018951416015625,
-0.0031585693359375,
-0.0195770263671875,
0.0095367431640625,
0.02032470703125,
-0.0152740478515625,
-0.05047607421875,
0.01332855224609375,
-0.0022830963134765625,
-0.0274658203125,
0.003726959228515625,
0.01247406005859375,
0.0015687942504882812,
0.02923583984375,
-0.0050048828125,
-0.0028667449951171875,
-0.0184326171875,
-0.00814056396484375,
-0.00330352783203125,
0.00766754150390625,
0.00203704833984375,
-0.044677734375,
-0.002674102783203125,
-0.0194854736328125,
-0.0149688720703125,
0.01050567626953125,
-0.005634307861328125,
0.0147857666015625,
0.00556182861328125,
0.021148681640625,
-0.0029926300048828125,
-0.00014269351959228516,
0.01348876953125,
0.01251983642578125,
-0.025665283203125,
-0.02069091796875,
-0.0021266937255859375,
0.0012722015380859375,
-0.0141754150390625,
0.0034961700439453125,
-0.005802154541015625,
0.007450103759765625,
0.00731658935546875,
-0.007678985595703125,
0.0267486572265625,
0.00482177734375,
0.016082763671875,
-0.0080718994140625,
-0.00400543212890625,
0.021942138671875,
0.0031280517578125,
0.0132293701171875,
-0.0330810546875,
0.0096588134765625,
-0.00815582275390625,
-0.0295867919921875,
-0.016204833984375,
0.020660400390625,
0.0131683349609375,
-0.031585693359375,
0.005435943603515625,
-0.0347900390625,
0.02044677734375,
-0.02825927734375,
-0.0013341903686523438,
0.004627227783203125,
0.0297088623046875,
-0.018096923828125,
-0.04779052734375,
0.0088653564453125,
-0.0211181640625,
-0.03289794921875,
0.00691986083984375,
-0.05157470703125,
0.0169219970703125,
-0.0252532958984375,
-0.009002685546875,
0.01084136962890625,
-0.0025768280029296875,
-0.028717041015625,
-0.01467132568359375,
0.004802703857421875,
-0.00635528564453125,
0.00809478759765625,
0.0026226043701171875,
-0.0013589859008789062,
0.019866943359375,
-0.0027923583984375,
0.0128631591796875,
0.0005064010620117188,
0.01511383056640625,
-0.009796142578125,
0.00215911865234375,
-0.0003085136413574219,
-0.010345458984375,
0.01025390625,
-0.00916290283203125,
-0.00838470458984375,
-0.022674560546875,
-0.0158233642578125,
-0.0173797607421875,
-0.0034236907958984375,
-0.025177001953125,
-0.019989013671875,
-0.010009765625,
-0.0288238525390625,
0.0285186767578125,
0.0226287841796875,
0.01425933837890625,
-0.0211029052734375,
-0.0017032623291015625,
0.02740478515625,
0.003856658935546875,
0.020538330078125,
-0.0282745361328125,
-0.01003265380859375,
-0.003345489501953125,
0.017669677734375,
-0.0284271240234375,
0.0019550323486328125,
0.0071563720703125,
0.007205963134765625,
0.0007557868957519531,
0.00302886962890625,
-0.011962890625,
0.034912109375,
-0.02655029296875,
-0.0178985595703125,
0.0038433074951171875,
0.0018138885498046875,
-0.01165771484375,
-0.021148681640625,
-0.00839996337890625,
0.006664276123046875,
0.00327301025390625,
-0.0291900634765625,
0.0011339187622070312,
-0.00009566545486450195,
-0.036529541015625,
-0.009490966796875,
0.00771331787109375,
0.01241302490234375,
-0.01094818115234375,
-0.00072479248046875,
0.06365966796875,
-0.00850677490234375,
0.023590087890625,
-0.0233001708984375,
0.0218963623046875,
0.0241241455078125,
0.019012451171875,
0.006084442138671875,
-0.01824951171875,
0.033935546875,
0.01265716552734375,
0.01287078857421875,
0.0008606910705566406,
-0.04241943359375,
0.002368927001953125,
-0.016204833984375,
0.016998291015625,
0.003589630126953125,
0.005374908447265625,
0.0221099853515625,
-0.021881103515625,
0.01143646240234375,
-0.0021572113037109375,
-0.0306243896484375,
-0.0019178390502929688,
-0.00966644287109375,
0.01021575927734375,
-0.037841796875,
-0.055816650390625,
0.03704833984375,
-0.03546142578125,
0.012908935546875,
0.01346588134765625,
0.00047707557678222656,
0.0084991455078125,
-0.0178680419921875,
-0.045257568359375,
-0.01222991943359375,
0.0070953369140625,
-0.0215911865234375,
0.007537841796875,
-0.00823974609375,
0.0110015869140625,
-0.0014095306396484375,
0.0259552001953125,
-0.0004296302795410156,
-0.024322509765625,
0.0184326171875,
0.0008759498596191406,
-0.00263214111328125,
0.0229339599609375,
-0.01849365234375,
0.0003764629364013672,
-0.0034885406494140625,
0.017913818359375,
0.022674560546875,
-0.0120391845703125,
-0.020904541015625,
0.019989013671875,
0.01776123046875,
0.002288818359375,
-0.039581298828125,
-0.01328277587890625,
0.027313232421875,
0.01212310791015625,
0.00925445556640625,
0.01119232177734375,
0.0102996826171875,
-0.004398345947265625,
0.0120391845703125,
0.01470947265625,
-0.026275634765625,
0.016021728515625,
0.0148162841796875,
0.02215576171875,
-0.018829345703125,
-0.006076812744140625,
0.0222625732421875,
-0.009796142578125,
0.0222015380859375,
-0.009185791015625,
0.049530029296875,
0.00872802734375,
0.013427734375,
-0.01800537109375,
0.0005869865417480469,
0.007442474365234375,
-0.0239410400390625,
0.005767822265625,
0.0112152099609375,
0.0128021240234375,
0.0280303955078125,
-0.03143310546875,
0.03033447265625,
-0.00579833984375,
0.0079345703125,
-0.01434326171875,
0.0226287841796875,
0.004764556884765625,
0.021331787109375,
-0.00992584228515625,
0.0244598388671875,
0.032806396484375,
-0.025146484375,
0.0079803466796875,
-0.0191650390625,
0.001712799072265625,
-0.004302978515625,
0.0352783203125,
0.0008525848388671875,
0.0028553009033203125,
0.009185791015625,
-0.025543212890625,
-0.030517578125,
0.0287322998046875,
-0.0200653076171875,
0.0361328125,
0.041412353515625,
-0.03448486328125,
-0.00591278076171875,
0.012420654296875,
-0.042510986328125,
0.0284576416015625,
-0.0018863677978515625,
-0.002105712890625,
-0.014892578125,
-0.0178985595703125,
-0.03753662109375,
0.0281219482421875,
-0.043487548828125,
0.022613525390625,
-0.00614166259765625,
0.022003173828125,
0.01806640625,
0.013336181640625,
-0.00801849365234375,
0.00540924072265625,
0.007244110107421875,
0.0007357597351074219,
0.0158843994140625,
0.025115966796875,
-0.0242767333984375,
-0.015380859375,
-0.01116180419921875,
-0.025115966796875,
-0.032684326171875,
0.032989501953125,
0.00005918741226196289,
-0.01995849609375,
-0.01540374755859375,
0.023193359375,
-0.0037689208984375,
-0.00028705596923828125,
-0.01442718505859375,
0.007450103759765625,
0.03167724609375,
-0.00955963134765625,
0.0117645263671875,
0.00832366943359375,
-0.0159912109375,
0.00247955322265625,
0.0154266357421875,
0.00659942626953125,
-0.00540924072265625,
-0.00305938720703125,
-0.036590576171875,
-0.04132080078125,
0.023529052734375,
0.0003025531768798828,
-0.0002541542053222656,
-0.0440673828125,
-0.006175994873046875,
-0.00897979736328125,
0.005706787109375,
-0.032958984375,
0.0124664306640625,
0.0181732177734375,
-0.0023174285888671875,
0.006519317626953125,
0.0296478271484375,
0.026519775390625,
-0.025909423828125,
-0.00188446044921875,
-0.02374267578125,
0.022003173828125,
0.0114288330078125,
-0.0216064453125,
0.0093231201171875,
-0.014190673828125,
0.0258331298828125,
0.0072021484375,
0.0321044921875,
-0.018157958984375,
0.0241546630859375,
-0.01407623291015625,
0.0128021240234375,
-0.0033550262451171875,
0.0099029541015625,
0.004150390625,
-0.0038471221923828125,
-0.006923675537109375,
-0.00887298583984375,
0.01203155517578125,
0.031219482421875,
0.00897979736328125,
0.0002849102020263672,
0.032135009765625,
0.006488800048828125,
-0.037567138671875,
0.0012111663818359375,
-0.033477783203125,
0.0088653564453125,
-0.006168365478515625,
0.00839996337890625,
-0.0301513671875,
-0.0178985595703125,
0.005802154541015625,
0.00653076171875,
-0.03057861328125,
-0.0233612060546875,
-0.007251739501953125,
0.007328033447265625,
-0.04974365234375,
-0.0302276611328125,
-0.004627227783203125,
0.0181427001953125,
0.00215911865234375,
0.0060272216796875,
-0.016845703125,
0.01824951171875,
0.006595611572265625,
-0.044891357421875,
0.005413055419921875,
-0.005527496337890625,
-0.0179290771484375,
-0.0018873214721679688,
-0.01097869873046875,
-0.0013513565063476562,
0.046905517578125,
0.0231170654296875,
-0.0404052734375,
-0.004695892333984375,
0.006561279296875,
-0.0413818359375,
0.02215576171875,
0.0160980224609375,
-0.009124755859375,
-0.008544921875,
0.0196533203125,
-0.007656097412109375,
0.01125335693359375,
0.026092529296875,
0.01505279541015625,
0.005283355712890625,
-0.007312774658203125,
0.010711669921875,
0.0131378173828125,
-0.0018939971923828125,
0.030548095703125,
-0.02142333984375,
-0.013275146484375,
0.0262603759765625,
0.00949859619140625,
0.023284912109375,
0.022735595703125,
0.0188446044921875,
0.027252197265625,
0.004802703857421875,
0.0141143798828125,
0.0299224853515625,
-0.0186004638671875,
0.00827789306640625,
-0.020172119140625,
-0.01207733154296875,
0.0171661376953125,
-0.00445556640625,
0.00681304931640625,
0.016021728515625,
-0.0811767578125,
-0.0116119384765625,
0.0085906982421875,
0.01727294921875,
-0.0172119140625,
-0.05908203125,
-0.023712158203125,
0.004116058349609375,
-0.0322265625,
0.019775390625,
0.036895751953125,
-0.027496337890625,
-0.006134033203125,
-0.014923095703125,
-0.0160675048828125,
0.0121917724609375,
-0.002521514892578125,
-0.0141448974609375,
0.00225067138671875,
-0.0305938720703125,
0.0208587646484375,
-0.024261474609375,
0.019989013671875,
0.0025043487548828125,
0.0491943359375,
-0.0305328369140625,
0.004802703857421875,
0.01099395751953125,
0.02703857421875,
0.0033740997314453125,
-0.021759033203125,
0.01355743408203125,
-0.01226043701171875,
0.015655517578125,
-0.0015430450439453125,
0.01186370849609375,
-0.0157928466796875,
0.01314544677734375,
0.00901031494140625,
-0.0101470947265625,
0.02716064453125,
0.02239990234375,
0.00978851318359375,
-0.038330078125,
-0.0092315673828125,
-0.032440185546875,
0.045074462890625,
-0.01000213623046875,
-0.0374755859375,
-0.0472412109375,
-0.0192413330078125,
0.044647216796875,
-0.05908203125,
0.0141754150390625,
-0.0193634033203125,
-0.0184478759765625,
0.0240478515625,
-0.002422332763671875,
0.0259857177734375,
-0.0022220611572265625,
0.03424072265625,
-0.0161285400390625,
-0.016754150390625,
0.0016021728515625,
-0.050384521484375,
0.00623321533203125,
0.0322265625,
-0.026031494140625,
-0.006641387939453125,
0.01020050048828125,
-0.0012617111206054688,
0.007526397705078125,
-0.0167694091796875,
0.031829833984375,
0.0013151168823242188,
-0.0199127197265625,
-0.025299072265625,
0.0090789794921875,
0.0087890625,
0.01276397705078125,
0.02044677734375,
-0.023345947265625,
0.00566864013671875,
-0.003292083740234375,
0.006618499755859375,
0.0224151611328125,
0.031707763671875,
-0.032745361328125,
-0.007305145263671875,
0.034912109375,
-0.0003247261047363281,
0.01467132568359375,
-0.018707275390625,
0.0117645263671875,
0.02484130859375,
0.0254058837890625,
0.0026264190673828125,
-0.0149383544921875,
-0.01377105712890625,
-0.04888916015625,
-0.027252197265625,
-0.0249786376953125,
0.006633758544921875,
0.0184173583984375,
-0.0064239501953125,
0.0050811767578125,
-0.00208282470703125,
0.01143646240234375,
-0.006374359130859375,
0.0229034423828125,
-0.0219879150390625,
0.0302276611328125,
-0.00948333740234375,
0.01082611083984375,
0.027557373046875,
-0.004917144775390625,
0.004138946533203125,
0.01186370849609375,
0.01190948486328125,
0.03253173828125,
-0.00482177734375,
-0.01206207275390625,
0.002407073974609375,
0.0022792816162109375,
-0.018402099609375,
-0.0245819091796875,
-0.00576019287109375,
-0.00850677490234375,
-0.0499267578125,
-0.00609588623046875,
0.0264892578125,
-0.0216064453125,
-0.0347900390625,
0.0160369873046875,
-0.0018701553344726562,
-0.01502227783203125,
-0.036834716796875,
-0.0352783203125,
0.003326416015625,
-0.0296478271484375,
0.00759124755859375,
-0.0096435546875,
-0.0146331787109375,
-0.00418853759765625,
0.0015611648559570312,
0.00922393798828125,
-0.02154541015625,
0.0142822265625,
0.0100555419921875,
0.000038564205169677734,
-0.00998687744140625,
0.02337646484375,
-0.020477294921875,
-0.0275421142578125,
0.01537322998046875,
0.0007715225219726562,
0.0018053054809570312,
-0.00868988037109375,
-0.018310546875,
0.0020313262939453125,
-0.00836944580078125,
-0.0058135986328125,
-0.06011962890625,
0.034820556640625,
0.02862548828125,
-0.01030731201171875,
0.00510406494140625,
0.005260467529296875,
-0.004283905029296875,
0.0148162841796875,
-0.026458740234375,
-0.0005402565002441406,
-0.01496124267578125,
0.02008056640625,
-0.0211334228515625,
-0.0164794921875,
0.00447845458984375,
-0.02581787109375,
0.004451751708984375,
0.00624847412109375,
0.007381439208984375,
-0.0173187255859375,
-0.00302886962890625,
-0.0396728515625,
0.007213592529296875,
-0.005229949951171875,
-0.00982666015625,
0.0194854736328125,
-0.00847625732421875,
0.03253173828125,
0.0028285980224609375,
0.043792724609375,
0.0005159378051757812,
0.01045989990234375,
0.0099334716796875,
-0.061676025390625,
0.0254974365234375,
0.028289794921875,
0.016204833984375,
-0.03070068359375,
-0.031524658203125,
-0.050384521484375,
0.0159759521484375,
0.0244598388671875,
-0.0062408447265625,
0.01116943359375,
-0.03515625,
-0.0187225341796875,
-0.01324462890625,
0.052978515625,
-0.0137176513671875,
-0.005130767822265625,
0.0203857421875,
-0.01364898681640625,
0.019378662109375,
0.002956390380859375,
-0.0223541259765625,
0.00566864013671875,
-0.01279449462890625,
-0.0052337646484375,
-0.010009765625,
0.02960205078125,
-0.039459228515625,
0.03717041015625,
0.0003960132598876953,
-0.012420654296875,
-0.00914764404296875,
-0.0038299560546875,
-0.0135040283203125,
0.0016069412231445312,
-0.00983428955078125,
0.006137847900390625,
0.00372314453125,
0.01025390625,
-0.0232086181640625,
0.015777587890625,
-0.0238494873046875,
-0.012603759765625,
-0.0164337158203125,
-0.032073974609375,
0.009552001953125,
-0.0076904296875,
-0.01233673095703125,
-0.01099395751953125,
-0.0133819580078125,
0.016143798828125,
-0.01486968994140625,
-0.0094757080078125,
0.00881195068359375,
0.035430908203125,
-0.0207977294921875,
0.0010137557983398438,
0.0162200927734375,
0.00757598876953125,
-0.0091400146484375,
-0.0003631114959716797,
0.011993408203125,
0.0031986236572265625,
-0.0193939208984375,
-0.02294921875,
0.0026721954345703125,
-0.008514404296875,
-0.01157379150390625,
0.024444580078125,
0.0257568359375,
-0.0102996826171875,
-0.04443359375,
-0.00815582275390625,
0.0078887939453125,
0.0673828125,
-0.01398468017578125,
-0.0203857421875,
-0.01342010498046875,
-0.0039825439453125,
-0.0174102783203125,
0.007762908935546875,
0.0035037994384765625,
-0.01100921630859375,
0.0175933837890625,
-0.0035247802734375,
0.0161285400390625,
0.01436614990234375,
-0.0031585693359375,
-0.005390167236328125,
0.001556396484375,
-0.028106689453125,
0.01155853271484375,
-0.0278167724609375,
0.040191650390625,
0.011566162109375,
0.003932952880859375,
-0.0084381103515625,
-0.0004494190216064453,
0.0189666748046875,
0.00980377197265625,
0.03509521484375,
0.0171966552734375,
-0.01291656494140625,
-0.022491455078125,
-0.005268096923828125,
-0.0095672607421875,
0.0262298583984375,
-0.00710296630859375,
0.042022705078125,
-0.00044798851013183594,
0.0160369873046875,
0.0282440185546875,
0.0147857666015625,
-0.035888671875,
0.039398193359375,
0.01105499267578125,
0.0201263427734375,
-0.00852203369140625,
-0.003551483154296875,
-0.03192138671875,
0.00920867919921875,
-0.0129547119140625,
0.0202178955078125,
-0.01044464111328125,
0.0343017578125,
0.00942230224609375,
-0.023040771484375,
-0.032501220703125,
0.005321502685546875,
-0.046051025390625,
-0.038543701171875,
0.013763427734375,
-0.023712158203125,
-0.053375244140625,
0.01325225830078125,
0.030731201171875,
-0.03582763671875,
0.01824951171875,
-0.0338134765625,
-0.00519561767578125,
0.0130615234375,
-0.01214599609375,
0.0269317626953125,
0.0114593505859375,
0.037078857421875,
-0.003482818603515625,
-0.0013017654418945312,
0.0203704833984375,
-0.035980224609375,
-0.014190673828125,
-0.025390625,
0.055633544921875,
0.01555633544921875,
0.005748748779296875,
0.0239410400390625,
0.01904296875,
-0.004367828369140625,
-0.01837158203125,
-0.005657196044921875,
0.0084075927734375,
0.0010814666748046875,
-0.0034961700439453125,
-0.01546478271484375,
0.0130157470703125,
0.020782470703125,
-0.006610870361328125,
0.004772186279296875,
-0.018524169921875,
-0.0292816162109375,
-0.01445770263671875,
-0.031646728515625,
0.02423095703125,
0.0065765380859375,
-0.0105743408203125,
0.01226043701171875,
0.024444580078125,
0.010833740234375,
0.0169525146484375,
0.00832366943359375,
-0.00859832763671875,
0.0269775390625,
0.004970550537109375,
-0.016204833984375,
-0.037445068359375,
-0.018035888671875,
-0.00630950927734375,
-0.0196075439453125,
-0.01311492919921875,
0.0372314453125,
-0.007740020751953125,
0.0003497600555419922,
0.0006661415100097656,
0.00719451904296875,
0.0021305084228515625,
0.0024089813232421875,
-0.0006918907165527344,
0.0032253265380859375,
-0.022674560546875,
0.034210205078125,
-0.01235198974609375,
-0.02996826171875,
0.0114288330078125,
-0.004070281982421875,
0.0276641845703125,
-0.0192718505859375,
-0.0009083747863769531,
0.058349609375,
0.0262908935546875,
0.01215362548828125,
-0.01446533203125,
-0.0094146728515625,
0.01247406005859375,
0.001956939697265625,
-0.0017671585083007812,
-0.004878997802734375,
-0.0208282470703125,
-0.017547607421875,
-0.010772705078125,
-0.0340576171875,
-0.0251312255859375,
-0.0181427001953125,
0.0384521484375,
-0.0087432861328125,
0.018768310546875,
-0.01947021484375,
0.024261474609375,
0.00811767578125,
-0.0182647705078125,
-0.03204345703125,
0.0196380615234375,
0.009124755859375,
-0.0066375732421875,
0.020538330078125,
0.004669189453125,
0.01338958740234375,
-0.018402099609375,
-0.01392364501953125,
-0.00334930419921875,
-0.004985809326171875,
0.00807952880859375,
0.0081939697265625,
-0.0007128715515136719,
0.01165771484375,
-0.005146026611328125,
-0.00809478759765625,
-0.02459716796875,
-0.01763916015625,
-0.01096343994140625,
0.03533935546875,
0.00026488304138183594,
0.014007568359375,
0.03204345703125,
-0.0152587890625,
-0.00939178466796875,
0.01432037353515625,
0.01959228515625,
-0.006336212158203125,
-0.0164794921875,
-0.01490020751953125,
0.0170440673828125,
-0.001682281494140625,
-0.022064208984375,
0.001964569091796875,
0.0224151611328125,
0.005756378173828125,
0.0279388427734375,
-0.03045654296875,
0.007274627685546875,
-0.0002810955047607422,
-0.016326904296875,
-0.01145172119140625,
-0.042999267578125,
-0.014923095703125,
-0.00278472900390625,
-0.00339508056640625,
0.01708984375,
-0.017669677734375,
-0.02691650390625,
-0.0255889892578125,
0.0240631103515625,
0.0171356201171875,
0.0227203369140625,
-0.0069427490234375,
-0.0293426513671875,
-0.0228118896484375,
-0.00960540771484375,
0.013336181640625,
0.0201568603515625,
-0.0215911865234375,
0.007755279541015625,
-0.004047393798828125,
0.01247406005859375,
-0.01629638671875,
-0.001495361328125,
-0.0186920166015625,
0.0120849609375,
-0.01293182373046875,
-0.01114654541015625,
-0.0243072509765625,
0.0175933837890625,
-0.00531768798828125,
-0.00550079345703125,
0.0155487060546875,
0.01282501220703125,
-0.027252197265625,
0.017578125,
0.025634765625,
0.022674560546875,
-0.01035308837890625,
-0.0037822723388671875,
0.011627197265625,
-0.01849365234375,
-0.028656005859375,
0.0189971923828125,
-0.00833892822265625,
0.004119873046875,
0.0274658203125,
-0.00197601318359375,
0.005588531494140625,
0.004695892333984375,
-0.004138946533203125,
0.0293731689453125,
-0.0278167724609375,
0.00937652587890625,
-0.0223236083984375,
0.025665283203125,
-0.0156707763671875,
0.0022182464599609375,
-0.01268768310546875,
0.036163330078125,
0.033599853515625,
-0.00691986083984375,
-0.006305694580078125,
0.0261383056640625,
-0.00278472900390625,
0.01229095458984375,
-0.0242767333984375,
0.0096435546875,
-0.00974273681640625,
0.0004260540008544922,
-0.03448486328125,
-0.030792236328125,
-0.0160675048828125,
0.0260772705078125,
-0.0004742145538330078,
0.008056640625,
-0.021453857421875,
0.029876708984375,
-0.01023101806640625,
-0.0243988037109375,
0.0169677734375,
-0.01082611083984375,
0.01299285888671875,
-0.01216888427734375,
0.0272216796875,
0.033294677734375,
0.02935791015625,
-0.0080108642578125,
0.0224609375,
-0.009857177734375,
-0.004638671875,
-0.01263427734375,
0.0030879974365234375,
0.0175323486328125,
0.00970458984375,
0.0377197265625,
-0.025177001953125,
-0.0087890625,
-0.0099945068359375,
0.0233917236328125,
-0.01497650146484375,
0.015838623046875,
0.002391815185546875,
0.007659912109375,
0.005626678466796875,
-0.041015625,
-0.017364501953125,
0.02301025390625,
-0.012298583984375,
-0.01142120361328125,
0.022552490234375,
0.0184326171875,
-0.01131439208984375,
0.052520751953125,
0.0121002197265625,
0.052337646484375,
0.0115814208984375,
0.002777099609375,
-0.016815185546875,
0.0194244384765625,
0.0137939453125,
0.01103973388671875,
0.0131378173828125,
0.0243988037109375,
0.002750396728515625,
-0.006561279296875,
0.016998291015625,
-0.0031986236572265625,
-0.00815582275390625,
0.0134429931640625,
-0.028533935546875,
0.01418304443359375,
0.00836944580078125,
0.00390625,
0.02337646484375,
-0.00952911376953125,
0.026824951171875,
0.0017004013061523438,
0.00843048095703125,
-0.01020050048828125,
-0.037017822265625,
0.033935546875,
0.010223388671875,
0.0029239654541015625,
0.00725555419921875,
0.0004954338073730469,
-0.006381988525390625,
0.0191802978515625,
-0.00586700439453125,
-0.0161895751953125,
0.02410888671875,
-0.019195556640625,
-0.0111236572265625,
0.01546478271484375,
-0.006725311279296875,
-0.007659912109375,
0.0178070068359375,
-0.01317596435546875,
-0.0306854248046875,
0.0202178955078125,
-0.054229736328125,
-0.01155853271484375,
-0.0022411346435546875,
0.0011701583862304688,
0.0031890869140625,
0.0260772705078125,
-0.02178955078125,
0.0199432373046875,
0.044464111328125,
-0.0019702911376953125,
0.00191497802734375,
0.0158233642578125,
0.00017952919006347656,
-0.00669097900390625,
-0.009552001953125,
0.006866455078125,
-0.0216217041015625,
-0.0119171142578125,
0.0288238525390625,
0.00882720947265625,
0.017730712890625,
-0.031402587890625,
0.0214385986328125,
-0.01119232177734375,
-0.032135009765625,
-0.0447998046875,
0.0037384033203125,
-0.022705078125,
-0.00424957275390625,
0.00844573974609375,
0.0296630859375,
-0.0236053466796875,
-0.0287628173828125,
-0.0007910728454589844,
-0.0212554931640625,
-0.00858306884765625,
0.0004467964172363281,
-0.00658416748046875,
-0.0101470947265625,
-0.004840850830078125,
-0.019561767578125,
-0.01513671875,
-0.01064300537109375,
0.0204620361328125,
-0.0016307830810546875,
0.00705718994140625,
0.0154876708984375,
0.037078857421875,
0.035858154296875,
0.00060272216796875,
0.0114593505859375,
0.004550933837890625,
0.033660888671875,
0.029571533203125,
0.006092071533203125,
-0.01207733154296875,
0.03131103515625,
-0.0149688720703125,
0.00531768798828125,
0.008087158203125,
-0.011627197265625,
0.01528167724609375,
0.0025844573974609375,
-0.03570556640625,
-0.01078033447265625,
-0.0121307373046875,
0.01202392578125,
0.0311279296875,
-0.0154266357421875,
-0.030517578125,
0.0204315185546875,
0.006992340087890625,
-0.0013561248779296875,
0.032989501953125,
-0.0032100677490234375,
0.004253387451171875,
-0.00951385498046875,
0.017547607421875,
0.0162353515625,
-0.0252532958984375,
-0.0244903564453125,
-0.00336456298828125,
-0.006649017333984375,
0.01446533203125,
-0.01568603515625,
0.007717132568359375,
0.026275634765625,
-0.0136566162109375,
0.03570556640625,
-0.01004791259765625,
0.00759124755859375,
0.0045013427734375,
-0.016204833984375,
-0.01071929931640625,
-0.0203094482421875,
-0.0205535888671875,
-0.0262298583984375,
0.00499725341796875,
-0.0230712890625,
-0.000064849853515625,
-0.006793975830078125,
-0.0002491474151611328,
0.0027904510498046875,
0.0033359527587890625,
0.038909912109375,
-0.002368927001953125,
-0.021697998046875,
0.04229736328125,
-0.0194854736328125,
0.0124359130859375,
0.00890350341796875,
-0.00785064697265625,
-0.0105438232421875,
0.0191650390625,
0.0170745849609375,
-0.041656494140625,
0.0177154541015625,
-0.004665374755859375,
-0.01271820068359375,
-0.031890869140625,
-0.0241546630859375,
-0.0231170654296875,
0.0066070556640625,
-0.0103912353515625,
-0.031280517578125,
-0.0195159912109375,
-0.0220489501953125,
0.01332855224609375,
0.0310821533203125,
0.0516357421875,
0.015655517578125,
-0.013275146484375,
-0.008758544921875,
0.024383544921875,
0.0007224082946777344,
-0.02398681640625,
0.018035888671875,
0.01427459716796875,
-0.00160980224609375,
-0.00911712646484375,
0.0029449462890625,
-0.00339508056640625,
-0.007366180419921875,
0.017364501953125,
0.0226593017578125,
-0.00574493408203125,
-0.005615234375,
0.0178680419921875,
0.00850677490234375,
-0.03082275390625,
0.0005712509155273438,
-0.0137939453125,
-0.026763916015625,
0.0038166046142578125,
0.018157958984375,
0.0138397216796875,
-0.009857177734375,
-0.0004968643188476562,
0.01132965087890625,
-0.0009489059448242188,
-0.0190887451171875,
0.03680419921875,
0.0029506683349609375,
0.01483917236328125,
-0.01380157470703125,
0.007656097412109375,
0.00012242794036865234,
-0.01294708251953125,
0.0008678436279296875,
-0.023406982421875,
-0.01125335693359375,
-0.04052734375,
-0.016998291015625,
0.018707275390625,
0.022735595703125,
-0.00749969482421875,
-0.01442718505859375,
-0.0218963623046875,
0.015045166015625,
-0.032135009765625,
-0.0186614990234375,
0.0089263916015625,
-0.0101318359375,
0.01520538330078125,
-0.0015668869018554688,
-0.02099609375,
0.024322509765625,
-0.02081298828125,
0.0008711814880371094,
-0.01461029052734375,
-0.030517578125,
0.001537322998046875,
0.002899169921875,
-0.033782958984375,
-0.032135009765625,
-0.0163116455078125,
0.022064208984375,
0.0020885467529296875,
0.0162506103515625,
-0.0235595703125,
0.00775146484375,
0.0158233642578125,
-0.0023822784423828125,
-0.012298583984375,
-0.0078125,
-0.019805908203125,
0.0170440673828125,
0.00666046142578125,
0.0038204193115234375,
-0.017730712890625,
-0.023406982421875,
-0.010406494140625,
-0.005229949951171875,
-0.0213623046875,
0.006137847900390625,
0.0220489501953125,
-0.0167999267578125,
-0.005725860595703125,
-0.032867431640625,
-0.0120697021484375,
0.0217742919921875,
0.03460693359375,
0.0100250244140625,
-0.016448974609375,
0.005084991455078125,
0.01256561279296875,
0.0128326416015625,
-0.019134521484375,
-0.03375244140625,
0.004886627197265625,
-0.0172271728515625,
-0.0013875961303710938,
-0.007373809814453125,
-0.027191162109375,
0.0068511962890625,
0.0543212890625,
0.0002512931823730469,
-0.01102447509765625,
0.02325439453125,
0.008880615234375,
0.035552978515625,
-0.0266876220703125,
0.006988525390625,
-0.004497528076171875,
0.029266357421875,
-0.011199951171875,
-0.0184173583984375,
-0.0014190673828125,
0.01364898681640625,
0.035247802734375,
0.00644683837890625,
0.00341033935546875,
-0.0022830963134765625,
-0.0195770263671875,
0.00444793701171875,
0.001201629638671875,
0.0127410888671875,
-0.0274200439453125,
-0.00499725341796875,
-0.038848876953125,
0.0692138671875,
-0.033203125,
0.016357421875,
-0.029052734375,
0.01346588134765625,
-0.0193023681640625,
-0.005382537841796875,
-0.00930023193359375,
-0.005695343017578125,
0.016998291015625,
-0.0246429443359375,
-0.029754638671875,
0.0361328125,
-0.0031337738037109375,
0.06512451171875,
-0.0007009506225585938,
0.0008625984191894531,
0.0282135009765625,
-0.012359619140625,
0.0176849365234375,
0.02166748046875,
0.00897216796875,
0.00341796875,
-0.00675201416015625,
-0.0186309814453125,
-0.03192138671875,
-0.0053863525390625,
-0.0014324188232421875,
0.01214599609375,
-0.0102996826171875,
-0.0276031494140625,
0.0187835693359375,
-0.0023937225341796875,
-0.00263214111328125,
0.026458740234375,
-0.01222991943359375,
0.015777587890625,
-0.00397491455078125,
0.0111083984375,
0.0194244384765625,
-0.0006041526794433594,
-0.0004334449768066406,
-0.0231170654296875,
0.0102386474609375,
0.001682281494140625,
0.0306396484375,
-0.02178955078125,
-0.01202392578125,
-0.0218963623046875,
-0.04278564453125,
-0.046600341796875,
0.009368896484375,
0.0052947998046875,
0.03594970703125,
-0.047088623046875,
0.0160064697265625,
0.0285186767578125,
0.01448822021484375,
-0.006542205810546875,
-0.0416259765625,
-0.0372314453125,
-0.016448974609375,
-0.0009775161743164062,
0.038970947265625,
-0.040130615234375,
-0.005039215087890625,
-0.00957489013671875,
0.0013761520385742188,
0.01198577880859375,
-0.0038471221923828125,
0.00896453857421875,
-0.007137298583984375,
-0.02227783203125,
0.01340484619140625,
0.033355712890625,
0.0215911865234375,
-0.00943756103515625,
-0.005481719970703125,
-0.023040771484375,
-0.0004298686981201172,
0.0156707763671875,
0.0220489501953125,
-0.0289764404296875,
0.0021457672119140625,
-0.0107269287109375,
-0.00504302978515625,
0.0163116455078125,
0.002750396728515625,
0.0100555419921875,
0.0093231201171875,
-0.0020351409912109375,
0.00022292137145996094,
0.01165771484375,
0.0247344970703125,
0.006099700927734375,
0.00746917724609375,
-0.01435089111328125,
-0.0179901123046875,
0.016754150390625,
0.03155517578125,
-0.0006580352783203125,
-0.003879547119140625,
-0.00737762451171875,
-0.0028896331787109375,
-0.004253387451171875,
-0.0006194114685058594,
-0.0151519775390625,
-0.006000518798828125,
-0.0259552001953125,
-0.002193450927734375,
0.00760650634765625,
-0.0272674560546875,
0.0279083251953125,
-0.036285400390625,
0.0149993896484375,
-0.01019287109375,
0.0006041526794433594,
-0.0027027130126953125,
-0.0010890960693359375,
-0.005558013916015625,
-0.00653076171875,
-0.0281829833984375,
-0.00800323486328125,
-0.0242767333984375,
0.0017213821411132812,
-0.000640869140625,
-0.017303466796875,
0.037261962890625,
-0.0009403228759765625,
0.029205322265625,
0.0276031494140625,
0.0194549560546875,
-0.016143798828125,
-0.0034332275390625,
-0.01354217529296875,
0.004131317138671875,
-0.004871368408203125,
-0.00493621826171875,
-0.01195526123046875,
-0.0080108642578125,
-0.00212860107421875,
0.0024242401123046875,
-0.033843994140625,
0.03790283203125,
0.019317626953125,
-0.004161834716796875,
0.02593994140625,
0.01064300537109375,
0.0007581710815429688,
0.021575927734375,
-0.00640106201171875,
-0.0033779144287109375,
-0.0052032470703125,
0.0209808349609375,
0.00390625,
-0.0168914794921875,
0.0067291259765625,
0.0167388916015625,
0.005168914794921875,
-0.0252685546875,
-0.01068878173828125,
0.0030384063720703125,
-0.00585174560546875,
-0.01126861572265625,
0.00237274169921875,
0.00675201416015625,
0.005573272705078125,
0.0125885009765625,
-0.00894927978515625,
-0.03314208984375,
-0.01143646240234375,
0.03240966796875,
-0.0152587890625,
-0.0408935546875,
0.0479736328125,
0.0164031982421875,
-0.0052642822265625,
-0.0653076171875,
0.0098876953125,
0.0209808349609375,
-0.009613037109375,
0.002117156982421875,
0.0009317398071289062,
0.01483917236328125,
0.00345611572265625,
0.02423095703125,
-0.033203125,
-0.007633209228515625,
0.0275115966796875,
-0.010406494140625,
0.01226043701171875,
0.0232391357421875,
-0.00868988037109375,
-0.0188140869140625,
-0.01027679443359375,
0.0235595703125,
0.003326416015625,
-0.015594482421875,
-0.0204315185546875,
0.0150146484375,
-0.0145416259765625,
0.013153076171875,
0.0032787322998046875,
-0.0197906494140625,
-0.021759033203125,
-0.002140045166015625,
0.0467529296875,
-0.00505828857421875,
-0.0310211181640625,
0.0159149169921875,
-0.0472412109375,
0.0298919677734375,
0.0168914794921875,
-0.01104736328125,
-0.0211181640625,
0.01300048828125,
0.0184326171875,
0.00951385498046875,
-0.01226043701171875,
0.002552032470703125,
0.012176513671875,
-0.0032787322998046875,
0.0025768280029296875,
-0.00830841064453125,
0.01209259033203125,
-0.0159454345703125,
-0.0140228271484375,
0.01558685302734375,
0.01012420654296875,
0.00617218017578125,
-0.01605224609375,
-0.0138702392578125,
-0.00457000732421875,
-0.00469207763671875,
-0.011749267578125,
-0.00968170166015625,
0.01364898681640625,
0.002506256103515625,
-0.01543426513671875,
0.0171051025390625,
-0.00292205810546875,
0.0209197998046875,
-0.0074005126953125,
0.02325439453125,
0.01485443115234375,
0.0005393028259277344,
-0.030853271484375,
0.0041046142578125,
-0.0266571044921875,
0.0032329559326171875,
0.001399993896484375,
-0.0015096664428710938,
0.0018596649169921875,
-0.00001531839370727539,
0.0032672882080078125,
-0.0178985595703125,
0.013336181640625,
0.0032558441162109375,
0.0014886856079101562,
-0.00336456298828125,
0.00023865699768066406,
0.00759124755859375,
-0.02142333984375,
-0.035125732421875,
0.0001678466796875,
0.01416015625,
0.01267242431640625,
-0.0014009475708007812,
0.005504608154296875,
-0.0187530517578125,
0.018310546875,
-0.01165771484375,
-0.0206756591796875,
-0.0128631591796875,
0.02862548828125,
0.023712158203125,
0.0030078887939453125,
-0.0197906494140625,
0.0051116943359375,
-0.053741455078125,
0.053558349609375,
0.0010690689086914062,
0.00719451904296875,
0.0021152496337890625,
0.0240936279296875,
0.039581298828125,
-0.0260009765625,
0.0084381103515625,
-0.0094757080078125,
0.0239410400390625,
-0.01177978515625,
0.0185699462890625,
0.004608154296875,
0.0114288330078125,
0.0085601806640625,
0.00014579296112060547,
0.0017633438110351562,
0.011627197265625,
-0.015716552734375,
-0.050445556640625,
-0.01102447509765625,
0.0024471282958984375,
-0.03173828125,
0.00627899169921875,
-0.011566162109375,
-0.0240936279296875,
-0.01934814453125,
-0.011199951171875,
0.01139068603515625,
-0.0066070556640625,
0.0114593505859375,
-0.0176849365234375,
-0.0152587890625,
0.00505828857421875,
-0.01247406005859375,
0.0233154296875,
0.012298583984375,
-0.0009794235229492188,
0.00409698486328125,
0.0015687942504882812,
0.001903533935546875,
0.005580902099609375,
-0.0130157470703125,
0.00029277801513671875,
-0.0082550048828125,
0.045257568359375,
0.00531005859375,
-0.01062774658203125,
0.0234527587890625,
0.02783203125,
-0.0269622802734375,
-0.0042877197265625,
0.0031719207763671875,
-0.0144195556640625,
-0.007358551025390625,
0.004291534423828125,
0.0022182464599609375,
0.0030727386474609375,
0.0106048583984375,
-0.01837158203125,
-0.0034351348876953125,
-0.04229736328125,
-0.0037174224853515625,
0.0034942626953125,
0.0125885009765625,
0.00823211669921875,
0.004688262939453125,
-0.031341552734375,
-0.01702880859375,
-0.0286865234375,
0.0038204193115234375,
0.0130157470703125,
0.0125579833984375,
0.014617919921875,
-0.0031147003173828125,
-0.0208282470703125,
-0.00811004638671875,
0.00371551513671875,
-0.0169677734375,
0.02099609375,
0.01427459716796875,
-0.004608154296875,
0.01024627685546875,
-0.01049041748046875,
-0.032440185546875,
0.03387451171875,
-0.028106689453125,
-0.0307464599609375,
-0.01165008544921875,
-0.01470947265625,
-0.015106201171875,
0.0159759521484375,
-0.025665283203125,
-0.0207366943359375,
-0.006366729736328125,
-0.00019550323486328125,
0.0245361328125,
-0.004917144775390625,
0.007274627685546875,
-0.0201873779296875,
0.000051021575927734375,
0.00023245811462402344,
0.038726806640625,
-0.0187835693359375,
-0.01544952392578125,
0.032135009765625,
-0.005268096923828125,
-0.01983642578125,
0.00675201416015625,
0.0222015380859375,
0.01084136962890625,
-0.0036468505859375,
0.005092620849609375,
-0.02154541015625,
0.0173492431640625,
0.020904541015625,
-0.015899658203125,
0.0006709098815917969,
-0.00489044189453125,
0.0139923095703125,
-0.01351165771484375,
-0.0013093948364257812,
-0.03216552734375,
-0.030242919921875,
0.0091400146484375,
0.010162353515625,
0.0208892822265625,
-0.00830078125,
0.0121612548828125,
0.01000213623046875,
-0.0012006759643554688,
-0.033599853515625,
-0.01507568359375,
0.017425537109375,
0.021881103515625,
0.01043701171875,
-0.0228271484375,
-0.04168701171875,
0.0216522216796875,
-0.0046234130859375,
0.031341552734375,
-0.01151275634765625,
-0.00890350341796875,
-0.0266265869140625,
-0.014801025390625,
0.0032596588134765625,
-0.00901031494140625,
0.000362396240234375,
-0.0294342041015625,
0.00534820556640625,
0.006622314453125,
-0.01512908935546875,
0.027313232421875,
0.006072998046875,
-0.01134490966796875,
-0.00576019287109375,
0.0022563934326171875,
-0.0291595458984375,
0.03656005859375,
0.0053253173828125,
0.0186767578125,
-0.0150146484375,
0.04168701171875,
0.0009350776672363281,
-0.0243072509765625,
-0.0149993896484375,
-0.0010213851928710938,
0.01337432861328125,
-0.00007492303848266602,
-0.011688232421875,
0.02764892578125,
-0.01282501220703125,
-0.0023136138916015625,
0.00885772705078125,
-0.01389312744140625,
0.00742340087890625,
-0.0105438232421875,
0.0086669921875,
0.004924774169921875,
-0.0162353515625,
0.007274627685546875,
-0.0102386474609375,
0.0127105712890625,
-0.0005445480346679688,
-0.011383056640625,
0.018829345703125,
0.03033447265625,
0.0234832763671875,
0.00516510009765625,
-0.017059326171875,
-0.020416259765625,
-0.00806427001953125,
0.027252197265625,
0.01326751708984375,
-0.01332855224609375,
0.0218353271484375,
0.00617218017578125,
0.0450439453125,
0.01947021484375,
-0.001163482666015625,
-0.0025196075439453125,
0.007549285888671875,
0.0175018310546875,
0.004848480224609375,
-0.048736572265625,
0.00670623779296875,
0.0019502639770507812,
0.0091400146484375,
-0.00251007080078125,
-0.01181793212890625,
-0.0024280548095703125,
-0.004360198974609375,
-0.0034351348876953125,
-0.0015382766723632812,
0.0012111663818359375,
0.01375579833984375,
0.00949859619140625,
0.018798828125,
-0.01105499267578125,
0.0163726806640625,
-0.003856658935546875,
-0.0202178955078125,
0.00859832763671875,
-0.00470733642578125,
0.0174102783203125,
0.0133514404296875,
0.00888824462890625,
-0.0029468536376953125,
0.023651123046875,
-0.0203094482421875,
-0.00641632080078125,
-0.0007071495056152344,
-0.024169921875,
0.003978729248046875,
0.021270751953125,
-0.0142822265625,
0.00035190582275390625,
-0.01053619384765625,
-0.0106658935546875,
-0.0020618438720703125,
-0.042022705078125,
-0.019287109375,
-0.02288818359375,
-0.005847930908203125,
0.0201263427734375,
-0.0093994140625,
-0.01190185546875,
0.032958984375,
-0.0016565322875976562,
0.0430908203125,
-0.016448974609375,
-0.0017719268798828125,
-0.00954437255859375,
0.051483154296875,
-0.0011501312255859375,
0.002155303955078125,
0.00809478759765625,
-0.00872802734375,
0.0092315673828125,
0.0166015625,
-0.01288604736328125,
-0.0129547119140625,
0.0207061767578125,
-0.0093231201171875,
-0.0037841796875,
-0.01375579833984375,
0.02667236328125,
-0.015350341796875,
0.00022423267364501953,
0.0003173351287841797,
-0.0168609619140625,
0.0045013427734375,
0.007366180419921875,
0.01715087890625,
-0.0104522705078125,
0.0236358642578125,
0.0054168701171875,
0.004505157470703125,
0.01409149169921875,
0.023468017578125,
0.02679443359375,
-0.047210693359375,
-0.004779815673828125,
-0.040740966796875,
0.00461578369140625,
-0.045013427734375,
0.00930023193359375,
0.0328369140625,
0.00905609130859375,
-0.0028896331787109375,
-0.038970947265625,
-0.0116424560546875,
0.019927978515625,
0.013031005859375,
0.006717681884765625,
0.0108795166015625,
0.0224151611328125,
0.034088134765625,
-0.0030384063720703125,
0.0222625732421875,
0.021881103515625,
0.0122833251953125,
0.008941650390625,
-0.0177459716796875,
-0.01531219482421875,
0.0036373138427734375,
-0.026092529296875,
-0.0235137939453125,
-0.017181396484375,
-0.01355743408203125,
-0.0121307373046875,
0.01401519775390625,
-0.0173187255859375,
-0.0082244873046875,
0.0229644775390625,
0.01027679443359375,
0.046295166015625,
0.0335693359375,
-0.00518798828125,
-0.019989013671875,
-0.0347900390625,
0.01192474365234375,
-0.0279693603515625,
0.01288604736328125,
-0.0257415771484375,
-0.0165252685546875,
-0.0207977294921875,
0.02215576171875,
-0.026641845703125,
-0.0104217529296875,
-0.035614013671875,
0.00038242340087890625,
-0.007904052734375,
0.0161590576171875,
-0.02069091796875,
0.01555633544921875,
-0.005229949951171875,
-0.030242919921875,
0.01494598388671875,
-0.005611419677734375,
-0.0400390625,
-0.001018524169921875,
0.01335906982421875,
0.02056884765625,
-0.0186767578125,
0.0224761962890625,
-0.02252197265625,
-0.0033779144287109375,
0.0229339599609375,
-0.0249481201171875,
0.00945281982421875,
-0.00830078125,
0.033111572265625,
0.0163726806640625,
0.003040313720703125,
0.01490020751953125,
0.003917694091796875,
0.01019287109375,
0.0186767578125,
0.0158538818359375,
0.01239013671875,
-0.006443023681640625,
0.005519866943359375,
0.035888671875,
0.0278167724609375,
0.025604248046875,
-0.0254669189453125,
-0.021759033203125,
-0.025970458984375,
-0.0186767578125,
0.0150604248046875,
0.0184783935546875,
0.0029697418212890625,
0.015533447265625,
-0.0023937225341796875,
0.0251922607421875,
0.004642486572265625
] |
ours_499
|
We claim that the numbers are \( 3, 4, 5, 6, \) and \( 7 \), for a sum of \( 3+4+5+6+7=25 \). It is straightforward to check that these work by listing the \( n \) smallest prime numbers for these \( n \). Note that \( n=1 \) and \( n=2 \) do not work because the \( n \) smallest prime numbers are \(\{2\}\) and \(\{2,3\}\), respectively. Also, note that \( n=8 \) does not work. Now, we show that \( n \geq 9 \) does not work. Let \( p_{1}, p_{2}, \ldots \) be the prime numbers.
If \( n \geq 9 \) is even, \( n=2k \) for some \( k \geq 5 \). If \( n \) is the median of \( p_{1}, p_{2}, \ldots, p_{n} \), then
\[
n=\frac{p_{k}+p_{k+1}}{2} \Rightarrow p_{k}<2k.
\]
Since no even numbers larger than \( 2 \) are prime, any prime below \( 2k \) must be one of \(\{2,3,5,7,9, \ldots, 2k-1\}\), which has exactly \( k \) members, so if \( p_{k}<2k \), then \( p_{j}=2j-1 \) for \( j=2,3, \ldots, k \). However, this is false for \( j=5 \), so it cannot hold for \( k \geq 5 \), as desired.
Similarly, if \( n \geq 9 \) is odd, write \( n=2k-1 \) for some \( k \geq 5 \). If \( n \) is the median of the smallest \( n \) primes, we have \( p_{k}=2k-1 \) so \( p_{k}<2k \). From the same reasoning as earlier, this cannot hold for \( k \geq 5 \).
Thus, the answer is \(\boxed{25}\).
|
25
|
{
"competition": "us_comps",
"dataset": "Ours",
"posts": null,
"source": "OMOFall19Solns.md"
}
|
Compute the sum of all positive integers \( n \) such that the median of the \( n \) smallest prime numbers is \( n \).
|
[
"/Mathematics/DiscreteMathematics/GeneralDiscreteMathematics/DiscreteMath",
"/Mathematics/DiscreteMathematics/GeneralDiscreteMathematics/DiscreteMathematics",
"/Mathematics/NumberTheory/GeneralNumberTheory/ElementaryMethods",
"/Mathematics/NumberTheory/GeneralNumberTheory/ElementaryNumberTheory",
"/Mathematics/NumberTheory/GeneralNumberTheory/HigherArithmetic",
"/Mathematics/NumberTheory/GeneralNumberTheory/NumberTheory",
"/Mathematics/NumberTheory/Integers/Integer",
"/Mathematics/NumberTheory/Integers/PositiveInteger",
"/Mathematics/NumberTheory/Integers/Z",
"/Mathematics/NumberTheory/Integers/Z-Plus",
"/Mathematics/NumberTheory/PrimeNumbers/PrimeNumberSequences"
] |
Show that the median prime must be less than twice its index, forcing the first k primes to be the first k odd numbers, which fails for k≥5.
|
[
-0.0000027418136596679688,
0.0233917236328125,
0.006557464599609375,
0.04046630859375,
-0.00011247396469116211,
0.016632080078125,
-0.00350189208984375,
0.0291595458984375,
-0.000125885009765625,
-0.006565093994140625,
-0.010711669921875,
-0.0247802734375,
0.0017919540405273438,
-0.0028285980224609375,
-0.0209197998046875,
0.0070648193359375,
0.0295867919921875,
0.007434844970703125,
0.0199737548828125,
-0.0072021484375,
-0.0022144317626953125,
-0.0577392578125,
-0.040985107421875,
0.0181121826171875,
-0.0268707275390625,
-0.042938232421875,
-0.0190277099609375,
-0.03436279296875,
0.0184783935546875,
0.03466796875,
-0.04718017578125,
0.0030307769775390625,
-0.01593017578125,
-0.0165252685546875,
-0.001285552978515625,
0.002040863037109375,
-0.0202789306640625,
0.0021228790283203125,
0.01361846923828125,
-0.027862548828125,
-0.03466796875,
-0.004428863525390625,
0.0250701904296875,
0.0033664703369140625,
0.003284454345703125,
-0.0021209716796875,
0.0031452178955078125,
0.0037021636962890625,
-0.00431060791015625,
0.00787353515625,
-0.00238037109375,
0.0073089599609375,
0.01407623291015625,
-0.018524169921875,
-0.005504608154296875,
-0.069580078125,
0.01166534423828125,
0.005008697509765625,
-0.021148681640625,
0.0030994415283203125,
0.006801605224609375,
0.015960693359375,
-0.0144805908203125,
-0.01155853271484375,
0.00383758544921875,
-0.006076812744140625,
0.016265869140625,
-0.02569580078125,
0.0119476318359375,
-0.016937255859375,
0.014190673828125,
-0.0029048919677734375,
0.006439208984375,
0.0063018798828125,
0.021209716796875,
-0.00505828857421875,
-0.00860595703125,
0.012420654296875,
-0.0261993408203125,
-0.0092315673828125,
0.01119232177734375,
0.0078125,
-0.0012836456298828125,
0.04461669921875,
-0.0008392333984375,
0.01435089111328125,
0.004329681396484375,
-0.002918243408203125,
-0.006885528564453125,
-0.02093505859375,
0.0116119384765625,
0.03619384765625,
0.01174163818359375,
-0.019805908203125,
-0.0014066696166992188,
-0.00982666015625,
0.0177154541015625,
-0.006931304931640625,
-0.0158538818359375,
0.01328277587890625,
-0.00882720947265625,
-0.0078582763671875,
0.00882720947265625,
-0.0180511474609375,
-0.029998779296875,
-0.0009794235229492188,
-0.0305938720703125,
0.012481689453125,
-0.0243072509765625,
-0.0005345344543457031,
0.01230621337890625,
0.0145263671875,
0.004833221435546875,
0.0177459716796875,
0.0052642822265625,
0.00634002685546875,
0.02587890625,
0.0196685791015625,
-0.0020904541015625,
-0.014678955078125,
-0.0050201416015625,
0.0224151611328125,
-0.020294189453125,
0.01280975341796875,
-0.0027027130126953125,
-0.0174713134765625,
-0.0091094970703125,
-0.0199432373046875,
0.0232391357421875,
0.00382232666015625,
0.0263671875,
0.0002932548522949219,
-0.0562744140625,
-0.0200958251953125,
-0.042236328125,
-0.01529693603515625,
-0.00958251953125,
-0.0213775634765625,
-0.015106201171875,
-0.00579071044921875,
0.0016679763793945312,
-0.001773834228515625,
-0.004261016845703125,
-0.0029811859130859375,
0.005908966064453125,
0.012481689453125,
-0.00672149658203125,
-0.04833984375,
-0.007335662841796875,
-0.006168365478515625,
-0.01404571533203125,
-0.01812744140625,
0.01580810546875,
-0.005100250244140625,
-0.0186614990234375,
0.012451171875,
-0.0033473968505859375,
0.0297698974609375,
-0.00969696044921875,
0.008331298828125,
0.0168609619140625,
0.0009512901306152344,
-0.0215301513671875,
-0.0159912109375,
-0.01033782958984375,
-0.0098114013671875,
-0.007228851318359375,
0.0086517333984375,
-0.00638580322265625,
0.0044097900390625,
-0.0164794921875,
-0.00018358230590820312,
-0.0133819580078125,
-0.0010528564453125,
-0.0233612060546875,
-0.01708984375,
-0.00931549072265625,
0.00423431396484375,
-0.00525665283203125,
0.0142669677734375,
-0.0107574462890625,
-0.03350830078125,
0.025543212890625,
0.013275146484375,
-0.007904052734375,
-0.00926971435546875,
0.00006580352783203125,
-0.00698089599609375,
-0.0091552734375,
0.005619049072265625,
0.030548095703125,
0.033233642578125,
-0.01438140869140625,
-0.0047760009765625,
0.0136871337890625,
-0.0010776519775390625,
-0.00858306884765625,
-0.000946044921875,
0.0010013580322265625,
0.011962890625,
0.0144195556640625,
0.00797271728515625,
-0.004436492919921875,
0.01116943359375,
0.0007672309875488281,
-0.006076812744140625,
0.0052947998046875,
0.0082550048828125,
0.0008578300476074219,
0.00980377197265625,
0.03509521484375,
-0.0016698837280273438,
-0.0016183853149414062,
-0.0413818359375,
-0.010223388671875,
0.01485443115234375,
-0.01052093505859375,
-0.004016876220703125,
-0.00341033935546875,
-0.06524658203125,
0.0111846923828125,
0.01021575927734375,
0.01485443115234375,
-0.01641845703125,
-0.01617431640625,
-0.01270294189453125,
0.007526397705078125,
0.0029964447021484375,
-0.0014467239379882812,
0.005001068115234375,
0.017608642578125,
0.00897216796875,
0.0031299591064453125,
-0.0014638900756835938,
0.0134735107421875,
0.01273345947265625,
-0.0440673828125,
-0.006420135498046875,
0.0166778564453125,
-0.03778076171875,
0.07391357421875,
0.003360748291015625,
0.01438140869140625,
0.00830078125,
-0.0117340087890625,
0.0003724098205566406,
-0.0047454833984375,
-0.005687713623046875,
0.016204833984375,
-0.0008478164672851562,
0.01486968994140625,
0.00884246826171875,
-0.007511138916015625,
-0.0160675048828125,
0.0075836181640625,
0.005126953125,
-0.005825042724609375,
-0.042449951171875,
-0.01436614990234375,
-0.00835418701171875,
-0.0068359375,
-0.027923583984375,
-0.00827789306640625,
-0.0032253265380859375,
0.01568603515625,
-0.001247406005859375,
0.036346435546875,
-0.016754150390625,
-0.00522613525390625,
-0.017913818359375,
0.004199981689453125,
-0.017303466796875,
-0.0305023193359375,
0.01186370849609375,
0.04730224609375,
-0.007091522216796875,
0.002620697021484375,
0.0047454833984375,
-0.0008254051208496094,
0.0182037353515625,
0.008758544921875,
-0.037841796875,
0.01287078857421875,
0.0200347900390625,
0.007022857666015625,
-0.028472900390625,
0.0039825439453125,
-0.04510498046875,
-0.02294921875,
-0.001007080078125,
-0.00382232666015625,
0.0289459228515625,
-0.0206298828125,
0.005687713623046875,
0.041717529296875,
-0.020050048828125,
0.01392364501953125,
0.0010509490966796875,
0.017608642578125,
-0.00904083251953125,
0.00838470458984375,
-0.01277923583984375,
-0.003650665283203125,
-0.016326904296875,
-0.00833892822265625,
0.02587890625,
0.006885528564453125,
0.04058837890625,
0.0104827880859375,
-0.0254364013671875,
-0.01416778564453125,
0.0137786865234375,
0.0232391357421875,
0.00738525390625,
0.0105438232421875,
-0.0211944580078125,
-0.008270263671875,
-0.0012598037719726562,
-0.01776123046875,
-0.004161834716796875,
-0.00228118896484375,
-0.006855010986328125,
-0.00733184814453125,
-0.00283050537109375,
-0.0180206298828125,
-0.0200347900390625,
0.004863739013671875,
0.0014438629150390625,
-0.005702972412109375,
0.016876220703125,
-0.03656005859375,
-0.0040740966796875,
0.0301666259765625,
-0.01096343994140625,
-0.006175994873046875,
-0.0028362274169921875,
-0.0197601318359375,
0.0005054473876953125,
-0.01025390625,
-0.0016965866088867188,
0.01267242431640625,
-0.0218048095703125,
-0.00783538818359375,
0.02972412109375,
-0.008819580078125,
0.00295257568359375,
-0.0186614990234375,
0.0007467269897460938,
-0.0014429092407226562,
-0.0236053466796875,
-0.0096893310546875,
-0.00383758544921875,
0.0197906494140625,
-0.0230712890625,
-0.03656005859375,
0.00994110107421875,
-0.0121917724609375,
0.0018854141235351562,
0.0034389495849609375,
0.0304412841796875,
-0.00634002685546875,
-0.034332275390625,
-0.0158233642578125,
-0.0038738250732421875,
0.0057830810546875,
-0.022857666015625,
-0.004970550537109375,
-0.0028247833251953125,
-0.05181884765625,
-0.005062103271484375,
-0.025390625,
-0.0262451171875,
0.046905517578125,
-0.0182952880859375,
-0.07080078125,
0.002655029296875,
0.009429931640625,
-0.006969451904296875,
-0.0045013427734375,
0.0002951622009277344,
0.012237548828125,
-0.0087127685546875,
-0.00530242919921875,
0.037994384765625,
-0.0153045654296875,
0.0032787322998046875,
0.00933837890625,
-0.0235748291015625,
-0.039093017578125,
0.01236724853515625,
-0.01153564453125,
0.00977325439453125,
-0.0144195556640625,
0.0128173828125,
0.0241241455078125,
-0.0107269287109375,
0.004673004150390625,
0.03204345703125,
0.050018310546875,
-0.0027713775634765625,
-0.0216217041015625,
-0.0286712646484375,
-0.0286407470703125,
0.020111083984375,
-0.0057830810546875,
0.004791259765625,
0.0261688232421875,
-0.01035308837890625,
0.010284423828125,
-0.0075225830078125,
-0.0006837844848632812,
0.0171356201171875,
-0.0207672119140625,
-0.010955810546875,
-0.0034008026123046875,
0.01219940185546875,
-0.02203369140625,
-0.0006313323974609375,
-0.03533935546875,
0.01477813720703125,
0.0021686553955078125,
-0.038177490234375,
-0.03472900390625,
-0.006195068359375,
0.0244293212890625,
0.031494140625,
-0.0013904571533203125,
0.036407470703125,
0.0214080810546875,
0.00740814208984375,
0.00661468505859375,
0.0008301734924316406,
0.007640838623046875,
0.0178680419921875,
-0.00850677490234375,
0.031097412109375,
0.03143310546875,
0.00789642333984375,
-0.000030994415283203125,
0.0289154052734375,
0.0110321044921875,
-0.0203399658203125,
-0.01348114013671875,
0.0182342529296875,
-0.01690673828125,
-0.007015228271484375,
0.0099029541015625,
0.0201873779296875,
-0.0093994140625,
0.00836944580078125,
-0.006603240966796875,
-0.01983642578125,
-0.01322174072265625,
0.0084075927734375,
-0.0115203857421875,
-0.0023365020751953125,
-0.00927734375,
-0.012054443359375,
-0.005950927734375,
-0.01184844970703125,
-0.01318359375,
-0.0038909912109375,
-0.040191650390625,
0.0012083053588867188,
-0.0222015380859375,
0.0124664306640625,
0.02008056640625,
0.0034847259521484375,
-0.00664520263671875,
0.02764892578125,
-0.01543426513671875,
-0.01198577880859375,
0.00223541259765625,
-0.041229248046875,
-0.0216827392578125,
0.028167724609375,
-0.00672149658203125,
0.009063720703125,
-0.0291748046875,
-0.0045318603515625,
0.00687408447265625,
-0.00785064697265625,
-0.0155792236328125,
0.016510009765625,
-0.006175994873046875,
-0.0011348724365234375,
0.0128326416015625,
0.003261566162109375,
0.0122222900390625,
-0.03668212890625,
0.0174102783203125,
0.0025539398193359375,
-0.01425933837890625,
-0.0268096923828125,
-0.01507568359375,
-0.02490234375,
-0.00031375885009765625,
-0.0030345916748046875,
0.010589599609375,
-0.01256561279296875,
0.00875091552734375,
-0.0180206298828125,
-0.018035888671875,
0.04241943359375,
0.0046539306640625,
-0.0189208984375,
0.038421630859375,
0.0142364501953125,
0.0107879638671875,
0.0071563720703125,
-0.00689697265625,
0.006847381591796875,
0.01296234130859375,
-0.0467529296875,
0.004673004150390625,
-0.0171356201171875,
0.00485992431640625,
-0.005573272705078125,
-0.0035381317138671875,
0.005001068115234375,
-0.0322265625,
0.0016889572143554688,
0.0281982421875,
0.0290069580078125,
0.0277862548828125,
0.0170745849609375,
-0.0181427001953125,
-0.030181884765625,
0.0283050537109375,
0.01410675048828125,
-0.0091400146484375,
-0.0170745849609375,
0.0128326416015625,
0.0031604766845703125,
-0.050140380859375,
-0.0022830963134765625,
0.020050048828125,
0.01873779296875,
0.0311126708984375,
-0.00870513916015625,
-0.01885986328125,
-0.0341796875,
0.012969970703125,
0.0109710693359375,
-0.023681640625,
-0.0142669677734375,
-0.0290374755859375,
0.016815185546875,
0.01103973388671875,
0.0224456787109375,
0.034515380859375,
0.02972412109375,
-0.0224456787109375,
0.01239776611328125,
0.0040740966796875,
0.01274871826171875,
0.008270263671875,
0.049957275390625,
-0.0236053466796875,
0.003131866455078125,
0.01366424560546875,
-0.0050811767578125,
-0.0226593017578125,
0.016998291015625,
0.0005831718444824219,
-0.01081085205078125,
-0.0007367134094238281,
-0.0183868408203125,
-0.0182647705078125,
-0.01287841796875,
0.0288238525390625,
-0.010589599609375,
-0.0143585205078125,
-0.014556884765625,
-0.0521240234375,
-0.06280517578125,
-0.041229248046875,
-0.0107269287109375,
-0.007434844970703125,
-0.0302886962890625,
0.053314208984375,
0.0257415771484375,
0.0203704833984375,
-0.0011663436889648438,
0.01507568359375,
-0.00855255126953125,
0.00830841064453125,
0.00966644287109375,
0.01488494873046875,
0.0284576416015625,
-0.026214599609375,
-0.015838623046875,
0.008026123046875,
-0.0225830078125,
-0.022125244140625,
0.0062103271484375,
0.03460693359375,
-0.032867431640625,
0.0206298828125,
-0.005329132080078125,
0.018585205078125,
0.0030879974365234375,
-0.01248931884765625,
0.0227203369140625,
0.002582550048828125,
-0.002338409423828125,
-0.0066070556640625,
0.0178680419921875,
0.01523590087890625,
0.00438690185546875,
-0.010223388671875,
-0.025543212890625,
0.007709503173828125,
-0.0079193115234375,
0.00850677490234375,
0.0156707763671875,
-0.00489044189453125,
-0.0028362274169921875,
0.02056884765625,
-0.01593017578125,
0.0203399658203125,
0.0132904052734375,
-0.0085906982421875,
0.007694244384765625,
-0.01446533203125,
0.0017032623291015625,
0.0521240234375,
-0.006603240966796875,
-0.01139068603515625,
0.0040435791015625,
0.0009813308715820312,
-0.011627197265625,
-0.0198211669921875,
-0.00736236572265625,
-0.007080078125,
-0.0367431640625,
-0.02203369140625,
0.045440673828125,
-0.0175628662109375,
-0.0158843994140625,
-0.0016202926635742188,
0.0092010498046875,
0.0051116943359375,
-0.0418701171875,
-0.0234375,
-0.007568359375,
-0.0173492431640625,
0.03741455078125,
-0.00373077392578125,
0.01409149169921875,
0.0040435791015625,
-0.017486572265625,
0.008209228515625,
0.0201416015625,
0.04034423828125,
0.01197052001953125,
0.0343017578125,
-0.021575927734375,
0.0316162109375,
-0.031982421875,
-0.00496673583984375,
-0.0130615234375,
-0.007625579833984375,
-0.0099945068359375,
-0.030364990234375,
-0.0306854248046875,
0.0172119140625,
-0.00835418701171875,
-0.003871917724609375,
-0.0045013427734375,
-0.0333251953125,
-0.007144927978515625,
0.00991058349609375,
0.00896453857421875,
0.0015392303466796875,
-0.0159759521484375,
-0.009796142578125,
-0.01232147216796875,
0.01006317138671875,
0.0186004638671875,
-0.0085601806640625,
-0.00687408447265625,
0.0254058837890625,
-0.005542755126953125,
-0.0271759033203125,
0.0217742919921875,
-0.0189666748046875,
0.004436492919921875,
-0.00865936279296875,
0.0157623291015625,
0.003147125244140625,
0.00058746337890625,
-0.004520416259765625,
0.0081024169921875,
-0.00896453857421875,
-0.026885986328125,
0.0233612060546875,
-0.034942626953125,
-0.0274505615234375,
0.00574493408203125,
-0.003673553466796875,
-0.0086669921875,
0.0287628173828125,
-0.002819061279296875,
-0.004116058349609375,
0.0009331703186035156,
0.006290435791015625,
-0.006046295166015625,
-0.0229949951171875,
0.033111572265625,
0.0017490386962890625,
-0.004299163818359375,
-0.0150146484375,
-0.007503509521484375,
-0.01320648193359375,
0.0299224853515625,
-0.0086822509765625,
-0.0190582275390625,
-0.0189208984375,
0.0082244873046875,
-0.0496826171875,
-0.0002219676971435547,
0.005435943603515625,
0.0212554931640625,
0.030914306640625,
0.02435302734375,
0.0024394989013671875,
-0.0144195556640625,
-0.039886474609375,
-0.00630950927734375,
-0.0240936279296875,
-0.011871337890625,
-0.0127105712890625,
-0.00980377197265625,
-0.0210113525390625,
0.00628662109375,
0.037109375,
0.0200347900390625,
0.00354766845703125,
0.0191497802734375,
0.02215576171875,
-0.02288818359375,
0.0223541259765625,
-0.0098114013671875,
-0.012725830078125,
-0.009063720703125,
-0.00583648681640625,
-0.0158233642578125,
-0.004482269287109375,
-0.0307159423828125,
0.0082550048828125,
-0.0021991729736328125,
-0.00565338134765625,
-0.03887939453125,
-0.01416015625,
-0.01338958740234375,
0.00982666015625,
-0.0220794677734375,
0.0218353271484375,
0.013763427734375,
-0.035491943359375,
-0.01320648193359375,
-0.004116058349609375,
-0.0239715576171875,
0.0003705024719238281,
-0.0224151611328125,
-0.0265350341796875,
-0.01447296142578125,
-0.0212249755859375,
0.04510498046875,
-0.029052734375,
0.0223236083984375,
-0.020355224609375,
0.004718780517578125,
0.030120849609375,
0.015960693359375,
-0.026031494140625,
0.01299285888671875,
0.01163482666015625,
0.011077880859375,
0.0121917724609375,
0.01279449462890625,
0.0004410743713378906,
0.023284912109375,
0.0255584716796875,
0.0201568603515625,
0.01337432861328125,
-0.02459716796875,
0.01165008544921875,
-0.019622802734375,
0.0202178955078125,
0.0208282470703125,
0.00875091552734375,
-0.018402099609375,
-0.018310546875,
-0.0098419189453125,
-0.030853271484375,
-0.01152801513671875,
-0.00902557373046875,
-0.0200042724609375,
-0.003444671630859375,
-0.0098114013671875,
-0.01324462890625,
0.0190277099609375,
0.006072998046875,
-0.01548004150390625,
0.030120849609375,
-0.03564453125,
0.004047393798828125,
0.033538818359375,
0.0017919540405273438,
-0.01293182373046875,
-0.01416015625,
-0.01334381103515625,
0.0265045166015625,
-0.01526641845703125,
0.004985809326171875,
0.01105499267578125,
0.00901031494140625,
-0.0111083984375,
-0.000797271728515625,
0.0316162109375,
-0.0107879638671875,
-0.0163421630859375,
-0.026153564453125,
0.01088714599609375,
0.003505706787109375,
-0.032135009765625,
0.00374603271484375,
-0.022552490234375,
-0.0243072509765625,
-0.00919342041015625,
-0.021728515625,
0.0042724609375,
-0.0101318359375,
-0.031768798828125,
0.006885528564453125,
0.0196685791015625,
-0.01435089111328125,
0.042449951171875,
-0.0177001953125,
0.0145721435546875,
0.0016679763793945312,
-0.0030879974365234375,
0.01898193359375,
-0.01641845703125,
-0.0111083984375,
0.00785064697265625,
0.003597259521484375,
-0.01255035400390625,
0.023773193359375,
0.0083160400390625,
-0.004970550537109375,
0.00969696044921875,
-0.0014324188232421875,
0.0179595947265625,
0.0308990478515625,
-0.01525115966796875,
-0.0278472900390625,
-0.006206512451171875,
-0.0028057098388671875,
-0.052703857421875,
0.0024127960205078125,
-0.00907135009765625,
-0.01494598388671875,
-0.0252227783203125,
-0.0299224853515625,
-0.039306640625,
-0.0016698837280273438,
0.01506805419921875,
0.0264434814453125,
-0.052093505859375,
-0.0007371902465820312,
-0.00884246826171875,
0.0173797607421875,
-0.004459381103515625,
-0.006412506103515625,
0.03271484375,
0.03082275390625,
0.0240020751953125,
-0.01910400390625,
-0.01309967041015625,
-0.03582763671875,
-0.00896453857421875,
-0.0163726806640625,
-0.0176544189453125,
0.024688720703125,
0.012786865234375,
0.0003516674041748047,
-0.031005859375,
-0.0229644775390625,
-0.00986480712890625,
0.004283905029296875,
0.01129913330078125,
0.01169586181640625,
0.0265960693359375,
0.004405975341796875,
0.01262664794921875,
-0.0128021240234375,
-0.0212554931640625,
-0.0010700225830078125,
0.01263427734375,
0.036529541015625,
0.031524658203125,
-0.0030364990234375,
-0.04510498046875,
-0.0272216796875,
0.029998779296875,
0.01125335693359375,
-0.007305145263671875,
-0.0278778076171875,
0.011077880859375,
0.0565185546875,
0.01123046875,
-0.0616455078125,
0.0106658935546875,
-0.006473541259765625,
-0.015228271484375,
0.00684356689453125,
-0.01331329345703125,
0.0196533203125,
-0.0355224609375,
-0.008026123046875,
-0.053558349609375,
0.0277099609375,
-0.0194854736328125,
0.0009646415710449219,
-0.0189666748046875,
-0.00897979736328125,
-0.01424407958984375,
-0.0148162841796875,
-0.004604339599609375,
-0.03948974609375,
-0.0141143798828125,
-0.0181121826171875,
-0.0173797607421875,
0.0211181640625,
0.01453399658203125,
-0.0088348388671875,
0.00968170166015625,
-0.002132415771484375,
-0.035491943359375,
0.01421356201171875,
0.06378173828125,
-0.00948333740234375,
0.031829833984375,
-0.0126953125,
0.0289306640625,
-0.025482177734375,
-0.01018524169921875,
-0.0145416259765625,
-0.00479888916015625,
0.00015735626220703125,
-0.01617431640625,
0.0108489990234375,
0.02032470703125,
0.033294677734375,
-0.007476806640625,
-0.024566650390625,
-0.0176849365234375,
0.012054443359375,
0.0007829666137695312,
-0.03656005859375,
-0.028106689453125,
-0.00017344951629638672,
0.0010633468627929688,
0.01508331298828125,
0.0182952880859375,
0.03167724609375,
0.004802703857421875,
-0.023590087890625,
0.01617431640625,
0.0086822509765625,
-0.049468994140625,
0.002025604248046875,
0.01044464111328125,
-0.0298919677734375,
-0.00864410400390625,
0.0038013458251953125,
-0.0038242340087890625,
-0.0231475830078125,
0.03802490234375,
-0.032379150390625,
-0.022247314453125,
0.01328277587890625,
0.015899658203125,
0.04278564453125,
-0.053009033203125,
0.0045013427734375,
-0.035491943359375,
-0.04681396484375,
0.0240020751953125,
0.0164794921875,
-0.005985260009765625,
-0.021575927734375,
-0.007537841796875,
-0.006740570068359375,
0.0046234130859375,
0.035430908203125,
0.0137481689453125,
-0.006526947021484375,
0.003421783447265625,
0.015777587890625,
0.018798828125,
0.023223876953125,
0.01314544677734375,
0.0155487060546875,
0.00843048095703125,
0.0009169578552246094,
0.0036029815673828125,
-0.01038360595703125,
0.0264739990234375,
-0.02459716796875,
0.047210693359375,
-0.04266357421875,
0.04547119140625,
0.002635955810546875,
0.0233154296875,
-0.0188751220703125,
-0.0009317398071289062,
-0.004634857177734375,
-0.0126800537109375,
-0.03515625,
-0.01092529296875,
0.0234222412109375,
0.045135498046875,
-0.007266998291015625,
0.016845703125,
0.039642333984375,
0.00017654895782470703,
0.0092926025390625,
-0.014129638671875,
0.0089263916015625,
-0.004680633544921875,
-0.0086669921875,
-0.020477294921875,
0.054351806640625,
-0.038330078125,
0.01337432861328125,
0.0189971923828125,
-0.010467529296875,
0.017669677734375,
0.032989501953125,
0.0187225341796875,
0.006130218505859375,
-0.00836944580078125,
0.024169921875,
0.01049041748046875,
-0.039459228515625,
-0.022003173828125,
-0.00164794921875,
0.0168304443359375,
-0.0494384765625,
0.00655364990234375,
0.0014905929565429688,
0.01702880859375,
0.0002663135528564453,
0.029327392578125,
0.0009374618530273438,
0.0394287109375,
-0.00856781005859375,
-0.01171112060546875,
-0.0091094970703125,
-0.00470733642578125,
-0.0197296142578125,
0.0176544189453125,
-0.039093017578125,
0.0031642913818359375,
0.00716400146484375,
0.037200927734375,
-0.03173828125,
0.048370361328125,
-0.002674102783203125,
-0.04833984375,
-0.003879547119140625,
0.01305389404296875,
-0.0107269287109375,
-0.005893707275390625,
0.00888824462890625,
0.01515960693359375,
0.026885986328125,
0.00118255615234375,
-0.0401611328125,
-0.0018606185913085938,
-0.020904541015625,
0.049285888671875,
-0.01123046875,
-0.0037212371826171875,
0.0273895263671875,
-0.00917816162109375,
-0.02081298828125,
-0.02069091796875,
-0.01490020751953125,
-0.0290679931640625,
0.00885009765625,
0.00258636474609375,
0.0097808837890625,
0.0260772705078125,
0.0196685791015625,
-0.032562255859375,
0.001708984375,
0.0131072998046875,
-0.0238494873046875,
0.00482177734375,
0.0160369873046875,
0.0013551712036132812,
0.0042724609375,
0.0065155029296875,
-0.0008363723754882812,
0.0172882080078125,
-0.0270843505859375,
0.0205078125,
0.025146484375,
0.020660400390625,
-0.0159912109375,
-0.0018224716186523438,
0.005126953125,
-0.02374267578125,
0.0027523040771484375,
0.0228729248046875,
-0.01461029052734375,
0.00287628173828125,
0.0197601318359375,
-0.0002987384796142578,
-0.01007080078125,
-0.01416015625,
-0.0114898681640625,
-0.032073974609375,
0.0047149658203125,
0.00927734375,
-0.0079498291015625,
-0.003543853759765625,
0.01422882080078125,
0.0015153884887695312,
0.0003414154052734375,
-0.0154571533203125,
0.019989013671875,
-0.006832122802734375,
0.009674072265625,
-0.0213470458984375,
-0.01419830322265625,
0.0161895751953125,
0.00543975830078125,
-0.00980377197265625,
-0.009490966796875,
0.025604248046875,
-0.0241851806640625,
0.00994873046875,
0.0277252197265625,
-0.002960205078125,
-0.0236053466796875,
0.0205841064453125,
-0.01441192626953125,
-0.049774169921875,
-0.0007977485656738281,
0.01340484619140625,
-0.007488250732421875,
-0.01168060302734375,
0.01506805419921875,
0.00955963134765625,
0.002529144287109375,
0.0036983489990234375,
0.031524658203125,
-0.0038547515869140625,
-0.035186767578125,
-0.003818511962890625,
0.018402099609375,
0.0006279945373535156,
-0.00977325439453125,
0.010040283203125,
-0.0230865478515625,
-0.042572021484375,
0.0032520294189453125,
0.01189422607421875,
0.005809783935546875,
0.0010576248168945312,
0.0116119384765625,
-0.0067138671875,
-0.0200042724609375,
-0.0158538818359375,
-0.00173187255859375,
0.0308380126953125,
0.0180206298828125,
-0.0232391357421875,
-0.0003306865692138672,
-0.0226287841796875,
0.0243377685546875,
-0.004207611083984375,
-0.0300140380859375,
0.0200958251953125,
-0.0205535888671875,
0.003192901611328125,
-0.016693115234375,
0.006198883056640625,
-0.0236663818359375,
-0.0088653564453125,
-0.0160369873046875,
0.000011086463928222656,
-0.03192138671875,
-0.002506256103515625,
-0.01995849609375,
-0.020233154296875,
-0.038787841796875,
-0.0249481201171875,
-0.01134490966796875,
0.00730133056640625,
0.0008893013000488281,
0.01352691650390625,
0.00519561767578125,
0.00618743896484375,
-0.0197601318359375,
0.0115509033203125,
-0.01058197021484375,
0.00711822509765625,
0.036407470703125,
0.0181427001953125,
0.019805908203125,
-0.03814697265625,
0.006298065185546875,
-0.03778076171875,
-0.0212249755859375,
0.0022792816162109375,
0.0007448196411132812,
0.0007100105285644531,
0.0032901763916015625,
-0.0036182403564453125,
-0.031707763671875,
0.010528564453125,
-0.01013946533203125,
0.0168304443359375,
0.022735595703125,
-0.005268096923828125,
-0.00374603271484375,
0.0224761962890625,
0.0064697265625,
-0.011962890625,
0.0016412734985351562,
0.0256195068359375,
0.0262451171875,
0.0202178955078125,
-0.044830322265625,
0.0006756782531738281,
-0.0037822723388671875,
0.017486572265625,
0.02618408203125,
0.011810302734375,
-0.034942626953125,
-0.0135040283203125,
-0.0219879150390625,
-0.033721923828125,
-0.0225982666015625,
0.009552001953125,
-0.037322998046875,
-0.004657745361328125,
-0.01343536376953125,
-0.006656646728515625,
0.031585693359375,
0.0066680908203125,
-0.0052490234375,
-0.00823211669921875,
0.0115509033203125,
0.0211944580078125,
-0.00510406494140625,
-0.0048980712890625,
0.01263427734375,
-0.03521728515625,
0.00310516357421875,
0.030303955078125,
0.0005774497985839844,
0.0032482147216796875,
0.0273284912109375,
0.0017528533935546875,
-0.0045928955078125,
0.0276947021484375,
-0.032196044921875,
-0.0307769775390625,
-0.01369476318359375,
-0.00457000732421875,
0.00986480712890625,
-0.021881103515625,
-0.040252685546875,
0.035125732421875,
0.017303466796875,
-0.011505126953125,
-0.0164794921875,
-0.0167236328125,
-0.0169677734375,
0.021575927734375,
0.0186920166015625,
-0.00576019287109375,
0.0176239013671875,
-0.0162200927734375,
-0.0211181640625,
-0.00312042236328125,
-0.04400634765625,
-0.00583648681640625,
-0.007602691650390625,
0.005725860595703125,
0.0081939697265625,
-0.0230255126953125,
0.0196685791015625,
-0.032379150390625,
-0.01271820068359375,
-0.022430419921875,
0.0014028549194335938,
-0.00446319580078125,
-0.0085601806640625,
-0.00611114501953125,
0.02606201171875,
0.005084991455078125,
0.0178375244140625,
0.03662109375,
0.04443359375,
-0.0149688720703125,
0.0180816650390625,
-0.0010242462158203125,
-0.00386810302734375,
-0.0399169921875,
-0.047332763671875,
0.0088958740234375,
-0.0192413330078125,
0.00905609130859375,
0.0033721923828125,
0.0175628662109375,
-0.020843505859375,
-0.03729248046875,
0.0203857421875,
-0.0189056396484375,
-0.0048675537109375,
-0.00798797607421875,
0.007701873779296875,
0.0210418701171875,
-0.01495361328125,
0.0017242431640625,
-0.016571044921875,
0.041778564453125,
-0.003284454345703125,
0.0258331298828125,
-0.01009368896484375,
-0.027099609375,
0.0076446533203125,
0.07086181640625,
-0.003871917724609375,
0.04608154296875,
-0.0013513565063476562,
-0.016571044921875,
-0.0294952392578125,
0.00449371337890625,
0.0236358642578125,
-0.025115966796875,
0.03936767578125,
0.0179443359375,
0.00872039794921875,
0.007568359375,
-0.02490234375,
-0.0189361572265625,
0.0020618438720703125,
0.018280029296875,
0.0163116455078125,
-0.0254364013671875,
0.02337646484375,
-0.0121002197265625,
-0.007843017578125,
-0.018707275390625,
0.0204620361328125,
0.0169219970703125,
0.0297088623046875,
-0.006591796875,
-0.01291656494140625,
0.0253753662109375,
0.0007491111755371094,
-0.0090484619140625,
-0.0119476318359375,
0.00733184814453125,
-0.007137298583984375,
-0.0254669189453125,
0.0018529891967773438,
0.03173828125,
0.01529693603515625,
0.01995849609375,
0.013885498046875,
-0.00928497314453125,
-0.020477294921875,
-0.0188446044921875,
0.002315521240234375,
0.009033203125,
-0.007343292236328125,
0.00518035888671875,
-0.001583099365234375,
-0.017608642578125,
0.0287322998046875,
0.019317626953125,
0.001338958740234375,
0.012176513671875,
-0.023101806640625,
-0.0309295654296875,
0.0301666259765625,
-0.016998291015625,
-0.006977081298828125,
0.0288238525390625,
0.038848876953125,
-0.0211944580078125,
0.01247406005859375,
0.01247406005859375,
0.0179595947265625,
0.01053619384765625,
0.018096923828125,
0.004425048828125,
0.037628173828125,
0.00415802001953125,
-0.0096893310546875,
0.01403045654296875,
-0.0088348388671875,
-0.0013980865478515625,
0.01505279541015625,
-0.00797271728515625,
0.004734039306640625,
0.0172119140625,
-0.0093231201171875,
0.00555419921875,
-0.016357421875,
-0.00533294677734375,
-0.02374267578125,
-0.01294708251953125,
-0.0277252197265625,
-0.000021278858184814453,
-0.0101318359375,
0.01153564453125,
-0.0068817138671875,
-0.0059051513671875,
0.0232391357421875,
-0.0048370361328125,
-0.0123291015625,
-0.0335693359375,
0.002933502197265625,
0.02142333984375,
0.0059051513671875,
0.0167236328125,
0.0447998046875,
0.04486083984375,
-0.01531982421875,
0.01158905029296875,
-0.0026950836181640625,
0.024932861328125,
-0.0258026123046875,
0.01068115234375,
-0.0016889572143554688,
-0.031524658203125,
0.035552978515625,
-0.005611419677734375,
-0.00016069412231445312,
-0.01136016845703125,
-0.0079498291015625,
0.022705078125,
0.047332763671875,
0.0272064208984375,
-0.0220184326171875,
0.004199981689453125,
-0.004550933837890625,
0.00844573974609375,
-0.00603485107421875,
0.03729248046875,
0.0291748046875,
0.020050048828125,
0.03350830078125,
-0.01485443115234375,
-0.018524169921875,
0.032073974609375,
0.0048065185546875,
-0.031341552734375,
0.0121612548828125,
-0.00612640380859375,
-0.049713134765625,
0.003452301025390625,
-0.037353515625,
-0.0108184814453125,
0.0265045166015625,
-0.034454345703125,
-0.0200042724609375,
-0.01149749755859375,
-0.0025177001953125,
0.0215911865234375,
0.0203704833984375,
0.027191162109375,
-0.03900146484375,
-0.016998291015625,
-0.0011196136474609375,
-0.015167236328125,
-0.005313873291015625,
-0.002506256103515625,
-0.001575469970703125,
-0.003643035888671875,
-0.007343292236328125,
0.0012903213500976562,
-0.0156402587890625,
0.0144805908203125,
-0.00710296630859375,
-0.0028591156005859375,
-0.020355224609375,
-0.030609130859375,
0.01007080078125,
0.00876617431640625,
0.0260162353515625,
-0.0255889892578125,
0.00464630126953125,
-0.01385498046875,
0.016082763671875,
0.03692626953125,
-0.005016326904296875,
-0.0034084320068359375,
-0.01507568359375,
-0.042755126953125,
0.01166534423828125,
-0.017059326171875,
-0.03765869140625,
-0.0264739990234375,
-0.0007691383361816406,
0.0097808837890625,
0.0023746490478515625,
0.02630615234375,
0.035736083984375,
0.0011882781982421875,
-0.01097869873046875,
0.0196380615234375,
0.0194854736328125,
-0.00972747802734375,
0.003673553466796875,
0.0060577392578125,
-0.0017099380493164062,
0.020751953125,
0.0016813278198242188,
-0.0256195068359375,
0.0205535888671875,
-0.0044403076171875,
0.0198822021484375,
0.0033626556396484375,
-0.041900634765625,
0.00946807861328125,
-0.00902557373046875,
-0.01031494140625,
0.0426025390625,
0.00836181640625,
0.0278472900390625,
0.0036773681640625,
0.0028533935546875,
0.00492095947265625,
0.0006632804870605469,
-0.004482269287109375,
-0.00970458984375,
-0.0001990795135498047,
0.022247314453125,
-0.02056884765625,
0.01136016845703125,
-0.0223541259765625,
0.018707275390625,
-0.01337432861328125,
0.006343841552734375,
0.01666259765625,
-0.007274627685546875,
0.01457977294921875,
-0.006069183349609375,
-0.0034580230712890625,
0.007297515869140625,
0.0083160400390625,
0.0191802978515625,
-0.00667572021484375,
-0.0038318634033203125,
0.01436614990234375,
0.0145263671875,
-0.0154876708984375,
-0.007503509521484375,
0.0280303955078125,
-0.0007476806640625,
0.008148193359375,
0.0099334716796875,
-0.0093841552734375,
0.00396728515625,
0.0019664764404296875,
-0.006103515625,
0.006710052490234375,
-0.032623291015625,
-0.0013456344604492188,
0.025177001953125,
-0.0028514862060546875,
0.034820556640625,
0.0010366439819335938,
-0.03387451171875,
0.0300140380859375,
-0.01352691650390625,
-0.02264404296875,
0.01493072509765625,
0.00698089599609375,
0.043914794921875,
0.0266876220703125,
-0.00015664100646972656,
-0.02716064453125,
0.0232391357421875,
-0.0252685546875,
0.01486968994140625,
0.00986480712890625,
-0.004192352294921875,
0.04046630859375,
0.0017852783203125,
0.0005192756652832031,
0.006439208984375,
0.005218505859375,
0.0177459716796875,
0.035430908203125,
0.00911712646484375,
0.0080108642578125,
0.006824493408203125,
-0.0012378692626953125,
0.0222320556640625,
-0.0006780624389648438,
-0.01494598388671875,
-0.003078460693359375,
0.003017425537109375,
0.0015811920166015625,
-0.01018524169921875,
0.021026611328125,
-0.006725311279296875,
-0.027099609375,
0.0190887451171875,
-0.006298065185546875,
0.005687713623046875,
0.0184783935546875,
-0.021484375,
0.0213623046875,
-0.0197296142578125,
0.00725555419921875,
0.0100555419921875,
-0.0134735107421875,
-0.0180511474609375,
-0.02703857421875,
0.037628173828125,
0.01522064208984375,
0.0047760009765625,
-0.00852203369140625,
0.0038433074951171875,
-0.0137939453125,
-0.0223236083984375,
-0.0242156982421875,
0.009918212890625,
-0.031890869140625,
-0.0261993408203125,
-0.00324249267578125,
-0.00537872314453125,
0.007633209228515625,
-0.0018768310546875,
-0.00429534912109375,
0.0001850128173828125,
0.0213165283203125,
0.0223846435546875,
0.019989013671875,
0.026123046875,
-0.010894775390625,
0.019500732421875,
-0.002285003662109375,
-0.0286102294921875,
-0.016021728515625,
-0.00672149658203125,
0.003032684326171875,
0.0134124755859375,
-0.01380157470703125,
-0.00986480712890625,
0.0073394775390625,
-0.022430419921875,
0.00048089027404785156,
0.0179595947265625,
-0.0163116455078125,
0.003833770751953125,
-0.018768310546875,
-0.0207672119140625,
0.015411376953125,
0.0035266876220703125,
0.00244903564453125,
-0.00018525123596191406,
-0.00356292724609375,
0.031829833984375,
-0.014373779296875,
-0.0196075439453125,
-0.007144927978515625,
-0.0003306865692138672,
-0.0175933837890625,
0.0213775634765625,
0.029815673828125,
0.03533935546875,
-0.00038623809814453125,
0.025634765625,
0.01079559326171875,
0.06439208984375,
0.0296783447265625,
-0.01290130615234375,
-0.00911712646484375,
0.0037136077880859375,
0.0159759521484375,
0.025848388671875,
0.001293182373046875,
-0.011993408203125,
0.0257415771484375,
-0.0187835693359375,
0.0367431640625,
-0.0187835693359375,
-0.01395416259765625,
0.0147857666015625,
-0.01334381103515625,
-0.01995849609375,
0.0029811859130859375,
-0.0304718017578125,
-0.004119873046875,
0.0122528076171875,
-0.0224609375,
0.01514434814453125,
-0.006999969482421875,
0.0019512176513671875,
0.01534271240234375,
0.01099395751953125,
-0.012176513671875,
0.01181793212890625,
0.003383636474609375,
-0.002590179443359375,
-0.01367950439453125,
0.01338958740234375,
-0.0163116455078125,
0.0182952880859375,
-0.0117645263671875,
0.0160369873046875,
-0.0306396484375,
-0.005519866943359375,
0.0246124267578125,
-0.007778167724609375,
0.01776123046875,
0.00371551513671875,
0.0183563232421875,
-0.01081085205078125,
-0.0097503662109375,
0.0179290771484375,
-0.01476287841796875,
-0.021026611328125,
0.01154327392578125,
0.0019292831420898438,
0.02764892578125,
0.006328582763671875,
0.00858306884765625,
0.01763916015625,
0.0062103271484375,
0.00786590576171875,
0.0278472900390625,
0.0167388916015625,
0.0267333984375,
-0.022674560546875,
-0.018585205078125,
0.014373779296875,
-0.017242431640625,
-0.00665283203125,
-0.0010480880737304688,
-0.00968170166015625,
-0.0034465789794921875,
0.0018901824951171875,
0.0004265308380126953,
0.01383209228515625,
0.013214111328125,
-0.02386474609375,
-0.0269775390625,
-0.01168060302734375,
0.010955810546875,
0.001049041748046875,
-0.004657745361328125,
-0.001789093017578125,
-0.0008759498596191406,
0.016754150390625,
0.02996826171875,
0.0033588409423828125,
-0.01220703125,
-0.0015859603881835938,
-0.0021190643310546875,
-0.0084075927734375,
-0.0088043212890625,
-0.049163818359375,
0.036041259765625,
0.01190185546875,
0.019439697265625,
0.0185546875,
-0.0171051025390625,
0.038665771484375,
0.0161590576171875,
-0.0009975433349609375,
-0.0034313201904296875,
0.01343536376953125,
-0.014312744140625,
-0.011505126953125,
-0.007656097412109375,
-0.0172119140625,
0.003253936767578125,
-0.01448822021484375,
-0.044586181640625,
0.000522613525390625,
-0.0255889892578125,
-0.0004868507385253906,
0.031463623046875,
-0.0134429931640625,
0.060943603515625,
0.019683837890625,
-0.020599365234375,
0.0295257568359375,
-0.01007080078125,
-0.0146484375,
-0.0259246826171875,
0.0146942138671875,
-0.0298309326171875,
0.003570556640625,
0.0096282958984375,
0.00926971435546875,
0.0048065185546875,
0.00919342041015625,
-0.038818359375,
0.02471923828125,
0.0084228515625,
-0.0189361572265625,
-0.032562255859375,
0.0012664794921875,
0.0401611328125,
-0.042510986328125,
-0.060821533203125,
-0.0031280517578125,
-0.01110076904296875,
0.0053863525390625,
0.01123809814453125,
-0.031097412109375,
-0.01239013671875,
-0.038787841796875,
0.0233306884765625,
-0.0014247894287109375,
-0.00873565673828125,
0.0151824951171875,
0.0069732666015625,
-0.00013971328735351562,
0.00942230224609375,
-0.0031681060791015625,
-0.020416259765625,
0.0005269050598144531,
0.0128936767578125,
-0.0166778564453125,
0.02587890625,
0.01776123046875,
-0.0004296302795410156,
-0.01605224609375,
-0.0153656005859375,
0.025054931640625,
-0.016082763671875,
-0.035430908203125,
0.0065765380859375,
-0.01245880126953125,
0.0160980224609375,
0.0025577545166015625,
0.010711669921875,
0.0096435546875,
0.0144500732421875,
0.003932952880859375,
-0.002559661865234375,
0.0080413818359375,
-0.0299835205078125,
-0.030120849609375,
0.01922607421875,
0.019989013671875,
0.02276611328125,
0.015167236328125,
-0.00894927978515625,
0.024200439453125,
-0.018310546875,
0.01331329345703125,
-0.01425933837890625,
-0.01210784912109375,
-0.01111602783203125,
0.006702423095703125,
0.0091094970703125,
-0.01401519775390625,
0.0162200927734375,
0.019439697265625,
-0.00684356689453125,
-0.0230712890625,
0.012451171875,
0.05029296875,
0.01332855224609375,
-0.00832366943359375,
-0.0048370361328125,
0.01032257080078125,
0.020782470703125,
0.00415802001953125,
0.005199432373046875,
-0.005123138427734375,
0.0032215118408203125,
0.0408935546875,
0.01149749755859375,
0.00708770751953125,
0.0100555419921875,
0.0281982421875,
-0.000004172325134277344,
-0.0367431640625,
-0.047149658203125,
0.0123748779296875,
0.01140594482421875,
-0.01541900634765625,
-0.011505126953125,
0.0038661956787109375,
0.00925445556640625,
-0.00608062744140625,
-0.006618499755859375,
-0.045623779296875,
-0.01183319091796875,
0.04241943359375,
0.004337310791015625,
-0.03948974609375,
-0.0280609130859375,
0.003124237060546875,
0.024322509765625,
-0.00246429443359375,
0.057159423828125,
-0.022857666015625,
0.01165771484375,
0.0170440673828125,
-0.008148193359375,
0.048095703125,
0.01025390625,
0.0244598388671875,
0.01319122314453125,
-0.0129241943359375,
-0.0253753662109375,
0.006885528564453125,
-0.0171661376953125,
0.016448974609375,
0.0108642578125,
-0.008819580078125,
0.0026874542236328125,
0.0031490325927734375,
-0.00431060791015625,
-0.00876617431640625,
-0.0008525848388671875,
0.0243682861328125,
-0.0088043212890625,
-0.01837158203125,
-0.02972412109375,
-0.01302337646484375,
0.024017333984375,
-0.01451873779296875,
-0.0208740234375,
-0.0211944580078125,
0.00463104248046875,
0.00847625732421875,
-0.0179290771484375,
-0.003704071044921875,
-0.04241943359375,
-0.0241546630859375,
-0.01396942138671875,
0.0259857177734375,
-0.0214691162109375,
0.003936767578125,
-0.0203704833984375,
0.0009565353393554688,
0.00024068355560302734,
-0.00525665283203125,
0.0025234222412109375,
-0.022003173828125,
-0.02752685546875,
0.00444793701171875,
-0.00104522705078125,
0.0200347900390625,
-0.001739501953125,
-0.00028777122497558594,
-0.0255584716796875,
0.0180511474609375,
0.012054443359375,
-0.001987457275390625,
-0.005313873291015625,
0.053009033203125,
-0.007495880126953125,
-0.0283355712890625,
0.0291290283203125,
0.03155517578125,
0.006130218505859375,
0.003978729248046875,
-0.0374755859375,
-0.035400390625,
0.003131866455078125,
0.0294952392578125,
-0.0129241943359375,
0.01171875,
-0.0271148681640625,
-0.039947509765625,
0.0197601318359375,
0.01715087890625,
0.029052734375,
0.0040740966796875,
0.0323486328125,
0.0209503173828125,
-0.0023345947265625,
0.00582122802734375,
0.01690673828125,
0.007526397705078125,
0.0082244873046875,
-0.0020503997802734375,
-0.01751708984375,
0.0228118896484375,
-0.002655029296875,
0.00391387939453125,
-0.00545501708984375,
-0.002445220947265625,
0.005710601806640625,
0.0030155181884765625,
-0.0006456375122070312,
0.036041259765625,
-0.0247344970703125,
-0.01052093505859375,
0.00047087669372558594,
-0.0275115966796875,
-0.0014667510986328125,
0.0025882720947265625,
0.022125244140625,
-0.01396942138671875,
0.016754150390625,
-0.00090789794921875,
-0.0165252685546875,
-0.00885772705078125,
0.0013141632080078125,
-0.0230255126953125,
0.023529052734375,
-0.0039005279541015625,
-0.01165771484375,
-0.01071929931640625,
0.002162933349609375,
0.006725311279296875,
0.0382080078125,
0.036590576171875,
-0.0018157958984375,
0.012481689453125,
-0.035400390625,
0.006427764892578125,
0.0007467269897460938,
-0.01485443115234375,
-0.0224151611328125,
0.0133209228515625,
0.0009584426879882812,
-0.0008635520935058594,
-0.00666046142578125,
-0.0128021240234375,
0.00402069091796875,
0.0169677734375,
-0.0067291259765625,
0.00516510009765625,
-0.0017414093017578125,
-0.0044708251953125,
-0.0010290145874023438,
0.0182952880859375,
-0.00975799560546875,
0.0167694091796875,
0.002346038818359375,
0.0276947021484375,
-0.0118255615234375,
-0.002899169921875,
-0.0269775390625,
-0.0017452239990234375,
0.026458740234375,
0.005901336669921875,
-0.023956298828125,
0.03179931640625,
0.01395416259765625,
-0.012969970703125,
0.00971221923828125,
-0.0161285400390625,
-0.02557373046875,
-0.0164642333984375,
0.0190887451171875,
-0.0256195068359375,
-0.02935791015625,
0.0168914794921875,
-0.006839752197265625,
-0.031707763671875,
0.0372314453125,
-0.01200103759765625,
-0.0127410888671875,
-0.0147857666015625,
0.0154876708984375,
0.0250091552734375,
-0.01025390625,
0.0038318634033203125,
-0.0225372314453125,
-0.0113067626953125,
-0.0187835693359375,
0.04156494140625,
0.00786590576171875,
-0.015716552734375,
0.0273895263671875,
-0.0093994140625,
-0.0172119140625,
0.05828857421875,
0.0087890625,
-0.0007638931274414062,
-0.01447296142578125,
0.02569580078125,
-0.022491455078125,
0.016845703125,
-0.007488250732421875,
0.0210113525390625,
-0.026214599609375,
-0.0188446044921875,
0.04266357421875,
-0.0045623779296875,
-0.01432037353515625,
0.0005350112915039062,
-0.004108428955078125,
0.00414276123046875,
0.002437591552734375,
0.01044464111328125,
-0.0016527175903320312,
0.01873779296875,
-0.01220703125,
-0.00927734375,
-0.0179443359375,
0.0253143310546875,
-0.00528717041015625,
0.0035858154296875,
0.03216552734375,
0.01226806640625,
0.00887298583984375,
0.026641845703125,
0.002506256103515625,
-0.00555419921875,
0.0172882080078125,
-0.0236968994140625,
0.01654052734375,
-0.0166473388671875,
-0.01087188720703125,
-0.007293701171875,
-0.0198211669921875,
-0.01568603515625,
0.01113128662109375,
0.01092529296875,
-0.030975341796875,
-0.0030689239501953125,
-0.0115966796875,
-0.00006526708602905273,
0.0219573974609375,
-0.02728271484375,
0.0146636962890625,
0.040557861328125,
0.0026035308837890625,
-0.009613037109375,
-0.001861572265625,
0.000621795654296875,
-0.006099700927734375,
-0.018402099609375,
-0.0005497932434082031,
-0.032470703125,
-0.0176849365234375,
0.017608642578125,
-0.0235137939453125,
0.019287109375,
-0.025726318359375,
-0.0018253326416015625,
0.013916015625,
0.0088653564453125,
-0.007457733154296875,
-0.004550933837890625,
0.010498046875,
0.01071929931640625,
0.0023651123046875,
-0.00934600830078125,
-0.012786865234375,
0.007755279541015625,
-0.01568603515625,
-0.018585205078125,
-0.005947113037109375,
-0.0115509033203125,
-0.005420684814453125,
-0.003337860107421875,
0.03887939453125,
-0.0198211669921875,
-0.0013570785522460938,
0.002201080322265625,
0.004474639892578125,
-0.0026454925537109375,
0.026611328125,
0.01611328125,
0.0234832763671875,
0.019989013671875,
-0.00279998779296875,
-0.007137298583984375,
-0.00004649162292480469,
0.01200103759765625,
0.00496673583984375,
-0.0142364501953125,
0.0010833740234375,
0.0233001708984375,
0.013702392578125,
0.0172271728515625,
0.00910186767578125,
0.003147125244140625,
-0.00618743896484375,
0.00533294677734375,
-0.0131072998046875,
0.0211944580078125,
0.012603759765625,
-0.01214599609375,
-0.01204681396484375,
-0.007106781005859375,
-0.0245361328125,
0.011199951171875,
-0.00905609130859375,
-0.0193328857421875,
-0.0024814605712890625,
-0.0233001708984375,
0.0274810791015625,
-0.011810302734375,
0.00232696533203125,
0.0025501251220703125,
-0.01142120361328125,
0.007274627685546875,
-0.0186309814453125,
0.01471710205078125,
-0.0014753341674804688,
0.0107269287109375,
0.0166473388671875,
0.00435638427734375,
0.01155853271484375,
0.03289794921875,
-0.01348114013671875,
-0.0129852294921875,
-0.034515380859375,
0.017303466796875,
0.042083740234375,
0.031494140625,
0.018890380859375,
0.0306854248046875,
-0.03045654296875,
-0.005615234375,
-0.0015039443969726562,
0.00470733642578125,
0.0288848876953125,
0.0330810546875,
-0.0009131431579589844,
-0.00695037841796875,
0.016815185546875,
-0.007610321044921875,
0.0009055137634277344,
0.00958251953125,
0.00821685791015625,
0.007312774658203125,
0.017303466796875,
0.047149658203125,
0.00971221923828125,
-0.026458740234375,
-0.0133056640625,
-0.0266265869140625,
0.0242767333984375,
0.00479888916015625,
-0.007183074951171875,
0.023651123046875,
0.043121337890625,
-0.01453399658203125,
-0.019500732421875,
0.00556182861328125,
0.021697998046875,
0.040374755859375,
-0.0259857177734375,
0.00852203369140625,
0.00487518310546875,
0.0174560546875,
-0.01177215576171875,
0.00518798828125,
0.01038360595703125,
-0.043182373046875,
-0.0144805908203125,
0.0121307373046875,
-0.003032684326171875,
0.00847625732421875,
-0.00881195068359375,
-0.02069091796875,
-0.01285552978515625,
-0.01439666748046875,
0.0126800537109375,
-0.0018558502197265625,
-0.030548095703125,
0.0019006729125976562,
-0.0163421630859375,
-0.00726318359375,
0.0272216796875,
0.00278472900390625,
-0.0162200927734375,
-0.002651214599609375,
-0.007663726806640625,
-0.0284423828125,
-0.013153076171875,
-0.01233673095703125,
0.003093719482421875,
-0.005863189697265625,
-0.0098419189453125,
0.0256500244140625,
0.0149993896484375,
0.014892578125,
0.00983428955078125,
0.032196044921875,
0.0200042724609375,
-0.002918243408203125,
0.0093231201171875,
-0.02508544921875,
-0.001605987548828125,
-0.016204833984375,
-0.01922607421875,
0.0086212158203125,
0.0264434814453125,
0.0231781005859375,
-0.0054931640625,
0.020782470703125,
-0.03192138671875,
-0.003444671630859375,
-0.0003991127014160156,
0.0029888153076171875,
0.0161590576171875,
-0.018310546875,
-0.01007843017578125,
-0.0304107666015625,
-0.01641845703125,
0.01039886474609375,
-0.00017261505126953125,
-0.035186767578125,
0.0006289482116699219,
-0.025115966796875,
-0.03912353515625,
0.0006723403930664062,
-0.0226898193359375,
-0.0264434814453125,
-0.0032215118408203125,
-0.0005178451538085938,
0.01285552978515625,
-0.031646728515625,
0.0272674560546875,
0.01056671142578125,
-0.005939483642578125,
0.01503753662109375,
-0.00342559814453125,
-0.00119781494140625,
-0.02294921875,
-0.0191650390625,
-0.00945281982421875,
-0.028961181640625,
0.0132598876953125,
0.00756072998046875,
0.005100250244140625,
-0.00858306884765625,
-0.0246429443359375,
-0.0439453125,
0.0012884140014648438,
-0.0143280029296875,
-0.0277862548828125,
0.00832366943359375,
-0.0282745361328125,
-0.0275421142578125,
-0.0161590576171875,
0.0141754150390625,
-0.0148468017578125,
0.0093536376953125,
0.01702880859375,
0.02716064453125,
0.0245208740234375,
-0.019622802734375,
-0.0095672607421875,
0.0023899078369140625,
-0.0240020751953125,
0.0158538818359375,
0.0312347412109375,
0.016815185546875,
0.002529144287109375,
-0.0194091796875,
0.00418853759765625,
0.007152557373046875,
0.049163818359375,
0.0289459228515625,
-0.04058837890625,
0.03900146484375,
0.0070343017578125,
0.00885009765625,
0.025238037109375,
-0.0173797607421875,
-0.0013971328735351562,
-0.01309967041015625,
0.009552001953125,
0.012176513671875,
0.00783538818359375,
-0.00560760498046875,
-0.0173492431640625,
-0.028289794921875,
0.007106781005859375,
-0.0177001953125,
0.0273895263671875,
0.036590576171875,
0.03631591796875,
0.00604248046875,
0.0183563232421875,
-0.0267791748046875,
0.0196380615234375,
0.040557861328125,
-0.009185791015625,
0.00641632080078125,
-0.0225372314453125,
-0.01508331298828125,
0.005176544189453125,
0.005962371826171875,
0.028533935546875,
0.033721923828125,
-0.0026493072509765625,
0.00786590576171875,
0.00035762786865234375,
0.0027408599853515625,
0.01013946533203125,
0.0138397216796875,
-0.030975341796875,
-0.01435089111328125,
-0.00238800048828125,
-0.055694580078125,
0.028350830078125,
0.013885498046875,
0.013885498046875,
0.0006704330444335938,
0.00305938720703125,
0.01045989990234375,
-0.034912109375,
-0.00543212890625,
0.0021762847900390625,
-0.0223388671875,
-0.0007510185241699219,
0.0036373138427734375,
-0.015777587890625,
0.01050567626953125,
-0.0281219482421875,
-0.01360321044921875,
0.00801849365234375,
0.03857421875,
0.005176544189453125,
-0.014739990234375,
-0.003780364990234375,
0.0175323486328125,
-0.006183624267578125,
-0.00513458251953125,
0.017974853515625,
0.00634765625,
-0.005764007568359375,
-0.00699615478515625,
0.03759765625,
0.0182952880859375,
0.005062103271484375,
0.0099029541015625,
0.0023956298828125,
-0.0157012939453125,
0.0426025390625,
-0.02435302734375,
-0.01092529296875,
0.00662994384765625,
0.01087188720703125,
-0.0127105712890625,
0.0261688232421875,
-0.01050567626953125,
-0.01334381103515625,
0.038787841796875,
-0.009002685546875,
-0.0262298583984375,
-0.0163116455078125,
-0.03790283203125,
-0.01904296875,
-0.009185791015625,
0.007709503173828125,
0.0224456787109375,
0.035675048828125,
0.0303802490234375,
-0.05609130859375,
-0.0215301513671875,
0.00695037841796875,
0.0438232421875,
-0.004425048828125,
-0.01352691650390625,
0.005519866943359375,
-0.01004791259765625,
0.01316070556640625,
-0.0088043212890625,
0.003265380859375,
-0.006572723388671875,
-0.032745361328125,
-0.0264892578125,
0.01432037353515625,
-0.0244140625,
0.007526397705078125,
-0.05194091796875,
-0.044281005859375,
-0.01377105712890625,
-0.004119873046875,
0.05224609375,
-0.0093994140625,
-0.01129150390625,
0.032958984375,
-0.006561279296875,
0.0517578125,
-0.00989532470703125,
-0.0289459228515625,
-0.00537872314453125,
-0.0190277099609375,
0.0211029052734375,
-0.019287109375,
-0.0246734619140625,
-0.0098419189453125,
-0.011810302734375,
0.0017566680908203125,
-0.01140594482421875,
0.00931549072265625,
-0.00897979736328125,
0.005504608154296875,
-0.00885009765625,
-0.00571441650390625,
0.0316162109375,
-0.01605224609375,
0.00701141357421875,
0.0222625732421875,
-0.0167999267578125,
-0.0179595947265625,
-0.0020542144775390625,
-0.0430908203125,
-0.002483367919921875,
-0.043731689453125,
0.010711669921875,
0.00803375244140625,
0.0246734619140625,
-0.038665771484375,
-0.003631591796875,
-0.002506256103515625,
0.0025920867919921875,
-0.0021686553955078125,
0.0347900390625,
0.0163726806640625,
0.039825439453125,
0.0035247802734375,
0.003925323486328125,
-0.0267791748046875,
0.006099700927734375,
0.004467010498046875,
0.0181121826171875,
-0.008697509765625,
0.01445770263671875,
-0.014404296875,
0.0394287109375,
0.0201416015625,
0.0301361083984375,
-0.005519866943359375,
-0.0225830078125,
0.007488250732421875,
-0.0001627206802368164,
-0.0122833251953125,
-0.007556915283203125,
-0.02294921875,
0.0025501251220703125,
0.01904296875,
0.0157470703125,
0.043670654296875
] |
ours_500
|
The possible areas of triangle \( ABC \) are given by the expression \(\pm 13 \pm 14 \pm 15\), where at most one minus sign is used. This is because the area of triangle \( ABC \) can be expressed as the sum of the areas of triangles \( BPC, CPA, \) and \( APB \), with the possibility of one of these areas being subtracted if point \( P \) is inside triangle \( ABC \).
The desired sum of all possible values for the area of triangle \( ABC \) is calculated as follows:
\[
2(13 + 14 + 15) = 84
\]
Thus, the sum of all possible values for the area of triangle \( ABC \) is \(\boxed{84}\).
|
84
|
{
"competition": "us_comps",
"dataset": "Ours",
"posts": null,
"source": "OMOFall19Solns.md"
}
|
Let \( A, B, C, \) and \( P \) be points in the plane such that no three of them are collinear. Suppose that the areas of triangles \( BPC, CPA, \) and \( APB \) are \( 13, 14, \) and \( 15, \) respectively. Compute the sum of all possible values for the area of triangle \( ABC \).
|
[
"/Mathematics/Geometry/PlaneGeometry/Triangles",
"/Mathematics/Geometry/Points/GeneralPosition"
] |
Use signed areas to write area(ABC) as the sum of the three sub‑triangle areas, allowing one negative sign when P lies inside the triangle.
|
[
0.00012576580047607422,
-0.03277587890625,
0.0207366943359375,
0.021087646484375,
0.0005984306335449219,
-0.0128936767578125,
0.00952911376953125,
-0.0023937225341796875,
0.007419586181640625,
-0.059051513671875,
-0.017730712890625,
-0.000006616115570068359,
-0.00847625732421875,
0.005321502685546875,
-0.0175933837890625,
-0.01540374755859375,
-0.01290130615234375,
-0.0196075439453125,
0.0256805419921875,
-0.0036258697509765625,
-0.0038547515869140625,
-0.0106353759765625,
-0.048797607421875,
0.037200927734375,
0.0016641616821289062,
-0.0100250244140625,
-0.01995849609375,
-0.0058441162109375,
-0.002033233642578125,
0.0026035308837890625,
-0.028900146484375,
-0.01282501220703125,
-0.0014247894287109375,
-0.0287322998046875,
0.00018846988677978516,
0.016693115234375,
-0.0028858184814453125,
-0.007266998291015625,
-0.009368896484375,
-0.064697265625,
0.0006003379821777344,
0.01143646240234375,
0.0125579833984375,
0.01308441162109375,
0.0212554931640625,
0.024139404296875,
0.0076446533203125,
0.0198822021484375,
-0.0228729248046875,
0.01369476318359375,
0.00858306884765625,
0.016510009765625,
-0.01285552978515625,
-0.0147857666015625,
-0.0097503662109375,
-0.057159423828125,
0.011077880859375,
-0.005496978759765625,
-0.01355743408203125,
0.0123748779296875,
-0.004962921142578125,
0.007221221923828125,
-0.0120697021484375,
-0.015960693359375,
0.004787445068359375,
-0.004611968994140625,
-0.0237884521484375,
-0.061981201171875,
0.003543853759765625,
-0.0103759765625,
0.04681396484375,
-0.023712158203125,
0.0282745361328125,
0.0143890380859375,
0.0225677490234375,
-0.01285552978515625,
-0.0031261444091796875,
0.0033016204833984375,
0.0016937255859375,
0.01202392578125,
0.00464630126953125,
-0.0039825439453125,
-0.001071929931640625,
-0.0316162109375,
0.01983642578125,
-0.004974365234375,
-0.009552001953125,
0.004291534423828125,
0.01538848876953125,
-0.004344940185546875,
0.012298583984375,
-0.01558685302734375,
-0.0287628173828125,
-0.00717926025390625,
-0.0010585784912109375,
-0.0035247802734375,
0.00965118408203125,
-0.0029773712158203125,
-0.01139068603515625,
0.00853729248046875,
-0.019500732421875,
-0.00750732421875,
0.03411865234375,
-0.033172607421875,
-0.0014543533325195312,
-0.009033203125,
-0.007007598876953125,
0.00943756103515625,
-0.0024166107177734375,
-0.017242431640625,
0.0130615234375,
-0.00949859619140625,
0.005008697509765625,
0.020538330078125,
0.034881591796875,
-0.003711700439453125,
0.005512237548828125,
-0.00679779052734375,
-0.0156402587890625,
-0.00415802001953125,
-0.0069580078125,
0.0248565673828125,
0.02642822265625,
0.0215301513671875,
0.01132965087890625,
-0.0215911865234375,
-0.00832366943359375,
-0.0179443359375,
-0.0282135009765625,
0.008819580078125,
0.0212860107421875,
-0.005985260009765625,
-0.0228729248046875,
-0.0185699462890625,
-0.052337646484375,
0.011474609375,
-0.0106964111328125,
-0.0136871337890625,
-0.002285003662109375,
-0.01605224609375,
-0.0071258544921875,
-0.0048370361328125,
0.00241851806640625,
-0.00710296630859375,
-0.0011415481567382812,
-0.01380157470703125,
0.0082244873046875,
-0.0252685546875,
0.00510406494140625,
0.0019683837890625,
-0.0026702880859375,
-0.020782470703125,
0.0035839080810546875,
0.0230560302734375,
0.0026416778564453125,
-0.02081298828125,
-0.0038394927978515625,
0.0142822265625,
0.022430419921875,
0.0036869049072265625,
-0.0188751220703125,
-0.007251739501953125,
-0.016510009765625,
0.0018663406372070312,
0.0063018798828125,
-0.012939453125,
-0.0027008056640625,
0.025177001953125,
-0.03106689453125,
0.01256561279296875,
0.0216064453125,
0.0013971328735351562,
0.00562286376953125,
0.00687408447265625,
-0.0088043212890625,
0.005100250244140625,
0.00026988983154296875,
0.0231475830078125,
-0.02056884765625,
0.01837158203125,
-0.002994537353515625,
-0.0252838134765625,
0.02349853515625,
0.00021708011627197266,
0.00458526611328125,
0.005523681640625,
0.007709503173828125,
0.0280914306640625,
0.01497650146484375,
0.014251708984375,
-0.0305023193359375,
-0.009429931640625,
-0.0128173828125,
0.00616455078125,
0.0236663818359375,
-0.01308441162109375,
-0.061981201171875,
0.0232391357421875,
-0.0026645660400390625,
0.0021343231201171875,
0.0032482147216796875,
0.0123443603515625,
0.00821685791015625,
-0.005764007568359375,
-0.0161590576171875,
-0.00958251953125,
0.01153564453125,
0.00289154052734375,
-0.0027923583984375,
0.00656890869140625,
0.0090484619140625,
0.0178070068359375,
-0.00855255126953125,
-0.00406646728515625,
-0.00208282470703125,
-0.010101318359375,
-0.020233154296875,
0.0033435821533203125,
-0.00421142578125,
-0.0257720947265625,
0.00711822509765625,
0.0012664794921875,
-0.004558563232421875,
-0.0024013519287109375,
-0.0119476318359375,
0.023651123046875,
0.01275634765625,
-0.0024051666259765625,
0.0037841796875,
0.0123443603515625,
-0.015899658203125,
-0.0064849853515625,
-0.007442474365234375,
0.01763916015625,
-0.0251617431640625,
-0.0138092041015625,
-0.046295166015625,
-0.00659942626953125,
0.0161285400390625,
-0.0302581787109375,
0.04437255859375,
-0.0160369873046875,
0.0186767578125,
0.010894775390625,
-0.00815582275390625,
-0.00090789794921875,
0.017120361328125,
-0.0255889892578125,
-0.01079559326171875,
0.0030765533447265625,
-0.03973388671875,
0.0171356201171875,
-0.00678253173828125,
-0.017547607421875,
-0.0181732177734375,
0.0116119384765625,
0.0217742919921875,
-0.0028362274169921875,
-0.002178192138671875,
-0.02484130859375,
-0.0016756057739257812,
-0.01364898681640625,
-0.01068878173828125,
-0.010528564453125,
0.00893402099609375,
0.035125732421875,
-0.00006145238876342773,
0.0097198486328125,
0.01386260986328125,
-0.013671875,
0.006252288818359375,
-0.041595458984375,
-0.0264739990234375,
-0.01372528076171875,
0.0268096923828125,
-0.00435638427734375,
-0.001171112060546875,
0.01568603515625,
0.0202789306640625,
-0.003631591796875,
-0.0001558065414428711,
0.00585174560546875,
0.0123748779296875,
0.0192718505859375,
-0.019317626953125,
0.004993438720703125,
0.01122283935546875,
-0.0206756591796875,
0.0233612060546875,
0.02301025390625,
0.00927734375,
0.0021514892578125,
-0.00522613525390625,
-0.0113067626953125,
0.0394287109375,
-0.009796142578125,
0.010955810546875,
0.03448486328125,
0.0028133392333984375,
0.01910400390625,
0.0419921875,
-0.0275115966796875,
-0.002124786376953125,
0.0175018310546875,
0.007350921630859375,
0.0173492431640625,
0.007099151611328125,
-0.0008525848388671875,
0.00742340087890625,
-0.034515380859375,
0.01279449462890625,
-0.00832366943359375,
0.0003657341003417969,
-0.0006146430969238281,
-0.004016876220703125,
-0.038055419921875,
-0.005268096923828125,
0.0222930908203125,
-0.01194000244140625,
-0.01103973388671875,
0.0085296630859375,
-0.005817413330078125,
0.0181121826171875,
0.004070281982421875,
0.033782958984375,
-0.01953125,
0.017120361328125,
0.005832672119140625,
0.03009033203125,
0.02691650390625,
-0.01548004150390625,
0.00908660888671875,
0.003139495849609375,
-0.01084136962890625,
-0.025146484375,
-0.0286865234375,
-0.006534576416015625,
0.014068603515625,
0.006755828857421875,
0.0031681060791015625,
0.016998291015625,
-0.005702972412109375,
0.0189666748046875,
-0.0130767822265625,
0.026092529296875,
0.0292816162109375,
-0.00551605224609375,
0.00704193115234375,
-0.0296173095703125,
0.008087158203125,
-0.01531982421875,
-0.0009603500366210938,
0.01605224609375,
0.01238250732421875,
-0.0203399658203125,
0.01451873779296875,
-0.007598876953125,
-0.01690673828125,
-0.004962921142578125,
0.015777587890625,
-0.0018682479858398438,
-0.00711822509765625,
-0.0218658447265625,
-0.005767822265625,
-0.0170745849609375,
-0.00580596923828125,
-0.007205963134765625,
-0.00348663330078125,
-0.031585693359375,
-0.01123046875,
-0.00846099853515625,
0.00577545166015625,
0.01294708251953125,
0.0055694580078125,
0.024871826171875,
-0.018341064453125,
0.0132293701171875,
-0.005096435546875,
-0.0086212158203125,
-0.0093994140625,
-0.021331787109375,
-0.0105133056640625,
-0.006862640380859375,
0.02752685546875,
-0.02374267578125,
0.0049285888671875,
0.0015420913696289062,
0.0053558349609375,
-0.0194244384765625,
0.0034427642822265625,
-0.0087127685546875,
0.01494598388671875,
0.001499176025390625,
-0.0132904052734375,
0.007236480712890625,
-0.0369873046875,
-0.0069732666015625,
0.005535125732421875,
0.04730224609375,
-0.032135009765625,
-0.0390625,
0.0026721954345703125,
0.01383209228515625,
-0.0263214111328125,
0.005832672119140625,
-0.0189361572265625,
-0.01520538330078125,
0.049041748046875,
-0.0034847259521484375,
-0.01152801513671875,
0.0244903564453125,
0.023193359375,
0.0109100341796875,
0.0018787384033203125,
-0.0305633544921875,
-0.005863189697265625,
0.0174713134765625,
0.01461029052734375,
0.021820068359375,
0.003025054931640625,
0.00909423828125,
-0.015350341796875,
0.0251312255859375,
-0.0155487060546875,
0.0082855224609375,
0.023193359375,
-0.0215911865234375,
0.0174560546875,
0.004547119140625,
-0.0277099609375,
0.035858154296875,
-0.0037212371826171875,
-0.0172882080078125,
0.032012939453125,
-0.007320404052734375,
0.0166168212890625,
0.01255035400390625,
-0.005584716796875,
0.01178741455078125,
0.0175323486328125,
-0.0041046142578125,
0.01326751708984375,
0.00737762451171875,
0.0131988525390625,
0.0130767822265625,
0.01439666748046875,
0.00876617431640625,
0.005176544189453125,
0.039215087890625,
-0.0253143310546875,
-0.0210113525390625,
-0.017578125,
0.013946533203125,
-0.021514892578125,
-0.032501220703125,
0.014984130859375,
0.0328369140625,
-0.041900634765625,
-0.0230560302734375,
-0.0165252685546875,
0.0094757080078125,
0.00553131103515625,
0.0007214546203613281,
0.0266571044921875,
-0.01287841796875,
0.01355743408203125,
-0.03125,
0.0308990478515625,
0.065185546875,
0.00426483154296875,
-0.000911712646484375,
-0.02789306640625,
0.004947662353515625,
-0.027435302734375,
-0.01107025146484375,
0.0204925537109375,
0.0170135498046875,
-0.006237030029296875,
-0.02239990234375,
0.0173187255859375,
-0.01206207275390625,
0.01079559326171875,
-0.0306243896484375,
0.01023101806640625,
-0.001865386962890625,
0.023681640625,
-0.0104217529296875,
-0.01047515869140625,
0.0011854171752929688,
-0.05303955078125,
-0.01229095458984375,
0.03424072265625,
-0.0362548828125,
-0.0215301513671875,
-0.042633056640625,
-0.0263214111328125,
0.00511932373046875,
-0.0017747879028320312,
0.00714111328125,
0.00730133056640625,
0.004131317138671875,
-0.021575927734375,
0.024261474609375,
0.01422119140625,
-0.0079193115234375,
-0.017608642578125,
0.0517578125,
0.0019407272338867188,
0.020843505859375,
0.005367279052734375,
0.0167999267578125,
0.0253448486328125,
0.008148193359375,
-0.048980712890625,
0.0024700164794921875,
0.002758026123046875,
0.01451873779296875,
0.004058837890625,
-0.00981903076171875,
0.0701904296875,
-0.039031982421875,
0.01444244384765625,
0.02001953125,
-0.0080718994140625,
-0.002002716064453125,
0.03387451171875,
-0.025634765625,
-0.02691650390625,
0.0008015632629394531,
-0.018218994140625,
0.032867431640625,
-0.003810882568359375,
-0.0167236328125,
-0.00580596923828125,
-0.035400390625,
0.00821685791015625,
-0.005886077880859375,
0.0022106170654296875,
0.03399658203125,
0.0075836181640625,
-0.0087432861328125,
-0.01543426513671875,
0.0160369873046875,
-0.02606201171875,
-0.04266357421875,
0.00890350341796875,
-0.00934600830078125,
0.01177978515625,
-0.006992340087890625,
-0.0064544677734375,
-0.00638580322265625,
0.020416259765625,
0.005046844482421875,
-0.0076141357421875,
-0.054290771484375,
-0.015655517578125,
0.0273284912109375,
0.056640625,
-0.02008056640625,
0.01038360595703125,
0.0169830322265625,
0.01110076904296875,
0.0306854248046875,
0.01151275634765625,
-0.021820068359375,
-0.0019683837890625,
0.030303955078125,
-0.0218963623046875,
-0.01153564453125,
-0.031341552734375,
-0.0261077880859375,
-0.003780364990234375,
0.0220489501953125,
-0.021514892578125,
0.0287322998046875,
-0.03216552734375,
-0.0210723876953125,
-0.015716552734375,
0.04962158203125,
-0.028778076171875,
0.0196075439453125,
-0.01308441162109375,
-0.0004184246063232422,
-0.00849151611328125,
-0.00756072998046875,
-0.0235443115234375,
-0.0177154541015625,
-0.00533294677734375,
-0.0023021697998046875,
0.0009145736694335938,
-0.0362548828125,
0.0280303955078125,
0.014190673828125,
-0.0042266845703125,
-0.03424072265625,
-0.03973388671875,
0.016357421875,
0.01546478271484375,
-0.0034122467041015625,
0.0112457275390625,
-0.007778167724609375,
0.029937744140625,
-0.018096923828125,
0.024444580078125,
-0.0019550323486328125,
0.032318115234375,
-0.011932373046875,
-0.004817962646484375,
0.02032470703125,
0.020355224609375,
-0.01953125,
-0.03131103515625,
-0.0015974044799804688,
0.016815185546875,
0.01031494140625,
0.0058135986328125,
-0.04022216796875,
0.0061187744140625,
-0.03155517578125,
0.005397796630859375,
-0.0030078887939453125,
0.02105712890625,
-0.0174713134765625,
0.045196533203125,
0.0039043426513671875,
-0.008575439453125,
0.01317596435546875,
-0.02703857421875,
0.01332855224609375,
-0.0472412109375,
-0.00592803955078125,
-0.0248260498046875,
-0.0272979736328125,
0.00955963134765625,
-0.030242919921875,
-0.01207733154296875,
0.0004925727844238281,
0.01091766357421875,
-0.04852294921875,
-0.00099945068359375,
0.016326904296875,
0.0178070068359375,
-0.006298065185546875,
-0.019989013671875,
-0.032928466796875,
-0.00223541259765625,
-0.00286865234375,
0.0133056640625,
0.022979736328125,
0.03118896484375,
-0.0199432373046875,
0.024688720703125,
0.0067138671875,
0.01174163818359375,
0.0157470703125,
-0.01348876953125,
-0.052276611328125,
-0.00766754150390625,
0.03472900390625,
0.020233154296875,
-0.007198333740234375,
-0.0015583038330078125,
0.013092041015625,
0.0131378173828125,
-0.0124359130859375,
0.00583648681640625,
-0.01189422607421875,
-0.015655517578125,
-0.00989532470703125,
0.0197906494140625,
-0.022918701171875,
-0.00678253173828125,
-0.0164947509765625,
0.004787445068359375,
0.0005693435668945312,
0.0017023086547851562,
-0.043914794921875,
0.00643157958984375,
0.0117950439453125,
-0.0036869049072265625,
-0.0114593505859375,
0.005584716796875,
0.053466796875,
0.01552581787109375,
0.004150390625,
0.010467529296875,
0.0084228515625,
-0.004329681396484375,
0.00283050537109375,
-0.027130126953125,
0.0240020751953125,
0.00445556640625,
-0.0292816162109375,
0.0080718994140625,
0.0005273818969726562,
-0.007282257080078125,
0.00283050537109375,
-0.00954437255859375,
0.015899658203125,
-0.01629638671875,
0.03887939453125,
-0.033355712890625,
0.01117706298828125,
-0.00598907470703125,
-0.021484375,
-0.013458251953125,
-0.01043701171875,
0.0015153884887695312,
-0.02392578125,
-0.004329681396484375,
-0.050567626953125,
-0.004436492919921875,
-0.0219268798828125,
-0.01435089111328125,
0.003978729248046875,
-0.018157958984375,
-0.0171356201171875,
-0.0067901611328125,
-0.01361846923828125,
-0.028228759765625,
-0.02215576171875,
0.0207672119140625,
-0.00400543212890625,
0.0012950897216796875,
0.005107879638671875,
0.005176544189453125,
-0.0008392333984375,
-0.0240478515625,
-0.00103759765625,
0.02301025390625,
0.0024204254150390625,
-0.043609619140625,
0.0242767333984375,
0.0112762451171875,
-0.0140838623046875,
0.0011415481567382812,
-0.034820556640625,
-0.03961181640625,
0.0132598876953125,
-0.00024056434631347656,
0.008087158203125,
-0.06146240234375,
0.0230712890625,
0.01311492919921875,
-0.01514434814453125,
-0.0170135498046875,
-0.0321044921875,
-0.004314422607421875,
-0.011962890625,
0.00955963134765625,
0.03863525390625,
-0.0026988983154296875,
-0.01221466064453125,
-0.00479888916015625,
-0.0137939453125,
-0.0011148452758789062,
-0.003917694091796875,
-0.004917144775390625,
-0.01251983642578125,
0.01349639892578125,
-0.00518798828125,
-0.011016845703125,
0.0102081298828125,
-0.02880859375,
-0.0055694580078125,
-0.0024261474609375,
0.0146942138671875,
-0.013946533203125,
-0.01209259033203125,
0.01904296875,
-0.0056610107421875,
-0.00997161865234375,
-0.00009918212890625,
0.0261993408203125,
0.0114593505859375,
-0.01318359375,
-0.05010986328125,
-0.005767822265625,
0.03265380859375,
-0.007049560546875,
-0.0009183883666992188,
0.004085540771484375,
-0.010986328125,
0.0169677734375,
-0.00531768798828125,
0.036468505859375,
-0.0158843994140625,
0.0179443359375,
0.02423095703125,
-0.0292205810546875,
0.04840087890625,
0.0236053466796875,
0.010406494140625,
0.01413726806640625,
0.0244140625,
-0.041534423828125,
-0.0212554931640625,
-0.03912353515625,
0.0150604248046875,
0.0050506591796875,
0.00965118408203125,
-0.01444244384765625,
-0.01496124267578125,
0.04083251953125,
0.06536865234375,
0.00838470458984375,
-0.00017273426055908203,
0.0209197998046875,
-0.03082275390625,
0.006656646728515625,
-0.00330352783203125,
0.03411865234375,
0.031982421875,
-0.0102081298828125,
0.0027751922607421875,
-0.03607177734375,
0.00873565673828125,
-0.01343536376953125,
-0.0007739067077636719,
0.01788330078125,
-0.0246429443359375,
0.014434814453125,
0.00014150142669677734,
-0.033355712890625,
-0.0283355712890625,
0.01364898681640625,
0.01384735107421875,
-0.0160369873046875,
0.01605224609375,
-0.0093231201171875,
0.002880096435546875,
-0.0019102096557617188,
-0.04034423828125,
-0.006900787353515625,
-0.03173828125,
-0.0150299072265625,
0.0030689239501953125,
0.0159454345703125,
-0.0187835693359375,
-0.03790283203125,
0.03741455078125,
0.029296875,
0.01488494873046875,
-0.0009336471557617188,
0.005428314208984375,
-0.020965576171875,
0.0151214599609375,
0.0224151611328125,
0.046173095703125,
-0.018035888671875,
-0.00673675537109375,
0.021453857421875,
-0.0307464599609375,
0.034576416015625,
-0.0218658447265625,
-0.0131683349609375,
0.0172119140625,
0.03131103515625,
0.00733184814453125,
-0.004199981689453125,
0.0188751220703125,
-0.0213470458984375,
0.0150146484375,
-0.009124755859375,
-0.0139312744140625,
-0.00199127197265625,
0.0013856887817382812,
-0.0213470458984375,
0.020355224609375,
-0.00336456298828125,
0.036407470703125,
-0.021087646484375,
-0.0209808349609375,
-0.02154541015625,
0.0182037353515625,
0.0428466796875,
0.030792236328125,
0.03326416015625,
0.0467529296875,
0.01064300537109375,
0.01509857177734375,
-0.0017976760864257812,
-0.02093505859375,
0.0191650390625,
-0.0286712646484375,
-0.0364990234375,
0.036224365234375,
0.001895904541015625,
0.01367950439453125,
-0.004856109619140625,
-0.006229400634765625,
-0.02313232421875,
-0.026947021484375,
-0.023712158203125,
0.00830078125,
-0.0102386474609375,
-0.00020229816436767578,
-0.03826904296875,
0.0170440673828125,
-0.01397705078125,
-0.01483917236328125,
-0.004749298095703125,
-0.006839752197265625,
0.006587982177734375,
-0.016204833984375,
-0.03570556640625,
-0.026824951171875,
-0.0034885406494140625,
0.0146484375,
0.0419921875,
-0.01071929931640625,
0.006221771240234375,
0.0170135498046875,
0.0303497314453125,
0.023712158203125,
0.02301025390625,
0.016754150390625,
0.00495147705078125,
-0.031524658203125,
-0.01690673828125,
-0.019439697265625,
0.013458251953125,
0.0034084320068359375,
-0.03082275390625,
0.0028133392333984375,
-0.041748046875,
0.01456451416015625,
0.0005497932434082031,
-0.04437255859375,
0.01045989990234375,
-0.00036907196044921875,
0.0262298583984375,
0.007175445556640625,
-0.0106964111328125,
-0.0258941650390625,
-0.01291656494140625,
-0.0117034912109375,
-0.025726318359375,
-0.0009598731994628906,
0.003566741943359375,
-0.01361846923828125,
0.001129150390625,
-0.0189056396484375,
0.023590087890625,
0.0125579833984375,
-0.01428985595703125,
-0.018157958984375,
0.0174102783203125,
-0.002582550048828125,
-0.0011043548583984375,
-0.0227813720703125,
0.00911712646484375,
0.0218048095703125,
-0.00836944580078125,
0.00112152099609375,
-0.01430511474609375,
0.0211029052734375,
0.009613037109375,
-0.01354217529296875,
0.01251220703125,
0.053131103515625,
-0.01049041748046875,
-0.003330230712890625,
0.0083160400390625,
-0.01702880859375,
0.0008997917175292969,
0.021636962890625,
0.04779052734375,
0.0304107666015625,
0.00885772705078125,
0.016571044921875,
-0.0024356842041015625,
-0.01119232177734375,
-0.0256805419921875,
-0.01476287841796875,
-0.01407623291015625,
0.0177459716796875,
0.00522613525390625,
0.035888671875,
-0.01197052001953125,
-0.04888916015625,
-0.0003809928894042969,
0.01482391357421875,
0.00070953369140625,
-0.01531219482421875,
-0.0120849609375,
0.0117645263671875,
0.003215789794921875,
0.042694091796875,
0.00547027587890625,
0.00437164306640625,
0.036865234375,
0.01194000244140625,
0.00380706787109375,
-0.01351165771484375,
0.0017795562744140625,
0.0222625732421875,
-0.0208740234375,
0.00804901123046875,
-0.0287322998046875,
-0.0293121337890625,
0.0265655517578125,
-0.0034656524658203125,
-0.0082244873046875,
0.01224517822265625,
0.004337310791015625,
0.00312042236328125,
0.0172576904296875,
0.022308349609375,
0.0189666748046875,
-0.03216552734375,
0.0186309814453125,
0.0163726806640625,
0.0159149169921875,
-0.0026092529296875,
0.044097900390625,
-0.00928497314453125,
0.00870513916015625,
-0.05096435546875,
0.04241943359375,
-0.0172119140625,
-0.04449462890625,
-0.0258026123046875,
-0.035003662109375,
0.0133514404296875,
-0.0131072998046875,
0.0023632049560546875,
-0.0220184326171875,
-0.01166534423828125,
-0.0019741058349609375,
-0.0232086181640625,
-0.005817413330078125,
0.005191802978515625,
-0.0145263671875,
0.0265045166015625,
-0.01861572265625,
0.00936126708984375,
-0.008575439453125,
0.0029277801513671875,
-0.0082550048828125,
-0.006740570068359375,
0.00490570068359375,
-0.0064239501953125,
-0.036651611328125,
-0.01806640625,
-0.0124664306640625,
-0.01366424560546875,
0.0013217926025390625,
-0.00951385498046875,
0.0181732177734375,
0.02252197265625,
-0.003559112548828125,
-0.00995635986328125,
-0.0160980224609375,
-0.0026149749755859375,
0.021484375,
-0.0204925537109375,
0.0294342041015625,
0.0256805419921875,
0.01727294921875,
0.021820068359375,
-0.0362548828125,
0.0023288726806640625,
-0.0318603515625,
0.0174713134765625,
0.00919342041015625,
-0.00954437255859375,
-0.0213165283203125,
-0.0016202926635742188,
0.0240020751953125,
-0.038238525390625,
-0.005176544189453125,
0.014556884765625,
-0.009490966796875,
0.00514984130859375,
-0.0013141632080078125,
-0.02484130859375,
-0.0206298828125,
-0.0247650146484375,
0.0118560791015625,
-0.00841522216796875,
0.0251007080078125,
-0.03521728515625,
0.02618408203125,
0.013214111328125,
0.054229736328125,
-0.005245208740234375,
-0.02606201171875,
0.0222320556640625,
-0.0182647705078125,
-0.00079345703125,
-0.004039764404296875,
-0.01262664794921875,
0.0198211669921875,
0.0211944580078125,
0.005157470703125,
0.0235137939453125,
0.0228271484375,
0.0115509033203125,
-0.0205841064453125,
-0.025115966796875,
0.0372314453125,
0.016510009765625,
0.01006317138671875,
0.00397491455078125,
-0.0222015380859375,
-0.019805908203125,
0.0229339599609375,
0.0004353523254394531,
0.0013484954833984375,
-0.01165008544921875,
0.03717041015625,
0.01212310791015625,
0.01629638671875,
-0.0006456375122070312,
-0.005947113037109375,
-0.026031494140625,
-0.028472900390625,
0.00646209716796875,
0.00014460086822509766,
0.00939178466796875,
-0.003170013427734375,
0.01055908203125,
0.0029087066650390625,
0.0032958984375,
-0.00389862060546875,
0.019622802734375,
-0.007541656494140625,
-0.01531982421875,
-0.0112152099609375,
0.029693603515625,
-0.0103607177734375,
-0.006511688232421875,
-0.0027866363525390625,
0.026641845703125,
0.01003265380859375,
0.0205841064453125,
-0.024261474609375,
0.00991058349609375,
-0.0172119140625,
-0.01151275634765625,
0.02490234375,
0.00908660888671875,
-0.025787353515625,
0.01001739501953125,
-0.0106964111328125,
-0.034393310546875,
0.0189056396484375,
0.0027599334716796875,
-0.006378173828125,
-0.0196075439453125,
0.01229095458984375,
0.00855255126953125,
0.0372314453125,
0.0091094970703125,
-0.0037384033203125,
-0.0289306640625,
-0.01605224609375,
0.019378662109375,
-0.0017881393432617188,
-0.02362060546875,
-0.00039505958557128906,
0.0234832763671875,
0.033050537109375,
0.00024235248565673828,
0.0113525390625,
0.0007715225219726562,
0.037384033203125,
-0.03485107421875,
0.04376220703125,
-0.0017747879028320312,
0.0114288330078125,
0.0163421630859375,
0.00318145751953125,
-0.00873565673828125,
0.0011587142944335938,
-0.02008056640625,
-0.027923583984375,
0.021026611328125,
-0.004413604736328125,
-0.00693511962890625,
-0.01219940185546875,
0.005474090576171875,
-0.0193023681640625,
0.00864410400390625,
-0.0157012939453125,
0.0184173583984375,
-0.0142669677734375,
-0.0219879150390625,
-0.01560211181640625,
0.0282135009765625,
0.01142120361328125,
-0.00376129150390625,
-0.00421142578125,
-0.002758026123046875,
0.0175018310546875,
-0.023162841796875,
0.029449462890625,
-0.05181884765625,
-0.007503509521484375,
-0.0009589195251464844,
-0.0061798095703125,
-0.0323486328125,
-0.00742340087890625,
0.006221771240234375,
-0.0024814605712890625,
0.01293182373046875,
0.0430908203125,
-0.003753662109375,
-0.00302886962890625,
0.014373779296875,
-0.0037670135498046875,
0.00238800048828125,
0.0002980232238769531,
0.04071044921875,
0.00913238525390625,
-0.007213592529296875,
0.02215576171875,
0.0004794597625732422,
-0.00380706787109375,
-0.0216064453125,
0.0049591064453125,
0.0167236328125,
-0.002437591552734375,
-0.0019006729125976562,
-0.0107421875,
-0.048614501953125,
0.026885986328125,
0.0211181640625,
0.00618743896484375,
0.0173187255859375,
0.0318603515625,
-0.006977081298828125,
0.04461669921875,
-0.0272064208984375,
-0.0452880859375,
0.0016908645629882812,
0.000255584716796875,
-0.0168914794921875,
0.00830841064453125,
-0.022705078125,
-0.004703521728515625,
-0.0278472900390625,
-0.01451873779296875,
0.030517578125,
-0.0042724609375,
-0.036773681640625,
-0.0238494873046875,
-0.022979736328125,
0.038848876953125,
0.004001617431640625,
0.01236724853515625,
-0.00986480712890625,
-0.0207061767578125,
-0.0193634033203125,
0.01061248779296875,
0.0289764404296875,
0.0032558441162109375,
0.00930023193359375,
-0.022735595703125,
0.017242431640625,
0.0162200927734375,
-0.02874755859375,
-0.0007276535034179688,
0.019256591796875,
0.0009646415710449219,
-0.0172119140625,
0.01364898681640625,
0.021697998046875,
0.02203369140625,
0.00039839744567871094,
0.0037059783935546875,
-0.003383636474609375,
0.0233001708984375,
-0.005710601806640625,
-0.005290985107421875,
0.0009927749633789062,
-0.014495849609375,
-0.0272064208984375,
0.0150909423828125,
-0.01450347900390625,
-0.01397705078125,
0.0222015380859375,
-0.0006003379821777344,
-0.0016393661499023438,
-0.0095977783203125,
-0.0249481201171875,
0.014678955078125,
-0.0284576416015625,
-0.002231597900390625,
0.00897979736328125,
-0.0012102127075195312,
0.0008988380432128906,
0.01959228515625,
-0.0261993408203125,
-0.038330078125,
-0.01259613037109375,
-0.00585174560546875,
0.043853759765625,
0.011962890625,
-0.007843017578125,
-0.0144195556640625,
0.00267791748046875,
0.01507568359375,
-0.00632476806640625,
-0.003879547119140625,
0.01617431640625,
0.02001953125,
0.00324249267578125,
0.005401611328125,
-0.01126861572265625,
0.009674072265625,
0.0187530517578125,
-0.0146484375,
0.0257110595703125,
-0.007843017578125,
-0.01064300537109375,
-0.004589080810546875,
-0.053558349609375,
0.0246734619140625,
-0.0208892822265625,
0.006725311279296875,
-0.0276947021484375,
0.0076751708984375,
0.01172637939453125,
-0.0001742839813232422,
-0.03662109375,
-0.01044464111328125,
-0.0214996337890625,
0.01561737060546875,
0.005313873291015625,
0.005641937255859375,
-0.0325927734375,
-0.00313568115234375,
0.00986480712890625,
0.0160369873046875,
0.0278778076171875,
0.010467529296875,
-0.0280303955078125,
-0.0127105712890625,
0.01483917236328125,
0.0271759033203125,
-0.00789642333984375,
0.00218963623046875,
0.0258941650390625,
-0.0190277099609375,
-0.0423583984375,
0.0154266357421875,
0.0279541015625,
-0.033203125,
0.01812744140625,
0.00015342235565185547,
-0.00914764404296875,
0.041778564453125,
-0.046600341796875,
-0.01502227783203125,
0.04071044921875,
0.0128936767578125,
0.0111083984375,
-0.0084686279296875,
0.036773681640625,
-0.00662994384765625,
-0.01444244384765625,
0.01409149169921875,
0.0156707763671875,
0.0192718505859375,
0.018157958984375,
-0.024261474609375,
-0.00218963623046875,
-0.00724029541015625,
-0.0258026123046875,
0.02093505859375,
0.0273590087890625,
-0.01511383056640625,
0.0240020751953125,
-0.02508544921875,
0.003276824951171875,
-0.005008697509765625,
0.01177978515625,
-0.00457000732421875,
0.006946563720703125,
-0.016876220703125,
-0.0178985595703125,
-0.053497314453125,
-0.0220184326171875,
-0.007411956787109375,
-0.0013151168823242188,
-0.0019016265869140625,
-0.017852783203125,
-0.0302276611328125,
-0.00521087646484375,
0.002040863037109375,
-0.0098114013671875,
0.033233642578125,
-0.005374908447265625,
-0.033111572265625,
-0.0124053955078125,
0.0191650390625,
-0.0189056396484375,
0.0022678375244140625,
0.00959014892578125,
0.00095367431640625,
0.0056610107421875,
0.011474609375,
-0.00907135009765625,
0.01104736328125,
0.0258026123046875,
0.03167724609375,
0.0306396484375,
-0.00580596923828125,
-0.01025390625,
-0.0143890380859375,
-0.015045166015625,
-0.01422882080078125,
0.033233642578125,
-0.021636962890625,
-0.0033931732177734375,
-0.01058197021484375,
-0.005252838134765625,
0.0037841796875,
0.0164642333984375,
0.01360321044921875,
-0.0088958740234375,
-0.016998291015625,
-0.0163116455078125,
0.00031757354736328125,
0.00994110107421875,
-0.003665924072265625,
0.0015573501586914062,
0.00629425048828125,
0.0173492431640625,
-0.0142669677734375,
-0.0135955810546875,
0.028717041015625,
0.006000518798828125,
-0.003253936767578125,
0.0338134765625,
0.0017862319946289062,
0.04522705078125,
0.01537322998046875,
0.0186767578125,
0.0152435302734375,
-0.00363922119140625,
-0.00555419921875,
0.0030574798583984375,
-0.00811767578125,
0.008636474609375,
-0.01418304443359375,
-0.02349853515625,
-0.0240020751953125,
0.00603485107421875,
-0.0433349609375,
-0.025604248046875,
-0.0036029815673828125,
0.00643157958984375,
0.02947998046875,
0.005779266357421875,
0.0289306640625,
0.003322601318359375,
-0.01232147216796875,
-0.028472900390625,
0.00884246826171875,
-0.005096435546875,
0.01922607421875,
-0.0119781494140625,
-0.0107879638671875,
-0.04644775390625,
0.036376953125,
0.0155487060546875,
-0.03961181640625,
-0.0128631591796875,
0.006221771240234375,
-0.024169921875,
0.035003662109375,
0.00400543212890625,
0.024200439453125,
0.036590576171875,
-0.0172576904296875,
0.0010023117065429688,
-0.01165008544921875,
0.003238677978515625,
0.024871826171875,
0.0178985595703125,
0.00489044189453125,
-0.0523681640625,
-0.0192718505859375,
-0.0037364959716796875,
0.040283203125,
0.0056304931640625,
-0.02081298828125,
-0.009857177734375,
-0.0299072265625,
0.0243072509765625,
-0.0010366439819335938,
0.0430908203125,
0.01161956787109375,
0.01373291015625,
-0.03729248046875,
-0.01474761962890625,
-0.00008767843246459961,
0.0263824462890625,
-0.009521484375,
0.0024280548095703125,
-0.00732421875,
0.0162353515625,
-0.04730224609375,
-0.0228424072265625,
-0.022186279296875,
-0.000005900859832763672,
-0.001270294189453125,
0.0168609619140625,
0.006580352783203125,
0.0011692047119140625,
-0.01500701904296875,
-0.0290985107421875,
-0.004261016845703125,
-0.01947021484375,
0.01580810546875,
-0.02276611328125,
0.01425933837890625,
0.0037288665771484375,
-0.0423583984375,
-0.0144500732421875,
0.0023040771484375,
0.0259246826171875,
-0.0110015869140625,
0.0117034912109375,
0.0010137557983398438,
-0.03521728515625,
0.022247314453125,
-0.01105499267578125,
0.003437042236328125,
0.041168212890625,
-0.0036163330078125,
0.0209197998046875,
-0.00896453857421875,
0.01277923583984375,
-0.024169921875,
-0.0007224082946777344,
0.007568359375,
0.04107666015625,
0.0154571533203125,
-0.00347900390625,
0.018585205078125,
-0.00013375282287597656,
0.01468658447265625,
0.0019683837890625,
0.00777435302734375,
0.00963592529296875,
-0.01059722900390625,
0.00312042236328125,
-0.04388427734375,
0.019927978515625,
-0.0011758804321289062,
0.0152740478515625,
-0.0145111083984375,
0.0131988525390625,
0.031524658203125,
-0.00855255126953125,
0.0107879638671875,
-0.0014944076538085938,
0.00583648681640625,
-0.0233154296875,
-0.0203399658203125,
0.0106353759765625,
0.0021457672119140625,
0.0205230712890625,
0.0341796875,
-0.007755279541015625,
-0.019805908203125,
0.0075225830078125,
-0.0003566741943359375,
-0.004993438720703125,
-0.035247802734375,
-0.021209716796875,
0.01262664794921875,
0.00901031494140625,
0.0372314453125,
0.03009033203125,
0.01160430908203125,
0.009185791015625,
-0.038330078125,
0.00839996337890625,
-0.0272674560546875,
0.0175933837890625,
-0.00872039794921875,
-0.0209197998046875,
0.01078033447265625,
-0.008697509765625,
-0.006206512451171875,
0.0184326171875,
0.0396728515625,
0.02313232421875,
-0.0054931640625,
0.0077667236328125,
-0.020294189453125,
0.005123138427734375,
0.007781982421875,
-0.00524139404296875,
0.018341064453125,
-0.00321197509765625,
0.0036449432373046875,
-0.006748199462890625,
0.05615234375,
-0.003673553466796875,
0.01291656494140625,
-0.003963470458984375,
0.0051116943359375,
-0.036102294921875,
-0.0095672607421875,
0.00786590576171875,
0.0182037353515625,
-0.00128173828125,
0.01407623291015625,
0.01287078857421875,
-0.007175445556640625,
0.0190887451171875,
0.053558349609375,
0.0107269287109375,
0.006008148193359375,
-0.01474761962890625,
-0.011505126953125,
0.00907135009765625,
0.0005884170532226562,
-0.01113128662109375,
0.01152801513671875,
0.005340576171875,
-0.006443023681640625,
-0.002471923828125,
-0.0200653076171875,
0.017578125,
0.005306243896484375,
0.0251312255859375,
-0.00429534912109375,
-0.0167694091796875,
-0.00891876220703125,
-0.0007681846618652344,
0.01678466796875,
0.0029239654541015625,
0.005702972412109375,
0.0184478759765625,
0.0081329345703125,
0.03839111328125,
-0.0078582763671875,
0.019989013671875,
-0.001338958740234375,
-0.0035991668701171875,
-0.0006814002990722656,
0.006122589111328125,
-0.045928955078125,
0.0025634765625,
0.0037174224853515625,
-0.01027679443359375,
0.01507568359375,
-0.0007929801940917969,
-0.026092529296875,
-0.0023403167724609375,
-0.0019931793212890625,
0.020965576171875,
0.008819580078125,
-0.0189056396484375,
0.03204345703125,
0.0078125,
-0.014434814453125,
0.003665924072265625,
0.00945281982421875,
0.031585693359375,
-0.006938934326171875,
0.0074615478515625,
0.023101806640625,
0.01337432861328125,
-0.0013704299926757812,
-0.0186920166015625,
0.00066375732421875,
0.0013637542724609375,
-0.022247314453125,
-0.007568359375,
-0.01983642578125,
0.017120361328125,
1.7881393432617188e-7,
-0.008148193359375,
-0.01422119140625,
-0.01314544677734375,
0.006130218505859375,
-0.013336181640625,
-0.005680084228515625,
-0.0157470703125,
0.0257720947265625,
0.022430419921875,
0.0172271728515625,
0.0175628662109375,
-0.00757598876953125,
-0.037322998046875,
0.0304107666015625,
0.00536346435546875,
0.03448486328125,
0.01294708251953125,
-0.0145111083984375,
-0.0117340087890625,
0.0035877227783203125,
-0.00421142578125,
0.02001953125,
0.019073486328125,
0.01776123046875,
0.02252197265625,
0.0308380126953125,
-0.035003662109375,
-0.0099945068359375,
-0.0232696533203125,
-0.046905517578125,
0.033294677734375,
-0.02362060546875,
-0.0166473388671875,
0.026519775390625,
0.00917816162109375,
0.01146697998046875,
0.03033447265625,
-0.00940704345703125,
-0.0028095245361328125,
-0.028350830078125,
-0.000957489013671875,
-0.0203857421875,
0.009613037109375,
0.0114593505859375,
0.01104736328125,
-0.015838623046875,
0.01727294921875,
-0.039581298828125,
-0.0017957687377929688,
0.031219482421875,
0.01062774658203125,
-0.004779815673828125,
-0.0164337158203125,
0.0162506103515625,
-0.0193023681640625,
-0.030029296875,
0.020111083984375,
-0.02398681640625,
0.0041656494140625,
0.03253173828125,
-0.0012693405151367188,
-0.0225830078125,
-0.0232391357421875,
-0.007541656494140625,
-0.006977081298828125,
-0.0019207000732421875,
-0.004261016845703125,
0.0255889892578125,
-0.0033969879150390625,
-0.00939178466796875,
0.0019664764404296875,
-0.0034027099609375,
0.0274658203125,
-0.02099609375,
-0.007129669189453125,
0.0035266876220703125,
-0.01715087890625,
0.005504608154296875,
-0.0157470703125,
-0.0206451416015625,
0.0212554931640625,
-0.0182647705078125,
-0.01204681396484375,
-0.0208892822265625,
-0.004421234130859375,
0.0014667510986328125,
-0.0279388427734375,
0.029449462890625,
0.0159149169921875,
-0.0047149658203125,
-0.0140380859375,
0.01161956787109375,
0.01043701171875,
0.0333251953125,
0.00605010986328125,
-0.0318603515625,
0.00688934326171875,
-0.003551483154296875,
-0.032623291015625,
0.0140838623046875,
-0.012298583984375,
-0.00638580322265625,
-0.036773681640625,
-0.0047454833984375,
-0.01294708251953125,
-0.005733489990234375,
0.00010484457015991211,
-0.00904083251953125,
-0.010162353515625,
-0.01354217529296875,
0.0180206298828125,
-0.02398681640625,
0.01068115234375,
-0.041412353515625,
-0.00553131103515625,
-0.006809234619140625,
0.01079559326171875,
0.0003719329833984375,
0.0226287841796875,
0.007244110107421875,
-0.006267547607421875,
0.02142333984375,
-0.0233917236328125,
-0.007343292236328125,
0.03607177734375,
-0.01389312744140625,
-0.00980377197265625,
-0.0164337158203125,
0.021636962890625,
0.006267547607421875,
0.005462646484375,
0.01113128662109375,
0.0123291015625,
-0.00699615478515625,
-0.03466796875,
-0.015838623046875,
0.0106201171875,
-0.01287841796875,
-0.052581787109375,
-0.0011835098266601562,
0.0008192062377929688,
-0.00592041015625,
-0.0017633438110351562,
-0.02264404296875,
-0.0139923095703125,
-0.004840850830078125,
-0.01129150390625,
-0.0252532958984375,
-0.01079559326171875,
0.0203857421875,
0.037750244140625,
0.01122283935546875,
-0.0236968994140625,
-0.01088714599609375,
0.026763916015625,
-0.03668212890625,
-0.0066680908203125,
-0.03485107421875,
-0.0158843994140625,
-0.012664794921875,
0.0148773193359375,
0.00450897216796875,
-0.004150390625,
0.02874755859375,
0.029022216796875,
0.01264190673828125,
0.01158905029296875,
0.011260986328125,
-0.00037384033203125,
0.01239776611328125,
-0.007762908935546875,
-0.0190582275390625,
-0.00559234619140625,
0.033538818359375,
-0.0275421142578125,
0.019622802734375,
0.00543212890625,
0.02362060546875,
-0.02734375,
0.0240478515625,
0.01568603515625,
-0.026702880859375,
0.00531768798828125,
-0.0006403923034667969,
-0.00220489501953125,
-0.032440185546875,
0.02020263671875,
0.01116943359375,
0.0047607421875,
-0.006015777587890625,
0.0084381103515625,
0.0008764266967773438,
0.0030078887939453125,
-0.035308837890625,
0.00478363037109375,
0.0028362274169921875,
-0.0267486572265625,
-0.004245758056640625,
0.05706787109375,
0.00652313232421875,
-0.0030460357666015625,
0.01776123046875,
0.016357421875,
0.0028553009033203125,
-0.009552001953125,
-0.008544921875,
-0.006809234619140625,
0.036407470703125,
0.0152587890625,
-0.01062774658203125,
-0.0228118896484375,
0.020111083984375,
0.017425537109375,
0.0106048583984375,
0.0103302001953125,
-0.01959228515625,
-0.0086517333984375,
-0.0038509368896484375,
-0.003818511962890625,
-0.00951385498046875,
-0.0168609619140625,
0.02764892578125,
-0.022918701171875,
0.0185699462890625,
-0.004241943359375,
0.02545166015625,
-0.004634857177734375,
-0.00974273681640625,
-0.0230560302734375,
0.005290985107421875,
0.0205841064453125,
-0.017242431640625,
-0.01358795166015625,
-0.0299072265625,
-0.01641845703125,
0.006763458251953125,
0.028411865234375,
0.0213623046875,
-0.01392364501953125,
0.02581787109375,
-0.013824462890625,
-0.0170440673828125,
0.0154266357421875,
0.0032196044921875,
0.0211181640625,
-0.0081787109375,
-0.02520751953125,
-0.00555419921875,
-0.01427459716796875,
-0.004261016845703125,
0.003631591796875,
-0.01311492919921875,
0.011077880859375,
-0.020721435546875,
0.032135009765625,
-0.0100860595703125,
-0.02349853515625,
0.01033782958984375,
0.021697998046875,
0.0010881423950195312,
-0.027862548828125,
-0.0156402587890625,
-0.049224853515625,
-0.00737762451171875,
0.028045654296875,
-0.01470947265625,
0.0109405517578125,
-0.0092926025390625,
-0.0316162109375,
0.01812744140625,
0.01377105712890625,
-0.034210205078125,
-0.00949859619140625,
-0.0164031982421875,
0.019012451171875,
-0.003490447998046875,
0.0175323486328125,
-0.0026187896728515625,
0.0012874603271484375,
0.030181884765625,
0.003559112548828125,
-0.0037899017333984375,
-0.0140380859375,
-0.027313232421875,
0.0021762847900390625,
0.0174102783203125,
-0.01190948486328125,
-0.02227783203125,
0.00461578369140625,
-0.01096343994140625,
0.0017633438110351562,
-0.006378173828125,
-0.002227783203125,
0.00815582275390625,
0.0104217529296875,
-0.0118408203125,
-0.0093994140625,
0.0188446044921875,
0.022674560546875,
-0.0283355712890625,
0.0036945343017578125,
-0.0206146240234375,
-0.038604736328125,
-0.00409698486328125,
0.008544921875,
-0.01611328125,
0.0243988037109375,
0.0102386474609375,
-0.01241302490234375,
-0.005146026611328125,
0.0215606689453125,
-0.016632080078125,
0.00030875205993652344,
0.01727294921875,
0.0010175704956054688,
-0.012847900390625,
0.019805908203125,
0.051055908203125,
0.013641357421875,
0.00809478759765625,
-0.0018682479858398438,
0.022552490234375,
0.01446533203125,
0.017547607421875,
0.00859832763671875,
-0.0224456787109375,
-0.01325225830078125,
0.0038051605224609375,
0.0167236328125,
0.004940032958984375,
0.0231170654296875,
-0.015655517578125,
0.023468017578125,
0.015472412109375,
-0.01410675048828125,
0.029266357421875,
-0.01517486572265625,
-0.0225982666015625,
0.00142669677734375,
-0.012603759765625,
0.005702972412109375,
-0.036407470703125,
-0.005794525146484375,
-0.01467132568359375,
-0.0235443115234375,
-0.0139312744140625,
-0.0052947998046875,
0.017242431640625,
-0.006481170654296875,
-0.013214111328125,
-0.0099945068359375,
0.005603790283203125,
0.045928955078125,
-0.010223388671875,
0.0009360313415527344,
-0.003467559814453125,
-0.021697998046875,
0.0203704833984375,
0.01055908203125,
-0.0037250518798828125,
0.01739501953125,
0.00249481201171875,
0.0230712890625,
-0.01036834716796875,
-0.00846099853515625,
0.01202392578125,
-0.00860595703125,
0.0313720703125,
-0.02618408203125,
-0.007648468017578125,
0.01255035400390625,
-0.016571044921875,
0.02081298828125,
-0.010986328125,
-0.01338958740234375,
-0.001705169677734375,
0.004558563232421875,
-0.019134521484375,
-0.0178375244140625,
-0.028045654296875,
-0.003269195556640625,
0.0103302001953125,
0.0223388671875,
-0.0175628662109375,
0.00580596923828125,
0.0151519775390625,
-0.0104827880859375,
0.0064239501953125,
0.0230560302734375,
-0.01390838623046875,
-0.00865936279296875,
0.011566162109375,
0.006801605224609375,
-0.040771484375,
-0.01526641845703125,
-0.00983428955078125,
0.0010366439819335938,
0.04180908203125,
-0.0268096923828125,
-0.004180908203125,
-0.034149169921875,
0.0002446174621582031,
0.031646728515625,
0.0177764892578125,
0.00531005859375,
-0.030364990234375,
0.01227569580078125,
0.016632080078125,
-0.01175689697265625,
-0.0109100341796875,
-0.0189208984375,
0.0186004638671875,
-0.00374603271484375,
0.01053619384765625,
0.021209716796875,
-0.0015935897827148438,
0.0160369873046875,
-0.01313018798828125,
0.01132965087890625,
-0.030059814453125,
0.0224761962890625,
0.009185791015625,
-0.00335693359375,
-0.0232696533203125,
-0.00891876220703125,
-0.0086669921875,
0.0003116130828857422,
-0.0146484375,
-0.00035452842712402344,
0.034637451171875,
-0.01091766357421875,
-0.019317626953125,
0.0222625732421875,
-0.01410675048828125,
0.0241851806640625,
0.0004150867462158203,
0.023681640625,
-0.02276611328125,
0.01529693603515625,
0.0154876708984375,
0.0111236572265625,
0.0103759765625,
0.0285491943359375,
-0.018402099609375,
-0.0214996337890625,
0.0287322998046875,
0.04058837890625,
0.019561767578125,
-0.004352569580078125,
-0.000179290771484375,
0.00494384765625,
-0.0181427001953125,
0.0056915283203125,
-0.0181427001953125,
-0.000009298324584960938,
-0.01273345947265625,
0.01849365234375,
-0.01360321044921875,
-0.022735595703125,
0.0157012939453125,
-0.0116119384765625,
-0.018707275390625,
0.0005664825439453125,
0.037261962890625,
0.0089874267578125,
0.0221710205078125,
0.01554107666015625,
0.01450347900390625,
0.033721923828125,
-0.028778076171875,
-0.01837158203125,
-0.0022754669189453125,
-0.023895263671875,
-0.0003802776336669922,
0.018768310546875,
-0.018524169921875,
-0.011932373046875,
-0.0611572265625,
0.02252197265625,
-0.0012712478637695312,
0.023834228515625,
0.0110626220703125,
-0.0249481201171875,
0.0028247833251953125,
0.00580596923828125,
-0.0256195068359375,
-0.018585205078125,
-0.013763427734375,
0.031890869140625,
0.01059722900390625,
0.0002720355987548828,
0.0158538818359375,
-0.006000518798828125,
-0.02496337890625,
-0.008331298828125,
0.00516510009765625,
-0.01251220703125,
0.0214691162109375,
-0.00647735595703125,
-0.0234222412109375,
0.01336669921875,
0.0247802734375,
-0.03662109375,
0.033050537109375,
-0.00311279296875,
0.016998291015625,
-0.00080108642578125,
0.0386962890625,
0.0161895751953125,
0.0084381103515625,
0.01396942138671875,
-0.005603790283203125,
0.01412200927734375,
0.0005979537963867188,
-0.0108642578125,
0.0283050537109375,
0.024627685546875,
0.018341064453125,
0.0150299072265625,
-0.022552490234375,
0.017303466796875,
-0.00487518310546875,
-0.006877899169921875,
-0.005573272705078125,
-0.01776123046875,
-0.00244140625,
0.034759521484375,
-0.035125732421875,
-0.0207672119140625,
-0.018768310546875,
-0.046722412109375,
0.032470703125,
-0.031646728515625,
-0.0047454833984375,
0.005504608154296875,
-0.0006036758422851562,
0.004364013671875,
-0.0012178421020507812,
0.018890380859375,
0.0200653076171875,
-0.033233642578125,
0.012298583984375,
0.031158447265625,
-0.03106689453125,
0.005954742431640625,
-0.01031494140625,
0.00566864013671875,
-0.009674072265625,
0.01038360595703125,
-0.001331329345703125,
-0.019195556640625,
0.0088958740234375,
0.0159149169921875,
0.00923919677734375,
-0.01450347900390625,
0.02703857421875,
0.0136871337890625,
0.0196685791015625,
-0.03338623046875,
-0.0099639892578125,
-0.022552490234375,
0.0296478271484375,
-0.038726806640625,
0.021728515625,
0.00487518310546875,
-0.004497528076171875,
0.0183868408203125,
0.01898193359375,
0.027587890625,
-0.01401519775390625,
-0.044586181640625,
0.021331787109375,
-0.0164337158203125,
-0.019866943359375,
-0.01213836669921875,
-0.0138092041015625,
-0.018218994140625,
0.01284027099609375,
-0.01157379150390625,
0.0110931396484375,
-0.013946533203125,
-0.0062713623046875,
0.00981903076171875,
0.03143310546875,
-0.01678466796875,
0.0008263587951660156,
-0.0077362060546875,
0.0081787109375,
0.011474609375,
-0.002544403076171875,
0.0020046234130859375,
-0.0025577545166015625,
0.004474639892578125,
-0.00853729248046875,
0.024627685546875,
0.015655517578125,
-0.0160369873046875,
-0.00684356689453125,
0.0046844482421875,
-0.032440185546875,
0.0183563232421875,
-0.0007371902465820312,
-0.004299163818359375,
-0.0234527587890625,
0.037811279296875,
-0.005313873291015625,
-0.005641937255859375,
0.01045989990234375,
0.041534423828125,
-0.01485443115234375,
-0.003665924072265625,
0.0226593017578125,
0.036865234375,
0.005107879638671875,
-0.0205078125,
0.02362060546875,
0.03375244140625,
0.03143310546875,
0.023651123046875,
0.018829345703125,
0.0198211669921875,
-0.038909912109375,
0.0252838134765625,
-0.0238037109375,
-0.004421234130859375,
0.017578125,
-0.0259552001953125,
-0.0310211181640625,
-0.033538818359375,
-0.00611114501953125,
0.0086669921875,
-0.0290374755859375,
0.0254058837890625,
-0.0027942657470703125,
0.011444091796875,
0.0217742919921875,
-0.01296234130859375,
0.048309326171875,
0.00007408857345581055,
-0.00511932373046875,
-0.0117950439453125,
0.007503509521484375,
0.0250701904296875,
-0.016357421875,
-0.020355224609375,
0.0063934326171875,
-0.0100860595703125,
0.006832122802734375,
0.03887939453125,
-0.024444580078125,
0.01535797119140625,
-0.06304931640625,
-0.029815673828125,
0.01232147216796875,
-0.0217742919921875,
0.0239105224609375,
0.0012350082397460938,
0.015869140625,
-0.0136871337890625,
0.004360198974609375,
-0.037506103515625,
0.0230560302734375,
-0.0139617919921875,
0.039794921875,
0.007625579833984375,
-0.0211944580078125,
0.01151275634765625,
0.018524169921875,
-0.022613525390625,
-0.0189208984375,
-0.032958984375,
0.01367950439453125,
-0.01250457763671875,
0.01059722900390625,
-0.024200439453125,
-0.00908660888671875,
-0.002590179443359375,
-0.01029205322265625,
0.0038509368896484375,
0.0081939697265625,
0.004772186279296875,
0.0093994140625,
-0.0007576942443847656,
0.0219573974609375,
-0.02520751953125,
0.00621795654296875,
0.00562286376953125,
0.00362396240234375,
0.00788116455078125,
0.01312255859375,
0.042327880859375,
0.0496826171875,
-0.020721435546875,
0.021636962890625,
0.0283203125,
0.0252532958984375,
0.021759033203125,
0.00720977783203125,
0.0221405029296875,
0.026611328125,
0.01253509521484375,
0.0119476318359375,
-0.0396728515625,
-0.016326904296875,
0.00789642333984375,
0.00814056396484375,
0.039276123046875,
-0.017578125,
0.0189056396484375,
0.0143585205078125,
0.02276611328125,
0.0139923095703125,
-0.003185272216796875,
0.00627899169921875,
-0.0017948150634765625,
0.005397796630859375,
0.00649261474609375,
0.01763916015625,
-0.01116180419921875,
-0.0086212158203125,
0.03143310546875,
-0.0115509033203125,
0.0011682510375976562,
-0.0186309814453125,
-0.01291656494140625,
0.007293701171875,
-0.021148681640625,
0.030914306640625,
-0.009002685546875,
-0.0300140380859375,
-0.0039825439453125,
0.007030487060546875,
-0.043060302734375,
0.00984954833984375,
0.00675201416015625,
0.0086669921875,
0.00848388671875,
0.0204620361328125,
-0.02862548828125,
0.0267486572265625,
0.0286712646484375,
-0.007602691650390625,
0.04473876953125,
-0.01207733154296875,
0.022003173828125,
0.00522613525390625,
-0.00022649765014648438,
-0.00536346435546875,
-0.007007598876953125,
-0.0279693603515625,
0.0045318603515625,
0.032806396484375,
0.0290374755859375,
-0.031494140625,
-0.03948974609375,
-0.006443023681640625,
0.0289764404296875,
0.0013551712036132812,
-0.03790283203125,
0.0010166168212890625,
0.0256805419921875,
-0.003570556640625,
0.0386962890625,
-0.01204681396484375,
-0.00604248046875,
0.036590576171875,
-0.0126800537109375,
-0.009368896484375,
0.00414276123046875,
0.0069122314453125,
-0.01166534423828125,
0.0031795501708984375,
-0.0175628662109375,
0.0264129638671875,
0.0187835693359375,
0.0007233619689941406,
0.0194244384765625,
-0.01136016845703125,
-0.00873565673828125,
0.007030487060546875,
0.01099395751953125,
0.008575439453125,
0.00559234619140625,
0.01192474365234375,
-0.01200103759765625,
-0.019439697265625,
-0.0271148681640625,
0.009246826171875,
-0.01184844970703125,
-0.01513671875,
0.0233154296875,
-0.0201416015625,
-0.0037631988525390625,
-0.04345703125,
-0.0299224853515625,
-0.04193115234375,
0.00705718994140625,
-0.00479888916015625,
-0.0099639892578125,
0.0030193328857421875,
-0.0137481689453125,
-0.0156402587890625,
-0.039764404296875,
0.007266998291015625,
-0.038116455078125,
-0.005428314208984375,
-0.039886474609375,
0.0235748291015625,
0.005496978759765625,
-0.038970947265625,
-0.01934814453125,
-0.0589599609375,
-0.0003559589385986328,
0.007312774658203125,
0.0085601806640625,
-0.00019621849060058594,
-0.025604248046875,
-0.00033092498779296875,
-0.00614166259765625,
0.0247039794921875,
0.006317138671875,
-0.036407470703125,
-0.0240936279296875,
-0.006641387939453125,
0.016448974609375,
-0.00954437255859375,
-0.0016632080078125,
-0.037322998046875,
0.006378173828125,
-0.02105712890625,
-0.00499725341796875,
0.0208282470703125,
-0.00492095947265625,
-0.00495147705078125,
-0.0205078125,
0.00965118408203125,
0.026214599609375,
-0.0007891654968261719,
-0.006633758544921875,
0.00496673583984375,
-0.051177978515625,
0.005031585693359375,
0.000008761882781982422,
0.0174102783203125,
-0.03778076171875,
-0.00775146484375,
0.01195526123046875,
0.006137847900390625,
0.020904541015625,
-0.00341033935546875,
0.01407623291015625,
-0.0099029541015625,
-0.004154205322265625,
-0.03009033203125,
0.04486083984375,
0.020751953125,
0.01248931884765625,
-0.026092529296875,
0.00980377197265625,
0.006885528564453125,
0.00614166259765625,
0.032318115234375,
-0.01146697998046875,
-0.00792694091796875,
-0.043365478515625,
-0.01493072509765625,
0.00010591745376586914,
-0.00870513916015625,
0.0036525726318359375,
-0.00429534912109375,
0.031341552734375,
0.0181884765625,
0.026123046875,
0.03369140625,
-0.00234222412109375,
0.00905609130859375,
0.0180816650390625,
0.01219940185546875,
0.04461669921875,
-0.0038394927978515625
] |
ours_502
|
There are \(3^3 - 2^3 = 19\) ways that at least one of them played Rock, and among them, there are 3 ways to have two Papers and one Rock. Among the \(19 - 3 = 16\) remaining possibilities, 6 of them have the three hands appear once each, and 3 of them have two Rocks and one Scissors. Therefore, the desired probability is \(\frac{9}{16}\). The answer is \(916\).
\(\boxed{916}\)
|
916
|
{
"competition": "us_comps",
"dataset": "Ours",
"posts": null,
"source": "OMOFall19Solns.md"
}
|
Maryssa, Stephen, and Cynthia played a game. Each of them independently privately chose one of Rock, Paper, and Scissors at random, with all three choices being equally likely. Given that at least one of them chose Rock and at most one of them chose Paper, the probability that exactly one of them chose Scissors can be expressed as \(\frac{m}{n}\) for relatively prime positive integers \(m\) and \(n\). Compute \(100m+n\).
|
[
"/Mathematics/DiscreteMathematics/Combinatorics/Enumeration",
"/Mathematics/DiscreteMathematics/Combinatorics/GeneralCombinatorics",
"/Mathematics/DiscreteMathematics/GeneralDiscreteMathematics/DiscreteMath",
"/Mathematics/DiscreteMathematics/GeneralDiscreteMathematics/DiscreteMathematics",
"/Mathematics/DiscreteMathematics/GeneralDiscreteMathematics/FiniteMathematics",
"/Mathematics/ProbabilityandStatistics/Probability/ConditionalProbability",
"/Mathematics/ProbabilityandStatistics/Probability/MultiplicationPrinciple",
"/Mathematics/ProbabilityandStatistics/Probability/SampleSpace"
] |
Count the outcomes satisfying the given constraints by complement, then enumerate the cases with exactly one Scissors.
|
[
-0.00005078315734863281,
-0.00450897216796875,
-0.0296630859375,
-0.027099609375,
-0.00004404783248901367,
0.0162353515625,
0.002361297607421875,
-0.0285186767578125,
0.0101318359375,
0.0025959014892578125,
0.00463104248046875,
-0.0257720947265625,
-0.0030803680419921875,
-0.045501708984375,
-0.0294952392578125,
-0.037933349609375,
0.0132904052734375,
0.01367950439453125,
-0.01483154296875,
-0.0006060600280761719,
-0.01097869873046875,
-0.0131378173828125,
-0.0028076171875,
0.0005583763122558594,
0.040191650390625,
-0.003780364990234375,
-0.016571044921875,
0.023651123046875,
0.004436492919921875,
0.01270294189453125,
-0.0282440185546875,
-0.039276123046875,
0.0026569366455078125,
0.006542205810546875,
-0.00035119056701660156,
0.00763702392578125,
0.003505706787109375,
0.0028553009033203125,
0.0006909370422363281,
-0.045135498046875,
-0.00681304931640625,
0.039520263671875,
-0.0030460357666015625,
-0.0010547637939453125,
-0.01172637939453125,
-0.008636474609375,
-0.0012836456298828125,
0.0345458984375,
0.010040283203125,
0.018798828125,
-0.00016677379608154297,
0.020782470703125,
-0.028167724609375,
-0.00677490234375,
0.00518798828125,
-0.07989501953125,
-0.01425933837890625,
-0.0002409219741821289,
-0.0021381378173828125,
-0.033447265625,
0.004302978515625,
-0.0247039794921875,
-0.0003294944763183594,
-0.01065826416015625,
-0.002140045166015625,
-0.0073089599609375,
0.001667022705078125,
-0.055694580078125,
0.0093841552734375,
-0.0277252197265625,
0.0270843505859375,
0.0096435546875,
-0.0270538330078125,
0.01113128662109375,
0.046661376953125,
0.0054779052734375,
-0.0009732246398925781,
0.017486572265625,
-0.00896453857421875,
0.01605224609375,
0.007053375244140625,
0.011474609375,
0.006275177001953125,
0.0274810791015625,
0.015899658203125,
0.0000883340835571289,
0.0229339599609375,
0.0023708343505859375,
0.0188446044921875,
-0.03021240234375,
-0.0004038810729980469,
0.058868408203125,
0.0223388671875,
0.0295257568359375,
-0.0004754066467285156,
-0.01277923583984375,
-0.0014858245849609375,
-0.01116180419921875,
-0.017181396484375,
0.00563812255859375,
-0.00702667236328125,
-0.004467010498046875,
0.044219970703125,
0.009002685546875,
-0.0272064208984375,
-0.0292510986328125,
-0.002689361572265625,
0.028717041015625,
-0.0106353759765625,
0.021087646484375,
-0.00539398193359375,
-0.00626373291015625,
0.0005059242248535156,
0.00557708740234375,
-0.00732421875,
0.0090179443359375,
0.01445770263671875,
0.0036773681640625,
-0.0193328857421875,
0.045623779296875,
-0.01654052734375,
0.0025691986083984375,
-0.0127105712890625,
0.003032684326171875,
0.004169464111328125,
0.03887939453125,
-0.0142364501953125,
-0.027984619140625,
0.019866943359375,
0.0041046142578125,
-0.021514892578125,
-0.01018524169921875,
-0.0011730194091796875,
-0.00815582275390625,
-0.05621337890625,
0.01491546630859375,
0.019287109375,
0.0024013519287109375,
-0.01535797119140625,
0.007358551025390625,
-0.0054168701171875,
-0.01629638671875,
-0.0024127960205078125,
0.0009708404541015625,
-0.01323699951171875,
0.00994873046875,
0.002017974853515625,
-0.049072265625,
-0.00478363037109375,
0.0006165504455566406,
0.0016326904296875,
-0.005451202392578125,
0.004825592041015625,
0.0113525390625,
-0.00653076171875,
0.0223236083984375,
0.0157318115234375,
0.01165008544921875,
0.0017843246459960938,
0.0016183853149414062,
-0.012115478515625,
-0.0075225830078125,
-0.004695892333984375,
0.051513671875,
0.0029277801513671875,
0.00870513916015625,
-0.0189666748046875,
0.0115814208984375,
0.00435638427734375,
0.00705718994140625,
0.0234375,
-0.002017974853515625,
-0.01666259765625,
-0.0088348388671875,
-0.006710052490234375,
0.0005340576171875,
-0.01410675048828125,
-0.01364898681640625,
-0.006160736083984375,
0.04058837890625,
0.006011962890625,
-0.0176239013671875,
0.00458526611328125,
-0.002079010009765625,
-0.0206756591796875,
-0.002536773681640625,
0.01500701904296875,
-0.0025806427001953125,
0.00971221923828125,
0.023193359375,
-0.008758544921875,
-0.032440185546875,
-0.0108795166015625,
0.01947021484375,
0.002681732177734375,
-0.02264404296875,
-0.021270751953125,
-0.002765655517578125,
0.0428466796875,
-0.00838470458984375,
0.005603790283203125,
-0.006587982177734375,
-0.001018524169921875,
-0.0021419525146484375,
-0.001438140869140625,
0.0133514404296875,
0.012847900390625,
-0.0011053085327148438,
0.01140594482421875,
0.0156707763671875,
-0.01226806640625,
0.00600433349609375,
-0.0019245147705078125,
-0.0116119384765625,
-0.00991058349609375,
-0.0113525390625,
-0.01125335693359375,
-0.0006451606750488281,
-0.01312255859375,
-0.056427001953125,
-0.01354217529296875,
-0.0088348388671875,
0.0037708282470703125,
-0.00860595703125,
-0.0093536376953125,
-0.0050048828125,
-0.0239715576171875,
-0.0078125,
-0.00562286376953125,
-0.016876220703125,
0.0168914794921875,
-0.005825042724609375,
0.0027008056640625,
-0.004268646240234375,
-0.0160064697265625,
0.01120758056640625,
0.00390625,
-0.0228424072265625,
0.016021728515625,
-0.000010013580322265625,
0.047515869140625,
-0.019744873046875,
-0.0008487701416015625,
0.00827789306640625,
-0.0215911865234375,
-0.01290130615234375,
0.00616455078125,
-0.01354217529296875,
0.01192474365234375,
-0.019195556640625,
-0.00664520263671875,
-0.0138702392578125,
-0.002849578857421875,
-0.020355224609375,
-0.016937255859375,
-0.0256195068359375,
0.01174163818359375,
-0.020599365234375,
-0.0120697021484375,
0.00412750244140625,
0.00907135009765625,
-0.0035572052001953125,
-0.010711669921875,
-0.011199951171875,
0.0070037841796875,
0.0296173095703125,
0.060394287109375,
-0.0026912689208984375,
0.0237274169921875,
-0.023895263671875,
0.00479888916015625,
-0.01519775390625,
-0.0241851806640625,
0.0022830963134765625,
-0.0014133453369140625,
0.01238250732421875,
-0.00160980224609375,
-0.000005602836608886719,
0.0074005126953125,
0.009521484375,
-0.00675201416015625,
0.01143646240234375,
-0.0276336669921875,
0.0006036758422851562,
0.018280029296875,
-0.0013561248779296875,
-0.01470947265625,
-0.009521484375,
-0.0139617919921875,
0.0032806396484375,
-0.0058135986328125,
0.0219573974609375,
0.0030460357666015625,
0.0007677078247070312,
-0.00853729248046875,
-0.040283203125,
-0.0013599395751953125,
0.00818634033203125,
0.0037250518798828125,
-0.0013151168823242188,
0.01324462890625,
0.0089569091796875,
0.0052032470703125,
0.040313720703125,
-0.037506103515625,
0.02630615234375,
0.00688934326171875,
-0.007144927978515625,
0.041595458984375,
0.0045166015625,
0.011444091796875,
0.01178741455078125,
0.022918701171875,
0.006328582763671875,
-0.002048492431640625,
-0.0311126708984375,
0.0157928466796875,
0.0169677734375,
-0.01137542724609375,
0.04010009765625,
0.00771331787109375,
-0.00621795654296875,
-0.024139404296875,
-0.006031036376953125,
0.032958984375,
-0.009674072265625,
0.0015020370483398438,
0.03179931640625,
-0.00823974609375,
0.002044677734375,
0.006313323974609375,
0.0029144287109375,
0.02532958984375,
-0.024322509765625,
-0.01136016845703125,
0.0002968311309814453,
-0.002185821533203125,
0.0301666259765625,
-0.023040771484375,
0.0022220611572265625,
0.009124755859375,
-0.006103515625,
0.0021820068359375,
-0.0264434814453125,
0.02056884765625,
0.0072479248046875,
0.0021266937255859375,
0.01163482666015625,
-0.003772735595703125,
-0.005779266357421875,
-0.017486572265625,
0.01282501220703125,
-0.0007576942443847656,
0.0080718994140625,
-0.04302978515625,
-0.00727081298828125,
0.01186370849609375,
0.0202789306640625,
-0.0088348388671875,
0.007640838623046875,
0.01146697998046875,
-0.00972747802734375,
-0.010589599609375,
-0.0157012939453125,
0.0090179443359375,
-0.00955963134765625,
0.0054931640625,
0.0305938720703125,
0.002445220947265625,
-0.01340484619140625,
-0.037384033203125,
0.01788330078125,
0.0027370452880859375,
-0.03289794921875,
0.0015382766723632812,
-0.02532958984375,
-0.0015773773193359375,
-0.016937255859375,
-0.0155029296875,
0.007450103759765625,
-0.00959014892578125,
0.025177001953125,
-0.008453369140625,
0.03350830078125,
-0.0413818359375,
-0.0048828125,
0.042327880859375,
-0.033966064453125,
-0.025115966796875,
-0.00299835205078125,
0.006336212158203125,
0.0008897781372070312,
0.0034275054931640625,
-0.00720977783203125,
0.0167083740234375,
-0.0254974365234375,
0.00016248226165771484,
0.0012445449829101562,
0.0202484130859375,
-0.027801513671875,
-0.02337646484375,
-0.01546478271484375,
0.004642486572265625,
-0.008544921875,
0.01103973388671875,
-0.003265380859375,
-0.0075836181640625,
0.03125,
-0.002552032470703125,
-0.0222015380859375,
-0.019012451171875,
0.0036792755126953125,
0.00955963134765625,
0.0391845703125,
-0.0211334228515625,
0.0021305084228515625,
0.0200042724609375,
0.006160736083984375,
-0.03350830078125,
-0.01373291015625,
-0.01184844970703125,
-0.0305938720703125,
-0.01325225830078125,
-0.003997802734375,
0.021820068359375,
0.041351318359375,
0.00984954833984375,
0.0010728836059570312,
-0.02911376953125,
0.01294708251953125,
-0.0282135009765625,
-0.003082275390625,
-0.0063934326171875,
0.022186279296875,
-0.03375244140625,
0.051544189453125,
-0.01354217529296875,
-0.0021762847900390625,
-0.0196533203125,
-0.0103302001953125,
-0.001220703125,
-0.050140380859375,
-0.00533294677734375,
0.0018768310546875,
0.0250701904296875,
0.00598907470703125,
-0.0257110595703125,
0.0194244384765625,
-0.04345703125,
0.02593994140625,
-0.0018930435180664062,
-0.0031833648681640625,
0.0013399124145507812,
-0.0341796875,
-0.01110076904296875,
0.0017061233520507812,
0.00949859619140625,
-0.009857177734375,
0.00998687744140625,
-0.0232391357421875,
-0.0121307373046875,
0.0289459228515625,
0.0217742919921875,
-0.0038623809814453125,
0.0306396484375,
0.0038299560546875,
-0.008819580078125,
0.018951416015625,
-0.029632568359375,
0.05157470703125,
-0.0200653076171875,
0.0006322860717773438,
-0.0238037109375,
-0.00916290283203125,
-0.0423583984375,
-0.0009312629699707031,
-0.023223876953125,
-0.006633758544921875,
-0.0062408447265625,
-0.006927490234375,
-0.0113983154296875,
0.0251922607421875,
-0.0165252685546875,
0.06756591796875,
-0.005466461181640625,
0.01332855224609375,
0.006084442138671875,
-0.006175994873046875,
-0.042724609375,
-0.0504150390625,
-0.00286865234375,
0.0268096923828125,
-0.04876708984375,
0.0055084228515625,
-0.04296875,
0.02398681640625,
0.0145263671875,
0.01512908935546875,
-0.002300262451171875,
0.0192718505859375,
0.0226593017578125,
-0.0350341796875,
0.019683837890625,
0.0084228515625,
-0.0159759521484375,
0.00638580322265625,
0.0235137939453125,
-0.00275421142578125,
-0.0174407958984375,
-0.007415771484375,
0.00799560546875,
0.00021159648895263672,
0.007312774658203125,
-0.01467132568359375,
0.021514892578125,
0.0260162353515625,
-0.0089263916015625,
-0.01459503173828125,
0.002132415771484375,
0.01535797119140625,
-0.032684326171875,
0.0243377685546875,
0.02227783203125,
-0.0284423828125,
-0.00470733642578125,
0.0252838134765625,
-0.003902435302734375,
0.01222991943359375,
-0.0227203369140625,
-0.00983428955078125,
0.019805908203125,
-0.0158843994140625,
0.004123687744140625,
-0.0225982666015625,
-0.04486083984375,
-0.0161285400390625,
-0.011810302734375,
-0.00994873046875,
-0.0007266998291015625,
0.0167694091796875,
-0.008636474609375,
-0.014007568359375,
-0.0023860931396484375,
-0.0288238525390625,
-0.02935791015625,
-0.035980224609375,
-0.0107421875,
0.002696990966796875,
0.0113525390625,
0.00260162353515625,
0.02398681640625,
0.03302001953125,
-0.037567138671875,
-0.0163116455078125,
-0.0278167724609375,
0.014312744140625,
-0.00923919677734375,
0.03021240234375,
-0.010345458984375,
0.004726409912109375,
0.0263671875,
-0.039794921875,
0.0207366943359375,
0.01019287109375,
-0.004993438720703125,
0.0180511474609375,
-0.0276641845703125,
0.00684356689453125,
0.0166168212890625,
-0.028106689453125,
-0.00778961181640625,
-0.0092620849609375,
-0.0094451904296875,
0.0452880859375,
0.0265655517578125,
0.004833221435546875,
-0.01245880126953125,
0.003971099853515625,
0.01125335693359375,
-0.0224456787109375,
0.01541900634765625,
0.013824462890625,
-0.01568603515625,
0.0271148681640625,
0.0220184326171875,
0.01220703125,
0.014984130859375,
-0.000017821788787841797,
0.0352783203125,
-0.005756378173828125,
-0.0206298828125,
0.01224517822265625,
0.031341552734375,
0.020843505859375,
-0.025115966796875,
0.0119476318359375,
0.029449462890625,
-0.0105743408203125,
-0.0048370361328125,
-0.0013380050659179688,
0.011322021484375,
-0.0085296630859375,
-0.00579071044921875,
-0.004238128662109375,
-0.0191802978515625,
-0.0105438232421875,
-0.00933837890625,
0.021484375,
0.0269317626953125,
-0.01120758056640625,
-0.04693603515625,
0.016571044921875,
0.00042057037353515625,
0.022247314453125,
0.01324462890625,
-0.0167694091796875,
0.011566162109375,
-0.0073699951171875,
-0.0180206298828125,
-0.0308074951171875,
0.0229034423828125,
0.0257110595703125,
0.0101165771484375,
0.02752685546875,
-0.0263671875,
0.006847381591796875,
-0.019256591796875,
-0.0164947509765625,
0.01203155517578125,
-0.00513458251953125,
0.0112152099609375,
-0.0017309188842773438,
0.00647735595703125,
0.0247955322265625,
-0.01229095458984375,
-0.0113067626953125,
0.003055572509765625,
-0.005115509033203125,
-0.013275146484375,
-0.043914794921875,
0.01317596435546875,
0.0178985595703125,
0.023468017578125,
-0.030517578125,
-0.00836944580078125,
-0.00853729248046875,
-0.0072174072265625,
0.018951416015625,
-0.00955963134765625,
0.0015878677368164062,
-0.00226593017578125,
0.0073699951171875,
0.0006165504455566406,
0.0291290283203125,
-0.01554107666015625,
0.00839996337890625,
-0.0195770263671875,
-0.037353515625,
0.00785064697265625,
-0.0220947265625,
-0.00372314453125,
-0.035919189453125,
0.0116119384765625,
-0.0120697021484375,
0.0205841064453125,
-0.0307464599609375,
0.01418304443359375,
-0.0182952880859375,
-0.01324462890625,
0.002655029296875,
-0.0048980712890625,
0.01059722900390625,
0.009796142578125,
-0.004119873046875,
0.0178985595703125,
-0.0254058837890625,
0.0088653564453125,
0.00113677978515625,
-0.021697998046875,
0.039642333984375,
-0.0026092529296875,
-0.001567840576171875,
0.027923583984375,
-0.053314208984375,
-0.016082763671875,
0.0022029876708984375,
0.03509521484375,
-0.00861358642578125,
0.02496337890625,
0.01446533203125,
0.01203155517578125,
0.02410888671875,
-0.0274810791015625,
0.03961181640625,
0.01050567626953125,
-0.00524139404296875,
0.00433349609375,
0.0177154541015625,
-0.0145263671875,
-0.049835205078125,
0.001194000244140625,
-0.015228271484375,
0.0008778572082519531,
-0.00580596923828125,
0.0048675537109375,
0.0091705322265625,
0.00766754150390625,
-0.006595611572265625,
-0.0245208740234375,
0.0107421875,
-0.0380859375,
-0.0034275054931640625,
-0.029327392578125,
0.01535797119140625,
-0.018707275390625,
-0.0406494140625,
0.0108489990234375,
-0.0084075927734375,
-0.0003294944763183594,
0.0176239013671875,
0.004459381103515625,
0.007598876953125,
-0.0031909942626953125,
-0.00286102294921875,
0.0181732177734375,
-0.0275115966796875,
0.01450347900390625,
-0.03082275390625,
-0.00148773193359375,
0.01102447509765625,
-0.01422882080078125,
-0.0172119140625,
0.025299072265625,
-0.003143310546875,
-0.00970458984375,
-0.033966064453125,
-0.0202178955078125,
-0.05999755859375,
0.00482177734375,
0.01485443115234375,
0.04022216796875,
-0.00720977783203125,
0.0304718017578125,
-0.0005559921264648438,
0.019256591796875,
-0.01221466064453125,
0.015625,
0.01337432861328125,
0.0230712890625,
-0.0269775390625,
0.01544952392578125,
-0.0232696533203125,
0.0014934539794921875,
-0.01351165771484375,
-0.033966064453125,
0.0000712275505065918,
0.0017957687377929688,
0.033050537109375,
-0.00443267822265625,
0.0201416015625,
-0.0091552734375,
-0.0264892578125,
-0.006610870361328125,
-0.01197052001953125,
0.037841796875,
-0.0019369125366210938,
-0.0276641845703125,
0.0009694099426269531,
-0.01165008544921875,
0.02142333984375,
-0.021759033203125,
-0.0006909370422363281,
-0.01274871826171875,
-0.0011692047119140625,
0.0265045166015625,
-0.01386260986328125,
-0.02813720703125,
0.00655364990234375,
0.02044677734375,
-0.03997802734375,
-0.0239105224609375,
-0.01131439208984375,
0.01641845703125,
0.01198577880859375,
0.0229644775390625,
0.0106658935546875,
-0.01306915283203125,
-0.0226898193359375,
-0.0159912109375,
-0.00885009765625,
0.0587158203125,
-0.0060882568359375,
0.01373291015625,
0.029998779296875,
-0.006824493408203125,
-0.016998291015625,
-0.0171356201171875,
-0.03900146484375,
-0.0008883476257324219,
0.005664825439453125,
-0.01468658447265625,
-0.0218505859375,
-0.005462646484375,
0.0235595703125,
0.024749755859375,
-0.0226898193359375,
0.0078277587890625,
0.03399658203125,
-0.000060439109802246094,
0.0213470458984375,
0.006511688232421875,
0.0012569427490234375,
-0.00882720947265625,
-0.0110321044921875,
-0.010498046875,
-0.03643798828125,
0.0179595947265625,
0.0034999847412109375,
-0.011474609375,
-0.01071929931640625,
-0.000843048095703125,
0.025909423828125,
-0.00901031494140625,
0.016754150390625,
-0.003688812255859375,
-0.0131988525390625,
0.00040411949157714844,
0.03253173828125,
0.005519866943359375,
-0.0016965866088867188,
0.01404571533203125,
-0.0202484130859375,
-0.0474853515625,
-0.01134490966796875,
-0.0197601318359375,
0.014617919921875,
-0.015716552734375,
0.035003662109375,
0.01184844970703125,
0.002140045166015625,
0.0031871795654296875,
0.0201416015625,
0.0005731582641601562,
0.00891876220703125,
0.06207275390625,
-0.010284423828125,
0.00202178955078125,
-0.01085662841796875,
0.0220184326171875,
0.01666259765625,
0.005718231201171875,
0.016937255859375,
-0.023956298828125,
0.01824951171875,
0.004665374755859375,
-0.0009965896606445312,
0.0135345458984375,
0.0014829635620117188,
-0.00769805908203125,
-0.022125244140625,
0.039154052734375,
-0.0014505386352539062,
0.043548583984375,
-0.0484619140625,
0.0026912689208984375,
0.016387939453125,
-0.0297698974609375,
0.002933502197265625,
0.001674652099609375,
-0.0226898193359375,
0.01206207275390625,
-0.01461029052734375,
0.0227813720703125,
-0.0100555419921875,
0.0026874542236328125,
0.03216552734375,
0.0031604766845703125,
-0.0103759765625,
-0.0138397216796875,
-0.002422332763671875,
0.017852783203125,
-0.0101318359375,
-0.05120849609375,
-0.0121002197265625,
-0.02520751953125,
0.0020389556884765625,
0.0251922607421875,
-0.004058837890625,
-0.00925445556640625,
-0.033233642578125,
-0.0020122528076171875,
-0.0006704330444335938,
0.003673553466796875,
0.01491546630859375,
-0.0029010772705078125,
0.027984619140625,
-0.0007305145263671875,
-0.032989501953125,
-0.009735107421875,
-0.007526397705078125,
0.01245880126953125,
0.00838470458984375,
-0.0204925537109375,
0.0210113525390625,
0.0163116455078125,
-0.0316162109375,
-0.017364501953125,
-0.01215362548828125,
0.01081085205078125,
0.00809478759765625,
-0.019439697265625,
0.0238800048828125,
-0.00955963134765625,
0.0225830078125,
-0.0010385513305664062,
-0.0009984970092773438,
0.01514434814453125,
0.00444793701171875,
-0.00435638427734375,
0.007266998291015625,
0.02569580078125,
0.001377105712890625,
-0.0310821533203125,
0.0012884140014648438,
0.0163116455078125,
-0.013519287109375,
-0.000041365623474121094,
0.0001424551010131836,
-0.019805908203125,
-0.0146942138671875,
-0.0261993408203125,
0.0291290283203125,
0.0093536376953125,
0.027191162109375,
0.003032684326171875,
0.033966064453125,
-0.016937255859375,
0.0019426345825195312,
0.014434814453125,
0.02301025390625,
-0.0419921875,
0.0164642333984375,
-0.034393310546875,
0.0290679931640625,
0.046478271484375,
0.00439453125,
0.02252197265625,
0.028564453125,
-0.0286712646484375,
-0.0176849365234375,
-0.0053558349609375,
0.0022106170654296875,
-0.01088714599609375,
-0.0160980224609375,
0.00004875659942626953,
-0.04864501953125,
-0.00048732757568359375,
-0.01110076904296875,
-0.029205322265625,
-0.017974853515625,
0.04248046875,
-0.0050201416015625,
-0.0177001953125,
-0.0195770263671875,
-0.007568359375,
0.0174407958984375,
0.003894805908203125,
0.0017547607421875,
-0.01338958740234375,
-0.0017538070678710938,
0.0008826255798339844,
0.0006389617919921875,
-0.037994384765625,
-0.0196075439453125,
0.0035305023193359375,
-0.007808685302734375,
-0.005146026611328125,
0.0243072509765625,
0.036865234375,
0.0154876708984375,
-0.047882080078125,
0.0021953582763671875,
0.037445068359375,
-0.0047760009765625,
-0.0180816650390625,
-0.00366973876953125,
0.06146240234375,
-0.0252532958984375,
0.00382232666015625,
-0.0097808837890625,
0.01496124267578125,
0.022674560546875,
-0.0251922607421875,
0.01861572265625,
-0.01151275634765625,
-0.013641357421875,
0.0166778564453125,
-0.0272216796875,
-0.00975799560546875,
-0.00707244873046875,
-0.01497650146484375,
0.0005879402160644531,
0.006572723388671875,
0.0072784423828125,
0.0308837890625,
-0.00428009033203125,
0.003459930419921875,
-0.0024242401123046875,
0.0013866424560546875,
0.0213623046875,
-0.0238800048828125,
-0.00893402099609375,
-0.009521484375,
0.0021915435791015625,
-0.00335693359375,
-0.006198883056640625,
-0.005001068115234375,
0.00982666015625,
-0.014984130859375,
0.01059722900390625,
0.012176513671875,
0.0103912353515625,
-0.029388427734375,
-0.0011959075927734375,
0.001010894775390625,
-0.03582763671875,
-0.0264892578125,
-0.036529541015625,
0.03662109375,
0.0117340087890625,
0.0057830810546875,
0.004547119140625,
0.0275115966796875,
0.005405426025390625,
0.01505279541015625,
-0.01157379150390625,
0.01116180419921875,
-0.01023101806640625,
0.0234527587890625,
-0.0036106109619140625,
0.005214691162109375,
0.0258941650390625,
0.00016689300537109375,
-0.0106048583984375,
-0.0159912109375,
-0.020416259765625,
-0.0220489501953125,
0.0160980224609375,
-0.0091705322265625,
0.01528167724609375,
-0.00412750244140625,
0.01165771484375,
-0.0013494491577148438,
-0.015869140625,
-0.0209197998046875,
0.04119873046875,
-0.0092010498046875,
-0.0006804466247558594,
-0.0192413330078125,
0.0043182373046875,
-0.019195556640625,
-0.003536224365234375,
-0.0008378028869628906,
-0.0325927734375,
-0.01294708251953125,
-0.0189208984375,
0.000980377197265625,
-0.0140838623046875,
-0.0160064697265625,
-0.007602691650390625,
-0.02313232421875,
0.01244354248046875,
-0.034515380859375,
0.002498626708984375,
-0.0003924369812011719,
-0.0027065277099609375,
0.0005450248718261719,
-0.031219482421875,
-0.003086090087890625,
0.0177001953125,
-0.0112762451171875,
0.0328369140625,
-0.0185089111328125,
0.01904296875,
0.01715087890625,
0.0199432373046875,
0.01031494140625,
-0.0115814208984375,
0.006374359130859375,
0.01800537109375,
-0.0019121170043945312,
0.001155853271484375,
0.00531005859375,
0.006328582763671875,
0.00699615478515625,
0.0023040771484375,
-0.0079193115234375,
0.017181396484375,
0.0105133056640625,
0.0090484619140625,
-0.031768798828125,
0.032684326171875,
-0.0251312255859375,
0.0020084381103515625,
-0.02984619140625,
0.005298614501953125,
0.005435943603515625,
0.0228271484375,
-0.006122589111328125,
-0.0165863037109375,
0.01122283935546875,
0.03729248046875,
0.00605010986328125,
0.016265869140625,
-0.0298309326171875,
-0.007205963134765625,
-0.045013427734375,
-0.0335693359375,
-0.0096435546875,
0.0065765380859375,
-0.00788116455078125,
0.023529052734375,
0.0038738250732421875,
0.016265869140625,
0.00917816162109375,
0.036773681640625,
0.01898193359375,
-0.0113983154296875,
0.0009169578552246094,
0.020050048828125,
0.00034332275390625,
0.0251007080078125,
-0.009307861328125,
-0.0175018310546875,
0.006221771240234375,
0.0207061767578125,
0.0035457611083984375,
0.031402587890625,
0.0007662773132324219,
-0.00981903076171875,
-0.017852783203125,
0.0128936767578125,
-0.01273345947265625,
-0.022491455078125,
0.00675201416015625,
-0.031829833984375,
-0.0200042724609375,
0.00807952880859375,
0.0360107421875,
0.03790283203125,
0.01122283935546875,
0.010498046875,
-0.00835418701171875,
0.0005688667297363281,
0.00591278076171875,
-0.00368499755859375,
-0.0112152099609375,
0.004680633544921875,
-0.00682830810546875,
0.004482269287109375,
0.022216796875,
-0.00716400146484375,
-0.0015745162963867188,
-0.01154327392578125,
-0.032379150390625,
0.007404327392578125,
-0.0025768280029296875,
0.002948760986328125,
-0.041046142578125,
0.0230865478515625,
-0.0009312629699707031,
0.0167694091796875,
0.01024627685546875,
0.0021381378173828125,
-0.017303466796875,
0.01551055908203125,
-0.0028018951416015625,
-0.026092529296875,
-0.00278472900390625,
0.0011148452758789062,
-0.01079559326171875,
-0.02105712890625,
0.019073486328125,
-0.0023250579833984375,
-0.0007309913635253906,
0.01458740234375,
-0.00461578369140625,
0.0229339599609375,
-0.0523681640625,
-0.0258941650390625,
-0.016082763671875,
0.0006728172302246094,
-0.0005331039428710938,
0.01003265380859375,
0.0174560546875,
0.02117919921875,
-0.01003265380859375,
0.0121612548828125,
0.00009864568710327148,
-0.018646240234375,
0.0252685546875,
-0.0162506103515625,
-0.006565093994140625,
0.00914764404296875,
0.0017642974853515625,
0.0253143310546875,
-0.00858306884765625,
0.01114654541015625,
0.004421234130859375,
-0.00341796875,
0.020416259765625,
-0.0212249755859375,
-0.0142974853515625,
-0.0126800537109375,
0.06768798828125,
-0.006488800048828125,
-0.0152130126953125,
-0.0068206787109375,
0.009979248046875,
0.004398345947265625,
-0.0129241943359375,
0.040374755859375,
0.0305633544921875,
0.0183563232421875,
0.00852203369140625,
-0.0208892822265625,
-0.021087646484375,
0.0226898193359375,
0.003570556640625,
0.000431060791015625,
-0.0044708251953125,
0.0173187255859375,
-0.032012939453125,
-0.01189422607421875,
0.0025501251220703125,
-0.0292816162109375,
-0.028900146484375,
0.026336669921875,
-0.0019931793212890625,
0.00000476837158203125,
0.0012044906616210938,
0.01479339599609375,
0.0161590576171875,
-0.0004260540008544922,
0.03973388671875,
-0.01145172119140625,
0.022613525390625,
0.0178985595703125,
0.0195465087890625,
0.03955078125,
0.0299072265625,
0.0295562744140625,
0.0003674030303955078,
-0.0238800048828125,
-0.0170745849609375,
-0.023345947265625,
0.0183868408203125,
-0.021209716796875,
-0.00749969482421875,
-0.0181884765625,
-0.0233917236328125,
0.00814056396484375,
-0.036468505859375,
0.0113677978515625,
-0.00615692138671875,
-0.0033168792724609375,
-0.0074462890625,
-0.0009565353393554688,
0.0173187255859375,
0.0252838134765625,
0.00931549072265625,
-0.0199432373046875,
0.0168914794921875,
0.018768310546875,
0.0170440673828125,
-0.009307861328125,
-0.04107666015625,
-0.035980224609375,
-0.008636474609375,
0.02386474609375,
-0.01384735107421875,
0.00696563720703125,
-0.010772705078125,
-0.014007568359375,
-0.0262298583984375,
-0.0225372314453125,
0.00870513916015625,
0.032012939453125,
-0.032073974609375,
-0.01207733154296875,
0.0269775390625,
-0.0020008087158203125,
-0.0035247802734375,
0.006206512451171875,
0.026947021484375,
-0.031402587890625,
-0.01534271240234375,
-0.027801513671875,
0.0023555755615234375,
0.0191497802734375,
-0.00150299072265625,
-0.0189208984375,
0.01343536376953125,
-0.019256591796875,
0.015899658203125,
-0.032623291015625,
0.011444091796875,
0.005443572998046875,
0.01230621337890625,
0.00637054443359375,
-0.01190948486328125,
-0.024505615234375,
0.0102081298828125,
0.0037174224853515625,
0.0166168212890625,
-0.028717041015625,
0.013641357421875,
-0.005352020263671875,
-0.0362548828125,
-0.0004973411560058594,
-0.0189361572265625,
0.0179290771484375,
0.0134735107421875,
-0.01236724853515625,
-0.0328369140625,
0.0259246826171875,
-0.04010009765625,
-0.01177215576171875,
0.0068206787109375,
-0.0188751220703125,
0.00019359588623046875,
-0.002307891845703125,
-0.0128631591796875,
-0.01270294189453125,
0.025543212890625,
0.0098724365234375,
0.00005716085433959961,
-0.0023632049560546875,
-0.00769805908203125,
-0.02557373046875,
-0.01971435546875,
0.0271148681640625,
0.004421234130859375,
-0.02459716796875,
0.0399169921875,
0.06964111328125,
-0.03558349609375,
-0.0170440673828125,
-0.00832366943359375,
-0.0180816650390625,
-0.0017070770263671875,
0.006946563720703125,
-0.00798797607421875,
0.0081024169921875,
-0.026641845703125,
-0.00716400146484375,
0.007030487060546875,
-0.054931640625,
-0.008087158203125,
0.0005154609680175781,
0.0219268798828125,
-0.0208282470703125,
-0.0272674560546875,
0.00009620189666748047,
0.0309600830078125,
-0.017333984375,
0.01087188720703125,
0.0066070556640625,
-0.005084991455078125,
0.0006608963012695312,
-0.037384033203125,
0.003536224365234375,
-0.030975341796875,
0.0140838623046875,
0.0263824462890625,
0.000392913818359375,
-0.01165771484375,
-0.005977630615234375,
-0.022705078125,
-0.0118560791015625,
-0.0186767578125,
-0.004650115966796875,
-0.006366729736328125,
-0.041229248046875,
0.0033416748046875,
0.0225372314453125,
0.004848480224609375,
-0.00797271728515625,
-0.0171051025390625,
0.018768310546875,
0.007122039794921875,
0.0118560791015625,
-0.009796142578125,
-0.0281219482421875,
0.0084228515625,
-0.0035495758056640625,
-0.0079345703125,
0.0075531005859375,
0.014984130859375,
-0.0278472900390625,
0.01110076904296875,
0.00113677978515625,
0.0015420913696289062,
0.010772705078125,
0.0012111663818359375,
-0.0029125213623046875,
0.005466461181640625,
0.0064849853515625,
-0.0030574798583984375,
0.00724029541015625,
-0.023406982421875,
-0.000934600830078125,
-0.003101348876953125,
-0.032135009765625,
0.0028820037841796875,
-0.034423828125,
0.018310546875,
-0.0170135498046875,
0.00862884521484375,
0.006366729736328125,
-0.004680633544921875,
0.02490234375,
-0.0189056396484375,
0.00811004638671875,
0.0028285980224609375,
-0.031982421875,
0.038848876953125,
-0.01461029052734375,
0.004528045654296875,
0.00013589859008789062,
0.00884246826171875,
-0.04595947265625,
-0.0242156982421875,
-0.028564453125,
-0.0007848739624023438,
0.01256561279296875,
0.032958984375,
0.00196075439453125,
0.0238494873046875,
0.01276397705078125,
0.00411224365234375,
-0.015167236328125,
-0.00215911865234375,
0.01091766357421875,
0.0035839080810546875,
-0.019073486328125,
0.0102691650390625,
-0.0199127197265625,
-0.018096923828125,
0.01107025146484375,
-0.00701141357421875,
-0.0157012939453125,
-0.01284027099609375,
-0.025634765625,
0.020111083984375,
-0.0232696533203125,
0.027191162109375,
-0.0113983154296875,
-0.006046295166015625,
0.0164337158203125,
-0.031036376953125,
-0.028045654296875,
-0.01274871826171875,
0.04449462890625,
-0.00972747802734375,
-0.0213165283203125,
-0.0185546875,
-0.0009593963623046875,
-0.036407470703125,
-0.0156097412109375,
0.00876617431640625,
-0.00850677490234375,
-0.0212554931640625,
0.01078033447265625,
-0.0100250244140625,
-0.0010881423950195312,
-0.00839996337890625,
-0.0051727294921875,
0.0150604248046875,
-0.019805908203125,
0.012908935546875,
0.0148773193359375,
0.03131103515625,
-0.004119873046875,
-0.0269317626953125,
0.007236480712890625,
0.005229949951171875,
0.0261993408203125,
0.011505126953125,
-0.02740478515625,
-0.0189208984375,
-0.0038623809814453125,
0.0197906494140625,
-0.051300048828125,
0.006763458251953125,
-0.0107421875,
-0.029296875,
-0.01580810546875,
-0.009246826171875,
-0.03961181640625,
0.033294677734375,
0.0020122528076171875,
0.022003173828125,
-0.0048675537109375,
0.0225372314453125,
0.0098419189453125,
0.03228759765625,
-0.00547027587890625,
0.005496978759765625,
-0.013671875,
-0.009979248046875,
-0.0170745849609375,
0.032623291015625,
-0.0081329345703125,
-0.027557373046875,
0.0246734619140625,
0.00766754150390625,
-0.003932952880859375,
-0.01080322265625,
0.00664520263671875,
0.01230621337890625,
0.00873565673828125,
-0.01392364501953125,
0.020751953125,
0.016998291015625,
0.009918212890625,
0.007114410400390625,
-0.00695037841796875,
-0.004535675048828125,
0.015899658203125,
-0.013671875,
0.0028476715087890625,
0.0238800048828125,
0.0231170654296875,
0.0036182403564453125,
0.0246734619140625,
0.034942626953125,
-0.00295257568359375,
0.004573822021484375,
-0.006195068359375,
-0.00872039794921875,
0.005756378173828125,
-0.017364501953125,
0.0257720947265625,
0.004108428955078125,
-0.0186004638671875,
0.0168609619140625,
0.0049896240234375,
0.0014190673828125,
-0.027496337890625,
-0.005401611328125,
-0.0125274658203125,
0.013671875,
0.0010204315185546875,
-0.0186614990234375,
0.0205230712890625,
0.00809478759765625,
-0.01401519775390625,
0.00960540771484375,
-0.033447265625,
-0.0019140243530273438,
0.058929443359375,
-0.0308380126953125,
0.0240325927734375,
0.032958984375,
0.027984619140625,
-0.009857177734375,
-0.0085906982421875,
-0.02667236328125,
-0.0211029052734375,
-0.005443572998046875,
0.01239013671875,
-0.0066070556640625,
0.007541656494140625,
0.021942138671875,
0.029693603515625,
0.016693115234375,
0.0004303455352783203,
0.005794525146484375,
0.03350830078125,
0.0261688232421875,
-0.01413726806640625,
0.0006709098815917969,
-0.002071380615234375,
-0.001617431640625,
-0.007717132568359375,
-0.0208282470703125,
0.0182647705078125,
-0.03314208984375,
0.01396942138671875,
0.0176544189453125,
0.0020351409912109375,
0.0191650390625,
0.0125579833984375,
0.036834716796875,
-0.0258331298828125,
0.035858154296875,
0.01470184326171875,
0.05377197265625,
-0.0068511962890625,
0.0113067626953125,
0.0134124755859375,
0.0212554931640625,
0.0064544677734375,
-0.034698486328125,
0.0078887939453125,
0.03680419921875,
-0.0308990478515625,
0.0244293212890625,
0.0019311904907226562,
-0.0162811279296875,
0.01898193359375,
0.0146942138671875,
0.0265655517578125,
-0.0190582275390625,
0.001678466796875,
0.034332275390625,
0.00786590576171875,
0.01055908203125,
0.015777587890625,
0.018096923828125,
0.0016803741455078125,
0.028228759765625,
0.003284454345703125,
0.011688232421875,
0.0072784423828125,
0.01071929931640625,
-0.0128173828125,
-0.01751708984375,
-0.026580810546875,
0.018951416015625,
0.0011844635009765625,
0.03009033203125,
0.0279541015625,
-0.02386474609375,
-0.02056884765625,
-0.01279449462890625,
0.0511474609375,
0.0006556510925292969,
0.0004363059997558594,
0.0341796875,
0.00508880615234375,
-0.00980377197265625,
-0.0295867919921875,
0.008941650390625,
-0.04119873046875,
0.023223876953125,
0.020782470703125,
0.0088043212890625,
-0.0301971435546875,
0.0025157928466796875,
-0.003082275390625,
0.003520965576171875,
-0.0080108642578125,
0.0190277099609375,
-0.00545501708984375,
0.0009908676147460938,
-0.0205230712890625,
-0.041229248046875,
0.01442718505859375,
-0.0028629302978515625,
0.042755126953125,
-0.002349853515625,
0.0113677978515625,
-0.029632568359375,
0.019439697265625,
0.034088134765625,
-0.0233612060546875,
-0.0136566162109375,
0.00428009033203125,
-0.01837158203125,
-0.0012722015380859375,
0.009552001953125,
0.0133514404296875,
-0.022705078125,
0.006092071533203125,
-0.01114654541015625,
0.012298583984375,
0.0108184814453125,
-0.01078033447265625,
0.01456451416015625,
0.0028743743896484375,
0.0084991455078125,
0.0478515625,
-0.003002166748046875,
0.006374359130859375,
-0.0004191398620605469,
-0.004924774169921875,
-0.0216217041015625,
0.005832672119140625,
0.0245361328125,
0.0198974609375,
-0.0149688720703125,
0.01436614990234375,
0.03369140625,
0.0091094970703125,
0.0197601318359375,
0.01812744140625,
0.00742340087890625,
0.049163818359375,
0.00354766845703125,
-0.015899658203125,
-0.01318359375,
-0.01702880859375,
-0.0202789306640625,
0.0186614990234375,
0.0002903938293457031,
-0.02911376953125,
-0.0401611328125,
-0.022552490234375,
0.052398681640625,
-0.0077362060546875,
0.0018815994262695312,
-0.0131683349609375,
0.0159912109375,
0.0019893646240234375,
0.012359619140625,
-0.01076507568359375,
0.0026950836181640625,
-0.0123138427734375,
0.0034618377685546875,
0.0035610198974609375,
-0.01983642578125,
0.00737762451171875,
0.0218353271484375,
-0.0364990234375,
-0.01041412353515625,
0.00527191162109375,
0.0199432373046875,
0.031982421875,
-0.0049285888671875,
0.01273345947265625,
-0.034881591796875,
0.004711151123046875,
-0.0262908935546875,
-0.0284271240234375,
0.0028934478759765625,
-0.02117919921875,
-0.037872314453125,
0.00887298583984375,
0.00650787353515625,
0.0005168914794921875,
-0.0158233642578125,
-0.00222015380859375,
0.0028438568115234375,
-0.0037078857421875,
0.039337158203125,
-0.00594329833984375,
0.022064208984375,
0.00859832763671875,
-0.00815582275390625,
-0.007625579833984375,
0.007659912109375,
-0.00899505615234375,
0.01617431640625,
-0.005527496337890625,
0.00785064697265625,
0.0179290771484375,
0.0088043212890625,
0.01061248779296875,
0.0200958251953125,
-0.0247039794921875,
-0.0247344970703125,
0.01117706298828125,
-0.01367950439453125,
-0.01192474365234375,
-0.0300140380859375,
-0.021575927734375,
-0.0140533447265625,
-0.026824951171875,
-0.0017843246459960938,
-0.007724761962890625,
0.0254058837890625,
0.026153564453125,
-0.00904083251953125,
-0.03216552734375,
0.0088348388671875,
0.02252197265625,
-0.032867431640625,
-0.0008435249328613281,
-0.0215911865234375,
-0.01003265380859375,
0.01415252685546875,
-0.0299072265625,
0.00130462646484375,
0.0295257568359375,
0.0007295608520507812,
-0.003131866455078125,
-0.01287078857421875,
0.0008134841918945312,
-0.03265380859375,
-0.01430511474609375,
0.0059356689453125,
-0.02545166015625,
-0.026824951171875,
-0.034759521484375,
0.0017452239990234375,
-0.025970458984375,
0.002758026123046875,
0.0233917236328125,
-0.0469970703125,
0.02178955078125,
-0.04388427734375,
-0.032745361328125,
0.00901031494140625,
0.029998779296875,
-0.003612518310546875,
-0.0204315185546875,
0.0009293556213378906,
-0.00951385498046875,
-0.0180511474609375,
-0.004520416259765625,
0.00852203369140625,
-0.01255035400390625,
-0.0125885009765625,
0.015838623046875,
-0.022796630859375,
0.0223846435546875,
-0.0270538330078125,
0.0296478271484375,
0.027923583984375,
-0.0127716064453125,
-0.043731689453125,
-0.0174407958984375,
0.01837158203125,
0.0023632049560546875,
0.0369873046875,
0.00833892822265625,
-0.00335693359375,
-0.0108184814453125,
0.01056671142578125,
0.01274871826171875,
-0.040130615234375,
-0.04595947265625,
0.02850341796875,
-0.0200653076171875,
-0.0294342041015625,
-0.0081329345703125,
-0.02490234375,
-0.032562255859375,
-0.0213775634765625,
0.016693115234375,
-0.003597259521484375,
0.0300445556640625,
-0.0017404556274414062,
0.002197265625,
0.0036640167236328125,
0.005096435546875,
0.00044727325439453125,
0.013427734375,
0.0244140625,
-0.03436279296875,
0.0250091552734375,
0.0273590087890625,
0.037139892578125,
0.00879669189453125,
0.006183624267578125,
0.00787353515625,
-0.0012607574462890625,
0.00904083251953125,
-0.006481170654296875,
0.00682830810546875,
0.0272979736328125,
0.0278778076171875,
0.012451171875,
-0.0300140380859375,
-0.0007014274597167969,
0.0155792236328125,
0.00719451904296875,
0.0184326171875,
0.04931640625,
0.021331787109375,
0.005092620849609375,
0.0015687942504882812,
0.0206146240234375,
0.011260986328125,
0.0132293701171875,
0.0164947509765625,
0.01448822021484375,
-0.01220703125,
0.0153656005859375,
0.0160980224609375,
0.00754547119140625,
-0.004604339599609375,
0.006954193115234375,
0.0012216567993164062,
0.01158905029296875,
0.0283660888671875,
0.042205810546875,
0.008544921875,
-0.007354736328125,
-0.01171112060546875,
0.010101318359375,
0.0012226104736328125,
0.0218963623046875,
0.007122039794921875,
0.031646728515625,
0.037872314453125,
-0.01528167724609375,
0.0106048583984375,
-0.006366729736328125,
-0.01305389404296875,
-0.0183563232421875,
0.0157623291015625,
-0.01326751708984375,
-0.0040283203125,
-0.032440185546875,
0.0150146484375,
-0.041473388671875,
0.01253509521484375,
0.0261383056640625,
0.0160980224609375,
-0.01161956787109375,
-0.002880096435546875,
-0.03521728515625,
-0.00511932373046875,
-0.01309967041015625,
0.0252685546875,
-0.0596923828125,
0.00440216064453125,
-0.004451751708984375,
-0.0215911865234375,
0.024688720703125,
0.02093505859375,
0.023193359375,
-0.003833770751953125,
-0.006092071533203125,
0.00833892822265625,
-0.0083160400390625,
-0.0035419464111328125,
-0.043426513671875,
-0.001926422119140625,
0.0019817352294921875,
0.01444244384765625,
-0.023834228515625,
0.0027332305908203125,
-0.02569580078125,
-0.029510498046875,
-0.0186614990234375,
0.0133514404296875,
-0.0282745361328125,
-0.03289794921875,
-0.01087188720703125,
-0.006298065185546875,
-0.0010652542114257812,
-0.01202392578125,
0.0145416259765625,
-0.00817108154296875,
-0.00257110595703125,
-0.0290374755859375,
0.00969696044921875,
0.018035888671875,
-0.005126953125,
-0.0213470458984375,
-0.0025997161865234375,
-0.01064300537109375,
-0.002048492431640625,
0.0221405029296875,
0.019012451171875,
0.022247314453125,
0.01491546630859375,
-0.017059326171875,
0.00910186767578125,
-0.0399169921875,
0.003734588623046875,
0.01265716552734375,
-0.00008082389831542969,
-0.00226593017578125,
0.021820068359375,
-0.01273345947265625,
-0.015899658203125,
0.0241546630859375,
0.006732940673828125,
0.045440673828125,
0.0087432861328125,
-0.0080413818359375,
0.0005283355712890625,
-0.0170135498046875,
-0.021026611328125,
-0.034881591796875,
-0.00295257568359375,
-0.0211944580078125,
0.01383209228515625,
-0.0195770263671875,
-0.01543426513671875,
-0.005863189697265625,
0.012451171875,
-0.0024433135986328125,
-0.045562744140625,
-0.02191162109375,
0.0289459228515625,
-0.016265869140625,
-0.01271820068359375,
-0.01461029052734375,
-0.01113128662109375,
0.022979736328125,
0.03814697265625,
-0.0030345916748046875,
0.006549835205078125,
-0.0094757080078125,
-0.003765106201171875,
0.0083160400390625,
0.037078857421875,
-0.0021419525146484375,
0.007480621337890625,
-0.004131317138671875,
0.00431060791015625,
0.0118255615234375,
0.0019435882568359375,
0.00258636474609375,
-0.0162353515625,
-0.034027099609375,
0.024566650390625,
-0.0237579345703125,
-0.00435638427734375,
0.0036029815673828125,
0.0163116455078125,
-0.00403594970703125,
0.00366973876953125,
0.0252227783203125,
-0.00949859619140625,
0.00045871734619140625,
-0.0023899078369140625,
-0.0162506103515625,
-0.0386962890625,
-0.0011339187622070312,
-0.0031681060791015625,
0.02410888671875,
-0.0194854736328125,
-0.003604888916015625,
0.00151824951171875,
-0.00891876220703125,
0.006763458251953125,
-0.014190673828125,
0.01137542724609375,
0.032257080078125,
0.03948974609375,
-0.00299835205078125,
-0.0021381378173828125,
-0.0041656494140625,
0.055206298828125,
-0.01861572265625,
-0.005680084228515625,
0.0158233642578125,
-0.01824951171875,
-0.006702423095703125,
0.0343017578125,
0.0181121826171875,
-0.00146484375,
-0.006839752197265625,
0.01189422607421875,
0.0160980224609375,
0.020233154296875,
-0.0209197998046875,
0.0084075927734375,
0.0178985595703125,
-0.00025963783264160156,
-0.0150299072265625,
0.002887725830078125,
0.01494598388671875,
-0.004100799560546875,
0.01491546630859375,
-0.0169677734375,
0.00623321533203125,
-0.01094818115234375,
0.024200439453125,
-0.0474853515625,
0.0214385986328125,
-0.05169677734375,
-0.0310211181640625,
-0.00972747802734375,
-0.0153045654296875,
-0.005786895751953125,
0.01250457763671875,
0.03668212890625,
0.008026123046875,
-0.00707244873046875,
0.0217742919921875,
0.01110076904296875,
-0.01024627685546875,
0.0211181640625,
0.00206756591796875,
-0.0003082752227783203,
0.021240234375,
0.00899505615234375,
-0.0172271728515625,
0.0005445480346679688,
-0.0164031982421875,
-0.01629638671875,
0.01556396484375,
-0.0193023681640625,
-0.005207061767578125,
0.006336212158203125,
-0.0279388427734375,
-0.014801025390625,
-0.018585205078125,
0.00383758544921875,
-0.01812744140625,
0.0213775634765625,
-0.01568603515625,
0.0034961700439453125,
0.03594970703125,
0.002506256103515625,
-0.0135040283203125,
-0.0060577392578125,
-0.0059356689453125,
0.004009246826171875,
-0.0172576904296875,
0.01031494140625,
-0.039794921875,
0.0016622543334960938,
-0.0158538818359375,
0.0190582275390625,
-0.027862548828125,
-0.00872039794921875,
-0.0192718505859375,
0.029876708984375,
-0.0289154052734375,
0.009674072265625,
0.00896453857421875,
0.00914764404296875,
0.0106353759765625,
0.007965087890625,
0.01474761962890625,
-0.00878143310546875,
0.0174102783203125,
0.0254974365234375,
0.0252227783203125,
0.0294952392578125,
0.002101898193359375,
-0.004184722900390625,
0.005397796630859375,
0.0149383544921875,
-0.0307769775390625,
0.0037899017333984375,
0.0020236968994140625,
0.054351806640625,
0.0090179443359375,
-0.04083251953125,
-0.02044677734375,
0.02008056640625,
0.031646728515625,
0.001434326171875,
-0.01248931884765625,
0.0012426376342773438,
-0.006107330322265625,
0.01531982421875,
0.01168060302734375,
0.01219940185546875,
-0.019683837890625,
0.029815673828125,
-0.00739288330078125,
-0.01128387451171875,
0.031646728515625,
0.0179901123046875,
-0.022186279296875,
0.01177215576171875,
-0.0333251953125,
0.0007104873657226562,
0.006748199462890625,
0.0123748779296875,
-0.01435089111328125,
-0.01505279541015625,
-0.005023956298828125,
0.01529693603515625,
0.041839599609375,
-0.0094757080078125,
-0.048980712890625,
-0.007678985595703125,
0.024261474609375,
0.0049591064453125,
-0.01025390625,
-0.0115203857421875,
-0.0228118896484375,
-0.01873779296875,
0.01122283935546875,
-0.0084075927734375,
0.043212890625,
-0.017547607421875,
0.00923919677734375,
-0.01129150390625,
0.021514892578125,
-0.03619384765625,
0.01611328125,
-0.0216064453125,
-0.0030517578125,
-0.0048980712890625,
0.00823211669921875,
0.0045318603515625,
0.0004754066467285156,
-0.0031337738037109375,
-0.01392364501953125,
0.01345062255859375,
0.0190277099609375,
-0.022308349609375,
0.01611328125,
0.00014531612396240234,
0.003284454345703125,
-0.018524169921875,
-0.030670166015625,
0.023468017578125,
0.005596160888671875,
-0.0259552001953125,
-0.00878143310546875,
0.0369873046875,
-0.0099945068359375,
0.007480621337890625,
0.0240325927734375,
-0.0014638900756835938,
-0.0081634521484375,
0.0087127685546875,
0.00754547119140625,
-0.036468505859375,
-0.007015228271484375,
-0.027130126953125,
-0.0007333755493164062,
0.0013456344604492188,
-0.0162811279296875,
-0.006481170654296875,
-0.00018846988677978516,
0.010528564453125,
0.003787994384765625,
0.0258636474609375,
0.00873565673828125,
0.00878143310546875,
0.0037250518798828125,
-0.01947021484375,
-0.007648468017578125,
0.0261993408203125,
0.0160064697265625,
-0.0151519775390625,
0.006717681884765625,
0.026031494140625,
0.01560211181640625,
0.01036834716796875,
0.035491943359375,
-0.0357666015625,
-0.01007843017578125,
-0.040985107421875,
-0.0003871917724609375,
-0.0025157928466796875,
0.006107330322265625,
-0.044036865234375,
0.0260162353515625,
0.030364990234375,
-0.0090179443359375,
0.0090789794921875,
0.0020694732666015625,
0.0263671875,
0.029693603515625,
0.0141448974609375,
0.024658203125,
-0.0257415771484375,
0.03326416015625,
0.0108795166015625,
-0.0017080307006835938,
-0.003444671630859375,
0.0243682861328125,
-0.0206298828125,
-0.0079345703125,
-0.0159912109375,
-0.01044464111328125,
0.01220703125,
0.033203125,
-0.0279083251953125,
0.03887939453125,
0.00334930419921875,
-0.016693115234375,
0.006374359130859375,
-0.0037326812744140625,
-0.01397705078125,
-0.0141448974609375,
0.014739990234375,
-0.01274871826171875,
0.0053253173828125,
0.019866943359375,
0.0031070709228515625,
0.0004858970642089844,
-0.00981903076171875,
-0.0215606689453125,
-0.0020599365234375,
-0.0015039443969726562,
-0.02386474609375,
0.00855255126953125,
0.025054931640625,
-0.006740570068359375,
-0.0182952880859375,
0.01168060302734375,
0.01641845703125,
-0.0009412765502929688,
0.001953125,
0.018218994140625,
-0.0033550262451171875,
0.006534576416015625,
-0.0171661376953125,
-0.00786590576171875,
0.0025196075439453125,
0.0030765533447265625,
-0.00894927978515625,
-0.004795074462890625,
0.032135009765625,
0.00093841552734375,
-0.0016622543334960938,
0.01438140869140625,
-0.0006775856018066406,
-0.0269012451171875,
0.0146942138671875,
-0.0274200439453125,
-0.0057525634765625,
0.016693115234375,
-0.00861358642578125,
-0.015838623046875,
0.00015366077423095703,
-0.004974365234375,
-0.01506805419921875,
0.00447845458984375,
-0.03167724609375,
0.0087890625,
0.00033020973205566406,
-0.00449371337890625,
0.0005660057067871094,
0.0245819091796875,
0.002696990966796875,
0.034759521484375,
0.0107574462890625,
-0.0299224853515625,
0.0259857177734375,
0.01444244384765625,
0.0222625732421875,
-0.0196533203125,
0.005859375,
-0.0306243896484375,
0.009124755859375,
0.0095062255859375,
0.01276397705078125,
-0.032440185546875,
-0.0198516845703125,
-0.03228759765625,
0.01251220703125,
0.0028324127197265625,
-0.0115203857421875,
-0.010711669921875,
0.00409698486328125,
0.0021762847900390625,
0.0034027099609375,
-0.0128631591796875,
0.004947662353515625,
0.0081024169921875,
-0.0242462158203125,
0.0111083984375,
-0.02215576171875,
-0.00594329833984375,
-0.0023250579833984375,
0.0236358642578125,
-0.01363372802734375,
0.0159454345703125,
-0.049530029296875,
-0.0179290771484375,
-0.022552490234375,
0.020263671875,
-0.00417327880859375,
0.0237884521484375,
-0.01427459716796875,
0.006931304931640625,
-0.0174407958984375,
-0.01045989990234375,
0.026702880859375,
0.006183624267578125,
0.035369873046875,
0.0127410888671875,
0.043182373046875,
-0.01413726806640625,
-0.02130126953125,
0.0006566047668457031,
-0.0072174072265625,
0.0028057098388671875,
0.047515869140625,
-0.0137481689453125,
-0.006351470947265625,
-0.00811767578125,
0.04412841796875,
-0.005275726318359375,
-0.0355224609375,
0.0226287841796875,
-0.00380706787109375,
0.01134490966796875,
-0.01678466796875,
-0.032806396484375,
0.036529541015625,
0.0248260498046875,
-0.020355224609375,
-0.00112152099609375,
0.0207061767578125,
-0.0308990478515625,
0.003948211669921875,
-0.0007381439208984375,
-0.01386260986328125,
-0.004573822021484375,
0.007381439208984375,
0.001186370849609375,
0.01287841796875,
-0.00658416748046875,
0.01007080078125,
-0.0088348388671875,
-0.024169921875,
0.0161895751953125,
0.0098724365234375,
0.035888671875,
0.016815185546875,
-0.0099945068359375,
0.004932403564453125,
0.007232666015625,
-0.018402099609375,
-0.007137298583984375,
-0.0198822021484375,
-0.0033397674560546875,
-0.02685546875,
0.03009033203125,
-0.0273895263671875,
-0.01445770263671875,
0.0360107421875,
-0.05523681640625,
0.01776123046875,
0.0167999267578125,
0.00858306884765625,
-0.034271240234375,
-0.01343536376953125,
0.0062408447265625,
-0.02679443359375,
0.000408172607421875,
0.0179901123046875,
-0.006084442138671875,
0.04412841796875,
-0.01099395751953125,
-0.0240325927734375,
-0.01233673095703125,
0.0303497314453125,
-0.0312347412109375,
-0.01995849609375,
-0.01300811767578125,
-0.00482177734375,
0.016357421875,
0.033538818359375,
0.00431060791015625,
0.03955078125,
0.0099945068359375,
-0.016143798828125,
0.0168304443359375,
0.006549835205078125,
0.0121002197265625,
-0.0152740478515625,
0.0158843994140625,
0.004093170166015625,
0.00968170166015625,
0.0077667236328125,
0.011077880859375,
0.01444244384765625,
-0.003780364990234375,
0.02227783203125,
-0.025177001953125,
0.033203125,
0.0030689239501953125,
0.02154541015625,
-0.00919342041015625,
-0.021942138671875,
-0.047760009765625,
-0.06512451171875,
0.03759765625,
-0.019683837890625,
-0.044036865234375,
0.01285552978515625,
0.0168609619140625,
0.004634857177734375,
0.017547607421875,
-0.035980224609375,
-0.02850341796875,
0.02667236328125,
-0.003154754638671875,
0.007099151611328125,
0.0292510986328125,
0.020355224609375,
0.0286712646484375,
-0.002735137939453125,
0.026641845703125,
-0.00812530517578125,
0.00495147705078125,
-0.03155517578125,
0.005218505859375,
0.0168304443359375,
-0.0203094482421875,
-0.053436279296875,
-0.0006318092346191406,
-0.01465606689453125,
-0.0016679763793945312,
0.0158538818359375,
-0.0087432861328125,
-0.041961669921875,
0.0220184326171875,
0.004810333251953125,
0.01319122314453125,
0.006824493408203125,
0.0210418701171875,
0.00400543212890625,
-0.006954193115234375,
0.01983642578125,
-0.0362548828125,
-0.01763916015625,
-0.00502777099609375,
-0.023101806640625,
-0.02154541015625,
0.018890380859375,
0.04669189453125,
-0.0201568603515625,
-0.005802154541015625,
-0.037322998046875,
0.01152801513671875,
-0.01088714599609375,
0.00411224365234375,
0.0259246826171875,
0.00002187490463256836,
-0.02398681640625,
-0.00963592529296875,
0.021331787109375,
-0.0176849365234375,
-0.01532745361328125,
-0.01033782958984375,
-0.0034160614013671875,
-0.00394439697265625,
0.00441741943359375,
-0.0252685546875,
0.0014104843139648438,
0.0219268798828125,
-0.036285400390625,
0.037506103515625,
0.042205810546875,
0.034942626953125,
0.0099639892578125,
-0.020233154296875,
-0.0068359375,
0.002140045166015625,
-0.004917144775390625,
0.0306396484375,
0.0195159912109375,
0.0009479522705078125,
0.05450439453125,
-0.0233001708984375,
-0.028045654296875,
-0.0037326812744140625,
0.0174713134765625,
-0.046844482421875,
-0.0230712890625,
0.01041412353515625,
-0.007579803466796875,
0.02044677734375,
-0.0006704330444335938,
-0.04425048828125,
-0.01548004150390625,
0.0179290771484375,
-0.0096588134765625,
0.0265655517578125
] |
ours_503
|
Let \(g = \operatorname{gcd}(m, n)\), \(a = \frac{m}{g}\), and \(b = \frac{n}{g}\). By definition, \(\operatorname{gcd}(a, b) = 1\). The equation becomes:
\[
g a b + g = g a + g b + 30
\]
Simplifying, we have:
\[
g(a-1)(b-1) = 30
\]
Since \(g\) must be odd (otherwise \(a\) and \(b\) would both be even, contradicting \(\operatorname{gcd}(a, b) = 1\)), we consider the following cases:
**Case 1: \(g = 1\)**
\((a-1)(b-1) = 30\), giving solutions:
\[
(a, b) = (2, 31), (3, 16), (4, 11), (6, 7), (7, 6), (11, 4), (16, 3), (31, 2)
\]
Thus, \((m, n) = (2, 31), (3, 16), (4, 11), (6, 7), (7, 6), (11, 4), (16, 3), (31, 2)\).
**Case 2: \(g = 3\)**
\((a-1)(b-1) = 10\), giving solutions:
\[
(a, b) = (2, 11), (3, 6), (6, 3), (11, 2)
\]
Only \((a, b) = (2, 11), (11, 2)\) satisfy \(\operatorname{gcd}(a, b) = 1\), so:
\((m, n) = (6, 33), (33, 6)\).
**Case 3: \(g = 5\)**
\((a-1)(b-1) = 6\), giving solutions:
\[
(a, b) = (2, 7), (3, 4), (4, 3), (7, 2)
\]
Thus, \((m, n) = (10, 35), (15, 20), (20, 15), (35, 10)\).
**Case 4: \(g = 15\)**
\((a-1)(b-1) = 2\), giving solutions:
\[
(a, b) = (2, 3), (3, 2)
\]
Thus, \((m, n) = (30, 45), (45, 30)\).
In total, there are 16 solutions. Therefore, the number of ordered pairs \((m, n)\) is \(\boxed{16}\).
|
16
|
{
"competition": "us_comps",
"dataset": "Ours",
"posts": null,
"source": "OMOFall19Solns.md"
}
|
Compute the number of ordered pairs \((m, n)\) of positive integers that satisfy the equation \(\operatorname{lcm}(m, n) + \operatorname{gcd}(m, n) = m + n + 30\).
|
[
"/Mathematics/Algebra/NumberTheory/Arithmetic/GeneralArithmetic",
"/Mathematics/Algebra/NumberTheory/DiophantineEquations/Diophantine",
"/Mathematics/Algebra/NumberTheory/DiophantineEquations/DiophantineEquation",
"/Mathematics/Algebra/NumberTheory/GeneralNumberTheory/ElementaryMethods",
"/Mathematics/Algebra/NumberTheory/GeneralNumberTheory/ElementaryNumberTheory",
"/Mathematics/Algebra/NumberTheory/GeneralNumberTheory/NumberTheory",
"/Mathematics/Algebra/NumberTheory/Integers/Integer",
"/Mathematics/Algebra/NumberTheory/Integers/N",
"/Mathematics/Algebra/NumberTheory/Integers/NonnegativeInteger",
"/Mathematics/Algebra/NumberTheory/Integers/PositiveInteger",
"/Mathematics/Algebra/NumberTheory/Integers/WholeNumber",
"/Mathematics/Algebra/NumberTheory/Integers/Z",
"/Mathematics/Algebra/NumberTheory/Integers/Z-Plus",
"/Mathematics/DiscreteMathematics/Combinatorics/Enumeration",
"/Mathematics/DiscreteMathematics/DivisionProblems/SubsetSumProblem",
"/Mathematics/NumberTheory/Arithmetic/GeneralArithmetic",
"/Mathematics/NumberTheory/Arithmetic/MultiplicationandDivision",
"/Mathematics/NumberTheory/DiophantineEquations/Diophantine",
"/Mathematics/NumberTheory/DiophantineEquations/DiophantineEquation",
"/Mathematics/NumberTheory/GeneralNumberTheory/ElementaryMethods",
"/Mathematics/NumberTheory/GeneralNumberTheory/ElementaryNumberTheory",
"/Mathematics/NumberTheory/GeneralNumberTheory/HigherArithmetic",
"/Mathematics/NumberTheory/GeneralNumberTheory/NumberTheory"
] |
Express m and n as g·a and g·b with gcd(a,b)=1, then rewrite the equation to obtain the factorisation g·(a−1)·(b−1)=30.
|
[
0.0000794529914855957,
-0.0304718017578125,
0.0204925537109375,
-0.005035400390625,
0.0003726482391357422,
0.028076171875,
-0.007598876953125,
0.0035953521728515625,
0.015777587890625,
0.00223541259765625,
0.0289459228515625,
-0.006366729736328125,
0.00102996826171875,
-0.00827789306640625,
-0.019317626953125,
0.01519012451171875,
0.0050506591796875,
0.01702880859375,
-0.017181396484375,
-0.00496673583984375,
-0.01155853271484375,
0.0058135986328125,
-0.0212860107421875,
0.005584716796875,
0.00612640380859375,
-0.004566192626953125,
-0.0191802978515625,
0.0264434814453125,
-0.01233673095703125,
0.032684326171875,
0.0093841552734375,
-0.020904541015625,
-0.0352783203125,
-0.0309906005859375,
-0.0024890899658203125,
0.01248931884765625,
0.00921630859375,
0.002864837646484375,
-0.004169464111328125,
-0.02435302734375,
-0.007274627685546875,
0.010711669921875,
0.004169464111328125,
0.0142822265625,
-0.0120391845703125,
-0.006565093994140625,
-0.0032978057861328125,
-0.01474761962890625,
-0.0229949951171875,
-0.005870819091796875,
-0.00411224365234375,
0.00812530517578125,
-0.054351806640625,
0.0016508102416992188,
0.0079803466796875,
-0.065673828125,
0.059051513671875,
0.00839996337890625,
-0.0269012451171875,
0.0193634033203125,
-0.006229400634765625,
0.015899658203125,
-0.029541015625,
-0.007793426513671875,
-0.007354736328125,
-0.01087188720703125,
-0.0210113525390625,
-0.0303192138671875,
0.0084075927734375,
0.0033550262451171875,
0.0374755859375,
-0.048675537109375,
-0.006046295166015625,
0.0214385986328125,
0.0097503662109375,
0.003139495849609375,
-0.006732940673828125,
0.01477813720703125,
-0.009124755859375,
0.020172119140625,
0.0110321044921875,
0.0267791748046875,
0.00730133056640625,
-0.0124664306640625,
0.0009417533874511719,
-0.0005745887756347656,
0.0128173828125,
-0.0016260147094726562,
0.031219482421875,
0.0017490386962890625,
-0.00151824951171875,
0.0240478515625,
-0.01194000244140625,
-0.002300262451171875,
-0.0005474090576171875,
-0.0027332305908203125,
0.0167694091796875,
-0.0067901611328125,
0.005084991455078125,
-0.0022449493408203125,
0.004573822021484375,
-0.0032558441162109375,
0.040069580078125,
-0.005733489990234375,
-0.01268768310546875,
-0.012542724609375,
-0.00807952880859375,
0.003223419189453125,
-0.0196685791015625,
0.00881195068359375,
-0.007350921630859375,
0.0028247833251953125,
0.04681396484375,
0.0257720947265625,
0.0095062255859375,
0.004756927490234375,
0.036468505859375,
0.004795074462890625,
-0.007030487060546875,
0.0296630859375,
-0.0007238388061523438,
-0.0015916824340820312,
-0.0206451416015625,
0.0258941650390625,
0.01074981689453125,
-0.015167236328125,
-0.0219268798828125,
-0.036712646484375,
-0.004863739013671875,
-0.0027256011962890625,
0.00595855712890625,
-0.01708984375,
-0.017425537109375,
-0.01222991943359375,
-0.04638671875,
0.0308990478515625,
0.004253387451171875,
0.01399993896484375,
-0.019744873046875,
-0.0106353759765625,
0.003009796142578125,
-0.0165557861328125,
-0.00788116455078125,
-0.01317596435546875,
-0.0024871826171875,
-0.0246124267578125,
-0.003986358642578125,
-0.01087188720703125,
0.0018529891967773438,
-0.02056884765625,
-0.01192474365234375,
-0.0088958740234375,
0.01097869873046875,
-0.018524169921875,
-0.018768310546875,
0.0056610107421875,
0.004032135009765625,
0.01983642578125,
-0.01320648193359375,
0.01593017578125,
-0.0003247261047363281,
-0.00009500980377197266,
0.00200653076171875,
0.0022029876708984375,
0.009063720703125,
-0.0033245086669921875,
0.004047393798828125,
0.02398681640625,
0.0010747909545898438,
-0.01149749755859375,
-0.0004112720489501953,
0.00872039794921875,
0.013824462890625,
-0.0175323486328125,
0.03070068359375,
-0.014068603515625,
0.016143798828125,
0.029998779296875,
-0.005817413330078125,
0.0164642333984375,
0.021881103515625,
-0.041412353515625,
0.0242156982421875,
0.0032520294189453125,
-0.004932403564453125,
-0.0208587646484375,
-0.011383056640625,
0.0069732666015625,
0.01212310791015625,
0.0158233642578125,
0.0010213851928710938,
-0.0182037353515625,
-0.013580322265625,
-0.0036373138427734375,
0.01067352294921875,
0.016357421875,
-0.0107574462890625,
-0.0226593017578125,
0.0360107421875,
0.0097808837890625,
-0.0045623779296875,
-0.00893402099609375,
0.0024261474609375,
-0.0177001953125,
0.01125335693359375,
-0.0235443115234375,
-0.0148162841796875,
-0.01067352294921875,
0.0062255859375,
-0.007686614990234375,
0.0036106109619140625,
0.009796142578125,
-0.005096435546875,
-0.00650787353515625,
-0.019378662109375,
0.0126953125,
-0.0184478759765625,
-0.00882720947265625,
0.0037975311279296875,
-0.02703857421875,
-0.006130218505859375,
-0.0106964111328125,
-0.002666473388671875,
-0.01155853271484375,
-0.0153656005859375,
-0.004703521728515625,
-0.0117034912109375,
0.0133514404296875,
-0.005767822265625,
-0.00690460205078125,
0.01265716552734375,
0.0213623046875,
0.0007777214050292969,
-0.01052093505859375,
0.0080108642578125,
-0.0212554931640625,
-0.03228759765625,
0.002353668212890625,
0.0200042724609375,
-0.0260162353515625,
0.021575927734375,
-0.0131683349609375,
-0.01404571533203125,
-0.0215911865234375,
-0.0213623046875,
0.00618743896484375,
0.0021839141845703125,
-0.007801055908203125,
0.0081634521484375,
-0.025177001953125,
-0.01239013671875,
0.0181427001953125,
-0.014495849609375,
-0.0188751220703125,
0.006092071533203125,
0.007671356201171875,
0.0020904541015625,
0.012725830078125,
-0.037322998046875,
-0.0071563720703125,
0.0013628005981445312,
-0.05865478515625,
-0.0071563720703125,
0.0021038055419921875,
-0.022216796875,
0.0213775634765625,
-0.0087890625,
0.0005755424499511719,
0.0010013580322265625,
0.012908935546875,
0.012451171875,
-0.0035610198974609375,
-0.0229339599609375,
-0.0015249252319335938,
0.007511138916015625,
0.011444091796875,
-0.01526641845703125,
0.001190185546875,
0.0140838623046875,
-0.00553131103515625,
0.0300750732421875,
-0.01251983642578125,
-0.0270233154296875,
0.0167236328125,
-0.017364501953125,
-0.026702880859375,
0.03277587890625,
-0.0233001708984375,
-0.006877899169921875,
-0.0034275054931640625,
-0.00272369384765625,
-0.01885986328125,
-0.00457763671875,
-0.0058441162109375,
0.046478271484375,
-0.0212554931640625,
-0.016693115234375,
-0.00942230224609375,
0.0212554931640625,
0.0091705322265625,
0.0206756591796875,
-0.01126861572265625,
-0.006107330322265625,
-0.00347137451171875,
-0.006061553955078125,
0.01372528076171875,
-0.006343841552734375,
0.002506256103515625,
-0.004726409912109375,
-0.023406982421875,
-0.0132293701171875,
-0.0035457611083984375,
-0.00023758411407470703,
0.01113128662109375,
-0.01038360595703125,
-0.0227508544921875,
-0.022674560546875,
-0.00004953145980834961,
-0.0088653564453125,
0.0155029296875,
0.0238800048828125,
-0.01593017578125,
-0.0016422271728515625,
0.0119476318359375,
0.015960693359375,
0.0144195556640625,
-0.0005497932434082031,
0.017578125,
-0.04541015625,
0.0270843505859375,
-0.00203704833984375,
0.0028533935546875,
-0.01202392578125,
-0.04937744140625,
-0.021575927734375,
0.02947998046875,
-0.0196533203125,
0.0179595947265625,
0.00823974609375,
-0.004878997802734375,
0.0105133056640625,
-0.031585693359375,
0.022186279296875,
-0.00862884521484375,
-0.01910400390625,
0.00959014892578125,
0.00457000732421875,
0.01232147216796875,
0.02557373046875,
-0.0298614501953125,
0.02264404296875,
0.022064208984375,
0.0206756591796875,
-0.012664794921875,
-0.00152587890625,
-0.00846099853515625,
0.000766754150390625,
-0.00846099853515625,
-0.0018987655639648438,
0.045135498046875,
0.0042724609375,
-0.0184783935546875,
-0.004791259765625,
0.0037593841552734375,
0.06060791015625,
-0.03424072265625,
0.0006356239318847656,
0.00955963134765625,
-0.00803375244140625,
0.00492095947265625,
-0.0240020751953125,
-0.018035888671875,
0.0286407470703125,
-0.01364898681640625,
0.00008493661880493164,
0.0171356201171875,
0.033905029296875,
-0.005413055419921875,
0.0285186767578125,
-0.0013303756713867188,
-0.002620697021484375,
0.0160064697265625,
0.01544189453125,
0.0295257568359375,
-0.0257720947265625,
-0.013824462890625,
0.0124969482421875,
-0.024078369140625,
-0.0107421875,
0.0206298828125,
-0.0045928955078125,
0.033447265625,
-0.012451171875,
-0.01229095458984375,
-0.007152557373046875,
-0.0248870849609375,
0.00214385986328125,
0.03277587890625,
0.027862548828125,
-0.008026123046875,
-0.0177764892578125,
0.0230560302734375,
-0.00946807861328125,
0.00746917724609375,
0.0221099853515625,
-0.003936767578125,
-0.0069732666015625,
-0.0146484375,
0.01885986328125,
0.002979278564453125,
-0.006496429443359375,
0.0097198486328125,
-0.006496429443359375,
-0.024658203125,
-0.016448974609375,
-0.02508544921875,
0.002574920654296875,
-0.0237884521484375,
-0.034423828125,
-0.0207672119140625,
-0.024871826171875,
-0.05450439453125,
0.0020961761474609375,
-0.037384033203125,
0.0233612060546875,
0.028656005859375,
-0.0219268798828125,
0.024627685546875,
-0.00896453857421875,
0.005950927734375,
0.00643157958984375,
-0.0391845703125,
0.01284027099609375,
0.02911376953125,
0.01204681396484375,
0.0272979736328125,
-0.0027313232421875,
-0.00012433528900146484,
-0.00730133056640625,
-0.006870269775390625,
-0.0271453857421875,
-0.018341064453125,
-0.002960205078125,
-0.0031585693359375,
0.01861572265625,
0.01641845703125,
-0.0015621185302734375,
0.036041259765625,
-0.024566650390625,
0.0357666015625,
-0.003948211669921875,
-0.00658416748046875,
-0.04534912109375,
0.0089111328125,
-0.0078277587890625,
0.004764556884765625,
-0.01053619384765625,
0.0104827880859375,
0.0018701553344726562,
0.00182342529296875,
-0.0136871337890625,
0.01238250732421875,
-0.0278472900390625,
0.0110626220703125,
-0.0382080078125,
0.00928497314453125,
-0.0268096923828125,
-0.0145111083984375,
-0.0168304443359375,
0.0106353759765625,
0.0003857612609863281,
-0.0026721954345703125,
-0.01024627685546875,
0.007537841796875,
-0.060760498046875,
0.0145111083984375,
-0.0214385986328125,
-0.0107879638671875,
-0.00797271728515625,
-0.01284027099609375,
0.00988006591796875,
-0.0102386474609375,
-0.004520416259765625,
-0.00830078125,
0.025665283203125,
0.01305389404296875,
0.0156402587890625,
-0.007061004638671875,
0.002208709716796875,
-0.02532958984375,
0.019073486328125,
0.0121307373046875,
-0.052734375,
-0.0338134765625,
0.0094451904296875,
-0.0206298828125,
0.00443267822265625,
0.00301361083984375,
-0.0211029052734375,
-0.004573822021484375,
0.035430908203125,
-0.0310211181640625,
-0.00818634033203125,
0.01107025146484375,
-0.00415802001953125,
-0.0090484619140625,
0.0265350341796875,
-0.0161590576171875,
-0.04156494140625,
0.006500244140625,
0.01300048828125,
0.01508331298828125,
-0.00634765625,
-0.006191253662109375,
0.01300811767578125,
-0.007640838623046875,
0.01506805419921875,
-0.0232086181640625,
0.03778076171875,
-0.0016736984252929688,
-0.032867431640625,
-0.0445556640625,
0.021942138671875,
0.00974273681640625,
0.0291748046875,
0.01500701904296875,
-0.009368896484375,
-0.0546875,
0.036041259765625,
-0.0169677734375,
-0.0208587646484375,
-0.017059326171875,
-0.0047149658203125,
-0.0045013427734375,
-0.03485107421875,
0.02105712890625,
-0.0032138824462890625,
0.001850128173828125,
0.036865234375,
0.0400390625,
0.0316162109375,
-0.0244293212890625,
-0.025421142578125,
-0.017059326171875,
-0.006160736083984375,
-0.002147674560546875,
-0.00896453857421875,
0.0217742919921875,
0.0069427490234375,
0.01552581787109375,
0.0002951622009277344,
0.01186370849609375,
-0.00927734375,
0.0321044921875,
-0.00982666015625,
0.0014562606811523438,
-0.006282806396484375,
0.034088134765625,
-0.005016326904296875,
0.006439208984375,
0.0192413330078125,
-0.0007519721984863281,
0.03607177734375,
-0.0009918212890625,
0.0341796875,
-0.01218414306640625,
-0.00830078125,
-0.00994110107421875,
0.0024566650390625,
-0.0277099609375,
-0.00020325183868408203,
-0.0054779052734375,
0.00937652587890625,
0.0103759765625,
0.01160430908203125,
0.020965576171875,
0.00799560546875,
0.02301025390625,
0.0068817138671875,
0.0070343017578125,
0.0345458984375,
0.01416778564453125,
-0.0170135498046875,
0.01389312744140625,
0.009002685546875,
0.03594970703125,
0.005023956298828125,
0.036224365234375,
0.0232391357421875,
-0.009521484375,
-0.0038299560546875,
-0.003887176513671875,
-0.003292083740234375,
-0.01480865478515625,
-0.00952911376953125,
-0.013702392578125,
0.039703369140625,
0.0096282958984375,
0.0026645660400390625,
0.0067291259765625,
0.0141448974609375,
0.006366729736328125,
-0.03289794921875,
0.019805908203125,
-0.0330810546875,
0.02020263671875,
0.0270843505859375,
0.0226898193359375,
-0.01377105712890625,
0.01059722900390625,
-0.004955291748046875,
-0.01490020751953125,
0.01003265380859375,
0.003986358642578125,
0.009429931640625,
0.032470703125,
-0.0008625984191894531,
-0.0092620849609375,
0.00350189208984375,
-0.011444091796875,
-0.00836944580078125,
0.01349639892578125,
0.0031719207763671875,
0.004180908203125,
0.0026397705078125,
0.00186920166015625,
0.01055908203125,
-0.041259765625,
0.0245819091796875,
0.0146331787109375,
-0.024169921875,
0.005954742431640625,
0.0224761962890625,
-0.0015773773193359375,
0.00992584228515625,
-0.01763916015625,
-0.017242431640625,
0.0092620849609375,
-0.018280029296875,
-0.01163482666015625,
0.0294952392578125,
0.01505279541015625,
0.0205078125,
-0.0419921875,
0.004119873046875,
0.0113677978515625,
-0.006237030029296875,
-0.0207061767578125,
-0.03167724609375,
-0.004390716552734375,
-0.0352783203125,
-0.00698089599609375,
0.005344390869140625,
0.0279083251953125,
0.0137481689453125,
0.0338134765625,
0.00072479248046875,
-0.0225372314453125,
0.00988006591796875,
-0.0244598388671875,
0.00867462158203125,
-0.01206207275390625,
-0.006183624267578125,
0.0031871795654296875,
-0.0288238525390625,
-0.0034999847412109375,
0.058624267578125,
0.005035400390625,
-0.00865936279296875,
-0.024200439453125,
0.025604248046875,
-0.041351318359375,
0.00981903076171875,
-0.01251983642578125,
-0.0240325927734375,
-0.010986328125,
-0.0006051063537597656,
-0.0019445419311523438,
0.033905029296875,
0.0396728515625,
-0.020416259765625,
0.0219573974609375,
0.01861572265625,
-0.01284027099609375,
-0.01049041748046875,
0.01137542724609375,
0.01389312744140625,
-0.01531219482421875,
-0.0234832763671875,
-0.0002180337905883789,
-0.0188446044921875,
-0.0157012939453125,
-0.03692626953125,
0.010528564453125,
0.0206451416015625,
-0.0171051025390625,
0.02740478515625,
-0.0283660888671875,
0.014434814453125,
-0.0259552001953125,
0.02020263671875,
-0.00250244140625,
0.006500244140625,
-0.0085906982421875,
0.00905609130859375,
-0.01177978515625,
-0.0322265625,
0.007598876953125,
-0.01300048828125,
0.0179595947265625,
-0.02056884765625,
0.00986480712890625,
-0.0122528076171875,
0.014739990234375,
-0.0249481201171875,
0.002971649169921875,
0.01434326171875,
0.019378662109375,
0.0159912109375,
-0.035430908203125,
-0.01540374755859375,
0.01123809814453125,
-0.0236358642578125,
-0.0171966552734375,
0.01873779296875,
0.0206146240234375,
0.0277557373046875,
-0.0305328369140625,
-0.01445770263671875,
0.001369476318359375,
-0.01551055908203125,
0.007305145263671875,
0.00482177734375,
-0.041839599609375,
-0.0307769775390625,
-0.04266357421875,
-0.0042266845703125,
-0.0186767578125,
-0.02349853515625,
0.00078582763671875,
0.0308837890625,
-0.00213623046875,
0.004436492919921875,
-0.0198516845703125,
0.016448974609375,
-0.01270294189453125,
0.021942138671875,
0.007343292236328125,
0.022735595703125,
-0.00009083747863769531,
0.01030731201171875,
-0.04083251953125,
-0.0140228271484375,
-0.039642333984375,
-0.0207977294921875,
-0.042327880859375,
-0.0036487579345703125,
-0.020050048828125,
-0.00019931793212890625,
-0.0025787353515625,
-0.0041961669921875,
0.0272979736328125,
-0.0186614990234375,
-0.0038280487060546875,
0.0036258697509765625,
-0.026275634765625,
-0.01508331298828125,
-0.021026611328125,
-0.0557861328125,
0.0026092529296875,
-0.041259765625,
0.0217742919921875,
-0.0010814666748046875,
-0.006641387939453125,
-0.013671875,
0.0223541259765625,
-0.0438232421875,
0.00249481201171875,
0.04766845703125,
-0.01200103759765625,
0.029815673828125,
0.021331787109375,
0.032196044921875,
0.006744384765625,
-0.030517578125,
-0.00615692138671875,
-0.00890350341796875,
-0.00492095947265625,
0.0144805908203125,
0.007091522216796875,
0.004100799560546875,
-0.0302886962890625,
-0.0236358642578125,
0.00445556640625,
-0.006946563720703125,
0.0036067962646484375,
-0.0159759521484375,
-0.0007658004760742188,
-0.052520751953125,
-0.017822265625,
-0.028167724609375,
-0.027801513671875,
0.0008134841918945312,
0.006999969482421875,
0.004299163818359375,
-0.02001953125,
0.0257720947265625,
-0.0060577392578125,
-0.008148193359375,
0.0179443359375,
0.0252685546875,
0.0008096694946289062,
-0.0098419189453125,
-0.0122222900390625,
0.031585693359375,
0.006374359130859375,
0.0061187744140625,
-0.0028324127197265625,
-0.004199981689453125,
0.00550079345703125,
0.013153076171875,
0.039306640625,
0.0191650390625,
-0.021820068359375,
-0.027496337890625,
-0.01219940185546875,
-0.0017309188842773438,
0.00955963134765625,
0.0235748291015625,
-0.0146484375,
0.0235137939453125,
0.0011606216430664062,
-0.034454345703125,
0.0286712646484375,
0.00034356117248535156,
0.00807952880859375,
0.022308349609375,
0.028167724609375,
0.0083770751953125,
-0.005641937255859375,
0.0027866363525390625,
0.0016546249389648438,
-0.006488800048828125,
0.00112152099609375,
0.0132598876953125,
0.01227569580078125,
-0.01169586181640625,
0.01296234130859375,
0.03253173828125,
-0.002288818359375,
0.0234832763671875,
0.00634002685546875,
-0.01113128662109375,
-0.00849151611328125,
0.0195770263671875,
0.0175628662109375,
-0.0014257431030273438,
0.01409912109375,
0.004852294921875,
-0.00022077560424804688,
-0.0190277099609375,
-0.006927490234375,
-0.0008864402770996094,
0.00421905517578125,
-0.0212554931640625,
-0.004047393798828125,
0.0036163330078125,
-0.018524169921875,
0.0304107666015625,
0.0025997161865234375,
0.010955810546875,
-0.0036373138427734375,
0.019073486328125,
-0.005435943603515625,
0.028656005859375,
0.018890380859375,
-0.00681304931640625,
0.01800537109375,
0.038909912109375,
0.0081939697265625,
0.04034423828125,
-0.0194854736328125,
-0.04705810546875,
0.0163116455078125,
-0.018218994140625,
-0.029876708984375,
-0.01021575927734375,
0.0260772705078125,
-0.0136871337890625,
-0.034759521484375,
-0.01418304443359375,
0.00405120849609375,
0.007488250732421875,
-0.01114654541015625,
0.004299163818359375,
0.0021495819091796875,
-0.004520416259765625,
-0.018280029296875,
0.022796630859375,
-0.0223541259765625,
0.0014123916625976562,
-0.01120758056640625,
0.014068603515625,
0.03839111328125,
-0.0015478134155273438,
-0.0071563720703125,
-0.006439208984375,
-0.0015163421630859375,
0.004741668701171875,
0.00002276897430419922,
-0.038818359375,
-0.022125244140625,
0.01016998291015625,
0.019744873046875,
-0.024261474609375,
-0.050018310546875,
-0.0142364501953125,
-0.017242431640625,
0.00783538818359375,
-0.0192108154296875,
0.0322265625,
-0.0166015625,
0.0193634033203125,
-0.0084991455078125,
-0.047607421875,
0.0068817138671875,
-0.004825592041015625,
0.0131683349609375,
-0.06329345703125,
-0.01506805419921875,
0.00409698486328125,
0.0145416259765625,
0.00959014892578125,
0.022186279296875,
0.021636962890625,
0.02679443359375,
-0.022308349609375,
-0.0193939208984375,
-0.005908966064453125,
0.00804901123046875,
-0.0291748046875,
0.019561767578125,
0.0277099609375,
0.022857666015625,
0.0185546875,
0.0244140625,
-0.01184844970703125,
-0.00186920166015625,
0.00479888916015625,
-0.0205535888671875,
-0.009765625,
-0.009490966796875,
-0.00980377197265625,
0.027099609375,
-0.0076904296875,
-0.006893157958984375,
0.01338958740234375,
-0.01071929931640625,
-0.0049896240234375,
-0.0036907196044921875,
-0.0006985664367675781,
0.007259368896484375,
-0.03448486328125,
0.010040283203125,
0.020294189453125,
0.0076141357421875,
-0.0192108154296875,
0.0027103424072265625,
0.01053619384765625,
-0.005283355712890625,
-0.004116058349609375,
-0.036773681640625,
-0.0036563873291015625,
-0.0285491943359375,
-0.019744873046875,
0.00885009765625,
-0.045623779296875,
0.0256500244140625,
0.0096893310546875,
-0.01091766357421875,
-0.03521728515625,
0.0261993408203125,
-0.0187835693359375,
-0.0175933837890625,
0.0006165504455566406,
0.01727294921875,
0.0015850067138671875,
-0.0001302957534790039,
0.01409149169921875,
-0.0269317626953125,
-0.0309906005859375,
0.0230712890625,
-0.001010894775390625,
0.0160369873046875,
-0.00007355213165283203,
-0.0033893585205078125,
0.00742340087890625,
0.0076446533203125,
0.000629425048828125,
0.02581787109375,
-0.042236328125,
0.0016031265258789062,
0.00125885009765625,
0.0097808837890625,
0.00644683837890625,
-0.03704833984375,
0.0203094482421875,
0.0134124755859375,
-0.04302978515625,
0.0196990966796875,
0.0098724365234375,
-0.019012451171875,
-0.01204681396484375,
0.0081939697265625,
-0.0008492469787597656,
0.040802001953125,
0.01018524169921875,
0.033233642578125,
-0.042236328125,
0.0193023681640625,
-0.00859832763671875,
-0.0020389556884765625,
-0.023193359375,
-0.00815582275390625,
-0.019317626953125,
-0.0020694732666015625,
-0.01399993896484375,
-0.0167236328125,
0.02667236328125,
0.0163116455078125,
-0.0035228729248046875,
0.0039215087890625,
-0.00551605224609375,
-0.004913330078125,
-0.038726806640625,
-0.012176513671875,
-0.00748443603515625,
-0.03631591796875,
0.0161590576171875,
-0.00217437744140625,
-0.015106201171875,
0.00032210350036621094,
0.045166015625,
0.0014324188232421875,
0.017913818359375,
0.00209808349609375,
0.01302337646484375,
0.029541015625,
0.00960540771484375,
0.0214996337890625,
-0.01285552978515625,
-0.007320404052734375,
-0.036376953125,
0.006488800048828125,
-0.01311492919921875,
0.0133514404296875,
-0.0018634796142578125,
-0.0172271728515625,
0.0303497314453125,
0.0202484130859375,
-0.0124969482421875,
0.0047760009765625,
0.0053253173828125,
-0.008209228515625,
0.004894256591796875,
-0.03173828125,
-0.027984619140625,
-0.0099945068359375,
-0.02490234375,
0.01169586181640625,
-0.044891357421875,
0.008148193359375,
0.0233612060546875,
0.01300811767578125,
-0.006862640380859375,
0.0001575946807861328,
0.0265045166015625,
-0.01348114013671875,
-0.00965118408203125,
-0.024322509765625,
0.04541015625,
-0.0106048583984375,
-0.0247344970703125,
0.0260467529296875,
-0.003383636474609375,
0.0142669677734375,
-0.027099609375,
0.0000616312026977539,
0.0176849365234375,
0.00939178466796875,
0.006954193115234375,
-0.00862884521484375,
-0.004909515380859375,
-0.01131439208984375,
-0.0123443603515625,
0.01229095458984375,
0.0294647216796875,
-0.00899505615234375,
0.0220794677734375,
-0.0145721435546875,
-0.00013387203216552734,
0.047637939453125,
0.0172271728515625,
0.004657745361328125,
-0.019775390625,
0.006855010986328125,
0.027496337890625,
0.006378173828125,
-0.0146484375,
0.006313323974609375,
-0.05157470703125,
0.01084136962890625,
0.036773681640625,
0.020599365234375,
-0.0170745849609375,
-0.021759033203125,
-0.045196533203125,
-0.023406982421875,
0.00867462158203125,
-0.004177093505859375,
0.0294952392578125,
0.0104827880859375,
-0.01061248779296875,
0.02374267578125,
-0.00977325439453125,
0.0070953369140625,
0.0304107666015625,
-0.005950927734375,
-0.00786590576171875,
-0.00914764404296875,
-0.005901336669921875,
-0.00420379638671875,
0.0012187957763671875,
-0.027496337890625,
-0.0009446144104003906,
0.02935791015625,
0.002178192138671875,
-0.0158843994140625,
0.01541900634765625,
-0.0074310302734375,
-0.000024318695068359375,
-0.00994110107421875,
0.0102386474609375,
-0.002471923828125,
-0.0220794677734375,
-0.00951385498046875,
0.0010547637939453125,
-0.0116729736328125,
0.0246734619140625,
-0.00238037109375,
-0.00624847412109375,
0.00014591217041015625,
-0.0205230712890625,
0.01264190673828125,
-0.016082763671875,
-0.01629638671875,
0.016632080078125,
-0.0316162109375,
0.018463134765625,
-0.0171051025390625,
0.026123046875,
-0.0282135009765625,
0.030609130859375,
0.0166778564453125,
-0.0304107666015625,
-0.0264434814453125,
-0.006702423095703125,
0.0165863037109375,
-0.011688232421875,
0.0297698974609375,
-0.01549530029296875,
-0.009613037109375,
0.0175018310546875,
0.013427734375,
-0.01055908203125,
0.01177215576171875,
0.0068511962890625,
-0.0033092498779296875,
-0.0289764404296875,
-0.00858306884765625,
-0.04852294921875,
0.00397491455078125,
-0.009246826171875,
0.002201080322265625,
-0.0140380859375,
-0.0018177032470703125,
0.005237579345703125,
-0.036041259765625,
-0.0286102294921875,
0.001438140869140625,
-0.024627685546875,
-0.0032405853271484375,
-0.0306549072265625,
-0.01337432861328125,
0.0176239013671875,
0.0245208740234375,
-0.0152130126953125,
-0.006343841552734375,
-0.01049041748046875,
-0.00481414794921875,
0.01654052734375,
0.01544952392578125,
-0.036773681640625,
-0.0176849365234375,
-0.003925323486328125,
0.0015649795532226562,
0.01476287841796875,
0.006256103515625,
-0.017059326171875,
0.006198883056640625,
0.001811981201171875,
-0.03955078125,
-0.0041351318359375,
-0.00730133056640625,
0.01152801513671875,
-0.0002803802490234375,
0.0279998779296875,
-0.00852203369140625,
-0.0021514892578125,
0.01541900634765625,
0.01363372802734375,
0.0296173095703125,
0.007785797119140625,
0.00615692138671875,
-0.004497528076171875,
0.006439208984375,
-0.0220489501953125,
0.044952392578125,
0.023834228515625,
-0.01166534423828125,
0.0264739990234375,
-0.01165008544921875,
-0.002197265625,
0.020721435546875,
0.01241302490234375,
-0.020111083984375,
0.0105438232421875,
0.01403045654296875,
0.0284271240234375,
0.00811767578125,
0.00489044189453125,
0.0295867919921875,
-0.0103759765625,
-0.0013980865478515625,
0.036651611328125,
-0.0157928466796875,
-0.01427459716796875,
0.0024356842041015625,
0.0099029541015625,
0.0097808837890625,
0.0230865478515625,
0.037017822265625,
0.007083892822265625,
-0.0208740234375,
0.0071868896484375,
-0.0161895751953125,
0.006839752197265625,
-0.0056915283203125,
0.0017566680908203125,
0.0281829833984375,
0.004550933837890625,
0.0163116455078125,
-0.0010576248168945312,
0.00809478759765625,
-0.00765228271484375,
0.022705078125,
-0.0222015380859375,
-0.00022995471954345703,
-0.033599853515625,
0.0272674560546875,
0.0216827392578125,
0.00965118408203125,
-0.00009632110595703125,
0.0245361328125,
-0.0140380859375,
-0.004825592041015625,
0.0155487060546875,
-0.02880859375,
-0.02398681640625,
-0.031005859375,
-0.051055908203125,
0.00679779052734375,
0.02191162109375,
0.010528564453125,
-0.0169525146484375,
0.02691650390625,
0.00127410888671875,
0.0276947021484375,
-0.0115203857421875,
0.004863739013671875,
0.0020599365234375,
0.025238037109375,
0.004703521728515625,
0.033599853515625,
-0.0183258056640625,
-0.01103973388671875,
0.0030345916748046875,
-0.017791748046875,
0.0051422119140625,
-0.00785064697265625,
0.0131683349609375,
-0.00708770751953125,
0.01464080810546875,
-0.0086517333984375,
-0.003932952880859375,
0.01226806640625,
0.0250396728515625,
0.0004930496215820312,
-0.0155487060546875,
0.017059326171875,
0.0242156982421875,
0.00958251953125,
0.02618408203125,
0.007442474365234375,
0.00841522216796875,
-0.01433563232421875,
0.01421356201171875,
-0.031890869140625,
-0.053955078125,
0.00014102458953857422,
-0.0251312255859375,
0.035308837890625,
-0.0185089111328125,
0.01084136962890625,
-0.006092071533203125,
0.00843048095703125,
-0.045135498046875,
-0.0235137939453125,
-0.00494384765625,
0.01467132568359375,
-0.027740478515625,
0.0036373138427734375,
-0.0188140869140625,
-0.004421234130859375,
-0.017547607421875,
0.018402099609375,
-0.0239105224609375,
0.034423828125,
-0.0001819133758544922,
-0.0188446044921875,
0.0019550323486328125,
0.020782470703125,
-0.0084686279296875,
-0.006885528564453125,
-0.011138916015625,
0.04364013671875,
-0.05169677734375,
0.0180816650390625,
-0.00414276123046875,
-0.03411865234375,
0.023834228515625,
0.0063629150390625,
-0.02923583984375,
0.0129547119140625,
-0.01702880859375,
0.0020694732666015625,
0.0233306884765625,
-0.01181793212890625,
0.00830841064453125,
0.002262115478515625,
0.0367431640625,
-0.01523590087890625,
0.0021495819091796875,
-0.0195159912109375,
-0.0013742446899414062,
0.0179901123046875,
-0.026123046875,
-0.007747650146484375,
-0.00019824504852294922,
0.00356292724609375,
-0.017974853515625,
-0.01434326171875,
-0.0229339599609375,
0.0130157470703125,
-0.00623321533203125,
0.0239410400390625,
-0.00679779052734375,
-0.038360595703125,
0.0243377685546875,
0.0027866363525390625,
0.010009765625,
-0.0216827392578125,
-0.032196044921875,
-0.03338623046875,
0.00441741943359375,
-0.0014591217041015625,
0.0008740425109863281,
0.01399993896484375,
0.004009246826171875,
-0.00894927978515625,
0.0200347900390625,
0.020751953125,
-0.014404296875,
0.0286102294921875,
0.0095672607421875,
0.0224456787109375,
0.022308349609375,
-0.0184326171875,
0.004604339599609375,
0.0390625,
0.0146331787109375,
-0.0029144287109375,
0.016021728515625,
-0.01226043701171875,
0.053985595703125,
-0.00925445556640625,
0.006336212158203125,
-0.01520538330078125,
0.0086517333984375,
0.007686614990234375,
0.019622802734375,
-0.0029659271240234375,
-0.0026226043701171875,
-0.024383544921875,
0.01131439208984375,
-0.031768798828125,
0.007106781005859375,
-0.00983428955078125,
0.0279693603515625,
-0.020843505859375,
0.016326904296875,
0.0144805908203125,
-0.005413055419921875,
0.017181396484375,
-0.004390716552734375,
0.020660400390625,
-0.0190887451171875,
0.015777587890625,
-0.037109375,
-0.01534271240234375,
-0.01540374755859375,
-0.043426513671875,
-0.0175323486328125,
0.009368896484375,
0.0080718994140625,
0.009185791015625,
0.0303192138671875,
0.00738525390625,
0.053436279296875,
0.036590576171875,
-0.02734375,
-0.0123291015625,
0.0208892822265625,
0.0159759521484375,
-0.0048675537109375,
-0.02093505859375,
0.005832672119140625,
0.0576171875,
-0.00542449951171875,
0.001819610595703125,
-0.0094146728515625,
-0.037628173828125,
-0.00888824462890625,
0.056427001953125,
0.0153961181640625,
0.0058135986328125,
0.01247406005859375,
0.0135650634765625,
-0.019287109375,
-0.00942230224609375,
-0.0128173828125,
-0.006786346435546875,
0.01220703125,
0.0155181884765625,
0.034912109375,
-0.002681732177734375,
-0.00614166259765625,
-0.00612640380859375,
-0.004425048828125,
-0.0294189453125,
-0.001678466796875,
-0.042144775390625,
-0.01190948486328125,
-0.0035648345947265625,
-0.0258331298828125,
-0.003173828125,
0.032012939453125,
-0.0202484130859375,
-0.004161834716796875,
0.028076171875,
-0.005695343017578125,
-0.005474090576171875,
0.024993896484375,
0.0229644775390625,
-0.01345062255859375,
-0.004085540771484375,
0.01641845703125,
-0.00370025634765625,
0.006732940673828125,
0.0134124755859375,
-0.00600433349609375,
-0.004302978515625,
0.0258941650390625,
0.0001977682113647461,
0.01453399658203125,
0.0112762451171875,
0.005252838134765625,
-0.0234222412109375,
-0.002483367919921875,
0.0008950233459472656,
0.032073974609375,
-0.01812744140625,
0.0256195068359375,
-0.01319122314453125,
-0.0294036865234375,
-0.040191650390625,
0.00844573974609375,
0.007404327392578125,
-0.00785064697265625,
0.017333984375,
0.0172119140625,
-0.01012420654296875,
0.0181121826171875,
0.002559661865234375,
-0.054290771484375,
-0.0114593505859375,
-0.005268096923828125,
-0.005588531494140625,
-0.015625,
-0.006622314453125,
-0.004299163818359375,
-0.008209228515625,
-0.00628662109375,
-0.0034027099609375,
-0.004322052001953125,
-0.0399169921875,
0.009246826171875,
-0.00634002685546875,
0.00141143798828125,
0.028778076171875,
-0.03643798828125,
-0.021331787109375,
-0.00506591796875,
0.037994384765625,
0.0404052734375,
0.008697509765625,
0.00547027587890625,
0.0078125,
0.034332275390625,
-0.02679443359375,
-0.006969451904296875,
-0.028594970703125,
0.01206207275390625,
0.03106689453125,
0.004146575927734375,
-0.0158843994140625,
-0.021453857421875,
0.006229400634765625,
0.01407623291015625,
0.016326904296875,
0.007236480712890625,
0.00229644775390625,
-0.006404876708984375,
0.006496429443359375,
-0.014678955078125,
0.03363037109375,
-0.01342010498046875,
0.0194549560546875,
-0.004486083984375,
0.01375579833984375,
0.01369476318359375,
-0.003231048583984375,
-0.00971221923828125,
-0.010589599609375,
0.006092071533203125,
0.0004930496215820312,
0.01203155517578125,
0.0023555755615234375,
0.0097503662109375,
0.02264404296875,
0.0142059326171875,
0.02618408203125,
0.011749267578125,
-0.0122528076171875,
0.007762908935546875,
0.0111236572265625,
0.0180511474609375,
-0.0194091796875,
-0.00543212890625,
0.007354736328125,
0.0088348388671875,
-0.0313720703125,
0.0073699951171875,
-0.044403076171875,
-0.0179290771484375,
0.0032024383544921875,
-0.0019626617431640625,
0.0244598388671875,
-0.019683837890625,
0.01166534423828125,
-0.0012798309326171875,
-0.0004200935363769531,
0.016754150390625,
-0.022796630859375,
0.005649566650390625,
0.0042572021484375,
0.002239227294921875,
-0.011962890625,
0.04925537109375,
0.002227783203125,
0.0031833648681640625,
0.0301055908203125,
-0.00429534912109375,
0.00455474853515625,
0.0258331298828125,
0.01296234130859375,
0.034820556640625,
-0.013092041015625,
-0.0052947998046875,
-0.00664520263671875,
0.01274871826171875,
-0.007171630859375,
0.0460205078125,
-0.0034732818603515625,
0.0018520355224609375,
-0.0027942657470703125,
0.016754150390625,
0.033538818359375,
0.017608642578125,
-0.0004706382751464844,
0.04827880859375,
0.00014770030975341797,
0.01812744140625,
-0.01078033447265625,
0.026214599609375,
-0.006198883056640625,
-0.0038509368896484375,
-0.01457977294921875,
-0.0177001953125,
0.007434844970703125,
-0.0213623046875,
0.00037407875061035156,
0.005771636962890625,
0.004184722900390625,
-0.0035858154296875,
-0.0208740234375,
-0.00801849365234375,
-0.016387939453125,
-0.00772857666015625,
0.0018644332885742188,
-0.0165557861328125,
-0.01549530029296875,
-0.00994110107421875,
-0.0304412841796875,
-0.00527191162109375,
0.00305938720703125,
-0.037109375,
0.0291900634765625,
0.0230560302734375,
-0.0070037841796875,
-0.0251312255859375,
0.056121826171875,
0.0252685546875,
-0.0251007080078125,
0.0239105224609375,
-0.035614013671875,
-0.008758544921875,
0.0112152099609375,
0.031280517578125,
0.0155792236328125,
-0.00572967529296875,
-0.0040283203125,
-0.006214141845703125,
0.01593017578125,
-0.028167724609375,
0.0172882080078125,
0.005077362060546875,
-0.007732391357421875,
-0.029052734375,
0.0151824951171875,
-0.04638671875,
-0.0156097412109375,
0.007030487060546875,
0.01464080810546875,
0.00618743896484375,
0.00949859619140625,
0.00960540771484375,
0.020660400390625,
0.01168060302734375,
-0.01033782958984375,
0.047210693359375,
-0.057525634765625,
-0.0197906494140625,
0.01220703125,
-0.025848388671875,
0.0196533203125,
0.006778717041015625,
0.01175689697265625,
0.027862548828125,
0.007495880126953125,
0.027191162109375,
0.00487518310546875,
-0.015899658203125,
0.0272979736328125,
0.034332275390625,
-0.00624847412109375,
0.041015625,
0.00026869773864746094,
-0.00811767578125,
0.0228729248046875,
-0.00838470458984375,
-0.0195770263671875,
-0.004730224609375,
-0.032562255859375,
0.05218505859375,
0.020233154296875,
-0.0433349609375,
-0.0282745361328125,
-0.003398895263671875,
0.00499725341796875,
0.041595458984375,
-0.040191650390625,
0.0014886856079101562,
0.017059326171875,
0.005535125732421875,
-0.012725830078125,
0.00783538818359375,
0.049560546875,
-0.0005826950073242188,
-0.036163330078125,
-0.021514892578125,
-0.0166168212890625,
0.017120361328125,
-0.025787353515625,
0.0178985595703125,
-0.0017108917236328125,
0.01483917236328125,
-0.0135498046875,
0.0159454345703125,
0.01953125,
0.016326904296875,
-0.00018525123596191406,
-0.0157318115234375,
-0.037109375,
0.003368377685546875,
-0.01247406005859375,
0.024993896484375,
-0.03411865234375,
-0.06109619140625,
0.01302337646484375,
-0.007297515869140625,
0.03167724609375,
-0.034942626953125,
0.01372528076171875,
0.003246307373046875,
-0.0086822509765625,
-0.02569580078125,
-0.0016336441040039062,
0.0126953125,
0.004444122314453125,
0.0036716461181640625,
-0.03253173828125,
-0.030029296875,
0.006801605224609375,
-0.01873779296875,
0.01116943359375,
0.0030727386474609375,
0.0169525146484375,
-0.042236328125,
0.004734039306640625,
0.034515380859375,
0.0041351318359375,
0.0006890296936035156,
-0.03118896484375,
0.003376007080078125,
-0.004268646240234375,
-0.0029468536376953125,
-0.01393890380859375,
-0.0260467529296875,
-0.019989013671875,
-0.01349639892578125,
0.03472900390625,
0.00023627281188964844,
-0.0208892822265625,
0.0021114349365234375,
-0.004726409912109375,
0.0004336833953857422,
-0.02410888671875,
-0.0130462646484375,
0.0245361328125,
-0.01235198974609375,
0.0109100341796875,
0.0125732421875,
0.0178680419921875,
0.0086669921875,
-0.003597259521484375,
-0.00917816162109375,
-0.032257080078125,
-0.002582550048828125,
-0.036224365234375,
0.0098419189453125,
0.01062774658203125,
0.003631591796875,
-0.015228271484375,
0.0038242340087890625,
0.01531982421875,
-0.0321044921875,
-0.0034236907958984375,
-0.01348876953125,
0.04583740234375,
-0.026763916015625,
0.0048065185546875,
0.01136016845703125,
-0.04168701171875,
0.040313720703125,
0.0036907196044921875,
-0.00557708740234375,
-0.01043701171875,
0.046630859375,
-0.050384521484375,
-0.00836944580078125,
0.0187835693359375,
-0.00606536865234375,
-0.003971099853515625,
-0.0115203857421875,
-0.0013179779052734375,
0.0013904571533203125,
0.030792236328125,
-0.005298614501953125,
-0.00696563720703125,
-0.01441192626953125,
0.01277923583984375,
-0.0034961700439453125,
-0.0300750732421875,
-0.02166748046875,
-0.01715087890625,
0.0177459716796875,
-0.01477813720703125,
0.005100250244140625,
0.018524169921875,
0.01154327392578125,
0.00311279296875,
-0.01462554931640625,
-0.0242462158203125,
-0.0075225830078125,
0.00655364990234375,
-0.0251312255859375,
0.00994110107421875,
-0.01535797119140625,
0.00997161865234375,
-0.00872802734375,
-0.0016841888427734375,
0.03271484375,
-0.004344940185546875,
0.02667236328125,
0.0003407001495361328,
0.001926422119140625,
0.01377105712890625,
0.00795745849609375,
-0.0009531974792480469,
0.038299560546875,
-0.02490234375,
-0.0041961669921875,
-0.01885986328125,
0.028717041015625,
0.005126953125,
-0.00788116455078125,
-0.001766204833984375,
-0.029388427734375,
-0.04296875,
0.00826263427734375,
-0.0045928955078125,
-0.0169219970703125,
-0.009857177734375,
0.0051116943359375,
0.016387939453125,
0.007671356201171875,
0.00524139404296875,
0.0262603759765625,
-0.023529052734375,
0.02191162109375,
-0.006744384765625,
-0.0158233642578125,
-0.010406494140625,
-0.00005263090133666992,
-0.0092010498046875,
0.0047149658203125,
-0.0273895263671875,
0.04827880859375,
-0.0025043487548828125,
-0.0106658935546875,
-0.000023186206817626953,
0.033203125,
-0.021240234375,
-0.0259857177734375,
0.018798828125,
0.042724609375,
0.026611328125,
-0.0080108642578125,
0.00872802734375,
-0.01837158203125,
-0.0020847320556640625,
0.0052642822265625,
0.04425048828125,
0.020050048828125,
-0.0069580078125,
-0.0268402099609375,
0.0004611015319824219,
-0.0133209228515625,
-0.00553131103515625,
-0.0130767822265625,
-0.0048980712890625,
-0.032440185546875,
-0.0179595947265625,
-0.00792694091796875,
-0.005123138427734375,
-0.033447265625,
-0.02093505859375,
-0.0102996826171875,
0.00572967529296875,
0.01537322998046875,
-0.0399169921875,
-0.00250244140625,
0.0045166015625,
0.004398345947265625,
0.0138092041015625,
-0.0141143798828125,
0.0302886962890625,
-0.03790283203125,
0.0025234222412109375,
0.0216522216796875,
-0.01436614990234375,
-0.0012140274047851562,
-0.007843017578125,
0.01519012451171875,
-0.00995635986328125,
-0.005764007568359375,
0.005218505859375,
-0.0207366943359375,
-0.031036376953125,
0.03265380859375,
0.0061492919921875,
-0.026885986328125,
-0.016357421875,
0.018951416015625,
0.0005540847778320312,
-0.017181396484375,
0.00745391845703125,
-0.0157318115234375,
-0.01248931884765625,
0.024993896484375,
-0.0018320083618164062,
-0.0203399658203125,
0.00267791748046875,
-0.0308990478515625,
0.00890350341796875,
0.034698486328125,
-0.01358795166015625,
-0.0265960693359375,
-0.0158843994140625,
-0.0255279541015625,
-0.016815185546875,
0.01113128662109375,
-0.029510498046875,
-0.00543212890625,
-0.02288818359375,
-0.01763916015625,
-0.00951385498046875,
0.007762908935546875,
0.0204315185546875,
-0.005153656005859375,
-0.0257110595703125,
-0.043121337890625,
-0.01470184326171875,
-0.0153656005859375,
-0.01125335693359375,
0.0041351318359375,
-0.0124969482421875,
-0.00482177734375,
0.00241851806640625,
0.0009369850158691406,
0.0003795623779296875,
-0.005970001220703125,
-0.000732421875,
0.0035152435302734375,
-0.00441741943359375,
0.041961669921875,
0.01514434814453125,
-0.01206207275390625,
-0.0300140380859375,
-0.00754547119140625,
-0.00528717041015625,
-0.00897216796875,
0.00193023681640625,
0.04571533203125,
-0.004817962646484375,
0.01824951171875,
-0.00734710693359375,
0.020721435546875,
0.00376129150390625,
-0.005657196044921875,
-0.034210205078125,
-0.00893402099609375,
0.0105743408203125,
-0.01355743408203125,
-0.006378173828125,
0.0276641845703125,
-0.015625,
0.01044464111328125,
-0.01303863525390625,
0.00913238525390625,
0.0132293701171875,
0.005054473876953125,
-0.0200653076171875,
0.008941650390625,
0.026214599609375,
-0.0178375244140625,
0.0030460357666015625,
-0.01555633544921875,
-0.0386962890625,
-0.0017261505126953125,
0.01531982421875,
0.015869140625,
0.0247650146484375,
-0.02447509765625,
-0.003726959228515625,
-0.02484130859375,
-0.006732940673828125,
0.00537872314453125,
-0.0033512115478515625,
0.025634765625,
-0.007770538330078125,
0.005413055419921875,
-0.041900634765625,
-0.038543701171875,
0.0278167724609375,
0.005275726318359375,
0.025054931640625,
0.035186767578125,
0.01203155517578125,
0.005016326904296875,
0.0001577138900756836,
0.0498046875,
0.031982421875,
0.00899505615234375,
0.004878997802734375,
0.02703857421875,
-0.0056304931640625,
-0.01497650146484375,
-0.01302337646484375,
-0.0106658935546875,
-0.01922607421875,
0.012786865234375,
0.04095458984375,
0.0168609619140625,
-0.0267181396484375,
0.0225067138671875,
0.020233154296875,
-0.007068634033203125,
0.007568359375,
-0.004543304443359375,
-0.01551055908203125,
0.019805908203125,
0.0012960433959960938,
-0.020660400390625,
-0.01319122314453125,
0.006256103515625,
0.008331298828125,
0.007610321044921875,
-0.007251739501953125,
0.00016176700592041016,
0.00794219970703125,
0.00902557373046875,
0.0012960433959960938,
-0.0232696533203125,
-0.00777435302734375,
-0.018157958984375,
0.0082550048828125,
-0.01155853271484375,
-0.028533935546875,
0.0183868408203125,
0.013519287109375,
-0.0047149658203125,
-0.022308349609375,
0.0011129379272460938,
0.01424407958984375,
-0.0030117034912109375,
0.006412506103515625,
-0.01206207275390625,
-0.0153350830078125,
-0.0247650146484375,
0.0241546630859375,
0.026153564453125,
0.0036029815673828125,
-0.00826263427734375,
0.0021457672119140625,
-0.034942626953125,
0.0022106170654296875,
0.017181396484375,
-0.023345947265625,
-0.024261474609375,
-0.00836181640625,
-0.017578125,
-0.00685882568359375,
0.01364898681640625,
-0.017333984375,
-0.0170440673828125,
-0.001804351806640625,
0.0207672119140625,
-0.0173797607421875,
0.007556915283203125,
0.0264739990234375,
0.0028133392333984375,
-0.00634002685546875,
-0.01222991943359375,
0.022430419921875,
-0.00890350341796875,
-0.01910400390625,
0.005535125732421875,
-0.017547607421875,
0.0102386474609375,
0.0185699462890625,
0.00399017333984375,
-0.048492431640625,
0.054443359375,
0.0262298583984375,
0.0190887451171875,
-0.00652313232421875,
-0.00994110107421875,
-0.00426483154296875,
-0.009765625,
0.007472991943359375,
-0.01849365234375,
-0.006931304931640625,
0.0161895751953125,
0.001800537109375,
-0.01078033447265625,
0.024017333984375,
0.01214599609375,
0.00238037109375,
-0.00836181640625,
-0.00959014892578125,
-0.01238250732421875,
-0.0228729248046875,
-0.007320404052734375,
0.0217132568359375,
-0.002635955810546875,
0.0068511962890625,
0.003444671630859375,
0.019317626953125,
0.0006113052368164062,
0.015777587890625,
-0.007476806640625,
-0.0282135009765625,
0.0189971923828125,
0.0208587646484375,
-0.0052490234375,
0.0014095306396484375,
0.049041748046875,
-0.0153961181640625,
0.0009598731994628906,
0.01119232177734375,
-0.0212249755859375,
-0.00330352783203125,
-0.005199432373046875,
-0.00873565673828125,
0.02825927734375,
0.0283966064453125,
0.00629425048828125,
0.00982666015625,
0.00775146484375,
0.004886627197265625,
0.0007991790771484375,
0.02935791015625,
-0.022674560546875,
0.025115966796875,
-0.027679443359375,
0.01242828369140625,
0.001171112060546875,
0.0002110004425048828,
-0.0159149169921875,
0.0007405281066894531,
-0.011688232421875,
0.0159912109375,
0.01422882080078125,
0.00400543212890625,
0.032257080078125,
0.0458984375,
0.004364013671875,
0.007457733154296875,
-0.011993408203125,
0.0279541015625,
-0.0240325927734375,
0.0231475830078125,
-0.0236663818359375,
0.00800323486328125,
-0.0143585205078125,
-0.005283355712890625,
-0.004581451416015625,
-0.00505828857421875,
0.03509521484375,
-0.003795623779296875,
0.064453125,
0.01580810546875,
0.0037174224853515625,
-0.0030517578125,
-0.0423583984375,
-0.045989990234375,
0.0006184577941894531,
-0.0211029052734375,
0.01122283935546875,
0.0025234222412109375,
-0.0382080078125,
-0.007450103759765625,
0.0177459716796875,
-0.0078277587890625,
-0.032501220703125,
0.006351470947265625,
-0.01561737060546875,
0.01025390625,
-0.007053375244140625,
0.0167236328125,
-0.01161956787109375,
-0.018402099609375,
0.01837158203125,
0.0125274658203125,
0.00959014892578125,
-0.01079559326171875,
0.0190277099609375,
0.0134124755859375,
-0.0063934326171875,
-0.0149993896484375,
0.010498046875,
-0.0023288726806640625,
0.035186767578125,
-0.05078125,
0.0077972412109375,
-0.002643585205078125,
0.0248260498046875,
0.0400390625,
0.0146942138671875,
0.0240936279296875,
0.01023101806640625,
0.0202484130859375,
0.004726409912109375,
0.0196075439453125,
-0.02685546875,
0.0009965896606445312,
-0.0127105712890625,
0.019622802734375,
0.0007843971252441406,
0.044464111328125,
0.002567291259765625,
0.0141754150390625,
-0.01837158203125,
-0.038604736328125,
0.01446533203125,
-0.0028858184814453125,
-0.0088958740234375,
0.004543304443359375,
-0.01544952392578125,
0.0205841064453125,
-0.0341796875,
0.055938720703125,
0.02508544921875,
-0.0175018310546875,
-0.00225830078125,
0.01507568359375,
-0.00516510009765625,
0.046844482421875,
0.042022705078125,
0.02813720703125,
0.00020623207092285156,
-0.00727081298828125,
0.02679443359375,
0.0299072265625,
0.00313568115234375,
-0.0032520294189453125,
0.019683837890625,
-0.0084686279296875,
-0.0078277587890625,
-0.0120391845703125,
-0.00429534912109375,
0.00443267822265625,
0.0164947509765625,
0.007518768310546875,
-0.034027099609375,
0.005428314208984375,
0.0252227783203125,
0.00852203369140625,
-0.029266357421875,
-0.0235748291015625,
0.00539398193359375,
-0.03173828125,
0.040252685546875,
0.0174407958984375,
-0.0196685791015625,
-0.0018291473388671875,
0.0189056396484375,
-0.01517486572265625,
-0.00533294677734375,
-0.03192138671875,
-0.00124359130859375,
-0.0114288330078125,
0.019927978515625,
0.00626373291015625,
0.0094146728515625,
0.0238189697265625,
-0.0201873779296875,
-0.0188446044921875,
0.023223876953125,
-0.00506591796875,
0.01264190673828125,
-0.0224609375,
-0.0016565322875976562,
0.04071044921875,
0.03118896484375,
0.006561279296875,
0.0179443359375,
0.0244293212890625,
0.0152435302734375,
-0.011932373046875,
-0.00218963623046875,
-0.0110015869140625,
-0.04742431640625,
0.008209228515625,
-0.0078887939453125,
0.0310516357421875,
-0.01117706298828125,
0.0294952392578125,
-0.0081024169921875,
-0.02685546875,
-0.0031986236572265625,
0.00539398193359375,
-0.02685546875,
-0.0037670135498046875,
0.00699615478515625,
0.00870513916015625,
0.0109405517578125,
-0.0183868408203125,
-0.0266265869140625,
0.02984619140625,
0.01372528076171875,
0.006744384765625,
-0.0137481689453125,
-0.00261688232421875,
0.0235137939453125,
0.01428985595703125,
-0.007114410400390625,
-0.007778167724609375,
-0.005649566650390625,
-0.004058837890625,
0.00920867919921875,
-0.0263214111328125,
-0.02020263671875,
-0.0009150505065917969,
0.04425048828125,
0.005031585693359375,
-0.00757598876953125,
-0.01212310791015625,
0.00923919677734375,
-0.00616455078125,
-0.01262664794921875,
-0.03070068359375,
0.00634002685546875,
0.0026397705078125,
0.003997802734375,
-0.0230865478515625,
-0.0028896331787109375,
-0.00689697265625,
0.0007352828979492188,
0.0276947021484375,
0.015960693359375,
0.04278564453125,
-0.05731201171875,
-0.007076263427734375,
0.0186767578125,
0.0037822723388671875,
0.01262664794921875,
0.00481414794921875,
0.002651214599609375,
-0.00390625,
0.01128387451171875,
-0.021026611328125,
0.005329132080078125,
0.0249481201171875,
0.0408935546875,
-0.01910400390625,
0.031341552734375,
0.012939453125,
0.0225372314453125,
0.04296875,
-0.029815673828125,
0.0172271728515625,
0.018890380859375,
0.0265350341796875,
0.01255035400390625,
-0.032806396484375,
0.043426513671875,
-0.03973388671875,
-0.00753021240234375,
-0.005847930908203125,
-0.0006847381591796875,
0.023956298828125,
0.0116119384765625,
-0.00519561767578125,
-0.0012426376342773438,
0.023773193359375,
-0.0008111000061035156,
0.04412841796875,
-0.00643157958984375,
0.0019197463989257812,
0.0389404296875,
0.0087738037109375,
-0.023834228515625,
0.01068115234375,
-0.00531768798828125,
0.0196533203125,
0.0229339599609375,
0.0014209747314453125,
-0.017852783203125,
-0.005207061767578125,
-0.01139068603515625,
0.04486083984375,
-0.014404296875,
0.01458740234375,
-0.007091522216796875,
0.010955810546875,
-0.017547607421875,
-0.001972198486328125,
0.0372314453125,
-0.0181427001953125,
-0.01166534423828125,
0.0241241455078125,
0.018096923828125,
0.026763916015625,
-0.00811004638671875,
0.044403076171875,
-0.0109405517578125,
0.01145172119140625,
-0.005886077880859375,
-0.01324462890625,
-0.005413055419921875,
-0.01678466796875,
-0.005870819091796875,
0.0029964447021484375,
0.0027599334716796875,
0.045196533203125,
-0.022705078125,
-0.0203094482421875,
-0.00799560546875,
0.0143890380859375,
0.0178375244140625,
0.00749969482421875,
0.0009374618530273438,
0.00971221923828125,
-0.0291900634765625,
0.01180267333984375,
-0.01007080078125,
0.0192108154296875,
-0.0157318115234375,
-0.0137481689453125,
-0.0062408447265625,
0.0196990966796875,
-0.0030364990234375,
0.001068115234375,
0.041046142578125,
-0.0149078369140625,
-0.005115509033203125,
-0.035858154296875,
0.0223541259765625,
0.02001953125,
0.052734375,
-0.01123809814453125,
-0.0284576416015625,
-0.06781005859375,
-0.00952911376953125,
0.0382080078125,
-0.0257415771484375,
-0.004817962646484375,
0.0299224853515625,
0.01544952392578125,
0.003910064697265625,
-0.008544921875,
-0.0011339187622070312,
-0.021087646484375,
-0.0101318359375,
-0.04461669921875,
-0.017242431640625,
0.01097869873046875,
0.022552490234375,
-0.0006260871887207031,
0.000007331371307373047,
0.00153350830078125,
-0.01654052734375,
-0.01242828369140625,
-0.0266876220703125,
-0.031646728515625,
0.00930023193359375,
-0.049163818359375,
-0.0240478515625,
-0.044219970703125,
-0.006622314453125,
-0.017608642578125,
0.018218994140625,
-0.0022830963134765625,
-0.0350341796875,
0.011749267578125,
0.0163421630859375,
-0.0017852783203125,
0.0183868408203125,
-0.0286102294921875,
0.006877899169921875,
-0.03350830078125,
0.062347412109375,
-0.0211334228515625,
0.01557159423828125,
-0.0005955696105957031,
0.0017528533935546875,
0.0033130645751953125,
-0.016357421875,
-0.0221710205078125,
-0.0306243896484375,
-0.01959228515625,
0.00566864013671875,
-0.003704071044921875,
-0.0074005126953125,
0.0076141357421875,
0.0236663818359375,
0.007022857666015625,
-0.0171356201171875,
0.02996826171875,
-0.005397796630859375,
-0.022430419921875,
-0.01381683349609375,
-0.0037670135498046875,
0.0014734268188476562,
0.00757598876953125,
-0.007534027099609375,
-0.0208587646484375,
-0.006504058837890625,
0.002994537353515625,
-0.04931640625,
0.0008153915405273438,
0.00911712646484375,
0.035186767578125,
0.01203155517578125,
-0.0254669189453125,
-0.005672454833984375,
-0.0016078948974609375,
0.02545166015625,
-0.0191802978515625,
0.00518798828125,
0.0257568359375,
0.00823211669921875,
-0.013885498046875,
0.0028972625732421875,
0.0009126663208007812,
-0.003307342529296875,
-0.0321044921875,
0.021484375,
-0.00861358642578125,
0.007366180419921875,
0.0243988037109375,
-0.0059967041015625,
-0.0032711029052734375,
0.0172271728515625,
0.007720947265625,
0.01253509521484375,
0.024810791015625
] |
ours_504
|
After one move, the ant is at one of the four points \((1,0)\), \((0,1)\), \((-1,0)\), \((0,-1)\). At each of these four points, there is a \(\frac{7}{16}\) probability of reaching a point where it stops after two moves, and a \(\frac{9}{16}\) probability it returns to one of these four points again. This means that the expected number of moves starting from any of these four points is \(2 \cdot \frac{16}{7} = \frac{32}{7}\). Therefore, the original expectation is \(\frac{32}{7} + 1 = \frac{39}{7}\). Thus, the answer is \(3907\).
\(\boxed{3907}\)
|
3907
|
{
"competition": "us_comps",
"dataset": "Ours",
"posts": null,
"source": "OMOFall19Solns.md"
}
|
An ant starts at the origin of the Cartesian coordinate plane. Each minute it moves randomly one unit in one of the directions up, down, left, or right, with all four directions being equally likely; its direction each minute is independent of its direction in any previous minutes. It stops when it reaches a point \((x, y)\) such that \(|x|+|y|=3\). The expected number of moves it makes before stopping can be expressed as \(\frac{m}{n}\) for relatively prime positive integers \(m\) and \(n\). Compute \(100m+n\).
|
[
"/Mathematics/DiscreteMathematics/Combinatorics/LatticePathsandPolygons",
"/Mathematics/DiscreteMathematics/GeneralDiscreteMathematics/DiscreteMath",
"/Mathematics/DiscreteMathematics/GeneralDiscreteMathematics/DiscreteMathematics",
"/Mathematics/ProbabilityandStatistics/Probability/ConditionalProbability",
"/Mathematics/ProbabilityandStatistics/RandomWalks/RandomWalk",
"/Mathematics/ProbabilityandStatistics/RandomWalks/RandomWalk2-Dimensional"
] |
Condition on being at a Manhattan distance 1 point and use the two‑step exit probability to solve for the expected remaining moves.
|
[
-0.00010544061660766602,
-0.01049041748046875,
0.03369140625,
-0.037994384765625,
-0.0005979537963867188,
0.0355224609375,
0.0162200927734375,
0.0095367431640625,
-0.005466461181640625,
0.0219268798828125,
0.04058837890625,
0.0150909423828125,
-0.0039215087890625,
0.0240936279296875,
0.0216064453125,
-0.02581787109375,
-0.0225982666015625,
0.0177154541015625,
0.00492095947265625,
0.006732940673828125,
-0.0140228271484375,
-0.029205322265625,
-0.0302734375,
-0.004047393798828125,
-0.0273590087890625,
-0.0184783935546875,
-0.01312255859375,
0.0278472900390625,
-0.0014925003051757812,
0.0224151611328125,
-0.030517578125,
0.012603759765625,
0.0484619140625,
0.007274627685546875,
-0.001964569091796875,
0.004665374755859375,
0.0023956298828125,
0.007015228271484375,
-0.002597808837890625,
-0.0190582275390625,
0.00044846534729003906,
0.0013380050659179688,
-0.005401611328125,
0.01934814453125,
-0.0027866363525390625,
-0.0176849365234375,
-0.01161956787109375,
-0.02752685546875,
0.01123046875,
-0.008392333984375,
-0.00013720989227294922,
0.0167999267578125,
-0.0007290840148925781,
-0.018890380859375,
-0.0452880859375,
-0.0648193359375,
0.006832122802734375,
-0.00208282470703125,
-0.010711669921875,
-0.0193939208984375,
0.0016527175903320312,
-0.00591278076171875,
0.0198211669921875,
-0.0032787322998046875,
-0.0028514862060546875,
-0.0107421875,
-0.0007491111755371094,
-0.016510009765625,
0.00545501708984375,
-0.0124359130859375,
0.002437591552734375,
0.004863739013671875,
-0.0081939697265625,
0.0300140380859375,
0.032440185546875,
-0.006809234619140625,
-0.002986907958984375,
0.01538848876953125,
-0.00832366943359375,
0.01493072509765625,
0.0035037994384765625,
0.0022640228271484375,
-0.00879669189453125,
-0.0200958251953125,
0.01212310791015625,
0.04241943359375,
-0.0044708251953125,
0.0015096664428710938,
0.02685546875,
-0.024261474609375,
-0.00258636474609375,
-0.005138397216796875,
0.006649017333984375,
-0.0204620361328125,
-0.002147674560546875,
0.01125335693359375,
0.01053619384765625,
-0.0031948089599609375,
-0.005092620849609375,
-0.0012369155883789062,
-0.01421356201171875,
0.0026302337646484375,
0.0274505615234375,
-0.00669097900390625,
-0.00618743896484375,
-0.0037059783935546875,
-0.0306396484375,
-0.007198333740234375,
0.003887176513671875,
0.01953125,
-0.00017571449279785156,
-0.001422882080078125,
0.03094482421875,
-0.00038743019104003906,
0.009063720703125,
0.004024505615234375,
-0.0126190185546875,
-0.0017766952514648438,
-0.0026264190673828125,
0.00943756103515625,
0.0019054412841796875,
0.0004508495330810547,
-0.0015287399291992188,
0.0015382766723632812,
-0.0153656005859375,
-0.00539398193359375,
0.00911712646484375,
0.0155181884765625,
0.020355224609375,
0.0138092041015625,
-0.0043792724609375,
-0.010009765625,
-0.0161895751953125,
-0.0236053466796875,
-0.06365966796875,
0.00010889768600463867,
-0.0007848739624023438,
-0.01523590087890625,
-0.01364898681640625,
-0.016204833984375,
0.021697998046875,
-0.0011653900146484375,
0.01580810546875,
-0.029998779296875,
0.00710296630859375,
0.0005135536193847656,
0.0148162841796875,
-0.05999755859375,
0.009765625,
0.011627197265625,
-0.00913238525390625,
-0.01497650146484375,
0.0079345703125,
0.01004791259765625,
-0.0049591064453125,
-0.0227813720703125,
-0.0089569091796875,
-0.0298004150390625,
-0.0143890380859375,
0.0078582763671875,
0.01401519775390625,
-0.0199737548828125,
0.0217437744140625,
0.046295166015625,
-0.0020809173583984375,
0.01119232177734375,
-0.016448974609375,
0.016204833984375,
0.003543853759765625,
0.0251312255859375,
0.0172271728515625,
-0.005645751953125,
-0.0069732666015625,
-0.0158538818359375,
0.003932952880859375,
0.0070648193359375,
0.00446319580078125,
-0.0174407958984375,
-0.01763916015625,
0.0198516845703125,
-0.011260986328125,
-0.0289306640625,
0.01464080810546875,
-0.00760650634765625,
0.0180206298828125,
0.0063018798828125,
0.00431060791015625,
-0.0026073455810546875,
0.0258331298828125,
0.0143280029296875,
-0.00799560546875,
-0.0032482147216796875,
0.0031490325927734375,
-0.017333984375,
0.00011974573135375977,
0.0078277587890625,
-0.0269622802734375,
0.005374908447265625,
0.028045654296875,
0.011688232421875,
-0.006732940673828125,
-0.00959014892578125,
-0.006763458251953125,
0.008636474609375,
-0.0022411346435546875,
-0.0004355907440185547,
0.01076507568359375,
-0.0130767822265625,
-0.006252288818359375,
0.003627777099609375,
0.002628326416015625,
0.0218505859375,
-0.006931304931640625,
-0.01434326171875,
-0.0037822723388671875,
0.023284912109375,
-0.0005049705505371094,
-0.011566162109375,
0.010406494140625,
-0.0193023681640625,
0.01471710205078125,
0.009552001953125,
0.0042724609375,
0.004459381103515625,
-0.007076263427734375,
-0.0016508102416992188,
-0.006015777587890625,
-0.00397491455078125,
0.01248931884765625,
0.0031871795654296875,
0.0214080810546875,
0.020050048828125,
0.005489349365234375,
-0.01454925537109375,
0.0005822181701660156,
-0.0014133453369140625,
-0.042266845703125,
-0.01517486572265625,
0.00238800048828125,
-0.00707244873046875,
0.0064849853515625,
0.00653076171875,
0.016387939453125,
-0.00640106201171875,
-0.00304412841796875,
0.0022106170654296875,
-0.0006308555603027344,
-0.0167999267578125,
0.0088348388671875,
-0.005489349365234375,
-0.0220794677734375,
0.0243072509765625,
-0.0169219970703125,
-0.0246734619140625,
8.940696716308594e-7,
-0.00345611572265625,
-0.0050506591796875,
0.01274871826171875,
-0.005802154541015625,
0.0141448974609375,
-0.0233917236328125,
0.035064697265625,
-0.00467681884765625,
0.01235198974609375,
-0.004352569580078125,
-0.00052642822265625,
-0.003879547119140625,
-0.0011053085327148438,
0.007717132568359375,
-0.0158538818359375,
0.0086212158203125,
0.0017852783203125,
-0.011260986328125,
0.00243377685546875,
-0.024566650390625,
-0.0185394287109375,
0.004253387451171875,
0.004764556884765625,
0.023193359375,
0.0004863739013671875,
0.0128173828125,
-0.0279693603515625,
0.004150390625,
-0.00296783447265625,
0.009857177734375,
-0.01290130615234375,
-0.007747650146484375,
-0.019775390625,
-0.0303192138671875,
0.00299835205078125,
-0.00811767578125,
0.0239715576171875,
-0.0035762786865234375,
0.0142059326171875,
0.0157012939453125,
-0.032257080078125,
0.01261138916015625,
0.00853729248046875,
-0.004650115966796875,
-0.003910064697265625,
0.036407470703125,
-0.00910186767578125,
-0.00064849853515625,
0.006732940673828125,
0.00962066650390625,
0.039581298828125,
0.01111602783203125,
-0.0134429931640625,
-0.010589599609375,
-0.0269012451171875,
-0.00124359130859375,
0.01727294921875,
-0.0024204254150390625,
-0.015869140625,
-0.0221099853515625,
-0.032501220703125,
0.0014753341674804688,
0.0230865478515625,
-0.0135345458984375,
-0.0195770263671875,
0.0269317626953125,
0.0057220458984375,
-0.01548004150390625,
0.0224456787109375,
0.03131103515625,
-0.0095367431640625,
-0.012115478515625,
0.01042938232421875,
-0.01555633544921875,
0.002101898193359375,
0.0194244384765625,
-0.00530242919921875,
0.0306243896484375,
-0.01861572265625,
-0.0078582763671875,
-0.00460052490234375,
-0.007259368896484375,
0.0303802490234375,
-0.0021514892578125,
-0.00000762939453125,
-0.007442474365234375,
0.01027679443359375,
0.0287933349609375,
-0.03387451171875,
0.005069732666015625,
0.01262664794921875,
-0.01160430908203125,
0.005641937255859375,
0.0005049705505371094,
-0.022613525390625,
0.004589080810546875,
0.02239990234375,
-0.007965087890625,
0.0010309219360351562,
-0.033966064453125,
0.00348663330078125,
0.01439666748046875,
-0.0170745849609375,
0.004642486572265625,
0.021209716796875,
0.0168304443359375,
-0.0171661376953125,
-0.006305694580078125,
-0.01148223876953125,
0.0294189453125,
0.00726318359375,
-0.027618408203125,
-0.005977630615234375,
-0.05645751953125,
0.0019989013671875,
0.0164947509765625,
0.0211029052734375,
0.0132293701171875,
-0.003162384033203125,
0.0093536376953125,
0.01143646240234375,
0.045379638671875,
-0.01552581787109375,
0.002269744873046875,
-0.007427215576171875,
-0.00970458984375,
0.043060302734375,
0.007335662841796875,
0.027923583984375,
-0.0211944580078125,
0.00933837890625,
-0.0018529891967773438,
-0.0379638671875,
-0.0303955078125,
-0.0055999755859375,
-0.0118865966796875,
-0.001708984375,
-0.00949859619140625,
0.01020050048828125,
-0.0323486328125,
-0.008758544921875,
-0.005603790283203125,
-0.0022602081298828125,
0.02679443359375,
-0.01776123046875,
-0.00124359130859375,
0.01003265380859375,
-0.0229949951171875,
0.0245361328125,
0.01123809814453125,
0.001590728759765625,
0.00864410400390625,
-0.0003857612609863281,
-0.0153961181640625,
0.01526641845703125,
-0.01238250732421875,
-0.0011310577392578125,
0.002727508544921875,
0.007793426513671875,
-0.01102447509765625,
0.0218353271484375,
0.0013952255249023438,
0.005847930908203125,
0.019378662109375,
-0.0252685546875,
-0.006977081298828125,
-0.020477294921875,
-0.03662109375,
-0.00891876220703125,
0.03924560546875,
0.002941131591796875,
-0.00818634033203125,
0.0252685546875,
-0.0404052734375,
-0.0167694091796875,
-0.00007635354995727539,
0.04364013671875,
0.0213775634765625,
0.05609130859375,
-0.01145172119140625,
0.0189666748046875,
0.0479736328125,
-0.031494140625,
-0.0310821533203125,
0.01009368896484375,
0.0035419464111328125,
0.00881195068359375,
-0.03607177734375,
-0.01541900634765625,
-0.01386260986328125,
0.0092620849609375,
0.027313232421875,
0.0198211669921875,
0.01605224609375,
0.0105438232421875,
-0.0042266845703125,
-0.035797119140625,
0.0144500732421875,
-0.0323486328125,
-0.020477294921875,
0.031219482421875,
0.01035308837890625,
-0.03680419921875,
-0.00611114501953125,
-0.011474609375,
0.0186614990234375,
-0.0287322998046875,
-0.02862548828125,
0.006855010986328125,
-0.038177490234375,
0.0037174224853515625,
-0.0299835205078125,
-0.006366729736328125,
0.0147552490234375,
-0.03558349609375,
-0.01678466796875,
-0.0565185546875,
-0.0231170654296875,
0.007389068603515625,
-0.01470184326171875,
0.0264739990234375,
0.0213775634765625,
0.018768310546875,
-0.0174102783203125,
-0.028350830078125,
-0.007221221923828125,
0.0149383544921875,
0.04217529296875,
0.070556640625,
0.032684326171875,
0.0024280548095703125,
0.0257568359375,
-0.0031871795654296875,
0.0106201171875,
-0.044158935546875,
0.0243988037109375,
0.027862548828125,
-0.041900634765625,
-0.0127105712890625,
-0.007656097412109375,
0.02679443359375,
-0.00047016143798828125,
-0.017974853515625,
-0.0264129638671875,
-0.00038886070251464844,
0.035003662109375,
0.03497314453125,
-0.0166168212890625,
0.04034423828125,
0.01305389404296875,
0.01629638671875,
0.048431396484375,
0.000530242919921875,
0.019805908203125,
0.033233642578125,
-0.0182342529296875,
0.01494598388671875,
0.00910186767578125,
-0.0260467529296875,
0.0350341796875,
-0.0225372314453125,
0.01500701904296875,
-0.0122833251953125,
-0.00439453125,
0.00203704833984375,
-0.037200927734375,
0.0133819580078125,
0.00991058349609375,
-0.004001617431640625,
-0.0178070068359375,
-0.00939178466796875,
-0.019775390625,
-0.01129150390625,
-0.0309600830078125,
0.01177215576171875,
0.000904083251953125,
-0.0270538330078125,
-0.0298004150390625,
-0.0177154541015625,
0.010986328125,
0.0098724365234375,
-0.0016546249389648438,
-0.0205230712890625,
0.028411865234375,
-0.005245208740234375,
-0.0032863616943359375,
-0.0087890625,
-0.0092620849609375,
-0.013946533203125,
0.02349853515625,
0.0003209114074707031,
0.0161895751953125,
0.032989501953125,
-0.03228759765625,
-0.01000213623046875,
0.026458740234375,
0.0175323486328125,
-0.02294921875,
-0.01210784912109375,
-0.01139068603515625,
0.0116729736328125,
0.0309295654296875,
0.0089569091796875,
-0.00551605224609375,
-0.00550079345703125,
-0.0081787109375,
-0.003093719482421875,
0.00809478759765625,
0.01403045654296875,
0.00984954833984375,
-0.00855255126953125,
0.014312744140625,
0.024444580078125,
0.0160675048828125,
-0.029571533203125,
0.006069183349609375,
-0.01439666748046875,
-0.004550933837890625,
-0.0287322998046875,
0.0219573974609375,
0.0003616809844970703,
-0.0264434814453125,
-0.005718231201171875,
-0.02557373046875,
-0.02056884765625,
-0.0005693435668945312,
0.00347137451171875,
0.003215789794921875,
0.026092529296875,
0.0030994415283203125,
0.0014209747314453125,
0.0221710205078125,
0.036956787109375,
0.0012006759643554688,
0.0007643699645996094,
0.00762939453125,
0.0482177734375,
0.0301361083984375,
-0.0017261505126953125,
-0.003643035888671875,
-0.0210113525390625,
-0.034027099609375,
-0.014556884765625,
-0.0013370513916015625,
-0.0178985595703125,
0.0009088516235351562,
0.01026153564453125,
-0.020294189453125,
0.015350341796875,
-0.0027561187744140625,
0.033660888671875,
-0.00251007080078125,
-0.00786590576171875,
-0.0038204193115234375,
0.0103607177734375,
0.00820159912109375,
0.0194091796875,
-0.01317596435546875,
0.007747650146484375,
0.04437255859375,
-0.002994537353515625,
-0.0069580078125,
-0.007160186767578125,
0.0014972686767578125,
-0.01003265380859375,
-0.006114959716796875,
-0.006824493408203125,
-0.006137847900390625,
-0.0098114013671875,
-0.000010311603546142578,
0.0128631591796875,
0.0252685546875,
-0.0037326812744140625,
0.00569915771484375,
0.0032787322998046875,
0.003993988037109375,
0.00830841064453125,
0.01479339599609375,
-0.00653839111328125,
-0.00791168212890625,
-0.049072265625,
-0.035858154296875,
-0.01334381103515625,
-0.05035400390625,
0.008270263671875,
0.005214691162109375,
0.00841522216796875,
0.020599365234375,
-0.032501220703125,
-0.00677490234375,
0.0228729248046875,
0.0270233154296875,
-0.01959228515625,
-0.037078857421875,
0.012847900390625,
-0.033172607421875,
0.0020599365234375,
-0.0243377685546875,
-0.0008931159973144531,
-0.038421630859375,
0.002056121826171875,
-0.0193939208984375,
-0.021240234375,
0.01837158203125,
-0.021240234375,
0.05706787109375,
0.028594970703125,
-0.022247314453125,
-0.0171356201171875,
-0.00882720947265625,
-0.04644775390625,
0.013458251953125,
-0.019622802734375,
0.007419586181640625,
-0.0004673004150390625,
0.0177459716796875,
-0.02459716796875,
-0.004459381103515625,
-0.00830841064453125,
-0.005596160888671875,
0.0234527587890625,
-0.019866943359375,
0.01059722900390625,
0.026336669921875,
-0.02093505859375,
-0.01116943359375,
0.00696563720703125,
0.03399658203125,
-0.0119476318359375,
0.009796142578125,
0.02783203125,
0.0174713134765625,
0.040252685546875,
0.0272064208984375,
0.006557464599609375,
-0.0090789794921875,
0.02056884765625,
-0.049835205078125,
0.00009453296661376953,
0.0234832763671875,
-0.0212554931640625,
-0.0228271484375,
0.0179290771484375,
-0.016693115234375,
0.003742218017578125,
0.038787841796875,
-0.0267486572265625,
0.00899505615234375,
-0.0091705322265625,
-0.003978729248046875,
-0.000591278076171875,
0.0031032562255859375,
-0.00020802021026611328,
-0.0121002197265625,
0.0213470458984375,
-0.01279449462890625,
-0.0300140380859375,
0.01020050048828125,
-0.004474639892578125,
-0.0304718017578125,
-0.04107666015625,
0.0150909423828125,
-0.01153564453125,
0.002223968505859375,
0.0263824462890625,
-0.034271240234375,
0.0355224609375,
-0.01219940185546875,
-0.01194000244140625,
0.016143798828125,
-0.01233673095703125,
-0.0272369384765625,
-0.0172576904296875,
-0.032928466796875,
-0.035064697265625,
-0.00237274169921875,
0.01375579833984375,
0.045318603515625,
-0.032745361328125,
-0.01611328125,
-0.04486083984375,
-0.0004839897155761719,
-0.018951416015625,
-0.00604248046875,
-0.00496673583984375,
0.0423583984375,
-0.007434844970703125,
0.0208282470703125,
-0.0313720703125,
0.005908966064453125,
-0.00865936279296875,
-0.005771636962890625,
0.0202178955078125,
0.00921630859375,
0.03472900390625,
0.033905029296875,
-0.0297698974609375,
0.005893707275390625,
-0.0006766319274902344,
-0.02325439453125,
0.01044464111328125,
-0.006313323974609375,
-0.005329132080078125,
0.0108184814453125,
-0.0038814544677734375,
-0.00860595703125,
0.01490020751953125,
0.0045928955078125,
-0.0143890380859375,
0.0170745849609375,
0.01314544677734375,
0.0096282958984375,
0.0169677734375,
0.00576019287109375,
-0.00891876220703125,
-0.047454833984375,
-0.012420654296875,
0.0302734375,
-0.0018873214721679688,
0.0033664703369140625,
-0.0007596015930175781,
-0.042816162109375,
-0.00293731689453125,
0.04730224609375,
-0.040374755859375,
0.0192413330078125,
-0.01024627685546875,
0.005748748779296875,
-0.000060677528381347656,
0.004611968994140625,
0.00743865966796875,
0.01153564453125,
-0.0005197525024414062,
0.00811767578125,
0.029205322265625,
0.0008029937744140625,
-0.00565338134765625,
0.018463134765625,
-0.0137786865234375,
0.028839111328125,
-0.044281005859375,
0.006847381591796875,
-0.0382080078125,
0.022216796875,
0.039642333984375,
0.007076263427734375,
-0.01483917236328125,
0.01454925537109375,
0.016632080078125,
0.02325439453125,
0.003154754638671875,
0.0004012584686279297,
0.004955291748046875,
-0.0224151611328125,
0.00600433349609375,
0.005401611328125,
-0.007106781005859375,
-0.0193328857421875,
0.005626678466796875,
-0.0038852691650390625,
-0.0017347335815429688,
0.044830322265625,
0.0287933349609375,
0.014190673828125,
0.0269317626953125,
0.0010251998901367188,
0.0340576171875,
0.0203094482421875,
-0.006195068359375,
-0.00146484375,
-0.006824493408203125,
-0.022308349609375,
0.001434326171875,
0.010223388671875,
0.005657196044921875,
-0.00048232078552246094,
0.011993408203125,
-0.01299285888671875,
0.00504302978515625,
-0.001979827880859375,
-0.0012340545654296875,
0.0129547119140625,
0.0271453857421875,
0.0001938343048095703,
-0.0116729736328125,
-0.037689208984375,
0.01308441162109375,
-0.0166168212890625,
0.00179290771484375,
0.0218658447265625,
0.00266265869140625,
0.0284271240234375,
-0.0267486572265625,
0.0262451171875,
0.0007472038269042969,
0.0171966552734375,
0.021942138671875,
-0.0211334228515625,
0.0195159912109375,
0.008819580078125,
0.03759765625,
0.0350341796875,
0.03369140625,
-0.044891357421875,
-0.0321044921875,
0.005344390869140625,
-0.02227783203125,
0.0172119140625,
-0.039703369140625,
-0.0224609375,
0.004024505615234375,
-0.0014390945434570312,
-0.04168701171875,
0.015960693359375,
0.0035266876220703125,
0.013031005859375,
0.006420135498046875,
0.0217742919921875,
0.06292724609375,
-0.0101470947265625,
0.0133514404296875,
0.0147247314453125,
-0.027252197265625,
0.0498046875,
-0.0159912109375,
0.01226806640625,
-0.007274627685546875,
-0.020172119140625,
0.0214996337890625,
0.00957489013671875,
-0.0262298583984375,
0.00489044189453125,
0.0059356689453125,
0.004299163818359375,
-0.0160369873046875,
0.0172576904296875,
-0.004940032958984375,
0.005428314208984375,
-0.0164794921875,
0.01216888427734375,
-0.0252532958984375,
-0.037109375,
-0.005382537841796875,
0.002155303955078125,
-0.0218658447265625,
-0.033905029296875,
-0.031768798828125,
-0.001735687255859375,
0.0281219482421875,
-0.0237579345703125,
-0.0256805419921875,
-0.00716400146484375,
-0.004390716552734375,
-0.006771087646484375,
-0.03936767578125,
-0.006259918212890625,
0.00145721435546875,
0.009674072265625,
0.03314208984375,
-0.0093841552734375,
0.01000213623046875,
0.028411865234375,
0.025634765625,
-0.0242462158203125,
-0.0083160400390625,
0.00638580322265625,
0.019744873046875,
-0.00757598876953125,
-0.026275634765625,
0.03173828125,
-0.00783538818359375,
0.01003265380859375,
0.0225677490234375,
-0.01392364501953125,
0.01023101806640625,
-0.01363372802734375,
0.025115966796875,
0.007232666015625,
-0.00974273681640625,
-0.021392822265625,
0.0025634765625,
-0.030242919921875,
-0.0390625,
0.00737762451171875,
-0.0006856918334960938,
-0.00013971328735351562,
0.003936767578125,
-0.0017566680908203125,
0.037872314453125,
0.005031585693359375,
-0.004669189453125,
-0.00997161865234375,
-0.0124359130859375,
-0.0305633544921875,
-0.0188751220703125,
-0.007110595703125,
-0.0195770263671875,
-0.047210693359375,
0.0232696533203125,
-0.034332275390625,
-0.0210113525390625,
0.0125579833984375,
-0.032958984375,
-0.015655517578125,
0.0065155029296875,
0.00740814208984375,
0.0021991729736328125,
-0.040924072265625,
-0.02630615234375,
0.0227508544921875,
-0.01445770263671875,
0.0164031982421875,
-0.0166015625,
-0.01160430908203125,
0.025054931640625,
0.0016841888427734375,
-0.0328369140625,
-0.0227203369140625,
-0.03753662109375,
-0.0341796875,
-0.005985260009765625,
-0.0223541259765625,
0.04254150390625,
0.023406982421875,
0.0035610198974609375,
-0.0279388427734375,
0.02459716796875,
0.0116424560546875,
0.01146697998046875,
0.00737762451171875,
-0.0011796951293945312,
0.009063720703125,
-0.044189453125,
0.040069580078125,
0.0089874267578125,
0.019073486328125,
0.0028705596923828125,
-0.009124755859375,
0.01287841796875,
-0.0193634033203125,
-0.01485443115234375,
-0.0210723876953125,
0.007312774658203125,
0.0016355514526367188,
-0.0140380859375,
0.008819580078125,
0.00537109375,
0.01039886474609375,
-0.0047454833984375,
-0.0269317626953125,
-0.033538818359375,
-0.00475311279296875,
-0.004467010498046875,
0.00797271728515625,
0.0092926025390625,
-0.00945281982421875,
-0.00862884521484375,
0.00939178466796875,
0.00939178466796875,
-0.0196685791015625,
-0.0038051605224609375,
0.0011730194091796875,
0.008392333984375,
-0.050628662109375,
0.01023101806640625,
-0.0193634033203125,
-0.0273590087890625,
-0.016693115234375,
-0.0257568359375,
-0.005733489990234375,
-0.027740478515625,
0.0030651092529296875,
-0.00022876262664794922,
0.034515380859375,
0.0020236968994140625,
0.0015897750854492188,
-0.0222625732421875,
-0.03045654296875,
0.009796142578125,
0.00856781005859375,
0.006908416748046875,
-0.02252197265625,
0.0278472900390625,
-0.0031032562255859375,
-0.0212554931640625,
-0.041656494140625,
-0.00775146484375,
0.004474639892578125,
-0.0073699951171875,
0.0129547119140625,
-0.046234130859375,
-0.016448974609375,
-0.001331329345703125,
-0.0018157958984375,
0.0239105224609375,
-0.014617919921875,
0.02130126953125,
-0.0087890625,
-0.03369140625,
0.01157379150390625,
-0.0105743408203125,
0.0000591278076171875,
-0.01678466796875,
0.01342010498046875,
0.0157318115234375,
-0.003936767578125,
-0.00640869140625,
-0.0206298828125,
-0.03363037109375,
0.00782012939453125,
-0.032562255859375,
-0.0135498046875,
0.010223388671875,
0.031158447265625,
0.03302001953125,
-0.03997802734375,
0.01512908935546875,
-0.01468658447265625,
-0.01174163818359375,
0.00629425048828125,
0.02081298828125,
-0.00949859619140625,
0.006336212158203125,
-0.01328277587890625,
0.01052093505859375,
0.0016641616821289062,
0.016510009765625,
-0.0247344970703125,
-0.0003554821014404297,
0.03326416015625,
-0.002010345458984375,
-0.0103759765625,
0.03509521484375,
0.009185791015625,
0.0229339599609375,
-0.0237579345703125,
0.0182037353515625,
0.005710601806640625,
0.0189666748046875,
0.00479888916015625,
-0.0207672119140625,
0.037200927734375,
0.01201629638671875,
0.0037937164306640625,
-0.0210113525390625,
0.01165008544921875,
0.043426513671875,
-0.0072479248046875,
0.03460693359375,
0.002288818359375,
-0.0111083984375,
-0.0163116455078125,
0.0290069580078125,
-0.0198516845703125,
-0.01233673095703125,
-0.0009255409240722656,
0.0345458984375,
0.024658203125,
0.0150146484375,
-0.0086212158203125,
0.009735107421875,
-0.00438690185546875,
-0.016082763671875,
-0.01168060302734375,
0.0191650390625,
-0.0277557373046875,
0.018798828125,
-0.01262664794921875,
-0.0067138671875,
0.0165863037109375,
-0.0111083984375,
-0.0076446533203125,
-0.0418701171875,
-0.0270538330078125,
0.0266876220703125,
-0.025360107421875,
0.031982421875,
0.0167236328125,
0.004001617431640625,
-0.005950927734375,
-0.0010318756103515625,
-0.0018177032470703125,
-0.0206756591796875,
0.01371002197265625,
-0.01322174072265625,
-0.0101318359375,
0.0179443359375,
-0.00621795654296875,
-0.01031494140625,
-0.022369384765625,
-0.01020050048828125,
0.0027942657470703125,
-0.00945281982421875,
0.036651611328125,
0.004573822021484375,
-0.02178955078125,
0.023284912109375,
-0.020355224609375,
0.0293731689453125,
-0.02203369140625,
-0.025360107421875,
-0.038818359375,
-0.01300811767578125,
0.00872802734375,
0.00609588623046875,
0.013641357421875,
-0.00069427490234375,
-0.005466461181640625,
0.00858306884765625,
-0.0158843994140625,
-0.00762176513671875,
-0.05059814453125,
-0.004917144775390625,
-0.0224761962890625,
0.031951904296875,
-0.0036449432373046875,
-0.021453857421875,
0.01080322265625,
-0.01617431640625,
-0.019012451171875,
0.00615692138671875,
0.026641845703125,
0.01202392578125,
-0.040863037109375,
-0.0210113525390625,
-0.040191650390625,
0.032470703125,
0.0038700103759765625,
-0.007274627685546875,
0.007648468017578125,
-0.007843017578125,
0.02386474609375,
-0.007068634033203125,
-0.03045654296875,
-0.019805908203125,
-0.03302001953125,
0.000020563602447509766,
0.00032138824462890625,
0.01479339599609375,
-0.0201873779296875,
0.02703857421875,
-0.01308441162109375,
-0.0119171142578125,
0.008209228515625,
-0.0037403106689453125,
-0.01288604736328125,
-0.01296234130859375,
-0.0126190185546875,
-0.0051727294921875,
0.0026721954345703125,
0.00942230224609375,
-0.005275726318359375,
0.038543701171875,
-0.008575439453125,
0.002918243408203125,
0.00740814208984375,
-0.0012235641479492188,
0.025665283203125,
-0.01367950439453125,
0.034271240234375,
-0.01094818115234375,
0.01776123046875,
-0.0184173583984375,
-0.022247314453125,
-0.0213165283203125,
0.0200958251953125,
0.0186920166015625,
-0.0009222030639648438,
0.0124359130859375,
-0.030120849609375,
-0.0396728515625,
-0.02606201171875,
0.0167236328125,
0.01023101806640625,
0.007328033447265625,
0.0218963623046875,
0.0225677490234375,
0.0029296875,
0.0246124267578125,
-0.036529541015625,
-0.00951385498046875,
-0.0066070556640625,
0.0194091796875,
-0.01541900634765625,
0.0311431884765625,
-0.00693511962890625,
0.045745849609375,
-0.0006308555603027344,
0.002124786376953125,
0.049163818359375,
0.0019016265869140625,
0.00170135498046875,
0.00688934326171875,
-0.0188446044921875,
0.025634765625,
0.0186614990234375,
0.02569580078125,
0.01354217529296875,
0.0133209228515625,
-0.010284423828125,
-0.012603759765625,
0.02813720703125,
0.0064544677734375,
-0.0263519287109375,
-0.03863525390625,
0.0007119178771972656,
0.011199951171875,
-0.0045623779296875,
-0.002033233642578125,
0.0024242401123046875,
-0.0085601806640625,
0.0230712890625,
0.018798828125,
-0.0247802734375,
0.023834228515625,
0.04254150390625,
0.0311126708984375,
-0.0025348663330078125,
0.00376129150390625,
0.0035800933837890625,
0.049407958984375,
0.0165252685546875,
-0.0239410400390625,
-0.0193023681640625,
-0.0020542144775390625,
-0.02142333984375,
0.039154052734375,
-0.0130462646484375,
-0.016021728515625,
-0.00011211633682250977,
-0.0123291015625,
-0.0210113525390625,
0.06280517578125,
-0.01220703125,
0.0113067626953125,
-0.0191192626953125,
0.03729248046875,
0.013824462890625,
0.04144287109375,
-0.031219482421875,
0.0053558349609375,
-0.03363037109375,
-0.0090789794921875,
0.018585205078125,
0.004390716552734375,
-0.00701141357421875,
-0.0156707763671875,
0.0081634521484375,
-0.03363037109375,
-0.0160369873046875,
-0.027252197265625,
-0.002147674560546875,
0.005817413330078125,
-0.006801605224609375,
-0.0310821533203125,
-0.012054443359375,
-0.01212310791015625,
-0.01641845703125,
0.005260467529296875,
0.01201629638671875,
-0.01084136962890625,
0.0014629364013671875,
0.005580902099609375,
-0.0100860595703125,
-0.0004100799560546875,
-0.02252197265625,
0.01190948486328125,
-0.0162811279296875,
-0.01232147216796875,
0.0054779052734375,
0.0005373954772949219,
-0.0290374755859375,
-0.004268646240234375,
-0.0020847320556640625,
0.0186767578125,
0.018646240234375,
0.010162353515625,
-0.01491546630859375,
0.00927734375,
0.00756072998046875,
0.0271453857421875,
0.02655029296875,
0.002002716064453125,
0.0131072998046875,
-0.052276611328125,
-0.007904052734375,
0.035797119140625,
-0.0166778564453125,
0.005352020263671875,
-0.00004982948303222656,
-0.002696990966796875,
-0.052459716796875,
0.02734375,
-0.0132904052734375,
-0.034576416015625,
-0.01300811767578125,
-0.0036487579345703125,
0.00009196996688842773,
0.036346435546875,
-0.021240234375,
0.0114593505859375,
0.03363037109375,
-0.003803253173828125,
0.019989013671875,
-0.00836181640625,
0.0007715225219726562,
-0.025909423828125,
-0.03485107421875,
-0.0325927734375,
0.0128173828125,
-0.00965118408203125,
0.0157623291015625,
0.0163421630859375,
0.0028247833251953125,
-0.0214996337890625,
-0.010162353515625,
-0.013397216796875,
-0.01280975341796875,
0.02337646484375,
0.0013437271118164062,
0.00414276123046875,
0.00608062744140625,
-0.0177459716796875,
-0.01084136962890625,
-0.029083251953125,
-0.0220947265625,
-0.00620269775390625,
0.00787353515625,
-0.031585693359375,
-0.003368377685546875,
-0.011199951171875,
0.008880615234375,
0.01114654541015625,
0.02935791015625,
-0.022613525390625,
0.01558685302734375,
-0.010711669921875,
-0.0308380126953125,
-0.02960205078125,
-0.0050048828125,
0.005306243896484375,
0.0019092559814453125,
0.01161956787109375,
-0.005756378173828125,
-0.024871826171875,
0.03692626953125,
-0.007289886474609375,
0.0057220458984375,
0.0245361328125,
0.018096923828125,
-0.0002465248107910156,
0.00942230224609375,
-0.01132965087890625,
0.041015625,
0.0026073455810546875,
-0.0053558349609375,
0.0006899833679199219,
0.01030731201171875,
-0.0183868408203125,
-0.0144500732421875,
-0.01435089111328125,
-0.0268096923828125,
-0.0197296142578125,
0.0302581787109375,
0.016998291015625,
0.016357421875,
0.019134521484375,
-0.01502227783203125,
0.0265960693359375,
-0.024169921875,
0.0229034423828125,
0.01336669921875,
0.0097198486328125,
-0.036865234375,
-0.016754150390625,
-0.006732940673828125,
-0.015838623046875,
-0.00644683837890625,
0.00008314847946166992,
0.004604339599609375,
-0.0270843505859375,
0.0135498046875,
0.00914764404296875,
-0.0002930164337158203,
0.040924072265625,
0.00969696044921875,
-0.0025920867919921875,
0.007061004638671875,
-0.005279541015625,
-0.01108551025390625,
-0.01392364501953125,
-0.00638580322265625,
0.014892578125,
0.000020802021026611328,
0.033599853515625,
-0.0131072998046875,
-0.0185394287109375,
0.01446533203125,
-0.00885772705078125,
-0.0124664306640625,
0.0219879150390625,
0.00618743896484375,
0.00690460205078125,
-0.0153350830078125,
-0.0160369873046875,
0.00018715858459472656,
-0.00799560546875,
0.0037841796875,
0.0140228271484375,
-0.02227783203125,
-0.028839111328125,
-0.037872314453125,
0.01143646240234375,
-0.00450897216796875,
-0.00994873046875,
-0.03009033203125,
0.005062103271484375,
0.001491546630859375,
0.0018091201782226562,
-0.00850677490234375,
0.0218963623046875,
-0.006984710693359375,
-0.0106048583984375,
0.0154266357421875,
-0.0012788772583007812,
-0.01065826416015625,
-0.025634765625,
0.014251708984375,
0.0285491943359375,
-0.0227508544921875,
-0.0248870849609375,
-0.015960693359375,
0.029998779296875,
0.01064300537109375,
-0.0161590576171875,
-0.03472900390625,
-0.026885986328125,
-0.00423431396484375,
0.01114654541015625,
0.044189453125,
0.022125244140625,
0.00971221923828125,
-0.007659912109375,
-0.016845703125,
-0.0022220611572265625,
0.00002771615982055664,
0.0167083740234375,
0.0239410400390625,
-0.0015239715576171875,
-0.00939178466796875,
-0.047821044921875,
0.0006527900695800781,
-0.0005664825439453125,
0.0169219970703125,
0.0009908676147460938,
-0.01454925537109375,
-0.038604736328125,
0.04327392578125,
0.0211029052734375,
-0.04266357421875,
0.0033321380615234375,
-0.006641387939453125,
-0.00432586669921875,
-0.02081298828125,
-0.01032257080078125,
-0.0008816719055175781,
-0.0017299652099609375,
-0.0248870849609375,
0.03546142578125,
-0.0013170242309570312,
-0.0318603515625,
0.005767822265625,
0.01611328125,
-0.019195556640625,
0.0020542144775390625,
-0.03076171875,
-0.0081787109375,
0.00008279085159301758,
0.007709503173828125,
0.004413604736328125,
-0.0010461807250976562,
-0.0019445419311523438,
-0.009063720703125,
-0.0090789794921875,
0.008087158203125,
0.006793975830078125,
-0.01551055908203125,
0.0304412841796875,
0.040985107421875,
-0.039886474609375,
-0.0264129638671875,
-0.002960205078125,
0.0198516845703125,
0.0004398822784423828,
-0.016815185546875,
0.02520751953125,
0.0074462890625,
-0.0169219970703125,
0.01073455810546875,
-0.0306549072265625,
-0.04205322265625,
0.016204833984375,
0.0184326171875,
-0.00975799560546875,
0.0159759521484375,
0.0239105224609375,
0.0343017578125,
0.0185394287109375,
-0.0014009475708007812,
-0.0194091796875,
-0.01181793212890625,
0.005462646484375,
0.02423095703125,
0.01316070556640625,
0.019073486328125,
0.020263671875,
0.037841796875,
-0.01085662841796875,
-0.0137176513671875,
-0.016632080078125,
0.022735595703125,
0.014007568359375,
0.01348114013671875,
-0.01071929931640625,
-0.0087738037109375,
0.0051116943359375,
-0.01029205322265625,
0.00173187255859375,
-0.036865234375,
0.01441192626953125,
0.0105743408203125,
0.026885986328125,
0.025787353515625,
-0.0098724365234375,
-0.01751708984375,
0.01056671142578125,
0.0022144317626953125,
0.01953125,
0.0082550048828125,
0.00809478759765625,
-0.037322998046875,
0.0173187255859375,
-0.0008001327514648438,
0.04327392578125,
-0.0255126953125,
-0.003513336181640625,
0.002376556396484375,
0.020477294921875,
0.0235137939453125,
-0.00281524658203125,
-0.0136566162109375,
0.023468017578125,
-0.01288604736328125,
-0.01702880859375,
0.019439697265625,
0.01110076904296875,
0.017242431640625,
0.03387451171875,
-0.038360595703125,
-0.0234527587890625,
-0.00438690185546875,
0.00799560546875,
0.05157470703125,
-0.004856109619140625,
0.0019140243530273438,
0.0103912353515625,
-0.027435302734375,
-0.00003331899642944336,
0.00785064697265625,
0.0165252685546875,
-0.0176849365234375,
0.01153564453125,
0.00839996337890625,
-0.01885986328125,
-0.000652313232421875,
-0.0093841552734375,
0.01708984375,
-0.00896453857421875,
0.017730712890625,
-0.0035839080810546875,
-0.06353759765625,
-0.016448974609375,
0.0162506103515625,
-0.00039076805114746094,
-0.01215362548828125,
0.005298614501953125,
0.003986358642578125,
0.01605224609375,
-0.037353515625,
-0.025177001953125,
0.0031490325927734375,
0.005832672119140625,
0.020751953125,
0.0205230712890625,
-0.0254058837890625,
0.0193939208984375,
0.035614013671875,
0.036376953125,
-0.0202178955078125,
0.0206756591796875,
-0.0158843994140625,
-0.0020732879638671875,
-0.0207672119140625,
0.0008859634399414062,
0.00959014892578125,
0.035491943359375,
0.01678466796875,
0.01422882080078125,
-0.0204620361328125,
-0.0171051025390625,
0.006732940673828125,
0.004669189453125,
0.003414154052734375,
-0.01482391357421875,
-0.004177093505859375,
-0.00696563720703125,
-0.0278778076171875,
0.00518035888671875,
0.0010528564453125,
-0.049713134765625,
-0.00377655029296875,
0.00013768672943115234,
-0.0183868408203125,
0.0015840530395507812,
0.00583648681640625,
-0.006443023681640625,
-0.0233612060546875,
-0.005191802978515625,
-0.0034275054931640625,
0.01099395751953125,
0.00948333740234375,
0.0257110595703125,
0.00946807861328125,
0.0280914306640625,
0.0300140380859375,
0.03546142578125,
-0.0085906982421875,
-0.027587890625,
0.01337432861328125,
-0.01189422607421875,
0.03143310546875,
0.01094818115234375,
-0.0032806396484375,
0.011077880859375,
0.0007758140563964844,
0.01824951171875,
0.0165252685546875,
0.0145263671875,
0.01435089111328125,
0.01056671142578125,
0.01190185546875,
-0.019287109375,
-0.007293701171875,
-0.028533935546875,
-0.0056610107421875,
0.060577392578125,
0.0101318359375,
0.0214385986328125,
-0.0015077590942382812,
0.031951904296875,
0.0264739990234375,
0.02972412109375,
0.0007634162902832031,
0.0007162094116210938,
-0.0210723876953125,
0.0009908676147460938,
-0.0011358261108398438,
0.004085540771484375,
0.00878143310546875,
0.01019287109375,
-0.0187225341796875,
0.0182037353515625,
0.02972412109375,
-0.012908935546875,
0.031158447265625,
-0.012725830078125,
0.038909912109375,
-0.01396942138671875,
0.003452301025390625,
0.0251007080078125,
-0.0254364013671875,
0.005496978759765625,
-0.0288238525390625,
-0.02081298828125,
-0.0002970695495605469,
0.014617919921875,
0.0121002197265625,
-0.022674560546875,
0.0290985107421875,
-0.005352020263671875,
0.004009246826171875,
0.0035343170166015625,
0.03668212890625,
0.0016040802001953125,
-0.01776123046875,
0.01410675048828125,
-0.00958251953125,
-0.00002372264862060547,
0.0273590087890625,
0.01020050048828125,
-0.002735137939453125,
-0.033447265625,
0.0130615234375,
-0.0134735107421875,
-0.01186370849609375,
0.03143310546875,
-0.00830078125,
-0.0116119384765625,
-0.0108795166015625,
-0.0227813720703125,
-0.034423828125,
0.009063720703125,
0.004302978515625,
0.0039520263671875,
-0.01171875,
0.01751708984375,
-0.0098876953125,
-0.00890350341796875,
-0.0011568069458007812,
-0.004596710205078125,
-0.038970947265625,
-0.00244140625,
0.002452850341796875,
-0.01007080078125,
0.02044677734375,
-0.0186767578125,
0.035400390625,
0.0019893646240234375,
-0.01873779296875,
-0.019989013671875,
-0.017791748046875,
0.01107025146484375,
-0.00368499755859375,
-0.0071868896484375,
-0.0082855224609375,
-0.0167236328125,
-0.032958984375,
0.00696563720703125,
-0.0055084228515625,
0.034698486328125,
-0.007343292236328125,
-0.0097198486328125,
-0.0312042236328125,
0.0008530616760253906,
0.020843505859375,
-0.00894927978515625,
0.0186614990234375,
0.0091552734375,
-0.00806427001953125,
-0.0079345703125,
-0.0179901123046875,
-0.00881195068359375,
0.0106201171875,
0.0157470703125,
-0.0104827880859375,
0.0182037353515625,
0.01116943359375,
-0.005939483642578125,
-0.0012178421020507812,
0.0144195556640625,
-0.003192901611328125,
0.0262451171875,
0.027862548828125,
-0.0258636474609375,
0.01678466796875,
-0.0149078369140625,
0.02874755859375,
-0.022613525390625,
-0.03021240234375,
-0.004215240478515625,
0.01325225830078125,
0.021881103515625,
-0.0172271728515625,
-0.02783203125,
-0.0010118484497070312,
-0.0016565322875976562,
-0.01885986328125,
0.0097808837890625,
-0.039276123046875,
0.01678466796875,
0.004070281982421875,
-0.009735107421875,
-0.021026611328125,
0.015716552734375,
0.03717041015625,
-0.0220184326171875,
0.00635528564453125,
-0.0202789306640625,
-0.0024547576904296875,
0.01605224609375,
0.00957489013671875,
-0.021270751953125,
0.0220947265625,
0.004589080810546875,
-0.011871337890625,
-0.005855560302734375,
-0.01947021484375,
-0.035003662109375,
0.031982421875,
-0.019256591796875,
-0.01305389404296875,
0.0096588134765625,
0.031890869140625,
0.0226898193359375,
-0.01026153564453125,
0.0110626220703125,
-0.0014410018920898438,
0.011962890625,
-0.01280975341796875,
-0.0046234130859375,
-0.0107269287109375,
-0.0172119140625,
-0.0170440673828125,
0.031524658203125,
0.00928497314453125,
-0.02618408203125,
-0.0010585784912109375,
-0.00617218017578125,
-0.046966552734375,
0.032958984375,
-0.006351470947265625,
-0.0139007568359375,
-0.00725555419921875,
0.041778564453125,
-0.0184478759765625,
0.022552490234375,
0.00331878662109375,
-0.00875091552734375,
0.008636474609375,
-0.0102386474609375,
0.0263519287109375,
-0.028106689453125,
0.021270751953125,
0.0009665489196777344,
-0.01250457763671875,
0.0301971435546875,
0.004100799560546875,
0.00807952880859375,
0.018890380859375,
0.03057861328125,
-0.007762908935546875,
0.00513458251953125,
-0.016143798828125,
0.01763916015625,
0.01076507568359375,
-0.0005655288696289062,
0.0214385986328125,
-0.00868988037109375,
0.010833740234375,
-0.0245361328125,
0.014434814453125,
0.00754547119140625,
-0.01172637939453125,
-0.014312744140625,
0.01904296875,
-0.0145111083984375,
-0.0167388916015625,
-0.0209197998046875,
0.002071380615234375,
-0.0194244384765625,
-0.0204925537109375,
0.0310211181640625,
0.030548095703125,
-0.034332275390625,
0.01525115966796875,
0.0126495361328125,
-0.014923095703125,
0.0170135498046875,
-0.000009655952453613281,
0.02008056640625,
-0.01288604736328125,
0.0110626220703125,
-0.02459716796875,
-0.016815185546875,
-0.03912353515625,
0.0183868408203125,
-0.00992584228515625,
-0.006137847900390625,
0.00637054443359375,
-0.036773681640625,
0.0225982666015625,
-0.02813720703125,
0.0221099853515625,
0.0138702392578125,
-0.01554107666015625,
0.024810791015625,
0.037994384765625,
-0.023834228515625,
-0.01065826416015625,
0.00611114501953125,
-0.0292205810546875,
-0.0035686492919921875,
0.0007252693176269531,
0.035003662109375,
0.01183319091796875,
-0.0200347900390625,
-0.00882720947265625,
-0.048583984375,
-0.039459228515625,
-0.02606201171875,
0.0265655517578125,
0.03521728515625,
0.0017843246459960938,
0.014892578125,
0.0309906005859375,
0.0306396484375,
-0.004467010498046875,
-0.019287109375,
-0.0341796875,
-0.005031585693359375,
0.00855255126953125,
0.0306854248046875,
-0.023345947265625,
0.0027332305908203125,
-0.01337432861328125,
-0.0079193115234375,
0.0218353271484375,
-0.0079345703125,
0.022186279296875,
0.0212249755859375,
-0.004547119140625,
-0.00695037841796875,
-0.002925872802734375,
0.0228424072265625,
-0.0252685546875,
-0.005252838134765625,
0.005279541015625,
-0.00001138448715209961,
-0.006744384765625,
0.007427215576171875,
-0.0159759521484375,
0.0179443359375,
-0.004550933837890625,
-0.0106658935546875,
0.004459381103515625,
0.022216796875,
-0.0149688720703125,
0.0249481201171875,
-0.0390625,
-0.01218414306640625,
0.0095672607421875,
0.00786590576171875,
-0.001110076904296875,
0.016357421875,
-0.0321044921875,
-0.0194244384765625,
0.02490234375,
0.0194091796875,
0.05145263671875,
0.0005249977111816406,
0.01560211181640625,
0.0004265308380126953,
-0.0305023193359375,
0.0007333755493164062,
0.004638671875,
0.005657196044921875,
-0.0401611328125,
-0.008453369140625,
-0.02044677734375,
-0.0179443359375,
0.0162506103515625,
-0.032440185546875,
-0.0014753341674804688,
-0.00775909423828125,
-0.02020263671875,
0.0254669189453125,
0.00986480712890625,
0.049041748046875,
-0.0386962890625,
-0.0240478515625,
-0.007068634033203125,
0.0202484130859375,
0.0026111602783203125,
-0.016082763671875,
-0.020751953125,
0.02752685546875,
0.0207366943359375,
0.029449462890625,
-0.00948333740234375,
0.02557373046875,
0.0072479248046875,
-0.0170135498046875,
-0.01027679443359375,
-0.0020771026611328125,
0.01076507568359375,
0.01140594482421875,
-0.01531982421875,
0.005504608154296875,
-0.0023040771484375,
-0.0295867919921875,
-0.0002856254577636719,
0.004909515380859375,
0.04559326171875,
-0.005340576171875,
-0.014892578125,
-0.0100860595703125,
0.01082611083984375,
0.0022144317626953125,
0.00994873046875,
0.004619598388671875,
0.0152435302734375,
-0.0007600784301757812,
-0.0095672607421875,
0.01184844970703125,
0.0252227783203125,
-0.004306793212890625,
-0.007183074951171875,
0.0007328987121582031,
0.00328826904296875,
0.034088134765625,
0.021087646484375,
-0.0281982421875,
0.0024166107177734375,
-0.0160980224609375,
-0.0026111602783203125,
-0.0281829833984375,
-0.0010128021240234375,
-0.03143310546875,
0.0043487548828125,
0.01361846923828125,
0.022705078125,
-0.057403564453125,
0.046905517578125,
0.031280517578125,
-0.0208892822265625,
-0.014892578125,
0.0149993896484375,
0.0078125,
0.017547607421875,
0.027008056640625,
-0.00713348388671875,
-0.0300445556640625,
-0.01204681396484375,
0.025299072265625,
-0.035247802734375,
-0.005046844482421875,
-0.00899505615234375,
-0.0042572021484375,
-0.0235595703125,
0.0257110595703125,
-0.01303863525390625,
0.00859832763671875,
0.0180816650390625,
0.00868988037109375,
-0.0243682861328125,
-0.003810882568359375,
0.03607177734375,
0.01091766357421875,
-0.010589599609375,
-0.0081329345703125,
0.00586700439453125,
0.043701171875,
0.00308990478515625,
0.006290435791015625,
0.01114654541015625,
-0.0209197998046875,
-0.0082244873046875,
0.031646728515625,
-0.0157318115234375,
0.0367431640625,
0.01265716552734375,
0.03289794921875,
-0.048248291015625,
-0.0037593841552734375,
0.0175628662109375,
0.00812530517578125,
0.012908935546875,
-0.00643157958984375,
0.002376556396484375,
-0.0177764892578125,
-0.0013742446899414062,
0.039947509765625,
-0.01050567626953125,
0.0141754150390625,
0.0007266998291015625,
-0.011749267578125,
-0.0027923583984375,
0.022308349609375,
-0.0012674331665039062,
0.04412841796875,
0.0232391357421875,
0.022918701171875,
-0.0036487579345703125,
-0.02392578125,
-0.0147705078125,
0.0291290283203125,
0.006946563720703125,
-0.01178741455078125,
0.032012939453125,
-0.004520416259765625,
0.025146484375,
-0.00681304931640625,
-0.00551605224609375,
-0.00833892822265625,
-0.0266571044921875,
0.004566192626953125,
-0.00063323974609375,
0.0291748046875,
0.01520538330078125,
0.006420135498046875,
-0.00804901123046875,
-0.0013980865478515625,
-0.036529541015625,
-0.0265655517578125,
-0.0127716064453125,
0.023101806640625,
-0.0232086181640625,
-0.01873779296875,
-0.0197296142578125,
0.004116058349609375,
-0.0305328369140625,
-0.0117950439453125,
-0.02996826171875,
-0.0018329620361328125,
0.0184326171875,
0.0010423660278320312,
-0.0016336441040039062,
-0.036834716796875,
0.01093292236328125,
-0.03228759765625,
0.0117340087890625,
-0.0037517547607421875,
0.00724029541015625,
-0.0139617919921875,
0.0094146728515625,
-0.014984130859375,
0.004192352294921875,
-0.0259552001953125,
0.00344085693359375,
0.0018110275268554688,
0.0131988525390625,
0.0116119384765625,
0.029937744140625,
0.01953125,
-0.007244110107421875,
-0.01087188720703125,
-0.016357421875,
0.01611328125,
-0.001293182373046875,
-0.02880859375,
0.01513671875,
-0.004802703857421875,
0.0178985595703125,
0.00859832763671875,
-0.0197296142578125,
0.0296630859375,
-0.01441192626953125,
0.0128173828125,
0.0034027099609375,
0.0201568603515625,
-0.0178375244140625,
-0.0171356201171875,
0.0020427703857421875,
-0.0072479248046875,
-0.00412750244140625,
-0.023406982421875,
-0.00534820556640625,
-0.030364990234375,
0.007541656494140625,
0.016448974609375,
-0.00421142578125,
0.041534423828125,
-0.028076171875,
0.008392333984375,
0.0210723876953125,
-0.0143890380859375,
0.02630615234375,
0.0107269287109375,
-0.0023937225341796875,
0.0163116455078125,
-0.0208892822265625,
0.0011987686157226562,
0.006938934326171875,
-0.0071563720703125,
0.0265350341796875,
-0.00009268522262573242,
-0.00634765625,
0.0185089111328125,
0.01522064208984375,
-0.0195465087890625,
0.025604248046875,
0.0008096694946289062,
-0.04156494140625,
-0.0144500732421875,
0.02178955078125,
-0.0254364013671875,
0.016143798828125,
-0.007106781005859375,
-0.017547607421875,
0.0012378692626953125,
-0.005657196044921875,
-0.020263671875,
0.025787353515625,
0.0111083984375,
0.0007605552673339844,
-0.0174560546875,
0.0114288330078125,
-0.039947509765625,
-0.006061553955078125,
-0.00347137451171875,
-0.0294036865234375,
0.0333251953125,
0.0218505859375,
-0.024322509765625,
0.002574920654296875,
-0.0117645263671875,
0.0033111572265625,
0.042144775390625,
0.0000015497207641601562,
0.01617431640625,
-0.018157958984375,
0.00785064697265625,
-0.0210723876953125,
-0.018768310546875,
0.01256561279296875,
-0.011566162109375,
-0.015960693359375,
0.0024967193603515625,
-0.003917694091796875,
-0.0264892578125,
-0.0254669189453125,
-0.004711151123046875,
0.007091522216796875,
0.0045013427734375,
-0.010284423828125,
0.00994110107421875,
-0.026458740234375,
-0.0234832763671875,
-0.007747650146484375,
0.0090789794921875,
0.0015287399291992188,
0.0023021697998046875,
0.0186004638671875,
0.0286407470703125,
0.010467529296875,
-0.009185791015625,
-0.0197906494140625,
0.0037078857421875,
-0.002849578857421875,
-0.01467132568359375,
0.0268707275390625,
0.0237579345703125,
0.01251983642578125,
0.0207366943359375,
0.0046539306640625,
0.0076904296875,
-0.0019140243530273438,
0.01358795166015625,
-0.01183319091796875,
-0.0352783203125,
-0.042449951171875,
-0.035308837890625,
-0.017822265625,
0.01078033447265625,
0.02239990234375,
0.00003325939178466797,
-0.015472412109375,
-0.0102996826171875,
0.01036834716796875,
-0.0261688232421875,
-0.0099029541015625,
0.031036376953125,
0.00047397613525390625,
0.0164031982421875,
-0.00264739990234375,
-0.01255035400390625,
0.0184173583984375,
-0.01152801513671875,
-0.00029468536376953125,
0.01105499267578125,
0.00925445556640625,
-0.00048661231994628906,
0.0288238525390625,
0.01200103759765625,
-0.0013666152954101562,
-0.01415252685546875,
-0.0203399658203125,
0.007678985595703125,
0.0187225341796875,
-0.0091400146484375,
0.009307861328125,
0.010101318359375,
-0.0208282470703125,
-0.034698486328125,
-0.00005829334259033203,
0.006160736083984375,
-0.006717681884765625,
0.0206756591796875,
0.0018978118896484375,
0.0233917236328125,
0.0154876708984375,
-0.0245819091796875,
-0.018829345703125,
0.0041961669921875,
-0.0168304443359375,
0.01056671142578125,
-0.0221710205078125,
-0.00553131103515625,
0.00934600830078125,
-0.03314208984375,
0.017608642578125,
0.0102081298828125,
-0.015899658203125,
0.01413726806640625,
-0.005786895751953125,
0.0271453857421875,
0.008636474609375,
-0.017425537109375,
0.0285491943359375,
-0.0025787353515625,
-0.007198333740234375,
-0.0169525146484375,
-0.0160675048828125,
0.026947021484375,
0.0294189453125,
0.0051116943359375,
0.0154571533203125,
-0.044403076171875,
-0.0012073516845703125,
-0.002048492431640625,
0.0214385986328125,
0.00467681884765625,
-0.0006589889526367188,
0.0174407958984375,
0.023590087890625,
0.0255126953125,
0.02435302734375,
-0.020843505859375,
0.01593017578125,
0.00968170166015625,
0.026397705078125,
-0.01323699951171875,
-0.0018129348754882812,
0.036590576171875,
-0.01235198974609375,
0.0261383056640625,
0.006259918212890625,
-0.032958984375,
-0.006656646728515625,
0.0159759521484375,
0.01104736328125,
-0.02947998046875,
0.003765106201171875,
-0.0259246826171875,
0.007419586181640625,
0.017242431640625,
-0.0006618499755859375,
-0.00521087646484375,
-0.0139007568359375,
0.002735137939453125,
0.020172119140625,
-0.0172882080078125,
0.005107879638671875,
0.00836944580078125,
-0.0164947509765625,
0.0029239654541015625,
0.03643798828125,
-0.042633056640625,
-0.01364898681640625,
0.01513671875,
-0.005641937255859375,
0.0005841255187988281,
-0.01348876953125,
-0.0233001708984375,
-0.0157470703125,
0.0011777877807617188,
-0.0020885467529296875,
0.0205230712890625,
0.0142822265625,
-0.037017822265625,
-0.04339599609375,
0.038970947265625,
0.00795745849609375,
-0.0229949951171875,
0.0290985107421875,
0.0195465087890625,
-0.00531768798828125,
0.053924560546875,
0.03857421875,
0.0011835098266601562,
-0.0225067138671875,
0.02081298828125,
0.0244903564453125,
-0.036956787109375,
-0.00015246868133544922,
-0.00859832763671875,
0.0056304931640625,
0.00215911865234375,
-0.01084136962890625,
-0.000046133995056152344,
0.0241851806640625,
-0.036376953125,
0.035736083984375,
-0.0069732666015625,
-0.0026721954345703125,
-0.00023066997528076172,
-0.007450103759765625,
0.004604339599609375,
-0.00696563720703125,
0.01201629638671875,
0.0098419189453125,
0.0293731689453125,
-0.0224456787109375,
-0.0085601806640625,
-0.0128326416015625,
0.0275726318359375,
0.00919342041015625,
0.01093292236328125,
0.0048828125,
0.003917694091796875,
-0.033172607421875,
-0.016510009765625,
-0.00565338134765625,
-0.01197052001953125,
0.00246429443359375,
0.029815673828125,
0.01238250732421875,
-0.0176544189453125,
0.0162506103515625,
-0.025238037109375,
-0.0062408447265625,
0.0225067138671875,
0.01056671142578125,
-0.0160064697265625,
0.01947021484375,
0.00954437255859375,
-0.0056304931640625,
0.0174560546875,
0.01361846923828125,
-0.0280303955078125,
-0.02459716796875,
-0.0189056396484375,
0.0211181640625,
-0.0206756591796875,
-0.07891845703125,
-0.03338623046875,
0.01154327392578125,
-0.0360107421875,
-0.004184722900390625,
0.0212554931640625,
-0.0185394287109375,
-0.04229736328125,
-0.01812744140625,
0.015167236328125,
0.005275726318359375,
0.0255889892578125,
0.007488250732421875,
-0.040069580078125,
-0.016754150390625,
-0.0110015869140625,
-0.0377197265625,
-0.0186920166015625,
-0.009735107421875,
0.0280914306640625,
0.019378662109375,
-0.01526641845703125,
0.0022182464599609375,
0.0192108154296875,
0.0148162841796875,
-0.01763916015625,
-0.0018854141235351562,
0.0247344970703125,
-0.0011320114135742188,
-0.01549530029296875,
0.0156707763671875,
-0.046112060546875,
0.032958984375,
0.017578125,
0.014312744140625,
-0.005084991455078125,
-0.000789642333984375,
0.0014715194702148438,
-0.0142364501953125,
0.01293182373046875,
-0.005153656005859375,
0.015380859375,
0.0066070556640625,
-0.0254364013671875,
0.00887298583984375,
0.0135345458984375,
0.03668212890625,
0.019866943359375,
-0.004779815673828125,
0.024627685546875,
-0.005710601806640625,
-0.01568603515625,
0.0224609375,
0.0269775390625,
-0.0004620552062988281,
0.0179595947265625,
-0.00782012939453125,
-0.019927978515625,
-0.033843994140625,
0.02349853515625,
0.0034046173095703125,
0.03729248046875,
0.005733489990234375,
0.0245361328125,
0.0090484619140625,
0.00435638427734375,
-0.00020122528076171875,
0.031829833984375,
0.0012273788452148438,
0.04931640625,
0.0007462501525878906
] |
ours_505
|
Suppose \(n\) is nonzero. Consider placing the singers into groups such that if for some two people \(x\) and \(y\), \(x\) wishes to perform right after \(y\), then \(x\) and \(y\) are in the same group. Note that each of these groups can be ordered in exactly one way, since every person, other than one person, is performing immediately after a fixed person in the group. (Each group can be ordered in at least one way, as \(n \neq 0\)). Then, if there are \(g\) groups, we can see that \(n = g!\).
Thus \(n\) is among \(10!, 9!, \ldots, 1!\). It is not hard to show that all these can be achieved. Now, the product is
\[
10! \times 9! \times \cdots \times 2! \times 1!
\]
To compute the answer, Legendre's formula gives an answer of
\[
\begin{gathered}
\left(\left\lfloor\frac{10}{2}\right\rfloor+\left\lfloor\frac{10}{4}\right\rfloor + \ldots\right) + \left(\left\lfloor\frac{9}{2}\right\rfloor+\left\lfloor\frac{9}{4}\right\rfloor + \ldots\right) + \ldots + \left(\left\lfloor\frac{1}{2}\right\rfloor+\left\lfloor\frac{1}{4}\right\rfloor + \ldots\right) \\
= 8 + 7 + 7 + 4 + 4 + 3 + 3 + 1 + 1 + 0 = 38.
\end{gathered}
\]
Thus, the largest nonnegative integer \(k\) such that \(2^k\) divides \(p\) is \(\boxed{38}\).
|
38
|
{
"competition": "us_comps",
"dataset": "Ours",
"posts": null,
"source": "OMOFall19Solns.md"
}
|
At a concert, 10 singers will perform. For each singer \(x\), either there is a singer \(y\) such that \(x\) wishes to perform right after \(y\), or \(x\) has no preferences at all. Suppose that there are \(n\) ways to order the singers such that no singer has an unsatisfied preference, and let \(p\) be the product of all possible nonzero values of \(n\). Compute the largest nonnegative integer \(k\) such that \(2^{k}\) divides \(p\).
|
[
"/Mathematics/DiscreteMathematics/Combinatorics/Enumeration",
"/Mathematics/DiscreteMathematics/Combinatorics/GeneralCombinatorics",
"/Mathematics/DiscreteMathematics/GeneralDiscreteMathematics/DiscreteMath",
"/Mathematics/DiscreteMathematics/GeneralDiscreteMathematics/DiscreteMathematics",
"/Mathematics/NumberTheory/GeneralNumberTheory/ElementaryNumberTheory",
"/Mathematics/NumberTheory/GeneralNumberTheory/HigherArithmetic",
"/Mathematics/NumberTheory/GeneralNumberTheory/NumberTheory",
"/Mathematics/NumberTheory/Integers/Integer",
"/Mathematics/NumberTheory/Integers/NonnegativeInteger",
"/Mathematics/NumberTheory/Integers/PositiveInteger",
"/Mathematics/NumberTheory/Numbers"
] |
Treat the “wants‑after” relations as forming fixed chains, so the singers are partitioned into blocks whose internal order is forced and the total order count is the factorial of the number of blocks.
|
[
0.00003629922866821289,
0.01239776611328125,
-0.002239227294921875,
0.006946563720703125,
0.0001062154769897461,
-0.0096588134765625,
0.05694580078125,
-0.01568603515625,
0.00821685791015625,
0.00891876220703125,
0.045196533203125,
-0.015899658203125,
-0.0036144256591796875,
-0.03265380859375,
-0.06573486328125,
-0.0281982421875,
0.0577392578125,
0.03485107421875,
-0.047149658203125,
-0.004856109619140625,
-0.008636474609375,
-0.0157928466796875,
-0.00031280517578125,
0.056396484375,
0.0298309326171875,
-0.04620361328125,
-0.018798828125,
-0.004329681396484375,
-0.0199432373046875,
-0.03857421875,
-0.0157318115234375,
-0.0257720947265625,
-0.005584716796875,
-0.0266571044921875,
0.00131988525390625,
0.01454925537109375,
0.006153106689453125,
-0.0029697418212890625,
-0.001392364501953125,
-0.0128631591796875,
-0.0030841827392578125,
0.005390167236328125,
0.007785797119140625,
-0.004512786865234375,
-0.0391845703125,
0.00522613525390625,
0.004421234130859375,
0.01293182373046875,
-0.0023517608642578125,
0.0044097900390625,
-0.0134124755859375,
0.01490020751953125,
-0.01496124267578125,
-0.0121917724609375,
-0.019805908203125,
-0.08856201171875,
0.0088958740234375,
-0.00400543212890625,
0.0252838134765625,
-0.0196075439453125,
0.008880615234375,
0.0013475418090820312,
0.01163482666015625,
-0.0125579833984375,
-0.0014219284057617188,
-0.01482391357421875,
-0.00785064697265625,
-0.00937652587890625,
-0.001735687255859375,
-0.009185791015625,
0.0098419189453125,
-0.01325225830078125,
-0.0103302001953125,
0.00518798828125,
0.0301055908203125,
-0.01250457763671875,
0.0012807846069335938,
-0.0162200927734375,
0.001461029052734375,
0.0102996826171875,
-0.006694793701171875,
0.01338958740234375,
-0.0010118484497070312,
0.0241241455078125,
0.01023101806640625,
-0.021148681640625,
0.0216522216796875,
-0.00860595703125,
0.0093841552734375,
-0.0116424560546875,
0.005527496337890625,
0.00449371337890625,
0.01250457763671875,
-0.004123687744140625,
0.0019483566284179688,
-0.0046844482421875,
0.009429931640625,
-0.014617919921875,
-0.019866943359375,
0.019134521484375,
-0.0034313201904296875,
-0.0021686553955078125,
-0.006103515625,
-0.0031871795654296875,
-0.042083740234375,
-0.014495849609375,
-0.0020198822021484375,
0.017333984375,
-0.00812530517578125,
-0.01250457763671875,
0.00958251953125,
0.0004897117614746094,
0.032257080078125,
-0.01953125,
-0.007404327392578125,
0.005352020263671875,
0.0052947998046875,
-0.0220184326171875,
-0.00319671630859375,
0.0080413818359375,
0.0028705596923828125,
0.0099334716796875,
-0.00879669189453125,
0.0237884521484375,
0.01084136962890625,
-0.0024814605712890625,
-0.002719879150390625,
-0.00786590576171875,
0.0129547119140625,
-0.0025424957275390625,
0.007110595703125,
0.0059967041015625,
-0.0186920166015625,
-0.0171661376953125,
0.00653839111328125,
-0.0005292892456054688,
-0.0018310546875,
0.005496978759765625,
0.03204345703125,
0.00083160400390625,
0.017333984375,
-0.0169677734375,
0.0005307197570800781,
0.0181121826171875,
-0.008209228515625,
0.049041748046875,
-0.0013275146484375,
-0.02935791015625,
-0.0007452964782714844,
-0.00873565673828125,
0.0010385513305664062,
-0.00543975830078125,
0.024871826171875,
0.0059356689453125,
0.00348663330078125,
0.0256500244140625,
0.0024547576904296875,
0.00661468505859375,
0.004673004150390625,
-0.0092620849609375,
-0.00797271728515625,
-0.0078277587890625,
-0.0032520294189453125,
0.0355224609375,
-0.02001953125,
0.012054443359375,
0.00858306884765625,
-0.01409149169921875,
0.006465911865234375,
0.022735595703125,
0.01290130615234375,
-0.005695343017578125,
0.002758026123046875,
-0.0208587646484375,
-0.0085296630859375,
-0.00479888916015625,
-0.0037364959716796875,
0.0015497207641601562,
0.0010805130004882812,
0.0020771026611328125,
0.007720947265625,
-0.0300445556640625,
-0.015045166015625,
0.01450347900390625,
0.001064300537109375,
0.004238128662109375,
-0.007183074951171875,
0.0067596435546875,
0.01543426513671875,
0.00391387939453125,
0.00466156005859375,
-0.0033740997314453125,
-0.003971099853515625,
0.0153045654296875,
-0.007106781005859375,
0.00598907470703125,
-0.0182037353515625,
0.01537322998046875,
0.044769287109375,
0.006778717041015625,
0.01132965087890625,
0.01424407958984375,
-0.01702880859375,
0.0176849365234375,
-0.003047943115234375,
-0.00511932373046875,
0.01287078857421875,
-0.0223846435546875,
0.01422882080078125,
-0.0001552104949951172,
-0.00004476308822631836,
-0.032379150390625,
0.002132415771484375,
-0.028900146484375,
0.0028209686279296875,
-0.00726318359375,
-0.01488494873046875,
0.01080322265625,
0.0087738037109375,
-0.04302978515625,
0.01297760009765625,
0.0063323974609375,
0.004924774169921875,
-0.00878143310546875,
0.00852203369140625,
0.0021991729736328125,
0.01151275634765625,
-0.00630950927734375,
0.0031147003173828125,
0.0037097930908203125,
0.01374053955078125,
0.00751495361328125,
-0.0027561187744140625,
0.0018205642700195312,
0.00852203369140625,
0.0008978843688964844,
0.01143646240234375,
-0.002437591552734375,
0.01313018798828125,
-0.0118408203125,
0.03485107421875,
-0.0193939208984375,
-0.00939178466796875,
0.0013217926025390625,
-0.0174407958984375,
0.0016498565673828125,
0.00566864013671875,
-0.006244659423828125,
-0.00350189208984375,
-0.017486572265625,
-0.0275421142578125,
-0.0000851750373840332,
-0.002552032470703125,
0.0001608133316040039,
-0.0223541259765625,
-0.0163726806640625,
0.00354766845703125,
-0.028045654296875,
0.004611968994140625,
0.001010894775390625,
0.0007548332214355469,
-0.02264404296875,
0.005710601806640625,
-0.0287322998046875,
-0.01238250732421875,
-0.0154571533203125,
0.0266876220703125,
0.0032176971435546875,
0.01366424560546875,
-0.01287841796875,
0.047149658203125,
-0.0030536651611328125,
-0.004909515380859375,
0.0216827392578125,
-0.00542449951171875,
0.009674072265625,
-0.0007586479187011719,
0.010345458984375,
-0.00019478797912597656,
-0.01910400390625,
0.01183319091796875,
0.0017032623291015625,
-0.05169677734375,
0.00010538101196289062,
-0.00707244873046875,
-0.004974365234375,
-0.00569915771484375,
-0.02099609375,
0.00978851318359375,
0.00505828857421875,
-0.00835418701171875,
-0.0111083984375,
-0.0103912353515625,
-0.01290130615234375,
0.03741455078125,
-0.068603515625,
-0.009002685546875,
0.005359649658203125,
0.0176239013671875,
-0.0057830810546875,
0.019927978515625,
-0.0270233154296875,
0.0154571533203125,
-0.0024433135986328125,
0.0026874542236328125,
0.01317596435546875,
0.003993988037109375,
-0.0020599365234375,
-0.056640625,
0.0149383544921875,
-0.010711669921875,
0.0145111083984375,
0.00960540771484375,
0.00827789306640625,
0.0301055908203125,
-0.0087890625,
-0.005672454833984375,
0.0158233642578125,
-0.01258087158203125,
0.0139007568359375,
-0.0041656494140625,
-0.019195556640625,
-0.0015316009521484375,
0.0101470947265625,
0.00894927978515625,
-0.019317626953125,
-0.00926971435546875,
0.0172576904296875,
-0.044830322265625,
0.04461669921875,
-0.061798095703125,
0.004604339599609375,
-0.016815185546875,
-0.01519012451171875,
-0.0177154541015625,
0.015655517578125,
-0.006488800048828125,
0.0207977294921875,
0.007671356201171875,
0.006244659423828125,
-0.00914764404296875,
0.002590179443359375,
0.01126861572265625,
0.02972412109375,
0.004276275634765625,
0.0274505615234375,
-0.0149383544921875,
-0.0011119842529296875,
-0.0219268798828125,
0.026702880859375,
0.013031005859375,
0.00811767578125,
0.0178680419921875,
0.005084991455078125,
-0.0177459716796875,
0.0173492431640625,
-0.03131103515625,
0.00478363037109375,
-0.0166473388671875,
0.0230865478515625,
-0.0016345977783203125,
-0.0013647079467773438,
0.01488494873046875,
-0.0114898681640625,
0.0136566162109375,
0.006084442138671875,
-0.0148773193359375,
0.0187225341796875,
-0.050262451171875,
-0.0170135498046875,
0.0033397674560546875,
0.0251617431640625,
0.0232696533203125,
-0.04461669921875,
-0.051422119140625,
-0.0030384063720703125,
-0.0085601806640625,
0.020782470703125,
-0.03045654296875,
-0.000324249267578125,
0.0039825439453125,
0.040618896484375,
-0.0038890838623046875,
0.0379638671875,
-0.0014257431030273438,
-0.0038852691650390625,
0.003875732421875,
-0.03265380859375,
-0.034820556640625,
0.01468658447265625,
-0.0250701904296875,
-0.003185272216796875,
-0.016082763671875,
0.00027060508728027344,
0.0364990234375,
-0.055511474609375,
-0.0010251998901367188,
0.025482177734375,
0.02301025390625,
-0.0205230712890625,
0.004528045654296875,
0.01244354248046875,
-0.0003771781921386719,
-0.0030364990234375,
0.01488494873046875,
-0.020965576171875,
-0.00548553466796875,
-0.0016155242919921875,
0.0187225341796875,
-0.01245880126953125,
0.0235748291015625,
0.0007700920104980469,
0.010467529296875,
0.005039215087890625,
0.0218963623046875,
-0.00920867919921875,
0.0447998046875,
0.000058770179748535156,
-0.052642822265625,
-0.006923675537109375,
0.0038967132568359375,
-0.0091094970703125,
0.02020263671875,
-0.0141754150390625,
0.0167388916015625,
0.026153564453125,
-0.0235443115234375,
0.022430419921875,
0.028900146484375,
-0.01151275634765625,
0.00453948974609375,
-0.0352783203125,
0.0018968582153320312,
0.0020198822021484375,
0.0197601318359375,
0.048553466796875,
-0.012664794921875,
-0.0191650390625,
0.00797271728515625,
-0.01354217529296875,
0.00716400146484375,
-0.00942230224609375,
0.0011796951293945312,
-0.01702880859375,
-0.003818511962890625,
0.0026721954345703125,
-0.01097869873046875,
0.0016374588012695312,
-0.0180816650390625,
0.021575927734375,
-0.0014581680297851562,
-0.044281005859375,
0.006984710693359375,
-0.0252227783203125,
0.0224761962890625,
0.028411865234375,
0.0027561187744140625,
0.007633209228515625,
-0.030548095703125,
-0.022918701171875,
0.01342010498046875,
-0.0253753662109375,
-0.005794525146484375,
-0.00803375244140625,
-0.0233306884765625,
0.0090484619140625,
-0.019134521484375,
0.019500732421875,
0.035980224609375,
0.0008440017700195312,
-0.02655029296875,
-0.00708770751953125,
0.00798797607421875,
0.0132293701171875,
-0.0548095703125,
0.029083251953125,
0.0045013427734375,
0.033599853515625,
-0.01540374755859375,
-0.016845703125,
0.01169586181640625,
-0.012969970703125,
-0.006591796875,
0.0008854866027832031,
0.0049896240234375,
0.00026535987854003906,
0.02935791015625,
-0.004108428955078125,
-0.03948974609375,
-0.01007080078125,
-0.0287628173828125,
0.04656982421875,
-0.0340576171875,
-0.01293182373046875,
0.01983642578125,
-0.05487060546875,
0.019683837890625,
-0.0094146728515625,
-0.0011949539184570312,
0.01129150390625,
0.0260009765625,
-0.027740478515625,
-0.010772705078125,
0.01337432861328125,
0.01348114013671875,
-0.0033779144287109375,
0.048492431640625,
0.0163726806640625,
-0.0146331787109375,
-0.0259552001953125,
-0.0013589859008789062,
-0.000012874603271484375,
0.006175994873046875,
-0.0219573974609375,
0.0007576942443847656,
-0.0135650634765625,
0.0124969482421875,
-0.0184783935546875,
0.016937255859375,
0.0400390625,
-0.0225677490234375,
-0.0026302337646484375,
0.01885986328125,
0.0227813720703125,
0.002696990966796875,
0.0232696533203125,
0.0250396728515625,
-0.00020134449005126953,
0.01495361328125,
-0.005275726318359375,
-0.005237579345703125,
-0.034942626953125,
0.00859832763671875,
-0.020904541015625,
-0.033721923828125,
-0.01290130615234375,
0.0226898193359375,
-0.0251007080078125,
-0.00078582763671875,
0.0174102783203125,
0.002384185791015625,
0.020843505859375,
0.01934814453125,
0.00699615478515625,
-0.032928466796875,
-0.016357421875,
-0.008575439453125,
0.0087738037109375,
-0.002773284912109375,
0.0037059783935546875,
-0.01983642578125,
-0.005268096923828125,
0.0114898681640625,
-0.035400390625,
0.0079498291015625,
-0.0109405517578125,
0.020294189453125,
0.0030517578125,
-0.0090179443359375,
-0.01258087158203125,
-0.0103912353515625,
0.02642822265625,
0.0066070556640625,
-0.0112457275390625,
-0.00836944580078125,
-0.0013570785522460938,
-0.01331329345703125,
0.0227203369140625,
-0.00855255126953125,
-0.036224365234375,
-0.01061248779296875,
0.0008840560913085938,
0.00286865234375,
-0.005435943603515625,
-0.01114654541015625,
-0.0084228515625,
0.001247406005859375,
-0.0085601806640625,
0.0102081298828125,
-0.004322052001953125,
0.01385498046875,
0.03875732421875,
-0.02264404296875,
0.0038547515869140625,
0.0278472900390625,
-0.01171875,
-0.010833740234375,
-0.006381988525390625,
0.00766754150390625,
0.02911376953125,
-0.01258087158203125,
-0.01092529296875,
-0.0158538818359375,
-0.00972747802734375,
0.04290771484375,
-0.031768798828125,
0.03472900390625,
-0.0019350051879882812,
0.0218658447265625,
0.0010118484497070312,
0.024871826171875,
-0.02197265625,
-0.00482177734375,
0.007610321044921875,
-0.011383056640625,
-0.0020809173583984375,
-0.01515960693359375,
0.0274200439453125,
-0.0235595703125,
0.0060272216796875,
-0.0082550048828125,
-0.016998291015625,
0.0228729248046875,
-0.001415252685546875,
0.038330078125,
-0.0032806396484375,
0.006946563720703125,
-0.01242828369140625,
0.027252197265625,
-0.038848876953125,
-0.0214080810546875,
0.0179290771484375,
-0.010345458984375,
0.0186309814453125,
0.032989501953125,
-0.0234222412109375,
0.0033054351806640625,
-0.002002716064453125,
0.019195556640625,
0.006618499755859375,
-0.0325927734375,
-0.016326904296875,
0.023681640625,
-0.0205841064453125,
-0.01457977294921875,
0.004108428955078125,
0.00775146484375,
0.025238037109375,
-0.0014200210571289062,
-0.00893402099609375,
0.0015058517456054688,
0.021697998046875,
0.005191802978515625,
-0.05889892578125,
-0.0101470947265625,
0.03448486328125,
0.0013151168823242188,
-0.00666046142578125,
0.00661468505859375,
-0.0038967132568359375,
-0.0027065277099609375,
-0.040863037109375,
-0.004009246826171875,
-0.00312042236328125,
-0.022735595703125,
0.016937255859375,
0.032806396484375,
-0.01462554931640625,
0.0111236572265625,
0.0212860107421875,
0.00901031494140625,
0.0088043212890625,
0.028564453125,
0.00765228271484375,
-0.019500732421875,
0.002727508544921875,
0.0170135498046875,
0.01557159423828125,
0.036590576171875,
0.007793426513671875,
0.003986358642578125,
-0.027008056640625,
0.034332275390625,
0.006381988525390625,
0.03857421875,
-0.019134521484375,
0.0064544677734375,
-0.00521087646484375,
-0.0085906982421875,
0.037750244140625,
-0.01012420654296875,
0.01108551025390625,
0.0557861328125,
-0.0178985595703125,
-0.00274658203125,
0.008575439453125,
0.0003476142883300781,
-0.034454345703125,
0.0014314651489257812,
0.0169219970703125,
0.0141448974609375,
0.0091705322265625,
-0.038970947265625,
0.0166778564453125,
-0.01163482666015625,
0.00861358642578125,
0.0129241943359375,
0.0034923553466796875,
-0.03546142578125,
0.028839111328125,
0.018646240234375,
0.00806427001953125,
-0.0030651092529296875,
0.003265380859375,
0.031982421875,
-0.0034008026123046875,
0.0019989013671875,
0.01189422607421875,
-0.0244293212890625,
-0.0018415451049804688,
-0.02838134765625,
-0.039306640625,
-0.04180908203125,
-0.0077667236328125,
-0.0286407470703125,
0.022064208984375,
0.011962890625,
0.0203704833984375,
0.0260772705078125,
0.0082244873046875,
-0.022979736328125,
0.0022640228271484375,
-0.010650634765625,
-0.0263671875,
0.01210784912109375,
-0.00919342041015625,
-0.0238494873046875,
-0.049163818359375,
-0.03436279296875,
0.009613037109375,
0.00928497314453125,
-0.0005884170532226562,
0.01139068603515625,
-0.01983642578125,
-0.053955078125,
-0.0254058837890625,
0.0295867919921875,
-0.0452880859375,
-0.0172271728515625,
-0.01428985595703125,
0.0291748046875,
-0.00708770751953125,
0.01233673095703125,
-0.0082244873046875,
-0.0245513916015625,
-0.003368377685546875,
0.01007080078125,
-0.004070281982421875,
-0.0123138427734375,
-0.033416748046875,
0.01275634765625,
0.032012939453125,
0.00508880615234375,
-0.019256591796875,
-0.0246734619140625,
-0.0003809928894042969,
0.01232147216796875,
-0.0106964111328125,
0.03521728515625,
-0.0147247314453125,
-0.04052734375,
-0.00403594970703125,
0.0146026611328125,
-0.0001271963119506836,
0.00316619873046875,
0.01035308837890625,
-0.038238525390625,
-0.0200958251953125,
-0.031707763671875,
0.0218963623046875,
-0.0236358642578125,
-0.004383087158203125,
-0.0025806427001953125,
0.006679534912109375,
0.0068206787109375,
0.003734588623046875,
-0.0027256011962890625,
0.0014181137084960938,
0.01517486572265625,
-0.03826904296875,
-0.022247314453125,
-0.0210113525390625,
-0.008392333984375,
-0.01336669921875,
-0.01885986328125,
-0.01904296875,
0.002658843994140625,
-0.01953125,
0.0071563720703125,
-0.0019588470458984375,
0.0273284912109375,
0.0001856088638305664,
-0.019195556640625,
0.0010166168212890625,
-0.041748046875,
0.0096588134765625,
-0.0078887939453125,
-0.01177978515625,
-0.00495147705078125,
0.02069091796875,
0.012115478515625,
-0.03875732421875,
-0.0086822509765625,
0.0228729248046875,
0.01099395751953125,
-0.00926971435546875,
0.0119781494140625,
-0.005847930908203125,
-0.006603240966796875,
0.01959228515625,
0.0036869049072265625,
-0.005519866943359375,
0.029693603515625,
-0.029052734375,
0.0210418701171875,
-0.0029277801513671875,
-0.01309967041015625,
0.005096435546875,
-0.00444793701171875,
0.006244659423828125,
-0.00998687744140625,
0.01995849609375,
0.027740478515625,
-0.01509857177734375,
-0.01546478271484375,
0.002681732177734375,
0.0191497802734375,
0.0205535888671875,
-0.0111236572265625,
-0.00452423095703125,
-0.01485443115234375,
-0.0008788108825683594,
-0.0169219970703125,
0.00717926025390625,
-0.006694793701171875,
-0.0221099853515625,
0.0081329345703125,
0.0023059844970703125,
0.00047278404235839844,
-0.04913330078125,
-0.0242919921875,
0.01538848876953125,
0.019744873046875,
-0.035552978515625,
0.03460693359375,
-0.003936767578125,
-0.02001953125,
-0.017730712890625,
0.007659912109375,
0.017913818359375,
0.00742340087890625,
0.0297088623046875,
-0.027587890625,
-0.0024547576904296875,
-0.01224517822265625,
0.01959228515625,
0.031890869140625,
-0.00506591796875,
-0.025726318359375,
0.0035266876220703125,
0.0154266357421875,
-0.000054717063903808594,
0.0201416015625,
0.0024013519287109375,
0.00946807861328125,
-0.018798828125,
-0.0010042190551757812,
-0.016082763671875,
0.01145172119140625,
-0.0165557861328125,
-0.006134033203125,
0.005519866943359375,
0.029754638671875,
-0.0085906982421875,
0.0289154052734375,
-0.0018625259399414062,
0.006134033203125,
0.006862640380859375,
0.01372528076171875,
0.016815185546875,
-0.009552001953125,
0.005191802978515625,
0.000013649463653564453,
0.032745361328125,
0.016448974609375,
0.01213836669921875,
0.036590576171875,
-0.0227203369140625,
0.00830841064453125,
-0.0153045654296875,
0.03118896484375,
0.010894775390625,
-0.020904541015625,
-0.0048828125,
0.01287841796875,
-0.01690673828125,
-0.006900787353515625,
-0.016021728515625,
0.004589080810546875,
-0.035491943359375,
-0.00688934326171875,
0.007503509521484375,
0.004932403564453125,
0.035125732421875,
0.001964569091796875,
-0.0251312255859375,
-0.015350341796875,
0.0095367431640625,
0.016998291015625,
0.015716552734375,
-0.0243072509765625,
0.007602691650390625,
0.0211639404296875,
-0.038330078125,
-0.0362548828125,
-0.00980377197265625,
-0.00875091552734375,
-0.004634857177734375,
0.00739288330078125,
0.05633544921875,
0.0083465576171875,
-0.0199432373046875,
0.00673675537109375,
-0.00439453125,
0.007171630859375,
-0.019073486328125,
-0.00968170166015625,
-0.011322021484375,
-0.0291748046875,
-0.003948211669921875,
0.00496673583984375,
0.052764892578125,
-0.004459381103515625,
0.01291656494140625,
0.0215301513671875,
0.03680419921875,
0.00799560546875,
0.007671356201171875,
0.01280975341796875,
-0.0067138671875,
-0.01296234130859375,
0.031646728515625,
-0.0194244384765625,
-0.000050008296966552734,
0.01181793212890625,
0.0157318115234375,
0.0157623291015625,
0.015899658203125,
-0.027191162109375,
-0.0296783447265625,
-0.01401519775390625,
-0.0004696846008300781,
-0.040679931640625,
0.0217132568359375,
0.01233673095703125,
0.020965576171875,
0.002559661865234375,
0.00986480712890625,
0.004779815673828125,
-0.0330810546875,
-0.0149993896484375,
-0.0031375885009765625,
-0.0302734375,
0.035064697265625,
-0.02081298828125,
0.0523681640625,
-0.006885528564453125,
-0.0026454925537109375,
0.03582763671875,
-0.012725830078125,
-0.0310516357421875,
0.0265045166015625,
0.0088653564453125,
-0.050567626953125,
-0.0211639404296875,
0.0206146240234375,
0.0008373260498046875,
-0.017608642578125,
0.037445068359375,
-0.00530242919921875,
-0.048828125,
0.00118255615234375,
0.01213836669921875,
-0.016143798828125,
0.0252532958984375,
0.01314544677734375,
-0.0137786865234375,
-0.0015964508056640625,
0.0094146728515625,
0.0019989013671875,
-0.0343017578125,
0.00832366943359375,
0.006191253662109375,
0.0108795166015625,
0.004669189453125,
-0.01190185546875,
0.02716064453125,
-0.0148162841796875,
0.0097503662109375,
-0.0037899017333984375,
-0.03167724609375,
0.01629638671875,
0.005687713623046875,
-0.0100250244140625,
0.01273345947265625,
-0.040771484375,
0.0018148422241210938,
0.013397216796875,
-0.013153076171875,
0.0187835693359375,
0.0078277587890625,
0.01372528076171875,
-0.04071044921875,
-0.004985809326171875,
-0.0147247314453125,
-0.0086669921875,
0.018280029296875,
0.008941650390625,
-0.020599365234375,
-0.01641845703125,
-0.01163482666015625,
0.016571044921875,
-0.0169677734375,
-0.0204315185546875,
0.0011091232299804688,
0.0233917236328125,
-0.027679443359375,
0.01043701171875,
0.0250091552734375,
-0.0307159423828125,
0.0308990478515625,
-0.012420654296875,
0.01409912109375,
-0.01297760009765625,
-0.0150604248046875,
-0.00785064697265625,
0.0115966796875,
-0.0168914794921875,
-0.004085540771484375,
-0.0184326171875,
-0.0185089111328125,
0.00787353515625,
0.03167724609375,
-0.0182952880859375,
0.0201263427734375,
-0.0250396728515625,
0.0243682861328125,
0.002685546875,
-0.0322265625,
-0.01375579833984375,
0.01200103759765625,
0.03265380859375,
-0.0174102783203125,
-0.01812744140625,
-0.01654052734375,
0.0296173095703125,
0.03692626953125,
-0.005634307861328125,
-0.0209197998046875,
0.038360595703125,
0.005031585693359375,
0.006107330322265625,
0.0288543701171875,
0.0014276504516601562,
0.0234832763671875,
-0.015655517578125,
-0.017547607421875,
0.005893707275390625,
-0.0218963623046875,
-0.002788543701171875,
-0.036376953125,
0.0032863616943359375,
0.0188446044921875,
-0.02490234375,
0.01473236083984375,
0.00951385498046875,
0.0369873046875,
-0.0024166107177734375,
0.00203704833984375,
-0.019439697265625,
-0.001033782958984375,
0.004150390625,
-0.0305328369140625,
0.0160980224609375,
0.0077667236328125,
0.021728515625,
-0.01122283935546875,
-0.0158538818359375,
0.00797271728515625,
-0.026824951171875,
-0.0239105224609375,
0.0005693435668945312,
0.00753021240234375,
0.019927978515625,
0.02215576171875,
0.0130462646484375,
-0.0299835205078125,
-0.00859832763671875,
-0.0222625732421875,
0.00015282630920410156,
-0.0142974853515625,
0.01403045654296875,
0.0203094482421875,
-0.0167694091796875,
-0.0033206939697265625,
0.00839996337890625,
-0.0281524658203125,
0.0233154296875,
-0.007720947265625,
0.01459503173828125,
-0.047576904296875,
0.002620697021484375,
-0.01263427734375,
0.0136566162109375,
0.01097869873046875,
0.0234527587890625,
-0.0302581787109375,
-0.049041748046875,
-0.0269775390625,
-0.0293731689453125,
0.04498291015625,
0.0230560302734375,
0.002101898193359375,
0.0295562744140625,
-0.0118408203125,
-0.0123138427734375,
-0.00711822509765625,
-0.02947998046875,
-0.017578125,
0.031951904296875,
-0.0299530029296875,
0.0030612945556640625,
0.004177093505859375,
-0.0206146240234375,
-0.0124664306640625,
0.005901336669921875,
-0.0088043212890625,
-0.01018524169921875,
0.00904083251953125,
-0.051544189453125,
-0.02301025390625,
0.0024929046630859375,
-0.04248046875,
-0.020477294921875,
-0.03765869140625,
0.0022754669189453125,
-0.022064208984375,
-0.0110626220703125,
0.005584716796875,
-0.004749298095703125,
-0.018798828125,
0.00972747802734375,
0.00691986083984375,
0.01444244384765625,
0.01218414306640625,
0.001575469970703125,
0.0014600753784179688,
-0.020416259765625,
0.01419830322265625,
0.032073974609375,
-0.0006818771362304688,
-0.0090484619140625,
0.002498626708984375,
-0.00777435302734375,
-0.00931549072265625,
-0.0026760101318359375,
0.020904541015625,
0.03961181640625,
0.0003650188446044922,
0.018585205078125,
-0.0193023681640625,
0.0013360977172851562,
-0.01215362548828125,
0.036163330078125,
-0.024627685546875,
-0.005199432373046875,
-0.0045318603515625,
0.00429534912109375,
-0.0209197998046875,
0.03619384765625,
-0.0699462890625,
0.039398193359375,
0.03302001953125,
-0.0025539398193359375,
0.00011771917343139648,
-0.01702880859375,
0.01319122314453125,
-0.041839599609375,
-0.042327880859375,
0.0081329345703125,
0.00035834312438964844,
-0.0188140869140625,
0.024078369140625,
-0.004230499267578125,
-0.005481719970703125,
0.00551605224609375,
-0.03643798828125,
-0.00862884521484375,
-0.0166778564453125,
-0.004138946533203125,
-0.01806640625,
0.0038585662841796875,
-0.01363372802734375,
-0.0167236328125,
-0.0333251953125,
0.005771636962890625,
-0.01499176025390625,
-0.004383087158203125,
0.0012617111206054688,
0.0175323486328125,
-0.0010194778442382812,
-0.021636962890625,
-0.0208740234375,
0.01139068603515625,
0.0165557861328125,
-0.007717132568359375,
0.032745361328125,
0.0005846023559570312,
-0.0169219970703125,
-0.013275146484375,
0.0139007568359375,
0.013824462890625,
0.0033016204833984375,
0.007049560546875,
-0.0160675048828125,
0.002788543701171875,
-0.035919189453125,
0.0408935546875,
-0.0076904296875,
0.003910064697265625,
0.04205322265625,
-0.0250396728515625,
-0.0179595947265625,
-0.0308685302734375,
-0.041412353515625,
0.00801849365234375,
-0.00405120849609375,
0.02191162109375,
-0.023834228515625,
0.034332275390625,
-0.040863037109375,
-0.02276611328125,
0.0260772705078125,
0.0013561248779296875,
0.016143798828125,
-0.0029697418212890625,
-0.03375244140625,
-0.00476837158203125,
-0.0195465087890625,
-0.005859375,
-0.0241546630859375,
0.024139404296875,
-0.004947662353515625,
0.00009334087371826172,
0.0170440673828125,
-0.0504150390625,
0.006168365478515625,
-0.0086669921875,
0.0015163421630859375,
0.0103607177734375,
0.007045745849609375,
0.010040283203125,
-0.0111236572265625,
-0.00308990478515625,
-0.01006317138671875,
0.009490966796875,
0.010040283203125,
-0.0203857421875,
-0.007556915283203125,
0.0247955322265625,
0.0287017822265625,
-0.007755279541015625,
0.005649566650390625,
0.0213470458984375,
0.00421905517578125,
-0.030181884765625,
-0.004604339599609375,
-0.0245513916015625,
0.016448974609375,
-0.016845703125,
-0.04266357421875,
0.01155853271484375,
0.006710052490234375,
0.00899505615234375,
-0.0200653076171875,
0.0235137939453125,
0.006809234619140625,
0.0258941650390625,
-0.0233154296875,
0.038665771484375,
0.015716552734375,
-0.01293182373046875,
-0.0156097412109375,
0.0037364959716796875,
-0.008880615234375,
0.0004734992980957031,
0.0233917236328125,
0.003940582275390625,
0.0035552978515625,
-0.01001739501953125,
-0.00647735595703125,
-0.026123046875,
0.0260162353515625,
-0.0204010009765625,
0.0023403167724609375,
-0.00771331787109375,
0.018524169921875,
0.01561737060546875,
0.0222930908203125,
-0.0037822723388671875,
0.0035228729248046875,
0.03216552734375,
0.0146026611328125,
0.007110595703125,
0.006320953369140625,
0.00894927978515625,
-0.00560760498046875,
-0.0232696533203125,
-0.0101470947265625,
0.0250244140625,
-0.0089263916015625,
-0.0018720626831054688,
-0.00563812255859375,
0.0160980224609375,
0.0003895759582519531,
-0.0181427001953125,
-0.033782958984375,
-0.00638580322265625,
-0.018463134765625,
-0.0278167724609375,
-0.007106781005859375,
-0.031829833984375,
-0.0290374755859375,
-0.0108184814453125,
-0.0224609375,
0.00876617431640625,
0.0555419921875,
0.00009709596633911133,
-0.000039517879486083984,
-0.02532958984375,
-0.00982666015625,
0.044586181640625,
-0.002521514892578125,
-0.007167816162109375,
-0.0007328987121582031,
0.0147552490234375,
-0.0150909423828125,
0.0241851806640625,
0.0229339599609375,
-0.031341552734375,
0.051910400390625,
0.0181732177734375,
0.018768310546875,
-0.0012197494506835938,
-0.038238525390625,
0.0225982666015625,
0.036895751953125,
-0.006195068359375,
0.01226043701171875,
-0.0012369155883789062,
0.01116943359375,
-0.0131072998046875,
-0.00862884521484375,
-0.00826263427734375,
0.05682373046875,
-0.005222320556640625,
0.010162353515625,
-0.01114654541015625,
-0.007228851318359375,
-0.026031494140625,
-0.0103607177734375,
-0.039581298828125,
-0.0040283203125,
0.0014638900756835938,
0.04840087890625,
-0.0268402099609375,
0.0199127197265625,
-0.006927490234375,
-0.01047515869140625,
-0.0010061264038085938,
-0.0289764404296875,
-0.01023101806640625,
-0.0254058837890625,
-0.004802703857421875,
-0.010467529296875,
0.032806396484375,
-0.0172271728515625,
-0.002223968505859375,
-0.00827789306640625,
0.0237884521484375,
0.01473236083984375,
0.00556182861328125,
-0.005146026611328125,
0.020782470703125,
-0.00107574462890625,
0.00213623046875,
0.00982666015625,
-0.009613037109375,
-0.01297760009765625,
-0.006866455078125,
0.0251922607421875,
-0.018280029296875,
-0.0188751220703125,
0.0008788108825683594,
0.02197265625,
-0.00662994384765625,
0.020355224609375,
-0.004177093505859375,
-0.0111083984375,
-0.01293182373046875,
-0.0177459716796875,
-0.00215911865234375,
-0.005138397216796875,
0.00952911376953125,
-0.006439208984375,
-0.014892578125,
0.0230255126953125,
-0.034393310546875,
0.00762939453125,
0.031463623046875,
-0.0036830902099609375,
0.0034275054931640625,
0.0021724700927734375,
-0.001552581787109375,
0.01367950439453125,
0.0171051025390625,
-0.00147247314453125,
0.029632568359375,
-0.0010309219360351562,
-0.0131378173828125,
0.00687408447265625,
-0.007724761962890625,
-0.027618408203125,
0.00725555419921875,
0.0254058837890625,
-0.0031642913818359375,
0.0192108154296875,
0.0256195068359375,
0.019927978515625,
0.01308441162109375,
0.012908935546875,
-0.004940032958984375,
-0.0173492431640625,
0.0107879638671875,
-0.0244293212890625,
0.0054779052734375,
0.042694091796875,
0.029083251953125,
0.0089263916015625,
-0.0023899078369140625,
-0.029541015625,
-0.015716552734375,
-0.02935791015625,
0.0122222900390625,
0.0025310516357421875,
-0.0114288330078125,
-0.0016469955444335938,
-0.0146636962890625,
0.0014524459838867188,
-0.023712158203125,
-0.034423828125,
0.0021381378173828125,
-0.035308837890625,
0.011138916015625,
0.010711669921875,
-0.00019872188568115234,
-0.028900146484375,
0.011505126953125,
0.0204010009765625,
-0.024627685546875,
-0.004413604736328125,
-0.01433563232421875,
0.0011157989501953125,
-0.005611419677734375,
-0.0027904510498046875,
-0.043701171875,
-0.033172607421875,
-0.009521484375,
-0.0215911865234375,
-0.0144195556640625,
-0.0189056396484375,
0.014923095703125,
0.0100250244140625,
-0.0062713623046875,
-0.014434814453125,
0.013916015625,
0.02349853515625,
-0.007633209228515625,
-0.010772705078125,
0.006122589111328125,
-0.023284912109375,
-0.0027370452880859375,
-0.006664276123046875,
-0.0118408203125,
0.04937744140625,
0.00655364990234375,
-0.0059967041015625,
-0.005218505859375,
0.00991058349609375,
0.0098724365234375,
0.01506805419921875,
0.01477813720703125,
0.01065826416015625,
0.00815582275390625,
0.0095672607421875,
-0.03045654296875,
0.03082275390625,
0.01184844970703125,
-0.0161285400390625,
-0.00206756591796875,
-0.01000213623046875,
-0.01483154296875,
-0.005977630615234375,
-0.0004987716674804688,
-0.0323486328125,
-0.00001728534698486328,
0.0177154541015625,
-0.025726318359375,
-0.0005192756652832031,
-0.003108978271484375,
0.002777099609375,
-0.00850677490234375,
-0.03961181640625,
-0.0008153915405273438,
0.00562286376953125,
0.00865936279296875,
-0.00039386749267578125,
0.01415252685546875,
0.005451202392578125,
-0.00032448768615722656,
-0.00875091552734375,
-0.01122283935546875,
0.01023101806640625,
-0.0190582275390625,
0.008941650390625,
-0.03863525390625,
0.0291595458984375,
0.0158233642578125,
0.0008635520935058594,
-0.009124755859375,
-0.0347900390625,
0.019805908203125,
-0.0212860107421875,
-0.02069091796875,
-0.0282135009765625,
-0.024505615234375,
0.03594970703125,
-0.0078582763671875,
-0.01313018798828125,
-0.01885986328125,
0.006626129150390625,
-0.007335662841796875,
0.008941650390625,
0.00007736682891845703,
0.002971649169921875,
0.0179595947265625,
-0.0017004013061523438,
0.009979248046875,
0.016693115234375,
-0.0272979736328125,
-0.0142669677734375,
0.0184478759765625,
-0.036224365234375,
0.02398681640625,
-0.0007433891296386719,
0.0244293212890625,
-0.024993896484375,
0.00218963623046875,
0.0152740478515625,
-0.0011653900146484375,
0.01433563232421875,
-0.011810302734375,
0.0011014938354492188,
0.01343536376953125,
-0.0042877197265625,
-0.010345458984375,
0.0004329681396484375,
0.01275634765625,
0.01702880859375,
0.028533935546875,
0.01248931884765625,
-0.028228759765625,
0.01532745361328125,
0.0168914794921875,
0.005191802978515625,
0.0208892822265625,
-0.032745361328125,
0.027496337890625,
-0.02972412109375,
0.0019817352294921875,
-0.01534271240234375,
0.004711151123046875,
-0.0195770263671875,
-0.0258941650390625,
-0.016754150390625,
0.004573822021484375,
0.0201873779296875,
0.01291656494140625,
0.00972747802734375,
0.0158538818359375,
-0.031280517578125,
0.0100250244140625,
0.0197906494140625,
0.033660888671875,
0.00804901123046875,
-0.01499176025390625,
0.0218048095703125,
-0.0011014938354492188,
-0.00017595291137695312,
0.0262298583984375,
0.01403045654296875,
-0.006214141845703125,
0.049774169921875,
-0.03167724609375,
-0.0205841064453125,
0.005504608154296875,
0.0010309219360351562,
0.00405120849609375,
-0.032562255859375,
0.0230865478515625,
0.022705078125,
0.024993896484375,
-0.01268768310546875,
-0.0198974609375,
0.0152130126953125,
0.033416748046875,
-0.0015153884887695312,
-0.015655517578125,
0.0160675048828125,
0.003261566162109375,
0.01274871826171875,
0.01155853271484375,
-0.02850341796875,
0.006603240966796875,
-0.0241851806640625,
0.00009530782699584961,
-0.017059326171875,
-0.0096435546875,
-0.0002560615539550781,
0.0198211669921875,
0.03802490234375,
-0.024261474609375,
0.0265655517578125,
-0.033843994140625,
0.0182952880859375,
0.0194091796875,
-0.0053863525390625,
0.03729248046875,
0.0259552001953125,
-0.0396728515625,
0.0228118896484375,
0.05511474609375,
0.0267181396484375,
-0.0084991455078125,
0.00988006591796875,
-0.008819580078125,
0.00537872314453125,
-0.019775390625,
-0.01323699951171875,
0.0006098747253417969,
0.0174102783203125,
0.03729248046875,
-0.00693511962890625,
-0.0026073455810546875,
-0.0172119140625,
0.0012292861938476562,
-0.020111083984375,
-0.00374603271484375,
-0.00322723388671875,
0.011474609375,
-0.0313720703125,
-0.0115966796875,
0.003940582275390625,
-0.0037517547607421875,
0.01419830322265625,
-0.0249786376953125,
-0.01546478271484375,
0.0221405029296875,
-0.027069091796875,
-0.00750732421875,
-0.0072784423828125,
0.01197052001953125,
0.0216827392578125,
0.017242431640625,
-0.0247955322265625,
0.00244903564453125,
0.029876708984375,
-0.02569580078125,
0.019256591796875,
-0.0205078125,
0.0261993408203125,
-0.01486968994140625,
-0.0081024169921875,
-0.009246826171875,
0.01983642578125,
0.031494140625,
0.028076171875,
-0.0281982421875,
0.0082855224609375,
0.00472259521484375,
-0.0186920166015625,
0.003025054931640625,
-0.036346435546875,
0.00656890869140625,
0.0102996826171875,
-0.00848388671875,
0.01038360595703125,
0.00484466552734375,
-0.01837158203125,
0.0150604248046875,
-0.00577545166015625,
-0.0384521484375,
-0.0259246826171875,
0.002471923828125,
-0.0057220458984375,
-0.016571044921875,
0.0162811279296875,
0.018829345703125,
0.0228118896484375,
-0.0122528076171875,
-0.01390838623046875,
-0.0040130615234375,
-0.0017147064208984375,
-0.0191192626953125,
-0.033599853515625,
0.0084686279296875,
0.00717926025390625,
0.0234222412109375,
0.0189361572265625,
-0.005535125732421875,
-0.0175933837890625,
0.021728515625,
0.00307464599609375,
0.0014219284057617188,
0.002071380615234375,
-0.01030731201171875,
0.0225677490234375,
0.0025730133056640625,
-0.0157012939453125,
-0.004665374755859375,
0.008209228515625,
-0.00022935867309570312,
-0.03961181640625,
-0.006542205810546875,
0.0031070709228515625,
0.005222320556640625,
-0.017791748046875,
-0.01068878173828125,
0.01071929931640625,
0.01277923583984375,
0.007213592529296875,
-0.0253448486328125,
0.0272216796875,
-0.006801605224609375,
-0.00917816162109375,
-0.014404296875,
0.033660888671875,
-0.00933074951171875,
-0.0272064208984375,
0.0006504058837890625,
0.03009033203125,
-0.04156494140625,
-0.00910186767578125,
-0.00754547119140625,
-0.0267333984375,
0.00897216796875,
-0.0133514404296875,
-0.00850677490234375,
-0.00414276123046875,
-0.02874755859375,
0.00815582275390625,
0.007053375244140625,
0.032562255859375,
0.0027179718017578125,
-0.0154266357421875,
-0.0210723876953125,
0.032867431640625,
0.0158843994140625,
0.0090179443359375,
0.0024566650390625,
0.0256500244140625,
0.0124359130859375,
-0.003482818603515625,
-0.0036334991455078125,
0.0130767822265625,
-0.0050506591796875,
0.013092041015625,
0.0048828125,
0.00669097900390625,
-0.03326416015625,
0.0021114349365234375,
0.0277557373046875,
0.0008101463317871094,
-0.02337646484375,
0.0204315185546875,
0.0185699462890625,
0.02154541015625,
0.02825927734375,
-0.0295867919921875,
0.0127716064453125,
-0.00586700439453125,
0.008026123046875,
-0.01299285888671875,
-0.04339599609375,
0.0221710205078125,
-0.0311431884765625,
0.005985260009765625,
-0.005245208740234375,
0.004276275634765625,
-0.0168914794921875,
0.0171051025390625,
0.007289886474609375,
-0.0007147789001464844,
-0.0367431640625,
-0.03485107421875,
-0.01146697998046875,
0.040802001953125,
0.0181884765625,
-0.0252838134765625,
-0.0125885009765625,
-0.032470703125,
0.0256195068359375,
-0.0035991668701171875,
0.004558563232421875,
0.023895263671875,
-0.0059051513671875,
0.01056671142578125,
-0.028350830078125,
-0.0191497802734375,
0.06268310546875,
-0.00366973876953125,
0.006793975830078125,
-0.0286712646484375,
-0.027618408203125,
-0.0131683349609375,
0.00930023193359375,
-0.021942138671875,
-0.00765228271484375,
-0.00669097900390625,
0.0101776123046875,
0.0029811859130859375,
-0.0130157470703125,
-0.01442718505859375,
0.029052734375,
0.029052734375,
-0.02374267578125,
0.005645751953125,
0.0191802978515625,
-0.037994384765625,
-0.0010213851928710938,
-0.0041961669921875,
-0.00017833709716796875,
0.034912109375,
-0.034912109375,
0.0095367431640625,
0.0133819580078125,
0.036346435546875,
0.013214111328125,
0.01119232177734375,
-0.0034465789794921875,
0.0227203369140625,
-0.0157012939453125,
0.006198883056640625,
0.0020542144775390625,
-0.0296173095703125,
-0.0218505859375,
0.035797119140625,
0.011810302734375,
0.01137542724609375,
0.01383209228515625,
0.021881103515625,
-0.006366729736328125,
-0.0173187255859375,
0.00959014892578125,
0.005481719970703125,
-0.0077362060546875,
0.0146026611328125,
0.01552581787109375,
0.0159454345703125,
0.00019669532775878906,
0.0043487548828125,
0.00344085693359375,
0.0009307861328125,
0.01178741455078125,
-0.004123687744140625,
-0.0032291412353515625,
0.006256103515625,
0.0408935546875,
0.0161895751953125,
-0.04229736328125,
-0.03289794921875,
-0.03338623046875,
0.00800323486328125,
0.0169830322265625,
0.027069091796875,
-0.0189666748046875,
-0.02642822265625,
0.03173828125,
-0.0037021636962890625,
0.01316070556640625,
-0.01751708984375,
-0.0236663818359375,
0.00004935264587402344,
0.0285491943359375,
-0.020599365234375,
0.024932861328125,
0.01218414306640625,
-0.01410675048828125,
0.01099395751953125,
-0.0005002021789550781,
0.0129852294921875,
-0.0220184326171875,
-0.0162200927734375,
-0.024505615234375,
-0.031158447265625,
0.027923583984375,
-0.0198974609375,
0.035919189453125,
-0.003387451171875,
0.0225067138671875,
-0.0014142990112304688,
-0.026214599609375,
0.04486083984375,
0.0167694091796875,
-0.02142333984375,
-0.024078369140625,
-0.0193634033203125,
0.0011949539184570312,
-0.0020751953125,
-0.02154541015625,
-0.0040740966796875,
0.0269927978515625,
0.01067352294921875,
-0.01074981689453125,
0.03558349609375,
0.00817108154296875,
0.0034923553466796875,
0.0159454345703125,
0.0098114013671875,
-0.0094757080078125,
-0.01177978515625,
-0.0284423828125,
0.0308074951171875,
0.016937255859375,
-0.0151824951171875,
-0.01398468017578125,
0.0288543701171875,
0.0157318115234375,
-0.0287017822265625,
0.01345062255859375,
-0.0038299560546875,
-0.03369140625,
-0.0182647705078125,
-0.0108795166015625,
-0.03704833984375,
0.00704193115234375,
0.0196075439453125,
-0.0049896240234375,
0.035675048828125,
0.0125885009765625,
0.0009465217590332031,
-0.02447509765625,
-0.0007243156433105469,
-0.035369873046875,
-0.005374908447265625,
-0.0203704833984375,
0.01348876953125,
-0.001316070556640625,
-0.027862548828125,
0.01442718505859375,
-0.0178070068359375,
0.0022335052490234375,
0.021026611328125,
0.0253753662109375,
0.01007080078125,
-0.013763427734375,
0.0185089111328125,
0.01519775390625,
0.0281524658203125,
-0.01451873779296875,
-0.01311492919921875,
-0.025726318359375,
-0.0182037353515625,
-0.0055694580078125,
0.02301025390625,
-0.0516357421875,
0.024383544921875,
-0.01898193359375,
-0.0212249755859375,
0.006046295166015625,
0.0116119384765625,
-0.014434814453125,
0.0221405029296875,
0.01186370849609375,
-0.0276336669921875,
0.01381683349609375,
0.03472900390625,
-0.03240966796875,
-0.00330352783203125,
-0.0307464599609375,
0.00226593017578125,
-0.032318115234375,
0.03802490234375,
0.01366424560546875,
-0.004329681396484375,
0.006069183349609375,
0.041717529296875,
0.01522064208984375,
0.015228271484375,
-0.00433349609375,
-0.006610870361328125,
-0.01052093505859375,
-0.004978179931640625,
-0.0111236572265625,
-0.015777587890625,
0.031097412109375,
-0.01438140869140625,
-0.01326751708984375,
0.02154541015625,
0.037994384765625,
-0.0285491943359375,
0.002277374267578125,
0.004367828369140625,
0.00484466552734375,
-0.01363372802734375,
-0.008697509765625,
0.016693115234375,
-0.0031108856201171875,
-0.007724761962890625,
0.0295257568359375,
-0.0093994140625,
-0.0271148681640625,
0.00690460205078125,
0.0256805419921875,
0.00173187255859375,
-0.030059814453125,
-0.0159149169921875,
-0.005649566650390625,
-0.01206207275390625,
-0.0254364013671875,
-0.036468505859375,
-0.015472412109375,
-0.0164947509765625,
0.00612640380859375,
0.01983642578125,
-0.006946563720703125,
0.028228759765625,
-0.0155181884765625,
-0.0155792236328125,
0.01776123046875,
0.0183868408203125,
0.019500732421875,
0.00927734375,
-0.020721435546875,
0.003650665283203125,
0.0103607177734375,
0.016571044921875,
0.0022449493408203125,
-0.0083465576171875,
0.01537322998046875,
-0.015899658203125,
0.0379638671875,
0.0005736351013183594,
-0.003780364990234375,
0.00982666015625,
0.05828857421875,
-0.037628173828125,
-0.01904296875,
-0.019256591796875,
-0.00714111328125,
0.0030574798583984375,
0.005626678466796875,
0.01404571533203125,
-0.005096435546875,
0.019317626953125,
-0.0016527175903320312,
-0.02447509765625,
0.006122589111328125,
0.00036072731018066406,
-0.0082244873046875,
-0.020538330078125,
0.0078582763671875,
-0.00019168853759765625,
-0.0093841552734375,
0.03729248046875,
-0.01763916015625,
-0.0288543701171875,
0.0194854736328125,
-0.02130126953125,
-0.0184478759765625,
-0.0119171142578125,
0.0151214599609375,
-0.021087646484375,
0.03289794921875,
0.019927978515625,
0.028961181640625,
-0.03076171875,
0.01238250732421875,
0.06396484375,
-0.005550384521484375,
-0.004383087158203125,
-0.007007598876953125,
0.0019664764404296875,
-0.0238800048828125,
-0.0195159912109375,
0.0174407958984375,
0.0201568603515625,
-0.02703857421875,
-0.0089569091796875,
-0.005092620849609375,
0.0254974365234375,
-0.0029449462890625,
-0.039581298828125,
0.001216888427734375,
0.0230255126953125,
0.0234527587890625,
0.0101318359375,
0.02618408203125,
-0.00705718994140625,
0.0033664703369140625,
0.0144195556640625,
0.00533294677734375,
-0.0164947509765625,
-0.005672454833984375,
-0.0027065277099609375,
0.0051727294921875,
-0.014373779296875,
0.01580810546875,
-0.01494598388671875,
0.03411865234375,
-0.0072174072265625,
-0.0094757080078125,
-0.0138397216796875,
-0.018310546875,
0.010345458984375,
0.013519287109375,
0.034820556640625,
-0.046173095703125,
-0.03857421875,
-0.00009590387344360352,
0.019439697265625,
0.000911712646484375,
0.0355224609375,
-0.0003781318664550781,
0.00766754150390625,
0.0198516845703125,
0.006099700927734375,
0.016845703125,
-0.014617919921875,
-0.0001837015151977539,
-0.00569915771484375,
-0.0206756591796875,
-0.0258941650390625,
0.00861358642578125,
0.0090789794921875,
0.02508544921875,
-0.0223541259765625,
-0.0294342041015625,
-0.007598876953125,
0.01477813720703125,
0.057281494140625,
-0.021484375,
-0.003810882568359375,
-0.022491455078125,
0.0250244140625,
-0.00704193115234375,
-0.02227783203125,
-0.005069732666015625,
-0.0203704833984375,
-0.0233917236328125,
-0.01110076904296875,
0.00389862060546875,
-0.0094451904296875,
-0.00254058837890625,
-0.00201416015625,
0.01407623291015625,
-0.005580902099609375,
0.035614013671875,
-0.0023212432861328125,
-0.0087127685546875,
-0.018310546875,
0.00756072998046875,
0.0001437664031982422,
0.0232391357421875,
0.04290771484375,
0.02008056640625,
0.003971099853515625,
0.05023193359375,
0.014862060546875,
-0.0017518997192382812,
-0.0147247314453125,
-0.0193023681640625,
0.038909912109375,
-0.006931304931640625,
-0.019683837890625,
-0.00524139404296875,
0.014862060546875,
0.0091094970703125,
0.00606536865234375,
0.0132598876953125,
0.0276947021484375,
-0.0001747608184814453,
-0.0143280029296875,
-0.0025787353515625,
-0.0006427764892578125,
-0.0110626220703125,
0.018829345703125,
-0.004878997802734375,
0.0233612060546875,
-0.0171356201171875,
0.0002894401550292969,
0.026275634765625,
0.004119873046875,
0.0166015625,
0.005950927734375,
0.0032176971435546875,
0.022735595703125,
-0.0124053955078125,
0.02679443359375,
0.023529052734375,
0.0027256011962890625,
0.02581787109375,
0.0251617431640625,
-0.0036373138427734375,
-0.0030498504638671875,
-0.0050048828125,
0.005031585693359375,
0.0015001296997070312,
0.0133819580078125,
-0.014129638671875,
0.006465911865234375,
-0.0028514862060546875,
0.0302276611328125,
-0.0120849609375,
0.024688720703125,
-0.0286865234375,
-0.006206512451171875,
0.050018310546875,
-0.0025234222412109375,
-0.008880615234375,
0.0205078125,
-0.0340576171875,
0.0095977783203125,
-0.0190277099609375,
-0.003337860107421875,
-0.0279693603515625,
0.00670623779296875,
0.01678466796875,
0.007232666015625,
0.005352020263671875,
-0.004772186279296875,
0.003597259521484375,
-0.0051727294921875,
0.01322174072265625,
0.001842498779296875,
-0.006622314453125,
0.006916046142578125,
0.0034637451171875,
-0.0187530517578125,
-0.0184783935546875,
0.0012454986572265625,
0.01470947265625,
0.0268096923828125,
-0.0030345916748046875,
-0.04266357421875,
0.0196533203125,
0.0234832763671875,
0.007251739501953125,
0.01374053955078125,
-0.0181884765625,
-0.0150146484375,
-0.01495361328125,
-0.01380157470703125,
-0.0096893310546875,
0.00983428955078125,
-0.01331329345703125,
0.00014162063598632812,
0.00701904296875,
-0.00972747802734375,
-0.00551605224609375,
0.01275634765625,
-0.02264404296875,
-0.0120849609375,
-0.01904296875,
0.0295867919921875,
-0.0040283203125,
-0.0156707763671875,
-0.013214111328125,
0.03594970703125,
0.01177215576171875,
-0.02099609375,
0.015167236328125,
0.02667236328125,
0.019561767578125,
-0.03985595703125,
0.00360107421875,
0.0259552001953125,
0.004299163818359375,
0.01078033447265625,
0.0137939453125,
0.01702880859375,
0.007045745849609375,
0.0185089111328125,
0.007080078125,
-0.047088623046875,
0.00565338134765625,
-0.0433349609375,
-0.0169525146484375,
0.004177093505859375,
0.033416748046875,
-0.0235595703125,
-0.039031982421875,
0.0271759033203125,
0.002197265625,
-0.00852203369140625,
0.01157379150390625,
-0.017730712890625,
0.01190948486328125,
0.0221099853515625,
-0.01447296142578125,
-0.016082763671875,
0.004383087158203125,
0.001987457275390625,
-0.006313323974609375,
-0.0029582977294921875,
0.0021305084228515625,
-0.00415802001953125,
-0.035675048828125,
0.052734375,
-0.0170440673828125,
0.016143798828125,
-0.03753662109375,
0.0034580230712890625,
0.00849151611328125,
0.0218505859375,
-0.032989501953125,
-0.006031036376953125,
0.0008497238159179688,
-0.004787445068359375,
0.0227508544921875,
0.005359649658203125,
-0.0001838207244873047,
-0.0012578964233398438,
0.025299072265625,
0.0193023681640625,
-0.01271820068359375,
-0.01617431640625,
-0.01049041748046875,
0.001155853271484375,
-0.001129150390625,
-0.029571533203125,
-0.015411376953125,
-0.01593017578125,
0.011810302734375,
-0.0217132568359375,
0.03485107421875,
-0.006168365478515625,
0.004695892333984375,
0.0121917724609375,
-0.006008148193359375,
-0.005695343017578125,
0.0217132568359375,
0.0190582275390625,
-0.0255889892578125,
-0.047576904296875,
-0.00482940673828125,
0.020538330078125,
0.002681732177734375,
-0.0128631591796875,
-0.0128173828125,
0.0299072265625,
0.0260009765625,
0.0031833648681640625,
-0.0239715576171875,
-0.0285797119140625,
0.0106353759765625,
0.03912353515625,
0.0236053466796875,
0.02484130859375,
0.01065826416015625,
0.0245208740234375,
0.015167236328125,
-0.02288818359375,
0.0012798309326171875,
-0.01220703125,
0.0084228515625,
0.0161895751953125,
-0.01276397705078125,
0.0104522705078125,
-0.008331298828125,
0.0062713623046875,
-0.0108489990234375,
0.0006985664367675781,
0.0219268798828125,
-0.00955963134765625,
0.0013790130615234375,
-0.03277587890625,
0.00244140625,
-0.00618743896484375,
-0.004215240478515625,
0.009307861328125,
-0.007671356201171875,
0.02081298828125,
0.01259613037109375,
-0.01399993896484375,
0.024139404296875,
0.029510498046875,
0.013092041015625,
0.002532958984375,
0.01515960693359375,
0.01319122314453125,
0.01459503173828125,
-0.001800537109375,
0.0145416259765625,
-0.01491546630859375,
0.013580322265625,
-0.019500732421875,
-0.0074920654296875,
-0.0130462646484375,
0.01251983642578125,
0.0106658935546875,
-0.034027099609375,
-0.01044464111328125,
-0.0024261474609375,
0.0244598388671875,
-0.01519775390625,
-0.000797271728515625,
0.0296630859375,
-0.039215087890625,
0.00860595703125,
0.038543701171875,
0.021881103515625,
0.026641845703125,
-0.043975830078125,
0.01044464111328125,
-0.0191802978515625,
0.0382080078125,
0.018951416015625,
-0.0240936279296875,
-0.0167999267578125,
0.0181121826171875,
-0.0006976127624511719,
0.020599365234375,
0.005435943603515625,
-0.01654052734375,
0.0163116455078125,
-0.01032257080078125,
-0.005855560302734375,
-0.01238250732421875,
0.00975799560546875,
-0.041900634765625,
-0.041290283203125,
-0.00963592529296875,
0.01296234130859375,
-0.00164794921875,
0.00921630859375,
0.0174560546875,
-0.007305145263671875,
0.0040283203125,
0.018463134765625,
0.01219940185546875,
-0.0245361328125,
0.0513916015625,
0.018768310546875,
-0.063232421875,
-0.02008056640625,
-0.01446533203125,
0.032012939453125,
-0.020233154296875,
0.0097808837890625,
0.0184173583984375,
0.016876220703125,
0.0030765533447265625,
-0.005863189697265625,
-0.047698974609375,
0.002857208251953125,
0.0150604248046875,
0.0162811279296875,
-0.020294189453125,
0.02880859375,
0.026824951171875,
-0.007488250732421875,
0.0013523101806640625,
-0.00420379638671875,
-0.0140380859375,
-0.0325927734375,
-0.0064697265625,
-0.0004925727844238281,
0.007694244384765625,
-0.01540374755859375,
-0.0362548828125,
-0.00313568115234375,
-0.00846099853515625,
0.006679534912109375,
-0.011383056640625,
-0.01202392578125,
-0.01367950439453125,
-0.032928466796875,
0.004886627197265625,
0.0135650634765625,
0.0219573974609375,
-0.046478271484375,
0.022247314453125,
-0.00574493408203125,
0.00716400146484375,
-0.0310516357421875,
0.0013742446899414062,
-0.01332855224609375,
-0.03375244140625,
0.01007080078125,
0.01316070556640625,
-0.0198822021484375,
-0.016937255859375,
-0.041168212890625,
-0.01457977294921875,
0.025299072265625,
-0.01214599609375,
-0.00763702392578125,
0.0163421630859375,
0.0287322998046875,
-0.047821044921875,
-0.004215240478515625,
0.008392333984375,
-0.006175994873046875,
0.0100250244140625,
-0.03533935546875,
0.0132904052734375,
0.008453369140625,
0.01457977294921875,
-0.00223541259765625,
0.047210693359375,
0.00457763671875,
-0.0281219482421875,
0.00652313232421875,
-0.025421142578125,
0.0187530517578125,
0.01520538330078125,
0.00879669189453125,
0.01617431640625,
-0.0206298828125,
0.016021728515625,
0.0027618408203125,
0.00862884521484375,
0.02679443359375,
-0.0265350341796875,
-0.00977325439453125,
-0.00493621826171875,
0.035675048828125,
0.00455474853515625,
-0.01061248779296875,
-0.017669677734375,
-0.0083160400390625,
0.0010900497436523438,
0.021270751953125,
0.0258941650390625,
-0.005107879638671875,
-0.01493072509765625,
0.0204315185546875,
-0.0025119781494140625,
-0.022430419921875
] |
ours_506
|
Since \(24678051\) has this property, it follows trivially that \(24678050\) does as well. Therefore, the third number is \(\boxed{24678050}\).
|
24678050
|
{
"competition": "us_comps",
"dataset": "Ours",
"posts": null,
"source": "OMOFall19Solns.md"
}
|
There are three eight-digit positive integers which are equal to the sum of the eighth powers of their digits. Given that two of the numbers are \(24678051\) and \(88593477\), compute the third number.
|
[
"/Mathematics/NumberTheory/GeneralNumberTheory/ElementaryNumberTheory",
"/Mathematics/NumberTheory/GeneralNumberTheory/NumberTheory",
"/Mathematics/NumberTheory/Numbers/LargeNumbers",
"/Mathematics/NumberTheory/Numbers/NumbersRepresentation",
"/Mathematics/NumberTheory/SpecialNumbers/Digit-RelatedNumbers",
"/Mathematics/RecreationalMathematics/Puzzles/Puzzle"
] |
Notice that changing the final digit from 1 to 0 reduces both the number and its digit‑eighth‑power sum by exactly 1, keeping the equality.
|
[
-0.00001430511474609375,
0.01435089111328125,
0.035125732421875,
0.0197601318359375,
-0.00008171796798706055,
0.02386474609375,
0.02783203125,
-0.0300750732421875,
0.0179595947265625,
-0.04541015625,
-0.0185699462890625,
-0.01471710205078125,
-0.0034961700439453125,
0.00724029541015625,
-0.03631591796875,
-0.0016307830810546875,
0.022735595703125,
0.0066070556640625,
-0.0096282958984375,
-0.0081024169921875,
-0.0156402587890625,
-0.0268402099609375,
-0.02008056640625,
0.007587432861328125,
-0.0237884521484375,
-0.0144195556640625,
-0.0261383056640625,
-0.0012331008911132812,
0.028533935546875,
-0.00482940673828125,
-0.0011806488037109375,
-0.0262908935546875,
-0.004840850830078125,
-0.00768280029296875,
-0.0009064674377441406,
-0.00833892822265625,
0.0170440673828125,
-0.0024394989013671875,
0.022247314453125,
-0.0071868896484375,
0.00039315223693847656,
0.0045318603515625,
-0.02960205078125,
0.0107574462890625,
-0.0255279541015625,
0.015869140625,
0.00036978721618652344,
-0.0418701171875,
-0.00803375244140625,
-0.01312255859375,
-0.0017547607421875,
0.010284423828125,
-0.020050048828125,
-0.0214996337890625,
-0.032562255859375,
-0.06085205078125,
-0.0182037353515625,
-0.002750396728515625,
-0.046112060546875,
0.004421234130859375,
0.010040283203125,
0.0275115966796875,
0.0005674362182617188,
-0.035064697265625,
0.0003132820129394531,
-0.005828857421875,
0.0192413330078125,
-0.025726318359375,
0.0029506683349609375,
0.009979248046875,
-0.0149993896484375,
-0.0172882080078125,
-0.0173492431640625,
0.01424407958984375,
0.030181884765625,
-0.00623321533203125,
-0.0108184814453125,
0.0082244873046875,
0.005954742431640625,
0.002490997314453125,
0.0007162094116210938,
-0.002391815185546875,
-0.0037136077880859375,
0.019500732421875,
0.010589599609375,
0.044219970703125,
-0.0162811279296875,
-0.005641937255859375,
0.03717041015625,
-0.01165008544921875,
0.004886627197265625,
0.00852203369140625,
-0.00396728515625,
0.006237030029296875,
-0.00727081298828125,
0.0084381103515625,
0.005275726318359375,
-0.01152801513671875,
-0.0087738037109375,
0.00920867919921875,
-0.00949859619140625,
-0.00937652587890625,
0.000904083251953125,
-0.0093536376953125,
-0.025970458984375,
-0.0036067962646484375,
-0.00502777099609375,
0.008209228515625,
-0.017425537109375,
0.006832122802734375,
0.00283050537109375,
0.00302886962890625,
-0.005176544189453125,
0.0394287109375,
-0.009521484375,
0.0037212371826171875,
0.0017986297607421875,
0.0108795166015625,
-0.0033817291259765625,
-0.01922607421875,
0.0003368854522705078,
0.01568603515625,
-0.0170745849609375,
-0.01218414306640625,
0.01438140869140625,
-0.0228424072265625,
-0.01084136962890625,
-0.00714874267578125,
0.0119476318359375,
0.0209503173828125,
0.019378662109375,
-0.0032749176025390625,
-0.0207672119140625,
-0.0298309326171875,
-0.087890625,
0.0009632110595703125,
0.006397247314453125,
-0.0074310302734375,
-0.0308074951171875,
-0.022491455078125,
0.005035400390625,
0.0089263916015625,
0.0181427001953125,
-0.0007348060607910156,
0.0144500732421875,
0.0229644775390625,
0.002155303955078125,
-0.019927978515625,
0.0233306884765625,
0.001873016357421875,
-0.0079193115234375,
0.0090179443359375,
0.00460052490234375,
0.0085601806640625,
0.003406524658203125,
0.00868988037109375,
0.006389617919921875,
0.0091705322265625,
-0.00934600830078125,
-0.006229400634765625,
-0.0009984970092773438,
-0.0083770751953125,
-0.0042724609375,
0.0017757415771484375,
-0.012359619140625,
-0.00151824951171875,
-0.0252227783203125,
-0.006221771240234375,
-0.018768310546875,
0.0081329345703125,
-0.01239013671875,
0.006221771240234375,
0.006011962890625,
-0.011322021484375,
-0.0004940032958984375,
-0.003658294677734375,
-0.01082611083984375,
0.013397216796875,
-0.01053619384765625,
0.015869140625,
0.005001068115234375,
-0.0472412109375,
0.032562255859375,
0.01496124267578125,
0.012603759765625,
-0.009552001953125,
-0.0119476318359375,
0.0034656524658203125,
0.0273590087890625,
0.0036563873291015625,
0.004055023193359375,
-0.01320648193359375,
-0.004566192626953125,
0.004962921142578125,
0.00045680999755859375,
-0.022247314453125,
-0.0177001953125,
0.0124969482421875,
0.07244873046875,
-0.00017380714416503906,
-0.01445770263671875,
0.0091400146484375,
-0.0008945465087890625,
0.010772705078125,
0.005634307861328125,
0.006519317626953125,
0.0060882568359375,
-0.0008959770202636719,
-0.0002994537353515625,
-0.00749969482421875,
-0.0017986297607421875,
0.0012502670288085938,
0.002933502197265625,
-0.045654296875,
-0.01070404052734375,
-0.00638580322265625,
-0.01428985595703125,
-0.01038360595703125,
0.0185699462890625,
-0.020355224609375,
0.0175933837890625,
0.014007568359375,
-0.007442474365234375,
0.00513458251953125,
-0.023590087890625,
0.006214141845703125,
-0.012542724609375,
0.0013399124145507812,
-0.00714111328125,
0.0091094970703125,
-0.0029754638671875,
0.0118255615234375,
-0.01043701171875,
0.004688262939453125,
0.002643585205078125,
0.00830078125,
-0.0196990966796875,
-0.025299072265625,
0.011199951171875,
-0.040191650390625,
0.058624267578125,
-0.013031005859375,
-0.0030155181884765625,
-0.0027027130126953125,
0.016357421875,
0.00467681884765625,
0.003772735595703125,
0.0003619194030761719,
0.0037689208984375,
-0.0222625732421875,
-0.00711822509765625,
0.018035888671875,
0.004917144775390625,
-0.0217437744140625,
-0.0209808349609375,
-0.01239776611328125,
0.0031490325927734375,
0.015380859375,
-0.0040435791015625,
-0.0067901611328125,
-0.0080413818359375,
-0.0287017822265625,
-0.01178741455078125,
-0.0019102096557617188,
-0.0022563934326171875,
0.006923675537109375,
0.0008177757263183594,
-0.0052947998046875,
0.01092529296875,
-0.0089263916015625,
0.0185089111328125,
-0.004535675048828125,
-0.005237579345703125,
0.00817108154296875,
0.038421630859375,
-0.0054779052734375,
-0.005645751953125,
0.0034503936767578125,
0.0182952880859375,
-0.0156707763671875,
0.004383087158203125,
-0.0205841064453125,
-0.01038360595703125,
0.0035228729248046875,
-0.01119232177734375,
0.01399993896484375,
0.055328369140625,
-0.007663726806640625,
-0.0304107666015625,
0.034942626953125,
-0.001438140869140625,
-0.00567626953125,
-0.03350830078125,
-0.00603485107421875,
0.053955078125,
-0.038543701171875,
0.0188140869140625,
-0.002956390380859375,
0.00759124755859375,
-0.002162933349609375,
0.03826904296875,
0.019012451171875,
-0.004322052001953125,
-0.01457977294921875,
-0.013671875,
0.018035888671875,
0.0159759521484375,
0.0086669921875,
-0.0347900390625,
-0.0165252685546875,
-0.01806640625,
0.0016613006591796875,
0.01113128662109375,
0.00847625732421875,
-0.0029010772705078125,
-0.040740966796875,
-0.001346588134765625,
0.026092529296875,
-0.017486572265625,
-0.020355224609375,
0.02911376953125,
0.005100250244140625,
-0.000012218952178955078,
0.00547027587890625,
0.004444122314453125,
0.0093994140625,
-0.004108428955078125,
-0.004364013671875,
-0.003307342529296875,
0.01776123046875,
-0.016876220703125,
0.0457763671875,
0.0028171539306640625,
-0.01556396484375,
-0.01027679443359375,
-0.0065460205078125,
0.0106048583984375,
0.0312042236328125,
-0.0215606689453125,
-0.0010843276977539062,
0.00957489013671875,
0.01445770263671875,
-0.0083160400390625,
0.006298065185546875,
-0.01042938232421875,
0.01082611083984375,
-0.0007252693176269531,
0.0052490234375,
-0.01097869873046875,
-0.0253448486328125,
-0.0172882080078125,
0.00302886962890625,
0.027252197265625,
-0.01462554931640625,
-0.045745849609375,
0.007442474365234375,
0.00012028217315673828,
0.0204315185546875,
0.019744873046875,
0.0116119384765625,
-0.0004799365997314453,
-0.0200042724609375,
0.0143585205078125,
-0.01416778564453125,
-0.00325775146484375,
-0.0183563232421875,
-0.0274200439453125,
0.0112152099609375,
-0.0243988037109375,
-0.00890350341796875,
-0.008209228515625,
-0.0278472900390625,
-0.017791748046875,
-0.0124053955078125,
-0.0104522705078125,
0.0019588470458984375,
0.0008139610290527344,
-0.0070648193359375,
-0.0005936622619628906,
-0.0097808837890625,
-0.007415771484375,
0.031494140625,
-0.0239715576171875,
0.016357421875,
0.0009303092956542969,
-0.0184783935546875,
-0.0049896240234375,
-0.03070068359375,
-0.0184173583984375,
0.0035915374755859375,
-0.0199737548828125,
0.0428466796875,
0.00356292724609375,
-0.021728515625,
0.033294677734375,
-0.0131988525390625,
0.00457763671875,
0.019195556640625,
0.032623291015625,
-0.01062774658203125,
-0.0261993408203125,
-0.01451873779296875,
-0.0174102783203125,
-0.00777435302734375,
-0.004161834716796875,
-0.017425537109375,
0.00167083740234375,
-0.0047149658203125,
0.0156402587890625,
0.0072021484375,
0.04833984375,
0.01029205322265625,
0.00646209716796875,
0.01727294921875,
-0.04876708984375,
-0.0161285400390625,
0.0169525146484375,
-0.032318115234375,
-0.00923919677734375,
-0.00359344482421875,
0.0243682861328125,
0.0208587646484375,
-0.00994873046875,
0.0200653076171875,
0.0178070068359375,
-0.00931549072265625,
-0.0440673828125,
0.027923583984375,
0.05474853515625,
-0.0246429443359375,
0.022705078125,
0.00746917724609375,
0.01241302490234375,
0.016998291015625,
-0.00672149658203125,
0.0282440185546875,
0.00435638427734375,
0.0008087158203125,
-0.05157470703125,
0.0163116455078125,
0.01425933837890625,
0.019500732421875,
0.0015163421630859375,
0.0091094970703125,
0.00836181640625,
-0.01558685302734375,
0.0242919921875,
-0.0032863616943359375,
-0.0223236083984375,
-0.012664794921875,
0.0030040740966796875,
-0.0284271240234375,
-0.0004222393035888672,
-0.017486572265625,
-0.048095703125,
-0.0005745887756347656,
0.0479736328125,
-0.0293731689453125,
-0.006008148193359375,
-0.0340576171875,
-0.0211181640625,
-0.004337310791015625,
-0.00040268898010253906,
0.01308441162109375,
-0.0262451171875,
-0.005523681640625,
-0.01230621337890625,
0.004673004150390625,
-0.0038204193115234375,
-0.0006341934204101562,
-0.0035037994384765625,
0.002899169921875,
-0.0086669921875,
-0.01300811767578125,
-0.01450347900390625,
0.0288543701171875,
-0.0008645057678222656,
0.0262908935546875,
-0.0134124755859375,
-0.003307342529296875,
0.04534912109375,
0.036895751953125,
0.003040313720703125,
0.01421356201171875,
0.00838470458984375,
0.0157928466796875,
0.0220794677734375,
0.012481689453125,
-0.028900146484375,
-0.0176544189453125,
0.047515869140625,
-0.0015935897827148438,
-0.0443115234375,
-0.0248260498046875,
-0.01434326171875,
-0.01203155517578125,
0.0276031494140625,
0.01187896728515625,
-0.0036449432373046875,
-0.000583648681640625,
0.0095367431640625,
-0.043609619140625,
0.0303955078125,
-0.00311279296875,
0.00402069091796875,
-0.0264892578125,
0.0260009765625,
-0.035919189453125,
0.0269775390625,
0.020111083984375,
0.01044464111328125,
0.009246826171875,
0.0194091796875,
-0.0296783447265625,
-0.0156097412109375,
-0.01123046875,
0.007549285888671875,
-0.040802001953125,
-0.0017786026000976562,
-0.0277862548828125,
-0.03778076171875,
-0.0164031982421875,
0.01111602783203125,
-0.00766754150390625,
0.0023288726806640625,
0.039642333984375,
0.01175689697265625,
-0.0097808837890625,
-0.0264129638671875,
0.022613525390625,
-0.0197296142578125,
0.004405975341796875,
0.0301971435546875,
0.00806427001953125,
-0.027923583984375,
-0.0167999267578125,
-0.00968170166015625,
-0.0283203125,
-0.00003600120544433594,
0.02081298828125,
-0.0088958740234375,
-0.0268096923828125,
0.006458282470703125,
-0.018157958984375,
-0.00601959228515625,
-0.0185394287109375,
-0.0198516845703125,
0.0426025390625,
-0.0252532958984375,
0.024810791015625,
0.00186920166015625,
0.0076904296875,
-0.01277923583984375,
0.0012063980102539062,
-0.03607177734375,
0.037078857421875,
0.050872802734375,
-0.00014543533325195312,
-0.001434326171875,
-0.0277099609375,
0.003932952880859375,
-0.039642333984375,
0.04229736328125,
0.03753662109375,
0.0200653076171875,
-0.0008463859558105469,
-0.0116424560546875,
-0.016632080078125,
0.0016298294067382812,
-0.05828857421875,
0.0098724365234375,
0.0242156982421875,
-0.006114959716796875,
-0.0012111663818359375,
0.0169525146484375,
-0.0006971359252929688,
-0.036834716796875,
0.00777435302734375,
-0.014129638671875,
-0.0012254714965820312,
0.0276336669921875,
0.022216796875,
0.0006322860717773438,
-0.0006709098815917969,
-0.01325225830078125,
0.002513885498046875,
-0.0037288665771484375,
0.00565338134765625,
0.0232086181640625,
-0.0091094970703125,
-0.014007568359375,
0.0032787322998046875,
-0.018157958984375,
0.0161895751953125,
0.0290374755859375,
-0.0287933349609375,
0.0005145072937011719,
-0.042236328125,
-0.0162811279296875,
0.0247802734375,
0.07196044921875,
-0.0030879974365234375,
-0.0034198760986328125,
-0.002925872802734375,
0.012847900390625,
-0.0214691162109375,
-0.0278472900390625,
0.021728515625,
-0.0157623291015625,
0.0220489501953125,
0.0092926025390625,
0.003292083740234375,
-0.0037822723388671875,
0.018646240234375,
0.039154052734375,
0.00855255126953125,
-0.0408935546875,
0.0021228790283203125,
0.008148193359375,
-0.00014925003051757812,
-0.00238800048828125,
-0.000743865966796875,
-0.0204925537109375,
0.0027637481689453125,
-0.00637054443359375,
-0.0423583984375,
0.0308685302734375,
-0.01202392578125,
0.0210113525390625,
-0.01297760009765625,
-0.0214691162109375,
0.023345947265625,
0.02105712890625,
0.0181732177734375,
0.01009368896484375,
-0.006130218505859375,
-0.0072174072265625,
0.03680419921875,
-0.038482666015625,
-0.02459716796875,
0.019866943359375,
-0.01230621337890625,
0.034881591796875,
-0.032470703125,
-0.006439208984375,
0.0301055908203125,
-0.0177764892578125,
0.04132080078125,
-0.0287017822265625,
0.003753662109375,
-0.005794525146484375,
0.05877685546875,
-0.0019989013671875,
0.01239013671875,
0.008331298828125,
0.0015354156494140625,
0.006450653076171875,
-0.01535797119140625,
0.036407470703125,
0.00276947021484375,
0.0208892822265625,
0.0154571533203125,
0.00817108154296875,
0.007843017578125,
-0.0183868408203125,
-0.04803466796875,
-0.0223846435546875,
-0.0128326416015625,
0.0121612548828125,
-0.0128326416015625,
0.01482391357421875,
0.0034885406494140625,
0.01462554931640625,
-0.0092620849609375,
0.023895263671875,
0.0006518363952636719,
-0.01213836669921875,
-0.0216827392578125,
0.0005955696105957031,
-0.003513336181640625,
-0.0233917236328125,
0.00988006591796875,
0.0171356201171875,
0.0211944580078125,
0.01070404052734375,
0.0462646484375,
0.018310546875,
0.0172882080078125,
0.0189208984375,
0.022125244140625,
0.01279449462890625,
-0.0229644775390625,
0.041595458984375,
0.03955078125,
0.01776123046875,
-0.00260162353515625,
0.01111602783203125,
0.030487060546875,
-0.005771636962890625,
-0.04656982421875,
0.02593994140625,
0.01094818115234375,
-0.00820159912109375,
-0.0049896240234375,
-0.040802001953125,
-0.0235443115234375,
0.0138092041015625,
0.00852203369140625,
-0.00887298583984375,
-0.0001881122589111328,
-0.0306243896484375,
-0.005626678466796875,
-0.04620361328125,
0.01361846923828125,
0.002468109130859375,
0.0145416259765625,
-0.0307159423828125,
-0.005481719970703125,
0.0058746337890625,
-0.0143280029296875,
-0.026397705078125,
0.01678466796875,
-0.01030731201171875,
0.02294921875,
-0.0018672943115234375,
0.026702880859375,
-0.0207061767578125,
-0.024444580078125,
-0.0301513671875,
0.019317626953125,
-0.00484466552734375,
-0.0245819091796875,
-0.00925445556640625,
0.024566650390625,
-0.015533447265625,
0.008056640625,
0.0081329345703125,
-0.0287017822265625,
-0.01190185546875,
0.0147552490234375,
-0.01290130615234375,
-0.003726959228515625,
0.0207366943359375,
-0.0041046142578125,
0.01226806640625,
0.00672149658203125,
-0.01132965087890625,
-0.0034275054931640625,
-0.010467529296875,
-0.038818359375,
0.0247039794921875,
-0.00870513916015625,
0.0421142578125,
-0.04071044921875,
-0.018096923828125,
-0.019989013671875,
0.0010700225830078125,
0.00557708740234375,
0.02777099609375,
0.0167083740234375,
-0.001270294189453125,
-0.0135498046875,
-0.028594970703125,
-0.03607177734375,
-0.007720947265625,
0.0226898193359375,
-0.04693603515625,
0.0089263916015625,
-0.009979248046875,
0.0263824462890625,
-0.01229095458984375,
-0.002040863037109375,
0.0265960693359375,
0.0128631591796875,
0.0079345703125,
-0.00884246826171875,
-0.042236328125,
0.0103759765625,
0.05816650390625,
-0.027435302734375,
0.00945281982421875,
0.0079803466796875,
-0.011566162109375,
0.007457733154296875,
-0.021484375,
-0.004131317138671875,
0.01282501220703125,
-0.00823974609375,
0.013580322265625,
-0.0288848876953125,
0.0182952880859375,
0.0164642333984375,
-0.01531219482421875,
0.0010271072387695312,
-0.01168060302734375,
-0.03338623046875,
0.005176544189453125,
-0.048370361328125,
-0.01326751708984375,
0.00011110305786132812,
0.01195526123046875,
-0.0221710205078125,
-0.006256103515625,
0.010406494140625,
0.013946533203125,
-0.011688232421875,
0.00690460205078125,
0.00957489013671875,
-0.0047760009765625,
0.038665771484375,
0.0288543701171875,
-0.00582122802734375,
-0.006732940673828125,
-0.030609130859375,
0.0017309188842773438,
-0.006237030029296875,
-0.01337432861328125,
0.02264404296875,
0.0194549560546875,
0.01184844970703125,
-0.007732391357421875,
0.0080108642578125,
-0.0019550323486328125,
0.0195159912109375,
-0.01427459716796875,
0.00139617919921875,
-0.0021305084228515625,
-0.04345703125,
0.0084991455078125,
-0.01451873779296875,
-0.0007443428039550781,
0.0133514404296875,
-0.0350341796875,
0.02392578125,
-0.008819580078125,
0.031280517578125,
0.0287933349609375,
-0.0072479248046875,
-0.0147552490234375,
0.017730712890625,
0.001239776611328125,
0.0140228271484375,
0.0189361572265625,
-0.039947509765625,
0.00044465065002441406,
-0.0170440673828125,
-0.01526641845703125,
0.0032901763916015625,
-0.004669189453125,
-0.003940582275390625,
0.01085662841796875,
0.03466796875,
-0.02325439453125,
0.0267333984375,
0.01058197021484375,
0.01218414306640625,
0.01296234130859375,
0.02508544921875,
0.005207061767578125,
-0.0113525390625,
-0.01409149169921875,
-0.044403076171875,
-0.01678466796875,
-0.0250396728515625,
0.04400634765625,
0.00027441978454589844,
0.0243682861328125,
-0.0245513916015625,
0.00962066650390625,
-0.00357818603515625,
0.0126953125,
0.01226043701171875,
0.0092926025390625,
0.00867462158203125,
0.025146484375,
0.00832366943359375,
0.0175018310546875,
0.0113067626953125,
0.01496124267578125,
-0.0023899078369140625,
0.0198822021484375,
-0.0445556640625,
0.00765228271484375,
-0.01404571533203125,
-0.01187896728515625,
0.02874755859375,
0.02520751953125,
0.0101470947265625,
0.004398345947265625,
-0.0165557861328125,
-0.00811004638671875,
-0.0024566650390625,
-0.01560211181640625,
-0.00027561187744140625,
0.007904052734375,
-0.0003948211669921875,
-0.009796142578125,
0.018280029296875,
0.006946563720703125,
-0.030517578125,
-0.01898193359375,
0.0287933349609375,
0.040740966796875,
0.046783447265625,
-0.01177978515625,
0.00551605224609375,
0.00884246826171875,
-0.00036406517028808594,
0.00787353515625,
-0.01230621337890625,
-0.026519775390625,
0.00217437744140625,
-0.0158843994140625,
0.035888671875,
-0.0181121826171875,
0.040313720703125,
-0.020782470703125,
0.0141448974609375,
0.00908660888671875,
-0.0230255126953125,
0.0223236083984375,
0.003528594970703125,
-0.038909912109375,
-0.01395416259765625,
0.00965118408203125,
-0.0308380126953125,
0.008056640625,
0.0004353523254394531,
-0.0203704833984375,
0.019561767578125,
0.01007843017578125,
0.033416748046875,
-0.00469207763671875,
0.017181396484375,
-0.005970001220703125,
0.014068603515625,
0.008026123046875,
-0.01959228515625,
-0.0291290283203125,
-0.01399993896484375,
-0.033111572265625,
-0.0229644775390625,
-0.0144195556640625,
0.00360870361328125,
-0.008056640625,
-0.01971435546875,
0.0035724639892578125,
-0.0022068023681640625,
-0.00777435302734375,
-0.005580902099609375,
-0.00141143798828125,
0.019989013671875,
-0.013092041015625,
-0.0205230712890625,
-0.0109710693359375,
-0.0095367431640625,
0.016510009765625,
0.003177642822265625,
-0.00891876220703125,
-0.015045166015625,
0.016845703125,
0.007366180419921875,
-0.04901123046875,
-0.0040130615234375,
-0.00040721893310546875,
-0.00527191162109375,
-0.012542724609375,
0.0011272430419921875,
-0.01983642578125,
0.011199951171875,
0.00045108795166015625,
-0.00797271728515625,
-0.0043182373046875,
-0.0168304443359375,
-0.00041937828063964844,
0.016632080078125,
-0.0296783447265625,
0.0301513671875,
0.0254058837890625,
-0.0010356903076171875,
-0.026702880859375,
0.01238250732421875,
-0.030548095703125,
-0.0248565673828125,
-0.0170440673828125,
0.01995849609375,
0.035247802734375,
-0.0220794677734375,
0.03326416015625,
-0.01056671142578125,
0.002716064453125,
0.0288238525390625,
0.00553131103515625,
0.024993896484375,
-0.007152557373046875,
0.01456451416015625,
-0.019866943359375,
0.0225982666015625,
0.041717529296875,
0.0082550048828125,
-0.00978851318359375,
0.00453948974609375,
-0.0032711029052734375,
0.019378662109375,
0.04473876953125,
-0.026519775390625,
0.0189971923828125,
-0.00569915771484375,
0.06268310546875,
0.0047607421875,
-0.03515625,
-0.013458251953125,
-0.0065155029296875,
0.0125274658203125,
-0.0203399658203125,
0.031280517578125,
0.0027713775634765625,
-0.004390716552734375,
-0.0394287109375,
-0.00826263427734375,
-0.002407073974609375,
-0.0187835693359375,
-0.029052734375,
-0.0288238525390625,
0.0139312744140625,
-0.030517578125,
0.025390625,
0.00946807861328125,
-0.01103973388671875,
0.0178375244140625,
-0.0019207000732421875,
-0.01265716552734375,
-0.00048804283142089844,
-0.00730133056640625,
0.006496429443359375,
-0.0184478759765625,
-0.019927978515625,
-0.017425537109375,
0.00966644287109375,
0.005802154541015625,
0.00510406494140625,
0.0128021240234375,
-0.00927734375,
-0.03173828125,
-0.02020263671875,
-0.036712646484375,
0.005588531494140625,
0.0184326171875,
-0.0212860107421875,
0.0014982223510742188,
0.02716064453125,
0.0304107666015625,
-0.032379150390625,
-0.021392822265625,
0.00664520263671875,
0.005313873291015625,
-0.0113525390625,
0.01042938232421875,
0.0266876220703125,
0.017730712890625,
-0.01861572265625,
-0.00439453125,
0.0242767333984375,
-0.0193634033203125,
0.004352569580078125,
0.0219268798828125,
-0.0259552001953125,
-0.003978729248046875,
0.0014715194702148438,
0.046875,
-0.026947021484375,
0.03216552734375,
0.015655517578125,
-0.024505615234375,
0.002338409423828125,
-0.034423828125,
0.01342010498046875,
-0.045654296875,
0.014984130859375,
0.0180816650390625,
0.0060272216796875,
0.032928466796875,
-0.037994384765625,
0.01287078857421875,
-0.0015058517456054688,
0.0240631103515625,
0.0016183853149414062,
0.0204315185546875,
-0.0095062255859375,
-0.01509857177734375,
0.0159912109375,
-0.013916015625,
-0.049285888671875,
-0.00209808349609375,
0.0133514404296875,
-0.0019664764404296875,
0.0039215087890625,
0.0219879150390625,
0.0179595947265625,
-0.017333984375,
-0.00926971435546875,
-0.00402069091796875,
0.0108184814453125,
-0.023773193359375,
-0.01947021484375,
0.0181732177734375,
0.00933837890625,
0.0004875659942626953,
0.0160369873046875,
0.0125579833984375,
-0.0281829833984375,
0.020660400390625,
0.011993408203125,
0.006809234619140625,
-0.0100250244140625,
0.0050201416015625,
-0.01537322998046875,
0.0005526542663574219,
0.0131683349609375,
0.00039386749267578125,
-0.005992889404296875,
0.0016345977783203125,
-0.00753021240234375,
-0.007171630859375,
-0.025543212890625,
-0.0033206939697265625,
0.0230255126953125,
0.0004973411560058594,
-0.0308990478515625,
0.0037097930908203125,
0.00522613525390625,
-0.0128631591796875,
0.02691650390625,
-0.024444580078125,
0.031524658203125,
-0.00817108154296875,
-0.01488494873046875,
-0.0144195556640625,
0.0256500244140625,
0.002338409423828125,
0.01416015625,
0.0211029052734375,
0.0012598037719726562,
-0.0168304443359375,
-0.006328582763671875,
-0.01068878173828125,
-0.036712646484375,
0.0180511474609375,
0.004390716552734375,
0.03076171875,
0.0204315185546875,
-0.00431060791015625,
-0.0294342041015625,
-0.01555633544921875,
0.007160186767578125,
-0.00476837158203125,
0.0045013427734375,
0.00601959228515625,
0.0125274658203125,
-0.0005192756652832031,
0.00467681884765625,
-0.0023479461669921875,
0.0093841552734375,
0.0292205810546875,
-0.054229736328125,
0.004032135009765625,
-0.004123687744140625,
0.013214111328125,
-0.0304107666015625,
-0.013275146484375,
-0.01081085205078125,
-0.040740966796875,
0.0164031982421875,
-0.00606536865234375,
0.018524169921875,
-0.01529693603515625,
0.0148773193359375,
-0.01187896728515625,
-0.00264739990234375,
0.01641845703125,
0.0176239013671875,
0.0054168701171875,
0.0284576416015625,
0.0021724700927734375,
-0.033599853515625,
0.0179290771484375,
0.0085906982421875,
0.01190185546875,
0.01372528076171875,
-0.009490966796875,
-0.0087890625,
0.00386810302734375,
-0.032623291015625,
0.01373291015625,
-0.0226593017578125,
-0.0114593505859375,
-0.028411865234375,
0.01340484619140625,
-0.0081939697265625,
-0.019805908203125,
-0.0257720947265625,
0.0256500244140625,
-0.017730712890625,
-0.00023543834686279297,
0.014984130859375,
0.0031528472900390625,
0.01111602783203125,
-0.0037593841552734375,
-0.00818634033203125,
0.0148773193359375,
-0.02154541015625,
-0.003726959228515625,
-0.01288604736328125,
-0.01052093505859375,
0.00958251953125,
-0.0246734619140625,
0.004329681396484375,
-0.01184844970703125,
-0.006626129150390625,
-0.01763916015625,
0.0115509033203125,
-0.01125335693359375,
0.0226287841796875,
0.0338134765625,
-0.01251220703125,
-0.01068878173828125,
-0.0109405517578125,
0.012481689453125,
-0.006145477294921875,
0.016357421875,
-0.0019931793212890625,
0.020904541015625,
-0.00618743896484375,
0.00742340087890625,
-0.035858154296875,
-0.0266265869140625,
-0.0249786376953125,
-0.016845703125,
0.033660888671875,
-0.003337860107421875,
-0.017059326171875,
0.0055999755859375,
0.004566192626953125,
0.0255889892578125,
0.01015472412109375,
0.00835418701171875,
-0.033538818359375,
0.0197296142578125,
-0.00980377197265625,
-0.004489898681640625,
0.007537841796875,
0.00995635986328125,
-0.0098419189453125,
-0.0156097412109375,
0.01384735107421875,
0.00679779052734375,
0.029388427734375,
-0.0268096923828125,
0.022857666015625,
-0.01396942138671875,
0.0220794677734375,
0.01261138916015625,
-0.043701171875,
0.0071258544921875,
-0.00018858909606933594,
-0.036712646484375,
0.02484130859375,
0.0186767578125,
0.00894927978515625,
0.029815673828125,
0.0110015869140625,
0.01450347900390625,
-0.01299285888671875,
0.0423583984375,
0.0015459060668945312,
-0.0111846923828125,
-0.034576416015625,
-0.059326171875,
-0.03485107421875,
-0.004749298095703125,
-0.0283966064453125,
0.0172882080078125,
0.016510009765625,
0.00665283203125,
0.010101318359375,
-0.032135009765625,
-0.0042724609375,
0.0120849609375,
0.00391387939453125,
0.0019931793212890625,
0.01129913330078125,
-0.00441741943359375,
-0.01157379150390625,
0.01483154296875,
-0.0189666748046875,
-0.00594329833984375,
0.0039215087890625,
-0.01348876953125,
0.0060882568359375,
-0.011505126953125,
0.0018568038940429688,
-0.013519287109375,
-0.0276336669921875,
-0.0153961181640625,
-0.007061004638671875,
-0.0292205810546875,
0.005176544189453125,
0.006732940673828125,
0.0011720657348632812,
-0.0545654296875,
0.0287017822265625,
0.0191650390625,
0.0253448486328125,
0.0015935897827148438,
0.033721923828125,
-0.0077362060546875,
-0.0153045654296875,
0.017578125,
-0.0223236083984375,
-0.0125732421875,
-0.008544921875,
0.01800537109375,
0.029296875,
0.009002685546875,
0.009613037109375,
-0.00969696044921875,
-0.028045654296875,
-0.031402587890625,
0.013427734375,
0.01448822021484375,
0.00579071044921875,
-0.000232696533203125,
-0.025543212890625,
-0.01284027099609375,
0.0016298294067382812,
0.01430511474609375,
0.0208587646484375,
-0.00748443603515625,
-0.006626129150390625,
-0.052734375,
-0.01302337646484375,
-0.00948333740234375,
-0.032135009765625,
-0.004505157470703125,
-0.0016145706176757812,
0.0201568603515625,
-0.01316070556640625,
0.0268096923828125,
0.0101776123046875,
-0.0125885009765625,
0.0259857177734375,
0.026031494140625,
0.016693115234375,
-0.01268768310546875,
0.0034332275390625,
-0.007640838623046875,
0.0218658447265625,
-0.004711151123046875,
0.0101776123046875,
-0.02142333984375,
0.0209197998046875,
-0.040802001953125,
0.01253509521484375,
0.0071258544921875,
0.00856781005859375,
0.016571044921875,
-0.01329803466796875,
0.0179901123046875,
-0.01035308837890625,
0.018463134765625,
0.0010004043579101562,
0.0027713775634765625,
0.00881195068359375,
0.003383636474609375,
0.0311126708984375,
0.01438140869140625,
-0.01174163818359375,
-0.006473541259765625,
0.0013608932495117188,
0.007091522216796875,
-0.008148193359375,
-0.005340576171875,
-0.0009002685546875,
0.0010528564453125,
0.006561279296875,
0.001750946044921875,
-0.00553131103515625,
0.0224456787109375,
-0.0090789794921875,
-0.00046634674072265625,
0.01165008544921875,
0.00041794776916503906,
-0.0219573974609375,
0.009521484375,
-0.01444244384765625,
-0.0401611328125,
0.0243682861328125,
0.01131439208984375,
-0.012786865234375,
0.0113372802734375,
0.010498046875,
0.0240325927734375,
-0.01861572265625,
0.017303466796875,
0.009246826171875,
-0.0389404296875,
0.0113677978515625,
0.0009512901306152344,
-0.0205535888671875,
-0.044769287109375,
0.0010919570922851562,
0.032012939453125,
0.00920867919921875,
-0.004871368408203125,
0.0016794204711914062,
-0.00891876220703125,
0.04376220703125,
0.005031585693359375,
-0.0271453857421875,
0.01470947265625,
-0.0182037353515625,
0.003574371337890625,
-0.0242156982421875,
-0.001873016357421875,
-0.023162841796875,
-0.0124969482421875,
0.0164794921875,
-0.003063201904296875,
-0.00991058349609375,
-0.021240234375,
0.0220947265625,
-0.055145263671875,
-0.0085906982421875,
0.0204620361328125,
-0.01250457763671875,
0.0084075927734375,
0.0073699951171875,
0.026336669921875,
0.028564453125,
0.033233642578125,
0.0037670135498046875,
0.0235137939453125,
0.00481414794921875,
0.016998291015625,
-0.009918212890625,
0.009674072265625,
-0.02984619140625,
-0.01751708984375,
-0.0272979736328125,
-0.0026073455810546875,
-0.025115966796875,
-0.00742340087890625,
0.0183563232421875,
-0.01218414306640625,
0.031768798828125,
0.001865386962890625,
-0.011505126953125,
0.00615692138671875,
-0.014129638671875,
-0.0156402587890625,
-0.046783447265625,
0.0201263427734375,
0.01549530029296875,
0.036773681640625,
0.0264739990234375,
-0.0258636474609375,
-0.03558349609375,
0.0150909423828125,
-0.0286865234375,
-0.0257110595703125,
-0.0182952880859375,
-0.01474761962890625,
-0.00614166259765625,
-0.01006317138671875,
-0.020721435546875,
0.0183868408203125,
0.018585205078125,
-0.01274871826171875,
0.0396728515625,
-0.033203125,
0.01372528076171875,
0.0172882080078125,
0.0170135498046875,
0.007472991943359375,
-0.0167999267578125,
-0.022369384765625,
-0.026519775390625,
0.0010986328125,
0.0521240234375,
-0.020172119140625,
-0.0019006729125976562,
0.0033931732177734375,
0.007015228271484375,
0.01099395751953125,
0.014495849609375,
0.00579071044921875,
-0.02069091796875,
-0.03125,
-0.006633758544921875,
-0.004291534423828125,
0.01454925537109375,
-0.001720428466796875,
0.01282501220703125,
0.0040130615234375,
-0.01111602783203125,
-0.0246429443359375,
0.01511383056640625,
-0.006771087646484375,
0.004283905029296875,
0.006114959716796875,
0.003467559814453125,
-0.015777587890625,
0.0149078369140625,
0.0261077880859375,
-0.001995086669921875,
-0.0178985595703125,
0.0266876220703125,
0.004344940185546875,
-0.0233917236328125,
-0.0217132568359375,
0.021636962890625,
-0.0092315673828125,
-0.02008056640625,
-0.00688934326171875,
0.007106781005859375,
-0.0172882080078125,
-0.01715087890625,
0.01947021484375,
-0.0108642578125,
0.001739501953125,
0.008544921875,
0.001399993896484375,
-0.018798828125,
-0.0103302001953125,
0.0091400146484375,
-0.01378631591796875,
-0.035125732421875,
0.0089874267578125,
-0.01322174072265625,
0.0004968643188476562,
0.033782958984375,
-0.00841522216796875,
0.023834228515625,
-0.0009212493896484375,
0.00308990478515625,
-0.017120361328125,
0.0003848075866699219,
0.02044677734375,
0.006465911865234375,
-0.01247406005859375,
0.0045166015625,
-0.020538330078125,
0.0018177032470703125,
-0.010498046875,
-0.033050537109375,
0.004817962646484375,
0.0006885528564453125,
0.0300750732421875,
-0.003604888916015625,
-0.00818634033203125,
-0.0222625732421875,
-0.0015077590942382812,
-0.00014209747314453125,
0.0231475830078125,
0.0169525146484375,
-0.0174713134765625,
0.00714111328125,
0.0299530029296875,
-0.02838134765625,
-0.003650665283203125,
-0.018341064453125,
0.0408935546875,
0.00824737548828125,
-0.0323486328125,
-0.030517578125,
0.013671875,
0.024932861328125,
0.0352783203125,
-0.00998687744140625,
-0.0053558349609375,
0.0088348388671875,
0.001392364501953125,
0.0193328857421875,
0.007030487060546875,
0.04339599609375,
0.0131378173828125,
-0.01438140869140625,
0.005054473876953125,
0.00238800048828125,
-0.0259246826171875,
0.00795745849609375,
0.0030727386474609375,
0.024200439453125,
-0.019073486328125,
0.00013065338134765625,
-0.0181427001953125,
0.0338134765625,
-0.0286865234375,
0.017120361328125,
0.029205322265625,
0.00243377685546875,
0.002910614013671875,
0.01529693603515625,
0.002166748046875,
-0.0244903564453125,
-0.0260467529296875,
0.0203704833984375,
-0.0291748046875,
-0.005401611328125,
0.0103607177734375,
0.0136260986328125,
0.04302978515625,
0.00982666015625,
-0.011077880859375,
-0.016876220703125,
0.0232086181640625,
0.0462646484375,
-0.0015077590942382812,
0.025299072265625,
0.005023956298828125,
0.021514892578125,
-0.0213775634765625,
-0.005832672119140625,
-0.0198822021484375,
0.020111083984375,
0.0133209228515625,
0.010345458984375,
0.0206146240234375,
-0.018341064453125,
-0.017333984375,
0.0065460205078125,
-0.018829345703125,
-0.01309967041015625,
-0.0224456787109375,
0.01263427734375,
-0.00856781005859375,
-0.0008144378662109375,
0.0214385986328125,
0.00820159912109375,
0.01059722900390625,
-0.0284576416015625,
0.0025196075439453125,
0.01203155517578125,
-0.055938720703125,
-0.0251312255859375,
0.00482177734375,
-0.006351470947265625,
0.027008056640625,
0.01398468017578125,
-0.00482177734375,
0.0192413330078125,
-0.00959014892578125,
0.0201416015625,
0.023162841796875,
0.01477813720703125,
-0.01082611083984375,
-0.004375457763671875,
0.00951385498046875,
0.0007658004760742188,
-0.0098724365234375,
-0.00484466552734375,
0.013092041015625,
0.013580322265625,
0.025726318359375,
0.01328277587890625,
-0.004741668701171875,
0.01421356201171875,
-0.01543426513671875,
-0.01806640625,
0.046295166015625,
-0.00428009033203125,
-0.034088134765625,
-0.0311126708984375,
0.03741455078125,
0.001323699951171875,
-0.0156402587890625,
-0.0191497802734375,
0.00360870361328125,
-0.0115509033203125,
-0.026092529296875,
0.0312347412109375,
-0.03729248046875,
0.0099945068359375,
0.01103973388671875,
-0.0264739990234375,
-0.0083770751953125,
0.0086212158203125,
0.0021648406982421875,
-0.010345458984375,
0.00576019287109375,
0.0269012451171875,
0.014373779296875,
-0.006023406982421875,
0.00608062744140625,
-0.0017175674438476562,
0.0169219970703125,
0.0102691650390625,
-0.012054443359375,
-0.00206756591796875,
-0.0010395050048828125,
-0.02801513671875,
0.0108184814453125,
-0.0212860107421875,
-0.028106689453125,
0.030059814453125,
0.039031982421875,
-0.0102081298828125,
-0.0288848876953125,
0.0015916824340820312,
0.01031494140625,
-0.0011625289916992188,
0.006603240966796875,
-0.0241851806640625,
0.0175323486328125,
-0.0185546875,
0.044281005859375,
-0.01226806640625,
0.007198333740234375,
0.0270538330078125,
-0.01462554931640625,
0.0006604194641113281,
-0.00012934207916259766,
0.0101470947265625,
-0.0263824462890625,
0.0171661376953125,
-0.0229034423828125,
-0.00521087646484375,
0.000675201416015625,
-0.0150604248046875,
0.018768310546875,
-0.003936767578125,
0.0251922607421875,
-0.03350830078125,
-0.006923675537109375,
0.0165252685546875,
-0.00049591064453125,
0.01241302490234375,
-0.04351806640625,
-0.0216522216796875,
-0.004764556884765625,
0.00099945068359375,
0.01654052734375,
-0.025787353515625,
-0.00443267822265625,
-0.00775909423828125,
-0.015472412109375,
0.003108978271484375,
0.030670166015625,
0.002887725830078125,
0.013214111328125,
0.007442474365234375,
0.0023174285888671875,
0.016357421875,
-0.0107269287109375,
-0.00024700164794921875,
0.017181396484375,
-0.033447265625,
-0.0168304443359375,
0.0102386474609375,
0.0269775390625,
0.0091705322265625,
-0.0439453125,
-0.036773681640625,
-0.0443115234375,
-0.00013566017150878906,
0.0028438568115234375,
0.00707244873046875,
-0.006439208984375,
0.01067352294921875,
-0.0102386474609375,
0.023193359375,
0.0113067626953125,
0.004119873046875,
0.0258636474609375,
-0.0103912353515625,
-0.03350830078125,
-0.005222320556640625,
-0.006626129150390625,
-0.03961181640625,
0.00737762451171875,
-0.00890350341796875,
-0.011932373046875,
-0.00032639503479003906,
-0.04144287109375,
0.0110015869140625,
0.01149749755859375,
-0.033050537109375,
-0.002094268798828125,
0.00022149085998535156,
-0.0257110595703125,
-0.052520751953125,
-0.01183319091796875,
0.0347900390625,
-0.033599853515625,
0.00376129150390625,
0.002544403076171875,
-0.011962890625,
0.0236053466796875,
0.004848480224609375,
0.052276611328125,
-0.0102996826171875,
0.0252838134765625,
0.021331787109375,
0.014739990234375,
0.0265960693359375,
-0.0012769699096679688,
-0.02587890625,
0.0115966796875,
0.0145263671875,
-0.0161285400390625,
0.003936767578125,
0.0210723876953125,
-0.01451873779296875,
-0.0199737548828125,
-0.013702392578125,
-0.00426483154296875,
0.005176544189453125,
-0.01328277587890625,
-0.004947662353515625,
0.0071563720703125,
0.004535675048828125,
-0.0105438232421875,
-0.02911376953125,
0.0011339187622070312,
-0.0228424072265625,
-0.03985595703125,
0.016632080078125,
-0.0025882720947265625,
-0.0036163330078125,
0.0260162353515625,
-0.006175994873046875,
-0.00037550926208496094,
-0.007152557373046875,
-0.040740966796875,
0.026153564453125,
-0.00745391845703125,
0.010406494140625,
-0.0178985595703125,
0.0024242401123046875,
-0.007289886474609375,
0.015838623046875,
0.0389404296875,
0.001605987548828125,
-0.003841400146484375,
-0.00949859619140625,
-0.0293731689453125,
-0.005970001220703125,
0.0251922607421875,
-0.0037250518798828125,
0.024322509765625,
-0.02752685546875,
-0.064453125,
-0.035797119140625,
-0.022857666015625,
-0.01953125,
-0.0004303455352783203,
-0.02099609375,
0.01361083984375,
-0.0007038116455078125,
0.0125274658203125,
-0.007266998291015625,
-0.05029296875,
-0.0207977294921875,
0.0216827392578125,
0.0006623268127441406,
-0.0049896240234375,
0.02557373046875,
0.0028438568115234375,
0.004543304443359375,
0.006252288818359375,
0.026702880859375,
0.00981903076171875,
-0.004642486572265625,
-0.01128387451171875,
0.0180816650390625,
-0.0075836181640625,
0.0125732421875,
0.0191497802734375,
0.046539306640625,
-0.035430908203125,
-0.013580322265625,
-0.0158233642578125,
0.00946807861328125,
-0.00083160400390625,
-0.0010471343994140625,
0.02154541015625,
-0.005916595458984375,
0.0406494140625,
0.01171875,
-0.017059326171875,
-0.01540374755859375,
-0.006076812744140625,
0.038726806640625,
0.044891357421875,
-0.00958251953125,
0.012603759765625,
-0.015533447265625,
-0.0183258056640625,
-0.027587890625,
0.029144287109375,
0.0091400146484375,
0.0072784423828125,
-0.026031494140625,
-0.007625579833984375,
0.031585693359375,
0.0291900634765625,
-0.0058135986328125,
-0.038818359375,
-0.0240020751953125,
0.0159454345703125,
0.000019252300262451172,
-0.01514434814453125,
-0.0248565673828125,
-0.00988006591796875,
-0.0018835067749023438,
0.036346435546875,
0.019195556640625,
0.018524169921875,
-0.01898193359375,
-0.0154876708984375,
0.00047326087951660156,
0.007221221923828125,
-0.01364898681640625,
0.0101165771484375,
0.005023956298828125,
0.02105712890625,
-0.03741455078125,
-0.005855560302734375,
0.01352691650390625,
0.0188751220703125,
0.0148773193359375,
-0.034820556640625,
0.0157623291015625,
0.004497528076171875,
0.006839752197265625,
0.0164794921875,
0.0159149169921875,
0.004795074462890625,
0.018341064453125,
0.0180816650390625,
0.005878448486328125,
-0.03741455078125,
-0.012451171875,
-0.0161590576171875,
-0.0258941650390625,
-0.0340576171875,
0.0252532958984375,
0.026458740234375,
0.0172576904296875,
-0.000469207763671875,
0.034637451171875,
-0.0029315948486328125,
-0.028778076171875,
-0.0146484375,
-0.0243072509765625,
0.0097503662109375,
0.01763916015625,
-0.01285552978515625,
0.00254058837890625,
0.017608642578125,
0.0289764404296875,
-0.0018796920776367188,
-0.0304107666015625,
0.019256591796875,
-0.0175323486328125,
0.00888824462890625,
0.048919677734375,
-0.0295562744140625,
-0.00787353515625,
-0.0155029296875,
0.01517486572265625,
0.0032711029052734375,
-0.03509521484375,
0.005779266357421875,
0.0218658447265625,
0.006900787353515625,
-0.01064300537109375,
0.035736083984375,
0.0029144287109375,
-0.0177154541015625,
0.002147674560546875,
-0.03057861328125,
-0.0284271240234375,
0.00313568115234375,
0.0017299652099609375,
-0.004306793212890625,
0.0157928466796875,
-0.01861572265625,
-0.01165008544921875,
0.0055694580078125,
0.01861572265625,
0.0093231201171875,
-0.01428985595703125,
-0.0084991455078125,
0.0145416259765625,
-0.0039825439453125,
0.01531982421875,
0.034759521484375,
0.0241851806640625,
-0.0050506591796875,
-0.0200958251953125,
0.05517578125,
0.02008056640625,
0.016326904296875,
-0.031890869140625,
-0.034210205078125,
-0.0021419525146484375,
0.03253173828125,
-0.0003948211669921875,
0.00782012939453125,
-0.01552581787109375,
-0.03228759765625,
0.005550384521484375,
-0.0291595458984375,
0.00466156005859375,
0.01345062255859375,
-0.0212249755859375,
0.007843017578125,
-0.03564453125,
0.00481414794921875,
-0.008056640625,
-0.02984619140625,
0.010040283203125,
-0.0285186767578125,
-0.01277923583984375,
0.0029964447021484375,
0.0127410888671875,
0.0108184814453125,
0.0206298828125,
0.005558013916015625,
-0.0019969940185546875,
0.01235198974609375,
0.014801025390625,
0.0214996337890625,
0.01067352294921875,
-0.0018711090087890625,
-0.0104827880859375,
-0.020965576171875,
0.01514434814453125,
-0.0016117095947265625,
-0.0200347900390625,
0.0029125213623046875,
0.006549835205078125,
0.034393310546875,
-0.024322509765625,
-0.01206207275390625,
-0.0173797607421875,
0.005565643310546875,
-0.00994110107421875,
0.009613037109375,
-0.032928466796875,
0.020233154296875,
0.034942626953125,
0.02301025390625,
-0.0017938613891601562,
-0.003772735595703125,
-0.00525665283203125,
-0.024688720703125,
0.0258941650390625,
-0.007472991943359375,
-0.01067352294921875,
0.01332855224609375,
0.044525146484375,
-0.009765625,
-0.01247406005859375,
0.01526641845703125,
-0.0297088623046875,
0.004474639892578125,
-0.0133056640625,
-0.022613525390625,
-0.03753662109375,
0.006793975830078125,
-0.044647216796875,
-0.0223388671875,
-0.0109710693359375,
-0.0288238525390625,
0.01306915283203125,
0.01708984375,
0.003078460693359375,
0.0182342529296875,
-0.0284271240234375,
-0.0017242431640625,
0.0305633544921875,
0.0108184814453125,
-0.00421905517578125,
-0.010284423828125,
-0.0233612060546875,
-0.0136260986328125,
-0.01366424560546875,
-0.0255584716796875,
-0.0362548828125,
0.046356201171875,
0.0168304443359375,
0.0057373046875,
0.048583984375,
-0.0221405029296875,
-0.04876708984375,
-0.00861358642578125,
-0.0031719207763671875,
-0.03955078125,
0.00452423095703125,
0.0198516845703125,
0.0020084381103515625,
0.0010700225830078125,
0.005523681640625,
-0.0172119140625,
0.037078857421875,
-0.04571533203125,
-0.009857177734375,
0.035614013671875,
0.0333251953125,
-0.029876708984375,
-0.001995086669921875,
-0.032867431640625,
-0.00344085693359375,
0.0184326171875,
0.0283660888671875,
-0.0280914306640625,
0.04620361328125,
0.012786865234375,
0.0364990234375,
0.005794525146484375,
0.0191497802734375,
-0.019012451171875,
0.000568389892578125,
0.00325775146484375,
-0.031890869140625,
-0.00617218017578125,
-0.015960693359375,
-0.00006747245788574219,
-0.0294342041015625,
-0.0035991668701171875,
-0.00690460205078125,
-0.00860595703125,
-0.00679779052734375,
-0.01666259765625,
0.005474090576171875,
-0.039337158203125,
-0.01470184326171875,
-0.0036907196044921875,
0.0240631103515625,
-0.00658416748046875,
0.02215576171875,
0.0272979736328125,
0.0180816650390625,
0.0280303955078125,
-0.005306243896484375,
-0.001415252685546875,
0.01548004150390625,
-0.0155487060546875,
-0.0164794921875,
0.0236053466796875,
-0.03546142578125,
0.0174560546875,
0.01255035400390625,
0.005252838134765625,
0.0139007568359375,
-0.0204315185546875,
-0.01128387451171875,
-0.0023250579833984375,
0.0287322998046875,
-0.036651611328125,
-0.01297760009765625,
0.019317626953125,
0.0227508544921875,
-0.03326416015625,
-0.0167083740234375,
-0.006336212158203125,
0.01227569580078125,
-0.027496337890625,
0.001148223876953125,
-0.00942230224609375,
0.032623291015625,
0.0248260498046875,
-0.0301361083984375,
0.006855010986328125,
-0.046112060546875,
-0.022552490234375,
-0.0220489501953125,
-0.0027179718017578125,
0.0116729736328125,
0.007495880126953125,
-0.0142974853515625,
0.034942626953125,
-0.0220947265625,
0.0185089111328125,
0.01041412353515625,
0.0111083984375,
0.04669189453125,
-0.007350921630859375,
-0.0253448486328125,
-0.021636962890625,
0.045867919921875,
-0.0090484619140625,
-0.0135955810546875,
-0.003513336181640625,
0.0247344970703125,
0.00457000732421875,
-0.0080108642578125,
0.008453369140625,
0.004177093505859375,
0.008148193359375,
-0.00251007080078125,
-0.00005841255187988281,
-0.0011138916015625,
0.00540924072265625,
-0.0084991455078125,
-0.03985595703125,
-0.0301513671875,
-0.008514404296875,
-0.01165771484375,
0.0030879974365234375,
-0.02880859375,
0.0250091552734375,
0.0185699462890625,
0.026580810546875,
0.0287017822265625,
-0.020538330078125,
-0.0004787445068359375,
0.0211639404296875,
-0.0030670166015625,
0.0259857177734375,
0.020965576171875,
-0.007160186767578125,
0.0055999755859375,
-0.0053863525390625,
0.03558349609375,
0.021026611328125,
0.0011234283447265625,
-0.0252685546875,
-0.01270294189453125,
0.00389862060546875,
0.0265655517578125,
-0.0018091201782226562,
0.0170745849609375,
-0.0096588134765625,
0.01401519775390625,
-0.0198974609375,
-0.0301055908203125,
0.0181732177734375,
-0.0303192138671875,
0.003772735595703125,
-0.052581787109375,
-0.048492431640625,
0.037445068359375,
-0.0082550048828125,
0.0164642333984375,
0.01319122314453125,
0.0025539398193359375,
0.0067291259765625,
-0.045623779296875,
0.01082611083984375,
-0.0211029052734375,
-0.0133819580078125,
0.017669677734375,
-0.0019245147705078125,
-0.019561767578125,
0.0343017578125,
-0.0181427001953125,
0.027374267578125,
0.01096343994140625,
0.0133209228515625,
0.004383087158203125,
0.01363372802734375,
0.00946807861328125,
0.00455474853515625,
-0.0111236572265625,
-0.0274505615234375,
-0.0173187255859375,
0.007633209228515625,
-0.00997161865234375,
0.0032062530517578125,
-0.0169677734375,
0.0047607421875,
0.036041259765625,
-0.0177764892578125,
-0.02587890625,
-0.03460693359375,
-0.0287628173828125,
0.00823974609375,
0.000812530517578125,
-0.00399017333984375,
-0.0204315185546875,
0.012420654296875,
0.0173492431640625,
0.004100799560546875,
-0.00353240966796875,
-0.014068603515625,
-0.0008974075317382812,
0.0049285888671875,
-0.0003178119659423828,
-0.004543304443359375,
0.0037937164306640625,
-0.0014982223510742188,
0.0277557373046875,
0.01153564453125,
0.0212554931640625,
-0.0017223358154296875,
0.006259918212890625,
0.0026226043701171875,
0.01265716552734375,
-0.0012235641479492188,
0.0207061767578125,
0.01155853271484375,
0.01149749755859375,
-0.01439666748046875,
-0.0254058837890625,
-0.009368896484375,
0.0027256011962890625,
0.0263519287109375,
-0.0083465576171875,
-0.020263671875,
-0.02313232421875,
-0.0128021240234375,
-0.035858154296875,
-0.02203369140625,
-0.0120391845703125,
0.0293426513671875,
0.00852203369140625,
-0.036376953125,
-0.03363037109375,
-0.01026153564453125,
0.007511138916015625,
0.02777099609375,
0.004520416259765625,
-0.004825592041015625,
0.007129669189453125,
-0.02618408203125,
-0.004467010498046875,
0.01259613037109375,
0.001270294189453125,
-0.019744873046875,
-0.0134429931640625,
0.00821685791015625,
-0.027130126953125,
0.005031585693359375,
-0.00292205810546875,
-0.0017690658569335938,
-0.00917816162109375,
0.0162353515625,
-0.01149749755859375,
0.027679443359375,
-0.0108795166015625,
0.00958251953125,
-0.023406982421875,
0.0202789306640625,
-0.00742340087890625,
-0.005573272705078125,
-0.01995849609375,
0.00029468536376953125,
-0.0017919540405273438,
0.0060577392578125,
0.01044464111328125,
0.005462646484375,
-0.02679443359375,
-0.010894775390625,
0.0109710693359375,
-0.01148223876953125,
0.01203155517578125,
-0.04595947265625,
-0.000286102294921875,
-0.010833740234375,
0.0362548828125,
0.04571533203125,
-0.01052093505859375,
-0.0002384185791015625,
-0.011199951171875,
-0.0025844573974609375,
0.0048065185546875,
0.00860595703125,
0.01319122314453125,
0.00646209716796875,
-0.00705718994140625,
0.0002613067626953125,
0.0243072509765625,
0.042816162109375,
0.01404571533203125,
-0.0278472900390625,
0.0005931854248046875,
0.01861572265625,
0.032257080078125,
0.0478515625,
-0.0257568359375,
-0.007579803466796875,
0.00006186962127685547,
-0.00646209716796875,
-0.01517486572265625,
-0.005523681640625,
-0.0082244873046875,
0.00455474853515625,
0.003437042236328125,
-0.0010929107666015625,
-0.044952392578125,
-0.00445556640625,
0.022552490234375,
-0.00595855712890625,
-0.0172576904296875,
-0.01446533203125,
-0.018798828125,
-0.01221466064453125,
0.0232086181640625,
-0.018096923828125,
0.0175323486328125,
-0.03424072265625,
-0.0252227783203125,
-0.00946807861328125,
0.0025539398193359375,
0.016387939453125,
0.01326751708984375,
0.029998779296875,
0.01300048828125,
0.001132965087890625,
-0.02294921875,
0.0188446044921875,
0.012969970703125,
0.00955963134765625,
0.025421142578125,
0.0284881591796875,
0.00940704345703125,
-0.00893402099609375,
0.00091552734375,
-0.01568603515625,
0.0192108154296875,
-0.02587890625,
0.0176849365234375,
-0.046417236328125,
0.004058837890625,
0.003971099853515625,
-0.01554107666015625,
0.003387451171875,
-0.0113677978515625,
-0.00714874267578125,
0.0333251953125,
-0.02508544921875,
0.01161956787109375,
-0.0290069580078125,
0.032989501953125,
-0.0287628173828125,
-0.022247314453125,
0.0010538101196289062,
0.0182037353515625,
-0.009063720703125,
-0.01015472412109375,
0.0010309219360351562,
0.01160430908203125,
0.003238677978515625,
-0.0142669677734375,
0.00847625732421875,
0.0116729736328125,
0.014495849609375,
0.00814056396484375,
-0.0007886886596679688,
0.0088958740234375,
0.0245208740234375,
0.0008902549743652344,
-0.01477813720703125,
0.011016845703125,
-0.01036834716796875,
-0.00653839111328125,
0.006229400634765625,
-0.0034999847412109375,
0.0028743743896484375,
0.0440673828125,
0.049530029296875,
-0.0082855224609375,
-0.01165008544921875,
-0.006908416748046875,
-0.0018978118896484375,
0.0029125213623046875,
-0.0037174224853515625,
0.00463104248046875,
-0.0111083984375,
-0.032470703125,
-0.004131317138671875,
-0.01140594482421875,
0.003536224365234375,
0.0183868408203125,
-0.002498626708984375,
-0.016265869140625,
-0.0023708343505859375,
0.00722503662109375,
0.0124664306640625,
0.00308990478515625,
-0.0101165771484375,
-0.02325439453125,
-0.0066680908203125,
-0.034942626953125,
0.00795745849609375,
-0.01000213623046875,
-0.01605224609375,
0.018707275390625,
-0.0115203857421875,
-0.00807952880859375,
-0.016387939453125,
0.0312347412109375,
-0.0151824951171875,
-0.0279693603515625,
0.0025463104248046875,
0.0311126708984375,
0.0264434814453125,
0.0002772808074951172,
0.011444091796875,
-0.027801513671875,
-0.0101776123046875,
0.00141143798828125,
-0.00943756103515625,
0.00942230224609375,
-0.0295562744140625,
-0.039520263671875,
0.01207733154296875,
-0.0111541748046875,
0.0037899017333984375,
-0.0153961181640625,
0.01169586181640625,
-0.0036067962646484375,
-0.00041937828063964844,
-0.0159149169921875,
-0.0229034423828125,
-0.0157318115234375,
0.028839111328125,
-0.031585693359375,
0.0032711029052734375,
-0.0113525390625,
-0.0167236328125,
-0.0262451171875,
-0.016510009765625,
0.0023441314697265625,
-0.0154266357421875,
-0.01251220703125,
-0.003955841064453125,
0.00144195556640625,
-0.007080078125,
-0.0303802490234375,
-0.0005674362182617188,
-0.006076812744140625,
0.00041294097900390625,
-0.01190185546875,
-0.00885772705078125,
0.0235748291015625,
-0.026947021484375,
-0.00380706787109375,
0.010833740234375,
0.0194854736328125,
0.00791168212890625,
-0.0202789306640625,
-0.0079803466796875,
-0.008697509765625,
-0.01068878173828125,
-0.021759033203125,
-0.00223541259765625,
0.00031948089599609375,
-0.000017642974853515625,
0.00533294677734375,
0.0029697418212890625,
-0.0004324913024902344,
0.03277587890625,
-0.025543212890625,
-0.0137786865234375,
0.0019464492797851562,
0.023956298828125
] |
ours_507
|
Set the radius of \(\gamma_{1}\) to be \(r\). Let the center of \(\gamma_{i}\) be \(O_{i}\), the foot of \(O_{1}\) onto \(\overline{B C}\) be \(X\), the midpoint of \(\overline{B C}\) be \(M\), and the center of \(A B C D E F\) be \(O\).
We now do some length chasing. Note \(O_{1} X=r\) and, because \(\triangle O_{1} X B\) is a \(30-60-90\) triangle, \(B X=r / \sqrt{3}\) and so \(C X=2-r / \sqrt{3}\). Moreover, \(\triangle O_{1} O_{2} O_{3}\) is equilateral with center \(O\) by symmetry, so \(O O_{1}=2 r / \sqrt{3}\). Finally, by extending sides \(B C, D E, F A\) to form an equilateral triangle, we have \(O M=\sqrt{3}\).
Then by the Pythagorean Theorem on right trapezoid \(X M O O_{1}\), we have
\[
\left(2-\frac{r}{\sqrt{3}}\right)^{2}+(\sqrt{3}-r)^{2}=\left(\frac{2 r}{\sqrt{3}}\right)^{2}
\]
which leads to \(r=\frac{7 \sqrt{3}}{10}\). Thus, the area of \(\gamma_{1}\) is \(\pi r^{2}=\frac{147 \pi}{100}\), so the answer is \(100 \cdot 147+100=14800\).
\(\boxed{14800}\)
|
14800
|
{
"competition": "us_comps",
"dataset": "Ours",
"posts": null,
"source": "OMOFall19Solns.md"
}
|
Convex equiangular hexagon \(A B C D E F\) has \(A B=C D=E F=1\) and \(B C=D E=F A=4\). Congruent and pairwise externally tangent circles \(\gamma_{1}, \gamma_{2},\) and \(\gamma_{3}\) are drawn such that \(\gamma_{1}\) is tangent to side \(\overline{A B}\) and side \(\overline{B C}\), \(\gamma_{2}\) is tangent to side \(\overline{C D}\) and side \(\overline{D E}\), and \(\gamma_{3}\) is tangent to side \(\overline{E F}\) and side \(\overline{F A}\). Then the area of \(\gamma_{1}\) can be expressed as \(\frac{m \pi}{n}\) for relatively prime positive integers \(m\) and \(n\). Compute \(100 m+n\).
|
[
"/Mathematics/Geometry/PlaneGeometry/Circles/Circle",
"/Mathematics/Geometry/PlaneGeometry/Circles/Circle-CircleTangents",
"/Mathematics/Geometry/PlaneGeometry/Circles/CircleTangentLine",
"/Mathematics/Geometry/PlaneGeometry/Circles/Radius",
"/Mathematics/Geometry/PlaneGeometry/Circles/TangentCircles",
"/Mathematics/Geometry/PlaneGeometry/Hexagons",
"/Mathematics/Geometry/PlaneGeometry/Polygons/ConvexPolygon",
"/Mathematics/Geometry/PlaneGeometry/Polygons/EquiangularPolygon",
"/Mathematics/Geometry/PlaneGeometry/Polygons/Hexagon",
"/Mathematics/Geometry/PlaneGeometry/Polygons/Polygon",
"/Mathematics/Geometry/PlaneGeometry/Polygons/SimplePolygon",
"/Mathematics/Geometry/PlaneGeometry/Triangles/SpecialTriangles"
] |
Use symmetry to see the circle centers form an equilateral triangle and relate the radius via 30‑60‑90 triangle distances to the sides.
|
[
0.00022649765014648438,
-0.0205841064453125,
-0.01091766357421875,
0.01171112060546875,
0.001247406005859375,
-0.004241943359375,
0.03436279296875,
0.021484375,
0.00855255126953125,
-0.020843505859375,
-0.01751708984375,
0.01030731201171875,
-0.00443267822265625,
0.0247650146484375,
-0.0081024169921875,
-0.0011653900146484375,
-0.03369140625,
-0.053070068359375,
0.03509521484375,
-0.0003650188446044922,
-0.011383056640625,
0.0177154541015625,
-0.06243896484375,
0.01425933837890625,
-0.0066070556640625,
-0.037933349609375,
-0.018341064453125,
0.034332275390625,
-0.00333404541015625,
0.00722503662109375,
-0.020294189453125,
0.00994873046875,
-0.0021381378173828125,
-0.0005431175231933594,
0.0019588470458984375,
0.016754150390625,
0.026031494140625,
0.003948211669921875,
-0.0196533203125,
-0.03851318359375,
0.00760650634765625,
0.0253448486328125,
-0.009185791015625,
0.0188446044921875,
-0.03424072265625,
0.039093017578125,
0.00605010986328125,
0.01016998291015625,
-0.03143310546875,
-0.002765655517578125,
0.008544921875,
0.0162200927734375,
-0.003208160400390625,
-0.0020771026611328125,
-0.02459716796875,
-0.050384521484375,
-0.0107574462890625,
-0.00818634033203125,
-0.0180511474609375,
0.00487518310546875,
0.0005369186401367188,
0.016998291015625,
-0.0221710205078125,
0.006256103515625,
-0.0006728172302246094,
-0.0018634796142578125,
0.0194091796875,
-0.0147552490234375,
0.01474761962890625,
0.009735107421875,
0.038330078125,
-0.045074462890625,
0.01654052734375,
0.022186279296875,
-0.0013856887817382812,
-0.01430511474609375,
-0.0039043426513671875,
0.004634857177734375,
-0.0029506683349609375,
0.007106781005859375,
0.0196990966796875,
0.00951385498046875,
0.0228424072265625,
-0.06427001953125,
0.00005638599395751953,
-0.023101806640625,
-0.00984954833984375,
0.00400543212890625,
0.02850341796875,
0.0104217529296875,
0.005733489990234375,
0.02093505859375,
-0.00897979736328125,
-0.0037078857421875,
0.0013952255249023438,
0.0030155181884765625,
0.02032470703125,
-0.006488800048828125,
-0.0257110595703125,
0.004001617431640625,
-0.024017333984375,
-0.0052642822265625,
0.007137298583984375,
-0.0293731689453125,
0.0034637451171875,
-0.01398468017578125,
-0.00789642333984375,
0.01384735107421875,
0.007511138916015625,
-0.003162384033203125,
-0.00411224365234375,
-0.0220489501953125,
0.035491943359375,
0.0163116455078125,
0.00875091552734375,
-0.0233154296875,
0.04486083984375,
-0.00543975830078125,
-0.00730133056640625,
0.0026569366455078125,
0.008026123046875,
0.0082550048828125,
0.0079498291015625,
0.009552001953125,
0.020904541015625,
-0.0253143310546875,
-0.004428863525390625,
-0.0279083251953125,
-0.04473876953125,
0.007656097412109375,
0.013031005859375,
0.00438690185546875,
-0.05352783203125,
-0.014434814453125,
-0.029083251953125,
0.0234832763671875,
-0.0004298686981201172,
0.00399017333984375,
-0.0215606689453125,
-0.01146697998046875,
-0.007320404052734375,
-0.01534271240234375,
0.01499176025390625,
-0.058502197265625,
0.0188751220703125,
-0.010101318359375,
0.00014078617095947266,
-0.03045654296875,
0.0090179443359375,
0.006031036376953125,
-0.012542724609375,
-0.01183319091796875,
0.01355743408203125,
0.02392578125,
-0.00789642333984375,
-0.0009589195251464844,
-0.004344940185546875,
0.01462554931640625,
0.01511383056640625,
-0.005695343017578125,
0.0126495361328125,
0.0008749961853027344,
0.0140380859375,
0.023834228515625,
-0.0008368492126464844,
-0.03179931640625,
0.007411956787109375,
0.0025730133056640625,
-0.012542724609375,
0.01513671875,
-0.00011909008026123047,
0.0033435821533203125,
-0.0006241798400878906,
-0.0104217529296875,
0.01416015625,
0.013031005859375,
-0.005664825439453125,
0.01800537109375,
-0.013153076171875,
0.01560211181640625,
0.017578125,
-0.0084991455078125,
0.0238800048828125,
-0.004207611083984375,
0.0142822265625,
0.02996826171875,
0.00974273681640625,
-0.002292633056640625,
0.00722503662109375,
0.00185394287109375,
0.00722503662109375,
-0.01531982421875,
-0.0059967041015625,
-0.0008635520935058594,
0.025054931640625,
0.01273345947265625,
-0.0246124267578125,
0.037445068359375,
0.026702880859375,
-0.005168914794921875,
-0.0198211669921875,
-0.002758026123046875,
0.0197906494140625,
0.0013408660888671875,
-0.0204315185546875,
-0.01214599609375,
0.00815582275390625,
-0.0030918121337890625,
-0.01727294921875,
0.00992584228515625,
-0.0038433074951171875,
0.0223236083984375,
0.0018968582153320312,
0.008819580078125,
-0.0146942138671875,
-0.008636474609375,
-0.0070648193359375,
0.006954193115234375,
0.0161895751953125,
-0.00372314453125,
0.01593017578125,
-0.007503509521484375,
0.003509521484375,
-0.0162200927734375,
-0.005126953125,
0.018890380859375,
0.025360107421875,
-0.006717681884765625,
0.0204010009765625,
-0.0141754150390625,
-0.0039520263671875,
0.025115966796875,
-0.00458526611328125,
-0.00215911865234375,
-0.006343841552734375,
-0.024139404296875,
-0.03375244140625,
-0.004638671875,
0.026275634765625,
0.003353118896484375,
0.0217742919921875,
-0.005107879638671875,
0.0113067626953125,
-0.0026988983154296875,
0.004199981689453125,
0.0005583763122558594,
0.029449462890625,
-0.003078460693359375,
0.0006937980651855469,
-0.01019287109375,
-0.0229949951171875,
0.01013946533203125,
0.00897979736328125,
-0.009307861328125,
-0.0158843994140625,
0.0254058837890625,
0.014373779296875,
-0.0067596435546875,
-0.0042572021484375,
-0.00667572021484375,
-0.0144805908203125,
-0.011322021484375,
-0.007038116455078125,
-0.005092620849609375,
-0.004116058349609375,
0.00803375244140625,
0.007781982421875,
0.003612518310546875,
0.0193634033203125,
-0.0082855224609375,
0.02642822265625,
-0.002071380615234375,
-0.0162353515625,
-0.007625579833984375,
-0.0251922607421875,
-0.018890380859375,
0.00948333740234375,
0.02020263671875,
0.0074462890625,
-0.000030159950256347656,
0.00823974609375,
-0.04400634765625,
-0.048980712890625,
0.0225982666015625,
-0.00018215179443359375,
-0.0209197998046875,
0.029296875,
-0.00806427001953125,
-0.00373077392578125,
0.02423095703125,
-0.00714111328125,
0.0144195556640625,
-0.00896453857421875,
-0.00772857666015625,
0.06488037109375,
-0.0215301513671875,
-0.005168914794921875,
0.01535797119140625,
0.0157623291015625,
0.006801605224609375,
0.0165557861328125,
-0.0247650146484375,
-0.001186370849609375,
0.01331329345703125,
0.032135009765625,
0.00923919677734375,
-0.012451171875,
-0.0196380615234375,
-0.010223388671875,
0.0040130615234375,
0.027313232421875,
0.0114593505859375,
0.001827239990234375,
0.007190704345703125,
-0.0220947265625,
-0.037139892578125,
-0.001735687255859375,
0.001201629638671875,
-0.0115966796875,
-0.001499176025390625,
0.00275421142578125,
0.016448974609375,
0.0198516845703125,
0.01174163818359375,
0.033905029296875,
-0.0120086669921875,
0.0057220458984375,
0.007724761962890625,
0.00981903076171875,
0.01396942138671875,
-0.004180908203125,
0.001094818115234375,
-0.0053253173828125,
-0.0176239013671875,
-0.01983642578125,
-0.00574493408203125,
0.004039764404296875,
0.005397796630859375,
0.0011463165283203125,
-0.0012760162353515625,
0.01055145263671875,
0.006336212158203125,
0.037506103515625,
-0.04071044921875,
-0.0197906494140625,
0.0279693603515625,
-0.0173492431640625,
0.0178375244140625,
-0.01386260986328125,
-0.043121337890625,
-0.0241241455078125,
-0.0016450881958007812,
0.0186767578125,
0.02703857421875,
-0.02105712890625,
0.013397216796875,
-0.0084686279296875,
0.0006761550903320312,
-0.00152587890625,
0.03240966796875,
0.01325225830078125,
-0.01041412353515625,
-0.001583099365234375,
0.0008330345153808594,
-0.0010461807250976562,
0.0102386474609375,
-0.00807952880859375,
-0.01227569580078125,
-0.03240966796875,
-0.01221466064453125,
0.0011119842529296875,
0.0007772445678710938,
-0.00858306884765625,
-0.00928497314453125,
0.019561767578125,
-0.01279449462890625,
0.018402099609375,
0.006923675537109375,
0.0047149658203125,
0.0032558441162109375,
-0.004833221435546875,
0.015380859375,
0.03826904296875,
0.031219482421875,
-0.0114898681640625,
0.01088714599609375,
0.03570556640625,
-0.042144775390625,
-0.0208587646484375,
-0.01502227783203125,
0.01197052001953125,
0.0167236328125,
-0.004711151123046875,
-0.029510498046875,
-0.00179290771484375,
-0.0278778076171875,
-0.00612640380859375,
0.00040221214294433594,
0.06317138671875,
-0.03326416015625,
-0.057220458984375,
0.0217437744140625,
0.00011450052261352539,
0.00954437255859375,
-0.00958251953125,
0.0153350830078125,
-0.024444580078125,
-0.0014743804931640625,
-0.01212310791015625,
0.007526397705078125,
-0.010894775390625,
0.011444091796875,
0.01425933837890625,
-0.0133514404296875,
-0.0007848739624023438,
0.006805419921875,
0.010986328125,
0.02471923828125,
0.003238677978515625,
0.014068603515625,
0.00978851318359375,
-0.0222930908203125,
0.01467132568359375,
-0.0194091796875,
0.022430419921875,
0.0194549560546875,
0.005817413330078125,
0.04132080078125,
-0.01255035400390625,
-0.0294342041015625,
0.028289794921875,
-0.029541015625,
-0.004425048828125,
0.019561767578125,
-0.01861572265625,
0.003963470458984375,
0.01641845703125,
-0.0192413330078125,
-0.00579833984375,
0.0120086669921875,
-0.0113525390625,
-0.0096893310546875,
-0.00267791748046875,
-0.0126953125,
-0.022613525390625,
0.006519317626953125,
0.01389312744140625,
0.0033702850341796875,
-0.02325439453125,
0.028533935546875,
-0.006435394287109375,
0.005077362060546875,
-0.0028171539306640625,
-0.0186614990234375,
0.004978179931640625,
-0.006862640380859375,
0.025970458984375,
-0.0277099609375,
-0.0124359130859375,
0.0271453857421875,
-0.0004439353942871094,
-0.01806640625,
-0.01464080810546875,
0.0032787322998046875,
-0.01136016845703125,
0.008544921875,
-0.0308990478515625,
0.0220489501953125,
0.007659912109375,
0.01064300537109375,
-0.0253753662109375,
-0.024566650390625,
-0.0015506744384765625,
-0.01336669921875,
-0.0260467529296875,
0.0221405029296875,
-0.007564544677734375,
0.00970458984375,
-0.00002378225326538086,
0.0032596588134765625,
-0.0235748291015625,
-0.00652313232421875,
-0.0270538330078125,
0.02667236328125,
0.0306549072265625,
-0.00653839111328125,
0.01666259765625,
0.0021228790283203125,
-0.024749755859375,
-0.023101806640625,
0.002330780029296875,
0.0419921875,
-0.00966644287109375,
-0.022186279296875,
-0.036956787109375,
-0.0205230712890625,
0.006633758544921875,
-0.0158538818359375,
0.0034275054931640625,
0.0226287841796875,
-0.023956298828125,
-0.01313018798828125,
-0.0174560546875,
0.00951385498046875,
0.01263427734375,
-0.04180908203125,
0.05609130859375,
-0.019012451171875,
0.0167236328125,
0.01433563232421875,
0.01074981689453125,
0.033111572265625,
0.023956298828125,
-0.022430419921875,
0.0135955810546875,
0.0211639404296875,
0.0125579833984375,
-0.01401519775390625,
-0.004749298095703125,
0.04400634765625,
-0.025360107421875,
0.01666259765625,
0.032379150390625,
0.01378631591796875,
-0.0078125,
0.0033130645751953125,
-0.036102294921875,
0.0003666877746582031,
-0.0010614395141601562,
-0.0190277099609375,
-0.01317596435546875,
-0.015411376953125,
-0.033233642578125,
0.018798828125,
-0.032470703125,
0.014862060546875,
0.004878997802734375,
0.0224609375,
0.01190948486328125,
-0.005054473876953125,
0.01568603515625,
-0.0095672607421875,
0.027008056640625,
0.0020599365234375,
0.0032329559326171875,
-0.01470184326171875,
-0.0084228515625,
0.00521087646484375,
0.005153656005859375,
0.0220184326171875,
0.0177154541015625,
0.02630615234375,
-0.01212310791015625,
0.0045013427734375,
-0.026763916015625,
0.014129638671875,
-0.017333984375,
-0.0199737548828125,
-0.01103973388671875,
0.002216339111328125,
0.0090789794921875,
0.0037212371826171875,
0.024810791015625,
0.00531005859375,
0.00016248226165771484,
-0.025970458984375,
0.01313018798828125,
0.00795745849609375,
-0.005401611328125,
-0.0118560791015625,
0.016204833984375,
0.00724029541015625,
0.00904083251953125,
0.014190673828125,
0.024200439453125,
-0.04815673828125,
-0.00391387939453125,
0.004146575927734375,
0.0219268798828125,
-0.02587890625,
0.00836181640625,
0.0149383544921875,
-0.006610870361328125,
-0.01236724853515625,
-0.000213623046875,
0.009124755859375,
0.03167724609375,
0.0132598876953125,
0.00007855892181396484,
-0.01192474365234375,
0.0037975311279296875,
0.0278778076171875,
0.022796630859375,
-0.02703857421875,
-0.0277557373046875,
-0.015655517578125,
0.01336669921875,
0.0181121826171875,
0.0128631591796875,
0.0296478271484375,
-0.0096435546875,
-0.034881591796875,
-0.0117950439453125,
0.001678466796875,
-0.018890380859375,
-0.006038665771484375,
0.01401519775390625,
0.01654052734375,
-0.0024814605712890625,
0.027099609375,
-0.00836944580078125,
-0.00722503662109375,
-0.0157318115234375,
0.0199432373046875,
0.0231475830078125,
-0.035003662109375,
-0.024017333984375,
-0.0169677734375,
-0.005733489990234375,
0.00992584228515625,
-0.013153076171875,
0.01239776611328125,
0.013916015625,
0.0283966064453125,
-0.01337432861328125,
0.001422882080078125,
-0.03448486328125,
-0.035003662109375,
-0.00725555419921875,
-0.0350341796875,
-0.03790283203125,
0.02130126953125,
-0.015716552734375,
-0.01537322998046875,
-0.03668212890625,
0.01146697998046875,
0.006237030029296875,
0.0122528076171875,
-0.0100860595703125,
-0.0247802734375,
0.0286407470703125,
-0.0007290840148925781,
0.01161956787109375,
-0.0242919921875,
-0.00975799560546875,
-0.0108184814453125,
0.0018863677978515625,
0.006008148193359375,
-0.0233612060546875,
0.0252685546875,
-0.00609588623046875,
0.01273345947265625,
0.0099029541015625,
0.040374755859375,
-0.00421142578125,
-0.0006456375122070312,
-0.0322265625,
-0.0256195068359375,
0.05169677734375,
0.037567138671875,
0.037994384765625,
0.00592041015625,
0.0120391845703125,
-0.0095062255859375,
0.00319671630859375,
0.0087127685546875,
-0.056182861328125,
-0.0133056640625,
-0.0253143310546875,
0.0285186767578125,
-0.0017681121826171875,
0.0166473388671875,
-0.04071044921875,
-0.00508880615234375,
0.0197906494140625,
0.039581298828125,
-0.00965118408203125,
-0.002986907958984375,
-0.0105743408203125,
-0.005504608154296875,
0.0035076141357421875,
0.0174102783203125,
0.05120849609375,
0.01751708984375,
-0.016448974609375,
0.051605224609375,
0.0230712890625,
-0.0016927719116210938,
0.009002685546875,
-0.03997802734375,
0.0124053955078125,
-0.000659942626953125,
-0.00844573974609375,
0.00818634033203125,
-0.0228271484375,
-0.027801513671875,
-0.007061004638671875,
-0.0141754150390625,
-0.00942230224609375,
-0.0106048583984375,
-0.007442474365234375,
-0.03973388671875,
0.0170440673828125,
-0.01611328125,
-0.01171112060546875,
-0.0259552001953125,
0.00960540771484375,
0.00812530517578125,
-0.0289306640625,
0.007110595703125,
-0.04327392578125,
-0.0146331787109375,
-0.00836944580078125,
-0.01312255859375,
-0.0035648345947265625,
-0.040924072265625,
-0.0311279296875,
-0.0254364013671875,
-0.003936767578125,
-0.0168304443359375,
0.0032062530517578125,
0.0206756591796875,
-0.0091552734375,
0.006969451904296875,
0.0253753662109375,
-0.035430908203125,
0.00394439697265625,
-0.050323486328125,
-0.0256195068359375,
0.005466461181640625,
0.00849151611328125,
-0.030609130859375,
0.0159759521484375,
0.004512786865234375,
-0.0269622802734375,
0.0131072998046875,
-0.01366424560546875,
-0.0254974365234375,
-0.022216796875,
0.0119781494140625,
0.04791259765625,
-0.0308685302734375,
0.0288238525390625,
0.0017719268798828125,
-0.00849151611328125,
-0.02191162109375,
-0.005908966064453125,
0.0078582763671875,
0.007770538330078125,
0.032470703125,
0.018585205078125,
0.0015201568603515625,
-0.0197601318359375,
-0.039459228515625,
-0.01102447509765625,
0.0027923583984375,
-0.015838623046875,
0.0107269287109375,
0.011688232421875,
-0.0233306884765625,
-0.0220947265625,
-0.018951416015625,
0.00847625732421875,
-0.040496826171875,
-0.0108795166015625,
-0.00951385498046875,
0.004421234130859375,
-0.0250396728515625,
-0.00356292724609375,
-0.00690460205078125,
-0.0106964111328125,
0.027191162109375,
0.02984619140625,
-0.00647735595703125,
0.021697998046875,
0.0037441253662109375,
-0.0335693359375,
-0.00585174560546875,
0.02618408203125,
-0.035888671875,
-0.00974273681640625,
0.01371002197265625,
0.0036945343017578125,
0.04107666015625,
-0.0187835693359375,
-0.01486968994140625,
0.00792694091796875,
0.0002689361572265625,
0.023895263671875,
-0.0170440673828125,
0.0283966064453125,
0.006256103515625,
0.006122589111328125,
0.009918212890625,
0.0094146728515625,
-0.0262451171875,
-0.0074462890625,
-0.011566162109375,
0.031402587890625,
-0.0191192626953125,
0.012054443359375,
-0.03765869140625,
-0.0256195068359375,
0.034698486328125,
0.0218505859375,
-0.00701141357421875,
-0.0104827880859375,
0.00205230712890625,
-0.0196075439453125,
0.004962921142578125,
0.0080413818359375,
0.01513671875,
0.0282440185546875,
0.005764007568359375,
-0.002002716064453125,
0.0006046295166015625,
-0.01049041748046875,
-0.0274658203125,
0.004215240478515625,
0.00635528564453125,
-0.0117645263671875,
0.01290130615234375,
-0.0214691162109375,
0.00844573974609375,
-0.0305023193359375,
0.0231170654296875,
-0.036224365234375,
-0.0045318603515625,
0.0045013427734375,
0.0155029296875,
0.032379150390625,
0.00038313865661621094,
-0.037322998046875,
0.0103607177734375,
-0.0595703125,
0.00655364990234375,
-0.0023441314697265625,
0.02227783203125,
-0.0159454345703125,
0.0016412734985351562,
0.024993896484375,
-0.005657196044921875,
0.0134735107421875,
0.0279998779296875,
0.03143310546875,
-0.02197265625,
-0.0036411285400390625,
0.0347900390625,
0.05389404296875,
0.0097808837890625,
-0.0024700164794921875,
0.002201080322265625,
-0.0197296142578125,
0.0230865478515625,
-0.005222320556640625,
-0.0041961669921875,
0.0253448486328125,
0.010772705078125,
0.011322021484375,
-0.036407470703125,
0.01165008544921875,
-0.007122039794921875,
0.02093505859375,
-0.0037136077880859375,
-0.006435394287109375,
0.0200347900390625,
-0.0216522216796875,
-0.013092041015625,
0.0273284912109375,
0.0019359588623046875,
0.00838470458984375,
-0.02276611328125,
-0.015289306640625,
0.0026111602783203125,
0.057952880859375,
0.015869140625,
0.010833740234375,
0.0166778564453125,
0.053253173828125,
-0.0176849365234375,
0.0222015380859375,
-0.041961669921875,
-0.00997161865234375,
-0.0014972686767578125,
-0.0246429443359375,
-0.0245513916015625,
0.03057861328125,
-0.0068206787109375,
0.007656097412109375,
-0.0160369873046875,
0.001384735107421875,
-0.04119873046875,
-0.0005221366882324219,
-0.0430908203125,
0.0257110595703125,
-0.0145721435546875,
0.00262451171875,
0.004856109619140625,
-0.023956298828125,
-0.01751708984375,
-0.00736236572265625,
0.0182647705078125,
0.0184173583984375,
0.00804901123046875,
-0.00336456298828125,
-0.015869140625,
-0.0263519287109375,
0.0018739700317382812,
0.0214996337890625,
0.02618408203125,
-0.013427734375,
0.01233673095703125,
0.020233154296875,
0.032012939453125,
0.0168914794921875,
0.005641937255859375,
-0.00769805908203125,
-0.016876220703125,
-0.036895751953125,
-0.0217132568359375,
-0.0203094482421875,
-0.004638671875,
0.0017938613891601562,
0.0247802734375,
0.0026607513427734375,
-0.041748046875,
-0.00548553466796875,
-0.003246307373046875,
-0.00951385498046875,
0.0188140869140625,
0.01043701171875,
0.01134490966796875,
0.0192413330078125,
-0.0024394989013671875,
-0.0281219482421875,
-0.009857177734375,
0.018646240234375,
-0.037353515625,
-0.01091766357421875,
-0.0287933349609375,
-0.0229339599609375,
0.0007090568542480469,
0.032958984375,
0.01253509521484375,
0.00669097900390625,
-0.0029754638671875,
-0.0227203369140625,
-0.0030651092529296875,
0.001293182373046875,
0.0050048828125,
0.0148468017578125,
0.01258087158203125,
0.003173828125,
0.0227508544921875,
-0.04461669921875,
-0.0199737548828125,
0.006801605224609375,
0.0174713134765625,
-0.003917694091796875,
-0.022186279296875,
0.03509521484375,
0.01432037353515625,
-0.01580810546875,
-0.00782012939453125,
0.012786865234375,
0.0208587646484375,
0.001361846923828125,
0.03009033203125,
0.00013935565948486328,
0.006011962890625,
0.026519775390625,
-0.01471710205078125,
-0.0413818359375,
-0.026580810546875,
-0.0142822265625,
0.01287078857421875,
0.036285400390625,
-0.0052337646484375,
0.03436279296875,
0.008087158203125,
-0.038238525390625,
0.037994384765625,
0.0031986236572265625,
0.00875091552734375,
-0.0113677978515625,
0.0003540515899658203,
-0.005523681640625,
0.00214385986328125,
0.045440673828125,
-0.0146026611328125,
0.0054779052734375,
0.045867919921875,
0.0113372802734375,
0.0267791748046875,
-0.003612518310546875,
0.03399658203125,
-0.029144287109375,
-0.017669677734375,
0.0308990478515625,
0.0010128021240234375,
-0.0280609130859375,
0.0000152587890625,
-0.00018107891082763672,
-0.0120086669921875,
0.024749755859375,
-0.0258026123046875,
-0.024749755859375,
0.025665283203125,
0.0243988037109375,
0.021636962890625,
-0.019927978515625,
0.0108489990234375,
0.020233154296875,
0.00482177734375,
-0.00777435302734375,
0.05718994140625,
-0.023590087890625,
0.0032482147216796875,
-0.0517578125,
0.005649566650390625,
0.002986907958984375,
-0.0023956298828125,
-0.041534423828125,
-0.032196044921875,
-0.007610321044921875,
-0.0150299072265625,
-0.0230712890625,
-0.006122589111328125,
0.00853729248046875,
-0.005031585693359375,
-0.01029205322265625,
0.040435791015625,
0.0070343017578125,
-0.006877899169921875,
-0.00969696044921875,
0.0007610321044921875,
0.0008139610290527344,
-0.0024738311767578125,
0.010284423828125,
0.01751708984375,
-0.00528717041015625,
0.01329803466796875,
0.00988006591796875,
-0.0259246826171875,
-0.035736083984375,
0.0191192626953125,
-0.0030574798583984375,
0.0033512115478515625,
-0.018096923828125,
0.034942626953125,
0.0189361572265625,
-0.014007568359375,
-0.015594482421875,
-0.001163482666015625,
0.023406982421875,
0.052490234375,
-0.020782470703125,
0.006565093994140625,
-0.01468658447265625,
-0.0015459060668945312,
0.0292205810546875,
-0.062255859375,
0.0168914794921875,
-0.0111236572265625,
0.017364501953125,
0.00296783447265625,
-0.0149993896484375,
-0.0220794677734375,
0.01104736328125,
-0.005702972412109375,
-0.03839111328125,
0.0292816162109375,
-0.01139068603515625,
-0.00689697265625,
0.0037250518798828125,
-0.03814697265625,
0.025177001953125,
-0.0168609619140625,
-0.0003075599670410156,
-0.007266998291015625,
0.0061187744140625,
-0.0059051513671875,
-0.04412841796875,
-0.0050506591796875,
0.0167694091796875,
0.03375244140625,
-0.0219879150390625,
0.0021190643310546875,
0.015625,
0.006866455078125,
-0.01198577880859375,
0.01258087158203125,
-0.02374267578125,
0.00926971435546875,
-0.0117950439453125,
0.00876617431640625,
-0.00018036365509033203,
0.040679931640625,
0.0164337158203125,
-0.01375579833984375,
-0.01934814453125,
0.0521240234375,
0.01447296142578125,
-0.0060882568359375,
0.024810791015625,
-0.0247650146484375,
-0.01033782958984375,
0.01702880859375,
-0.031768798828125,
0.0265045166015625,
-0.00846099853515625,
0.0199127197265625,
0.0269775390625,
0.0222625732421875,
-0.0021762847900390625,
-0.007190704345703125,
-0.0203704833984375,
0.0002732276916503906,
0.0105133056640625,
-0.0286865234375,
0.008758544921875,
0.028533935546875,
0.001018524169921875,
-0.00594329833984375,
0.0183868408203125,
-0.0254058837890625,
0.0015621185302734375,
-0.0031795501708984375,
-0.0166168212890625,
-0.01116943359375,
0.0157928466796875,
0.028533935546875,
-0.01126861572265625,
-0.0152435302734375,
-0.00936126708984375,
0.0290679931640625,
0.0178375244140625,
-0.0200347900390625,
0.00220489501953125,
-0.017486572265625,
-0.0011959075927734375,
0.03033447265625,
-0.005764007568359375,
-0.01486968994140625,
-0.03314208984375,
-0.032623291015625,
-0.0082550048828125,
-0.007602691650390625,
0.004802703857421875,
0.01561737060546875,
-0.044403076171875,
-0.0002875328063964844,
0.00518798828125,
-0.0171661376953125,
0.0028514862060546875,
0.00620269775390625,
-0.029571533203125,
-0.018157958984375,
0.003997802734375,
0.0036792755126953125,
0.00019621849060058594,
0.0237274169921875,
0.01287841796875,
0.021728515625,
-0.0130157470703125,
-0.00778961181640625,
0.0027065277099609375,
0.01465606689453125,
-0.027435302734375,
0.01065826416015625,
-0.01433563232421875,
-0.00891876220703125,
0.000728607177734375,
-0.007648468017578125,
-0.0183868408203125,
0.026397705078125,
-0.0271453857421875,
-0.0204315185546875,
0.00852203369140625,
0.0006170272827148438,
-0.046844482421875,
0.02593994140625,
0.0207061767578125,
-0.004802703857421875,
0.0251007080078125,
-0.0272216796875,
-0.01056671142578125,
-0.0161895751953125,
0.0175933837890625,
0.0142059326171875,
0.01207733154296875,
-0.0009851455688476562,
-0.0115203857421875,
-0.0182037353515625,
0.02862548828125,
-0.013397216796875,
-0.006732940673828125,
0.0022907257080078125,
-0.01291656494140625,
-0.024169921875,
0.007518768310546875,
0.02227783203125,
-0.0389404296875,
0.009063720703125,
0.0054779052734375,
0.01490020751953125,
0.01340484619140625,
0.034423828125,
-0.032867431640625,
-0.005580902099609375,
-0.0103912353515625,
-0.0160980224609375,
0.0198516845703125,
0.0020008087158203125,
0.0177764892578125,
-0.010894775390625,
-0.0195465087890625,
-0.00244140625,
-0.01276397705078125,
0.0005984306335449219,
0.01404571533203125,
0.0286102294921875,
0.0172576904296875,
-0.0224609375,
-0.01125335693359375,
-0.0229949951171875,
-0.032196044921875,
0.02703857421875,
0.0010824203491210938,
0.0154266357421875,
0.0274505615234375,
0.0022869110107421875,
0.005741119384765625,
0.0018157958984375,
-0.035247802734375,
-0.031341552734375,
-0.0207977294921875,
0.0201416015625,
-0.01432037353515625,
0.0015172958374023438,
-0.0179901123046875,
0.0138092041015625,
-0.0135955810546875,
-0.0294036865234375,
0.01074981689453125,
-0.0302886962890625,
-0.0269927978515625,
0.017669677734375,
-0.04302978515625,
0.0394287109375,
0.00913238525390625,
0.0286102294921875,
-0.032501220703125,
-0.018524169921875,
-0.003711700439453125,
-0.0011425018310546875,
-0.0006818771362304688,
-0.00540924072265625,
-0.00650787353515625,
-0.026947021484375,
-0.0093231201171875,
0.00589752197265625,
-0.01358795166015625,
-0.0027713775634765625,
-0.025360107421875,
-0.03143310546875,
-0.007091522216796875,
0.035736083984375,
0.00826263427734375,
-0.0077362060546875,
0.018218994140625,
0.0180511474609375,
-0.03570556640625,
0.037200927734375,
-0.0025730133056640625,
-0.013427734375,
0.0151214599609375,
-0.007053375244140625,
0.0172576904296875,
0.0194549560546875,
-0.04022216796875,
-0.005168914794921875,
0.031890869140625,
-0.0067596435546875,
-0.02862548828125,
0.004680633544921875,
0.031585693359375,
0.005680084228515625,
0.00013113021850585938,
0.0083160400390625,
0.008758544921875,
0.019775390625,
0.0214996337890625,
0.0233154296875,
0.0087738037109375,
-0.00849151611328125,
-0.0035400390625,
-0.0052337646484375,
0.0223388671875,
-0.004497528076171875,
-0.0183258056640625,
0.003154754638671875,
-0.00838470458984375,
0.00980377197265625,
-0.0006265640258789062,
-0.0030612945556640625,
0.008758544921875,
-0.0030918121337890625,
0.00844573974609375,
-0.01019287109375,
0.0019178390502929688,
0.01200103759765625,
0.032806396484375,
0.0018377304077148438,
0.0220794677734375,
0.0013437271118164062,
-0.0235443115234375,
-0.00815582275390625,
-0.039154052734375,
0.010528564453125,
-0.006404876708984375,
0.0061798095703125,
-0.02838134765625,
-0.00283050537109375,
-0.015960693359375,
-0.00257110595703125,
-0.0294342041015625,
-0.01227569580078125,
-0.0032138824462890625,
-0.0228729248046875,
-0.03533935546875,
0.01971435546875,
-0.023956298828125,
-0.011871337890625,
-0.01442718505859375,
-0.0057830810546875,
0.01337432861328125,
0.019256591796875,
-0.017608642578125,
-0.02166748046875,
0.00885009765625,
-0.00021886825561523438,
-0.00875091552734375,
-0.04608154296875,
0.00507354736328125,
-0.001544952392578125,
-0.060272216796875,
0.00058746337890625,
0.0152130126953125,
-0.04931640625,
0.00884246826171875,
0.005420684814453125,
0.00811767578125,
0.062164306640625,
-0.046234130859375,
0.0171966552734375,
-0.00018596649169921875,
0.047637939453125,
0.0030517578125,
0.034912109375,
0.00007909536361694336,
0.0080718994140625,
0.036865234375,
0.0236968994140625,
0.0369873046875,
0.012908935546875,
-0.0091400146484375,
-0.0167999267578125,
-0.0250396728515625,
-0.0178375244140625,
-0.0256195068359375,
0.01274871826171875,
-0.016326904296875,
-0.0158843994140625,
0.0265350341796875,
-0.01364898681640625,
-0.00894927978515625,
0.00655364990234375,
0.031890869140625,
0.018218994140625,
-0.01369476318359375,
-0.0198516845703125,
-0.007724761962890625,
-0.045013427734375,
0.01328277587890625,
0.0006093978881835938,
-0.004787445068359375,
-0.01922607421875,
0.016387939453125,
-0.0272216796875,
0.002841949462890625,
-0.005260467529296875,
-0.0260162353515625,
0.028076171875,
0.0005655288696289062,
-0.005229949951171875,
0.01116943359375,
-0.009490966796875,
-0.01474761962890625,
0.0162353515625,
0.0147857666015625,
0.011016845703125,
-0.012054443359375,
0.039215087890625,
0.0007472038269042969,
-0.00876617431640625,
-0.008087158203125,
0.01290130615234375,
0.0246429443359375,
-0.00414276123046875,
-0.0266571044921875,
0.006084442138671875,
0.01088714599609375,
-0.037353515625,
0.0163116455078125,
-0.0305633544921875,
-0.0235137939453125,
-0.00782012939453125,
-0.0241546630859375,
-0.0165252685546875,
0.0313720703125,
0.0200958251953125,
-0.036285400390625,
-0.00601959228515625,
0.0205841064453125,
0.002391815185546875,
0.020965576171875,
-0.03607177734375,
-0.0012378692626953125,
-0.01079559326171875,
0.00986480712890625,
-0.0004494190216064453,
0.0028171539306640625,
-0.005237579345703125,
-0.00119781494140625,
-0.0164337158203125,
0.0307159423828125,
0.00958251953125,
0.01436614990234375,
0.005218505859375,
0.0116424560546875,
-0.01244354248046875,
0.0170440673828125,
0.0188140869140625,
-0.0203704833984375,
0.0120391845703125,
0.0003674030303955078,
0.0233306884765625,
-0.00970458984375,
-0.023529052734375,
-0.0131683349609375,
-0.04071044921875,
-0.0286407470703125,
0.01476287841796875,
0.00904083251953125,
0.005146026611328125,
-0.0034275054931640625,
0.021087646484375,
-0.01325225830078125,
-0.0182952880859375,
0.005878448486328125,
0.004852294921875,
0.00550079345703125,
0.0333251953125,
0.01111602783203125,
-0.0033416748046875,
-0.02569580078125,
0.0061798095703125,
-0.01012420654296875,
-0.027374267578125,
-0.017974853515625,
0.0024280548095703125,
0.01090240478515625,
0.032806396484375,
-0.020477294921875,
0.00012302398681640625,
0.0218505859375,
0.03204345703125,
-0.005390167236328125,
-0.025115966796875,
-0.0233154296875,
0.0157318115234375,
-0.01519775390625,
0.0101165771484375,
-0.0016107559204101562,
-0.0065460205078125,
-0.0043792724609375,
0.019927978515625,
-0.0030689239501953125,
-0.00955963134765625,
-0.01165008544921875,
-0.0124664306640625,
-0.000141143798828125,
-0.00836944580078125,
0.030364990234375,
-0.035308837890625,
-0.0238800048828125,
-0.0101318359375,
-0.00507354736328125,
-0.005779266357421875,
0.0220794677734375,
-0.005634307861328125,
0.0158233642578125,
0.01288604736328125,
0.0367431640625,
-0.025482177734375,
-0.024932861328125,
-0.02471923828125,
0.00217437744140625,
0.005340576171875,
-0.0022125244140625,
-0.018768310546875,
0.0185699462890625,
0.0242919921875,
-0.0191192626953125,
-0.0061187744140625,
-0.0176849365234375,
0.0322265625,
0.03009033203125,
-0.00234222412109375,
0.0196380615234375,
0.0078125,
-0.007415771484375,
0.00323486328125,
0.00586700439453125,
0.0020160675048828125,
0.00911712646484375,
-0.01284027099609375,
0.0032825469970703125,
0.01165771484375,
-0.0141754150390625,
-0.00579071044921875,
0.0037708282470703125,
-0.00724029541015625,
-0.01061248779296875,
0.0010347366333007812,
-0.034576416015625,
-0.0162811279296875,
0.008026123046875,
-0.037567138671875,
0.0141754150390625,
-0.01258087158203125,
0.0012216567993164062,
0.04248046875,
0.0009083747863769531,
0.0125274658203125,
0.011260986328125,
-0.0036563873291015625,
0.026519775390625,
-0.006313323974609375,
0.0056610107421875,
-0.0209808349609375,
-0.01018524169921875,
0.0079803466796875,
-0.022857666015625,
-0.008148193359375,
0.0037994384765625,
0.0249176025390625,
-0.001811981201171875,
-0.022674560546875,
0.0165863037109375,
0.03997802734375,
-0.0310516357421875,
0.0180206298828125,
0.005565643310546875,
-0.0216064453125,
-0.00673675537109375,
-0.006072998046875,
-0.052459716796875,
0.0292816162109375,
-0.0198516845703125,
0.04254150390625,
-0.019439697265625,
-0.0306243896484375,
0.03460693359375,
0.03765869140625,
-0.011260986328125,
0.022003173828125,
0.0003120899200439453,
-0.005710601806640625,
-0.0014629364013671875,
-0.010833740234375,
0.0076751708984375,
0.004131317138671875,
0.0202789306640625,
0.02978515625,
-0.01029205322265625,
0.0182037353515625,
-0.0321044921875,
-0.005718231201171875,
0.016845703125,
0.00675201416015625,
0.0251312255859375,
-0.0089569091796875,
0.002796173095703125,
-0.00850677490234375,
0.007293701171875,
0.0027408599853515625,
0.00787353515625,
-0.0037078857421875,
-0.00007581710815429688,
0.0379638671875,
0.0027828216552734375,
-0.0083770751953125,
-0.0185089111328125,
0.018646240234375,
0.0251617431640625,
0.00548553466796875,
-0.0274658203125,
0.0016794204711914062,
0.007049560546875,
-0.0106048583984375,
0.0309600830078125,
-0.01122283935546875,
0.0027484893798828125,
0.00826263427734375,
-0.00304412841796875,
0.03363037109375,
0.0173797607421875,
0.0096435546875,
-0.004596710205078125,
-0.0318603515625,
0.0075225830078125,
-0.01372528076171875,
0.017486572265625,
0.005641937255859375,
0.00316619873046875,
0.00641632080078125,
0.0032329559326171875,
-0.0177764892578125,
0.00525665283203125,
0.0208740234375,
0.0303497314453125,
-0.00524139404296875,
-0.0288238525390625,
-0.023468017578125,
-0.002857208251953125,
0.026336669921875,
0.0012598037719726562,
0.0282745361328125,
0.0031795501708984375,
0.0184326171875,
0.0179443359375,
-0.0309906005859375,
-0.00336456298828125,
-0.0006732940673828125,
-0.00699615478515625,
0.0198211669921875,
0.0024852752685546875,
-0.01434326171875,
0.0220489501953125,
0.0191497802734375,
0.00311279296875,
-0.0003726482391357422,
0.0267486572265625,
-0.00102996826171875,
0.00527191162109375,
-0.01187896728515625,
0.0268096923828125,
0.0029392242431640625,
0.007007598876953125,
0.041290283203125,
0.01081085205078125,
0.021331787109375,
-0.01389312744140625,
-0.014495849609375,
-0.0050048828125,
0.0018825531005859375,
-0.02874755859375,
0.00044035911560058594,
0.0061492919921875,
-0.0328369140625,
-0.00433349609375,
0.0033016204833984375,
-0.01015472412109375,
-0.0269775390625,
0.0135955810546875,
-0.0116424560546875,
0.0074005126953125,
-0.002170562744140625,
-0.0210723876953125,
-0.03253173828125,
-0.018707275390625,
0.01041412353515625,
-0.0025272369384765625,
-0.0276641845703125,
0.01233673095703125,
0.005802154541015625,
0.03265380859375,
0.007640838623046875,
0.0150604248046875,
0.03729248046875,
-0.0289764404296875,
0.0196075439453125,
-0.0034332275390625,
0.029327392578125,
0.004673004150390625,
0.011566162109375,
-0.006317138671875,
0.019744873046875,
-0.039703369140625,
0.004940032958984375,
0.00714874267578125,
-0.0094451904296875,
0.013946533203125,
0.0206451416015625,
-0.00997161865234375,
0.005382537841796875,
-0.028961181640625,
0.0028076171875,
0.005588531494140625,
-0.03076171875,
-0.01165771484375,
0.0153961181640625,
-0.018096923828125,
0.0115966796875,
0.021331787109375,
0.01158905029296875,
0.0096588134765625,
-0.027099609375,
0.0012197494506835938,
-0.0165863037109375,
-0.0118408203125,
0.0279693603515625,
0.0211181640625,
-0.018280029296875,
0.00861358642578125,
-0.01739501953125,
-0.0084991455078125,
0.04901123046875,
-0.01128387451171875,
0.01436614990234375,
-0.03167724609375,
-0.020538330078125,
0.0119781494140625,
-0.0079803466796875,
0.0241546630859375,
-0.012908935546875,
-0.0206756591796875,
-0.004161834716796875,
0.01175689697265625,
0.0019521713256835938,
-0.004638671875,
-0.002010345458984375,
0.02587890625,
0.01702880859375,
0.023040771484375,
0.0194854736328125,
0.006427764892578125,
0.001018524169921875,
0.015411376953125,
-0.019287109375,
0.0098724365234375,
-0.0179443359375,
-0.004863739013671875,
0.0079193115234375,
-0.01422119140625,
-0.0083770751953125,
-0.035797119140625,
0.0116729736328125,
0.009368896484375,
-0.012664794921875,
0.0017986297607421875,
-0.0156707763671875,
-0.0036373138427734375,
-0.00839996337890625,
-0.00829315185546875,
0.020294189453125,
-0.01422119140625,
0.022308349609375,
-0.0129241943359375,
0.006717681884765625,
0.01678466796875,
0.006534576416015625,
0.00655364990234375,
-0.03631591796875,
0.032928466796875,
0.00927734375,
-0.039276123046875,
-0.01837158203125,
-0.041961669921875,
0.0245361328125,
-0.014923095703125,
0.038848876953125,
0.02764892578125,
0.0205230712890625,
0.00461578369140625,
0.0118560791015625,
-0.022186279296875,
-0.0255584716796875,
0.0136871337890625,
0.006481170654296875,
-0.0194091796875,
-0.042694091796875,
0.03009033203125,
-0.0122222900390625,
-0.0266571044921875,
-0.005451202392578125,
-0.010009765625,
0.009185791015625,
0.0036220550537109375,
0.017059326171875,
0.0031032562255859375,
-0.0198516845703125,
0.02557373046875,
-0.000774383544921875,
-0.032623291015625,
0.004543304443359375,
0.041046142578125,
0.01317596435546875,
0.018585205078125,
-0.007671356201171875,
-0.0072784423828125,
0.0015411376953125,
-0.018646240234375,
0.0050201416015625,
0.01180267333984375,
0.03143310546875,
-0.0244903564453125,
0.00742340087890625,
-0.008636474609375,
-0.00867462158203125,
-0.028533935546875,
-0.021728515625,
-0.0230560302734375,
-0.01517486572265625,
-0.017852783203125,
-0.0171051025390625,
-0.0294342041015625,
0.01377105712890625,
0.0080718994140625,
0.02301025390625,
-0.027801513671875,
0.003986358642578125,
0.0258941650390625,
0.01209259033203125,
0.01222991943359375,
-0.0177459716796875,
-0.00804901123046875,
-0.0144500732421875,
0.00963592529296875,
0.010223388671875,
-0.0014715194702148438,
0.005126953125,
0.04608154296875,
-0.004047393798828125,
0.0104827880859375,
0.0074310302734375,
-0.0165252685546875,
-0.0026645660400390625,
-0.0026397705078125,
-0.033905029296875,
-0.0242156982421875,
0.011810302734375,
-0.01617431640625,
0.0127410888671875,
-0.0131988525390625,
0.025360107421875,
-0.0211181640625,
-0.0126800537109375,
0.036895751953125,
-0.02569580078125,
0.005146026611328125,
-0.015777587890625,
0.021728515625,
0.0203704833984375,
-0.00457000732421875,
-0.031524658203125,
-0.00547027587890625,
-0.0203857421875,
-0.01727294921875,
-0.0120391845703125,
-0.003337860107421875,
-0.00788116455078125,
-0.025787353515625,
0.009033203125,
0.0198822021484375,
0.0230560302734375,
0.0085906982421875,
0.0243988037109375,
-0.006465911865234375,
-0.0233917236328125,
0.0186614990234375,
0.010406494140625,
0.0191802978515625,
0.007137298583984375,
0.01849365234375,
0.04638671875,
0.0222320556640625,
-0.01552581787109375,
-0.03497314453125,
0.0204010009765625,
0.004360198974609375,
0.00960540771484375,
0.04034423828125,
-0.02655029296875,
-0.0225830078125,
-0.00015842914581298828,
0.0017147064208984375,
0.002960205078125,
-0.00821685791015625,
-0.0142364501953125,
0.01381683349609375,
0.0306396484375,
-0.003108978271484375,
0.0019989013671875,
-0.006328582763671875,
-0.0282135009765625,
-0.0294342041015625,
-0.0106048583984375,
0.03533935546875,
0.016265869140625,
-0.01512908935546875,
-0.034820556640625,
-0.0242919921875,
0.02105712890625,
0.004520416259765625,
0.03851318359375,
-0.0295562744140625,
0.0134735107421875,
0.005527496337890625,
-0.01522064208984375,
-0.00371551513671875,
-0.00580596923828125,
0.00787353515625,
-0.027984619140625,
0.004207611083984375,
0.007556915283203125,
0.0013904571533203125,
-0.01080322265625,
0.0165557861328125,
0.0013885498046875,
0.0186767578125,
-0.018798828125,
0.008575439453125,
0.01788330078125,
-0.01678466796875,
-0.004833221435546875,
0.006465911865234375,
0.0102996826171875,
0.00426483154296875,
0.036834716796875,
-0.0269927978515625,
-0.008697509765625,
-0.003826141357421875,
0.0018291473388671875,
0.01806640625,
-0.004062652587890625,
0.01258087158203125,
-0.01947021484375,
0.009002685546875,
-0.042266845703125,
0.004425048828125,
-0.0221710205078125,
0.01468658447265625,
0.007259368896484375,
0.0247650146484375,
-0.0170135498046875,
0.01366424560546875,
0.027557373046875,
0.0225982666015625,
-0.01218414306640625,
-0.06353759765625,
-0.0077972412109375,
0.0093994140625,
0.000028371810913085938,
0.0009412765502929688,
-0.021636962890625,
0.01300048828125,
-0.02227783203125,
-0.0109710693359375,
-0.005527496337890625,
-0.0101470947265625,
0.0131378173828125,
0.04620361328125,
-0.020965576171875,
-0.01483154296875,
0.0166015625,
0.032928466796875,
-0.038116455078125,
0.005802154541015625,
-0.00728607177734375,
-0.0198822021484375,
-0.006008148193359375,
0.01528167724609375,
-0.05035400390625,
-0.01348114013671875,
-0.00739288330078125,
-0.009674072265625,
-0.005916595458984375,
0.0167694091796875,
-0.006923675537109375,
-0.01319122314453125,
-0.0163116455078125,
0.004638671875,
0.01131439208984375,
0.0156707763671875,
0.031036376953125,
0.004398345947265625,
-0.0107574462890625,
-0.0001875162124633789,
0.026123046875,
0.0435791015625,
0.00232696533203125,
-0.0222625732421875,
0.00621795654296875,
-0.024383544921875,
0.01311492919921875,
0.002208709716796875,
-0.0272216796875,
0.0234832763671875,
-0.0162353515625,
0.035369873046875,
-0.0181884765625,
-0.021514892578125,
0.0350341796875,
-0.01374053955078125,
0.00734710693359375,
0.001544952392578125,
0.0193634033203125,
0.0006623268127441406,
-0.021942138671875,
-0.04205322265625,
-0.0004303455352783203,
0.00787353515625,
-0.0328369140625,
-0.027435302734375,
0.006076812744140625,
0.0307464599609375,
0.00738525390625,
0.0235748291015625,
-0.017547607421875,
0.046112060546875,
0.017974853515625,
0.0034503936767578125,
0.008087158203125,
0.033905029296875,
0.00943756103515625,
0.014678955078125,
0.0009741783142089844,
0.01560211181640625,
0.031890869140625,
0.0018939971923828125,
0.0064849853515625,
0.0171661376953125,
-0.0174407958984375,
0.00977325439453125,
0.037994384765625,
0.01445770263671875,
0.0021915435791015625,
-0.0013494491577148438,
-0.0262298583984375,
-0.0189666748046875,
0.007556915283203125,
-0.0030345916748046875,
-0.0099334716796875,
-0.0037994384765625,
-0.015899658203125,
-0.0018863677978515625,
0.01494598388671875,
-0.011627197265625,
0.0052947998046875,
0.0196533203125,
0.0103759765625,
0.0015726089477539062,
-0.036651611328125,
0.007030487060546875,
0.0093231201171875,
-0.001068115234375,
-0.0023670196533203125,
0.0184783935546875,
0.032318115234375,
-0.0122528076171875,
-0.0225372314453125,
0.003818511962890625,
0.0128021240234375,
-0.00852203369140625,
0.01560211181640625,
-0.0005664825439453125,
0.0131988525390625,
-0.04791259765625,
-0.0287322998046875,
0.0216827392578125,
0.053070068359375,
-0.01276397705078125,
-0.0239410400390625,
-0.006679534912109375,
0.029022216796875,
-0.006916046142578125,
-0.020477294921875,
-0.0216064453125,
-0.0164642333984375,
-0.006275177001953125,
-0.00539398193359375,
-0.003017425537109375,
-0.0128173828125,
-0.0008087158203125,
-0.02362060546875,
-0.0219573974609375,
-0.0184173583984375,
0.0117950439453125,
0.0263671875,
-0.005756378173828125,
-0.01007843017578125,
0.005603790283203125,
-0.012359619140625,
0.01287078857421875,
-0.008575439453125,
-0.0029926300048828125,
0.0106048583984375,
-0.027435302734375,
0.0056610107421875,
-0.0135650634765625,
-0.047882080078125,
0.031951904296875,
0.0010385513305664062,
0.005275726318359375,
-0.0316162109375,
0.0205230712890625,
0.0036869049072265625,
0.0164031982421875,
-0.0075531005859375,
-0.011688232421875,
0.0219573974609375,
0.00121307373046875,
0.029052734375,
0.006259918212890625,
-0.020751953125,
0.0182342529296875,
0.0053863525390625,
0.00749969482421875,
-0.00695037841796875,
-0.01311492919921875,
-0.01169586181640625,
0.00408935546875,
-0.0070037841796875,
-0.001972198486328125,
-0.0313720703125,
-0.022857666015625,
0.00762939453125,
-0.0013246536254882812,
0.0138702392578125,
-0.002780914306640625,
0.0039520263671875,
0.023040771484375,
0.020050048828125,
0.01129913330078125,
0.0182342529296875,
0.03375244140625,
-0.01373291015625,
0.019256591796875,
0.00701141357421875,
-0.017913818359375,
-0.016357421875,
0.01434326171875,
-0.016448974609375,
0.020477294921875,
-0.037811279296875,
0.01381683349609375,
0.0260162353515625,
0.0211944580078125,
0.00937652587890625,
-0.0141754150390625,
-0.0098876953125,
-0.021759033203125,
-0.0186309814453125,
-0.0245513916015625,
-0.0275115966796875,
0.002445220947265625,
-0.00994873046875,
-0.0225677490234375,
0.035400390625,
-0.0012769699096679688,
-0.007358551025390625,
0.026275634765625,
0.007343292236328125,
0.0277557373046875,
0.00774383544921875,
-0.015411376953125,
-0.023773193359375,
-0.01282501220703125,
0.000025928020477294922,
-0.0330810546875,
0.0031414031982421875,
0.01678466796875,
0.02239990234375,
-0.003086090087890625,
0.031036376953125,
0.0203399658203125,
-0.01043701171875,
0.0156402587890625,
-0.0029392242431640625,
0.003887176513671875,
0.0188446044921875,
-0.031494140625,
0.019989013671875,
0.01165771484375,
-0.00904083251953125,
-0.01497650146484375,
0.0092926025390625,
0.0202484130859375,
-0.011138916015625,
-0.00881195068359375,
0.00543975830078125,
0.00351715087890625,
0.002017974853515625,
-0.01122283935546875,
0.0039215087890625,
-0.000751495361328125,
-0.017486572265625,
-0.004425048828125,
0.00798797607421875,
-0.02777099609375,
0.0078125,
0.01983642578125,
-0.0168304443359375,
0.010345458984375,
0.0161285400390625,
0.001071929931640625,
0.004993438720703125,
-0.018890380859375,
-0.0195465087890625,
0.033660888671875,
-0.0222930908203125,
0.014068603515625,
0.004123687744140625,
0.02655029296875,
0.019195556640625,
0.0178985595703125,
0.0015230178833007812,
-0.033477783203125,
0.01136016845703125,
0.034393310546875,
0.00371551513671875,
0.01335906982421875,
0.031463623046875,
-0.006591796875,
-0.003993988037109375,
-0.0428466796875,
0.0119171142578125,
0.0022296905517578125,
0.01393890380859375,
-0.03369140625,
0.0262603759765625,
0.00666046142578125,
-0.01422882080078125,
0.0153350830078125,
-0.0023822784423828125,
0.00681304931640625,
0.01485443115234375,
-0.0093231201171875,
-0.01441192626953125,
-0.013458251953125,
0.01141357421875,
-0.0210723876953125,
-0.01021575927734375,
0.00023496150970458984,
-0.002651214599609375,
-0.006885528564453125,
0.006214141845703125,
0.00943756103515625,
0.03955078125,
-0.0082550048828125,
0.0191192626953125,
0.00489044189453125,
0.01477813720703125,
0.01727294921875,
0.00690460205078125,
-0.0015230178833007812,
0.0040130615234375,
-0.00005942583084106445,
0.03778076171875,
0.0045623779296875,
-0.0269012451171875,
0.0073699951171875,
0.03021240234375,
-0.014190673828125,
-0.0012607574462890625,
-0.007411956787109375,
-0.00806427001953125,
-0.0086517333984375,
-0.00836944580078125,
-0.00566864013671875,
-0.01216888427734375,
0.0265045166015625,
0.003421783447265625,
-0.01117706298828125,
0.00991058349609375,
0.00940704345703125,
0.01308441162109375,
-0.00812530517578125,
-0.017059326171875,
0.02557373046875,
0.0027866363525390625,
-0.009246826171875,
0.0295257568359375,
0.03668212890625,
0.0054779052734375,
-0.006206512451171875,
0.05133056640625,
-0.004283905029296875,
-0.0008673667907714844,
0.0118560791015625,
-0.024139404296875,
-0.003757476806640625,
-0.019317626953125,
-0.0008826255798339844,
-0.052581787109375,
-0.041839599609375,
-0.00286865234375,
0.004833221435546875,
-0.0081024169921875,
-0.001434326171875,
-0.00608062744140625,
-0.01473236083984375,
-0.0207977294921875,
-0.0021514892578125,
0.0128936767578125,
-0.0041046142578125,
-0.005329132080078125,
-0.0179595947265625,
-0.0086517333984375,
0.0193328857421875,
0.020599365234375,
-0.045745849609375,
-0.0040130615234375,
0.008270263671875,
0.02227783203125,
0.06390380859375,
-0.023284912109375,
0.0034847259521484375,
-0.01971435546875,
-0.0237274169921875,
0.010162353515625,
0.00043487548828125,
-0.00670623779296875,
-0.009429931640625,
-0.0027866363525390625,
-0.01444244384765625,
0.04058837890625,
-0.0049896240234375,
-0.009185791015625,
0.019500732421875,
0.04052734375,
-0.032012939453125,
-0.0288543701171875,
-0.01137542724609375,
0.0106658935546875,
-0.03240966796875,
-0.018157958984375,
-0.020782470703125,
-0.033935546875,
-0.01641845703125,
0.0194244384765625,
-0.0198516845703125,
-0.032470703125,
-0.0078277587890625,
-0.00939178466796875,
-0.0019683837890625,
-0.0197601318359375,
0.007335662841796875,
0.0283660888671875,
-0.0305633544921875,
0.025543212890625,
-0.0028324127197265625,
0.000438690185546875,
-0.00894927978515625,
0.007503509521484375,
0.034942626953125,
0.0147552490234375,
0.032073974609375,
0.0080108642578125,
-0.005275726318359375,
0.0085601806640625,
0.01236724853515625,
0.0253753662109375,
0.0144500732421875,
-0.02301025390625,
-0.00753021240234375,
-0.00807952880859375,
0.00847625732421875,
0.034027099609375,
-0.0377197265625,
0.024871826171875,
-0.006725311279296875,
0.0252685546875,
-0.009185791015625,
-0.0257415771484375,
0.036285400390625,
0.00696563720703125,
-0.0049591064453125,
0.0303497314453125,
-0.003330230712890625,
0.022125244140625,
0.0026416778564453125,
-0.031982421875,
-0.0162506103515625,
-0.0191650390625,
0.015228271484375,
0.0222320556640625,
0.0293731689453125,
0.00634002685546875,
0.027679443359375,
-0.028961181640625,
-0.03558349609375,
0.0254974365234375,
-0.0211181640625,
0.031768798828125,
0.0156707763671875,
-0.02362060546875,
0.020721435546875,
-0.0190277099609375,
-0.0204010009765625,
0.028106689453125,
0.00731658935546875,
0.00821685791015625,
-0.01486968994140625,
0.0110321044921875,
-0.0259246826171875,
-0.023651123046875,
0.03558349609375,
0.0179443359375,
0.01374053955078125,
0.0066986083984375,
0.0250396728515625,
0.0078277587890625,
0.0195465087890625,
0.0260009765625,
0.0244140625,
-0.00006091594696044922,
0.031768798828125,
0.0006613731384277344,
0.0313720703125,
-0.00481414794921875,
-0.003383636474609375,
0.016754150390625,
0.007434844970703125,
0.0244293212890625,
-0.00749969482421875,
0.029266357421875,
0.01451873779296875,
0.0011548995971679688,
0.026275634765625,
-0.0213470458984375,
0.022125244140625,
0.06622314453125,
-0.0243682861328125,
0.004787445068359375,
-0.037445068359375,
0.0028743743896484375,
-0.015350341796875,
0.01023101806640625,
-0.00833892822265625,
0.002777099609375,
0.007167816162109375,
-0.0034580230712890625,
-0.004749298095703125,
-0.0121002197265625,
-0.0277557373046875,
-0.0115966796875,
0.0265350341796875,
-0.0037937164306640625,
0.0224151611328125,
0.026947021484375,
-0.002643585205078125,
-0.009063720703125,
-0.00811767578125,
0.0177459716796875,
-0.0061492919921875,
-0.0007004737854003906,
0.021484375,
-0.020263671875,
-0.0203399658203125,
-0.039459228515625,
-0.0117034912109375,
-0.00202178955078125,
-0.00870513916015625,
0.00557708740234375,
0.003673553466796875,
0.0285186767578125,
-0.00146484375,
-0.013397216796875,
-0.0084075927734375,
-0.01739501953125,
-0.007293701171875,
-0.00763702392578125,
-0.02166748046875,
0.0039043426513671875,
-0.0079803466796875,
-0.052520751953125,
-0.01479339599609375,
-0.01129913330078125,
-0.00478363037109375,
0.00017786026000976562,
0.01312255859375,
0.0102691650390625,
-0.0440673828125,
-0.04205322265625,
0.00431060791015625,
0.03790283203125,
0.000492095947265625,
-0.0274658203125,
-0.040130615234375,
-0.025665283203125,
0.0026950836181640625,
0.00989532470703125,
0.00693511962890625,
-0.02490234375,
0.0114593505859375,
0.01250457763671875,
0.02374267578125,
0.0264892578125,
-0.0202484130859375,
-0.00998687744140625,
-0.021728515625,
-0.0161285400390625,
0.0229339599609375,
0.01522064208984375,
-0.00426483154296875,
0.0345458984375,
-0.047821044921875,
0.0138397216796875,
0.029449462890625,
0.0008482933044433594,
-0.006755828857421875,
-0.01983642578125,
-0.00496673583984375,
-0.0189971923828125,
-0.01128387451171875,
-0.00875091552734375,
-0.0084381103515625,
0.0151519775390625,
-0.034149169921875,
-0.039642333984375,
0.029052734375,
0.00894927978515625,
0.0034618377685546875,
-0.026947021484375,
0.01403045654296875,
0.0333251953125,
0.007602691650390625,
0.0258331298828125,
0.011016845703125,
-0.0282135009765625,
-0.042236328125,
0.0281829833984375,
0.006572723388671875,
-0.016357421875,
0.0369873046875,
-0.001140594482421875,
0.00977325439453125,
0.00841522216796875,
0.0170440673828125,
0.0261993408203125,
0.003688812255859375,
0.03057861328125,
0.02276611328125,
-0.018402099609375,
0.0261077880859375,
0.0188446044921875
] |
ours_508
|
We claim that the values of \( m \) and \( t \) are \( m=1 \) and \( t=3 \).
We show that Vera can win after at most three turns if \( k=1 \). Let B represent a black square, and let W represent a white square.
Originally, the position is this:
\[
\begin{array}{ccccc}
W & W & W & W & W \\
W & W & W & W & W \\
W & W & B & W & W \\
W & W & W & W & W \\
W & W & W & W & W \\
\end{array}
\]
Then Marco makes it this:
\[
\begin{array}{ccccc}
W & W & W & W & W \\
W & W & B & W & W \\
W & B & W & B & W \\
W & W & B & W & W \\
W & W & W & W & W \\
\end{array}
\]
Then Vera swaps two white squares off in the distance so as not to affect the board, and Marco makes it this or something symmetric:
\[
\begin{array}{ccccc}
W & W & B & W & W \\
W & B & W & B & W \\
W & B & B & B & W \\
W & W & B & W & W \\
W & W & W & W & W \\
\end{array}
\]
Vera now makes it this:
\[
\begin{array}{ccccc}
W & W & W & W & W \\
W & B & B & B & W \\
W & B & B & B & W \\
W & W & B & W & W \\
W & W & W & W & W \\
\end{array}
\]
Marco is forced to make it this:
\[
\begin{array}{ccccc}
W & W & W & W & W \\
W & B & B & B & W \\
W & B & B & B & W \\
W & B & W & B & W \\
W & W & B & W & W \\
\end{array}
\]
Vera then makes it this:
\[
\begin{array}{ccccc}
W & W & W & W & W \\
W & B & B & B & W \\
W & B & B & B & W \\
W & B & B & B & W \\
W & W & W & W & W \\
\end{array}
\]
In this position, Vera wins. Thus Vera wins after at most three turns if \( k=1 \). Thus \( m=1 \) (since we cannot have \( k<1 \)), and \( t \leq 3 \).
Now, for \( k=1 \), it needs to be shown that Vera cannot guarantee that she wins after at most two turns. This is left as an exercise to the reader.
Thus, \( m=1 \) and \( t=3 \), as claimed. Thus, the answer is \( 100 \cdot 1 + 3 = 103 \).
\(\boxed{103}\)
|
103
|
{
"competition": "us_comps",
"dataset": "Ours",
"posts": null,
"source": "OMOFall19Solns.md"
}
|
Let \( k \) be a positive integer. Marco and Vera play a game on an infinite grid of square cells. At the beginning, only one cell is black and the rest are white. A turn in this game consists of the following: Marco moves first, and for every move, he must choose a cell which is black and which has more than two white neighbors. (Two cells are neighbors if they share an edge, so every cell has exactly four neighbors.) His move consists of making the chosen black cell white and turning all of its neighbors black if they are not already. Vera then performs the following action exactly \( k \) times: she chooses two cells that are neighbors to each other and swaps their colors (she is allowed to swap the colors of two white or of two black cells, though doing so has no effect). This, in totality, is a single turn. If Vera leaves the board so that Marco cannot choose a cell that is black and has more than two white neighbors, then Vera wins; otherwise, another turn occurs.
Let \( m \) be the minimal \( k \) value such that Vera can guarantee that she wins no matter what Marco does. For \( k=m \), let \( t \) be the smallest positive integer such that Vera can guarantee, no matter what Marco does, that she wins after at most \( t \) turns. Compute \( 100m + t \).
|
[
"/Mathematics/DiscreteMathematics/Combinatorics",
"/Mathematics/DiscreteMathematics/GeneralDiscreteMathematics/DiscreteMath",
"/Mathematics/DiscreteMathematics/GeneralDiscreteMathematics/DiscreteMathematics",
"/Mathematics/RecreationalMathematics/Games/GameTheory",
"/Mathematics/RecreationalMathematics/Games/GeneralGames",
"/Mathematics/RecreationalMathematics/Puzzles/Puzzle"
] |
Use one swap each turn to restrict Marco’s expansion and force a 3×3 solid black block, ensuring all black cells have ≤2 white neighbors within three turns.
|
[
0.0000069141387939453125,
-0.01305389404296875,
0.0236053466796875,
-0.05902099609375,
0.00016796588897705078,
0.032928466796875,
0.030181884765625,
-0.0013599395751953125,
0.01114654541015625,
0.05450439453125,
0.043243408203125,
-0.055816650390625,
0.0002574920654296875,
-0.00417327880859375,
-0.001232147216796875,
-0.0272064208984375,
-0.0252685546875,
0.0026149749755859375,
-0.01528167724609375,
0.0023365020751953125,
-0.023956298828125,
0.00519561767578125,
-0.0270538330078125,
0.028289794921875,
0.0002359151840209961,
-0.044525146484375,
-0.0212249755859375,
0.025604248046875,
0.0087127685546875,
-0.00989532470703125,
-0.029693603515625,
-0.00948333740234375,
0.039947509765625,
-0.0121307373046875,
-0.0005736351013183594,
-0.003509521484375,
0.009246826171875,
0.0022411346435546875,
-0.03350830078125,
-0.01255035400390625,
-0.0016241073608398438,
0.0225372314453125,
-0.00579833984375,
0.01398468017578125,
-0.0034389495849609375,
0.026031494140625,
-0.0036296844482421875,
0.0230712890625,
0.0046539306640625,
-0.0181121826171875,
-0.0164031982421875,
0.0222015380859375,
0.029571533203125,
-0.01392364501953125,
-0.0117340087890625,
-0.06585693359375,
0.00299835205078125,
-0.0030059814453125,
0.055694580078125,
-0.0149078369140625,
0.00811004638671875,
0.0258636474609375,
-0.00673675537109375,
-0.01666259765625,
0.002410888671875,
-0.004650115966796875,
0.0167236328125,
0.01284027099609375,
0.01070404052734375,
-0.0055389404296875,
0.0272979736328125,
-0.0005240440368652344,
0.00389862060546875,
0.0184173583984375,
0.0161895751953125,
-0.01715087890625,
-0.00904083251953125,
0.00782012939453125,
0.03765869140625,
-0.000415802001953125,
-0.031158447265625,
0.006927490234375,
0.0159454345703125,
0.00836181640625,
-0.0004992485046386719,
0.018707275390625,
0.0189056396484375,
-0.0018339157104492188,
0.02227783203125,
-0.02276611328125,
0.00812530517578125,
-0.01116180419921875,
0.0091552734375,
0.01218414306640625,
0.0107421875,
0.006092071533203125,
0.0115966796875,
-0.0081787109375,
-0.01151275634765625,
0.0005154609680175781,
-0.00452423095703125,
0.018646240234375,
0.005615234375,
-0.01338958740234375,
-0.037353515625,
-0.0182952880859375,
-0.03021240234375,
0.006465911865234375,
-0.0236358642578125,
0.005184173583984375,
0.0007119178771972656,
0.005950927734375,
0.036346435546875,
-0.03082275390625,
0.01189422607421875,
-0.0053558349609375,
0.0015649795532226562,
-0.00557708740234375,
0.00677490234375,
0.01122283935546875,
-0.0049591064453125,
0.01221466064453125,
-0.02349853515625,
0.01418304443359375,
0.01152801513671875,
-0.024627685546875,
-0.004909515380859375,
-0.0153045654296875,
0.01116943359375,
0.0111541748046875,
-0.01983642578125,
0.0033206939697265625,
-0.0305023193359375,
-0.0045623779296875,
-0.047943115234375,
0.018707275390625,
-0.01039886474609375,
-0.006717681884765625,
-0.005767822265625,
0.0031414031982421875,
0.0144805908203125,
-0.0092926025390625,
0.00888824462890625,
-0.0113372802734375,
-0.006134033203125,
0.01374053955078125,
0.013763427734375,
-0.0462646484375,
0.0175628662109375,
-0.010772705078125,
-0.008270263671875,
-0.00971221923828125,
0.04608154296875,
-0.01313018798828125,
-0.0201263427734375,
0.0183563232421875,
0.0008411407470703125,
-0.0008702278137207031,
0.0226593017578125,
-0.002285003662109375,
-0.00942230224609375,
-0.0107269287109375,
-0.0239715576171875,
0.09320068359375,
-0.0028285980224609375,
0.033935546875,
0.004150390625,
-0.00472259521484375,
-0.00428009033203125,
0.0098876953125,
-0.0012226104736328125,
-0.016204833984375,
-0.007904052734375,
-0.0110321044921875,
-0.0123291015625,
-0.01129150390625,
-0.01424407958984375,
-0.02734375,
-0.00255584716796875,
0.008758544921875,
0.018035888671875,
-0.049835205078125,
0.0174102783203125,
0.01033782958984375,
-0.0196380615234375,
-0.002349853515625,
-0.0007390975952148438,
0.0025806427001953125,
0.00980377197265625,
0.01007080078125,
0.0243072509765625,
-0.019866943359375,
0.0014677047729492188,
-0.004360198974609375,
-0.0186767578125,
0.0010433197021484375,
-0.019744873046875,
0.0146636962890625,
0.06219482421875,
0.0140838623046875,
-0.006191253662109375,
0.011383056640625,
-0.0111236572265625,
0.01035308837890625,
0.01363372802734375,
-0.0182037353515625,
0.00579071044921875,
-0.0144500732421875,
-0.00565338134765625,
0.00047969818115234375,
0.0015878677368164062,
-0.01507568359375,
-0.004077911376953125,
0.0067138671875,
-0.002658843994140625,
0.0160675048828125,
-0.0006117820739746094,
0.01050567626953125,
0.00888824462890625,
-0.02484130859375,
0.0025196075439453125,
0.0027618408203125,
-0.0009293556213378906,
-0.00205230712890625,
-0.0223236083984375,
0.006313323974609375,
0.0142974853515625,
-0.007015228271484375,
-0.009490966796875,
0.004840850830078125,
0.015838623046875,
0.0233001708984375,
-0.01132965087890625,
-0.0275726318359375,
-0.01959228515625,
0.007568359375,
0.01251220703125,
-0.023590087890625,
0.0103302001953125,
-0.0260772705078125,
0.0195465087890625,
-0.0011053085327148438,
-0.01045989990234375,
0.005962371826171875,
-0.01263427734375,
-0.007450103759765625,
-0.009124755859375,
0.00020706653594970703,
0.005218505859375,
0.0015935897827148438,
-0.010345458984375,
0.00965118408203125,
-0.009796142578125,
-0.0265960693359375,
-0.0276641845703125,
-0.00848388671875,
-0.0015821456909179688,
-0.01151275634765625,
-0.0156097412109375,
-0.0345458984375,
-0.02197265625,
-0.0178985595703125,
0.00958251953125,
0.004734039306640625,
0.005023956298828125,
-0.0233154296875,
0.010101318359375,
0.006999969482421875,
-0.006221771240234375,
-0.026123046875,
0.034027099609375,
0.001567840576171875,
-0.01068878173828125,
0.0171356201171875,
0.01534271240234375,
-0.02227783203125,
-0.005218505859375,
0.0055999755859375,
0.0117034912109375,
0.0028057098388671875,
0.0248870849609375,
-0.0185394287109375,
-0.0064697265625,
-0.004489898681640625,
-0.0019092559814453125,
0.0063323974609375,
-0.0201263427734375,
-0.01200103759765625,
-0.00841522216796875,
0.0048980712890625,
-0.01385498046875,
-0.0081939697265625,
0.005329132080078125,
-0.003787994384765625,
0.050384521484375,
-0.02093505859375,
-0.0010080337524414062,
0.01323699951171875,
0.01488494873046875,
-0.001544952392578125,
0.0057525634765625,
-0.008697509765625,
0.003803253173828125,
0.033782958984375,
-0.002330780029296875,
0.0030574798583984375,
0.0054779052734375,
-0.0029048919677734375,
-0.0196533203125,
-0.0221099853515625,
0.0243682861328125,
-0.01299285888671875,
-0.00922393798828125,
0.01132965087890625,
-0.016571044921875,
-0.027557373046875,
-0.014251708984375,
0.01467132568359375,
0.0121917724609375,
-0.0158538818359375,
-0.0025539398193359375,
-0.00933074951171875,
-0.004383087158203125,
-0.006259918212890625,
0.029144287109375,
-0.00856781005859375,
0.023529052734375,
0.0186614990234375,
0.003398895263671875,
0.00638580322265625,
0.002811431884765625,
0.003810882568359375,
0.0102691650390625,
0.012176513671875,
-0.0135040283203125,
0.0135955810546875,
-0.021087646484375,
0.034149169921875,
-0.00018775463104248047,
0.02978515625,
-0.01275634765625,
0.0145721435546875,
-0.0185089111328125,
-0.0706787109375,
-0.00982666015625,
-0.0073699951171875,
0.0074920654296875,
-0.00832366943359375,
-0.0037784576416015625,
0.0018091201782226562,
0.041229248046875,
0.0229644775390625,
-0.0243072509765625,
0.006378173828125,
0.0026149749755859375,
-0.00040149688720703125,
-0.0001571178436279297,
0.0212554931640625,
-0.004955291748046875,
-0.0007314682006835938,
0.00922393798828125,
-0.019378662109375,
-0.0009636878967285156,
-0.00960540771484375,
0.01534271240234375,
-0.00690460205078125,
-0.0279388427734375,
0.0168609619140625,
-0.0155029296875,
0.007640838623046875,
-0.0032215118408203125,
0.0293731689453125,
0.004848480224609375,
0.00010079145431518555,
-0.00876617431640625,
-0.00038909912109375,
0.009033203125,
0.0038394927978515625,
0.0087432861328125,
-0.008056640625,
0.0009722709655761719,
0.02099609375,
0.0311431884765625,
0.0306243896484375,
-0.023773193359375,
0.0020427703857421875,
0.001277923583984375,
-0.04193115234375,
-0.0035076141357421875,
0.01776123046875,
0.006992340087890625,
0.00995635986328125,
-0.007537841796875,
-0.0173797607421875,
0.01084136962890625,
0.0092010498046875,
-0.0023365020751953125,
0.0028820037841796875,
0.048309326171875,
-0.0156097412109375,
-0.01824951171875,
-0.01047515869140625,
0.00547027587890625,
0.0372314453125,
0.00553131103515625,
0.014892578125,
-0.016845703125,
0.00530242919921875,
-0.01226806640625,
0.006038665771484375,
0.00743865966796875,
-0.053436279296875,
0.03680419921875,
-0.019256591796875,
0.04180908203125,
-0.01158905029296875,
0.004154205322265625,
-0.002185821533203125,
-0.0224609375,
0.006328582763671875,
-0.0018568038940429688,
0.0084075927734375,
-0.007476806640625,
0.020233154296875,
-0.005588531494140625,
0.0260162353515625,
-0.0177764892578125,
0.022125244140625,
-0.03948974609375,
-0.0068359375,
-0.007251739501953125,
-0.006954193115234375,
0.01491546630859375,
0.04425048828125,
-0.003513336181640625,
0.04010009765625,
0.01922607421875,
-0.0167083740234375,
-0.026336669921875,
0.00180816650390625,
-0.0304718017578125,
-0.006229400634765625,
-0.0094451904296875,
0.0001914501190185547,
0.029510498046875,
0.0079803466796875,
0.02020263671875,
0.01187896728515625,
-0.05230712890625,
0.02044677734375,
-0.01026153564453125,
-0.0016736984252929688,
-0.005035400390625,
-0.00921630859375,
0.01363372802734375,
0.032928466796875,
0.0193634033203125,
-0.0175933837890625,
-0.0013484954833984375,
0.0023784637451171875,
0.005435943603515625,
-0.007099151611328125,
0.01403045654296875,
0.0217742919921875,
-0.038543701171875,
0.0038700103759765625,
-0.00690460205078125,
-0.022552490234375,
-0.0163421630859375,
0.0439453125,
-0.01270294189453125,
-0.0266265869140625,
0.0082244873046875,
0.01479339599609375,
-0.0030078887939453125,
0.0199127197265625,
-0.01213836669921875,
0.033721923828125,
-0.02593994140625,
-0.03369140625,
0.000579833984375,
0.00682830810546875,
0.00997161865234375,
0.05126953125,
0.009552001953125,
0.0118865966796875,
0.014190673828125,
-0.00992584228515625,
0.004428863525390625,
0.01446533203125,
0.000858306884765625,
0.02154541015625,
-0.010406494140625,
-0.002498626708984375,
-0.0290679931640625,
-0.0005307197570800781,
0.0084381103515625,
-0.01146697998046875,
-0.0273895263671875,
-0.0134429931640625,
-0.01324462890625,
0.01416015625,
-0.01296234130859375,
0.00826263427734375,
0.032806396484375,
-0.0038585662841796875,
0.00653076171875,
-0.02154541015625,
-0.00943756103515625,
-0.0150909423828125,
0.0048980712890625,
0.0390625,
-0.0089874267578125,
-0.01513671875,
0.03277587890625,
-0.0169219970703125,
0.004108428955078125,
-0.0044403076171875,
0.03668212890625,
0.038421630859375,
-0.004817962646484375,
-0.026031494140625,
0.0394287109375,
0.006755828857421875,
-0.00787353515625,
0.01029205322265625,
0.0095062255859375,
-0.0276336669921875,
0.0221405029296875,
0.007633209228515625,
0.0068359375,
0.019134521484375,
-0.0195770263671875,
0.0328369140625,
-0.025054931640625,
0.0096435546875,
0.004787445068359375,
-0.0137176513671875,
0.01861572265625,
0.00379180908203125,
0.02520751953125,
0.0051727294921875,
0.021209716796875,
-0.01348876953125,
0.00826263427734375,
-0.049407958984375,
-0.006885528564453125,
-0.007465362548828125,
-0.006275177001953125,
-0.0118865966796875,
-0.0003731250762939453,
0.027557373046875,
-0.05230712890625,
-0.0099029541015625,
-0.0221099853515625,
0.0131988525390625,
-0.01538848876953125,
-0.007030487060546875,
0.01617431640625,
0.0065155029296875,
-0.01134490966796875,
0.0413818359375,
0.0171356201171875,
0.0161895751953125,
0.018280029296875,
-0.03955078125,
-0.0053253173828125,
-0.010101318359375,
-0.0154876708984375,
-0.039276123046875,
-0.01483917236328125,
-0.03314208984375,
-0.007526397705078125,
-0.0194244384765625,
0.0008645057678222656,
0.00701904296875,
-0.035675048828125,
-0.01363372802734375,
-0.01493072509765625,
-0.007747650146484375,
0.039520263671875,
0.0218658447265625,
-0.023345947265625,
0.033538818359375,
0.0225830078125,
0.0159759521484375,
0.0184783935546875,
0.0088348388671875,
0.003963470458984375,
-0.007801055908203125,
0.013671875,
0.0308380126953125,
0.004077911376953125,
0.004131317138671875,
0.00432586669921875,
-0.0028247833251953125,
-0.031524658203125,
0.00177001953125,
-0.01035308837890625,
0.01209259033203125,
0.0377197265625,
-0.05816650390625,
-0.00954437255859375,
0.0271759033203125,
-0.036285400390625,
-0.01398468017578125,
0.021453857421875,
0.0213775634765625,
-0.0113983154296875,
0.0251617431640625,
0.01177215576171875,
0.01520538330078125,
0.003604888916015625,
0.00685882568359375,
-0.0032672882080078125,
-0.0037994384765625,
0.0175323486328125,
-0.036712646484375,
0.022430419921875,
-0.0237884521484375,
-0.0310821533203125,
-0.01433563232421875,
0.00666046142578125,
0.0026531219482421875,
-0.02252197265625,
-0.0090179443359375,
0.0086822509765625,
-0.0206298828125,
0.028961181640625,
0.0016126632690429688,
-0.021209716796875,
0.00855255126953125,
-0.001239776611328125,
-0.03704833984375,
0.004787445068359375,
0.00508880615234375,
0.005939483642578125,
0.02178955078125,
0.00266265869140625,
-0.007450103759765625,
0.002307891845703125,
-0.018157958984375,
0.0156707763671875,
-0.032806396484375,
-0.002124786376953125,
0.0028171539306640625,
-0.00582122802734375,
-0.0052947998046875,
-0.02740478515625,
-0.004222869873046875,
-0.0185699462890625,
-0.023101806640625,
-0.03802490234375,
-0.002460479736328125,
-0.022064208984375,
0.0028553009033203125,
-0.00336456298828125,
-0.0186614990234375,
0.00872802734375,
-0.01397705078125,
0.0269927978515625,
-0.01042938232421875,
-0.01151275634765625,
-0.012237548828125,
-0.034912109375,
-0.03997802734375,
-0.0187835693359375,
0.0254669189453125,
0.0212554931640625,
0.00635528564453125,
0.035003662109375,
0.013153076171875,
-0.0241546630859375,
0.0176239013671875,
0.028106689453125,
0.0125885009765625,
0.01247406005859375,
-0.0006632804870605469,
0.0178985595703125,
-0.004505157470703125,
0.00044155120849609375,
0.037933349609375,
0.04339599609375,
-0.02227783203125,
0.01425933837890625,
0.0145416259765625,
0.033721923828125,
-0.0030670166015625,
0.0177764892578125,
-0.0071868896484375,
0.0104522705078125,
0.028045654296875,
-0.01485443115234375,
0.00972747802734375,
-0.0099029541015625,
-0.01239776611328125,
0.0282745361328125,
0.022216796875,
-0.041778564453125,
0.03106689453125,
-0.018707275390625,
-0.034881591796875,
-0.00196075439453125,
-0.01255035400390625,
-0.0267486572265625,
-0.0271453857421875,
-0.0012340545654296875,
-0.028167724609375,
-0.019012451171875,
-0.0020732879638671875,
-0.04254150390625,
0.0119781494140625,
0.005535125732421875,
-0.004840850830078125,
-0.0130157470703125,
-0.013580322265625,
-0.00400543212890625,
0.028564453125,
0.0108642578125,
0.0046539306640625,
-0.0546875,
0.0235137939453125,
-0.03106689453125,
-0.01267242431640625,
0.0206756591796875,
-0.00966644287109375,
0.016265869140625,
-0.01415252685546875,
-0.0008363723754882812,
0.011016845703125,
0.0081024169921875,
-0.004604339599609375,
0.008209228515625,
-0.009918212890625,
-0.0369873046875,
0.00041222572326660156,
-0.008758544921875,
-0.03216552734375,
-0.003345489501953125,
-0.02099609375,
0.07415771484375,
-0.00919342041015625,
0.005886077880859375,
-0.005107879638671875,
0.02105712890625,
-0.011138916015625,
-0.0264434814453125,
-0.0012483596801757812,
-0.003055572509765625,
0.01436614990234375,
0.04449462890625,
0.01222991943359375,
-0.005596160888671875,
0.0147857666015625,
-0.016693115234375,
0.00870513916015625,
0.030029296875,
-0.005619049072265625,
0.0134735107421875,
0.0009708404541015625,
-0.028289794921875,
-0.012237548828125,
0.004886627197265625,
-0.00921630859375,
0.0091552734375,
-0.01554107666015625,
-0.02655029296875,
-0.01262664794921875,
0.00330352783203125,
-0.0002570152282714844,
-0.06207275390625,
-0.029144287109375,
0.007389068603515625,
0.0301666259765625,
0.0208587646484375,
0.0087738037109375,
-0.039276123046875,
-0.0032825469970703125,
0.0367431640625,
-0.0196075439453125,
-0.007793426513671875,
-0.0186767578125,
-0.04522705078125,
0.0089111328125,
-0.038421630859375,
-0.0177764892578125,
0.003665924072265625,
-0.00431060791015625,
0.01247406005859375,
0.0157928466796875,
0.04766845703125,
0.0175628662109375,
0.02935791015625,
0.0235443115234375,
0.01824951171875,
0.0105743408203125,
0.0185699462890625,
0.0006184577941894531,
0.02557373046875,
-0.0008454322814941406,
-0.00885772705078125,
-0.0069122314453125,
-0.0160369873046875,
-0.005947113037109375,
0.0206298828125,
-0.00792694091796875,
-0.014251708984375,
-0.00476837158203125,
-0.019561767578125,
-0.021087646484375,
0.006740570068359375,
-0.01103973388671875,
0.01654052734375,
-0.017578125,
0.00988006591796875,
-0.009063720703125,
-0.00125885009765625,
0.0391845703125,
-0.03131103515625,
0.0089263916015625,
-0.020538330078125,
0.0132904052734375,
0.005283355712890625,
0.01474761962890625,
-0.0088653564453125,
-0.0299224853515625,
0.01422882080078125,
0.03582763671875,
-0.0012760162353515625,
0.0008683204650878906,
-0.015838623046875,
0.01024627685546875,
-0.04052734375,
-0.004974365234375,
-0.00618743896484375,
-0.00815582275390625,
0.0143890380859375,
-0.00077056884765625,
-0.0103607177734375,
0.0030059814453125,
-0.01165008544921875,
0.0227813720703125,
-0.0243377685546875,
0.0186004638671875,
0.0166168212890625,
-0.00395965576171875,
0.0036296844482421875,
0.026611328125,
0.017974853515625,
0.007335662841796875,
-0.0168304443359375,
0.01715087890625,
-0.05596923828125,
0.0125579833984375,
0.034942626953125,
0.043548583984375,
0.00939178466796875,
0.005603790283203125,
-0.0067901611328125,
-0.044708251953125,
-0.00020122528076171875,
-0.024627685546875,
0.02630615234375,
-0.038787841796875,
0.00958251953125,
-0.0018587112426757812,
-0.016754150390625,
-0.0018568038940429688,
-0.00229644775390625,
-0.033721923828125,
0.0227203369140625,
-0.005840301513671875,
0.018951416015625,
0.0225372314453125,
0.0296173095703125,
0.0022449493408203125,
-0.0059051513671875,
-0.02630615234375,
0.0472412109375,
0.00955963134765625,
0.002399444580078125,
-0.01238250732421875,
-0.0012760162353515625,
-0.002254486083984375,
-0.0128631591796875,
-0.0118255615234375,
-0.0357666015625,
0.01055145263671875,
-0.01345062255859375,
-0.024688720703125,
0.0325927734375,
0.00830078125,
0.0027065277099609375,
-0.025177001953125,
-0.0019741058349609375,
0.015869140625,
-0.01727294921875,
-0.019073486328125,
0.0123748779296875,
-0.037506103515625,
-0.0325927734375,
-0.024169921875,
0.017333984375,
0.00933074951171875,
0.007656097412109375,
-0.005222320556640625,
-0.0238189697265625,
-0.009033203125,
0.024322509765625,
-0.02734375,
-0.0265045166015625,
-0.0223388671875,
0.021331787109375,
0.0110931396484375,
-0.00926971435546875,
0.00982666015625,
0.0005488395690917969,
0.0241546630859375,
-0.0096282958984375,
-0.01271820068359375,
0.0216827392578125,
-0.00797271728515625,
0.0082550048828125,
-0.003833770751953125,
0.005733489990234375,
-0.04364013671875,
-0.006961822509765625,
0.00142669677734375,
0.00421142578125,
0.017822265625,
0.0037555694580078125,
0.016845703125,
0.006870269775390625,
0.0017528533935546875,
0.00421142578125,
0.0210418701171875,
0.00823974609375,
-0.0071868896484375,
-0.0036144256591796875,
-0.0333251953125,
-0.016754150390625,
0.0167083740234375,
0.00870513916015625,
0.0234832763671875,
0.0286102294921875,
-0.010406494140625,
-0.00782012939453125,
-0.0296630859375,
-0.026641845703125,
0.0011148452758789062,
0.01148223876953125,
-0.01114654541015625,
-0.035675048828125,
0.01885986328125,
-0.04888916015625,
0.007472991943359375,
0.01776123046875,
-0.005573272705078125,
0.0284576416015625,
-0.0255126953125,
0.01242828369140625,
0.01824951171875,
0.006641387939453125,
0.01190948486328125,
-0.01453399658203125,
0.00981903076171875,
-0.0284423828125,
0.01264190673828125,
0.0257110595703125,
-0.0004565715789794922,
-0.0015735626220703125,
0.0110931396484375,
-0.01361846923828125,
-0.034149169921875,
-0.029876708984375,
0.0016269683837890625,
-0.029541015625,
0.0226287841796875,
-0.003108978271484375,
0.008453369140625,
-0.0059356689453125,
-0.004207611083984375,
0.0215606689453125,
-0.00957489013671875,
-0.01497650146484375,
0.0123748779296875,
0.034820556640625,
-0.004238128662109375,
0.00992584228515625,
-0.0034732818603515625,
-0.00492095947265625,
0.01250457763671875,
0.02301025390625,
0.0013799667358398438,
0.0089263916015625,
0.01059722900390625,
0.00843048095703125,
-0.0149383544921875,
0.006183624267578125,
0.004268646240234375,
-0.03375244140625,
-0.00975799560546875,
0.006679534912109375,
-0.006694793701171875,
0.0179901123046875,
-0.040130615234375,
-0.0139312744140625,
0.01678466796875,
-0.01255035400390625,
0.01486968994140625,
0.0029087066650390625,
-0.0125885009765625,
0.009765625,
-0.00989532470703125,
-0.00962066650390625,
0.017822265625,
0.0276336669921875,
-0.01212310791015625,
0.012420654296875,
-0.0021839141845703125,
0.0126495361328125,
0.0150146484375,
-0.046966552734375,
-0.00830078125,
0.01299285888671875,
-0.00984954833984375,
-0.00508880615234375,
-0.0021762847900390625,
0.0218048095703125,
0.0250244140625,
0.01477813720703125,
0.0171356201171875,
0.00881195068359375,
-0.01078033447265625,
-0.0242462158203125,
-0.0131072998046875,
-0.01806640625,
0.008148193359375,
-0.0277099609375,
-0.010162353515625,
0.0164337158203125,
0.025177001953125,
0.0037708282470703125,
0.017822265625,
0.01654052734375,
-0.0213165283203125,
-0.00101470947265625,
0.01207733154296875,
-0.007335662841796875,
0.0306549072265625,
-0.00494384765625,
0.00806427001953125,
-0.0014200210571289062,
-0.00414276123046875,
0.034149169921875,
-0.00687408447265625,
-0.00824737548828125,
-0.01493072509765625,
-0.0008320808410644531,
0.0279998779296875,
0.02789306640625,
-0.0092010498046875,
-0.0098114013671875,
0.006725311279296875,
-0.0025463104248046875,
-0.03070068359375,
-0.01497650146484375,
-0.006572723388671875,
-0.0177154541015625,
-0.00878143310546875,
-0.032440185546875,
0.024383544921875,
-0.0180206298828125,
-0.01116180419921875,
0.016632080078125,
0.037261962890625,
-0.006023406982421875,
0.0243072509765625,
-0.04022216796875,
0.0169525146484375,
-0.0208740234375,
0.0411376953125,
-0.048736572265625,
-0.0205078125,
0.01143646240234375,
0.006053924560546875,
-0.0299835205078125,
-0.0116729736328125,
-0.01325225830078125,
0.00476837158203125,
-0.014739990234375,
0.01415252685546875,
-0.01207733154296875,
-0.0179443359375,
0.017730712890625,
-0.01849365234375,
0.006622314453125,
-0.0104217529296875,
0.01200103759765625,
0.0151214599609375,
0.007358551025390625,
0.038909912109375,
-0.0045166015625,
0.0020599365234375,
0.01186370849609375,
-0.0198516845703125,
0.032073974609375,
0.02001953125,
-0.03070068359375,
-0.00047326087951660156,
-0.01111602783203125,
0.03253173828125,
-0.0193634033203125,
0.007129669189453125,
-0.0187530517578125,
0.0103607177734375,
0.0032196044921875,
-0.01506805419921875,
-0.0298309326171875,
0.03228759765625,
-0.006847381591796875,
0.01194000244140625,
-0.02923583984375,
0.0013580322265625,
0.0099029541015625,
-0.0034332275390625,
-0.01412200927734375,
-0.0264739990234375,
-0.004703521728515625,
-0.009246826171875,
-0.0153656005859375,
0.0253143310546875,
0.0243377685546875,
-0.061065673828125,
-0.0148468017578125,
-0.0204620361328125,
0.0005784034729003906,
0.008087158203125,
0.041168212890625,
-0.0224609375,
0.0264434814453125,
-0.0012712478637695312,
-0.0253448486328125,
0.005779266357421875,
0.010498046875,
0.00342559814453125,
-0.0022258758544921875,
-0.007045745849609375,
0.0704345703125,
0.020050048828125,
0.0071563720703125,
0.00586700439453125,
-0.0272674560546875,
-0.018035888671875,
-0.024017333984375,
0.01363372802734375,
-0.0207061767578125,
-0.02081298828125,
-0.0143280029296875,
0.0038547515869140625,
-0.0149078369140625,
-0.0275115966796875,
0.0134124755859375,
-0.0035572052001953125,
-0.0330810546875,
-0.0225067138671875,
0.015167236328125,
-0.0032672882080078125,
-0.0234527587890625,
-0.00991058349609375,
-0.01154327392578125,
-0.0193939208984375,
0.0208587646484375,
0.00885009765625,
-0.03924560546875,
-0.0167236328125,
0.0030117034912109375,
-0.0002148151397705078,
-0.0072021484375,
0.00025653839111328125,
-0.02362060546875,
0.0284881591796875,
0.0281829833984375,
0.0134124755859375,
-0.002361297607421875,
0.00653076171875,
-0.0102386474609375,
-0.011688232421875,
-0.0279083251953125,
0.0030975341796875,
-0.01334381103515625,
0.00476837158203125,
-0.0177459716796875,
-0.047698974609375,
0.006458282470703125,
0.0045013427734375,
-0.00528717041015625,
0.00801849365234375,
-0.001026153564453125,
0.0031909942626953125,
0.06732177734375,
-0.024200439453125,
-0.0178375244140625,
-0.026824951171875,
0.0155487060546875,
0.041778564453125,
-0.00010180473327636719,
0.02227783203125,
-0.013427734375,
0.01361083984375,
-0.005886077880859375,
0.00096893310546875,
0.0055084228515625,
-0.0158233642578125,
0.008087158203125,
-0.0105743408203125,
0.01016998291015625,
0.005710601806640625,
-0.0183563232421875,
-0.00739288330078125,
0.035064697265625,
-0.01010894775390625,
-0.0030040740966796875,
-0.0262298583984375,
0.008270263671875,
-0.002597808837890625,
-0.04071044921875,
0.049835205078125,
0.00006580352783203125,
-0.045196533203125,
0.05523681640625,
0.055328369140625,
0.00528717041015625,
-0.0301361083984375,
-0.0177001953125,
-0.0155792236328125,
-0.007068634033203125,
0.02227783203125,
-0.0166015625,
0.007472991943359375,
-0.0135650634765625,
-0.02130126953125,
0.03582763671875,
-0.006023406982421875,
0.0141143798828125,
-0.0168914794921875,
0.010772705078125,
0.0183258056640625,
-0.01007843017578125,
0.0166473388671875,
0.028045654296875,
0.01091766357421875,
-0.0191497802734375,
-0.01139068603515625,
0.0171051025390625,
-0.03265380859375,
0.01357269287109375,
-0.002429962158203125,
-0.013916015625,
0.004192352294921875,
-0.01560211181640625,
0.01361846923828125,
-0.036163330078125,
0.002536773681640625,
0.00021064281463623047,
0.01448822021484375,
0.0310821533203125,
0.0229339599609375,
0.003108978271484375,
-0.005283355712890625,
0.0277252197265625,
0.001964569091796875,
0.01477813720703125,
0.0555419921875,
-0.037506103515625,
0.00328826904296875,
0.0002765655517578125,
-0.047821044921875,
-0.01788330078125,
-0.01226806640625,
-0.024017333984375,
0.0178985595703125,
-0.017333984375,
-0.0032863616943359375,
-0.004154205322265625,
-0.01861572265625,
-0.02459716796875,
0.00872039794921875,
-0.03387451171875,
-0.0034732818603515625,
0.014251708984375,
0.0189208984375,
0.007640838623046875,
-0.00751495361328125,
0.0113067626953125,
-0.01442718505859375,
0.01558685302734375,
0.03363037109375,
0.014801025390625,
0.0201263427734375,
-0.00653076171875,
0.0019397735595703125,
0.0294036865234375,
0.00555419921875,
-0.00853729248046875,
-0.0179290771484375,
0.020355224609375,
0.0161590576171875,
-0.00669097900390625,
0.0019483566284179688,
0.00397491455078125,
0.0281524658203125,
0.037506103515625,
-0.0155029296875,
-0.00514984130859375,
0.0238494873046875,
0.01157379150390625,
0.0157928466796875,
-0.0179443359375,
-0.00439453125,
-0.0019054412841796875,
0.0289306640625,
-0.0223236083984375,
-0.01488494873046875,
0.037506103515625,
-0.0161285400390625,
-0.0233154296875,
0.0018405914306640625,
-0.020904541015625,
-0.01029205322265625,
-0.0024623870849609375,
-0.014892578125,
-0.00986480712890625,
0.036712646484375,
0.0045928955078125,
0.034027099609375,
0.029815673828125,
0.01433563232421875,
-0.0094451904296875,
-0.040557861328125,
-0.0167388916015625,
0.006542205810546875,
-0.0028285980224609375,
-0.00457000732421875,
0.0219573974609375,
0.038970947265625,
-0.0175628662109375,
0.03656005859375,
0.005023956298828125,
0.01090240478515625,
0.00258636474609375,
0.0010728836059570312,
-0.004177093505859375,
0.011932373046875,
-0.0199737548828125,
-0.0191650390625,
0.01123809814453125,
0.0198516845703125,
0.021484375,
0.0172119140625,
0.00197601318359375,
-0.001987457275390625,
0.0186614990234375,
-0.03985595703125,
0.0287322998046875,
-0.0038089752197265625,
0.00878143310546875,
0.03546142578125,
0.008575439453125,
0.00028228759765625,
-0.02105712890625,
-0.0067901611328125,
-0.002902984619140625,
-0.007678985595703125,
0.045654296875,
0.0036602020263671875,
0.0075225830078125,
-0.01099395751953125,
0.0078125,
-0.017730712890625,
-0.05426025390625,
-0.014617919921875,
-0.02081298828125,
-0.021453857421875,
-0.0179290771484375,
0.0284881591796875,
-0.004486083984375,
-0.0026912689208984375,
-0.01311492919921875,
0.01360321044921875,
-0.007221221923828125,
0.005062103271484375,
0.0003876686096191406,
-0.00572967529296875,
-0.009185791015625,
-0.0126190185546875,
-0.00965118408203125,
0.01080322265625,
-0.0210723876953125,
0.00020825862884521484,
0.0178680419921875,
0.01351165771484375,
-0.049072265625,
0.033782958984375,
0.00849151611328125,
-0.01739501953125,
-0.0006089210510253906,
0.00640869140625,
0.007762908935546875,
0.012542724609375,
-0.0157623291015625,
-0.031524658203125,
0.008758544921875,
-0.05364990234375,
0.017852783203125,
-0.0267333984375,
-0.0008912086486816406,
-0.0015516281127929688,
-0.007293701171875,
0.00829315185546875,
0.00799560546875,
-0.00864410400390625,
-0.033782958984375,
0.002353668212890625,
0.026763916015625,
0.022796630859375,
0.020294189453125,
0.0308685302734375,
-0.01279449462890625,
-0.01031494140625,
0.0215911865234375,
-0.01305389404296875,
-0.0118865966796875,
-0.0286712646484375,
-0.037261962890625,
-0.04107666015625,
0.0242156982421875,
0.007198333740234375,
-0.008392333984375,
-0.0016632080078125,
0.0188751220703125,
-0.01300048828125,
0.0167388916015625,
-0.01224517822265625,
-0.0117340087890625,
-0.0278778076171875,
0.003101348876953125,
-0.0072479248046875,
-0.019317626953125,
-0.005954742431640625,
0.0012941360473632812,
-0.028045654296875,
-0.006725311279296875,
0.039031982421875,
0.029876708984375,
-0.0086822509765625,
0.00995635986328125,
0.009246826171875,
0.0007429122924804688,
-0.01126861572265625,
-0.0215301513671875,
0.01020050048828125,
-0.032196044921875,
-0.0033054351806640625,
0.01161956787109375,
-0.003910064697265625,
-0.01319122314453125,
0.016204833984375,
0.0149688720703125,
-0.0091400146484375,
0.002025604248046875,
0.0190277099609375,
-0.00797271728515625,
-0.007022857666015625,
-0.03289794921875,
-0.0106048583984375,
0.0024566650390625,
-0.02301025390625,
0.015228271484375,
0.0029144287109375,
0.0018157958984375,
0.0182342529296875,
-0.019866943359375,
-0.019134521484375,
-0.01438140869140625,
-0.021209716796875,
-0.0300140380859375,
0.01103973388671875,
-0.00481414794921875,
0.0194244384765625,
-0.030731201171875,
-0.014862060546875,
-0.0014858245849609375,
-0.004299163818359375,
0.036285400390625,
0.0093994140625,
0.00010073184967041016,
-0.006053924560546875,
0.018829345703125,
-0.012847900390625,
-0.0161895751953125,
0.0226593017578125,
0.00592041015625,
-0.0033855438232421875,
0.00501251220703125,
-0.022674560546875,
0.0085601806640625,
0.0241241455078125,
-0.01203155517578125,
-0.00925445556640625,
-0.0244140625,
-0.006099700927734375,
0.0116424560546875,
-0.0280609130859375,
-0.0443115234375,
0.01515960693359375,
0.0026378631591796875,
-0.033477783203125,
0.01413726806640625,
-0.01410675048828125,
0.00812530517578125,
0.041290283203125,
-0.01097869873046875,
0.0233917236328125,
-0.0020847320556640625,
0.00946807861328125,
0.0048828125,
0.0198211669921875,
-0.00455474853515625,
0.00839996337890625,
-0.0244598388671875,
0.0205841064453125,
0.006664276123046875,
0.0072021484375,
0.017242431640625,
-0.01190948486328125,
0.0211944580078125,
0.0204315185546875,
-0.0029354095458984375,
0.000530242919921875,
0.03497314453125,
-0.004840850830078125,
-0.01519012451171875,
0.0181732177734375,
-0.0316162109375,
-0.0174560546875,
0.01041412353515625,
-0.002971649169921875,
0.0008544921875,
-0.036865234375,
0.0237579345703125,
-0.005157470703125,
-0.006343841552734375,
0.00917816162109375,
-0.033050537109375,
0.0102691650390625,
-0.0027618408203125,
0.034912109375,
-0.016754150390625,
-0.015655517578125,
-0.00850677490234375,
0.019775390625,
-0.006031036376953125,
0.00991058349609375,
-0.024169921875,
0.0271148681640625,
-0.019622802734375,
-0.0236053466796875,
-0.01187896728515625,
-0.01605224609375,
0.006015777587890625,
0.0062713623046875,
0.0230712890625,
0.0007920265197753906,
0.00336456298828125,
-0.006061553955078125,
-0.0154266357421875,
0.0309295654296875,
-0.0222930908203125,
0.038421630859375,
0.028167724609375,
-0.027801513671875,
0.009002685546875,
-0.0019683837890625,
0.0089111328125,
0.049285888671875,
0.0011577606201171875,
0.0118255615234375,
-0.025970458984375,
0.0152587890625,
-0.004489898681640625,
0.00788116455078125,
0.0012311935424804688,
0.034088134765625,
0.012451171875,
0.005161285400390625,
0.037078857421875,
-0.025146484375,
0.0240936279296875,
-0.0175933837890625,
-0.0252838134765625,
0.01215362548828125,
-0.01279449462890625,
0.0165557861328125,
0.0287017822265625,
0.0029144287109375,
0.01479339599609375,
-0.01416778564453125,
0.00041747093200683594,
-0.0136566162109375,
-0.003208160400390625,
-0.0181427001953125,
0.013946533203125,
-0.011962890625,
-0.0109710693359375,
0.001617431640625,
0.005176544189453125,
0.048004150390625,
-0.00138092041015625,
0.035797119140625,
0.057830810546875,
-0.0004553794860839844,
0.0005345344543457031,
0.0018825531005859375,
0.025634765625,
0.0211334228515625,
0.02398681640625,
0.0209503173828125,
-0.003002166748046875,
-0.0008683204650878906,
0.007709503173828125,
0.02801513671875,
-0.0025234222412109375,
0.0260009765625,
-0.01338958740234375,
-0.00943756103515625,
-0.024078369140625,
0.0263671875,
-0.02362060546875,
-0.0030040740966796875,
-0.00914764404296875,
-0.01407623291015625,
0.007640838623046875,
-0.035308837890625,
0.00475311279296875,
-0.0188140869140625,
-0.005802154541015625,
0.0233612060546875,
0.00789642333984375,
-0.018951416015625,
0.008575439453125,
0.0180206298828125,
-0.0093231201171875,
-0.033966064453125,
-0.00923919677734375,
-0.00994873046875,
-0.0047454833984375,
-0.0312347412109375,
0.017913818359375,
0.012939453125,
0.01364898681640625,
-0.02197265625,
0.006031036376953125,
0.01366424560546875,
-0.018646240234375,
-0.0016298294067382812,
0.01361846923828125,
0.004947662353515625,
-0.035186767578125,
-0.0296630859375,
-0.01338958740234375,
-0.026702880859375,
0.01019287109375,
-0.004779815673828125,
-0.0299224853515625,
-0.00489044189453125,
-0.005840301513671875,
-0.004680633544921875,
-0.0131072998046875,
0.002422332763671875,
-0.004642486572265625,
-0.0191650390625,
0.022216796875,
-0.00035262107849121094,
0.01036834716796875,
-0.02880859375,
0.026123046875,
-0.026702880859375,
-0.0034084320068359375,
0.00972747802734375,
0.047637939453125,
0.0008296966552734375,
-0.01352691650390625,
0.00347900390625,
0.0225677490234375,
0.039276123046875,
0.021392822265625,
0.0096893310546875,
-0.0187835693359375,
0.0277099609375,
0.006378173828125,
-0.0028133392333984375,
-0.003231048583984375,
0.0229644775390625,
0.03131103515625,
0.007568359375,
-0.0251007080078125,
0.0168609619140625,
-0.051666259765625,
-0.01270294189453125,
0.0224761962890625,
-0.0271759033203125,
-0.0025577545166015625,
0.00836944580078125,
-0.0074005126953125,
-0.00547027587890625,
-0.00701904296875,
0.007236480712890625,
0.004177093505859375,
-0.0257568359375,
0.0018396377563476562,
-0.01371002197265625,
0.0003304481506347656,
-0.02142333984375,
0.0125274658203125,
0.033538818359375,
-0.005771636962890625,
0.0260467529296875,
0.0260772705078125,
0.042144775390625,
0.007568359375,
0.033538818359375,
-0.0131683349609375,
-0.0158233642578125,
0.0226898193359375,
-0.007091522216796875,
0.03680419921875,
-0.0144195556640625,
-0.02362060546875,
-0.027984619140625,
-0.0059051513671875,
0.0237884521484375,
-0.032958984375,
0.03326416015625,
0.0089111328125,
-0.01010894775390625,
0.01184844970703125,
0.050628662109375,
-0.003017425537109375,
0.009796142578125,
0.01099395751953125,
-0.005626678466796875,
0.0228424072265625,
0.009552001953125,
0.0007767677307128906,
0.00528717041015625,
0.0024280548095703125,
-0.0205535888671875,
-0.005344390869140625,
0.00736236572265625,
0.00439453125,
0.0064849853515625,
-0.003284454345703125,
0.024810791015625,
0.01311492919921875,
-0.001148223876953125,
-0.0237579345703125,
0.0152587890625,
-0.030792236328125,
-0.01384735107421875,
0.00522613525390625,
0.025177001953125,
0.0285186767578125,
0.005962371826171875,
-0.00022149085998535156,
-0.0004355907440185547,
-0.00049591064453125,
-0.006534576416015625,
0.00974273681640625,
-0.0015621185302734375,
-0.0008230209350585938,
0.02667236328125,
0.011077880859375,
-0.00838470458984375,
-0.0086669921875,
0.04534912109375,
-0.00019538402557373047,
0.010101318359375,
-0.01520538330078125,
0.01483917236328125,
0.01477813720703125,
0.01399993896484375,
-0.01593017578125,
0.007236480712890625,
-0.007171630859375,
-0.0195770263671875,
-0.0031871795654296875,
0.028717041015625,
-0.0121612548828125,
0.022247314453125,
-0.01496124267578125,
0.002925872802734375,
0.02178955078125,
-0.031768798828125,
-0.0115203857421875,
-0.01580810546875,
-0.0102386474609375,
0.004077911376953125,
0.04071044921875,
-0.005329132080078125,
0.026519775390625,
0.0093841552734375,
-0.0056304931640625,
0.01776123046875,
0.002140045166015625,
-0.0014667510986328125,
0.00907135009765625,
0.0345458984375,
-0.0159149169921875,
0.00231170654296875,
-0.034515380859375,
-0.01351165771484375,
0.006954193115234375,
-0.03680419921875,
0.0003955364227294922,
0.003047943115234375,
0.0281524658203125,
-0.04052734375,
-0.0291900634765625,
0.012969970703125,
-0.0118408203125,
0.002490997314453125,
-0.03826904296875,
-0.044097900390625,
-0.002986907958984375,
0.029693603515625,
-0.01250457763671875,
-0.02484130859375,
0.021026611328125,
-0.00965118408203125,
0.00659942626953125,
0.034637451171875,
-0.032958984375,
0.007160186767578125,
0.0025730133056640625,
-0.01197052001953125,
0.0240478515625,
-0.0170745849609375,
0.0092620849609375,
-0.0106048583984375,
0.011871337890625,
-0.032012939453125,
0.0133209228515625,
0.0023784637451171875,
-0.00421905517578125,
-0.00806427001953125,
0.01320648193359375,
0.02142333984375,
0.0018014907836914062,
-0.016815185546875,
0.02655029296875,
0.0255279541015625,
-0.0028553009033203125,
-0.0007505416870117188,
0.005924224853515625,
0.007686614990234375,
0.01611328125,
-0.00963592529296875,
-0.005435943603515625,
0.020050048828125,
0.0139923095703125,
0.015716552734375,
-0.001132965087890625,
0.0176239013671875,
0.05120849609375,
0.02490234375,
0.0050506591796875,
0.0096588134765625,
0.0229339599609375,
-0.012176513671875,
0.01522064208984375,
0.010650634765625,
-0.016876220703125,
0.00879669189453125,
0.016204833984375,
0.0197601318359375,
-0.00794219970703125,
0.058441162109375,
0.0273590087890625,
-0.01155853271484375,
-0.0160980224609375,
-0.0034999847412109375,
0.001483917236328125,
0.0284576416015625,
0.014190673828125,
-0.00113677978515625,
-0.00513458251953125,
0.0243988037109375,
-0.02105712890625,
-0.0107879638671875,
-0.0082855224609375,
-0.022979736328125,
-0.01509857177734375,
0.017333984375,
-0.01264190673828125,
-0.0023956298828125,
-0.006500244140625,
0.0013790130615234375,
-0.0196685791015625,
-0.01276397705078125,
-0.0281982421875,
-0.009185791015625,
-0.0306396484375,
-0.01218414306640625,
0.0058441162109375,
0.00991058349609375,
-0.01142120361328125,
0.0311126708984375,
-0.016265869140625,
0.0011224746704101562,
-0.01395416259765625,
-0.0318603515625,
-0.004913330078125,
0.036163330078125,
-0.01161956787109375,
-0.0142669677734375,
-0.00612640380859375,
0.00519561767578125,
-0.0296783447265625,
0.0036182403564453125,
0.0002582073211669922,
-0.0214996337890625,
-0.019775390625,
-0.0256805419921875,
-0.02667236328125,
0.0127410888671875,
0.01093292236328125,
0.0253448486328125,
0.01085662841796875,
-0.0191650390625,
-0.0136871337890625,
0.0101318359375,
-0.031036376953125,
-0.0136871337890625,
-0.0014314651489257812,
0.00582122802734375,
0.01800537109375,
0.00432586669921875,
-0.03961181640625,
0.01507568359375,
0.006565093994140625,
-0.0198974609375,
-0.005596160888671875,
0.0155487060546875,
0.027984619140625,
0.0014867782592773438,
0.0160675048828125,
-0.0287322998046875,
0.0186309814453125,
0.021392822265625,
0.00215911865234375,
-0.00873565673828125,
-0.030975341796875,
-0.006938934326171875,
0.027496337890625,
-0.0089263916015625,
0.01180267333984375,
-0.0206298828125,
-0.0146636962890625,
-0.0306854248046875,
0.017730712890625,
0.010040283203125,
0.0034160614013671875,
0.0179901123046875,
0.042633056640625,
0.0030460357666015625,
0.0204315185546875,
0.0271148681640625,
0.010101318359375,
-0.0078277587890625,
-0.033203125,
-0.0032863616943359375,
-0.021453857421875,
-0.01629638671875,
0.01490020751953125,
-0.034027099609375,
0.000896453857421875,
-0.0028858184814453125,
-0.02880859375,
-0.01995849609375,
0.03570556640625,
-0.024871826171875,
0.0029449462890625,
-0.01160430908203125,
-0.01183319091796875,
0.009063720703125,
0.034210205078125,
-0.0009794235229492188,
-0.0226593017578125,
-0.0175933837890625,
0.0032939910888671875,
-0.0009503364562988281,
0.02886962890625,
0.04638671875,
-0.03253173828125,
-0.022003173828125,
0.0050048828125,
0.00696563720703125,
0.0089111328125,
0.004833221435546875,
0.026214599609375,
-0.04833984375,
0.0143890380859375,
-0.02783203125,
-0.043731689453125,
0.0269927978515625,
-0.022979736328125,
-0.01038360595703125,
-0.021026611328125,
0.01551055908203125,
-0.022796630859375,
-0.035247802734375,
0.00807952880859375,
-0.023101806640625,
0.01062774658203125,
0.005657196044921875,
-0.0114593505859375,
-0.00795745849609375,
-0.0180206298828125,
0.002529144287109375,
0.0085906982421875,
0.02008056640625,
0.01003265380859375,
0.01377105712890625,
0.0247955322265625,
-0.00077056884765625,
-0.00646209716796875,
0.00946807861328125,
-0.0058746337890625,
-0.0230560302734375,
0.0203704833984375,
0.0167236328125,
0.00815582275390625,
-0.007038116455078125,
-0.0089569091796875,
0.00756072998046875,
-0.006072998046875,
-0.003215789794921875,
0.021209716796875,
0.0167694091796875,
0.0192718505859375,
0.005107879638671875,
0.034332275390625,
0.006069183349609375,
-0.00920867919921875,
0.0007405281066894531,
-0.002162933349609375,
-0.00464630126953125,
-0.01125335693359375,
0.01271820068359375,
0.0190582275390625,
0.0258636474609375,
0.01210784912109375,
0.0033016204833984375,
-0.006244659423828125,
0.052978515625,
-0.0106353759765625,
-0.004444122314453125,
0.0137786865234375,
-0.0101776123046875,
0.0014781951904296875,
-0.0089569091796875,
0.00830841064453125,
-0.0029468536376953125,
0.025665283203125,
0.0196685791015625,
-0.018798828125,
0.01357269287109375,
-0.005573272705078125,
0.004154205322265625,
0.004108428955078125,
-0.00655364990234375,
0.0184326171875,
0.022491455078125,
0.005413055419921875,
-0.025604248046875,
-0.02496337890625,
-0.00368499755859375,
-0.01238250732421875,
0.001750946044921875,
-0.016693115234375,
-0.0016126632690429688,
-0.0175018310546875,
0.014190673828125,
0.017913818359375,
-0.005397796630859375,
0.007610321044921875,
-0.004364013671875,
0.0164794921875,
-0.0037021636962890625,
-0.0080413818359375,
-0.0021343231201171875,
0.01554107666015625,
-0.0291595458984375,
-0.032012939453125,
-0.0023975372314453125,
-0.0126800537109375,
0.01519012451171875,
0.024871826171875,
-0.00005030632019042969,
-0.0120086669921875,
0.0002949237823486328,
0.038665771484375,
-0.022674560546875,
0.018829345703125,
0.0198822021484375,
0.00940704345703125,
-0.0249176025390625,
0.028076171875,
-0.00382232666015625,
0.012969970703125,
0.00717926025390625,
0.0155029296875,
0.0335693359375,
-0.008453369140625,
0.007350921630859375,
0.0204620361328125,
0.0156097412109375,
-0.0171966552734375,
0.017333984375,
-0.0130157470703125,
-0.018157958984375,
0.0181732177734375,
-0.03497314453125,
0.0292510986328125,
-0.0020351409912109375,
-0.0027484893798828125,
0.00934600830078125,
-0.036895751953125,
-0.00670623779296875,
0.033355712890625,
0.006244659423828125,
0.01013946533203125,
-0.0172271728515625,
0.00403594970703125,
0.0004189014434814453,
0.0254669189453125,
0.0034351348876953125,
-0.01555633544921875,
-0.0237579345703125,
-0.021575927734375,
0.0083160400390625,
-0.0029659271240234375,
-0.00507354736328125,
-0.0004127025604248047,
0.0006651878356933594,
-0.038360595703125,
-0.00302886962890625,
0.01262664794921875,
0.002826690673828125,
0.0213165283203125,
0.0007581710815429688,
-0.002288818359375,
-0.0369873046875,
0.0106201171875,
0.007030487060546875,
-0.040191650390625,
-0.049652099609375,
0.004138946533203125,
-0.0238494873046875,
-0.01715087890625,
0.0313720703125,
-0.020294189453125,
0.008453369140625,
-0.01216888427734375,
0.007106781005859375,
-0.004756927490234375,
0.072509765625,
0.0200653076171875,
0.0169525146484375,
-0.03826904296875,
0.01421356201171875,
-0.035675048828125,
0.034515380859375,
0.0027370452880859375,
-0.00936126708984375,
-0.0237274169921875,
0.030670166015625,
-0.0211944580078125,
-0.01287078857421875,
0.0230865478515625,
-0.0280609130859375,
0.033599853515625,
0.00440216064453125,
-0.029815673828125,
0.04638671875,
0.003673553466796875,
0.06646728515625,
0.01751708984375,
-0.01253509521484375,
0.019378662109375,
-0.0114898681640625,
-0.020477294921875,
0.016510009765625,
-0.00438690185546875,
-0.0394287109375,
-0.033050537109375,
-0.00905609130859375,
0.0017499923706054688,
-0.01354217529296875,
0.0302581787109375,
0.0114898681640625,
-0.0009703636169433594,
0.0259552001953125,
-0.01210784912109375,
-0.00019621849060058594,
0.0099334716796875,
-0.001678466796875,
-0.00640106201171875,
-0.01027679443359375,
-0.004364013671875,
0.0098114013671875,
0.00028514862060546875,
-0.01206207275390625,
0.00809478759765625,
0.001201629638671875,
-0.0020961761474609375,
-0.020599365234375,
-0.00562286376953125,
0.01546478271484375,
0.0035114288330078125,
-0.00958251953125,
0.0406494140625,
-0.0115966796875,
0.033843994140625,
-0.0008516311645507812,
-0.0195465087890625,
0.014678955078125,
0.01110076904296875,
-0.006488800048828125,
-0.018707275390625,
-0.00740814208984375,
-0.01058197021484375,
0.0162200927734375,
-0.0259246826171875,
-0.030120849609375,
-0.00772857666015625,
0.01224517822265625,
-0.009429931640625,
-0.00931549072265625,
-0.0408935546875,
-0.032867431640625,
-0.02947998046875,
0.01788330078125,
-0.01282501220703125,
0.014984130859375,
-0.017852783203125,
-0.01374053955078125,
-0.01190948486328125,
-0.010650634765625,
0.005359649658203125,
0.03887939453125,
0.006938934326171875,
-0.0272979736328125,
-0.032806396484375,
0.0004286766052246094,
0.0037517547607421875,
-0.021331787109375,
-0.00859832763671875,
-0.00972747802734375,
0.0012722015380859375,
0.003948211669921875,
0.0060272216796875,
0.009368896484375,
0.0033626556396484375,
0.0133056640625,
0.01316070556640625,
0.00667572021484375,
0.007549285888671875,
-0.0018777847290039062,
0.012359619140625,
-0.0277252197265625,
-0.004413604736328125,
-0.0040740966796875,
0.023223876953125,
-0.004119873046875,
-0.00763702392578125,
0.014801025390625,
0.01107025146484375,
0.01132965087890625,
-0.01163482666015625,
-0.002574920654296875,
-0.004917144775390625,
0.0037250518798828125,
0.0156402587890625,
0.018218994140625,
-0.016082763671875,
-0.0007185935974121094,
-0.0151519775390625,
0.00746917724609375,
0.01155853271484375,
-0.0015897750854492188,
0.0177154541015625,
-0.0147705078125,
0.02032470703125,
-0.035247802734375,
-0.0242462158203125,
-0.00881195068359375,
0.01079559326171875,
0.0241546630859375,
-0.017822265625,
0.0083465576171875,
0.0149688720703125,
-0.0020885467529296875,
-0.0673828125,
-0.01029205322265625,
-0.0220947265625,
0.0278472900390625,
0.0311126708984375,
0.005718231201171875,
-0.047454833984375,
0.0177154541015625,
-0.0113677978515625,
0.0125885009765625,
-0.034210205078125,
-0.01531982421875,
0.0033283233642578125,
0.01226806640625,
0.047027587890625,
0.005115509033203125,
0.006389617919921875,
0.0025310516357421875,
0.0164794921875,
0.032928466796875,
-0.024017333984375,
-0.0244598388671875,
-0.0015535354614257812,
-0.00885009765625,
-0.01727294921875,
-0.0101318359375,
0.01202392578125,
0.01325225830078125,
-0.01552581787109375,
0.0093994140625,
0.0217742919921875,
0.0027408599853515625,
-0.0086669921875,
-0.0240631103515625,
-0.00978851318359375,
0.002559661865234375,
0.01303863525390625,
-0.0175323486328125,
-0.0207366943359375,
-0.0306549072265625,
-0.040802001953125,
0.0016040802001953125,
0.005939483642578125,
-0.005474090576171875,
-0.019622802734375,
0.01512908935546875,
-0.01788330078125,
-0.01055145263671875,
0.0207061767578125,
-0.00905609130859375,
0.03521728515625,
0.01898193359375,
0.004436492919921875,
0.00025177001953125,
-0.01146697998046875,
0.0062103271484375,
0.0034427642822265625,
-0.00048732757568359375,
-0.0333251953125,
0.0213775634765625,
-0.0164031982421875,
0.0065460205078125,
0.035858154296875,
-0.010345458984375,
0.010650634765625,
0.005931854248046875,
0.0009479522705078125,
0.0355224609375,
-0.016265869140625,
0.01195526123046875,
-0.0097503662109375,
-0.0029354095458984375,
-0.0025386810302734375,
-0.0271759033203125,
0.0034637451171875,
0.0386962890625,
0.00543212890625,
0.039031982421875,
0.0014600753784179688,
-0.000705718994140625,
0.019775390625,
0.006572723388671875,
-0.05328369140625,
-0.010894775390625,
0.002513885498046875,
-0.006103515625,
-0.001186370849609375,
-0.003795623779296875,
0.01445770263671875,
-0.006404876708984375,
-0.015777587890625,
0.0209503173828125,
-0.0240478515625,
0.01190948486328125,
0.0142364501953125,
-0.0350341796875,
0.0079193115234375,
0.0304412841796875,
-0.0178680419921875,
-0.0200653076171875,
-0.0007238388061523438,
0.024139404296875,
-0.01483154296875,
-0.039764404296875,
-0.01474761962890625,
-0.0131378173828125,
0.032012939453125,
0.003871917724609375,
0.006778717041015625,
-0.0039825439453125,
-0.0296783447265625,
-0.0458984375,
0.0103912353515625,
0.0294189453125,
-0.0438232421875,
-0.004852294921875,
0.0087127685546875,
0.0018444061279296875,
0.044036865234375,
-0.0029087066650390625,
-0.0041351318359375,
-0.0175628662109375,
-0.0020542144775390625,
0.0006184577941894531,
-0.0171356201171875,
0.0092926025390625,
-0.021148681640625,
0.000286102294921875,
0.019134521484375,
0.012298583984375,
0.01532745361328125,
0.0117034912109375,
-0.0364990234375,
0.022857666015625,
-0.017578125,
0.0421142578125,
-0.011566162109375,
0.014373779296875,
-0.01506805419921875,
0.0161590576171875,
0.0035762786865234375,
0.017242431640625,
0.00691986083984375,
-0.046356201171875,
-0.018341064453125,
0.009368896484375,
-0.01165771484375,
-0.0268402099609375,
0.056854248046875,
-0.006328582763671875,
-0.0184783935546875,
-0.045166015625,
-0.0298614501953125,
0.0347900390625,
-0.007755279541015625,
-0.010040283203125,
0.026947021484375,
0.037689208984375,
0.0022182464599609375,
0.044677734375,
-0.0192413330078125,
-0.01331329345703125,
-0.012115478515625,
-0.00506591796875,
-0.013824462890625,
0.0162811279296875,
0.003997802734375,
0.011505126953125,
0.0186004638671875,
-0.0003590583801269531,
-0.00789642333984375,
-0.004398345947265625,
-0.033782958984375,
0.006683349609375,
0.015167236328125,
-0.05230712890625,
-0.0216827392578125,
0.0020465850830078125,
0.0068206787109375,
-0.003147125244140625,
0.03533935546875,
-0.0122222900390625,
-0.0261077880859375,
-0.0052490234375,
0.0018301010131835938,
0.00331878662109375,
0.0192108154296875,
0.004993438720703125,
0.00421142578125,
-0.020263671875,
0.01806640625,
-0.0205078125,
-0.00696563720703125,
-0.0172882080078125,
-0.00121307373046875,
-0.0062713623046875,
0.00965118408203125,
0.004558563232421875,
0.033233642578125,
-0.043701171875,
-0.0207366943359375,
-0.0177001953125,
-0.01373291015625,
0.0017213821411132812,
0.0087127685546875,
0.0197296142578125,
-0.056182861328125,
0.0029888153076171875,
-0.00624847412109375,
-0.01375579833984375,
-0.0069580078125,
-0.004642486572265625,
-0.0211334228515625,
-0.00754547119140625,
0.0208740234375,
0.00383758544921875,
-0.0201263427734375,
-0.014739990234375,
-0.0078582763671875,
0.0018815994262695312,
0.0306396484375,
0.0031490325927734375,
-0.00382232666015625,
-0.0168304443359375,
0.00408935546875,
-0.0006642341613769531,
0.0024929046630859375,
-0.0267181396484375,
0.0160064697265625,
0.021636962890625,
-0.0157470703125,
0.006458282470703125,
0.009185791015625,
0.0103302001953125,
0.02764892578125,
-0.0309906005859375,
0.0178680419921875,
-0.005397796630859375,
-0.035675048828125,
0.0286865234375,
0.007282257080078125,
-0.0165863037109375,
0.01299285888671875,
0.0034008026123046875,
0.0130767822265625,
0.0216064453125
] |
ours_509
|
Define \( I' \) to be the intersection of \( AI \) with the circumcircle of \( \triangle ABC \). By Simson lines, the foot of the altitude from \( I \) onto \( AB \), the foot of the altitude from \( I \) onto \( AC \), and the midpoint of \( BC \) are collinear.
Since \( I_BI_C \parallel PQ \) and both pass through the midpoint of \( BC \), they must be the same line. Thus, the reflection of \( A \) over \( I \) is \( I' \). Then \(\frac{AI'}{2} = II' = BI' = CI'\) by "Fact 5." Now, as \( I' \) lies on arc \( BC \) not containing \( A \), we have \( AB \cdot CI' + AC \cdot BI' = BC \cdot AI' \) by Ptolemy's theorem, which yields \( AB + AC = 2BC \). Then \( BC = \frac{39}{2} \), making the answer \( 3902 \).
\(\boxed{3902}\)
|
3902
|
{
"competition": "us_comps",
"dataset": "Ours",
"posts": null,
"source": "OMOFall19Solns.md"
}
|
Let \( \triangle ABC \) be a triangle with incenter \( I \) such that \( AB = 20 \) and \( AC = 19 \). Point \( P \neq A \) lies on line \( AB \) and point \( Q \neq A \) lies on line \( AC \). Suppose that \( IA = IP = IQ \) and that line \( PQ \) passes through the midpoint of side \( BC \). Suppose that \( BC = \frac{m}{n} \) for relatively prime positive integers \( m \) and \( n \). Compute \( 100m + n \).
|
[
"/Mathematics/Geometry/GeneralGeometry/EuclideanGeometry",
"/Mathematics/Geometry/GeneralGeometry/Geometry",
"/Mathematics/Geometry/PlaneGeometry/CircularTriangles/CircularTriangle",
"/Mathematics/Geometry/PlaneGeometry/Triangles/TriangleCenters",
"/Mathematics/Geometry/PlaneGeometry/Triangles/TriangleCircles",
"/Mathematics/Geometry/PlaneGeometry/Triangles/TriangleLines",
"/Mathematics/Geometry/Points/Midpoint",
"/Mathematics/Geometry/Points/SpecialPoint"
] |
Recognize that I lies on the circumcircle of ABC so PQ is the Simson line through the midpoint of BC, allowing a Ptolemy relation that yields AB+AC=2BC.
|
[
-0.00011581182479858398,
-0.030181884765625,
0.0301971435546875,
0.01395416259765625,
-0.00020062923431396484,
0.01261138916015625,
0.018402099609375,
0.042449951171875,
0.006069183349609375,
-0.01432037353515625,
0.039886474609375,
0.00769805908203125,
-0.0050506591796875,
0.009063720703125,
0.020172119140625,
-0.0157928466796875,
-0.0158538818359375,
-0.00801849365234375,
0.01250457763671875,
-0.00022459030151367188,
-0.007328033447265625,
-0.0067596435546875,
-0.043609619140625,
-0.00896453857421875,
-0.0263824462890625,
-0.00485992431640625,
-0.01201629638671875,
0.0149993896484375,
-0.0023174285888671875,
-0.0017681121826171875,
-0.0236053466796875,
-0.005542755126953125,
-0.011749267578125,
-0.0165863037109375,
0.0003650188446044922,
0.01197052001953125,
-0.0111541748046875,
0.0004673004150390625,
-0.04315185546875,
-0.03875732421875,
-0.0246124267578125,
0.02716064453125,
0.01018524169921875,
0.0205535888671875,
-0.004306793212890625,
-0.016510009765625,
-0.003376007080078125,
0.0027980804443359375,
0.0010900497436523438,
-0.01056671142578125,
0.004329681396484375,
0.01422882080078125,
-0.04205322265625,
0.0021495819091796875,
-0.01861572265625,
-0.037994384765625,
-0.003337860107421875,
0.0017366409301757812,
-0.00476837158203125,
-0.03399658203125,
0.00423431396484375,
0.00940704345703125,
0.0026378631591796875,
-0.016845703125,
-0.000499725341796875,
-0.007053375244140625,
0.001689910888671875,
-0.005687713623046875,
-0.0138397216796875,
-0.010650634765625,
0.04168701171875,
-0.0092926025390625,
0.007678985595703125,
0.0033435821533203125,
0.041290283203125,
-0.0034313201904296875,
-0.01406097412109375,
-0.0033168792724609375,
-0.004009246826171875,
0.00827789306640625,
-0.012786865234375,
0.0018215179443359375,
0.005428314208984375,
-0.041900634765625,
0.0222930908203125,
0.0084228515625,
-0.00385284423828125,
0.005767822265625,
0.0098419189453125,
-0.0167388916015625,
0.0070648193359375,
0.01031494140625,
-0.01201629638671875,
-0.01007843017578125,
0.00262451171875,
0.007556915283203125,
0.0173492431640625,
-0.0195159912109375,
-0.0202178955078125,
0.005130767822265625,
-0.022491455078125,
-0.0009069442749023438,
-0.01200103759765625,
-0.0175933837890625,
-0.005672454833984375,
-0.00527191162109375,
-0.0157623291015625,
0.00615692138671875,
-0.01093292236328125,
-0.0034770965576171875,
0.0012540817260742188,
0.0020008087158203125,
0.0276336669921875,
-0.00695037841796875,
0.01971435546875,
-0.01506805419921875,
0.039459228515625,
0.01364898681640625,
0.005916595458984375,
0.005435943603515625,
0.0018100738525390625,
0.01678466796875,
-0.0166168212890625,
0.023712158203125,
-0.0011625289916992188,
-0.0055084228515625,
-0.0084686279296875,
-0.01557159423828125,
-0.005218505859375,
-0.000926971435546875,
0.01087188720703125,
0.0088348388671875,
-0.037872314453125,
-0.03277587890625,
-0.048095703125,
0.0016450881958007812,
-0.017425537109375,
0.0003764629364013672,
-0.0114593505859375,
-0.01422882080078125,
0.0024623870849609375,
0.00913238525390625,
0.00528717041015625,
-0.06317138671875,
0.002765655517578125,
-0.056915283203125,
0.0089263916015625,
-0.0262603759765625,
0.0010938644409179688,
0.0008563995361328125,
-0.00809478759765625,
-0.01142120361328125,
0.013580322265625,
0.006900787353515625,
-0.006778717041015625,
-0.00867462158203125,
0.01094818115234375,
0.028472900390625,
0.021942138671875,
0.0107269287109375,
0.00684356689453125,
-0.01128387451171875,
-0.005657196044921875,
-0.00577545166015625,
-0.0081634521484375,
-0.00604248046875,
0.015869140625,
0.0121002197265625,
-0.0189971923828125,
-0.0024051666259765625,
0.0012102127075195312,
0.0159759521484375,
-0.004302978515625,
-0.01238250732421875,
-0.0048065185546875,
-0.0005550384521484375,
-0.0168609619140625,
0.00711822509765625,
-0.0225372314453125,
0.0226593017578125,
0.0006265640258789062,
-0.04150390625,
-0.004680633544921875,
0.002056121826171875,
-0.0085601806640625,
-0.0243072509765625,
-0.00323486328125,
0.00626373291015625,
0.0079345703125,
0.01264190673828125,
-0.03912353515625,
-0.025909423828125,
0.0015420913696289062,
-0.01220703125,
0.01800537109375,
-0.017333984375,
-0.0286407470703125,
0.004650115966796875,
0.0193328857421875,
0.0022907257080078125,
-0.0014257431030273438,
0.0015583038330078125,
0.0232391357421875,
-0.00689697265625,
-0.01366424560546875,
0.004077911376953125,
0.0192108154296875,
-0.011016845703125,
-0.02099609375,
0.00853729248046875,
0.021820068359375,
0.01678466796875,
-0.0128173828125,
-0.003749847412109375,
-0.00518798828125,
-0.014251708984375,
-0.0215301513671875,
0.01036834716796875,
-0.007450103759765625,
0.00830078125,
-0.001171112060546875,
-0.00250244140625,
0.0111846923828125,
-0.02825927734375,
-0.017578125,
0.004611968994140625,
0.004474639892578125,
-0.0009064674377441406,
0.00371551513671875,
0.01399993896484375,
-0.0082244873046875,
0.011260986328125,
-0.00670623779296875,
-0.005001068115234375,
-0.01152801513671875,
-0.00016450881958007812,
-0.0279541015625,
0.0084228515625,
0.012298583984375,
0.0062103271484375,
0.034576416015625,
-0.03167724609375,
0.00624847412109375,
-0.01477813720703125,
-0.003917694091796875,
-0.0106201171875,
0.007541656494140625,
-0.01043701171875,
-0.00278472900390625,
0.0058746337890625,
-0.00276947021484375,
0.0260162353515625,
-0.01715087890625,
-0.016143798828125,
-0.004688262939453125,
-0.00933837890625,
-0.0008549690246582031,
0.0024700164794921875,
-0.01593017578125,
0.004573822021484375,
-0.01325225830078125,
-0.013671875,
-0.0037078857421875,
-0.0108795166015625,
-0.0243988037109375,
0.0296630859375,
0.00537109375,
0.0239715576171875,
0.0163421630859375,
-0.01119232177734375,
0.038848876953125,
-0.026885986328125,
-0.005466461181640625,
0.0028095245361328125,
-0.0006508827209472656,
-0.03466796875,
-0.0000858306884765625,
-0.0002884864807128906,
0.01141357421875,
-0.01407623291015625,
0.0248260498046875,
-0.0152130126953125,
-0.030029296875,
0.0011911392211914062,
0.0213470458984375,
-0.01401519775390625,
-0.01386260986328125,
-0.0357666015625,
-0.0084381103515625,
-0.0028476715087890625,
-0.00844573974609375,
0.0113525390625,
-0.01568603515625,
-0.01010894775390625,
0.04595947265625,
-0.0008053779602050781,
-0.00908660888671875,
0.0247039794921875,
0.0160064697265625,
0.0033626556396484375,
0.0267181396484375,
-0.0030307769775390625,
0.007282257080078125,
0.0006246566772460938,
0.016082763671875,
0.014007568359375,
0.005451202392578125,
0.0176544189453125,
-0.01678466796875,
-0.0175628662109375,
-0.000007808208465576172,
0.01495361328125,
0.0005207061767578125,
0.00806427001953125,
-0.034454345703125,
-0.0298004150390625,
0.005336761474609375,
0.0004029273986816406,
-0.0162506103515625,
0.01708984375,
0.01366424560546875,
0.0316162109375,
-0.003643035888671875,
0.00228118896484375,
0.01453399658203125,
-0.0308990478515625,
-0.003444671630859375,
-0.0029010772705078125,
0.0277862548828125,
0.0411376953125,
-0.0083465576171875,
-0.01316070556640625,
-0.001251220703125,
-0.0024967193603515625,
0.01560211181640625,
0.00365447998046875,
0.00046634674072265625,
0.025238037109375,
-0.0017709732055664062,
-0.01239013671875,
0.016448974609375,
0.007244110107421875,
0.02630615234375,
-0.065673828125,
-0.0199127197265625,
0.0078277587890625,
-0.01343536376953125,
0.01146697998046875,
-0.03936767578125,
-0.029083251953125,
0.0140533447265625,
0.032623291015625,
0.028472900390625,
0.01488494873046875,
-0.007564544677734375,
-0.01531982421875,
0.0029392242431640625,
0.018218994140625,
-0.0194091796875,
0.009063720703125,
0.0131378173828125,
-0.00499725341796875,
-0.01059722900390625,
0.025177001953125,
-0.020416259765625,
0.01439666748046875,
-0.0321044921875,
0.00933837890625,
-0.0305938720703125,
0.004436492919921875,
-0.0172119140625,
-0.0175933837890625,
0.026885986328125,
-0.015350341796875,
-0.0015087127685546875,
0.0197296142578125,
-0.0257110595703125,
0.00897979736328125,
-0.002223968505859375,
-0.0032100677490234375,
0.0090789794921875,
-0.0186309814453125,
-0.0163726806640625,
0.0296173095703125,
-0.035308837890625,
0.009002685546875,
0.0099334716796875,
-0.044525146484375,
-0.0021820068359375,
0.0139617919921875,
-0.007965087890625,
0.00917816162109375,
-0.0164947509765625,
-0.018951416015625,
-0.034332275390625,
0.01561737060546875,
-0.003021240234375,
0.00646209716796875,
0.01416778564453125,
-0.0159759521484375,
-0.02752685546875,
-0.01285552978515625,
-0.0034694671630859375,
0.0006551742553710938,
0.00504302978515625,
-0.0006561279296875,
-0.003963470458984375,
0.0207366943359375,
-0.0161285400390625,
0.0282135009765625,
0.006450653076171875,
0.01021575927734375,
0.0173187255859375,
-0.02099609375,
-0.0242156982421875,
0.0229949951171875,
-0.01061248779296875,
-0.001556396484375,
-0.0007510185241699219,
-0.035064697265625,
0.0272369384765625,
-0.0295257568359375,
0.01361846923828125,
-0.0076904296875,
0.021331787109375,
0.0244903564453125,
-0.0013380050659179688,
0.048187255859375,
0.0159912109375,
-0.0003600120544433594,
0.032928466796875,
-0.006931304931640625,
-0.00466156005859375,
0.003604888916015625,
0.0103759765625,
-0.00330352783203125,
0.03509521484375,
0.0103302001953125,
0.0210113525390625,
0.0178070068359375,
-0.01445770263671875,
0.008392333984375,
-0.00203704833984375,
0.003635406494140625,
-0.0034942626953125,
0.02294921875,
-0.005077362060546875,
0.0031261444091796875,
-0.019378662109375,
0.002902984619140625,
-0.0063018798828125,
-0.046142578125,
0.0175933837890625,
-0.01474761962890625,
0.0004162788391113281,
0.0176239013671875,
0.041839599609375,
-0.03253173828125,
-0.027313232421875,
0.0296630859375,
-0.0263824462890625,
0.0152130126953125,
-0.0035037994384765625,
0.004749298095703125,
-0.059600830078125,
0.0049285888671875,
-0.0228729248046875,
0.006832122802734375,
0.000598907470703125,
-0.002899169921875,
0.0233154296875,
-0.031707763671875,
-0.023834228515625,
-0.033477783203125,
-0.032257080078125,
0.037200927734375,
0.00897979736328125,
0.004749298095703125,
-0.0322265625,
0.05517578125,
-0.0147705078125,
-0.0171661376953125,
-0.006336212158203125,
0.0009465217590332031,
0.0044097900390625,
0.00684356689453125,
0.027435302734375,
0.004032135009765625,
-0.01143646240234375,
-0.05255126953125,
0.007476806640625,
0.031005859375,
-0.019317626953125,
0.0016040802001953125,
-0.033905029296875,
-0.035369873046875,
0.0184173583984375,
-0.01192474365234375,
0.00435638427734375,
0.0082244873046875,
0.0300140380859375,
-0.0194854736328125,
-0.0035572052001953125,
0.0491943359375,
0.0015506744384765625,
-0.0509033203125,
0.045440673828125,
-0.006130218505859375,
0.033538818359375,
-0.035186767578125,
-0.00182342529296875,
0.00047397613525390625,
0.02386474609375,
-0.022216796875,
0.00867462158203125,
0.009063720703125,
-0.00841522216796875,
-0.0251617431640625,
0.029083251953125,
0.03997802734375,
-0.0242767333984375,
-0.00470733642578125,
-0.006153106689453125,
-0.006732940673828125,
0.020233154296875,
0.021759033203125,
-0.002410888671875,
-0.00514984130859375,
0.0202484130859375,
0.0030727386474609375,
0.0241546630859375,
-0.009857177734375,
-0.05780029296875,
0.0178985595703125,
0.0154266357421875,
0.027587890625,
-0.016937255859375,
-0.00421905517578125,
0.01364898681640625,
-0.00821685791015625,
-0.03692626953125,
-0.021331787109375,
-0.0111846923828125,
-0.0030670166015625,
0.016082763671875,
-0.01120758056640625,
-0.0272979736328125,
0.0012865066528320312,
-0.004734039306640625,
0.0235137939453125,
0.0172576904296875,
0.01174163818359375,
-0.027435302734375,
0.0206451416015625,
-0.03497314453125,
0.009857177734375,
-0.0290679931640625,
-0.0009388923645019531,
0.01568603515625,
0.0105438232421875,
0.026031494140625,
0.0012235641479492188,
0.040313720703125,
-0.0172882080078125,
-0.004848480224609375,
0.003780364990234375,
0.00928497314453125,
-0.02899169921875,
-0.03515625,
-0.031768798828125,
-0.0014600753784179688,
0.006683349609375,
-0.03277587890625,
0.00890350341796875,
0.024383544921875,
-0.0176544189453125,
-0.00707244873046875,
-0.01552581787109375,
0.0164642333984375,
-0.026885986328125,
0.0213470458984375,
0.023956298828125,
-0.01031494140625,
-0.0117034912109375,
0.0034198760986328125,
-0.0045318603515625,
0.00797271728515625,
-0.01209259033203125,
0.0093231201171875,
-0.00597381591796875,
0.001766204833984375,
0.00988006591796875,
0.0181121826171875,
-0.00750732421875,
0.0015783309936523438,
-0.010009765625,
0.026947021484375,
0.01213836669921875,
0.034149169921875,
-0.004688262939453125,
-0.0022373199462890625,
0.002323150634765625,
-0.03582763671875,
0.037872314453125,
-0.0224761962890625,
0.00749969482421875,
-0.040557861328125,
0.0183563232421875,
0.0195465087890625,
0.01739501953125,
0.0009212493896484375,
-0.005245208740234375,
0.00652313232421875,
0.01044464111328125,
-0.01169586181640625,
-0.01019287109375,
0.0021228790283203125,
0.020416259765625,
-0.00481414794921875,
0.0179595947265625,
0.008941650390625,
0.0108642578125,
-0.01239776611328125,
0.0265655517578125,
0.0048065185546875,
-0.0124359130859375,
-0.004116058349609375,
-0.031280517578125,
0.01389312744140625,
-0.0272064208984375,
0.00037670135498046875,
-0.0007457733154296875,
-0.0390625,
-0.026336669921875,
-0.02215576171875,
-0.020416259765625,
-0.01137542724609375,
0.01158905029296875,
0.0198516845703125,
-0.0146942138671875,
0.0167694091796875,
0.028472900390625,
0.01265716552734375,
-0.0745849609375,
-0.0308685302734375,
0.01690673828125,
-0.01047515869140625,
0.021148681640625,
0.0018892288208007812,
0.01502227783203125,
0.0058135986328125,
-0.03009033203125,
0.020294189453125,
0.0027008056640625,
0.035858154296875,
-0.006336212158203125,
-0.005664825439453125,
-0.02423095703125,
0.0308685302734375,
-0.0112457275390625,
0.01169586181640625,
0.00434112548828125,
-0.00388336181640625,
-0.0131988525390625,
-0.0267333984375,
-0.0025920867919921875,
-0.047027587890625,
-0.02679443359375,
0.0160675048828125,
0.037689208984375,
0.015228271484375,
-0.024444580078125,
0.01546478271484375,
-0.003253936767578125,
0.0081787109375,
0.007732391357421875,
-0.0161285400390625,
0.027862548828125,
0.01763916015625,
-0.0029773712158203125,
-0.0290374755859375,
0.0029201507568359375,
0.03131103515625,
-0.0011959075927734375,
-0.011260986328125,
0.034454345703125,
0.0162200927734375,
0.0177764892578125,
0.01165008544921875,
-0.0183563232421875,
-0.0033416748046875,
-0.004352569580078125,
-0.01213836669921875,
-0.014923095703125,
-0.0052642822265625,
-0.0105743408203125,
0.03057861328125,
-0.0205841064453125,
-0.033721923828125,
0.005916595458984375,
0.0205230712890625,
-0.0235443115234375,
0.00897216796875,
0.0132293701171875,
-0.0186767578125,
-0.03277587890625,
-0.0036220550537109375,
0.0294647216796875,
-0.050750732421875,
-0.0068206787109375,
-0.04779052734375,
-0.031982421875,
-0.00759124755859375,
-0.0003986358642578125,
-0.041748046875,
-0.019317626953125,
-0.01053619384765625,
0.0073089599609375,
-0.007305145263671875,
0.024200439453125,
-0.02447509765625,
0.01983642578125,
-0.00836944580078125,
-0.0232391357421875,
0.0226898193359375,
0.01061248779296875,
-0.014251708984375,
-0.01776123046875,
-0.0357666015625,
0.01030731201171875,
-0.0050201416015625,
0.0114288330078125,
0.03948974609375,
0.00028252601623535156,
-0.003749847412109375,
-0.0216217041015625,
-0.015838623046875,
-0.06158447265625,
-0.00008440017700195312,
-0.0016145706176757812,
0.032135009765625,
-0.011993408203125,
0.004703521728515625,
0.003131866455078125,
0.0065765380859375,
0.016571044921875,
-0.0003521442413330078,
-0.049896240234375,
0.006908416748046875,
0.01654052734375,
0.0232391357421875,
0.00620269775390625,
-0.0271148681640625,
-0.032928466796875,
-0.03509521484375,
-0.006465911865234375,
-0.021209716796875,
-0.036865234375,
0.01006317138671875,
0.0203704833984375,
-0.0242767333984375,
-0.005352020263671875,
0.032684326171875,
0.01201629638671875,
0.01302337646484375,
-0.01003265380859375,
-0.01171112060546875,
-0.01381683349609375,
-0.0208587646484375,
0.01456451416015625,
0.0025787353515625,
-0.0145263671875,
0.01297760009765625,
0.000896453857421875,
0.0057830810546875,
0.00930023193359375,
-0.061065673828125,
0.0145416259765625,
0.04327392578125,
-0.007965087890625,
0.0193023681640625,
-0.0014238357543945312,
-0.00370025634765625,
0.03253173828125,
-0.039794921875,
-0.0121917724609375,
-0.0126953125,
-0.01361846923828125,
0.00905609130859375,
0.004711151123046875,
0.006565093994140625,
0.002964019775390625,
0.0220794677734375,
-0.0133209228515625,
0.0008325576782226562,
0.00769805908203125,
-0.0166778564453125,
-0.0190887451171875,
-0.0262603759765625,
-0.016693115234375,
0.028594970703125,
-0.036102294921875,
-0.007534027099609375,
0.0247955322265625,
0.043701171875,
-0.0124969482421875,
-0.00943756103515625,
0.00738525390625,
-0.007511138916015625,
0.020294189453125,
0.006618499755859375,
-0.021240234375,
0.00482940673828125,
-0.00991058349609375,
-0.00022518634796142578,
-0.006702423095703125,
0.007526397705078125,
0.006999969482421875,
0.0041656494140625,
0.0202178955078125,
-0.032684326171875,
0.00782012939453125,
-0.03143310546875,
-0.0018672943115234375,
-0.040679931640625,
-0.0298614501953125,
0.00820159912109375,
0.023712158203125,
0.0049591064453125,
0.0011987686157226562,
0.00620269775390625,
-0.028076171875,
-0.00525665283203125,
-0.0191497802734375,
-0.030670166015625,
0.01482391357421875,
-0.019866943359375,
0.0157470703125,
-0.0416259765625,
-0.032501220703125,
0.0098724365234375,
-0.00579833984375,
0.00867462158203125,
0.032806396484375,
0.0259246826171875,
-0.0111083984375,
-0.002777099609375,
0.03271484375,
0.0081329345703125,
0.01053619384765625,
-0.0162506103515625,
0.00762939453125,
-0.027557373046875,
0.02880859375,
-0.034515380859375,
0.006931304931640625,
0.0180206298828125,
-0.00264739990234375,
-0.0139007568359375,
-0.00959014892578125,
-0.004871368408203125,
-0.0030956268310546875,
0.0010976791381835938,
0.0372314453125,
0.0054473876953125,
-0.0121612548828125,
0.00360870361328125,
-0.0090789794921875,
0.035369873046875,
0.0003879070281982422,
0.039703369140625,
-0.004543304443359375,
-0.00589752197265625,
0.01306915283203125,
-0.0005612373352050781,
0.0560302734375,
-0.029388427734375,
0.01250457763671875,
0.0247344970703125,
0.01263427734375,
0.01488494873046875,
-0.0159454345703125,
-0.034515380859375,
0.0227813720703125,
0.008270263671875,
0.001678466796875,
-0.00510406494140625,
0.009918212890625,
-0.0137176513671875,
-0.00939178466796875,
-0.0019817352294921875,
0.002735137939453125,
0.00843048095703125,
-0.05584716796875,
0.01485443115234375,
0.0102386474609375,
-0.0164031982421875,
0.0184173583984375,
0.0179443359375,
-0.0243377685546875,
0.011505126953125,
0.02020263671875,
0.0061798095703125,
-0.037567138671875,
-0.004138946533203125,
-0.0478515625,
-0.002899169921875,
-0.0013647079467773438,
-0.00917816162109375,
0.022705078125,
-0.0038089752197265625,
0.005619049072265625,
0.019439697265625,
0.027130126953125,
0.0196685791015625,
-0.0085296630859375,
-0.0141448974609375,
-0.0021495819091796875,
0.007198333740234375,
-0.0180816650390625,
0.0145721435546875,
0.006137847900390625,
-0.0046539306640625,
-0.01399993896484375,
0.01605224609375,
-0.01531982421875,
0.0024890899658203125,
0.005390167236328125,
-0.0202178955078125,
0.02838134765625,
-0.00033664703369140625,
0.0218963623046875,
-0.011322021484375,
-0.0286102294921875,
-0.03570556640625,
-0.0001678466796875,
-0.004344940185546875,
-0.021453857421875,
-0.0197296142578125,
-0.0380859375,
-0.01406097412109375,
-0.007579803466796875,
0.0228271484375,
0.00994110107421875,
0.0037670135498046875,
0.00876617431640625,
0.0037899017333984375,
0.045013427734375,
0.0242919921875,
-0.01763916015625,
-0.0014696121215820312,
-0.005168914794921875,
0.033599853515625,
0.028656005859375,
-0.0000026226043701171875,
0.00711822509765625,
0.0011873245239257812,
0.02020263671875,
-0.0018033981323242188,
-0.01220703125,
0.0237579345703125,
0.017547607421875,
0.007282257080078125,
0.03399658203125,
-0.0008692741394042969,
0.037750244140625,
0.0295867919921875,
0.013519287109375,
0.034912109375,
0.0010080337524414062,
0.00005459785461425781,
-0.01165008544921875,
-0.0034084320068359375,
-0.00994873046875,
-0.0009341239929199219,
-0.01049041748046875,
0.0014162063598632812,
0.01312255859375,
0.041259765625,
0.0017414093017578125,
-0.0606689453125,
0.007411956787109375,
-0.0116119384765625,
0.0015745162963867188,
0.0298309326171875,
0.01517486572265625,
0.0379638671875,
-0.0095672607421875,
0.04193115234375,
0.003627777099609375,
-0.0023193359375,
0.013336181640625,
-0.02972412109375,
0.0171356201171875,
-0.010162353515625,
0.013641357421875,
0.0048828125,
-0.023345947265625,
0.0158538818359375,
-0.0175323486328125,
-0.031341552734375,
-0.0019130706787109375,
0.00263214111328125,
-0.0026454925537109375,
-0.020050048828125,
-0.0236358642578125,
-0.0060272216796875,
0.00498199462890625,
-0.0013551712036132812,
0.03326416015625,
0.0002982616424560547,
0.011016845703125,
0.004718780517578125,
0.02191162109375,
-0.02203369140625,
0.0157623291015625,
-0.0004475116729736328,
0.019256591796875,
-0.046661376953125,
0.0156707763671875,
0.0217437744140625,
-0.0239105224609375,
-0.02996826171875,
-0.041778564453125,
0.033721923828125,
-0.0208282470703125,
-0.01317596435546875,
-0.0214691162109375,
0.03289794921875,
0.030303955078125,
-0.0163421630859375,
-0.007598876953125,
-0.016326904296875,
-0.03448486328125,
-0.00568389892578125,
-0.019439697265625,
-0.005985260009765625,
-0.0034008026123046875,
0.0296478271484375,
0.0013113021850585938,
-0.0070953369140625,
-0.00579833984375,
-0.01244354248046875,
-0.0194091796875,
-0.0396728515625,
0.00661468505859375,
0.0114898681640625,
0.00762939453125,
-0.0296478271484375,
-0.0135498046875,
0.019012451171875,
0.02349853515625,
-0.0158233642578125,
-0.00665283203125,
0.02838134765625,
0.015350341796875,
0.0115203857421875,
-0.01288604736328125,
-0.0020542144775390625,
0.01395416259765625,
0.0264434814453125,
-0.045074462890625,
-0.0093994140625,
-0.024078369140625,
0.0185394287109375,
-0.005390167236328125,
-0.0018777847290039062,
0.0230255126953125,
-0.0025386810302734375,
0.0137176513671875,
-0.052978515625,
-0.004344940185546875,
0.003353118896484375,
-0.01319122314453125,
0.0210418701171875,
-0.004032135009765625,
0.0011682510375976562,
-0.01522064208984375,
0.004486083984375,
-0.017181396484375,
0.0124969482421875,
0.00763702392578125,
-0.043731689453125,
0.005558013916015625,
0.039886474609375,
0.00777435302734375,
-0.00923919677734375,
-0.0440673828125,
0.0209197998046875,
-0.0182647705078125,
0.0030307769775390625,
-0.0157470703125,
0.00792694091796875,
-0.006496429443359375,
0.044921875,
-0.005840301513671875,
0.019378662109375,
0.00970458984375,
0.0413818359375,
-0.0150146484375,
0.0265960693359375,
0.02227783203125,
0.00841522216796875,
0.026092529296875,
0.0008754730224609375,
-0.027191162109375,
-0.0192413330078125,
0.00792694091796875,
-0.01561737060546875,
-0.0005249977111816406,
0.0006575584411621094,
0.0228729248046875,
0.03277587890625,
0.023590087890625,
-0.00826263427734375,
-0.00838470458984375,
-0.022064208984375,
-0.02154541015625,
0.01361083984375,
-0.0181732177734375,
0.0196075439453125,
0.005405426025390625,
-0.0099639892578125,
0.0167236328125,
-0.0039215087890625,
-0.0017185211181640625,
-0.0142669677734375,
-0.0021343231201171875,
-0.0117034912109375,
0.005344390869140625,
-0.00606536865234375,
0.0142059326171875,
-0.007663726806640625,
-0.0204925537109375,
-0.01544952392578125,
0.031646728515625,
-0.010345458984375,
-0.0203399658203125,
0.002593994140625,
-0.000667572021484375,
-0.005462646484375,
0.0027828216552734375,
0.0178680419921875,
-0.005390167236328125,
-0.0219268798828125,
0.0141448974609375,
-0.01293182373046875,
-0.0009131431579589844,
0.0242767333984375,
-0.004169464111328125,
-0.0133514404296875,
-0.005706787109375,
0.0156402587890625,
0.0196990966796875,
-0.0325927734375,
-0.025421142578125,
-0.0263214111328125,
-0.0194854736328125,
0.0157928466796875,
0.0017023086547851562,
-0.0274810791015625,
-0.0038356781005859375,
0.041900634765625,
0.0200042724609375,
-0.005985260009765625,
0.01244354248046875,
-0.006237030029296875,
0.00583648681640625,
0.0007443428039550781,
0.0340576171875,
0.007503509521484375,
-0.0185699462890625,
0.01535797119140625,
0.031463623046875,
-0.0230560302734375,
-0.01457977294921875,
-0.004207611083984375,
-0.0150299072265625,
-0.028472900390625,
-0.006015777587890625,
-0.024444580078125,
0.0345458984375,
0.02972412109375,
-0.004833221435546875,
-0.0084228515625,
-0.0062255859375,
-0.009124755859375,
0.0059661865234375,
-0.04107666015625,
-0.01213836669921875,
-0.0139923095703125,
-0.0137786865234375,
-0.01470947265625,
0.005054473876953125,
-0.00998687744140625,
0.041961669921875,
-0.02288818359375,
0.01277923583984375,
-0.013031005859375,
-0.000018477439880371094,
-0.007419586181640625,
0.0217132568359375,
-0.01654052734375,
-0.01219940185546875,
0.0186920166015625,
-0.0024242401123046875,
-0.00469970703125,
0.0313720703125,
-0.054840087890625,
-0.0023708343505859375,
0.0054168701171875,
-0.033050537109375,
0.01050567626953125,
-0.0587158203125,
0.02435302734375,
-0.011199951171875,
-0.0028400421142578125,
-0.01389312744140625,
-0.0018596649169921875,
-0.01519775390625,
-0.005096435546875,
0.01438140869140625,
-0.01338958740234375,
-0.01184844970703125,
-0.00872039794921875,
-0.0035648345947265625,
-0.012115478515625,
0.0183563232421875,
0.02801513671875,
0.02215576171875,
0.037384033203125,
0.03729248046875,
-0.0041656494140625,
0.0205078125,
-0.0037593841552734375,
-0.03240966796875,
0.0180816650390625,
0.0284576416015625,
-0.044952392578125,
0.0179443359375,
-0.01385498046875,
0.005420684814453125,
0.0177154541015625,
-0.0157470703125,
0.041351318359375,
-0.03216552734375,
-0.030548095703125,
-0.0141754150390625,
-0.06011962890625,
0.02606201171875,
-0.01393890380859375,
0.0009312629699707031,
0.00867462158203125,
0.0047149658203125,
-0.0154876708984375,
-0.0186004638671875,
0.00608062744140625,
0.03594970703125,
0.0248870849609375,
-0.01568603515625,
0.0005183219909667969,
-0.0133056640625,
0.0005784034729003906,
-0.035675048828125,
0.009796142578125,
0.011688232421875,
0.0021457672119140625,
0.048187255859375,
0.00891876220703125,
0.02459716796875,
-0.006435394287109375,
0.00856781005859375,
0.020294189453125,
0.03570556640625,
0.0181884765625,
-0.00879669189453125,
-0.01122283935546875,
-0.0165863037109375,
0.0153961181640625,
-0.00016641616821289062,
0.020965576171875,
-0.0091705322265625,
0.029052734375,
0.0081634521484375,
-0.037841796875,
-0.020599365234375,
-0.00995635986328125,
0.01483917236328125,
0.003376007080078125,
0.01496124267578125,
0.008392333984375,
0.044677734375,
0.0341796875,
0.0323486328125,
-0.01277923583984375,
-0.022552490234375,
-0.01522064208984375,
0.02984619140625,
0.039093017578125,
0.004871368408203125,
0.009613037109375,
-0.01190948486328125,
0.0360107421875,
-0.00048542022705078125,
-0.00829315185546875,
-0.02496337890625,
0.01120758056640625,
0.005802154541015625,
0.009063720703125,
0.0021762847900390625,
0.005435943603515625,
-0.00798797607421875,
0.0208282470703125,
0.0200042724609375,
0.04766845703125,
-0.004718780517578125,
0.0160369873046875,
-0.0170135498046875,
0.009124755859375,
0.01219940185546875,
0.0012674331665039062,
-0.004180908203125,
-0.0269317626953125,
-0.014923095703125,
-0.0206298828125,
0.00962066650390625,
-0.00868988037109375,
-0.0003180503845214844,
-0.02044677734375,
0.0009794235229492188,
0.005596160888671875,
0.0204925537109375,
-0.023345947265625,
0.01444244384765625,
0.0114898681640625,
0.036895751953125,
0.0244293212890625,
0.00202178955078125,
0.0307769775390625,
-0.01076507568359375,
-0.0081634521484375,
0.006710052490234375,
-0.01227569580078125,
0.0267181396484375,
0.004608154296875,
-0.01187896728515625,
-0.027252197265625,
0.00827789306640625,
-0.0037746429443359375,
-0.02752685546875,
-0.0036258697509765625,
0.0372314453125,
0.0079803466796875,
0.0281982421875,
-0.0406494140625,
-0.0179443359375,
-0.00896453857421875,
0.0269012451171875,
-0.00838470458984375,
0.0187225341796875,
0.01605224609375,
-0.00917816162109375,
0.00485992431640625,
-0.021148681640625,
0.05084228515625,
-0.0015020370483398438,
0.0069580078125,
-0.034820556640625,
-0.046966552734375,
-0.0350341796875,
-0.03839111328125,
0.01532745361328125,
0.021636962890625,
0.0157318115234375,
0.0159149169921875,
-0.01226043701171875,
-0.0202789306640625,
-0.0147857666015625,
-0.02899169921875,
0.0211944580078125,
0.01019287109375,
-0.007160186767578125,
-0.01531219482421875,
-0.0268402099609375,
0.004489898681640625,
0.022216796875,
0.0094757080078125,
-0.0159454345703125,
-0.0164337158203125,
-0.015655517578125,
0.0158233642578125,
0.01873779296875,
0.004329681396484375,
0.034698486328125,
0.01485443115234375,
-0.018798828125,
0.01403045654296875,
-0.0162353515625,
-0.01678466796875,
0.01152801513671875,
0.0091705322265625,
-0.0159912109375,
-0.0097503662109375,
0.01546478271484375,
0.0074462890625,
-0.0018444061279296875,
0.0063018798828125,
0.0011415481567382812,
0.01953125,
-0.0081939697265625,
-0.0282745361328125,
-0.0092926025390625,
-0.00948333740234375,
-0.02569580078125,
0.017333984375,
-0.04302978515625,
0.01107025146484375,
-0.054779052734375,
0.0218048095703125,
0.024261474609375,
-0.0010309219360351562,
0.00949859619140625,
-0.032379150390625,
0.0030670166015625,
0.011810302734375,
-0.00000864267349243164,
-0.00836944580078125,
-0.02325439453125,
-0.01250457763671875,
0.005954742431640625,
-0.0009794235229492188,
0.0279083251953125,
-0.00789642333984375,
-0.0002465248107910156,
-0.0113372802734375,
0.0024662017822265625,
0.044525146484375,
0.0079193115234375,
0.0313720703125,
0.007965087890625,
0.0023097991943359375,
0.01123809814453125,
0.01605224609375,
0.005741119384765625,
-0.0440673828125,
-0.00750732421875,
0.007354736328125,
0.035125732421875,
-0.0024662017822265625,
0.00223541259765625,
0.016845703125,
-0.020355224609375,
-0.019134521484375,
-0.005397796630859375,
0.00489044189453125,
-0.005741119384765625,
-0.003482818603515625,
0.0244598388671875,
0.01849365234375,
-0.046844482421875,
-0.03143310546875,
0.002674102783203125,
0.00270843505859375,
0.024139404296875,
-0.0072021484375,
0.03155517578125,
0.0153045654296875,
0.037933349609375,
-0.0055389404296875,
0.003948211669921875,
-0.0325927734375,
0.007083892822265625,
-0.00609588623046875,
0.0032825469970703125,
0.0026264190673828125,
-0.01380157470703125,
0.049560546875,
-0.01445770263671875,
-0.00957489013671875,
0.0032711029052734375,
-0.0164947509765625,
0.00730133056640625,
0.0233001708984375,
0.0297698974609375,
-0.01389312744140625,
-0.030792236328125,
0.005161285400390625,
0.0487060546875,
0.0006155967712402344,
0.006786346435546875,
-0.0060272216796875,
-0.03173828125,
0.0030460357666015625,
0.0257720947265625,
0.0286102294921875,
0.01171875,
0.003932952880859375,
-0.0264892578125,
0.0015201568603515625,
-0.0279083251953125,
0.043060302734375,
0.04290771484375,
0.0328369140625,
0.0058441162109375,
0.025970458984375,
-0.042022705078125,
-0.005908966064453125,
0.022308349609375,
-0.02081298828125,
0.0127716064453125,
0.0034942626953125,
-0.0277252197265625,
-0.029937744140625,
-0.006359100341796875,
-0.030609130859375,
-0.00406646728515625,
-0.01067352294921875,
-0.00232696533203125,
-0.012451171875,
0.005023956298828125,
0.02349853515625,
0.01751708984375,
0.0108184814453125,
0.0285491943359375,
0.0421142578125,
-0.026519775390625,
0.0208740234375,
-0.0033359527587890625,
0.011688232421875,
0.019683837890625,
-0.0281829833984375,
-0.00495147705078125,
0.036407470703125,
0.0117340087890625,
0.004901885986328125,
0.0047149658203125,
-0.015472412109375,
0.0167999267578125,
0.029022216796875,
-0.01096343994140625,
0.0180816650390625,
-0.024322509765625,
0.0145111083984375,
0.037109375,
-0.0208892822265625,
-0.00080108642578125,
0.019805908203125,
0.0267333984375,
0.02069091796875,
-0.0240325927734375,
0.0567626953125,
-0.005680084228515625,
-0.004852294921875,
-0.002742767333984375,
0.01194000244140625,
0.00911712646484375,
0.0158233642578125,
0.03680419921875,
0.01316070556640625,
-0.0111846923828125,
0.007717132568359375,
0.0208282470703125,
-0.0157470703125,
-0.025909423828125,
-0.030609130859375,
-0.0284881591796875,
0.01387786865234375,
0.029937744140625,
0.007495880126953125,
-0.026702880859375,
0.01544189453125,
0.0017681121826171875,
-0.00689697265625,
-0.00955963134765625,
0.013946533203125,
-0.002742767333984375,
0.01361846923828125,
-0.0158843994140625,
0.0146942138671875,
0.007793426513671875,
-0.0075531005859375,
-0.0182037353515625,
-0.004974365234375,
0.00897979736328125,
0.01375579833984375,
0.01062774658203125,
-0.007244110107421875,
0.034149169921875,
-0.01029205322265625,
-0.00934600830078125,
-0.00469970703125,
0.01546478271484375,
0.005859375,
-0.0192718505859375,
-0.01354217529296875,
-0.0189056396484375,
0.0021381378173828125,
0.0033321380615234375,
0.045135498046875,
0.00305938720703125,
-0.0212249755859375,
0.02490234375,
-0.012176513671875,
0.0275726318359375,
-0.008148193359375,
-0.0029811859130859375,
-0.0015916824340820312,
0.02099609375,
-0.004947662353515625,
0.0121307373046875,
0.0028858184814453125,
0.016845703125,
-0.0134429931640625,
-0.004638671875,
0.00754547119140625,
0.0013408660888671875,
-0.0048675537109375,
0.0592041015625,
-0.01404571533203125,
0.00855255126953125,
0.0218658447265625,
0.0226287841796875,
0.01166534423828125,
0.01406097412109375,
0.00868988037109375,
0.020538330078125,
-0.011199951171875,
-0.00893402099609375,
0.002696990966796875,
-0.00922393798828125,
-0.0165863037109375,
0.00655364990234375,
0.0178985595703125,
0.02044677734375,
-0.035858154296875,
-0.006114959716796875,
-0.00193023681640625,
-0.005615234375,
0.00531005859375,
0.0123138427734375,
0.00691986083984375,
0.0027027130126953125,
0.031158447265625,
-0.01395416259765625,
-0.0219268798828125,
0.0203704833984375,
-0.002117156982421875,
-0.0297698974609375,
-0.0013608932495117188,
-0.043701171875,
0.01200103759765625,
-0.024444580078125,
0.02069091796875,
0.0031299591064453125,
-0.004261016845703125,
-0.02294921875,
0.0015926361083984375,
-0.007762908935546875,
0.0079498291015625,
0.0026397705078125,
0.018096923828125,
-0.0099029541015625,
0.01125335693359375,
0.0302734375,
-0.005130767822265625,
0.003826141357421875,
-0.0079498291015625,
-0.0146026611328125,
-0.0201416015625,
-0.01303863525390625,
0.02593994140625,
-0.0139923095703125,
0.00257110595703125,
-0.0178375244140625,
-0.007579803466796875,
0.0012598037719726562,
0.016326904296875,
-0.01044464111328125,
-0.01273345947265625,
0.017913818359375,
-0.0294342041015625,
-0.0183868408203125,
-0.0087738037109375,
0.020477294921875,
-0.0058746337890625,
-0.0111236572265625,
-0.01221466064453125,
-0.0234222412109375,
0.0172271728515625,
0.004886627197265625,
0.045257568359375,
0.010040283203125,
-0.0401611328125,
0.022369384765625,
0.018218994140625,
0.0167236328125,
0.0178680419921875,
-0.0214385986328125,
-0.01007843017578125,
0.01224517822265625,
-0.01497650146484375,
-0.0102691650390625,
0.0033016204833984375,
-0.0276031494140625,
0.0188751220703125,
-0.00814056396484375,
-0.018707275390625,
0.009674072265625,
-0.0306396484375,
-0.0240325927734375,
0.0205230712890625,
-0.020751953125,
-0.016204833984375,
0.01395416259765625,
-0.0006527900695800781,
-0.0025997161865234375,
0.01349639892578125,
0.0223541259765625,
-0.004833221435546875,
-0.0207977294921875,
0.00016200542449951172,
-0.0090484619140625,
-0.012786865234375,
0.0082855224609375,
-0.0079803466796875,
-0.0225830078125,
0.034027099609375,
-0.0191192626953125,
-0.004375457763671875,
0.01166534423828125,
0.004222869873046875,
0.0190277099609375,
-0.004833221435546875,
0.016937255859375,
-0.020050048828125,
-0.0081787109375,
0.0313720703125,
-0.0017538070678710938,
-0.00196075439453125,
-0.004222869873046875,
-0.006847381591796875,
0.0208892822265625,
0.0128936767578125,
0.015380859375,
0.0217132568359375,
0.024871826171875,
0.032257080078125,
0.039886474609375,
0.0100555419921875,
0.004589080810546875,
-0.0318603515625,
0.00473785400390625,
0.0125579833984375,
-0.015869140625,
-0.030364990234375,
0.022552490234375,
0.0006475448608398438,
-0.0254058837890625,
-0.0056915283203125,
-0.00858306884765625,
0.0265350341796875,
-0.029052734375,
0.0254364013671875,
-0.01001739501953125,
-0.0168609619140625,
-0.0222625732421875,
-0.0244140625,
0.0262603759765625,
-0.00637054443359375,
0.01031494140625,
0.0207672119140625,
0.032623291015625,
0.02947998046875,
-0.0053863525390625,
0.017669677734375,
-0.0197296142578125,
0.031280517578125,
0.002788543701171875,
-0.01410675048828125,
0.0210723876953125,
-0.0081787109375,
0.03302001953125,
-0.022003173828125,
0.0063018798828125,
-0.009002685546875,
-0.0152740478515625,
0.001667022705078125,
-0.005260467529296875,
-0.0264892578125,
0.018402099609375,
-0.0027141571044921875,
0.02508544921875,
-0.02740478515625,
-0.00399017333984375,
0.0038127899169921875,
0.022247314453125,
-0.004650115966796875,
-0.0203094482421875,
-0.03497314453125,
0.020050048828125,
-0.01239776611328125,
0.0140533447265625,
-0.015960693359375,
-0.019622802734375,
0.0175323486328125,
0.006916046142578125,
0.00579833984375,
0.0121307373046875,
0.011322021484375,
-0.00861358642578125,
0.00882720947265625,
0.003322601318359375,
0.01053619384765625,
0.007755279541015625,
-0.003772735595703125,
-0.020782470703125,
0.0010862350463867188,
0.0229034423828125,
0.00168609619140625,
0.02252197265625,
-0.00843048095703125,
-0.00543212890625,
0.0005965232849121094,
-0.028594970703125,
-0.010406494140625,
-0.031341552734375,
0.00298309326171875,
-0.0253143310546875,
-0.0113983154296875,
-0.0014448165893554688,
0.0239410400390625,
0.0035533905029296875,
-0.035797119140625,
-0.0090179443359375,
0.0006275177001953125,
0.01561737060546875,
-0.018585205078125,
-0.0122833251953125,
0.01438140869140625,
0.0069427490234375,
0.006862640380859375,
0.030181884765625,
0.0016050338745117188,
0.057464599609375,
0.0198974609375,
-0.01141357421875,
0.0019178390502929688,
0.01021575927734375,
-0.004604339599609375,
0.0013227462768554688,
-0.0171051025390625,
-0.0006723403930664062,
0.03192138671875,
-0.0131378173828125,
-0.0230560302734375,
0.0034313201904296875,
0.0211639404296875,
0.00039267539978027344,
0.006832122802734375,
0.0014209747314453125,
0.025848388671875,
-0.042999267578125,
-0.020111083984375,
0.0237274169921875,
-0.001186370849609375,
0.0247955322265625,
-0.038726806640625,
-0.02032470703125,
-0.00653839111328125,
-0.0189056396484375,
0.00473785400390625,
-0.04437255859375,
-0.012420654296875,
-0.012054443359375,
-0.01421356201171875,
0.004058837890625,
-0.01374053955078125,
0.0151214599609375,
0.00177764892578125,
0.03265380859375,
-0.040740966796875,
0.0137481689453125,
-0.0010061264038085938,
-0.0173187255859375,
-0.004367828369140625,
-0.0255279541015625,
0.007534027099609375,
0.028717041015625,
0.010986328125,
0.0145111083984375,
0.00618743896484375,
0.0033130645751953125,
0.00916290283203125,
0.0250701904296875,
0.0189361572265625,
-0.02264404296875,
0.0146636962890625,
0.0012950897216796875,
-0.0027370452880859375,
-0.0003914833068847656,
-0.04986572265625,
0.01026153564453125,
-0.019622802734375,
0.027008056640625,
-0.03399658203125,
0.0262603759765625,
-0.0005707740783691406,
-0.019439697265625,
-0.003368377685546875,
-0.016143798828125,
-0.0075531005859375,
-0.012115478515625,
0.0115203857421875,
-0.0223541259765625,
-0.01470947265625,
0.0126190185546875,
-0.00762939453125,
0.040130615234375,
-0.016357421875,
0.006988525390625,
-0.016845703125,
-0.0035457611083984375,
0.01959228515625,
-0.00608062744140625,
-0.0016851425170898438,
0.0098419189453125,
0.0136260986328125,
-0.0188751220703125,
0.00904083251953125,
-0.00336456298828125,
0.031402587890625,
-0.0015411376953125,
0.037322998046875,
0.00809478759765625,
0.0057830810546875,
-0.0145263671875,
-0.0369873046875,
-0.01331329345703125,
0.00738525390625,
-0.004154205322265625,
0.0075225830078125,
0.01079559326171875,
-0.012451171875,
-0.04412841796875,
0.0135955810546875,
-0.0280914306640625,
-0.004901885986328125,
0.0081024169921875,
-0.03631591796875,
-0.004150390625,
0.030670166015625,
-0.0068817138671875,
-0.0025310516357421875,
-0.010650634765625,
0.00009894371032714844,
0.00601959228515625,
-0.0016460418701171875,
0.007366180419921875,
0.005786895751953125,
0.0230255126953125,
0.0074920654296875,
-0.005237579345703125,
-0.052001953125,
-0.0428466796875,
-0.01122283935546875,
0.01401519775390625,
-0.014373779296875,
-0.01629638671875,
-0.018524169921875,
0.0032100677490234375,
0.005344390869140625,
-0.0030841827392578125,
-0.006103515625,
-0.001262664794921875,
0.0022125244140625,
-0.01004791259765625,
0.0174102783203125,
-0.003688812255859375,
-0.009735107421875,
-0.004558563232421875,
0.0092010498046875,
0.027008056640625,
-0.039337158203125,
-0.0075836181640625,
0.0213470458984375,
-0.040435791015625,
0.05584716796875,
0.0155792236328125,
-0.005283355712890625,
0.0094451904296875,
0.047271728515625,
-0.0167083740234375,
-0.019622802734375,
0.0162353515625,
0.0024356842041015625,
-0.00447845458984375,
0.005859375,
0.013763427734375,
-0.0158843994140625,
0.01436614990234375,
-0.00521087646484375,
-0.007656097412109375,
0.0163116455078125,
0.017242431640625,
0.0178375244140625,
0.0235595703125,
-0.00047278404235839844,
0.0036106109619140625,
0.00359344482421875,
-0.0089569091796875,
0.030975341796875,
-0.0306396484375,
0.020843505859375,
-0.0007281303405761719,
-0.0034275054931640625,
0.0274658203125,
-0.035888671875,
-0.0119781494140625,
0.0166473388671875,
0.014984130859375,
-0.007556915283203125,
-0.006244659423828125,
0.0028839111328125,
-0.01352691650390625,
-0.01043701171875,
-0.0222015380859375,
-0.03863525390625,
0.03302001953125,
-0.01000213623046875,
-0.0178680419921875,
0.014556884765625,
-0.0120849609375,
0.04071044921875,
0.0267486572265625,
0.00595855712890625,
0.007129669189453125,
-0.00856781005859375,
-0.003753662109375,
-0.007717132568359375,
-0.027679443359375,
-0.0217132568359375,
-0.0197601318359375,
0.01128387451171875,
0.00894927978515625,
0.0087432861328125,
-0.0200653076171875,
0.0189666748046875,
0.0235595703125,
-0.01190948486328125,
-0.01312255859375,
-0.003932952880859375,
0.00899505615234375,
-0.0148162841796875,
-0.00827789306640625,
-0.043609619140625,
0.03192138671875,
0.002025604248046875,
-0.023681640625,
0.0014753341674804688,
0.019195556640625,
0.0011653900146484375,
0.0205078125,
-0.01021575927734375,
0.006969451904296875,
-0.0022335052490234375,
-0.016815185546875,
0.00354766845703125,
-0.00946807861328125,
-0.0180206298828125,
-0.0252227783203125,
-0.0197906494140625,
0.0019445419311523438,
-0.0230560302734375,
-0.032073974609375,
0.003276824951171875,
0.005401611328125,
-0.0269775390625,
-0.0032958984375,
-0.0005593299865722656,
0.00601959228515625,
-0.040313720703125,
-0.0110626220703125,
0.0032405853271484375,
0.009796142578125,
0.033111572265625,
-0.03765869140625,
-0.049468994140625,
0.0281829833984375,
0.0038089752197265625,
-0.0263671875,
-0.0172576904296875,
-0.00971221923828125,
0.0141448974609375,
-0.004520416259765625,
0.01439666748046875,
0.002056121826171875,
0.02947998046875,
0.01215362548828125,
0.0237274169921875,
-0.01287078857421875,
-0.00887298583984375,
-0.0019817352294921875,
-0.017669677734375,
-0.0196075439453125,
-0.0133209228515625,
-0.01337432861328125,
0.01122283935546875,
-0.015411376953125,
-0.01189422607421875,
0.014251708984375,
-0.01267242431640625,
-0.0141754150390625,
0.01110076904296875,
-0.00975799560546875,
0.037750244140625,
0.01369476318359375,
0.0215911865234375,
-0.01409149169921875,
0.0269012451171875,
0.031524658203125,
-0.0234832763671875,
0.0158538818359375,
-0.004169464111328125,
-0.005245208740234375,
-0.017913818359375,
0.04248046875,
0.0208740234375,
0.0255279541015625,
0.01364898681640625,
-0.004123687744140625,
-0.004871368408203125,
0.00644683837890625,
-0.007411956787109375,
-0.003936767578125,
0.0026836395263671875,
0.0040435791015625,
0.0297393798828125,
0.007671356201171875,
-0.01294708251953125,
-0.01531982421875,
-0.022796630859375,
0.01526641845703125,
0.0137786865234375,
-0.0028209686279296875,
-0.01317596435546875,
-0.018951416015625,
0.0202789306640625,
0.00383758544921875,
0.024505615234375,
0.0017795562744140625,
-0.01898193359375,
0.0278778076171875,
-0.02288818359375,
0.015289306640625,
0.02301025390625,
-0.039642333984375,
-0.00133514404296875,
-0.035400390625,
0.0270843505859375,
-0.0200958251953125,
0.0016489028930664062,
-0.00392913818359375,
0.0100860595703125,
-0.0094146728515625,
0.00212860107421875,
-0.0211944580078125,
-0.01306915283203125,
-0.0009927749633789062,
0.02569580078125,
0.0013713836669921875,
-0.00452423095703125,
-0.004467010498046875,
-0.00611114501953125,
-0.009735107421875,
-0.04071044921875,
-0.007160186767578125,
0.00876617431640625,
-0.00585174560546875,
-0.0022258758544921875,
-0.0007410049438476562,
0.0145721435546875,
-0.0091094970703125,
-0.01331329345703125,
0.0218963623046875,
0.00711822509765625,
0.01123809814453125,
-0.01215362548828125,
0.003337860107421875,
0.048095703125,
0.00762939453125,
0.0216217041015625,
-0.0196075439453125,
0.042388916015625,
0.04388427734375,
-0.0210418701171875,
0.01264190673828125,
0.0230865478515625,
0.015167236328125,
0.004894256591796875,
-0.01232147216796875,
-0.0102081298828125,
-0.0008940696716308594,
0.019439697265625,
0.01360321044921875,
0.004131317138671875,
-0.02056884765625,
0.0067901611328125,
-0.006130218505859375,
-0.015594482421875,
-0.01537322998046875,
-0.0008687973022460938,
-0.003253936767578125,
-0.0194549560546875,
0.017364501953125,
-0.00826263427734375,
-0.034423828125,
0.035064697265625,
0.0030994415283203125,
0.0330810546875,
-0.0003197193145751953,
-0.0264739990234375,
-0.0020198822021484375,
0.0201416015625,
-0.037445068359375,
0.0178985595703125,
-0.012603759765625,
0.0008745193481445312,
0.0278778076171875,
-0.0305938720703125,
-0.008087158203125,
-0.0028533935546875,
0.041259765625,
0.0280303955078125,
-0.0024566650390625,
-0.00435638427734375,
0.0177764892578125,
-0.01346588134765625,
0.014129638671875,
-0.0241851806640625,
0.0222320556640625,
-0.0181884765625,
0.01145172119140625,
-0.0013647079467773438,
0.0311126708984375,
-0.0245513916015625,
-0.0175323486328125,
-0.0077667236328125,
-0.0133514404296875,
0.035430908203125,
-0.0121307373046875,
-0.035491943359375,
-0.02276611328125,
-0.0034923553466796875,
0.01345062255859375,
0.0199127197265625,
-0.0225830078125,
-0.022216796875,
-0.005054473876953125,
-0.0059814453125,
-0.010711669921875,
0.00070953369140625,
0.025177001953125,
-0.01181793212890625,
-0.01255035400390625,
-0.0251922607421875,
-0.02655029296875,
-0.0022735595703125,
0.006702423095703125,
-0.0294952392578125,
-0.0343017578125,
0.006252288818359375,
0.045379638671875,
-0.004291534423828125,
0.0018835067749023438,
0.00958251953125,
0.0016269683837890625,
-0.0027866363525390625,
0.0126953125,
0.00414276123046875,
0.0206298828125,
-0.01352691650390625,
-0.00598907470703125,
-0.01279449462890625,
-0.0172119140625,
0.01473236083984375,
-0.00839996337890625,
-0.001331329345703125,
-0.01593017578125,
0.0042724609375,
-0.0079193115234375,
0.035064697265625,
-0.0019931793212890625,
-0.015777587890625,
0.01727294921875,
0.030029296875,
0.0273590087890625,
0.034088134765625,
0.0294036865234375,
-0.0116424560546875,
0.01186370849609375,
0.01183319091796875,
0.00879669189453125,
0.0130615234375,
0.005580902099609375,
-0.0245819091796875,
-0.010162353515625,
-0.0103759765625,
-0.025299072265625,
-0.02642822265625,
0.01010894775390625,
-0.0038318634033203125,
-0.057098388671875,
0.0246124267578125,
-0.0162506103515625,
-0.03192138671875,
-0.0050811767578125,
-0.0131683349609375,
0.029815673828125,
0.0174407958984375,
0.01548004150390625,
-0.01837158203125,
-0.0291900634765625,
-0.005474090576171875,
-0.0009446144104003906,
-0.00848388671875,
-0.00021016597747802734,
0.006214141845703125,
-0.00823211669921875,
0.047760009765625,
-0.01290130615234375,
-0.0015668869018554688,
-0.00881195068359375,
-0.032745361328125,
0.035888671875,
-0.0172882080078125,
0.00311279296875,
0.01163482666015625,
0.025146484375,
-0.00620269775390625,
0.01099395751953125,
-0.018829345703125,
-0.004848480224609375,
0.002033233642578125,
0.0122528076171875,
0.015960693359375,
-0.00543212890625,
0.007625579833984375,
0.004329681396484375,
0.0253143310546875,
-0.0014925003051757812,
-0.02728271484375,
0.007442474365234375,
-0.00522613525390625,
0.00891876220703125,
0.01136016845703125,
-0.0144805908203125,
-0.049957275390625,
0.0016908645629882812,
0.00832366943359375,
-0.035980224609375,
0.0037021636962890625,
0.00841522216796875,
-0.011474609375,
0.003932952880859375,
0.00873565673828125,
-0.0005397796630859375,
-0.0055694580078125,
-0.03704833984375,
0.0242462158203125,
0.0256195068359375,
0.02423095703125,
0.0031795501708984375,
-0.042938232421875,
-0.00452423095703125,
-0.0140228271484375,
0.01425933837890625,
0.01331329345703125,
-0.008087158203125,
0.0190582275390625,
0.0284576416015625,
0.0171356201171875,
0.025177001953125,
0.0145111083984375,
0.01213836669921875,
0.001392364501953125,
-0.0139617919921875,
0.030853271484375,
-0.052001953125,
-0.0028018951416015625,
0.00007891654968261719,
0.01690673828125,
0.04840087890625,
0.0015001296997070312,
0.029266357421875,
0.02410888671875,
-0.0183563232421875,
-0.000008881092071533203,
0.004596710205078125,
0.002880096435546875,
0.0262298583984375,
0.0198822021484375,
-0.007091522216796875,
0.0011119842529296875,
0.00797271728515625,
0.00661468505859375,
0.0177154541015625,
-0.01837158203125,
0.019012451171875,
-0.0070648193359375,
-0.043792724609375,
0.00860595703125,
-0.00438690185546875,
-0.041534423828125,
0.005786895751953125,
-0.00804901123046875,
-0.01461029052734375,
0.01422119140625,
0.0014400482177734375,
-0.044036865234375,
0.003139495849609375,
0.02862548828125,
0.0010967254638671875,
0.0125579833984375,
-0.0115203857421875,
0.0068511962890625,
-0.01922607421875,
0.0223541259765625,
0.035003662109375,
-0.00872039794921875,
0.00044465065002441406,
-0.0215606689453125,
0.01035308837890625,
0.035614013671875,
-0.01470947265625,
-0.033660888671875,
-0.0236053466796875,
0.0233154296875,
0.002468109130859375,
-0.01549530029296875,
0.0180511474609375,
0.01342010498046875,
0.026123046875,
0.03314208984375,
0.034149169921875,
0.02288818359375,
0.037445068359375,
-0.0233917236328125,
0.00550079345703125,
-0.005748748779296875,
-0.01666259765625,
-0.043060302734375,
0.0006327629089355469,
-0.0052337646484375,
0.01062774658203125,
0.002811431884765625,
-0.015960693359375,
0.0091400146484375,
0.0189666748046875,
-0.013336181640625,
0.00012302398681640625,
0.0065460205078125,
0.006992340087890625,
0.01461029052734375,
0.00408935546875,
-0.01287841796875,
-0.0249786376953125,
0.012237548828125,
0.007110595703125,
0.018798828125,
-0.0237579345703125,
0.00728607177734375,
-0.005878448486328125,
-0.000926971435546875,
-0.031158447265625,
-0.0190277099609375,
-0.047882080078125,
0.01445770263671875,
-0.0167388916015625,
-0.0007228851318359375,
0.032379150390625,
0.0037975311279296875,
0.0077667236328125,
0.0030841827392578125,
-0.0176239013671875,
-0.0311431884765625,
-0.03851318359375,
-0.01318359375,
0.00205230712890625,
-0.006954193115234375,
-0.05078125,
-0.035919189453125,
-0.032867431640625,
0.01541900634765625,
-0.0016736984252929688,
-0.00691986083984375,
-0.0177154541015625,
-0.020355224609375,
0.006061553955078125,
-0.00006949901580810547,
0.0243377685546875,
0.027984619140625,
-0.0082550048828125,
-0.01385498046875,
-0.0721435546875,
0.00934600830078125,
-0.02166748046875,
-0.0005536079406738281,
-0.0283203125,
0.006439208984375,
0.0125579833984375,
-0.0004487037658691406,
-0.0289154052734375,
-0.022491455078125,
-0.0193023681640625,
-0.025146484375,
0.0161285400390625,
0.0182342529296875,
-0.029327392578125,
-0.0250091552734375,
-0.0190277099609375,
-0.04510498046875,
0.0019702911376953125,
0.00026416778564453125,
0.0180206298828125,
-0.000736236572265625,
-0.048187255859375,
-0.01270294189453125,
0.0035533905029296875,
0.018707275390625,
-0.01303863525390625,
-0.01387786865234375,
0.01227569580078125,
0.005069732666015625,
-0.005496978759765625,
0.0364990234375,
0.020294189453125,
0.0171966552734375,
0.01153564453125,
-0.00839996337890625,
0.01172637939453125,
0.0137481689453125,
-0.006984710693359375,
-0.0064697265625,
-0.0261077880859375,
0.007495880126953125,
0.00940704345703125,
-0.01470184326171875,
0.00719451904296875,
-0.0009851455688476562,
0.005252838134765625,
0.01837158203125,
0.00475311279296875,
0.00301361083984375,
0.00006538629531860352,
0.021575927734375,
-0.0134124755859375,
-0.00045800209045410156,
0.014404296875,
0.0274505615234375,
-0.018890380859375
] |
ours_510
|
Solution. Let \( a(n) \) denote the least positive integer with digit sum \( n \). Partition the positive integers into chains:
\[
\begin{gathered}
a(1) = 1 \mapsto F(1) \mapsto F(F(1)) \mapsto F(F(F(1))) \mapsto \ldots \\
a(2) = 2 \mapsto F(2) \mapsto F(F(2)) \mapsto F(F(F(2))) \mapsto \ldots \\
\quad \vdots \\
a(10) = 19 \mapsto F(19) \mapsto F(F(19)) \mapsto F(F(F(19))) \mapsto \ldots
\end{gathered}
\]
A positive integer with digit sum \( n \) appears in the chain starting with \( a(n) \). Then \( F(\mathbb{N}) \) sends each positive integer to the next number in its chain. Thus, if \( X(n) \) is the least positive integer greater than 1000 with digit sum \( n \), we have:
\[
(F(1) + F(2) + \cdots + F(1000)) - (1 + 2 + \cdots + 1000) = \sum_{n=1}^{27}(X(n) - a(n))
\]
It is straightforward to show:
\[
a(n) = \overline{m \underbrace{9 \ldots 9}_{k \text{ 9's}}} \quad \text{where } n = 9k + m, \, 0 \leq m < 9; \quad X(n) =
\begin{cases}
10000 & \text{if } n = 1 \\
1000 + a(n-1) & \text{if } 2 \leq n \leq 27
\end{cases}
\]
In particular, \( X(n) - a(n-1) = 1000 \), so:
\[
\sum_{n=1}^{27}(X(n) - a(n)) = X(1) - a(27) + \sum_{n=2}^{27}(X(n) - a(n-1)) = 10000 - 999 + 26 \cdot 1000 = 35001
\]
Thus, \( F(1) + \cdots + F(1000) = 35001 + (1 + 2 + \cdots + 1000) = 535501 \).
\(\boxed{535501}\)
|
535501
|
{
"competition": "us_comps",
"dataset": "Ours",
"posts": null,
"source": "OMOFall19Solns.md"
}
|
Let \( F(n) \) denote the smallest positive integer greater than \( n \) whose sum of digits is equal to the sum of the digits of \( n \). For example, \( F(2019) = 2028 \). Compute \( F(1) + F(2) + \cdots + F(1000) \).
|
[
"/Mathematics/NumberTheory/GeneralNumberTheory/ElementaryMethods",
"/Mathematics/NumberTheory/GeneralNumberTheory/ElementaryNumberTheory",
"/Mathematics/NumberTheory/GeneralNumberTheory/HigherArithmetic",
"/Mathematics/NumberTheory/GeneralNumberTheory/NumberTheory",
"/Mathematics/NumberTheory/Integers/N",
"/Mathematics/NumberTheory/Integers/PositiveInteger",
"/Mathematics/NumberTheory/Integers/Z-Plus",
"/Mathematics/NumberTheory/NumberTheoreticFunctions/IntegerFunctions",
"/Mathematics/RecreationalMathematics/Puzzles/Puzzle"
] |
Group integers into chains by digit sum so that F moves to the next larger number in the same chain, turning the total sum into a sum of gaps between minimal and first >1000 numbers for each digit sum.
|
[
0.000013053417205810547,
0.029449462890625,
0.027130126953125,
0.0119781494140625,
-0.00023818016052246094,
-0.012359619140625,
0.060638427734375,
-0.039093017578125,
0.0169830322265625,
-0.032135009765625,
-0.0034465789794921875,
-0.0650634765625,
0.000774383544921875,
0.031982421875,
-0.0294647216796875,
-0.001171112060546875,
0.007366180419921875,
0.017059326171875,
0.0013399124145507812,
-0.00823974609375,
-0.0165252685546875,
0.00963592529296875,
-0.046356201171875,
-0.0190887451171875,
-0.033050537109375,
-0.0189666748046875,
-0.0303955078125,
0.0119171142578125,
0.0236358642578125,
-0.0445556640625,
0.0174713134765625,
-0.005382537841796875,
-0.01224517822265625,
-0.034576416015625,
-0.0011148452758789062,
-0.01160430908203125,
-0.017791748046875,
-0.0005359649658203125,
-0.0190277099609375,
0.016632080078125,
-0.01495361328125,
-0.0206756591796875,
-0.017608642578125,
0.00807952880859375,
-0.021331787109375,
-0.0069427490234375,
0.005084991455078125,
0.007579803466796875,
-0.0219573974609375,
-0.01367950439453125,
-0.00887298583984375,
0.001277923583984375,
-0.0276641845703125,
-0.004642486572265625,
-0.07672119140625,
-0.03826904296875,
0.0113067626953125,
0.00968170166015625,
0.00652313232421875,
-0.04071044921875,
-0.0014429092407226562,
0.005519866943359375,
-0.0204315185546875,
-0.01739501953125,
0.0016384124755859375,
-0.0095062255859375,
0.0287628173828125,
-0.0083160400390625,
0.00888824462890625,
0.0114288330078125,
0.021514892578125,
-0.0240020751953125,
-0.01995849609375,
0.03369140625,
0.0192718505859375,
-0.0132293701171875,
-0.005542755126953125,
-0.004627227783203125,
0.0162506103515625,
-0.018402099609375,
0.028656005859375,
0.003757476806640625,
0.017608642578125,
0.0206756591796875,
0.00426483154296875,
0.01041412353515625,
0.0208587646484375,
-0.00571441650390625,
0.046966552734375,
0.017181396484375,
-0.0020294189453125,
-0.01415252685546875,
0.0226593017578125,
0.0029754638671875,
0.0005612373352050781,
0.0096893310546875,
0.00844573974609375,
-0.004459381103515625,
0.0017366409301757812,
0.009185791015625,
-0.0248870849609375,
0.0015468597412109375,
0.02435302734375,
-0.017791748046875,
-0.042572021484375,
-0.0135345458984375,
-0.002552032470703125,
-0.0001634359359741211,
-0.031280517578125,
-0.002407073974609375,
-0.00042557716369628906,
0.0005507469177246094,
0.0108795166015625,
0.021881103515625,
-0.0198211669921875,
-0.0012578964233398438,
-0.0003218650817871094,
0.0229644775390625,
-0.00911712646484375,
-0.0215911865234375,
-0.005496978759765625,
0.00687408447265625,
-0.0082855224609375,
0.0256195068359375,
-0.0022735595703125,
-0.0097198486328125,
0.004180908203125,
-0.0196533203125,
0.0184173583984375,
0.01464080810546875,
0.021240234375,
0.006908416748046875,
-0.04559326171875,
-0.01018524169921875,
-0.0631103515625,
-0.0009050369262695312,
-0.005077362060546875,
-0.00600433349609375,
-0.009368896484375,
-0.0223388671875,
-0.01336669921875,
-0.006397247314453125,
0.01450347900390625,
0.0304412841796875,
0.0061492919921875,
0.01482391357421875,
0.007228851318359375,
-0.034393310546875,
0.0255126953125,
-0.0112762451171875,
0.00719451904296875,
0.00849151611328125,
0.01085662841796875,
0.0245819091796875,
0.00551605224609375,
0.017822265625,
0.004901885986328125,
0.006336212158203125,
-0.0185546875,
-0.000579833984375,
0.0033969879150390625,
0.00049591064453125,
-0.0032825469970703125,
-0.00016760826110839844,
-0.006336212158203125,
-0.0008769035339355469,
0.01006317138671875,
-0.003971099853515625,
-0.024444580078125,
0.0028018951416015625,
-0.00286865234375,
0.0097503662109375,
0.0064239501953125,
-0.0202484130859375,
0.005016326904296875,
-0.0188446044921875,
-0.006175994873046875,
-0.0142059326171875,
-0.0035686492919921875,
-0.0184173583984375,
0.00530242919921875,
-0.0171661376953125,
0.040374755859375,
0.01377105712890625,
0.01349639892578125,
-0.01363372802734375,
-0.00397491455078125,
0.01171875,
0.0155181884765625,
0.01189422607421875,
0.03704833984375,
-0.0135650634765625,
0.0028133392333984375,
-0.0031528472900390625,
-0.0087432861328125,
-0.022857666015625,
0.008270263671875,
0.006999969482421875,
0.0379638671875,
0.00601959228515625,
-0.0015163421630859375,
0.0268096923828125,
-0.034942626953125,
0.015167236328125,
0.0135040283203125,
-0.0171966552734375,
-0.0012006759643554688,
0.006977081298828125,
-0.00958251953125,
0.0014505386352539062,
0.009185791015625,
0.007297515869140625,
-0.01413726806640625,
0.01371002197265625,
-0.00897979736328125,
-0.00920867919921875,
0.002094268798828125,
-0.011322021484375,
0.0108184814453125,
-0.0290374755859375,
-0.0012464523315429688,
0.0044403076171875,
-0.007648468017578125,
-0.0082244873046875,
-0.0097198486328125,
-0.002422332763671875,
0.0012464523315429688,
-0.010345458984375,
-0.009368896484375,
0.00037860870361328125,
-0.0007443428039550781,
0.006763458251953125,
-0.011566162109375,
-0.0043487548828125,
-0.00858306884765625,
0.01525115966796875,
0.022064208984375,
-0.0234375,
0.01910400390625,
-0.0396728515625,
0.048004150390625,
-0.0099334716796875,
0.00765228271484375,
0.0036678314208984375,
-0.0007386207580566406,
-0.00823211669921875,
0.0024318695068359375,
0.005069732666015625,
0.01146697998046875,
-0.01001739501953125,
0.00852203369140625,
0.0034770965576171875,
-0.0211944580078125,
0.0016384124755859375,
0.012420654296875,
-0.0037441253662109375,
0.0004239082336425781,
-0.02801513671875,
-0.0174102783203125,
-0.0107269287109375,
0.0004417896270751953,
-0.01081085205078125,
0.01065826416015625,
0.004070281982421875,
0.00701904296875,
-0.0185089111328125,
-0.0231170654296875,
0.0269775390625,
-0.01055908203125,
0.000606536865234375,
0.016265869140625,
-0.01126861572265625,
-0.0069122314453125,
0.00023734569549560547,
0.0178070068359375,
-0.02532958984375,
-0.007251739501953125,
-0.0280914306640625,
-0.008453369140625,
0.0013017654418945312,
0.01287841796875,
-0.035736083984375,
-0.003986358642578125,
0.016021728515625,
0.0020160675048828125,
-0.010009765625,
-0.011260986328125,
0.0032062530517578125,
-0.006816864013671875,
-0.0014982223510742188,
0.00817108154296875,
-0.0277099609375,
0.005603790283203125,
-0.00858306884765625,
0.06256103515625,
-0.060272216796875,
0.01049041748046875,
0.01457977294921875,
-0.0093994140625,
-0.0192718505859375,
0.0269317626953125,
0.010772705078125,
-0.0202789306640625,
-0.03204345703125,
0.00037932395935058594,
0.001308441162109375,
0.00981903076171875,
0.015625,
-0.0361328125,
-0.022003173828125,
-0.003536224365234375,
-0.0160064697265625,
0.0206451416015625,
0.01001739501953125,
-0.0219573974609375,
-0.037353515625,
-0.0095672607421875,
0.01100921630859375,
-0.0124053955078125,
-0.028106689453125,
0.0186309814453125,
0.005916595458984375,
0.01529693603515625,
-0.004596710205078125,
-0.0311431884765625,
0.0123443603515625,
-0.0120086669921875,
0.004901885986328125,
-0.01346588134765625,
0.00848388671875,
-0.0148773193359375,
0.015289306640625,
0.01033782958984375,
-0.01078033447265625,
-0.0231475830078125,
0.0084075927734375,
-0.01959228515625,
0.006969451904296875,
-0.0005216598510742188,
-0.0003039836883544922,
-0.00008016824722290039,
-0.0185089111328125,
0.0021514892578125,
0.03076171875,
-0.0272216796875,
0.029144287109375,
0.0352783203125,
-0.0024509429931640625,
-0.0185394287109375,
-0.00438690185546875,
-0.015380859375,
0.004116058349609375,
-0.0076141357421875,
0.007747650146484375,
-0.032440185546875,
0.01404571533203125,
-0.020294189453125,
-0.00185394287109375,
0.0135955810546875,
0.02142333984375,
-0.0094146728515625,
-0.028717041015625,
0.01300811767578125,
0.021759033203125,
0.0207366943359375,
-0.01519775390625,
-0.005107879638671875,
-0.0019025802612304688,
-0.00931549072265625,
-0.01181793212890625,
0.007171630859375,
-0.0540771484375,
0.0016317367553710938,
-0.035369873046875,
-0.032806396484375,
0.0016565322875976562,
-0.00640869140625,
-0.01383209228515625,
-0.00757598876953125,
0.00031495094299316406,
-0.011474609375,
0.0499267578125,
-0.008514404296875,
0.026885986328125,
-0.036102294921875,
-0.01009368896484375,
0.0216064453125,
-0.036834716796875,
-0.0159454345703125,
-0.0189056396484375,
-0.01385498046875,
0.00872039794921875,
-0.0013685226440429688,
0.0114593505859375,
-0.0068511962890625,
-0.0002288818359375,
0.001861572265625,
0.036407470703125,
0.034942626953125,
-0.006378173828125,
0.0102691650390625,
-0.022705078125,
-0.0293121337890625,
0.03729248046875,
0.0037479400634765625,
-0.00614166259765625,
-0.0014667510986328125,
-0.00257110595703125,
0.0147705078125,
-0.0013027191162109375,
0.016876220703125,
0.021697998046875,
0.00011271238327026367,
-0.026580810546875,
0.0081024169921875,
0.0062713623046875,
-0.004718780517578125,
0.023651123046875,
-0.0246124267578125,
0.006580352783203125,
0.014739990234375,
-0.0153656005859375,
-0.01230621337890625,
0.0236358642578125,
0.0159912109375,
0.01385498046875,
-0.00652313232421875,
0.040374755859375,
0.0206451416015625,
0.0163116455078125,
0.039520263671875,
-0.0215606689453125,
0.0229949951171875,
0.01025390625,
-0.022308349609375,
-0.0146636962890625,
0.01849365234375,
0.0135955810546875,
-0.0254974365234375,
-0.004856109619140625,
0.008056640625,
0.01210784912109375,
0.021759033203125,
-0.021728515625,
-0.052032470703125,
0.006267547607421875,
0.0340576171875,
-0.005687713623046875,
0.0009026527404785156,
0.00742340087890625,
0.004428863525390625,
-0.0139007568359375,
0.003841400146484375,
0.01277923583984375,
-0.033966064453125,
-0.007038116455078125,
0.0167694091796875,
-0.009674072265625,
-0.016754150390625,
-0.028564453125,
-0.03631591796875,
-0.031707763671875,
-0.036895751953125,
-0.019622802734375,
-0.018341064453125,
0.01073455810546875,
0.01751708984375,
0.0033435821533203125,
0.0048675537109375,
0.00890350341796875,
0.0017690658569335938,
-0.031585693359375,
0.007904052734375,
-0.00485992431640625,
-0.030517578125,
0.0187225341796875,
-0.004398345947265625,
0.02978515625,
0.005275726318359375,
-0.03253173828125,
0.0277252197265625,
0.0084991455078125,
0.0123748779296875,
0.035125732421875,
-0.020660400390625,
0.005771636962890625,
0.025054931640625,
0.0081634521484375,
-0.0203704833984375,
0.006183624267578125,
0.0187530517578125,
0.0248870849609375,
-0.024322509765625,
-0.0287933349609375,
-0.01568603515625,
-0.0209503173828125,
-0.019500732421875,
0.0065765380859375,
0.0124969482421875,
-0.004405975341796875,
-0.0248565673828125,
-0.0261688232421875,
0.01464080810546875,
0.021087646484375,
-0.01529693603515625,
-0.017852783203125,
0.043792724609375,
-0.009674072265625,
0.02032470703125,
-0.01555633544921875,
0.005466461181640625,
-0.00025153160095214844,
-0.009796142578125,
-0.0285491943359375,
0.002513885498046875,
0.0022487640380859375,
0.00930023193359375,
-0.0030612945556640625,
-0.01715087890625,
0.0019216537475585938,
-0.035614013671875,
-0.021087646484375,
0.0149688720703125,
-0.01399993896484375,
0.007404327392578125,
0.0271148681640625,
0.01010894775390625,
0.0005946159362792969,
-0.002994537353515625,
0.016845703125,
0.0008220672607421875,
-0.0225372314453125,
0.01654052734375,
0.00838470458984375,
-0.031402587890625,
-0.02093505859375,
0.039154052734375,
0.023284912109375,
-0.007579803466796875,
0.0039520263671875,
-0.01837158203125,
-0.005229949951171875,
-0.029541015625,
-0.0014715194702148438,
-0.01543426513671875,
0.00528717041015625,
0.006107330322265625,
0.0255889892578125,
0.0081634521484375,
0.017852783203125,
-0.0168304443359375,
0.00799560546875,
0.021392822265625,
0.0188446044921875,
-0.005466461181640625,
0.021392822265625,
0.054443359375,
-0.016754150390625,
-0.012359619140625,
-0.00325775146484375,
0.00360107421875,
-0.031829833984375,
0.03936767578125,
0.0008220672607421875,
0.0118560791015625,
-0.02752685546875,
0.01910400390625,
0.016693115234375,
0.00867462158203125,
-0.023193359375,
-0.017486572265625,
0.0126495361328125,
-0.00502777099609375,
-0.01161956787109375,
-0.01407623291015625,
-0.03192138671875,
-0.03167724609375,
-0.019012451171875,
-0.0021076202392578125,
0.0032787322998046875,
0.0150604248046875,
0.00804901123046875,
0.00572967529296875,
-0.0413818359375,
0.007404327392578125,
-0.0033054351806640625,
0.022430419921875,
-0.032562255859375,
0.0054779052734375,
0.0091094970703125,
-0.0079345703125,
-0.0360107421875,
0.00013720989227294922,
-0.01849365234375,
0.0279083251953125,
-0.02001953125,
-0.02264404296875,
-0.041473388671875,
0.035247802734375,
-0.0215301513671875,
0.043121337890625,
-0.01485443115234375,
-0.00749969482421875,
0.0213165283203125,
-0.0004382133483886719,
-0.01641845703125,
0.0085296630859375,
0.01824951171875,
-0.00970458984375,
0.0235137939453125,
0.035614013671875,
-0.030975341796875,
0.0009584426879882812,
-0.009185791015625,
0.02252197265625,
0.004039764404296875,
0.01131439208984375,
0.0024662017822265625,
0.0037860870361328125,
0.002349853515625,
0.01103973388671875,
0.006305694580078125,
-0.0263824462890625,
0.0281219482421875,
-0.0153961181640625,
-0.042205810546875,
0.02642822265625,
0.00986480712890625,
0.00035119056701660156,
0.005542755126953125,
-0.025604248046875,
-0.0117645263671875,
-0.00380706787109375,
-0.010009765625,
-0.01129913330078125,
-0.015716552734375,
-0.00568389892578125,
0.03521728515625,
-0.0135040283203125,
-0.0189361572265625,
0.024688720703125,
0.034149169921875,
0.018402099609375,
-0.056121826171875,
-0.0029392242431640625,
0.031158447265625,
-0.027130126953125,
-0.00978851318359375,
-0.00897216796875,
0.02764892578125,
-0.035125732421875,
-0.0028476715087890625,
-0.0066986083984375,
0.01715087890625,
0.007518768310546875,
0.01238250732421875,
0.029296875,
-0.01934814453125,
0.04937744140625,
-0.0309600830078125,
0.02569580078125,
0.01537322998046875,
0.0175933837890625,
-0.00901031494140625,
-0.017059326171875,
-0.0013275146484375,
-0.0017910003662109375,
-0.00525665283203125,
0.0176239013671875,
-0.03057861328125,
-0.006046295166015625,
-0.048187255859375,
0.00875091552734375,
0.0245361328125,
0.01160430908203125,
-0.0157470703125,
-0.001049041748046875,
-0.033538818359375,
-0.03985595703125,
0.013580322265625,
-0.00890350341796875,
0.01049041748046875,
0.0272064208984375,
0.0085296630859375,
0.011688232421875,
0.0211181640625,
-0.007350921630859375,
0.0081024169921875,
-0.005558013916015625,
0.00766754150390625,
0.00634002685546875,
-0.0164642333984375,
0.01239776611328125,
0.0224761962890625,
0.0016632080078125,
-0.02740478515625,
0.0318603515625,
-0.00969696044921875,
-0.0014734268188476562,
-0.0016851425170898438,
-0.0169525146484375,
-0.006999969482421875,
0.0135955810546875,
0.0025177001953125,
0.00983428955078125,
-0.03326416015625,
-0.0233154296875,
-0.00533294677734375,
-0.03863525390625,
0.027374267578125,
0.00830078125,
0.00742340087890625,
-0.00982666015625,
0.0037670135498046875,
0.00650787353515625,
0.0394287109375,
-0.01045989990234375,
-0.005237579345703125,
0.01297760009765625,
-0.004489898681640625,
-0.04290771484375,
-0.0019989013671875,
0.0029296875,
0.01039886474609375,
0.0264739990234375,
0.0009336471557617188,
-0.020294189453125,
-0.01654052734375,
-0.02874755859375,
-0.00635528564453125,
0.0082855224609375,
-0.01052093505859375,
-0.004627227783203125,
-0.02764892578125,
-0.03558349609375,
0.00021088123321533203,
-0.00201416015625,
-0.014739990234375,
-0.004482269287109375,
-0.018035888671875,
0.037689208984375,
-0.0174102783203125,
0.03753662109375,
-0.0227813720703125,
-0.0002238750457763672,
-0.0025730133056640625,
0.007656097412109375,
0.007144927978515625,
-0.0244598388671875,
-0.00586700439453125,
-0.00481414794921875,
0.00603485107421875,
0.04937744140625,
-0.035888671875,
-0.0234832763671875,
-0.006439208984375,
-0.0011920928955078125,
0.0169525146484375,
-0.0136871337890625,
-0.0073394775390625,
-0.0303802490234375,
0.00795745849609375,
-0.0247039794921875,
-0.01541900634765625,
-0.01953125,
0.03564453125,
-0.046905517578125,
-0.025054931640625,
-0.0283203125,
0.021453857421875,
-0.004337310791015625,
-0.007659912109375,
0.01041412353515625,
0.0023860931396484375,
0.027252197265625,
-0.009063720703125,
-0.006256103515625,
0.01456451416015625,
0.0223236083984375,
-0.0308380126953125,
-0.00024962425231933594,
0.01029205322265625,
-0.0328369140625,
0.00360870361328125,
-0.0241241455078125,
0.00382232666015625,
0.0205078125,
-0.0030059814453125,
0.051177978515625,
-0.020233154296875,
0.01953125,
0.008453369140625,
-0.015106201171875,
0.000244140625,
-0.016265869140625,
-0.0015516281127929688,
0.015960693359375,
0.0072174072265625,
0.004123687744140625,
-0.000324249267578125,
0.0179290771484375,
-0.01001739501953125,
0.0202789306640625,
0.00896453857421875,
0.0246734619140625,
-0.03790283203125,
0.003143310546875,
0.003757476806640625,
0.011566162109375,
0.002532958984375,
0.03936767578125,
-0.010589599609375,
0.053253173828125,
0.003101348876953125,
0.022613525390625,
-0.026275634765625,
-0.020782470703125,
-0.0034198760986328125,
-0.00787353515625,
0.01331329345703125,
-0.01654052734375,
0.0248870849609375,
-0.0230560302734375,
-0.00724029541015625,
-0.00988006591796875,
0.01605224609375,
0.04541015625,
-0.0318603515625,
-0.004070281982421875,
0.015869140625,
-0.019378662109375,
0.0272979736328125,
-0.033477783203125,
0.043914794921875,
0.004669189453125,
-0.006969451904296875,
0.0276336669921875,
0.019378662109375,
0.0008516311645507812,
0.0299835205078125,
0.031463623046875,
0.0014753341674804688,
0.01255035400390625,
-0.0201568603515625,
-0.006900787353515625,
-0.0186004638671875,
0.007152557373046875,
0.01293182373046875,
-0.00930023193359375,
0.00247955322265625,
0.005519866943359375,
0.02142333984375,
-0.04315185546875,
0.0280609130859375,
-0.006671905517578125,
0.0287628173828125,
-0.003299713134765625,
0.0010957717895507812,
-0.005008697509765625,
-0.0584716796875,
-0.0107879638671875,
-0.03948974609375,
0.0016345977783203125,
-0.0190887451171875,
0.0159759521484375,
-0.0131072998046875,
-0.0112152099609375,
-0.0338134765625,
0.0021800994873046875,
-0.0029735565185546875,
-0.004161834716796875,
-0.01629638671875,
0.005886077880859375,
0.0004298686981201172,
0.00592803955078125,
0.025909423828125,
-0.00821685791015625,
-0.0133056640625,
0.0081939697265625,
0.01044464111328125,
0.0149078369140625,
-0.044921875,
-0.0201416015625,
0.0221099853515625,
-0.0258026123046875,
-0.00429534912109375,
0.0205230712890625,
-0.00414276123046875,
0.008636474609375,
-0.0245208740234375,
-0.00826263427734375,
-0.00931549072265625,
-0.0120086669921875,
0.001667022705078125,
0.027099609375,
0.0438232421875,
0.0108795166015625,
0.0208282470703125,
0.006755828857421875,
-0.0139007568359375,
-0.0093841552734375,
0.016632080078125,
0.0302886962890625,
0.01971435546875,
-0.0196685791015625,
-0.0384521484375,
0.01216888427734375,
0.027557373046875,
-0.007808685302734375,
-0.01395416259765625,
0.00045680999755859375,
0.01123046875,
0.0198211669921875,
0.0262908935546875,
-0.037628173828125,
-0.00571441650390625,
-0.0007815361022949219,
-0.0032482147216796875,
0.004421234130859375,
-0.03070068359375,
-0.00431060791015625,
-0.01605224609375,
-0.02642822265625,
-0.0206146240234375,
-0.0170135498046875,
0.0161590576171875,
0.02520751953125,
-0.01258087158203125,
-0.01045989990234375,
0.0199127197265625,
0.00424957275390625,
0.02655029296875,
0.01050567626953125,
0.0007305145263671875,
-0.0238800048828125,
0.00009369850158691406,
0.01255035400390625,
0.0075836181640625,
-0.0179290771484375,
0.01363372802734375,
-0.043060302734375,
-0.0030994415283203125,
-0.0270843505859375,
0.017852783203125,
-0.004390716552734375,
0.01953125,
-0.0031375885009765625,
0.0199737548828125,
-0.0251312255859375,
-0.0167694091796875,
-0.012847900390625,
0.0095672607421875,
-0.027191162109375,
0.0175323486328125,
-0.02947998046875,
-0.021209716796875,
-0.0194854736328125,
-0.0022411346435546875,
0.0038890838623046875,
-0.0258026123046875,
0.0152435302734375,
-0.0255279541015625,
-0.05517578125,
0.00342559814453125,
-0.0211029052734375,
0.011474609375,
0.0115203857421875,
0.00914764404296875,
0.00453948974609375,
0.019500732421875,
-0.0294189453125,
0.0020809173583984375,
0.003932952880859375,
-0.01371002197265625,
-0.006832122802734375,
-0.01558685302734375,
-0.0562744140625,
0.023468017578125,
-0.0028934478759765625,
0.003665924072265625,
-0.023590087890625,
0.043426513671875,
-0.0274505615234375,
0.00472259521484375,
-0.01038360595703125,
0.013031005859375,
0.047088623046875,
-0.0108489990234375,
-0.00524139404296875,
-0.006984710693359375,
-0.0190887451171875,
0.0230255126953125,
-0.0200653076171875,
0.0249786376953125,
-0.0183563232421875,
0.020782470703125,
-0.0015354156494140625,
-0.0086212158203125,
0.022796630859375,
-0.011810302734375,
-0.01690673828125,
0.016357421875,
0.0015516281127929688,
0.013397216796875,
0.0203094482421875,
-0.007335662841796875,
0.028594970703125,
0.00020015239715576172,
0.040191650390625,
0.046295166015625,
-0.04510498046875,
-0.015869140625,
-0.00981903076171875,
-0.0169219970703125,
0.006099700927734375,
0.029815673828125,
-0.036712646484375,
0.01100921630859375,
-0.033111572265625,
0.012420654296875,
0.003002166748046875,
0.0188446044921875,
-0.0117950439453125,
-0.034820556640625,
-0.015960693359375,
0.0034732818603515625,
0.0210113525390625,
0.0263824462890625,
-0.00952911376953125,
-0.006587982177734375,
0.0218658447265625,
0.0051116943359375,
0.00543975830078125,
-0.01861572265625,
-0.016021728515625,
-0.0193939208984375,
0.0003063678741455078,
-0.02069091796875,
0.0110626220703125,
-0.00560760498046875,
-0.006565093994140625,
0.0260467529296875,
-0.004619598388671875,
0.008941650390625,
0.0057220458984375,
-0.019622802734375,
0.043670654296875,
0.0088958740234375,
-0.0275421142578125,
-0.022430419921875,
0.026092529296875,
0.032073974609375,
-0.03216552734375,
-0.0093536376953125,
0.01389312744140625,
0.0294036865234375,
0.00684356689453125,
0.025146484375,
-0.002971649169921875,
0.01230621337890625,
-0.0006456375122070312,
0.0013589859008789062,
-0.005126953125,
0.0111541748046875,
-0.007549285888671875,
0.020599365234375,
-0.046051025390625,
0.01338958740234375,
-0.0296173095703125,
0.0203704833984375,
-0.035919189453125,
0.0193328857421875,
0.0196380615234375,
-0.03741455078125,
0.0275115966796875,
0.00008678436279296875,
0.007404327392578125,
-0.0194854736328125,
0.005859375,
-0.00189208984375,
-0.0014448165893554688,
0.01136016845703125,
-0.0462646484375,
0.00243377685546875,
0.01184844970703125,
0.0087432861328125,
0.00027441978454589844,
-0.00797271728515625,
-0.01226043701171875,
-0.0074310302734375,
-0.036895751953125,
-0.005992889404296875,
-0.0118560791015625,
-0.0178070068359375,
-0.00260162353515625,
-0.0032672882080078125,
0.0079498291015625,
0.03143310546875,
-0.01139068603515625,
-0.0008597373962402344,
-0.0306854248046875,
0.03497314453125,
0.00836944580078125,
-0.0130767822265625,
-0.006336212158203125,
0.01145172119140625,
-0.022552490234375,
0.0013751983642578125,
-0.0033245086669921875,
0.005229949951171875,
-0.0032825469970703125,
0.01213836669921875,
0.02728271484375,
-0.01488494873046875,
-0.0281829833984375,
-0.01117706298828125,
-0.031036376953125,
-0.0183258056640625,
-0.00872802734375,
-0.0266876220703125,
-0.0209197998046875,
0.01299285888671875,
0.046417236328125,
0.00927734375,
0.002613067626953125,
0.0234375,
-0.016693115234375,
-0.0150146484375,
0.01505279541015625,
-0.00830841064453125,
0.0208282470703125,
0.0271759033203125,
0.01348114013671875,
0.0035533905029296875,
0.0163116455078125,
-0.0182952880859375,
-0.020233154296875,
0.005153656005859375,
0.03936767578125,
-0.0014820098876953125,
-0.003643035888671875,
0.02093505859375,
-0.038116455078125,
0.002986907958984375,
-0.01082611083984375,
-0.007587432861328125,
0.01058197021484375,
0.04290771484375,
0.03485107421875,
0.021820068359375,
-0.00943756103515625,
0.00910186767578125,
-0.0204315185546875,
-0.0049591064453125,
-0.00824737548828125,
0.0240478515625,
0.00994110107421875,
-0.0254364013671875,
0.031585693359375,
-0.005992889404296875,
0.025848388671875,
-0.0185089111328125,
-0.00562286376953125,
0.01537322998046875,
-0.038238525390625,
0.01454925537109375,
0.005023956298828125,
-0.011077880859375,
0.00859832763671875,
-0.011016845703125,
-0.024505615234375,
-0.0172576904296875,
-0.007061004638671875,
0.0081024169921875,
0.005680084228515625,
-0.01433563232421875,
0.02081298828125,
-0.0286407470703125,
-0.00002282857894897461,
-0.0014371871948242188,
0.0369873046875,
0.0162506103515625,
-0.0110931396484375,
-0.0174102783203125,
-0.006000518798828125,
0.01009368896484375,
-0.0199432373046875,
0.00018012523651123047,
0.004932403564453125,
0.00453948974609375,
-0.0253448486328125,
-0.032012939453125,
0.0008344650268554688,
0.00726318359375,
-0.01204681396484375,
-0.0267333984375,
-0.00991058349609375,
0.0028133392333984375,
-0.0248260498046875,
0.0020427703857421875,
-0.004974365234375,
0.0341796875,
-0.042266845703125,
0.00804901123046875,
0.023681640625,
0.0120391845703125,
0.0020160675048828125,
0.004299163818359375,
-0.00746917724609375,
0.016845703125,
-0.0321044921875,
0.0101165771484375,
-0.040283203125,
-0.0011806488037109375,
0.0027790069580078125,
-0.0172119140625,
0.001941680908203125,
-0.038818359375,
0.00012934207916259766,
-0.006710052490234375,
0.00792694091796875,
-0.0386962890625,
0.0158843994140625,
0.011932373046875,
0.0012598037719726562,
-0.0035991668701171875,
-0.0189208984375,
0.030548095703125,
0.006557464599609375,
0.032623291015625,
0.009918212890625,
-0.0199432373046875,
0.002346038818359375,
0.003780364990234375,
-0.00997161865234375,
-0.049713134765625,
-0.00707244873046875,
0.01806640625,
0.0224456787109375,
0.0172119140625,
0.0186920166015625,
0.044464111328125,
0.0278472900390625,
-0.003154754638671875,
0.0574951171875,
-0.0142822265625,
-0.045013427734375,
0.01047515869140625,
-0.0234832763671875,
-0.0174560546875,
0.01010894775390625,
-0.012451171875,
-0.025054931640625,
-0.025787353515625,
0.0225830078125,
-0.0135040283203125,
0.0217742919921875,
-0.0007567405700683594,
0.0167236328125,
0.003429412841796875,
0.0198974609375,
0.0262451171875,
-0.036163330078125,
-0.00548553466796875,
0.0157470703125,
0.001087188720703125,
0.01218414306640625,
0.0291595458984375,
0.01959228515625,
0.01371002197265625,
-0.007228851318359375,
0.0186614990234375,
-0.0206756591796875,
0.0550537109375,
-0.00728607177734375,
0.0262451171875,
-0.016082763671875,
-0.0291900634765625,
0.01372528076171875,
-0.00676727294921875,
-0.017120361328125,
0.0279083251953125,
0.0067901611328125,
-0.028228759765625,
-0.002994537353515625,
-0.0163421630859375,
-0.0123748779296875,
0.023681640625,
-0.0200347900390625,
-0.0188751220703125,
0.00421905517578125,
-0.00327301025390625,
-0.028717041015625,
-0.0004143714904785156,
0.00435638427734375,
-0.008697509765625,
-0.00873565673828125,
-0.0162200927734375,
-0.00762176513671875,
-0.01251983642578125,
0.004657745361328125,
-0.0286102294921875,
-0.00107574462890625,
-0.016845703125,
-0.01140594482421875,
0.014892578125,
0.017059326171875,
0.002552032470703125,
-0.00701141357421875,
-0.00485992431640625,
-0.000043511390686035156,
0.01812744140625,
0.033447265625,
-0.0178985595703125,
0.03399658203125,
0.00799560546875,
-0.006938934326171875,
-0.0012054443359375,
-0.0269317626953125,
-0.006954193115234375,
0.01195526123046875,
0.0196990966796875,
-0.004817962646484375,
0.0241851806640625,
0.0262603759765625,
0.0021381378173828125,
-0.0396728515625,
-0.01203155517578125,
-0.01360321044921875,
-0.004344940185546875,
0.00894927978515625,
0.0280609130859375,
-0.0282745361328125,
-0.0157928466796875,
-0.007045745849609375,
0.00388336181640625,
-0.002288818359375,
0.017852783203125,
-0.00118255615234375,
-0.01377105712890625,
-0.022613525390625,
0.0063934326171875,
-0.01029205322265625,
0.017852783203125,
0.01352691650390625,
0.00321197509765625,
-0.0187530517578125,
0.007007598876953125,
0.02142333984375,
-0.01543426513671875,
0.017669677734375,
0.034210205078125,
0.00559234619140625,
0.004146575927734375,
0.00881195068359375,
-0.0284576416015625,
-0.0008854866027832031,
0.0310211181640625,
0.01105499267578125,
-0.0140533447265625,
0.044647216796875,
-0.032379150390625,
-0.02618408203125,
-0.0146331787109375,
0.02740478515625,
0.0251617431640625,
0.0080413818359375,
-0.01337432861328125,
0.012115478515625,
-0.0025119781494140625,
-0.01328277587890625,
0.0149383544921875,
-0.0194244384765625,
-0.0159454345703125,
0.0134124755859375,
-0.038421630859375,
-0.001190185546875,
0.0259857177734375,
-0.00508880615234375,
0.0283355712890625,
-0.00023114681243896484,
-0.032379150390625,
-0.01273345947265625,
-0.025787353515625,
-0.005550384521484375,
0.001651763916015625,
0.0035552978515625,
0.01180267333984375,
0.01227569580078125,
-0.021820068359375,
0.02642822265625,
-0.0153350830078125,
-0.01172637939453125,
0.0014171600341796875,
-0.0408935546875,
-0.044097900390625,
0.004924774169921875,
-0.02880859375,
-0.01296234130859375,
0.0310821533203125,
0.03076171875,
0.01296234130859375,
-0.0035114288330078125,
-0.00396728515625,
-0.0171356201171875,
-0.021881103515625,
0.0212249755859375,
-0.007904052734375,
0.01171112060546875,
-0.0005168914794921875,
0.00695037841796875,
-0.01177978515625,
0.0137176513671875,
-0.040069580078125,
0.006015777587890625,
-0.0155181884765625,
0.0330810546875,
-0.0225067138671875,
-0.01035308837890625,
0.023040771484375,
-0.01126861572265625,
0.0015916824340820312,
-0.016876220703125,
-0.0114288330078125,
-0.026885986328125,
0.00594329833984375,
0.0085601806640625,
0.0154876708984375,
0.004150390625,
-0.0275421142578125,
0.04119873046875,
-0.03375244140625,
-0.0285186767578125,
-0.0164031982421875,
-0.0338134765625,
0.02587890625,
0.026092529296875,
0.00865936279296875,
0.05438232421875,
0.0283355712890625,
-0.00653076171875,
0.024078369140625,
0.033477783203125,
0.02197265625,
0.0195770263671875,
-0.0112762451171875,
0.004734039306640625,
0.018341064453125,
-0.0088653564453125,
-0.018463134765625,
-0.0273895263671875,
-0.0197906494140625,
0.006855010986328125,
0.00556182861328125,
-0.005176544189453125,
0.00511932373046875,
0.00514984130859375,
-0.00203704833984375,
0.0157012939453125,
-0.0055084228515625,
-0.0262908935546875,
0.040679931640625,
0.0092620849609375,
-0.003658294677734375,
0.0106048583984375,
-0.0204620361328125,
-0.003025054931640625,
0.0030231475830078125,
-0.00366973876953125,
-0.0081939697265625,
-0.0267333984375,
0.005245208740234375,
0.0032863616943359375,
0.01470184326171875,
-0.0227508544921875,
-0.00942230224609375,
-0.00467681884765625,
-0.025482177734375,
0.008575439453125,
-0.01898193359375,
0.0113525390625,
0.00861358642578125,
0.0157470703125,
0.041351318359375,
-0.01763916015625,
-0.0113983154296875,
-0.024932861328125,
-0.0020751953125,
0.0056304931640625,
-0.0235443115234375,
0.006450653076171875,
-0.0268096923828125,
-0.01049041748046875,
0.031005859375,
-0.0013818740844726562,
0.02301025390625,
-0.0252532958984375,
0.0210113525390625,
0.01071929931640625,
-0.0162811279296875,
-0.0017795562744140625,
0.00522613525390625,
0.00704193115234375,
-0.019683837890625,
0.0045013427734375,
-0.025970458984375,
0.007549285888671875,
-0.004772186279296875,
0.027313232421875,
0.0009360313415527344,
-0.01708984375,
-0.0113983154296875,
-0.0155487060546875,
0.0059356689453125,
0.0030670166015625,
-0.0141754150390625,
-0.002079010009765625,
-0.028900146484375,
-0.0060882568359375,
-0.023681640625,
0.00791168212890625,
-0.006732940673828125,
-0.012603759765625,
0.0018415451049804688,
0.006984710693359375,
0.00235748291015625,
0.008575439453125,
-0.0191650390625,
-0.028411865234375,
0.01033782958984375,
0.0249786376953125,
-0.0178070068359375,
0.0064697265625,
0.011444091796875,
0.026123046875,
-0.01611328125,
-0.018951416015625,
-0.0183868408203125,
-0.0167388916015625,
0.00699615478515625,
0.0116119384765625,
-0.01300048828125,
-0.01438140869140625,
-0.01434326171875,
0.0126800537109375,
0.004695892333984375,
0.0056304931640625,
-0.0218505859375,
-0.0308380126953125,
-0.01885986328125,
0.0082550048828125,
-0.005367279052734375,
0.0204925537109375,
0.0162200927734375,
-0.01446533203125,
-0.004337310791015625,
-0.0249786376953125,
0.0517578125,
-0.01506805419921875,
-0.01360321044921875,
-0.000339508056640625,
0.013946533203125,
0.01351165771484375,
-0.00811767578125,
0.0084228515625,
0.0162353515625,
0.0046539306640625,
0.01206207275390625,
-0.007030487060546875,
-0.021820068359375,
-0.0173492431640625,
0.0302581787109375,
0.01690673828125,
0.02325439453125,
-0.041473388671875,
-0.022369384765625,
0.016448974609375,
0.026123046875,
-0.0243988037109375,
0.0022735595703125,
-0.026275634765625,
0.019744873046875,
0.02166748046875,
-0.00722503662109375,
0.04400634765625,
0.006011962890625,
-0.0174560546875,
0.01702880859375,
-0.00594329833984375,
-0.018096923828125,
-0.01517486572265625,
-0.017913818359375,
0.013946533203125,
0.0011129379272460938,
-0.009246826171875,
0.0022869110107421875,
0.039703369140625,
-0.026458740234375,
-0.00011873245239257812,
0.031097412109375,
-0.002353668212890625,
0.023040771484375,
0.036102294921875,
-0.0291748046875,
0.0090789794921875,
-0.0163116455078125,
0.0279388427734375,
0.00665283203125,
-0.0032596588134765625,
-0.0045166015625,
-0.004608154296875,
0.00836181640625,
0.0203704833984375,
-0.01151275634765625,
-0.0224761962890625,
-0.00962066650390625,
0.0242156982421875,
0.0297088623046875,
-0.003299713134765625,
0.017059326171875,
0.00011342763900756836,
-0.0226593017578125,
-0.00901031494140625,
-0.00782012939453125,
0.0206451416015625,
0.0288238525390625,
-0.012176513671875,
0.0214691162109375,
-0.0169525146484375,
-0.0270538330078125,
0.0291290283203125,
-0.001293182373046875,
-0.03289794921875,
-0.00568389892578125,
0.0091094970703125,
0.01383209228515625,
0.005962371826171875,
0.0233306884765625,
-0.01018524169921875,
0.0162353515625,
0.0277557373046875,
-0.0241546630859375,
-0.0003459453582763672,
-0.0247650146484375,
-0.03961181640625,
0.00945281982421875,
-0.0017185211181640625,
-0.00244903564453125,
0.0030975341796875,
-0.0293731689453125,
0.0235137939453125,
0.0221710205078125,
-0.007221221923828125,
0.003589630126953125,
0.01151275634765625,
-0.03179931640625,
-0.003887176513671875,
0.0174713134765625,
0.01470947265625,
0.01366424560546875,
-0.021575927734375,
-0.012237548828125,
-0.009185791015625,
-0.0019063949584960938,
-0.0230712890625,
0.0070953369140625,
-0.00829315185546875,
0.038360595703125,
-0.0037689208984375,
0.032989501953125,
-0.0341796875,
-0.039459228515625,
-0.01308441162109375,
0.06683349609375,
0.01525115966796875,
-0.021148681640625,
-0.009613037109375,
0.0213165283203125,
-0.009552001953125,
-0.0321044921875,
0.0136871337890625,
-0.006267547607421875,
0.008697509765625,
0.028076171875,
0.0022106170654296875,
0.0046234130859375,
0.00714874267578125,
-0.002674102783203125,
0.01262664794921875,
-0.0233001708984375,
0.06512451171875,
0.01338958740234375,
0.0024013519287109375,
0.0292816162109375,
0.018524169921875,
-0.0182037353515625,
0.024444580078125,
-0.023345947265625,
-0.01043701171875,
0.00958251953125,
-0.0014209747314453125,
0.01323699951171875,
-0.03436279296875,
-0.036956787109375,
0.05108642578125,
0.0242919921875,
-0.0271148681640625,
0.0203857421875,
0.0001989603042602539,
0.0026950836181640625,
-0.003063201904296875,
-0.0252685546875,
-0.02545166015625,
-0.01091766357421875,
0.018035888671875,
-0.0030994415283203125,
0.01019287109375,
0.0224761962890625,
0.006587982177734375,
-0.040740966796875,
0.0024852752685546875,
0.002582550048828125,
0.0064849853515625,
-0.042083740234375,
0.002925872802734375,
-0.0172882080078125,
0.01641845703125,
0.033050537109375,
-0.01413726806640625,
0.027130126953125,
-0.0078582763671875,
0.006397247314453125,
-0.0005125999450683594,
-0.012908935546875,
0.0028400421142578125,
-0.0181427001953125,
-0.0005564689636230469,
-0.02679443359375,
-0.029815673828125,
-0.02398681640625,
-0.0079345703125,
0.0161590576171875,
-0.0286712646484375,
-0.01885986328125,
0.01322174072265625,
-0.01227569580078125,
0.007770538330078125,
0.01444244384765625,
0.00042319297790527344,
0.0343017578125,
0.034149169921875,
-0.00659942626953125,
0.0288238525390625,
-0.0139923095703125,
0.005252838134765625,
-0.007518768310546875,
-0.0004115104675292969,
-0.0426025390625,
0.00829315185546875,
0.007671356201171875,
-0.006977081298828125,
-0.01116180419921875,
-0.0290374755859375,
-0.005802154541015625,
-0.0038890838623046875,
-0.005054473876953125,
0.035491943359375,
-0.025390625,
-0.00939178466796875,
0.01465606689453125,
-0.00627899169921875,
-0.00565338134765625,
0.033935546875,
0.01285552978515625,
-0.0145416259765625,
-0.0091094970703125,
-0.0299530029296875,
-0.00954437255859375,
-0.049591064453125,
-0.0018014907836914062,
-0.01036834716796875,
-0.00849151611328125,
0.01221466064453125,
-0.0092620849609375,
0.017852783203125,
-0.0011138916015625,
0.0184173583984375,
-0.016571044921875,
-0.01241302490234375,
-0.0168609619140625,
-0.043548583984375,
-0.00939178466796875,
0.01360321044921875,
0.0200958251953125,
0.018768310546875,
0.0205535888671875,
-0.010009765625,
-0.01161956787109375,
0.0017099380493164062,
0.03857421875,
0.00295257568359375,
0.033599853515625,
-0.0032711029052734375,
-0.00809478759765625,
0.025115966796875,
-0.034149169921875,
0.01873779296875,
0.006259918212890625,
0.03094482421875,
0.00922393798828125,
-0.0081024169921875,
0.00936126708984375,
-0.011749267578125,
-0.01125335693359375,
-0.0026073455810546875,
-0.0071868896484375,
0.023345947265625,
0.0262298583984375,
0.0012388229370117188,
-0.03289794921875,
0.0046234130859375,
-0.0176239013671875,
0.002079010009765625,
0.00371551513671875,
-0.01261138916015625,
-0.027587890625,
0.010894775390625,
0.007617950439453125,
-0.01190185546875,
0.0124053955078125,
0.00030732154846191406,
0.0118865966796875,
-0.003162384033203125,
-0.01043701171875,
0.01085662841796875,
-0.0003991127014160156,
-0.0264434814453125,
-0.01163482666015625,
-0.00981903076171875,
-0.0111846923828125,
-0.0035381317138671875,
0.0208587646484375,
-0.007457733154296875,
-0.01088714599609375,
-0.0005092620849609375,
-0.0096282958984375,
-0.004634857177734375,
0.0153656005859375,
0.01287841796875,
0.016082763671875,
0.004100799560546875,
-0.0277252197265625,
-0.0162200927734375,
0.0172882080078125,
0.006328582763671875,
-0.00572967529296875,
0.0010232925415039062,
0.000186920166015625,
0.0019092559814453125,
-0.0175933837890625,
-0.006748199462890625,
-0.020782470703125,
0.0169830322265625,
0.0310516357421875,
0.0025691986083984375,
0.025360107421875,
0.022247314453125,
-0.01270294189453125,
0.0069580078125,
0.0081329345703125,
0.0196685791015625,
0.039825439453125,
-0.038604736328125,
0.005031585693359375,
0.02374267578125,
-0.0028896331787109375,
-0.00719451904296875,
0.01043701171875,
0.0350341796875,
0.01027679443359375,
-0.007556915283203125,
0.01052093505859375,
0.033477783203125,
-0.0197906494140625,
-0.0016994476318359375,
0.0251922607421875,
-0.00109100341796875,
0.01399993896484375,
0.005046844482421875,
0.00946044921875,
-0.0107574462890625,
0.00011372566223144531,
0.0377197265625,
-0.01039886474609375,
-0.0184326171875,
0.033172607421875,
-0.01082611083984375,
0.015167236328125,
-0.021697998046875,
-0.0017232894897460938,
0.00566864013671875,
0.038818359375,
-0.03411865234375,
0.0082855224609375,
-0.002918243408203125,
0.031890869140625,
-0.004001617431640625,
-0.0287628173828125,
-0.003662109375,
0.00457000732421875,
0.022247314453125,
0.0034389495849609375,
-0.0260162353515625,
-0.0068817138671875,
0.00794219970703125,
0.026092529296875,
0.02276611328125,
0.0169830322265625,
-0.00720977783203125,
-0.0025997161865234375,
0.00820159912109375,
-0.00872802734375,
-0.00765228271484375,
-0.01110076904296875,
-0.002376556396484375,
0.0017061233520507812,
-0.009368896484375,
-0.01457977294921875,
0.02886962890625,
-0.0306549072265625,
0.010772705078125,
-0.020172119140625,
0.005435943603515625,
-0.006977081298828125,
-0.023590087890625,
0.01332855224609375,
-0.0097503662109375,
-0.01120758056640625,
0.00476837158203125,
0.007381439208984375,
-0.009033203125,
-0.018463134765625,
-0.0007829666137695312,
-0.00272369384765625,
-0.003635406494140625,
-0.0022220611572265625,
0.00969696044921875,
0.022491455078125,
-0.007442474365234375,
-0.01910400390625,
0.0390625,
-0.01395416259765625,
-0.048431396484375,
-0.01103973388671875,
-0.002719879150390625,
0.026458740234375,
0.018524169921875,
-0.02001953125,
-0.0271453857421875,
-0.0003972053527832031,
-0.0279693603515625,
-0.005611419677734375,
-0.02838134765625,
-0.0008349418640136719,
-0.006366729736328125,
0.0014057159423828125,
0.03472900390625,
-0.0171661376953125,
-0.011383056640625,
-0.00771331787109375,
0.037445068359375,
0.00556182861328125,
-0.0233001708984375,
-0.005054473876953125,
0.048828125,
-0.01318359375,
-0.01447296142578125,
-0.0128021240234375,
-0.003997802734375,
-0.004642486572265625,
-0.0216217041015625,
-0.0208892822265625,
-0.032379150390625,
-0.02435302734375,
0.01084136962890625,
-0.043304443359375,
0.039093017578125,
-0.0196075439453125,
-0.0156097412109375,
-0.00908660888671875,
0.0204010009765625,
-0.018035888671875,
0.01509857177734375,
0.0113677978515625,
-0.0008654594421386719,
0.0029850006103515625,
0.0014476776123046875,
-0.01119232177734375,
0.0182647705078125,
0.017913818359375,
-0.033416748046875,
0.041046142578125,
0.0017614364624023438,
-0.01262664794921875,
0.01255035400390625,
-0.017852783203125,
0.017730712890625,
0.056182861328125,
-0.006885528564453125,
0.01409912109375,
-0.001201629638671875,
-0.041473388671875,
0.027435302734375,
-0.004871368408203125,
-0.039093017578125,
0.03564453125,
-0.019134521484375,
0.0289306640625,
-0.01221466064453125,
-0.0025043487548828125,
-0.0204925537109375,
-0.02374267578125,
0.0016412734985351562,
-0.033355712890625,
-0.01318359375,
0.00316619873046875,
-0.0007596015930175781,
0.004428863525390625,
0.0127105712890625,
0.007572174072265625,
0.00481414794921875,
-0.030029296875,
0.013336181640625,
0.035919189453125,
0.034027099609375,
-0.02447509765625,
-0.02557373046875,
-0.0246124267578125,
0.029083251953125,
-0.00420379638671875,
-0.00864410400390625,
-0.0021839141845703125,
0.012908935546875,
0.0136871337890625,
-0.032012939453125,
-0.01385498046875,
-0.00860595703125,
0.02056884765625,
0.01166534423828125,
0.016448974609375,
0.02264404296875,
0.02099609375,
0.037994384765625,
0.0248565673828125,
-0.00478363037109375,
-0.01340484619140625,
0.01270294189453125,
0.00525665283203125,
0.01885986328125,
0.0038471221923828125,
-0.0294952392578125,
0.01336669921875,
0.0244140625,
-0.009857177734375,
0.0016775131225585938,
0.0159759521484375,
-0.0257568359375,
-0.0173797607421875,
0.0037860870361328125,
-0.01047515869140625,
-0.005886077880859375,
0.04974365234375,
-0.0246124267578125,
-0.0228271484375,
0.0222625732421875,
-0.01399993896484375,
0.00807952880859375,
0.0462646484375,
0.033599853515625,
-0.033935546875,
-0.032440185546875,
0.0032100677490234375,
0.016876220703125,
0.004512786865234375,
-0.01861572265625,
-0.004199981689453125,
-0.041046142578125,
-0.0066070556640625,
0.0214691162109375,
0.0019197463989257812,
-0.01522064208984375,
-0.00008869171142578125,
-0.00676727294921875,
0.0194549560546875,
0.0294189453125,
0.0080108642578125,
-0.010345458984375,
-0.0099029541015625,
0.0200653076171875,
-0.029876708984375,
-0.0274658203125,
0.0120391845703125,
0.00115966796875,
-0.00379180908203125,
-0.005565643310546875,
0.0126800537109375,
-0.030609130859375,
0.0022182464599609375,
-0.0225982666015625,
0.018341064453125,
0.01036834716796875,
0.0024471282958984375,
-0.00711822509765625,
-0.0241546630859375,
0.0291595458984375,
-0.0086669921875,
-0.0124053955078125,
-0.003719329833984375,
0.031951904296875,
-0.01125335693359375,
0.0175933837890625,
0.02752685546875,
-0.0118408203125,
0.00543212890625,
0.0168609619140625,
0.02130126953125,
-0.019989013671875,
0.01328277587890625,
-0.019866943359375,
0.00022876262664794922,
-0.0184173583984375,
0.01458740234375,
-0.01161956787109375,
-0.0230712890625,
-0.0066070556640625,
-0.0283660888671875,
0.0157012939453125,
-0.0226287841796875,
0.00838470458984375,
-0.0081024169921875,
0.01049041748046875,
-0.025634765625,
-0.0030956268310546875,
0.01055908203125,
-0.00687408447265625,
0.0246124267578125,
0.0028972625732421875,
-0.0216217041015625,
-0.0114898681640625,
-0.035125732421875,
-0.0084228515625,
0.026214599609375,
-0.054931640625,
0.01233673095703125,
0.052978515625,
0.01232147216796875,
0.015960693359375,
-0.018096923828125,
0.01959228515625,
0.00286102294921875,
0.0088653564453125,
-0.051116943359375,
-0.0304718017578125,
-0.01491546630859375,
-0.0185394287109375,
-0.0019330978393554688,
0.0119781494140625,
-0.01065826416015625,
-0.0268402099609375,
-0.023834228515625,
0.0009074211120605469,
-0.013336181640625,
-0.003505706787109375,
0.01922607421875,
0.0191192626953125,
0.0170440673828125,
-0.00955963134765625,
0.0233154296875,
-0.024261474609375,
0.021728515625,
-0.00843048095703125,
0.01104736328125,
-0.01702880859375,
0.0270843505859375,
0.006618499755859375,
0.014617919921875,
-0.0014638900756835938,
0.017974853515625,
0.01971435546875,
-0.007541656494140625,
0.0139312744140625,
-0.002979278564453125,
0.01343536376953125,
-0.0080718994140625,
-0.01873779296875,
-0.028656005859375,
-0.0143585205078125,
-0.017791748046875,
-0.006420135498046875,
0.0031452178955078125,
0.031829833984375,
-0.0026187896728515625,
-0.01354217529296875,
0.00856781005859375,
0.0276947021484375,
-0.0150604248046875,
-0.0027942657470703125,
-0.031036376953125,
0.0115814208984375,
-0.0229644775390625,
-0.0206451416015625,
0.01141357421875,
-0.0159149169921875,
0.016510009765625,
-0.0017337799072265625,
0.031982421875,
0.0167999267578125,
-0.007305145263671875,
0.0225830078125,
0.01110076904296875,
0.00601959228515625,
-0.036712646484375,
0.01354217529296875,
-0.0308380126953125,
0.010955810546875,
0.004627227783203125,
0.00164031982421875,
-0.0165252685546875,
-0.0079345703125,
0.0086212158203125,
-0.0107879638671875,
-0.004947662353515625,
0.023651123046875,
0.00756072998046875,
0.00815582275390625,
-0.0282135009765625,
-0.0010509490966796875,
0.0004436969757080078,
0.003810882568359375,
0.0285186767578125,
-0.0276336669921875,
0.0142822265625,
-0.0266876220703125,
-0.045257568359375,
0.0011892318725585938,
-0.0258636474609375,
0.00925445556640625,
0.0012502670288085938,
0.01922607421875,
0.00638580322265625,
-0.037506103515625,
0.01427459716796875,
-0.0136871337890625,
0.0310211181640625,
0.016387939453125,
-0.00330352783203125,
-0.01055908203125,
0.0104827880859375,
0.02215576171875,
0.03704833984375,
0.0008492469787597656,
0.0650634765625,
0.030029296875,
0.0260162353515625,
0.0029659271240234375,
0.0027923583984375,
0.005542755126953125,
-0.0180511474609375,
-0.01317596435546875,
-0.005954742431640625,
-0.00945281982421875,
-0.002811431884765625,
-0.004344940185546875,
0.0303192138671875,
0.017578125,
0.020416259765625,
0.0111541748046875,
0.0042724609375,
-0.06292724609375,
-0.00907135009765625,
-0.0039825439453125,
0.007251739501953125,
-0.0024566650390625,
-0.00888824462890625,
-0.0135040283203125,
0.0021991729736328125,
-0.01184844970703125,
-0.006458282470703125,
0.006336212158203125,
-0.0177001953125,
-0.01551055908203125,
0.0007576942443847656,
-0.0112762451171875,
-0.004909515380859375,
-0.0001800060272216797,
0.012420654296875,
0.0501708984375,
0.00897979736328125,
0.0080718994140625,
0.0007481575012207031,
0.01788330078125,
-0.0094451904296875,
0.01157379150390625,
-0.018035888671875,
-0.0023670196533203125,
0.02557373046875,
-0.0000010132789611816406,
0.0133209228515625,
-0.0006341934204101562,
-0.01934814453125,
0.0238037109375,
0.00814056396484375,
0.0048370361328125,
-0.00007605552673339844,
-0.01505279541015625,
-0.02178955078125,
-0.01491546630859375,
0.0263519287109375,
-0.0180511474609375,
-0.01983642578125,
-0.021881103515625,
0.00933074951171875,
-0.00977325439453125,
0.0241546630859375,
0.0186004638671875,
-0.016387939453125,
-0.00446319580078125,
0.0174102783203125,
0.0031681060791015625,
-0.006023406982421875,
0.0101165771484375,
-0.036468505859375,
-0.0279541015625,
0.009613037109375,
-0.01763916015625,
0.0003199577331542969,
0.0036163330078125,
-0.008087158203125,
-0.0150146484375,
0.0108184814453125,
0.0030689239501953125,
-0.0009055137634277344,
0.01873779296875,
0.0027179718017578125,
-0.03619384765625,
0.0286865234375,
0.01480865478515625,
-0.039794921875,
-0.01654052734375,
-0.008544921875,
0.00423431396484375,
-0.02935791015625,
0.0139007568359375,
0.0031032562255859375,
-0.0101318359375,
-0.0066986083984375,
-0.046051025390625,
-0.01081085205078125,
-0.00815582275390625,
-0.056549072265625,
0.0029163360595703125,
0.012176513671875,
0.01148223876953125,
0.01251983642578125,
-0.00006657838821411133,
0.0009775161743164062,
0.007602691650390625,
-0.021820068359375,
-0.005489349365234375,
-0.003353118896484375,
0.025604248046875,
-0.0180816650390625,
-0.023284912109375,
-0.01511383056640625,
0.013763427734375,
0.041473388671875,
0.028228759765625,
-0.04669189453125,
0.009857177734375,
0.006046295166015625,
0.03924560546875,
0.043609619140625,
-0.0307464599609375,
0.0161285400390625,
-0.00991058349609375,
0.012786865234375,
-0.01023101806640625,
-0.006618499755859375,
-0.002277374267578125,
-0.004558563232421875,
-0.0068206787109375,
0.006183624267578125,
-0.009796142578125,
-0.0213775634765625,
0.0002655982971191406,
0.037811279296875,
0.0004432201385498047,
0.004161834716796875,
-0.01007080078125,
0.00015807151794433594,
0.040008544921875,
-0.01496124267578125,
0.021392822265625,
-0.0228271484375,
0.0027027130126953125,
-0.004741668701171875,
0.0016374588012695312,
0.01415252685546875,
-0.013885498046875,
-0.01348114013671875,
-0.00775909423828125,
-0.0025730133056640625,
-0.0272369384765625,
-0.0007925033569335938,
0.019622802734375,
0.0014057159423828125,
-0.0249786376953125,
-0.02508544921875,
-0.004070281982421875,
0.0263671875,
0.00885772705078125,
-0.0215301513671875,
-0.00699615478515625,
0.00826263427734375,
0.019317626953125,
-0.046112060546875,
0.01371002197265625,
-0.00717926025390625,
-0.009307861328125,
-0.01155853271484375,
-0.0100250244140625,
-0.00695037841796875,
0.05474853515625,
-0.00736236572265625,
-0.0008358955383300781,
0.01183319091796875,
0.03961181640625,
-0.0152130126953125,
-0.04254150390625,
0.0172271728515625,
-0.011260986328125,
-0.003143310546875,
0.01364898681640625,
0.0181121826171875,
0.0001779794692993164,
-0.0190277099609375,
-0.005016326904296875,
-0.01198577880859375,
-0.00099945068359375,
0.03900146484375,
-0.034027099609375,
0.0185394287109375,
0.005420684814453125,
0.00536346435546875,
-0.0225677490234375,
-0.04315185546875,
-0.01247406005859375,
-0.005340576171875,
0.00691986083984375,
-0.038970947265625,
-0.01555633544921875,
0.00905609130859375,
0.05242919921875,
0.0236968994140625,
-0.037445068359375,
-0.040771484375,
-0.060028076171875,
0.0211181640625,
-0.004665374755859375,
0.0204620361328125,
-0.00406646728515625,
0.005329132080078125,
-0.0125579833984375,
-0.013458251953125,
0.0145721435546875,
-0.00183868408203125,
-0.000640869140625,
-0.032257080078125,
-0.01806640625,
-0.033050537109375,
-0.00867462158203125,
0.00009655952453613281,
0.01468658447265625,
-0.006763458251953125,
-0.01885986328125,
-0.0220184326171875,
-0.014892578125,
0.02642822265625,
0.00920867919921875,
-0.01291656494140625,
-0.0006976127624511719,
-0.0157623291015625,
-0.0005850791931152344,
-0.028076171875,
0.0296630859375,
0.004428863525390625,
-0.00792694091796875,
0.01218414306640625,
0.0244598388671875,
0.0207366943359375,
-0.0252685546875,
-0.0027713775634765625,
-0.01141357421875,
0.019378662109375,
0.0033855438232421875,
-0.03399658203125,
0.0103912353515625,
-0.013641357421875,
-0.035064697265625,
0.01238250732421875,
0.0076904296875,
-0.00981903076171875,
-0.00458526611328125,
-0.0078887939453125,
-0.005176544189453125,
0.003993988037109375,
-0.00026297569274902344,
-0.0160980224609375,
-0.011932373046875,
0.037384033203125,
-0.0289306640625,
0.007259368896484375,
-0.00017631053924560547,
-0.046600341796875,
0.004199981689453125,
-0.0235443115234375,
0.0081329345703125,
0.017669677734375,
0.005001068115234375,
0.0006976127624511719,
-0.0099945068359375,
-0.00798797607421875,
-0.0066070556640625,
0.004146575927734375,
0.0177001953125,
0.0201873779296875,
-0.0007014274597167969,
0.029876708984375,
-0.045806884765625,
-0.035064697265625,
-0.0026264190673828125,
-0.0110321044921875,
0.025909423828125,
-0.01311492919921875,
-0.0035495758056640625,
0.0022487640380859375,
-0.00676727294921875,
0.0135040283203125,
0.0207366943359375,
-0.01277923583984375,
0.00958251953125,
0.001079559326171875,
-0.0020294189453125,
0.0088958740234375,
0.0255279541015625,
0.0217132568359375,
-0.01274871826171875,
0.00734710693359375,
0.0215301513671875,
0.00820159912109375
] |
ours_512
|
Extend the sequence to \(F_{-1}, F_{-2}, \ldots\) such that \(F_{n+2}=F_{n+1}+F_{n}\) for all integers \(n\). Note that for all integers \(n\), \(F_{-n}=-(-1)^{n} F_{n}\).
Define the sequence \(X_{n}=F_{n+2020}-F_{n}\). Since \(X_{n}\) satisfies the recurrence \(X_{n}=X_{n-1}+X_{n-2}\), by the Euclidean Algorithm,
\[
\operatorname{gcd}\left(X_{n}, X_{n-1}\right)=\operatorname{gcd}\left(X_{n-1}+X_{n-2}, X_{n-1}\right)=\operatorname{gcd}\left(X_{n-2}, X_{n-1}\right)
\]
so for all \(n\),
\[
d=\operatorname{gcd}\left(X_{n}, X_{n+1}\right)
\]
Taking \(n=-1010\),
\[
d=\operatorname{gcd}\left(F_{1010}-F_{-1010}, F_{1011}-F_{1009}\right)=\operatorname{gcd}\left(2 F_{1010}, F_{1010}\right)=F_{1010}
\]
To compute \(F_{1010}\) modulo 1001, we must compute it modulo 7, 11, and 13. We have
\[
F_{0}, F_{1}, \ldots \equiv 0,1,1,2,3,5,1,6,0,6,6,5,4,2,6,1,0 \quad(\bmod 7)
\]
so it repeats every 16 in modulo 7. Thus,
\[
F_{1010} \equiv F_{1010-63 \cdot 16} \equiv F_{2} \equiv 1 \quad(\bmod 7)
\]
Similarly,
\[
F_{0}, F_{1}, \ldots=0,1,1,2,3,5,8,2,10,1,0,1, \ldots \quad(\bmod 11)
\]
so it repeats every 10 in \((\bmod 11)\), giving
\[
F_{1010} \equiv F_{0} \equiv 0 \quad(\bmod 11)
\]
For \((\bmod 13)\),
\[
F_{0}, F_{1}, \ldots \equiv 0,1,1,2,3,5,8,0,8,8,3,11,1,12,0,12,12,11,10,8,5,0,5,5,10,2,12,1,0,1, \ldots \quad(\bmod 13)
\]
meaning it repeats every 28 in \((\bmod 13)\), giving
\[
F_{1010} \equiv F_{1010-28 \cdot 36} \equiv F_{2} \equiv 1 \quad(\bmod 13)
\]
By the Chinese Remainder Theorem, we can compute the answer as \(638\).
\(\boxed{638}\)
|
638
|
{
"competition": "us_comps",
"dataset": "Ours",
"posts": null,
"source": "OMOFall19Solns.md"
}
|
The sequence of nonnegative integers \(F_{0}, F_{1}, F_{2}, \ldots\) is defined recursively as \(F_{0}=0, F_{1}=1\), and \(F_{n+2}=F_{n+1}+F_{n}\) for all integers \(n \geq 0\). Let \(d\) be the largest positive integer such that, for all integers \(n \geq 0\), \(d\) divides \(F_{n+2020}-F_{n}\). Compute the remainder when \(d\) is divided by \(1001\).
|
[
"/Mathematics/DiscreteMathematics/DivisionProblems/SegnersRecurrenceFormula",
"/Mathematics/DiscreteMathematics/RecurrenceEquations/LinearRecurrenceEquation",
"/Mathematics/DiscreteMathematics/RecurrenceEquations/RecurrenceEquation",
"/Mathematics/DiscreteMathematics/RecurrenceEquations/RecurrenceRelation",
"/Mathematics/DiscreteMathematics/RecurrenceEquations/RecursiveSequence",
"/Mathematics/NumberTheory/Congruences/ChineseRemainderTheorem",
"/Mathematics/NumberTheory/Congruences/Congruence",
"/Mathematics/NumberTheory/Congruences/Mod",
"/Mathematics/NumberTheory/Congruences/ModularArithmetic",
"/Mathematics/NumberTheory/Congruences/PisanoPeriod",
"/Mathematics/NumberTheory/Congruences/Residue",
"/Mathematics/NumberTheory/Divisors/Divides",
"/Mathematics/NumberTheory/Divisors/Divisible",
"/Mathematics/NumberTheory/Divisors/Divisor",
"/Mathematics/NumberTheory/Sequences/FibonacciDualTheorem"
] |
Show the common divisor equals a Fibonacci number by using the recurrence of the differences, then compute that Fibonacci term modulo 1001 via Pisano periods and CRT.
|
[
-0.00017702579498291016,
-0.003246307373046875,
0.048583984375,
0.0092620849609375,
-0.0008788108825683594,
0.02154541015625,
0.02880859375,
-0.033599853515625,
0.01300048828125,
0.019622802734375,
0.028656005859375,
-0.0648193359375,
0.00106048583984375,
0.0274658203125,
-0.053314208984375,
-0.0011930465698242188,
0.008392333984375,
0.0216827392578125,
-0.007080078125,
-0.007518768310546875,
-0.01052093505859375,
0.0036373138427734375,
-0.035919189453125,
0.032470703125,
-0.01233673095703125,
-0.026641845703125,
-0.01959228515625,
0.05828857421875,
0.008056640625,
0.01009368896484375,
-0.00736236572265625,
0.00662994384765625,
-0.01500701904296875,
-0.01568603515625,
0.00206756591796875,
-0.01419830322265625,
-0.04046630859375,
0.0009760856628417969,
0.01375579833984375,
-0.01302337646484375,
0.01224517822265625,
0.0218658447265625,
-0.00772857666015625,
0.0284423828125,
-0.0257415771484375,
0.00035119056701660156,
0.00004225969314575195,
-0.0082244873046875,
-0.00986480712890625,
-0.005939483642578125,
-0.00585174560546875,
0.002010345458984375,
-0.01331329345703125,
-0.0164337158203125,
-0.0355224609375,
-0.03955078125,
0.0182952880859375,
0.00775909423828125,
0.039093017578125,
-0.033447265625,
0.0004096031188964844,
-0.0137176513671875,
-0.036590576171875,
-0.007518768310546875,
-0.008209228515625,
-0.007904052734375,
0.015594482421875,
0.00879669189453125,
0.004360198974609375,
-0.00011146068572998047,
0.04180908203125,
0.00901031494140625,
-0.0246124267578125,
0.031646728515625,
0.035614013671875,
-0.02099609375,
-0.01561737060546875,
0.0216827392578125,
0.029754638671875,
-0.001918792724609375,
0.0011854171752929688,
0.0290069580078125,
0.02349853515625,
0.0233917236328125,
0.0190887451171875,
-0.0122222900390625,
-0.00811767578125,
-0.0031795501708984375,
0.0322265625,
0.0227813720703125,
-0.007488250732421875,
-0.0293426513671875,
0.0022430419921875,
0.01230621337890625,
0.005344390869140625,
0.01113128662109375,
0.0176544189453125,
-0.01392364501953125,
-0.007801055908203125,
0.004802703857421875,
-0.01258087158203125,
-0.0091705322265625,
0.0198211669921875,
-0.008636474609375,
-0.035430908203125,
-0.0027179718017578125,
-0.004638671875,
-0.00763702392578125,
-0.0013713836669921875,
0.0122528076171875,
0.0024547576904296875,
-0.007335662841796875,
0.031524658203125,
0.0009236335754394531,
-0.0109405517578125,
0.0037937164306640625,
0.0186614990234375,
0.019683837890625,
-0.0017299652099609375,
0.004512786865234375,
-0.006744384765625,
0.004367828369140625,
-0.01068115234375,
0.020965576171875,
0.00039124488830566406,
-0.040313720703125,
-0.006137847900390625,
-0.02398681640625,
-0.012969970703125,
0.00791168212890625,
0.003894805908203125,
-0.0037784576416015625,
-0.0244903564453125,
-0.035247802734375,
-0.039825439453125,
0.023681640625,
-0.01042938232421875,
-0.00971221923828125,
-0.005298614501953125,
-0.020599365234375,
-0.003910064697265625,
0.002105712890625,
-0.00045943260192871094,
-0.0176849365234375,
-0.013397216796875,
-0.0276031494140625,
0.0024871826171875,
-0.037933349609375,
0.024993896484375,
-0.004596710205078125,
0.007534027099609375,
-0.0027751922607421875,
0.03192138671875,
0.0193023681640625,
-0.01512908935546875,
0.0213165283203125,
0.0081939697265625,
0.002040863037109375,
-0.0011034011840820312,
0.00690460205078125,
0.01425933837890625,
0.008697509765625,
-0.02838134765625,
0.035064697265625,
0.0128936767578125,
-0.0166473388671875,
-0.0276336669921875,
-0.0282135009765625,
-0.0086212158203125,
-0.0230712890625,
0.01549530029296875,
0.00299835205078125,
0.005512237548828125,
-0.0182037353515625,
0.019989013671875,
-0.0159149169921875,
-0.002895355224609375,
-0.00450897216796875,
0.00116729736328125,
-0.0300140380859375,
0.024932861328125,
-0.03326416015625,
-0.0047149658203125,
-0.0024261474609375,
0.02435302734375,
-0.0287017822265625,
-0.00597381591796875,
0.0032444000244140625,
0.014678955078125,
0.010772705078125,
0.0053558349609375,
-0.0024776458740234375,
0.0225372314453125,
0.0167083740234375,
-0.01495361328125,
-0.01134490966796875,
0.0168304443359375,
0.01715087890625,
0.0304718017578125,
0.0176544189453125,
0.00009143352508544922,
0.021881103515625,
-0.0161590576171875,
0.004863739013671875,
-0.0005698204040527344,
-0.006317138671875,
0.021392822265625,
-0.0097198486328125,
0.0011930465698242188,
-0.00780487060546875,
0.00977325439453125,
-0.005413055419921875,
-0.0080413818359375,
-0.01328277587890625,
-0.0233154296875,
-0.01450347900390625,
-0.00295257568359375,
-0.0016155242919921875,
0.0274810791015625,
-0.016998291015625,
0.0099334716796875,
0.01270294189453125,
0.0021381378173828125,
0.003566741943359375,
-0.01428985595703125,
-0.01105499267578125,
0.0066680908203125,
-0.0150146484375,
-0.002956390380859375,
0.0169830322265625,
0.0197906494140625,
0.0179443359375,
-0.034515380859375,
0.01247406005859375,
0.025848388671875,
-0.0017595291137695312,
0.0263671875,
-0.0108795166015625,
0.00543212890625,
-0.0286407470703125,
-0.01004791259765625,
-0.0206451416015625,
-0.021209716796875,
-0.0017061233520507812,
-0.00699615478515625,
0.00728607177734375,
0.0055694580078125,
0.0017299652099609375,
-0.026031494140625,
-0.005710601806640625,
-0.0231781005859375,
0.0079193115234375,
-0.00095367431640625,
0.0194091796875,
-0.004703521728515625,
0.001964569091796875,
0.007007598876953125,
-0.0287933349609375,
-0.01824951171875,
0.0227508544921875,
-0.0018796920776367188,
-0.01264190673828125,
-0.019561767578125,
-0.0006012916564941406,
-0.0054931640625,
0.005596160888671875,
-0.0258636474609375,
0.0039215087890625,
0.0087432861328125,
-0.002124786376953125,
0.060699462890625,
0.0010194778442382812,
-0.00971221923828125,
0.0003223419189453125,
0.016357421875,
-0.0236358642578125,
-0.01959228515625,
0.00562286376953125,
-0.0177154541015625,
0.0210113525390625,
0.0005402565002441406,
-0.0214691162109375,
0.0111083984375,
0.003635406494140625,
0.0035533905029296875,
-0.0035724639892578125,
-0.016754150390625,
-0.0017032623291015625,
-0.0232086181640625,
0.0020694732666015625,
-0.00506591796875,
-0.0002582073211669922,
-0.01189422607421875,
0.006061553955078125,
0.061187744140625,
-0.01432037353515625,
0.00269317626953125,
0.050079345703125,
-0.00803375244140625,
-0.0217742919921875,
0.033599853515625,
0.006927490234375,
-0.0210723876953125,
-0.005443572998046875,
0.031951904296875,
-0.01256561279296875,
-0.0015134811401367188,
-0.005340576171875,
-0.001216888427734375,
-0.0196685791015625,
0.0028972625732421875,
-0.0131072998046875,
-0.00818634033203125,
-0.0038166046142578125,
-0.0197601318359375,
-0.026214599609375,
0.019866943359375,
0.005054473876953125,
-0.031951904296875,
-0.003879547119140625,
0.007259368896484375,
0.04638671875,
-0.004764556884765625,
0.01102447509765625,
-0.02154541015625,
-0.0157470703125,
0.018310546875,
-0.0222015380859375,
-0.0167999267578125,
0.0189666748046875,
-0.04217529296875,
0.0050506591796875,
0.0170745849609375,
-0.030426025390625,
-0.020477294921875,
0.0138092041015625,
0.0169677734375,
0.00620269775390625,
0.0164642333984375,
-0.0142974853515625,
-0.00009429454803466797,
0.0018148422241210938,
0.0086669921875,
-0.0107574462890625,
-0.0303955078125,
0.00931549072265625,
-0.01290130615234375,
-0.0035686492919921875,
0.0030117034912109375,
-0.003894805908203125,
0.00754547119140625,
0.00984954833984375,
-0.014495849609375,
-0.017120361328125,
0.0033664703369140625,
-0.00763702392578125,
-0.0017795562744140625,
0.021270751953125,
-0.0362548828125,
0.02960205078125,
-0.006206512451171875,
-0.00600433349609375,
-0.0118865966796875,
0.01119232177734375,
-0.006916046142578125,
-0.0212249755859375,
0.0019626617431640625,
-0.0006947517395019531,
-0.0287628173828125,
-0.00785064697265625,
-0.0021381378173828125,
-0.04058837890625,
0.02337646484375,
0.003215789794921875,
-0.02227783203125,
-0.005657196044921875,
-0.00510406494140625,
-0.00058746337890625,
0.0005893707275390625,
-0.0134124755859375,
0.00759124755859375,
0.057952880859375,
-0.018798828125,
0.01012420654296875,
-0.01849365234375,
-0.002811431884765625,
0.0216522216796875,
-0.0157318115234375,
-0.024383544921875,
0.01580810546875,
-0.0013780593872070312,
0.0155029296875,
-0.0200653076171875,
-0.01270294189453125,
-0.0347900390625,
0.0033702850341796875,
-0.00594329833984375,
0.00612640380859375,
0.0252838134765625,
0.004608154296875,
0.0014600753784179688,
-0.016937255859375,
-0.0251007080078125,
0.0182037353515625,
0.00817108154296875,
-0.0194244384765625,
-0.01241302490234375,
-0.01259613037109375,
-0.0159149169921875,
0.0113525390625,
0.0021038055419921875,
0.012939453125,
0.01189422607421875,
-0.0023212432861328125,
0.037139892578125,
-0.00006318092346191406,
-0.0031566619873046875,
-0.0212554931640625,
-0.048431396484375,
-0.01079559326171875,
-0.0174560546875,
-0.033477783203125,
0.023468017578125,
-0.01438140869140625,
-0.0005750656127929688,
0.01171875,
-0.00691986083984375,
0.031951904296875,
0.03857421875,
0.0019054412841796875,
0.001979827880859375,
-0.062286376953125,
0.022064208984375,
0.0291900634765625,
0.0026798248291015625,
0.01111602783203125,
-0.0173797607421875,
0.00672149658203125,
-0.0135955810546875,
0.0221710205078125,
0.0011148452758789062,
-0.0012569427490234375,
0.0157470703125,
-0.0126190185546875,
-0.040924072265625,
-0.00960540771484375,
-0.0197601318359375,
0.005741119384765625,
-0.0035953521728515625,
-0.0165557861328125,
-0.0095367431640625,
0.03466796875,
0.0145111083984375,
-0.010284423828125,
0.012664794921875,
0.025360107421875,
-0.0006570816040039062,
0.0222320556640625,
0.004581451416015625,
-0.007274627685546875,
-0.01349639892578125,
0.0128173828125,
-0.03692626953125,
-0.004604339599609375,
-0.01525115966796875,
-0.0259246826171875,
-0.017242431640625,
-0.025054931640625,
0.0169677734375,
0.0017156600952148438,
-0.0016641616821289062,
0.00213623046875,
0.005001068115234375,
0.0001913309097290039,
-0.044708251953125,
0.02337646484375,
0.0033512115478515625,
0.007617950439453125,
-0.03631591796875,
-0.0206298828125,
-0.0117034912109375,
-0.0139923095703125,
0.0119171142578125,
0.00629425048828125,
-0.0125274658203125,
0.0182342529296875,
0.0284881591796875,
-0.006160736083984375,
0.005519866943359375,
0.021026611328125,
-0.023345947265625,
0.0180816650390625,
-0.0227508544921875,
-0.01580810546875,
-0.029815673828125,
0.0206756591796875,
-0.0225982666015625,
0.0079498291015625,
-0.004840850830078125,
-0.01175689697265625,
-0.00301361083984375,
-0.04278564453125,
-0.03948974609375,
0.0199737548828125,
-0.01270294189453125,
-0.036285400390625,
0.01971435546875,
-0.017303466796875,
0.0213775634765625,
-0.028900146484375,
-0.009521484375,
0.0295867919921875,
0.0005588531494140625,
-0.01971435546875,
0.02471923828125,
0.00888824462890625,
0.019866943359375,
0.039886474609375,
0.0181732177734375,
0.01110076904296875,
0.00870513916015625,
0.041900634765625,
0.0005502700805664062,
-0.00894927978515625,
0.0184326171875,
0.007762908935546875,
0.0245361328125,
-0.0158233642578125,
0.01800537109375,
0.0049285888671875,
-0.0294342041015625,
-0.03155517578125,
-0.0011854171752929688,
0.01201629638671875,
-0.0083770751953125,
0.02197265625,
0.01421356201171875,
0.007373809814453125,
-0.0083770751953125,
0.00249481201171875,
-0.00516510009765625,
0.01125335693359375,
-0.035980224609375,
-0.041229248046875,
-0.00632476806640625,
-0.01013946533203125,
-0.0078277587890625,
0.024932861328125,
-0.006282806396484375,
-0.0133056640625,
-0.006191253662109375,
0.005046844482421875,
0.0005602836608886719,
-0.0010137557983398438,
-0.035919189453125,
0.004695892333984375,
-0.00774383544921875,
-0.01177978515625,
-0.021728515625,
0.01560211181640625,
0.0202178955078125,
0.000469207763671875,
0.0298309326171875,
-0.0215911865234375,
0.02142333984375,
-0.0215606689453125,
-0.0110931396484375,
0.01983642578125,
0.0010366439819335938,
-0.0555419921875,
0.034698486328125,
0.029388427734375,
0.0005145072937011719,
0.003826141357421875,
0.01163482666015625,
-0.0213165283203125,
-0.0034656524658203125,
-0.00982666015625,
0.0168609619140625,
0.0025081634521484375,
-0.0026340484619140625,
0.035552978515625,
-0.0123748779296875,
0.00666046142578125,
0.01210784912109375,
0.00730133056640625,
-0.0084075927734375,
0.0213470458984375,
-0.007587432861328125,
0.00018548965454101562,
-0.0110626220703125,
0.0020542144775390625,
-0.0249176025390625,
0.00644683837890625,
-0.004161834716796875,
-0.0020351409912109375,
-0.00009196996688842773,
0.0179443359375,
0.022064208984375,
-0.033447265625,
0.03277587890625,
-0.0037899017333984375,
-0.0291748046875,
0.006755828857421875,
-0.00980377197265625,
-0.00626373291015625,
-0.0037860870361328125,
0.0148468017578125,
-0.0012340545654296875,
0.0030002593994140625,
0.00673675537109375,
-0.0092010498046875,
-0.006748199462890625,
0.017303466796875,
0.010711669921875,
-0.007602691650390625,
0.01462554931640625,
-0.00910186767578125,
0.00412750244140625,
0.0140228271484375,
-0.02166748046875,
-0.01276397705078125,
-0.013671875,
0.031585693359375,
0.003814697265625,
-0.0175323486328125,
0.0084381103515625,
-0.01389312744140625,
-0.012603759765625,
-0.0099639892578125,
-0.052642822265625,
0.015655517578125,
0.0445556640625,
0.0035400390625,
0.003108978271484375,
0.006191253662109375,
-0.00948333740234375,
0.00414276123046875,
-0.00757598876953125,
-0.028289794921875,
0.01099395751953125,
0.0194091796875,
-0.011505126953125,
-0.0648193359375,
0.001041412353515625,
0.020111083984375,
-0.0172271728515625,
-0.028533935546875,
-0.0426025390625,
0.0252838134765625,
-0.0196990966796875,
0.0001976490020751953,
-0.0189056396484375,
-0.00534820556640625,
0.007518768310546875,
0.006519317626953125,
0.0224151611328125,
0.006290435791015625,
-0.0017709732055664062,
-0.02581787109375,
0.00836181640625,
-0.031280517578125,
0.0098876953125,
-0.0343017578125,
-0.00943756103515625,
0.016998291015625,
-0.0259246826171875,
-0.01506805419921875,
0.0452880859375,
0.00010544061660766602,
-0.00870513916015625,
-0.0252227783203125,
0.0194549560546875,
-0.0255126953125,
-0.004238128662109375,
-0.00363922119140625,
0.007381439208984375,
-0.01079559326171875,
0.017242431640625,
0.013702392578125,
0.007244110107421875,
0.022491455078125,
0.01641845703125,
0.0180511474609375,
0.021942138671875,
0.039703369140625,
-0.017669677734375,
0.00836181640625,
-0.016998291015625,
-0.00629425048828125,
0.0094146728515625,
0.0162353515625,
-0.004589080810546875,
-0.0035247802734375,
0.0078277587890625,
-0.0169677734375,
0.0245819091796875,
-0.00957489013671875,
-0.0236053466796875,
0.0037326812744140625,
0.007061004638671875,
-0.005977630615234375,
0.02618408203125,
0.0145263671875,
-0.009490966796875,
-0.03900146484375,
0.006061553955078125,
-0.01314544677734375,
-0.0615234375,
0.01041412353515625,
-0.0238189697265625,
-0.029449462890625,
-0.01062774658203125,
-0.0192413330078125,
-0.01537322998046875,
0.00789642333984375,
-0.00022554397583007812,
0.0418701171875,
-0.0210418701171875,
-0.0036182403564453125,
-0.044677734375,
0.00008040666580200195,
-0.04571533203125,
-0.01403045654296875,
0.0160675048828125,
0.0352783203125,
-0.016510009765625,
-0.0219573974609375,
-0.0175018310546875,
-0.010406494140625,
-0.00748443603515625,
0.005100250244140625,
-0.0139007568359375,
-0.0008263587951660156,
-0.039764404296875,
0.01654052734375,
0.037567138671875,
-0.01497650146484375,
0.03546142578125,
-0.01483154296875,
0.044647216796875,
0.01531219482421875,
0.02557373046875,
-0.01226806640625,
0.01045989990234375,
0.00682830810546875,
-0.002437591552734375,
-0.014190673828125,
0.018890380859375,
0.027862548828125,
0.046234130859375,
0.0020084381103515625,
0.0141448974609375,
-0.05560302734375,
-0.0048675537109375,
-0.01261138916015625,
0.0214691162109375,
-0.0175933837890625,
-0.0192108154296875,
0.00146484375,
-0.038116455078125,
-0.0086212158203125,
0.008209228515625,
0.0294647216796875,
0.005733489990234375,
-0.031829833984375,
-0.0243072509765625,
-0.001819610595703125,
-0.01390838623046875,
0.00939178466796875,
-0.033050537109375,
0.02032470703125,
0.0152587890625,
-0.0035762786865234375,
-0.0026416778564453125,
-0.0016117095947265625,
-0.03564453125,
0.021331787109375,
0.0399169921875,
-0.010833740234375,
0.0188751220703125,
0.0007319450378417969,
-0.034637451171875,
-0.01715087890625,
-0.0312347412109375,
-0.009124755859375,
0.0208892822265625,
-0.0009889602661132812,
0.02044677734375,
-0.005584716796875,
0.038787841796875,
0.006420135498046875,
0.02447509765625,
-0.026580810546875,
-0.037933349609375,
0.015838623046875,
0.0132598876953125,
0.007526397705078125,
-0.0312042236328125,
-0.0060882568359375,
0.04290771484375,
-0.0291748046875,
0.0030918121337890625,
0.02593994140625,
-0.0028476715087890625,
-0.019012451171875,
0.0036258697509765625,
0.0118560791015625,
-0.03582763671875,
-0.006561279296875,
-0.00534820556640625,
-0.0016269683837890625,
0.055694580078125,
0.00821685791015625,
-0.00363922119140625,
-0.01497650146484375,
0.03411865234375,
-0.0008969306945800781,
0.01036834716796875,
0.033843994140625,
-0.01165771484375,
0.00739288330078125,
-0.0024261474609375,
-0.00543212890625,
0.01088714599609375,
0.007274627685546875,
-0.01514434814453125,
0.032989501953125,
0.037322998046875,
0.005573272705078125,
0.005123138427734375,
0.034210205078125,
-0.0173492431640625,
-0.004795074462890625,
0.01910400390625,
0.007343292236328125,
-0.0076904296875,
0.0175628662109375,
-0.011993408203125,
-0.0021266937255859375,
0.0236663818359375,
-0.0063934326171875,
0.0094757080078125,
-0.0257415771484375,
0.0007085800170898438,
-0.04010009765625,
-0.01184844970703125,
0.00711822509765625,
0.0038604736328125,
-0.02996826171875,
0.0203857421875,
-0.00376129150390625,
-0.018768310546875,
-0.0033092498779296875,
-0.01393890380859375,
0.0309906005859375,
-0.01348114013671875,
-0.00583648681640625,
-0.0029888153076171875,
-0.041595458984375,
0.0205841064453125,
-0.00736236572265625,
0.0007662773132324219,
-0.015167236328125,
-0.0284423828125,
0.02215576171875,
-0.00455474853515625,
0.01451873779296875,
0.01806640625,
-0.01395416259765625,
0.004150390625,
0.024993896484375,
0.005931854248046875,
-0.018096923828125,
-0.01381683349609375,
-0.0014591217041015625,
-0.0178680419921875,
-0.0097198486328125,
-0.01168060302734375,
0.0161285400390625,
0.01025390625,
-0.028167724609375,
0.0053863525390625,
0.007061004638671875,
-0.03717041015625,
-0.003795623779296875,
0.0041656494140625,
0.020263671875,
0.0193939208984375,
-0.0158843994140625,
0.013671875,
-0.0168609619140625,
0.038726806640625,
-0.006500244140625,
-0.0015935897827148438,
0.00020062923431396484,
0.004611968994140625,
0.00916290283203125,
0.0147552490234375,
-0.0291900634765625,
-0.00356292724609375,
0.0036792755126953125,
0.0015039443969726562,
-0.01197052001953125,
-0.0013942718505859375,
-0.0247955322265625,
-0.024810791015625,
-0.0294952392578125,
0.0240478515625,
-0.00627899169921875,
0.0025997161865234375,
0.0231781005859375,
0.0025463104248046875,
0.014801025390625,
-0.041473388671875,
-0.01242828369140625,
-0.0027294158935546875,
0.007259368896484375,
0.01255035400390625,
-0.0013437271118164062,
-0.01226043701171875,
-0.00582122802734375,
0.024749755859375,
-0.0120086669921875,
-0.00807952880859375,
0.02740478515625,
-0.0062713623046875,
0.0176239013671875,
-0.049407958984375,
0.0141448974609375,
-0.0308074951171875,
0.0347900390625,
-0.0268096923828125,
0.0189361572265625,
0.0031948089599609375,
0.02874755859375,
0.0095672607421875,
0.018157958984375,
0.004505157470703125,
0.037567138671875,
-0.033782958984375,
0.00856781005859375,
0.04449462890625,
-0.0017681121826171875,
0.040863037109375,
0.007793426513671875,
-0.0154876708984375,
-0.0170745849609375,
-0.029388427734375,
-0.02099609375,
-0.0275726318359375,
-0.022918701171875,
-0.003856658935546875,
0.0276947021484375,
-0.0009984970092773438,
-0.00585174560546875,
-0.0193634033203125,
-0.005748748779296875,
0.01629638671875,
-0.022247314453125,
0.014984130859375,
0.00687408447265625,
-0.037933349609375,
0.0112762451171875,
0.00728607177734375,
0.017608642578125,
0.0027828216552734375,
0.012481689453125,
0.0191497802734375,
0.01169586181640625,
-0.031494140625,
-0.01439666748046875,
-0.0181884765625,
-0.02117919921875,
0.0245361328125,
-0.00872802734375,
-0.0206451416015625,
0.00669097900390625,
0.0245208740234375,
0.00984954833984375,
-0.00860595703125,
0.0285491943359375,
-0.0144500732421875,
-0.01580810546875,
-0.0004715919494628906,
0.06378173828125,
0.0152435302734375,
0.0047607421875,
-0.0007686614990234375,
0.00006026029586791992,
-0.012481689453125,
0.05157470703125,
-0.028228759765625,
0.0185546875,
0.028533935546875,
0.0169677734375,
-0.0231781005859375,
-0.01091766357421875,
-0.02001953125,
-0.00023257732391357422,
-0.02734375,
0.0009365081787109375,
-0.004619598388671875,
0.012725830078125,
-0.004062652587890625,
-0.0096893310546875,
0.024444580078125,
0.040191650390625,
0.011474609375,
0.01488494873046875,
-0.01447296142578125,
-0.0187835693359375,
-0.02142333984375,
-0.0034961700439453125,
0.01119232177734375,
-0.0081787109375,
0.0024394989013671875,
-0.0167236328125,
-0.0355224609375,
-0.0085906982421875,
0.0185546875,
0.025909423828125,
-0.0323486328125,
-0.00046706199645996094,
-0.01336669921875,
0.017486572265625,
-0.0097503662109375,
0.004016876220703125,
0.005889892578125,
0.003627777099609375,
0.0227508544921875,
-0.035400390625,
0.0017528533935546875,
-0.006195068359375,
-0.0121002197265625,
-0.01543426513671875,
-0.0189208984375,
0.00865936279296875,
0.01824951171875,
0.0025806427001953125,
-0.003002166748046875,
0.0418701171875,
0.0017757415771484375,
0.02203369140625,
0.01386260986328125,
-0.021209716796875,
0.011138916015625,
0.018035888671875,
-0.01392364501953125,
-0.0193939208984375,
0.01013946533203125,
0.0146484375,
-0.0146484375,
-0.0139617919921875,
0.0152130126953125,
-0.0005059242248535156,
0.036773681640625,
-0.01537322998046875,
-0.01934814453125,
0.020965576171875,
0.021331787109375,
-0.0102691650390625,
-0.032623291015625,
-0.03802490234375,
-0.0250396728515625,
0.0174102783203125,
0.00925445556640625,
-0.006809234619140625,
0.0170135498046875,
-0.00968170166015625,
-0.0031375885009765625,
-0.0032958984375,
-0.01071929931640625,
-0.020233154296875,
0.020111083984375,
0.0011434555053710938,
0.01238250732421875,
-0.0220489501953125,
-0.020355224609375,
-0.01233673095703125,
-0.007274627685546875,
-0.008392333984375,
-0.0462646484375,
-0.01105499267578125,
0.00545501708984375,
-0.021148681640625,
-0.007236480712890625,
-0.0203094482421875,
-0.01007843017578125,
-0.00904083251953125,
-0.02716064453125,
-0.0205535888671875,
-0.004871368408203125,
0.00787353515625,
0.0008912086486816406,
-0.031402587890625,
-0.02484130859375,
0.004795074462890625,
-0.015625,
0.0006690025329589844,
0.0131683349609375,
0.00891876220703125,
0.0213775634765625,
-0.0089874267578125,
0.00711822509765625,
0.00908660888671875,
-0.0190277099609375,
0.0213623046875,
-0.01308441162109375,
-0.0159454345703125,
0.00803375244140625,
0.0202789306640625,
-0.013427734375,
-0.0012121200561523438,
-0.0025787353515625,
0.0015268325805664062,
-0.0287933349609375,
0.004901885986328125,
-0.042510986328125,
-0.0166015625,
0.007381439208984375,
0.040252685546875,
0.00665283203125,
0.0038089752197265625,
0.0025081634521484375,
0.0120086669921875,
-0.00287628173828125,
-0.01275634765625,
-0.0283355712890625,
0.0228118896484375,
-0.01450347900390625,
0.0240478515625,
0.00969696044921875,
-0.028472900390625,
-0.0164947509765625,
0.00867462158203125,
-0.0205535888671875,
0.0176544189453125,
0.026123046875,
0.00579833984375,
0.01181793212890625,
-0.01218414306640625,
0.006805419921875,
-0.0008950233459472656,
-0.0184478759765625,
-0.00021696090698242188,
0.006267547607421875,
0.0200042724609375,
0.002109527587890625,
0.0125579833984375,
0.00592803955078125,
0.0144805908203125,
-0.0290985107421875,
0.01580810546875,
-0.0013265609741210938,
0.0296173095703125,
-0.0248260498046875,
0.0134124755859375,
-0.00783538818359375,
-0.004444122314453125,
-0.00902557373046875,
-0.030609130859375,
0.027191162109375,
0.0139312744140625,
-0.0260162353515625,
0.019775390625,
-0.005725860595703125,
0.0020313262939453125,
-0.06549072265625,
0.005825042724609375,
0.00043702125549316406,
-0.01102447509765625,
-0.0030155181884765625,
0.007080078125,
-0.014495849609375,
0.0035228729248046875,
0.022979736328125,
-0.01419830322265625,
-0.0245819091796875,
-0.003055572509765625,
-0.015869140625,
0.0082244873046875,
0.0023174285888671875,
-0.022979736328125,
0.038116455078125,
-0.003147125244140625,
-0.027557373046875,
0.0142059326171875,
0.0426025390625,
0.01192474365234375,
0.0138702392578125,
-0.006740570068359375,
-0.0013856887817382812,
0.0175933837890625,
-0.00864410400390625,
0.003505706787109375,
-0.029144287109375,
0.01314544677734375,
-0.0036220550537109375,
-0.0197296142578125,
-0.0171356201171875,
0.034759521484375,
-0.0024662017822265625,
-0.006351470947265625,
0.00677490234375,
0.010650634765625,
-0.004535675048828125,
0.0312347412109375,
-0.0242919921875,
0.0083160400390625,
-0.00124359130859375,
0.0198516845703125,
-0.007320404052734375,
-0.0201416015625,
0.0116729736328125,
-0.04034423828125,
0.0281829833984375,
0.0153350830078125,
-0.00795745849609375,
-0.016204833984375,
0.004364013671875,
-0.01332855224609375,
-0.033905029296875,
0.0193634033203125,
0.0036258697509765625,
-0.01038360595703125,
-0.019866943359375,
0.04296875,
0.00795745849609375,
0.004306793212890625,
-0.0114288330078125,
-0.045166015625,
-0.0194244384765625,
0.01430511474609375,
-0.01348876953125,
-0.0218353271484375,
0.011383056640625,
0.039276123046875,
0.00336456298828125,
0.02581787109375,
-0.0173492431640625,
0.045440673828125,
0.01422882080078125,
-0.0164794921875,
0.041961669921875,
-0.039947509765625,
-0.0238494873046875,
0.0167388916015625,
-0.00493621826171875,
0.00589752197265625,
-0.0049896240234375,
0.032745361328125,
-0.01557159423828125,
-0.00424957275390625,
-0.0136260986328125,
-0.02325439453125,
0.0175933837890625,
0.0171966552734375,
-0.01155853271484375,
-0.00335693359375,
-0.040008544921875,
-0.003330230712890625,
-0.036346435546875,
-0.0113983154296875,
0.00562286376953125,
-0.003299713134765625,
0.0016384124755859375,
0.0311279296875,
-0.004085540771484375,
0.020599365234375,
-0.007724761962890625,
-0.010711669921875,
0.027923583984375,
0.034942626953125,
-0.005298614501953125,
0.017913818359375,
-0.0091552734375,
-0.028045654296875,
0.01490020751953125,
0.0186920166015625,
-0.0030803680419921875,
0.03179931640625,
0.0457763671875,
0.0028285980224609375,
-0.0143585205078125,
-0.05426025390625,
-0.0272064208984375,
-0.007587432861328125,
-0.0241851806640625,
0.01332855224609375,
0.013214111328125,
-0.049102783203125,
0.005870819091796875,
7.152557373046875e-7,
0.00930023193359375,
0.034637451171875,
0.000408172607421875,
-0.0022640228271484375,
-0.0098114013671875,
0.0167999267578125,
-0.018646240234375,
-0.039337158203125,
0.019256591796875,
0.0157012939453125,
-0.01438140869140625,
0.00952911376953125,
0.0112762451171875,
0.002777099609375,
0.0054931640625,
0.003582000732421875,
-0.005115509033203125,
-0.0220489501953125,
-0.009429931640625,
0.0196990966796875,
0.019927978515625,
-0.01513671875,
-0.01430511474609375,
0.0006656646728515625,
-0.0272216796875,
0.0006532669067382812,
-0.0090484619140625,
0.0217132568359375,
-0.008697509765625,
0.0095672607421875,
0.0369873046875,
0.021759033203125,
-0.0251007080078125,
0.01494598388671875,
-0.0128936767578125,
-0.017578125,
-0.01155853271484375,
-0.0184478759765625,
-0.0214385986328125,
-0.0189056396484375,
-0.0245361328125,
-0.0019445419311523438,
0.01177215576171875,
0.034454345703125,
0.02508544921875,
-0.00689697265625,
-0.0447998046875,
-0.0167388916015625,
-0.0367431640625,
0.01224517822265625,
0.00972747802734375,
0.0181427001953125,
-0.04742431640625,
-0.0168304443359375,
0.0114898681640625,
-0.0205078125,
-0.00019216537475585938,
0.0025482177734375,
0.0400390625,
0.0199432373046875,
-0.00485992431640625,
-0.0246124267578125,
-0.00582122802734375,
0.026519775390625,
0.01094818115234375,
0.0006303787231445312,
0.0229949951171875,
-0.0210723876953125,
0.0112457275390625,
-0.027557373046875,
0.0180816650390625,
0.0274200439453125,
-0.0215911865234375,
0.00988006591796875,
0.0190887451171875,
-0.023895263671875,
-0.0265655517578125,
0.035247802734375,
-0.018463134765625,
0.003170013427734375,
0.021087646484375,
-0.01047515869140625,
-0.023895263671875,
-0.038482666015625,
-0.0285186767578125,
0.0177001953125,
0.01497650146484375,
-0.0209197998046875,
-0.00881195068359375,
-0.04327392578125,
-0.00876617431640625,
0.0175628662109375,
-0.004299163818359375,
0.04974365234375,
0.013916015625,
-0.020416259765625,
0.02783203125,
0.01108551025390625,
0.006908416748046875,
-0.031463623046875,
0.0217132568359375,
-0.01464080810546875,
0.019073486328125,
-0.01739501953125,
-0.00963592529296875,
0.04351806640625,
0.023956298828125,
0.006809234619140625,
-0.00440216064453125,
0.0113525390625,
-0.0017147064208984375,
-0.0240478515625,
0.024200439453125,
-0.0114288330078125,
0.02362060546875,
0.003997802734375,
-0.0047149658203125,
-0.011993408203125,
0.004894256591796875,
-0.04949951171875,
-0.005054473876953125,
-0.025543212890625,
0.014923095703125,
-0.016448974609375,
0.01021575927734375,
0.01035308837890625,
-0.02569580078125,
-0.023040771484375,
-0.007152557373046875,
0.0080413818359375,
-0.0200042724609375,
0.0029010772705078125,
-0.0062713623046875,
-0.0235595703125,
-0.01113128662109375,
-0.01427459716796875,
0.0034637451171875,
0.0017080307006835938,
-0.0297393798828125,
0.0005950927734375,
-0.0160064697265625,
-0.01045989990234375,
0.01690673828125,
-0.00666046142578125,
0.0217742919921875,
0.0264434814453125,
-0.0135040283203125,
-0.019012451171875,
0.01207733154296875,
0.0245361328125,
-0.0035381317138671875,
0.006359100341796875,
-0.0195770263671875,
0.0364990234375,
-0.0027179718017578125,
-0.0247955322265625,
-0.0158233642578125,
-0.0099639892578125,
0.0174713134765625,
0.0164794921875,
0.00505828857421875,
-0.009735107421875,
0.00966644287109375,
0.0190887451171875,
0.035919189453125,
-0.0256805419921875,
-0.0012884140014648438,
0.0036716461181640625,
0.0050048828125,
-0.0034160614013671875,
0.021270751953125,
-0.01139068603515625,
0.030914306640625,
0.0007605552673339844,
0.0228424072265625,
0.0096435546875,
-0.004360198974609375,
-0.034454345703125,
-0.005634307861328125,
-0.0011644363403320312,
-0.0110321044921875,
-0.00988006591796875,
0.019805908203125,
0.0015783309936523438,
0.01247406005859375,
-0.03717041015625,
0.007030487060546875,
0.01202392578125,
0.0183563232421875,
0.05181884765625,
0.0022125244140625,
-0.0189361572265625,
0.01299285888671875,
-0.0313720703125,
-0.00966644287109375,
-0.00719451904296875,
-0.00156402587890625,
-0.0005221366882324219,
0.0175933837890625,
0.035186767578125,
0.00748443603515625,
0.022430419921875,
-0.016998291015625,
-0.011566162109375,
-0.00409698486328125,
-0.03094482421875,
0.02520751953125,
0.0005769729614257812,
-0.00846099853515625,
-0.0241851806640625,
0.033477783203125,
-0.020965576171875,
-0.005504608154296875,
-0.01155853271484375,
0.0175323486328125,
-0.0127105712890625,
0.004619598388671875,
-0.00225067138671875,
-0.006237030029296875,
0.005584716796875,
-0.037628173828125,
-0.0135345458984375,
0.00897216796875,
-0.0183868408203125,
-0.00926971435546875,
-0.024627685546875,
0.0194091796875,
-0.032196044921875,
0.005207061767578125,
-0.004180908203125,
0.00873565673828125,
-0.0182647705078125,
0.01461029052734375,
-0.0355224609375,
-0.004093170166015625,
0.0231781005859375,
0.018829345703125,
-0.0260009765625,
-0.01580810546875,
0.004547119140625,
0.0284881591796875,
0.0291290283203125,
0.04486083984375,
0.002849578857421875,
-0.0166473388671875,
-0.005359649658203125,
0.016204833984375,
-0.007488250732421875,
-0.0136566162109375,
0.021026611328125,
0.01274871826171875,
0.0124664306640625,
0.0269775390625,
0.0024242401123046875,
0.0005955696105957031,
0.020294189453125,
0.0474853515625,
-0.01708984375,
0.0263671875,
0.0030517578125,
-0.03594970703125,
0.027862548828125,
-0.0197296142578125,
0.03961181640625,
0.0034122467041015625,
-0.054779052734375,
0.0032787322998046875,
-0.001247406005859375,
0.03448486328125,
0.015594482421875,
0.006252288818359375,
-0.00250244140625,
-0.00319671630859375,
-0.0016880035400390625,
-0.0099334716796875,
-0.0092926025390625,
-0.01209259033203125,
-0.004180908203125,
0.005237579345703125,
0.0275726318359375,
-0.0238494873046875,
-0.0082855224609375,
0.01800537109375,
-0.03131103515625,
-0.03497314453125,
-0.00560760498046875,
-0.01529693603515625,
-0.00444793701171875,
-0.01312255859375,
0.0015659332275390625,
0.0213470458984375,
-0.00693511962890625,
-0.01222991943359375,
0.0238189697265625,
-0.01136016845703125,
0.0042877197265625,
0.02557373046875,
0.003631591796875,
-0.0088653564453125,
-0.008148193359375,
-0.015716552734375,
0.0031280517578125,
0.022705078125,
0.03509521484375,
0.0007953643798828125,
-0.0034580230712890625,
-0.01216888427734375,
-0.0100555419921875,
-0.019927978515625,
-0.010223388671875,
-0.01258087158203125,
0.007648468017578125,
0.02532958984375,
0.0255126953125,
-0.000988006591796875,
0.005626678466796875,
0.00235748291015625,
-0.019775390625,
0.0165557861328125,
0.0006632804870605469,
-0.0296630859375,
0.01444244384765625,
0.00972747802734375,
0.014923095703125,
0.00225830078125,
0.0279083251953125,
0.040740966796875,
-0.0003178119659423828,
-0.01715087890625,
-0.0009093284606933594,
0.0273590087890625,
0.00592041015625,
0.0205535888671875,
-0.00203704833984375,
-0.046051025390625,
-0.0192718505859375,
0.043548583984375,
0.00252532958984375,
-0.05914306640625,
0.03179931640625,
-0.01325225830078125,
0.00153350830078125,
0.026458740234375,
0.03375244140625,
0.0182342529296875,
0.022918701171875,
-0.007007598876953125,
-0.0206146240234375,
0.012725830078125,
-0.0567626953125,
-0.004695892333984375,
0.0218505859375,
0.033538818359375,
0.0257568359375,
-0.006381988525390625,
-0.0009813308715820312,
0.0236968994140625,
0.03765869140625,
-0.00811004638671875,
0.021484375,
0.002628326416015625,
-0.0269317626953125,
-0.003955841064453125,
-0.00264739990234375,
0.0074310302734375,
0.0077056884765625,
0.0144500732421875,
0.00299835205078125,
0.0233154296875,
0.00458526611328125,
-0.02069091796875,
-0.0008373260498046875,
0.00708770751953125,
-0.00537872314453125,
-0.0167694091796875,
0.0084991455078125,
-0.0151214599609375,
0.00011777877807617188,
-0.0006914138793945312,
0.03143310546875,
-0.0169830322265625,
0.010040283203125,
-0.0211181640625,
0.0108184814453125,
0.0000737905502319336,
-0.01461029052734375,
-0.016143798828125,
-0.03302001953125,
-0.0013113021850585938,
-0.00142669677734375,
-0.006031036376953125,
0.0023365020751953125,
0.00026679039001464844,
-0.00598907470703125,
-0.0014848709106445312,
0.0014247894287109375,
0.0362548828125,
-0.007381439208984375,
-0.00628662109375,
0.0180816650390625,
0.051910400390625,
0.0028533935546875,
0.0013484954833984375,
-0.01183319091796875,
0.0096282958984375,
0.018524169921875,
0.018463134765625,
0.00197601318359375,
0.0218048095703125,
-0.04034423828125,
0.035736083984375,
0.0194549560546875,
-0.0214691162109375,
0.01161956787109375,
0.0005011558532714844,
-0.020416259765625,
-0.0015306472778320312,
-0.0194549560546875,
-0.031494140625,
0.0027751922607421875,
0.0008587837219238281,
0.0014371871948242188,
0.0099639892578125,
0.0347900390625,
0.01885986328125,
-0.033050537109375,
-0.0032100677490234375,
0.0012340545654296875,
-0.004520416259765625,
0.01175689697265625,
-0.01119232177734375,
-0.01396942138671875,
0.0179901123046875,
0.000873565673828125,
0.0206298828125,
-0.009674072265625,
0.002872467041015625,
-0.000598907470703125,
0.0083465576171875,
-0.0199737548828125,
0.0258636474609375,
-0.0264129638671875,
0.013885498046875,
0.004009246826171875,
-0.0009369850158691406,
-0.006130218505859375,
-0.0323486328125,
0.0277099609375,
0.01029205322265625,
-0.004276275634765625,
-0.002452850341796875,
-0.024627685546875,
0.0017271041870117188,
0.0235595703125,
-0.0044403076171875,
-0.00830078125,
-0.0028820037841796875,
-0.00859832763671875,
0.035186767578125,
-0.00440216064453125,
-0.017333984375,
0.021453857421875,
-0.01142120361328125,
-0.043212890625,
-0.0051116943359375,
-0.0169677734375,
-0.01052093505859375,
-0.0240478515625,
-0.0038127899169921875,
0.007457733154296875,
0.01202392578125,
0.0002925395965576172,
0.039825439453125,
-0.007411956787109375,
-0.01273345947265625,
-0.01387786865234375,
-0.00435638427734375,
-0.0029697418212890625,
0.030120849609375,
0.0170745849609375,
0.0033702850341796875,
-0.01507568359375,
0.01343536376953125,
-0.00540924072265625,
-0.001190185546875,
-0.01287078857421875,
-0.0017910003662109375,
0.0238800048828125,
0.0333251953125,
-0.01206207275390625,
0.018585205078125,
0.00794219970703125,
0.0152130126953125,
-0.01461029052734375,
-0.0130615234375,
0.01055145263671875,
-0.01485443115234375,
-0.0005502700805664062,
0.00469207763671875,
-0.005886077880859375,
-0.0165863037109375,
0.0129547119140625,
-0.00011283159255981445,
0.033477783203125,
-0.0120391845703125,
0.01313018798828125,
0.002460479736328125,
0.0115966796875,
0.018096923828125,
-0.00795745849609375,
0.019317626953125,
-0.012542724609375,
-0.0067901611328125,
0.00982666015625,
0.01258087158203125,
0.0120391845703125,
-0.019073486328125,
-0.002864837646484375,
0.00421905517578125,
0.0032215118408203125,
0.0013036727905273438,
-0.01861572265625,
0.0182037353515625,
0.00884246826171875,
-0.0019855499267578125,
-0.019073486328125,
-0.00977325439453125,
0.018341064453125,
0.0157470703125,
0.0038928985595703125,
-0.02020263671875,
-0.012176513671875,
0.020782470703125,
0.01311492919921875,
-0.0209503173828125,
0.0285186767578125,
0.0026493072509765625,
0.01898193359375,
0.01010894775390625,
-0.021392822265625,
0.0249786376953125,
-0.0036773681640625,
-0.0240020751953125,
0.0005903244018554688,
-0.00771331787109375,
0.0212860107421875,
0.01482391357421875,
0.0435791015625,
0.0010833740234375,
-0.007099151611328125,
0.0250244140625,
0.005275726318359375,
0.003475189208984375,
0.0028076171875,
0.009735107421875,
0.00262451171875,
0.03887939453125,
-0.033660888671875,
0.006252288818359375,
0.045013427734375,
-0.0179443359375,
0.01007843017578125,
0.00945281982421875,
0.001468658447265625,
-0.01404571533203125,
-0.00833892822265625,
-0.01995849609375,
-0.0159912109375,
-0.01464080810546875,
-0.0025730133056640625,
-0.0084686279296875,
-0.0008516311645507812,
-0.012176513671875,
-0.032012939453125,
-0.01552581787109375,
-0.0004558563232421875,
0.020050048828125,
0.01453399658203125,
-0.036376953125,
0.0296630859375,
0.017059326171875,
-0.00762939453125,
0.006778717041015625,
-0.0139312744140625,
0.01021575927734375,
-0.008392333984375,
-0.032196044921875,
0.00498199462890625,
-0.007843017578125,
-0.0204620361328125,
0.02978515625,
-0.01053619384765625,
0.021392822265625,
0.0277557373046875,
-0.0035419464111328125,
0.0069427490234375,
0.00754547119140625,
-0.0013589859008789062,
0.025177001953125,
-0.0185699462890625,
-0.000012576580047607422,
0.003753662109375,
-0.03125,
0.0279693603515625,
-0.0002739429473876953,
0.02294921875,
-0.00127410888671875,
0.0076446533203125,
-0.0208892822265625,
-0.0008363723754882812,
-0.0236968994140625,
0.0046539306640625,
-0.0186614990234375,
-0.042205810546875,
0.0285491943359375,
0.01003265380859375,
-0.0275726318359375,
-0.0207977294921875,
-0.047027587890625,
0.0258026123046875,
-0.017578125,
0.041229248046875,
0.016693115234375,
0.0209197998046875,
-0.027496337890625,
0.0105743408203125,
0.0110321044921875,
-0.007579803466796875,
0.0271759033203125,
0.0091552734375,
0.002620697021484375,
0.00998687744140625,
-0.01055908203125,
0.0126953125,
-0.003757476806640625,
0.001956939697265625,
-0.0081787109375,
0.020050048828125,
-0.002223968505859375,
-0.0325927734375,
-0.00811767578125,
0.0025730133056640625,
0.01471710205078125,
0.00829315185546875,
0.01496124267578125,
0.011749267578125,
0.015838623046875,
0.00197601318359375,
0.006603240966796875,
-0.0172882080078125,
0.0102691650390625,
-0.00740814208984375,
0.03271484375,
-0.00748443603515625,
-0.0016927719116210938,
-0.017913818359375,
-0.0104217529296875,
0.0284881591796875,
-0.01551055908203125,
-0.01543426513671875,
-0.0210723876953125,
0.0058746337890625,
0.03216552734375,
0.004673004150390625,
-0.002468109130859375,
0.026641845703125,
0.0021495819091796875,
-0.00714874267578125,
-0.032257080078125,
-0.0164947509765625,
-0.01776123046875,
-0.01224517822265625,
0.00402069091796875,
-0.0234832763671875,
-0.022308349609375,
-0.01727294921875,
-0.005634307861328125,
-0.0174102783203125,
-0.0024089813232421875,
0.00791168212890625,
0.033538818359375,
-0.041717529296875,
0.006134033203125,
0.0121307373046875,
0.01445770263671875,
-0.032470703125,
-0.003574371337890625,
-0.022674560546875,
0.0115966796875,
-0.009735107421875,
-0.0248565673828125,
-0.01177215576171875,
0.024810791015625,
-0.0107269287109375,
0.013916015625,
0.016510009765625,
0.0092010498046875,
-0.024566650390625,
0.0212860107421875,
-0.00284576416015625,
0.0143280029296875,
0.0245361328125,
0.0123138427734375,
-0.004184722900390625,
-0.00853729248046875,
-0.0110626220703125,
-0.006702423095703125,
0.03228759765625,
0.01334381103515625,
-0.044036865234375,
0.032684326171875,
0.0035610198974609375,
-0.0149688720703125,
0.0286712646484375,
-0.002376556396484375,
-0.0208740234375,
-0.03387451171875,
-0.04949951171875,
-0.003932952880859375,
-0.00826263427734375,
-0.0073394775390625,
-0.003299713134765625,
-0.0267333984375,
0.027618408203125,
-0.00995635986328125,
0.0008029937744140625,
-0.0228271484375,
0.017791748046875,
-0.0260467529296875,
-0.035736083984375,
-0.0027179718017578125,
0.02337646484375,
0.013427734375,
0.0190582275390625,
-0.03076171875,
-0.021636962890625,
-0.0241851806640625,
-0.028533935546875,
0.019378662109375,
0.043182373046875,
0.0087127685546875,
-0.0002560615539550781,
-0.01446533203125,
-0.003063201904296875,
0.0270233154296875,
-0.0256805419921875,
0.004268646240234375,
-0.00785064697265625,
0.01213836669921875,
0.0009679794311523438,
-0.031036376953125,
-0.0172576904296875,
0.042816162109375,
-0.0195770263671875,
0.005809783935546875,
0.00862884521484375,
0.0258636474609375,
0.017608642578125,
-0.01206207275390625,
-0.0002593994140625,
-0.004421234130859375,
-0.0048370361328125,
0.036163330078125,
0.00713348388671875,
-0.0009036064147949219,
0.038787841796875,
-0.0169830322265625,
0.044189453125,
0.01007080078125,
-0.0045166015625,
0.00457763671875,
0.019134521484375,
-0.040130615234375,
-0.046295166015625,
-0.0201873779296875,
0.0005016326904296875,
-0.005329132080078125,
-0.00209808349609375,
-0.00884246826171875,
-0.022216796875,
0.0008077621459960938,
-0.002864837646484375,
0.0204010009765625,
0.003910064697265625,
0.0031909942626953125,
-0.00023412704467773438,
-0.017822265625,
0.00839996337890625,
0.01812744140625,
0.00928497314453125,
0.0016384124755859375,
-0.007610321044921875,
-0.040679931640625,
-0.00408935546875,
0.0186767578125,
-0.0203704833984375,
-0.0125885009765625,
0.01477813720703125,
0.011474609375,
0.00858306884765625,
0.0019073486328125,
-0.0008912086486816406,
0.01288604736328125,
0.0157928466796875,
0.0343017578125,
-0.047332763671875,
-0.0289306640625,
0.0200347900390625,
-0.01068878173828125,
-0.0216064453125,
-0.0250091552734375,
0.016021728515625,
0.0010995864868164062,
0.002437591552734375,
0.0041961669921875,
0.0013151168823242188,
-0.0203857421875,
0.00457000732421875,
-0.01251220703125,
-0.008819580078125,
0.03106689453125,
-0.00521087646484375,
0.0172882080078125,
-0.021697998046875,
0.010345458984375,
-0.01146697998046875,
0.01171112060546875,
0.01160430908203125,
-0.00658416748046875,
0.01763916015625,
-0.0015411376953125,
-0.0182037353515625,
-0.0253753662109375,
0.040008544921875,
-0.00383758544921875,
0.020111083984375,
-0.0215301513671875,
0.0169677734375,
-0.00545501708984375,
-0.037872314453125,
-0.004486083984375,
0.035400390625,
0.036651611328125,
-0.003963470458984375,
0.00414276123046875,
0.00434112548828125,
-0.003757476806640625,
-0.0181427001953125,
0.01290130615234375,
-0.01059722900390625,
0.0040435791015625,
-0.0034160614013671875,
0.014434814453125,
0.0267333984375,
0.02301025390625,
0.01052093505859375,
-0.00586700439453125,
0.02960205078125,
-0.052337646484375,
-0.00542449951171875,
0.0254669189453125,
-0.01345062255859375,
0.00821685791015625,
-0.0216064453125,
-0.0030918121337890625,
0.0225982666015625,
-0.0206451416015625,
-0.016387939453125,
-0.035858154296875,
-0.033447265625,
0.0225372314453125,
-0.0074615478515625,
0.00428009033203125,
0.01438140869140625,
0.015655517578125,
-0.00759124755859375,
-0.0287322998046875,
-0.0183258056640625,
0.0092926025390625,
0.0197601318359375,
0.0019044876098632812,
-0.02264404296875,
0.007381439208984375,
0.01297760009765625,
-0.0167083740234375,
-0.0005640983581542969,
0.01509857177734375,
0.01140594482421875,
-0.04925537109375,
0.007137298583984375,
0.038543701171875,
-0.0203704833984375,
0.0014896392822265625,
-0.0121002197265625,
-0.019378662109375,
-0.0198822021484375,
0.0148773193359375,
-0.003337860107421875,
0.0143585205078125,
0.006160736083984375,
0.007778167724609375,
-0.038238525390625,
-0.0015573501586914062,
-0.0067596435546875,
-0.004199981689453125,
-0.003879547119140625,
0.01084136962890625,
0.0224609375,
-0.01340484619140625,
0.037017822265625,
0.027740478515625,
-0.024322509765625,
-0.0149383544921875,
-0.053924560546875,
0.009490966796875,
-0.010894775390625,
0.00872802734375,
0.011688232421875,
-0.01425933837890625,
0.0177154541015625,
-0.033935546875,
-0.014404296875,
-0.0258636474609375,
-0.0077056884765625,
0.0009741783142089844,
-0.001934051513671875,
0.01593017578125,
-0.0103302001953125,
0.024993896484375,
-0.035552978515625,
-0.0132598876953125,
-0.011993408203125,
-0.0174407958984375,
-0.00814056396484375,
0.0018596649169921875,
0.003398895263671875,
0.01093292236328125,
-0.004016876220703125,
0.0176239013671875,
-0.0143280029296875,
0.0181884765625,
-0.0138702392578125,
-0.0086517333984375,
0.018890380859375,
-0.00972747802734375,
0.03375244140625,
-0.048370361328125,
0.0261383056640625,
-0.0283966064453125,
-0.0246124267578125,
-0.01074981689453125,
-0.008209228515625,
-0.004650115966796875,
-0.023956298828125,
0.02362060546875,
0.00258636474609375,
-0.04559326171875,
-0.01470184326171875,
0.0024509429931640625,
0.0109100341796875,
0.017425537109375,
-0.004192352294921875,
-0.01328277587890625,
-0.0087127685546875,
-0.008544921875,
0.006900787353515625,
-0.0183563232421875,
0.041748046875,
-0.007495880126953125,
0.0156402587890625,
0.006378173828125,
0.01366424560546875,
-0.01226806640625,
0.0176239013671875,
0.01459503173828125,
-0.0213470458984375,
-0.043365478515625,
-0.005771636962890625,
-0.0013780593872070312,
-0.01389312744140625,
-0.02215576171875,
0.005786895751953125,
-0.0186920166015625,
0.0030574798583984375,
0.01038360595703125,
0.0292205810546875,
0.018951416015625,
0.003940582275390625,
-0.00997161865234375,
-0.0203704833984375,
0.0085296630859375,
-0.0186614990234375,
0.010101318359375,
-0.0228271484375,
0.03790283203125,
-0.023468017578125,
0.006618499755859375,
-0.0213775634765625,
0.0269317626953125,
0.01702880859375,
0.0175323486328125,
0.0227203369140625,
0.04180908203125,
0.00023233890533447266,
0.0017099380493164062,
0.0099945068359375,
0.0144195556640625,
0.00833892822265625,
0.0016231536865234375,
-0.004131317138671875,
0.0211639404296875,
-0.04290771484375,
-0.0232391357421875,
0.0043182373046875,
-0.00757598876953125,
0.019012451171875,
0.01068115234375,
-0.0090484619140625,
0.01078033447265625,
0.031036376953125,
-0.036651611328125,
-0.00769805908203125,
-0.00563812255859375,
0.0180816650390625,
-0.02374267578125,
-0.0184173583984375,
-0.023895263671875,
-0.0208892822265625,
0.0266265869140625,
0.035064697265625,
0.023651123046875,
0.003971099853515625,
0.02349853515625,
-0.01522064208984375,
0.04150390625,
0.00997161865234375,
0.0238800048828125,
-0.0213623046875,
-0.03466796875,
0.0026607513427734375,
-0.0162353515625,
-0.003383636474609375,
-0.0007410049438476562,
-0.0186004638671875,
0.01995849609375,
-0.0093231201171875,
-0.0223846435546875,
-0.0135650634765625,
-0.01152801513671875,
-0.0262298583984375,
-0.027191162109375,
0.0180816650390625,
0.0277862548828125,
-0.01432037353515625,
-0.0027942657470703125,
-0.0411376953125,
0.006832122802734375,
-0.0016527175903320312,
-0.00215911865234375,
0.020904541015625,
-0.04193115234375,
-0.002979278564453125,
-0.039886474609375,
-0.0157012939453125,
0.007205963134765625,
-0.03167724609375,
-0.0088043212890625,
-0.0017375946044921875,
0.007251739501953125,
-0.029571533203125,
-0.033477783203125,
0.00646209716796875,
0.0251922607421875,
-0.021484375,
-0.019561767578125,
0.03741455078125,
0.006458282470703125,
-0.004428863525390625,
-0.00971221923828125,
-0.0286865234375,
-0.006744384765625,
0.0040130615234375,
0.017578125,
-0.0084991455078125,
0.03582763671875,
-0.005939483642578125,
0.07818603515625,
0.033172607421875,
-0.016632080078125,
0.0129852294921875,
-0.006580352783203125,
0.00884246826171875,
-0.0268096923828125,
0.00917816162109375,
0.0017547607421875,
0.002758026123046875,
0.02191162109375,
0.031494140625,
0.002483367919921875,
-0.016571044921875,
0.01221466064453125,
0.01529693603515625,
0.0110626220703125,
0.007183074951171875,
-0.0322265625,
0.00470733642578125,
0.048370361328125,
0.0251922607421875,
0.0267486572265625,
-0.006710052490234375,
-0.02490234375,
0.013519287109375,
0.01519012451171875,
0.01153564453125,
-0.006805419921875,
-0.023162841796875,
0.0014123916625976562,
0.00605010986328125,
-0.0225677490234375,
0.00695037841796875,
0.01531982421875,
0.0022945404052734375,
-0.0031909942626953125,
-0.043548583984375,
-0.01163482666015625,
-0.010589599609375,
0.0267333984375,
-0.0180511474609375,
-0.006778717041015625,
0.05767822265625,
0.0014753341674804688,
-0.0085906982421875,
0.00015413761138916016,
0.04827880859375,
-0.01873779296875,
-0.0125274658203125,
-0.030609130859375,
0.01250457763671875,
0.037994384765625,
-0.022003173828125,
0.010711669921875,
-0.004901885986328125,
0.0065460205078125,
-0.041748046875,
-0.00310516357421875,
-0.004459381103515625,
-0.011627197265625,
-0.01058197021484375,
0.0219268798828125,
0.01531982421875,
0.006916046142578125,
0.0151214599609375,
-0.00981903076171875,
0.00408935546875,
-0.01189422607421875,
0.0355224609375,
0.0179443359375,
-0.0003299713134765625,
-0.041290283203125,
0.008056640625,
0.001605987548828125,
-0.0172271728515625,
0.010986328125,
-0.005809783935546875,
0.01320648193359375,
-0.03118896484375,
-0.051910400390625,
0.00612640380859375,
0.030792236328125,
-0.016754150390625,
-0.0175933837890625,
-0.03094482421875,
-0.0203704833984375,
0.022247314453125,
-0.02093505859375,
-0.01239776611328125,
0.020904541015625,
0.0030879974365234375,
-0.0127105712890625,
-0.0113525390625,
-0.033538818359375,
-0.02166748046875,
0.034698486328125,
0.0007967948913574219,
-0.015594482421875,
0.005168914794921875,
-0.00795745849609375,
0.0018787384033203125,
0.00844573974609375,
0.0013942718505859375,
-0.001544952392578125,
-0.0268402099609375,
0.009429931640625,
0.04010009765625,
-0.029541015625,
-0.04150390625,
-0.01302337646484375,
-0.01165008544921875,
0.0218658447265625,
-0.02093505859375,
-0.0014972686767578125,
-0.0031147003173828125,
-0.0189666748046875,
0.004764556884765625,
-0.0033626556396484375,
0.011138916015625,
0.0164337158203125,
-0.0168304443359375,
0.00377655029296875,
0.0190277099609375,
0.02935791015625,
-0.0101470947265625,
0.005901336669921875,
-0.048614501953125,
-0.05120849609375,
0.018890380859375,
-0.01061248779296875,
-0.0293426513671875,
0.0024871826171875,
-0.024383544921875,
0.007232666015625,
-0.0225830078125,
-0.01806640625,
-0.01467132568359375,
-0.003101348876953125,
0.037567138671875,
-0.005374908447265625,
-0.01045989990234375,
-0.0029735565185546875,
-0.00917816162109375,
0.04705810546875,
-0.0281219482421875,
0.01041412353515625,
0.00823211669921875,
0.031463623046875,
0.01214599609375,
0.008056640625,
-0.019744873046875,
-0.019500732421875,
-0.006175994873046875,
0.039825439453125,
0.0299835205078125,
-0.01824951171875,
0.006561279296875,
-0.0184326171875,
0.023651123046875,
0.0231475830078125,
-0.004383087158203125,
0.036407470703125,
-0.004848480224609375,
-0.00634765625,
0.00702667236328125,
-0.026947021484375,
0.02447509765625,
0.00994110107421875,
0.0105438232421875,
0.006870269775390625,
-0.01021575927734375,
-0.035308837890625,
-0.006908416748046875,
0.0245208740234375,
-0.035797119140625,
-0.0107574462890625,
-0.031646728515625,
0.01373291015625,
0.0013856887817382812
] |
ours_513
|
We first prove that \(\angle BPC = 60^\circ\). Note that \(\triangle MBD \sim \triangle DCN\). Now \(\frac{MB}{BC} = \frac{MB}{BD} = \frac{DC}{CN} = \frac{BC}{CN}\) and \(\angle MBC = 60^\circ = \angle BCN\), so \(\triangle MBC \sim \triangle BCN\). Then \(\angle BPC = 180^\circ - \angle NBC - \angle BCM = 180^\circ - \angle CMB - \angle BCM = \angle CBM = 60^\circ\), as claimed.
Then, \(P\) lies on the circumcircle of \(\triangle ABC\). Let \(O\) be the circumcenter of \(\triangle ABC\). By the Triangle Inequality, \(KP \leq KO + OP = 12 + 12\sqrt{3} = 12 + \sqrt{432}\), with equality when \(P\) is the intersection of ray \(\overrightarrow{KO}\) with the circumcircle of \(\triangle ABC\). (Using a phantom point argument, it is not hard to see that this position of \(P\) can be achieved.) The answer is then \(1200 + 432 = 1632\).
\(\boxed{1632}\)
|
1632
|
{
"competition": "us_comps",
"dataset": "Ours",
"posts": null,
"source": "OMOFall19Solns.md"
}
|
Let \( A, B, C, \) and \( D \) be points in the plane with \( AB = AC = BC = BD = CD = 36 \) and such that \( A \neq D \). Point \( K \) lies on segment \( AC \) such that \( AK = 2KC \). Point \( M \) lies on segment \( AB \), and point \( N \) lies on line \( AC \), such that \( D, M, \) and \( N \) are collinear. Let lines \( CM \) and \( BN \) intersect at \( P \). Then the maximum possible length of segment \( KP \) can be expressed in the form \( m+\sqrt{n} \) for positive integers \( m \) and \( n \). Compute \( 100m+n \).
|
[
"/Mathematics/Geometry/Distance/Point-PointDistance2-Dimensional",
"/Mathematics/Geometry/PlaneGeometry/Circles/Circle",
"/Mathematics/Geometry/PlaneGeometry/Circles/Circumcenter",
"/Mathematics/Geometry/PlaneGeometry/Circles/Concyclic",
"/Mathematics/Geometry/PlaneGeometry/Triangles/Cevians",
"/Mathematics/Geometry/PlaneGeometry/Triangles/SpecialTriangles",
"/Mathematics/Geometry/PlaneGeometry/Triangles/TriangleCenters",
"/Mathematics/Geometry/PlaneGeometry/Triangles/TriangleCircles"
] |
Show that ∠BPC = 60° so P lies on the circumcircle of ABC, then maximize KP by placing P on the ray KO, giving KP = KO + radius.
|
[
-0.00004595518112182617,
-0.024658203125,
0.0169830322265625,
0.0007004737854003906,
0.000033736228942871094,
0.0009055137634277344,
0.003948211669921875,
0.0029811859130859375,
0.00811767578125,
0.0023174285888671875,
-0.0031280517578125,
-0.0114593505859375,
-0.003612518310546875,
0.040802001953125,
-0.00284576416015625,
-0.03204345703125,
-0.00377655029296875,
-0.01515960693359375,
0.059051513671875,
-0.0018167495727539062,
-0.0188751220703125,
0.0026397705078125,
-0.046661376953125,
-0.0003745555877685547,
-0.00963592529296875,
-0.005916595458984375,
-0.02166748046875,
0.0146484375,
-0.0034465789794921875,
0.0128936767578125,
0.004245758056640625,
-0.041656494140625,
0.001190185546875,
-0.032958984375,
0.0017757415771484375,
0.01082611083984375,
0.017913818359375,
0.0024890899658203125,
-0.058074951171875,
-0.05804443359375,
0.019073486328125,
0.01297760009765625,
-0.0111083984375,
0.011962890625,
-0.0021495819091796875,
0.031524658203125,
-0.0013141632080078125,
-0.011138916015625,
-0.022216796875,
-0.00311279296875,
0.0047607421875,
0.0248565673828125,
-0.0211334228515625,
-0.005588531494140625,
0.0037097930908203125,
-0.035736083984375,
-0.017974853515625,
0.000591278076171875,
-0.01910400390625,
0.00701904296875,
-0.0027637481689453125,
0.00617218017578125,
0.01959228515625,
-0.018218994140625,
-0.00508880615234375,
-0.016632080078125,
-0.0174102783203125,
-0.04937744140625,
0.01314544677734375,
-0.0229339599609375,
0.01543426513671875,
-0.02740478515625,
0.022796630859375,
0.0307159423828125,
0.01214599609375,
-0.0013971328735351562,
-0.004657745361328125,
0.0013113021850585938,
-0.035003662109375,
0.01316070556640625,
0.00485992431640625,
0.0124053955078125,
-0.00469207763671875,
-0.04345703125,
0.005008697509765625,
0.0223236083984375,
-0.03582763671875,
0.0042877197265625,
0.00797271728515625,
-0.007320404052734375,
-0.005786895751953125,
-0.0009183883666992188,
-0.0160064697265625,
-0.02752685546875,
0.00879669189453125,
0.0016412734985351562,
0.020172119140625,
-0.0081329345703125,
-0.02386474609375,
-0.00026679039001464844,
-0.00698089599609375,
0.0037689208984375,
-0.00914764404296875,
-0.029266357421875,
-0.02105712890625,
-0.007556915283203125,
-0.009979248046875,
-0.006610870361328125,
-0.010498046875,
-0.004486083984375,
0.0013303756713867188,
-0.006023406982421875,
0.0174407958984375,
0.00957489013671875,
-0.01007843017578125,
-0.0200958251953125,
0.0082550048828125,
-0.00643157958984375,
0.0200958251953125,
0.01557159423828125,
0.0014753341674804688,
-0.0005936622619628906,
-0.0189971923828125,
0.017730712890625,
0.00010943412780761719,
-0.0108642578125,
0.0030384063720703125,
-0.026275634765625,
-0.0255279541015625,
0.014556884765625,
0.0115814208984375,
-0.00698089599609375,
-0.0276947021484375,
-0.023345947265625,
-0.0233154296875,
0.00878143310546875,
0.005401611328125,
0.00363922119140625,
-0.01404571533203125,
-0.00968170166015625,
-0.0021648406982421875,
0.0004248619079589844,
0.0021877288818359375,
-0.048095703125,
-0.006206512451171875,
-0.038360595703125,
-0.002796173095703125,
-0.0175018310546875,
-0.0068511962890625,
-0.004581451416015625,
-0.0115814208984375,
-0.00897216796875,
0.0267791748046875,
0.00586700439453125,
0.0009322166442871094,
-0.007068634033203125,
-0.0062408447265625,
0.006504058837890625,
0.0165252685546875,
-0.00749969482421875,
-0.0010662078857421875,
-0.01441192626953125,
0.01006317138671875,
0.0169219970703125,
0.01181793212890625,
-0.00811767578125,
0.015472412109375,
0.0013208389282226562,
-0.0181732177734375,
0.010711669921875,
0.00911712646484375,
-0.00894927978515625,
-0.0049591064453125,
0.00008553266525268555,
-0.010986328125,
0.00505828857421875,
0.0082855224609375,
0.00972747802734375,
-0.00878143310546875,
0.00684356689453125,
0.0208740234375,
-0.007198333740234375,
0.00592041015625,
0.01044464111328125,
0.0191802978515625,
-0.023529052734375,
-0.005741119384765625,
0.007083892822265625,
0.01171875,
0.015838623046875,
-0.0097198486328125,
-0.0297698974609375,
-0.0074920654296875,
-0.0072784423828125,
0.007274627685546875,
-0.01934814453125,
-0.021209716796875,
0.0080718994140625,
0.0186614990234375,
-0.00467681884765625,
0.002323150634765625,
-0.0193328857421875,
0.037139892578125,
-0.005828857421875,
-0.0146484375,
-0.004390716552734375,
0.01018524169921875,
-0.00921630859375,
-0.023956298828125,
0.00150299072265625,
0.0190582275390625,
0.002910614013671875,
-0.01190948486328125,
0.050567626953125,
0.00555419921875,
-0.01216888427734375,
-0.02764892578125,
-0.005222320556640625,
0.0015306472778320312,
-0.0225677490234375,
0.0206756591796875,
-0.01361083984375,
-0.0029468536376953125,
-0.0145111083984375,
-0.00862884521484375,
0.00797271728515625,
0.0027103424072265625,
-0.018646240234375,
0.028411865234375,
-0.00592041015625,
-0.007686614990234375,
0.0018062591552734375,
-0.0002237558364868164,
0.006683349609375,
-0.027069091796875,
-0.0138092041015625,
-0.02239990234375,
-0.0018377304077148438,
0.006694793701171875,
-0.02337646484375,
0.0687255859375,
-0.0218048095703125,
-0.006561279296875,
-0.009735107421875,
-0.00884246826171875,
-0.00262451171875,
0.005031585693359375,
-0.0223236083984375,
-0.00670623779296875,
0.0003712177276611328,
-0.0229644775390625,
0.0139923095703125,
-0.007232666015625,
-0.019287109375,
-0.0189056396484375,
0.0081787109375,
0.00321197509765625,
-0.0190887451171875,
-0.00812530517578125,
-0.00263214111328125,
-0.0256500244140625,
-0.0193023681640625,
-0.0026988983154296875,
-0.006198883056640625,
-0.0087432861328125,
0.0330810546875,
-0.00925445556640625,
0.007595062255859375,
0.00644683837890625,
-0.01129913330078125,
0.0202178955078125,
-0.0217742919921875,
-0.0207977294921875,
0.01450347900390625,
-0.02740478515625,
-0.020172119140625,
0.003814697265625,
0.02520751953125,
0.01186370849609375,
0.0034427642822265625,
0.00530242919921875,
0.0097808837890625,
-0.0211334228515625,
0.018157958984375,
-0.0152587890625,
-0.007472991943359375,
-0.01226806640625,
-0.0101318359375,
-0.0021209716796875,
0.042694091796875,
0.01238250732421875,
-0.011749267578125,
-0.005126953125,
-0.0268402099609375,
0.029998779296875,
-0.0251617431640625,
0.008056640625,
0.01192474365234375,
0.0037097930908203125,
0.009063720703125,
0.021392822265625,
-0.020263671875,
0.026397705078125,
0.004634857177734375,
0.01058197021484375,
0.01715087890625,
0.0081024169921875,
0.00997161865234375,
-0.0295562744140625,
-0.0011930465698242188,
0.01041412353515625,
0.006237030029296875,
-0.010406494140625,
-0.024932861328125,
-0.0125274658203125,
-0.0184478759765625,
-0.0007333755493164062,
0.0171051025390625,
-0.02386474609375,
0.01453399658203125,
0.00247955322265625,
0.001064300537109375,
0.0272216796875,
0.00858306884765625,
0.047882080078125,
-0.0239715576171875,
0.0188140869140625,
0.0246124267578125,
0.01114654541015625,
0.01605224609375,
-0.023681640625,
0.0112762451171875,
-0.0167083740234375,
-0.0056610107421875,
-0.0240325927734375,
-0.0004394054412841797,
-0.0032901763916015625,
0.01482391357421875,
-0.012420654296875,
0.01284027099609375,
0.028656005859375,
0.0097808837890625,
0.034454345703125,
-0.045257568359375,
-0.0190887451171875,
0.0189666748046875,
-0.0277862548828125,
-0.0080718994140625,
-0.04339599609375,
-0.019866943359375,
-0.02008056640625,
-0.0169677734375,
0.0106658935546875,
0.00461578369140625,
0.0023937225341796875,
0.005184173583984375,
0.01457977294921875,
0.01355743408203125,
-0.0222930908203125,
0.0154571533203125,
0.002620697021484375,
-0.021240234375,
-0.005367279052734375,
0.007114410400390625,
-0.0012950897216796875,
0.009307861328125,
-0.00652313232421875,
0.0005464553833007812,
-0.0484619140625,
0.0093841552734375,
-0.01959228515625,
0.032989501953125,
0.0206451416015625,
-0.0028285980224609375,
0.0165863037109375,
0.01094818115234375,
0.01393890380859375,
-0.0124359130859375,
0.0032634735107421875,
-0.01548004150390625,
-0.0066680908203125,
-0.0174102783203125,
0.00464630126953125,
0.03131103515625,
0.0007119178771972656,
-0.009735107421875,
0.01001739501953125,
-0.02960205078125,
-0.029205322265625,
0.0014696121215820312,
-0.0175018310546875,
0.0168609619140625,
-0.0026721954345703125,
0.0003643035888671875,
-0.0174102783203125,
-0.0292510986328125,
0.0064239501953125,
0.0198516845703125,
0.024017333984375,
-0.017974853515625,
-0.053497314453125,
0.00018346309661865234,
-0.011932373046875,
-0.04254150390625,
0.01334381103515625,
-0.0328369140625,
-0.01145172119140625,
0.0002505779266357422,
-0.0167388916015625,
0.0205535888671875,
-0.0089569091796875,
-0.004978179931640625,
-0.0127716064453125,
-0.012451171875,
-0.0221710205078125,
0.00972747802734375,
0.021087646484375,
0.01396942138671875,
0.017547607421875,
0.004924774169921875,
0.00838470458984375,
-0.02349853515625,
-0.01873779296875,
-0.005069732666015625,
0.0030803680419921875,
0.018524169921875,
-0.028076171875,
0.04144287109375,
0.0018339157104492188,
-0.0283660888671875,
0.0303497314453125,
0.02215576171875,
-0.004276275634765625,
0.0300140380859375,
-0.006420135498046875,
-0.008270263671875,
0.037567138671875,
-0.03253173828125,
-0.00081634521484375,
0.00830078125,
0.005199432373046875,
0.0008745193481445312,
0.006336212158203125,
0.00426483154296875,
0.021942138671875,
0.0132293701171875,
0.013153076171875,
0.018707275390625,
0.041107177734375,
0.0230255126953125,
-0.007091522216796875,
-0.0254974365234375,
0.0133209228515625,
-0.04144287109375,
-0.01540374755859375,
0.0335693359375,
0.01311492919921875,
-0.026580810546875,
-0.0228729248046875,
0.01358795166015625,
-0.018280029296875,
-0.00792694091796875,
-0.00942230224609375,
0.01873779296875,
-0.01387786865234375,
-0.019927978515625,
-0.004589080810546875,
0.0106353759765625,
0.01407623291015625,
0.004390716552734375,
0.006702423095703125,
-0.04779052734375,
-0.01904296875,
-0.0096588134765625,
-0.01422882080078125,
0.0070953369140625,
0.0200042724609375,
0.01245880126953125,
-0.0225067138671875,
0.0068511962890625,
-0.026397705078125,
0.01544189453125,
-0.024566650390625,
-0.00930023193359375,
-0.01230621337890625,
0.0269927978515625,
0.00919342041015625,
-0.00757598876953125,
-0.00736236572265625,
-0.052764892578125,
-0.0024585723876953125,
0.02978515625,
-0.022705078125,
-0.00838470458984375,
-0.00189208984375,
-0.026611328125,
0.023956298828125,
-0.016632080078125,
-0.007701873779296875,
-0.0225372314453125,
0.0377197265625,
-0.0113525390625,
-0.0321044921875,
0.031219482421875,
-0.007450103759765625,
-0.0254974365234375,
0.0174713134765625,
-0.024383544921875,
0.00766754150390625,
0.0269927978515625,
0.0325927734375,
0.0072479248046875,
0.0253143310546875,
-0.0350341796875,
0.0281524658203125,
-0.0031986236572265625,
0.012359619140625,
0.0034942626953125,
0.034637451171875,
0.01038360595703125,
-0.012481689453125,
0.0207366943359375,
0.0233917236328125,
0.0023784637451171875,
0.017333984375,
0.018951416015625,
-0.017822265625,
-0.01593017578125,
0.032928466796875,
-0.0084228515625,
0.03021240234375,
-0.0186309814453125,
-0.053924560546875,
0.0219573974609375,
-0.03399658203125,
0.0181884765625,
0.0156707763671875,
0.00647735595703125,
0.03411865234375,
-0.012542724609375,
0.01922607421875,
0.02337646484375,
-0.0137786865234375,
-0.004673004150390625,
-0.0024013519287109375,
0.0108184814453125,
-0.037078857421875,
-0.0134429931640625,
0.004375457763671875,
-0.027740478515625,
-0.01053619384765625,
-0.00762939453125,
-0.0238800048828125,
0.005512237548828125,
-0.0180511474609375,
-0.0013513565063476562,
-0.0172576904296875,
0.006175994873046875,
0.004039764404296875,
0.017913818359375,
0.01328277587890625,
-0.0158843994140625,
0.0211181640625,
-0.0012235641479492188,
0.011199951171875,
-0.01294708251953125,
0.021392822265625,
-0.0012140274047851562,
-0.00719451904296875,
-0.038177490234375,
-0.01898193359375,
0.0005025863647460938,
-0.0020694732666015625,
-0.0198974609375,
0.0292816162109375,
-0.040802001953125,
0.00775909423828125,
-0.0024547576904296875,
0.0155181884765625,
-0.0258026123046875,
0.0093994140625,
0.038848876953125,
-0.0236968994140625,
-0.043731689453125,
0.0008440017700195312,
0.01100921630859375,
0.0203399658203125,
0.019439697265625,
0.0037136077880859375,
-0.0210418701171875,
-0.0189971923828125,
0.055328369140625,
0.0251617431640625,
0.01763916015625,
-0.01029205322265625,
-0.039154052734375,
0.031768798828125,
0.0014123916625976562,
0.0163116455078125,
0.0020160675048828125,
0.02496337890625,
-0.006328582763671875,
0.0035400390625,
0.04315185546875,
-0.0010204315185546875,
0.0090484619140625,
-0.0018482208251953125,
0.0031147003173828125,
0.009796142578125,
0.00829315185546875,
-0.025543212890625,
-0.021514892578125,
-0.01061248779296875,
0.044769287109375,
-0.002239227294921875,
-0.0230560302734375,
-0.018829345703125,
-0.0170440673828125,
-0.007389068603515625,
0.00617218017578125,
-0.01190948486328125,
0.01509857177734375,
-0.0035839080810546875,
0.047149658203125,
-0.002765655517578125,
0.004962921142578125,
-0.0278472900390625,
-0.021087646484375,
0.013916015625,
-0.0282745361328125,
0.0022907257080078125,
0.02056884765625,
0.0175628662109375,
0.032135009765625,
-0.01074981689453125,
-0.0230255126953125,
0.00527191162109375,
0.00920867919921875,
-0.00992584228515625,
-0.004100799560546875,
0.017913818359375,
0.0075836181640625,
0.0089263916015625,
-0.053924560546875,
-0.018890380859375,
0.01061248779296875,
-0.03314208984375,
0.000537872314453125,
-0.0178680419921875,
-0.007434844970703125,
-0.01190185546875,
-0.010284423828125,
0.01617431640625,
0.040985107421875,
0.0131988525390625,
-0.03802490234375,
-0.005306243896484375,
-0.0125732421875,
0.035247802734375,
0.0189361572265625,
0.00498199462890625,
-0.0180816650390625,
0.0035381317138671875,
0.00251007080078125,
0.006622314453125,
0.021881103515625,
-0.043701171875,
-0.024627685546875,
-0.01136016845703125,
0.022247314453125,
0.0009636878967285156,
-0.01512908935546875,
0.014007568359375,
0.001483917236328125,
0.021209716796875,
-0.02166748046875,
-0.007740020751953125,
0.0170745849609375,
0.0022945404052734375,
-0.0167236328125,
-0.0210723876953125,
0.0093536376953125,
0.0231781005859375,
0.00928497314453125,
-0.01444244384765625,
0.041351318359375,
0.0112457275390625,
0.0015802383422851562,
0.01337432861328125,
-0.0019435882568359375,
-0.01129913330078125,
0.0130157470703125,
-0.0306854248046875,
0.0016021728515625,
0.00959014892578125,
-0.0027103424072265625,
-0.033172607421875,
-0.012237548828125,
-0.0086822509765625,
-0.00789642333984375,
0.0200042724609375,
-0.02777099609375,
0.0017576217651367188,
-0.0177764892578125,
-0.0181884765625,
-0.0237274169921875,
0.012115478515625,
0.039520263671875,
-0.01474761962890625,
-0.0012941360473632812,
-0.026763916015625,
-0.0116424560546875,
-0.0146484375,
-0.00795745849609375,
-0.016510009765625,
-0.06494140625,
-0.0106201171875,
-0.00127410888671875,
0.00901031494140625,
0.0082550048828125,
-0.01230621337890625,
0.0196075439453125,
-0.0263824462890625,
0.01146697998046875,
0.0223541259765625,
0.0202178955078125,
-0.036407470703125,
-0.0139007568359375,
-0.042572021484375,
0.003040313720703125,
-0.00836181640625,
-0.0125885009765625,
0.036163330078125,
-0.003055572509765625,
-0.02032470703125,
-0.01110076904296875,
-0.01236724853515625,
-0.036407470703125,
-0.013031005859375,
-0.006893157958984375,
0.06536865234375,
-0.014312744140625,
-0.00763702392578125,
-0.0197296142578125,
0.00394439697265625,
0.00044083595275878906,
-0.0253753662109375,
0.005176544189453125,
0.0014934539794921875,
0.01380157470703125,
0.02667236328125,
0.020233154296875,
0.0167388916015625,
-0.0230865478515625,
-0.0367431640625,
-0.00875091552734375,
0.0001327991485595703,
-0.03314208984375,
0.01238250732421875,
0.022003173828125,
0.00931549072265625,
0.032684326171875,
-0.00978851318359375,
-0.01103973388671875,
-0.01397705078125,
-0.005023956298828125,
0.0242919921875,
-0.0101470947265625,
-0.060455322265625,
-0.0328369140625,
-0.007213592529296875,
0.002857208251953125,
-0.0012378692626953125,
0.01284027099609375,
0.0167236328125,
0.0061798095703125,
-0.03009033203125,
-0.01531219482421875,
0.0037593841552734375,
-0.023101806640625,
-0.033233642578125,
0.0033931732177734375,
0.0181732177734375,
0.015777587890625,
-0.0272064208984375,
-0.000980377197265625,
-0.0028247833251953125,
0.0002522468566894531,
0.0168609619140625,
-0.01505279541015625,
0.0396728515625,
0.01004791259765625,
-0.0006222724914550781,
-0.032623291015625,
0.0262451171875,
-0.0218048095703125,
0.00859832763671875,
-0.021759033203125,
-0.0065155029296875,
0.0112762451171875,
0.00690460205078125,
-0.0208587646484375,
-0.0117950439453125,
0.005828857421875,
0.036956787109375,
-0.003276824951171875,
0.031585693359375,
0.0030765533447265625,
-0.0170440673828125,
-0.002269744873046875,
0.0236968994140625,
-0.0050811767578125,
0.027679443359375,
-0.024139404296875,
0.0016851425170898438,
-0.00543212890625,
0.0039215087890625,
0.01439666748046875,
-0.0222015380859375,
0.005428314208984375,
-0.01001739501953125,
0.0215911865234375,
-0.0204010009765625,
-0.0171661376953125,
-0.0154571533203125,
-0.0162200927734375,
-0.006122589111328125,
-0.004001617431640625,
-0.015777587890625,
0.01291656494140625,
-0.00995635986328125,
-0.004810333251953125,
-0.038116455078125,
-0.0175323486328125,
-0.03509521484375,
0.0164031982421875,
0.00565338134765625,
0.01715087890625,
-0.022918701171875,
0.004581451416015625,
-0.018768310546875,
-0.00262451171875,
0.003833770751953125,
0.004436492919921875,
0.035125732421875,
0.0048828125,
0.0001285076141357422,
0.05474853515625,
0.018646240234375,
0.0013856887817382812,
0.01355743408203125,
0.0188751220703125,
-0.0411376953125,
0.0261077880859375,
-0.03436279296875,
0.0008797645568847656,
0.015625,
0.0280303955078125,
-0.0165863037109375,
-0.01202392578125,
0.0261688232421875,
-0.0213775634765625,
0.0265350341796875,
0.024261474609375,
0.01305389404296875,
-0.00652313232421875,
0.01082611083984375,
-0.01346588134765625,
0.034149169921875,
-0.0180206298828125,
0.0200042724609375,
-0.0166778564453125,
-0.0330810546875,
-0.00861358642578125,
0.04742431640625,
-0.0013265609741210938,
0.000019669532775878906,
0.0245819091796875,
0.051910400390625,
0.0187835693359375,
0.01337432861328125,
-0.020263671875,
-0.00736236572265625,
-0.005840301513671875,
-0.0203399658203125,
-0.02520751953125,
0.0174407958984375,
-0.00887298583984375,
0.01235198974609375,
-0.01377105712890625,
0.00030541419982910156,
-0.0225830078125,
-0.0251007080078125,
-0.036041259765625,
0.04473876953125,
0.00884246826171875,
-0.0293121337890625,
-0.0295867919921875,
0.00669097900390625,
-0.008056640625,
0.003208160400390625,
-0.0047149658203125,
-0.036285400390625,
0.037994384765625,
0.0201568603515625,
-0.0191650390625,
-0.0269775390625,
0.0276336669921875,
0.006988525390625,
0.0227813720703125,
0.00872039794921875,
-0.020477294921875,
0.0019311904907226562,
0.00492095947265625,
0.01253509521484375,
0.0188140869140625,
0.004306793212890625,
-0.0179901123046875,
-0.0176849365234375,
-0.006092071533203125,
-0.008056640625,
-0.0101318359375,
0.022796630859375,
-0.0174713134765625,
0.023040771484375,
-0.0114288330078125,
0.01354217529296875,
0.0205078125,
-0.02886962890625,
0.0016641616821289062,
-0.007007598876953125,
0.0491943359375,
0.00801849365234375,
-0.00635528564453125,
-0.00870513916015625,
-0.0009908676147460938,
-0.01294708251953125,
-0.053863525390625,
-0.008056640625,
-0.044769287109375,
-0.00823211669921875,
-0.006595611572265625,
0.002597808837890625,
0.022247314453125,
0.00823211669921875,
-0.0155029296875,
-0.023345947265625,
-0.0090179443359375,
0.01751708984375,
-0.0252532958984375,
-0.0073089599609375,
0.007045745849609375,
-0.007152557373046875,
0.01235198974609375,
-0.01416778564453125,
-0.0248870849609375,
0.01108551025390625,
0.01184844970703125,
-0.0184783935546875,
-0.006244659423828125,
0.014892578125,
-0.0234375,
-0.02056884765625,
0.0019512176513671875,
0.01526641845703125,
0.026611328125,
0.010345458984375,
0.041259765625,
0.01055908203125,
-0.01715087890625,
0.00412750244140625,
-0.0194549560546875,
-0.00788116455078125,
-0.039886474609375,
-0.00774383544921875,
0.0037937164306640625,
-0.020111083984375,
0.019134521484375,
0.02325439453125,
0.00701904296875,
-0.02313232421875,
-0.0199127197265625,
0.034576416015625,
0.00226593017578125,
0.004703521728515625,
-0.009979248046875,
0.0139312744140625,
0.000030159950256347656,
0.03594970703125,
0.0050811767578125,
-0.00930023193359375,
0.0210113525390625,
0.0096282958984375,
-0.0006384849548339844,
0.00470733642578125,
0.004974365234375,
0.0120697021484375,
-0.006954193115234375,
0.0009274482727050781,
-0.049407958984375,
-0.04498291015625,
0.01406097412109375,
0.0200347900390625,
-0.00909423828125,
0.0032901763916015625,
-0.02557373046875,
0.00511932373046875,
0.037445068359375,
0.01180267333984375,
0.00621795654296875,
-0.0234527587890625,
-0.00270843505859375,
0.0004837512969970703,
0.020294189453125,
0.0037822723388671875,
0.035614013671875,
-0.007465362548828125,
0.037841796875,
-0.059844970703125,
0.04296875,
-0.007396697998046875,
-0.01532745361328125,
-0.0255889892578125,
-0.021575927734375,
0.037506103515625,
-0.0369873046875,
-0.00106048583984375,
-0.022918701171875,
-0.007038116455078125,
0.0179443359375,
-0.01128387451171875,
0.00875091552734375,
-0.047088623046875,
0.0174407958984375,
-0.009918212890625,
0.0005059242248535156,
-0.0205535888671875,
-0.0135955810546875,
-0.0003170967102050781,
0.0004432201385498047,
-0.01395416259765625,
0.01117706298828125,
0.009613037109375,
-0.044769287109375,
-0.0184783935546875,
-0.0071868896484375,
0.0035552978515625,
0.0160675048828125,
-0.038421630859375,
0.0022563934326171875,
0.00208282470703125,
0.032073974609375,
-0.004863739013671875,
0.003570556640625,
-0.00664520263671875,
0.0091705322265625,
0.002025604248046875,
-0.018646240234375,
-0.006885528564453125,
0.0195159912109375,
0.0278778076171875,
-0.0494384765625,
-0.030609130859375,
-0.006961822509765625,
0.024078369140625,
-0.00101470947265625,
-0.0213775634765625,
-0.0006203651428222656,
-0.0086822509765625,
0.0137786865234375,
-0.050537109375,
0.01540374755859375,
0.004596710205078125,
0.00005245208740234375,
0.01407623291015625,
-0.0122833251953125,
0.0008325576782226562,
-0.03094482421875,
0.02984619140625,
-0.020782470703125,
0.01690673828125,
0.0138397216796875,
-0.0259552001953125,
0.0029926300048828125,
0.01800537109375,
-0.007381439208984375,
-0.0163116455078125,
-0.0253753662109375,
-0.00913238525390625,
0.005321502685546875,
-0.006641387939453125,
0.0242767333984375,
-0.021636962890625,
-0.0252227783203125,
0.0137939453125,
0.0259857177734375,
0.01088714599609375,
0.0230255126953125,
0.03656005859375,
-0.018096923828125,
0.00624847412109375,
0.032470703125,
0.032562255859375,
0.037628173828125,
-0.001373291015625,
-0.053558349609375,
-0.01509857177734375,
0.01312255859375,
-0.0137176513671875,
0.0006670951843261719,
-0.0224761962890625,
0.01451873779296875,
0.0037212371826171875,
0.025390625,
-0.00423431396484375,
-0.01502227783203125,
-0.0288543701171875,
-0.0110015869140625,
0.00774383544921875,
0.009033203125,
0.0231781005859375,
0.00824737548828125,
0.016754150390625,
0.01244354248046875,
-0.0112762451171875,
-0.0003936290740966797,
0.007198333740234375,
0.0174102783203125,
-0.047576904296875,
0.0232391357421875,
-0.0230712890625,
-0.0040435791015625,
-0.0051727294921875,
-0.0172576904296875,
0.004726409912109375,
0.0260467529296875,
-0.00036907196044921875,
-0.025482177734375,
0.007625579833984375,
0.014892578125,
-0.0121307373046875,
-0.00418853759765625,
-0.0065765380859375,
-0.0110626220703125,
-0.0288848876953125,
0.01375579833984375,
-0.00809478759765625,
-0.00039196014404296875,
0.013214111328125,
-0.00939178466796875,
-0.0290985107421875,
0.0005540847778320312,
0.010406494140625,
0.021209716796875,
0.01505279541015625,
-0.0116729736328125,
0.0004968643188476562,
-0.0241241455078125,
-0.01184844970703125,
0.00926971435546875,
-0.004505157470703125,
-0.006809234619140625,
0.0244598388671875,
-0.00038695335388183594,
-0.017303466796875,
-0.0219573974609375,
-0.018951416015625,
0.0009975433349609375,
-0.01076507568359375,
0.032928466796875,
0.002285003662109375,
-0.034881591796875,
-0.005828857421875,
0.0214385986328125,
0.01079559326171875,
0.020477294921875,
-0.0179595947265625,
-0.0077972412109375,
0.0076141357421875,
-0.01007843017578125,
-0.0193023681640625,
0.0258636474609375,
0.0189361572265625,
0.004573822021484375,
0.016265869140625,
-0.0178070068359375,
-0.0053863525390625,
-0.0025348663330078125,
-0.02423095703125,
-0.007701873779296875,
-0.002605438232421875,
0.00574493408203125,
-0.0190887451171875,
-0.0011396408081054688,
0.0261993408203125,
0.0031681060791015625,
-0.0219573974609375,
0.0206146240234375,
-0.026824951171875,
0.0009751319885253906,
0.01026153564453125,
0.0095672607421875,
0.00350189208984375,
-0.0024127960205078125,
0.03173828125,
0.014404296875,
-0.00461578369140625,
0.052490234375,
-0.014251708984375,
-0.00534820556640625,
0.01227569580078125,
-0.007129669189453125,
0.0256805419921875,
-0.026458740234375,
0.0158843994140625,
-0.0025806427001953125,
0.0020923614501953125,
0.00170135498046875,
0.00305938720703125,
-0.003173828125,
-0.005847930908203125,
0.01412200927734375,
0.018035888671875,
-0.0133209228515625,
-0.03143310546875,
-0.034820556640625,
-0.01324462890625,
0.0469970703125,
0.01061248779296875,
-0.01508331298828125,
0.0294952392578125,
0.0229644775390625,
-0.004863739013671875,
-0.005802154541015625,
-0.0379638671875,
0.0094757080078125,
-0.01013946533203125,
0.0179595947265625,
-0.031158447265625,
0.01678466796875,
-0.0008835792541503906,
-0.01074981689453125,
-0.0248870849609375,
-0.0283355712890625,
0.029571533203125,
-0.0161285400390625,
-0.03741455078125,
0.0181732177734375,
-0.0252227783203125,
0.007656097412109375,
-0.008575439453125,
0.044830322265625,
-0.01421356201171875,
-0.009490966796875,
-0.0138702392578125,
-0.01399993896484375,
-0.0253143310546875,
0.0130615234375,
0.01654052734375,
-0.0235443115234375,
0.00229644775390625,
0.00482940673828125,
-0.032196044921875,
-0.0016460418701171875,
0.007568359375,
-0.0200347900390625,
-0.0172119140625,
0.02142333984375,
-0.0009617805480957031,
0.01213836669921875,
0.003749847412109375,
0.0244903564453125,
-0.00876617431640625,
0.0162506103515625,
0.0027027130126953125,
-0.003917694091796875,
0.00847625732421875,
-0.0186767578125,
-0.00428009033203125,
0.00846099853515625,
-0.025421142578125,
0.0174713134765625,
0.03326416015625,
-0.01268768310546875,
-0.0078582763671875,
-0.0034999847412109375,
-0.006809234619140625,
0.035888671875,
0.01006317138671875,
0.0019626617431640625,
0.004608154296875,
0.0225067138671875,
0.018035888671875,
0.03643798828125,
-0.050140380859375,
0.0108642578125,
-0.0062408447265625,
0.007457733154296875,
0.0231170654296875,
0.00211334228515625,
0.01047515869140625,
0.0080413818359375,
0.0069580078125,
-0.013946533203125,
0.0102996826171875,
-0.04083251953125,
0.0241241455078125,
0.0216064453125,
0.00397491455078125,
-0.0186920166015625,
0.0199127197265625,
-0.0008759498596191406,
0.02587890625,
-0.0008802413940429688,
0.044189453125,
0.0209808349609375,
0.0236663818359375,
-0.017730712890625,
-0.006649017333984375,
0.00778961181640625,
0.01511383056640625,
0.005634307861328125,
-0.018341064453125,
0.00004571676254272461,
0.004207611083984375,
-0.0047760009765625,
-0.0172882080078125,
0.0049591064453125,
-0.0248870849609375,
-0.0090789794921875,
-0.0164794921875,
0.01204681396484375,
0.002544403076171875,
0.00545501708984375,
0.00128173828125,
0.02972412109375,
0.029754638671875,
0.007228851318359375,
-0.0264434814453125,
-0.0071868896484375,
-0.0088653564453125,
-0.006671905517578125,
-0.01776123046875,
-0.0139923095703125,
0.033721923828125,
0.01568603515625,
-0.06072998046875,
0.032196044921875,
0.00469207763671875,
-0.027374267578125,
0.01531219482421875,
-0.005672454833984375,
-0.0262298583984375,
0.05645751953125,
-0.03912353515625,
0.02960205078125,
0.012542724609375,
0.0161590576171875,
0.0239715576171875,
-0.0025005340576171875,
0.0265655517578125,
-0.024749755859375,
0.02093505859375,
-0.0171356201171875,
0.00498199462890625,
-0.0006470680236816406,
-0.01224517822265625,
-0.030609130859375,
0.0022430419921875,
-0.01081085205078125,
-0.00754547119140625,
0.01904296875,
0.031524658203125,
-0.01715087890625,
0.015777587890625,
0.005634307861328125,
0.0297698974609375,
-0.003719329833984375,
0.0059356689453125,
-0.0193939208984375,
-0.013214111328125,
-0.024505615234375,
-0.0018777847290039062,
-0.029815673828125,
-0.002899169921875,
0.031585693359375,
0.0102691650390625,
0.002208709716796875,
0.00916290283203125,
0.0283050537109375,
-0.0011339187622070312,
0.00557708740234375,
-0.031982421875,
0.01087188720703125,
-0.00756072998046875,
-0.004543304443359375,
0.018768310546875,
0.01641845703125,
-0.006622314453125,
-0.006099700927734375,
0.04241943359375,
-0.016326904296875,
0.0029754638671875,
-0.0010824203491210938,
0.045196533203125,
-0.003299713134765625,
0.020965576171875,
-0.00616455078125,
0.027587890625,
0.01727294921875,
-0.0249786376953125,
0.028350830078125,
-0.0085601806640625,
-0.023406982421875,
0.00689697265625,
-0.01413726806640625,
-0.0170135498046875,
-0.0198516845703125,
-0.0048065185546875,
0.0180206298828125,
0.0100860595703125,
0.040191650390625,
-0.03948974609375,
-0.01125335693359375,
0.0247650146484375,
-0.01522064208984375,
0.0013561248779296875,
0.0019588470458984375,
-0.025787353515625,
0.007671356201171875,
0.0191802978515625,
-0.0081329345703125,
-0.0070343017578125,
0.0159912109375,
-0.0125579833984375,
-0.006877899169921875,
0.016510009765625,
-0.0029582977294921875,
0.005901336669921875,
0.00757598876953125,
-0.0152435302734375,
-0.0009765625,
0.00588226318359375,
0.0286407470703125,
-0.01153564453125,
0.004070281982421875,
0.007549285888671875,
0.04278564453125,
0.00809478759765625,
-0.0090789794921875,
0.002590179443359375,
-0.02972412109375,
-0.020355224609375,
0.04229736328125,
-0.0043792724609375,
0.01247406005859375,
-0.0230712890625,
-0.00586700439453125,
0.0180816650390625,
-0.042877197265625,
-0.01395416259765625,
-0.0098876953125,
0.0066986083984375,
0.05059814453125,
0.0252685546875,
0.01546478271484375,
-0.001384735107421875,
0.0200347900390625,
0.0084228515625,
-0.0015268325805664062,
0.0023822784423828125,
-0.00746917724609375,
-0.003971099853515625,
0.0297088623046875,
0.020111083984375,
-0.022796630859375,
0.024566650390625,
-0.01520538330078125,
0.0009684562683105469,
-0.0023174285888671875,
-0.01678466796875,
-0.03314208984375,
0.004344940185546875,
0.019195556640625,
-0.01276397705078125,
-0.035736083984375,
-0.0201568603515625,
0.036102294921875,
0.0030651092529296875,
-0.0164642333984375,
-0.030364990234375,
0.0081329345703125,
-0.0007987022399902344,
-0.01248931884765625,
0.027496337890625,
0.00848388671875,
-0.032501220703125,
0.01113128662109375,
0.0018405914306640625,
-0.041748046875,
0.00725555419921875,
0.012451171875,
0.0009608268737792969,
0.00940704345703125,
-0.00978851318359375,
-0.050872802734375,
-0.001689910888671875,
-0.0258636474609375,
0.006137847900390625,
-0.00988006591796875,
-0.005397796630859375,
-0.009246826171875,
-0.007808685302734375,
0.0079498291015625,
-0.01497650146484375,
0.007404327392578125,
-0.025909423828125,
-0.0219573974609375,
-0.01503753662109375,
-0.0206298828125,
-0.0059051513671875,
-0.0195159912109375,
-0.023162841796875,
0.0250091552734375,
0.0127105712890625,
-0.00823211669921875,
0.0271148681640625,
-0.001300811767578125,
-0.0038356781005859375,
0.0543212890625,
-0.0030078887939453125,
0.01209259033203125,
0.0258636474609375,
0.0015802383422851562,
0.00827789306640625,
-0.0014925003051757812,
0.00623321533203125,
-0.00998687744140625,
0.01082611083984375,
-0.00705718994140625,
0.0175323486328125,
-0.007232666015625,
-0.0036907196044921875,
0.0369873046875,
0.00399017333984375,
-0.0020275115966796875,
0.0123443603515625,
0.00609588623046875,
0.047637939453125,
0.003612518310546875,
-0.0098724365234375,
-0.0302734375,
0.0169525146484375,
0.0018682479858398438,
0.0026721954345703125,
0.0033111572265625,
-0.01800537109375,
0.0257415771484375,
-0.00498199462890625,
-0.01331329345703125,
0.00876617431640625,
0.024810791015625,
-0.0333251953125,
0.0085296630859375,
0.01190185546875,
-0.029022216796875,
-0.01280975341796875,
0.0224609375,
-0.00414276123046875,
0.0225372314453125,
-0.00879669189453125,
0.0264129638671875,
-0.038543701171875,
-0.033721923828125,
0.017059326171875,
0.0175323486328125,
0.0139923095703125,
0.0248260498046875,
0.0187530517578125,
0.0181884765625,
0.0161285400390625,
-0.01218414306640625,
0.0003981590270996094,
0.0019330978393554688,
0.0196990966796875,
0.009002685546875,
-0.007541656494140625,
0.039520263671875,
-0.0186920166015625,
0.01198577880859375,
-0.0008249282836914062,
0.025115966796875,
0.011871337890625,
-0.0033321380615234375,
0.01285552978515625,
-0.0272369384765625,
0.036895751953125,
0.01230621337890625,
0.033782958984375,
0.003383636474609375,
-0.0161590576171875,
0.0234832763671875,
0.00740814208984375,
0.0162811279296875,
-0.0119781494140625,
0.0011310577392578125,
0.0222015380859375,
0.0030574798583984375,
-0.005901336669921875,
0.009063720703125,
0.027618408203125,
-0.0028896331787109375,
-0.0095672607421875,
0.0289154052734375,
-0.0118865966796875,
-0.006198883056640625,
0.0282745361328125,
0.06585693359375,
0.0204925537109375,
0.0152130126953125,
0.01274871826171875,
-0.0033931732177734375,
-0.0270538330078125,
0.021087646484375,
0.012664794921875,
0.018951416015625,
0.034515380859375,
-0.0007815361022949219,
-0.007190704345703125,
-0.019744873046875,
0.0057525634765625,
0.00814056396484375,
0.03436279296875,
0.0028362274169921875,
-0.037933349609375,
-0.011199951171875,
-0.043670654296875,
-0.00205230712890625,
-0.00652313232421875,
0.0195159912109375,
0.01593017578125,
-0.01556396484375,
0.036712646484375,
-0.0244293212890625,
0.00026226043701171875,
0.00994110107421875,
-0.00013577938079833984,
0.01393890380859375,
0.020904541015625,
-0.04925537109375,
-0.027618408203125,
0.00821685791015625,
0.028106689453125,
-0.00519561767578125,
-0.0192718505859375,
0.00801849365234375,
-0.02667236328125,
-0.0222015380859375,
0.0003807544708251953,
-0.002117156982421875,
-0.0186309814453125,
0.01715087890625,
-0.016571044921875,
0.01531982421875,
0.0021457672119140625,
-0.014617919921875,
0.030731201171875,
-0.007251739501953125,
-0.03424072265625,
-0.00373077392578125,
0.001308441162109375,
0.0017404556274414062,
-0.0058746337890625,
0.0182647705078125,
-0.0101165771484375,
-0.01177215576171875,
-0.01238250732421875,
0.005260467529296875,
-0.005222320556640625,
0.00824737548828125,
-0.006805419921875,
-0.02996826171875,
0.0007205009460449219,
-0.006134033203125,
-0.01099395751953125,
-0.035675048828125,
0.003917694091796875,
0.027496337890625,
0.0021495819091796875,
0.04095458984375,
0.037994384765625,
0.01453399658203125,
-0.03887939453125,
0.0230560302734375,
0.002651214599609375,
0.048309326171875,
0.02569580078125,
-0.00824737548828125,
-0.010650634765625,
0.0259552001953125,
-0.0244293212890625,
0.00855255126953125,
0.02581787109375,
-0.028228759765625,
0.01427459716796875,
0.00724029541015625,
-0.033843994140625,
0.0171051025390625,
-0.04071044921875,
-0.005435943603515625,
0.0421142578125,
-0.0197601318359375,
-0.007080078125,
0.0200653076171875,
-0.000591278076171875,
0.0172576904296875,
0.0234527587890625,
0.0301666259765625,
0.01020050048828125,
-0.0246734619140625,
0.0029315948486328125,
-0.01300048828125,
0.0026340484619140625,
0.004764556884765625,
-0.00004309415817260742,
-0.002788543701171875,
0.024078369140625,
0.00260162353515625,
-0.02264404296875,
0.04437255859375,
0.012176513671875,
0.006816864013671875,
-0.0231781005859375,
-0.004032135009765625,
-0.00714111328125,
-0.007289886474609375,
0.038482666015625,
-0.0205535888671875,
-0.00293731689453125,
0.00991058349609375,
-0.01105499267578125,
0.021087646484375,
-0.0108642578125,
0.02178955078125,
0.0281524658203125,
-0.009307861328125,
0.019775390625,
0.02630615234375,
0.000025510787963867188,
-0.0143280029296875,
-0.0145416259765625,
-0.0357666015625,
0.0257568359375,
-0.010284423828125,
-0.005939483642578125,
0.01345062255859375,
0.00757598876953125,
0.0106964111328125,
-0.015899658203125,
-0.0010128021240234375,
0.007503509521484375,
-0.0289459228515625,
0.01345062255859375,
-0.0293121337890625,
-0.01111602783203125,
0.0224456787109375,
-0.0204620361328125,
0.034393310546875,
0.0166168212890625,
-0.01084136962890625,
0.002994537353515625,
0.031280517578125,
0.0242156982421875,
0.0108489990234375,
0.00971221923828125,
-0.006999969482421875,
0.01120758056640625,
-0.0275726318359375,
-0.035308837890625,
0.0174560546875,
-0.023162841796875,
0.019561767578125,
-0.02386474609375,
0.0167999267578125,
-0.007568359375,
-0.0018072128295898438,
-0.031005859375,
0.0153961181640625,
0.011627197265625,
0.0217437744140625,
0.0006747245788574219,
0.0197296142578125,
-0.00004869699478149414,
-0.0176544189453125,
-0.00010418891906738281,
0.01007080078125,
-0.023162841796875,
-0.01654052734375,
0.01441192626953125,
0.017486572265625,
-0.01171112060546875,
0.014617919921875,
-0.031585693359375,
0.0222015380859375,
0.036468505859375,
0.020050048828125,
-0.00043129920959472656,
0.01163482666015625,
0.03131103515625,
-0.00894927978515625,
0.01035308837890625,
0.01346588134765625,
0.01531219482421875,
-0.01116943359375,
-0.024444580078125,
0.00846099853515625,
-0.0240478515625,
0.01169586181640625,
-0.027923583984375,
0.011016845703125,
0.01039886474609375,
-0.0310211181640625,
-0.0283050537109375,
-0.0262298583984375,
-0.0022754669189453125,
-0.016815185546875,
0.01043701171875,
-0.01788330078125,
-0.026031494140625,
0.0246429443359375,
0.028778076171875,
0.0008835792541503906,
-0.0216522216796875,
-0.02960205078125,
0.036285400390625,
-0.00984954833984375,
-0.025115966796875,
-0.034759521484375,
-0.006412506103515625,
0.01042938232421875,
0.0283355712890625,
0.0018491744995117188,
0.00414276123046875,
0.038299560546875,
0.035430908203125,
-0.005222320556640625,
-0.01134490966796875,
0.0049591064453125,
0.0021514892578125,
0.006504058837890625,
-0.032928466796875,
-0.024810791015625,
-0.01222991943359375,
0.002178192138671875,
0.00943756103515625,
0.0078582763671875,
0.0038356781005859375,
0.0005192756652832031,
0.01483917236328125,
0.0208740234375,
0.0207672119140625,
-0.050262451171875,
-0.01398468017578125,
-0.022796630859375,
-0.002590179443359375,
0.00365447998046875,
-0.043701171875,
0.01009368896484375,
-0.0150909423828125,
0.009124755859375,
-0.01873779296875,
-0.0277862548828125,
0.00525665283203125,
-0.0213470458984375,
-0.0099334716796875,
0.0292816162109375,
-0.00959014892578125,
0.0167388916015625,
0.0245513916015625,
0.02362060546875,
0.0020122528076171875,
-0.00267791748046875,
-0.0038604736328125,
0.00738525390625,
-0.0050201416015625,
-0.020294189453125,
0.006549835205078125,
0.042755126953125,
0.028900146484375,
0.0160369873046875,
0.01006317138671875,
0.00007659196853637695,
-0.00592803955078125,
0.025146484375,
0.01544189453125,
-0.0038204193115234375,
-0.022064208984375,
0.0012903213500976562,
0.00986480712890625,
-0.01273345947265625,
-0.006771087646484375,
-0.00797271728515625,
0.003017425537109375,
0.0552978515625,
-0.01129913330078125,
0.0273895263671875,
-0.01236724853515625,
0.01690673828125,
0.0014886856079101562,
-0.0025348663330078125,
-0.031524658203125,
-0.024444580078125,
-0.00646209716796875,
0.00023627281188964844,
-0.00481414794921875,
0.0224609375,
-0.0145111083984375,
0.0384521484375,
-0.01263427734375,
-0.003509521484375,
-0.0148162841796875,
-0.0173492431640625,
0.037261962890625,
0.0031261444091796875,
0.01326751708984375,
-0.030548095703125,
0.0035648345947265625,
0.0017652511596679688,
0.029296875,
-0.025177001953125,
-0.00286865234375,
0.005367279052734375,
0.0309600830078125,
-0.02789306640625,
-0.0045318603515625,
0.0168304443359375,
-0.0260009765625,
0.01180267333984375,
0.01404571533203125,
-0.01189422607421875,
-0.021331787109375,
-0.0191192626953125,
-0.02154541015625,
-0.0257415771484375,
0.01401519775390625,
-0.0002256631851196289,
0.015594482421875,
-0.01114654541015625,
-0.03753662109375,
-0.0279693603515625,
-0.00884246826171875,
-0.0156402587890625,
-0.006549835205078125,
-0.00010019540786743164,
0.00528717041015625,
-0.0014972686767578125,
-0.00836944580078125,
0.0310516357421875,
0.01371002197265625,
0.01346588134765625,
0.01201629638671875,
-0.011932373046875,
-0.0292816162109375,
0.0033969879150390625,
-0.0071563720703125,
0.00666046142578125,
0.0226898193359375,
-0.025604248046875,
0.007488250732421875,
-0.0150299072265625,
-0.022125244140625,
-0.0013141632080078125,
-0.01214599609375,
0.01175689697265625,
0.01160430908203125,
0.0149078369140625,
-0.0037288665771484375,
0.0236053466796875,
0.01355743408203125,
-0.036102294921875,
0.04290771484375,
-0.01486968994140625,
-0.013092041015625,
-0.0023345947265625,
0.0121307373046875,
-0.0297393798828125,
0.014251708984375,
-0.0140228271484375,
0.018768310546875,
-0.006969451904296875,
0.03228759765625,
-0.00778961181640625,
0.00460052490234375,
0.0304718017578125,
-0.01059722900390625,
-0.004787445068359375,
0.0006513595581054688,
-0.005779266357421875,
-0.01519012451171875,
0.00787353515625,
-0.030792236328125,
-0.016876220703125,
0.04150390625,
0.01163482666015625,
-0.01219940185546875,
-0.0088958740234375,
0.0004374980926513672,
-0.017333984375,
-0.0012969970703125,
-0.019012451171875,
0.0011835098266601562,
-0.01085662841796875,
0.006595611572265625,
-0.0145111083984375,
-0.01837158203125,
0.0261077880859375,
-0.0251007080078125,
-0.0394287109375,
0.01551055908203125,
0.00981903076171875,
-0.00502777099609375,
-0.0014944076538085938,
-0.0175323486328125,
0.026947021484375,
0.01904296875,
-0.01110076904296875,
-0.01129913330078125,
0.042266845703125,
0.018890380859375,
0.0116424560546875,
0.0309600830078125,
0.010986328125,
0.037078857421875,
-0.005924224853515625,
0.0032176971435546875,
0.0218505859375,
-0.019195556640625,
0.01110076904296875,
0.0157928466796875,
-0.0105743408203125,
-0.0047607421875,
-0.0094757080078125,
0.0020542144775390625,
0.0121002197265625,
0.0184478759765625,
0.00289154052734375,
0.0301666259765625,
0.01099395751953125,
-0.01126861572265625,
0.0173492431640625,
-0.004974365234375,
-0.0245361328125,
-0.003452301025390625,
0.01300811767578125,
0.004741668701171875,
-0.00965118408203125,
0.0313720703125,
0.0005855560302734375,
0.00891876220703125,
0.00676727294921875,
-0.00888824462890625,
0.0262298583984375,
0.0458984375,
-0.01227569580078125,
0.0054779052734375,
-0.0007109642028808594,
0.0277099609375,
0.00981903076171875,
0.00022041797637939453,
-0.036407470703125,
0.00988006591796875,
-0.02386474609375,
-0.034332275390625,
-0.021484375,
0.015289306640625,
0.0404052734375,
-0.009002685546875,
0.0155029296875,
0.01149749755859375,
0.00647735595703125,
-0.04541015625,
-0.0213470458984375,
0.016815185546875,
0.00676727294921875,
0.017669677734375,
-0.0340576171875,
-0.0018339157104492188,
0.0214996337890625,
-0.0208740234375,
-0.0106048583984375,
-0.02581787109375,
0.0055999755859375,
-0.007541656494140625,
0.0280914306640625,
0.019775390625,
0.007534027099609375,
0.00688934326171875,
0.0093994140625,
0.0193328857421875,
-0.019500732421875,
0.0010519027709960938,
0.01456451416015625,
-0.0032062530517578125,
-0.01690673828125,
-0.0014095306396484375,
-0.00420379638671875,
0.00719451904296875,
-0.023834228515625,
-0.039642333984375,
0.01073455810546875,
-0.02325439453125,
-0.0211944580078125,
0.0169525146484375,
-0.017059326171875,
0.01317596435546875,
0.031951904296875,
0.026824951171875,
-0.040496826171875,
0.049407958984375,
0.01024627685546875,
0.023406982421875,
0.0038967132568359375,
0.023468017578125,
0.0015306472778320312,
-0.0221710205078125,
0.03985595703125,
0.01493072509765625,
0.0166015625,
-0.01256561279296875,
-0.00939178466796875,
0.01122283935546875,
-0.0202484130859375,
-0.006191253662109375,
-0.006114959716796875,
-0.00496673583984375,
-0.0195465087890625,
0.0235137939453125,
-0.0008358955383300781,
-0.00975799560546875,
0.03790283203125,
0.013427734375,
0.021514892578125,
0.0163421630859375,
0.0175933837890625,
-0.0005636215209960938,
0.00818634033203125,
0.00553131103515625,
-0.024383544921875,
0.016632080078125,
-0.0267486572265625,
0.00006461143493652344,
0.0224761962890625,
0.00116729736328125,
-0.0004744529724121094,
0.041717529296875,
-0.01464080810546875,
0.015899658203125,
-0.0244140625,
0.01055145263671875,
-0.0020923614501953125,
0.0032978057861328125,
-0.0030670166015625,
0.00788116455078125,
-0.0011205673217773438,
0.0007338523864746094,
-0.0159759521484375,
-0.006504058837890625,
-0.032012939453125,
0.0214691162109375,
0.01861572265625,
-0.00749969482421875,
-0.005828857421875,
-0.012176513671875,
0.0034046173095703125,
-0.006328582763671875,
-0.0179443359375,
0.0144500732421875,
0.00977325439453125,
-0.00008589029312133789,
0.005207061767578125,
-0.03472900390625,
-0.001064300537109375,
-0.0103607177734375,
0.037933349609375,
0.025665283203125,
0.0254974365234375,
-0.0141448974609375,
0.0265960693359375,
0.04327392578125,
-0.003330230712890625,
0.01287078857421875,
-0.01108551025390625,
0.0224761962890625,
0.026885986328125,
-0.01013946533203125,
0.050689697265625,
0.006866455078125,
0.0025577545166015625,
0.01096343994140625,
-0.006923675537109375,
0.0119171142578125,
-0.03741455078125,
-0.0170745849609375,
-0.0254364013671875,
0.0037841796875,
-0.0156402587890625,
0.0201416015625,
-0.0248565673828125,
0.01324462890625,
-0.029632568359375,
-0.01177215576171875,
0.0178070068359375,
-0.041839599609375,
0.01806640625,
-0.0037250518798828125,
-0.000469207763671875,
0.01355743408203125,
-0.01421356201171875,
0.01120758056640625,
0.00562286376953125,
0.00757598876953125,
0.01325225830078125,
0.005893707275390625,
-0.0185089111328125,
0.0092315673828125,
-0.001789093017578125,
0.01546478271484375,
0.0013885498046875,
-0.01285552978515625,
-0.0224761962890625,
-0.0209808349609375,
0.025299072265625,
0.0182037353515625,
-0.0029449462890625,
-0.0019683837890625,
0.0023517608642578125,
-0.0086212158203125,
0.01279449462890625,
-0.034271240234375,
0.032440185546875,
-0.0279541015625,
-0.001873016357421875,
-0.0306243896484375,
0.028076171875,
0.004337310791015625,
-0.00455474853515625,
-0.023895263671875,
0.00775146484375,
0.024749755859375,
-0.0019407272338867188,
-0.0290679931640625,
0.01152801513671875,
-0.00670623779296875,
0.01464080810546875,
0.003307342529296875,
0.0088348388671875,
-0.0249786376953125,
0.005340576171875,
-0.016326904296875,
-0.0081787109375,
0.0268096923828125,
0.00016605854034423828,
-0.00739288330078125,
0.01088714599609375,
-0.0218658447265625,
0.021484375,
-0.005096435546875,
0.0118865966796875,
0.0235595703125,
-0.0187225341796875,
0.025543212890625,
0.0238189697265625,
-0.01514434814453125,
-0.00601959228515625,
0.01189422607421875,
0.0198516845703125,
0.00713348388671875,
0.013885498046875,
0.01181793212890625,
0.0235748291015625,
-0.00998687744140625,
-0.00566864013671875,
-0.0237579345703125,
-0.0231781005859375,
0.0218963623046875,
-0.0080413818359375,
-0.033447265625,
-0.01360321044921875,
0.0135650634765625,
0.0079345703125,
-0.006061553955078125,
0.007427215576171875,
0.0017337799072265625,
0.02728271484375,
0.007488250732421875,
0.0172576904296875,
0.015716552734375,
0.0400390625,
0.027679443359375,
-0.0002830028533935547,
-0.0292816162109375,
-0.0018835067749023438,
0.027679443359375,
-0.0066375732421875,
0.0022411346435546875,
0.00432586669921875,
-0.00678253173828125,
-0.031341552734375,
-0.033538818359375,
0.022186279296875,
0.00833892822265625,
-0.04541015625,
0.0032978057861328125,
-0.020538330078125,
-0.0341796875,
0.003902435302734375,
0.0261077880859375,
0.054534912109375,
0.007572174072265625,
0.0248565673828125,
-0.03125,
-0.01032257080078125,
-0.00298309326171875,
0.00882720947265625,
-0.0306549072265625,
0.01515960693359375,
0.0019273757934570312,
-0.00312042236328125,
0.0458984375,
-0.026580810546875,
0.0017786026000976562,
-0.0259552001953125,
-0.01081085205078125,
0.0131988525390625,
-0.00882720947265625,
0.0256805419921875,
-0.012603759765625,
0.0092010498046875,
-0.006988525390625,
0.00922393798828125,
-0.006031036376953125,
-0.01514434814453125,
0.0389404296875,
0.0160980224609375,
-0.0091552734375,
-0.011474609375,
-0.004180908203125,
0.032135009765625,
-0.0035839080810546875,
0.0165252685546875,
0.007801055908203125,
-0.00963592529296875,
-0.026611328125,
0.01378631591796875,
-0.01284027099609375,
-0.030609130859375,
-0.0265350341796875,
-0.027923583984375,
0.005870819091796875,
-0.0090179443359375,
-0.0205078125,
0.0201416015625,
-0.0025196075439453125,
0.01422119140625,
0.00287628173828125,
-0.0000908970832824707,
0.0003247261047363281,
0.0013017654418945312,
0.032562255859375,
0.0088348388671875,
0.019439697265625,
0.00551605224609375,
-0.02386474609375,
0.003215789794921875,
-0.0003688335418701172,
0.022705078125,
0.03106689453125,
-0.01293182373046875,
0.01493072509765625,
0.034820556640625,
-0.00029015541076660156,
0.0157928466796875,
-0.0062408447265625,
0.0045013427734375,
0.004245758056640625,
0.01238250732421875,
0.01506805419921875,
-0.0322265625,
0.004802703857421875,
0.00988006591796875,
0.018218994140625,
0.053924560546875,
0.0093841552734375,
0.0131072998046875,
-0.01128387451171875,
-0.007732391357421875,
-0.0077667236328125,
-0.01358795166015625,
-0.000732421875,
-0.0007457733154296875,
0.0212860107421875,
-0.00791168212890625,
0.01233673095703125,
0.00463104248046875,
-0.0235443115234375,
0.053985595703125,
-0.00750732421875,
0.023345947265625,
0.004150390625,
-0.018463134765625,
0.01068878173828125,
0.02532958984375,
-0.026763916015625,
0.01548004150390625,
-0.022735595703125,
0.01800537109375,
0.0216827392578125,
0.011383056640625,
-0.020263671875,
-0.019744873046875,
0.016754150390625,
-0.0126495361328125,
-0.018402099609375,
-0.01702880859375,
-0.0223846435546875,
-0.0122222900390625,
0.00272369384765625,
0.03326416015625,
-0.0455322265625,
0.00777435302734375,
0.0223388671875,
0.0193023681640625,
0.0328369140625,
-0.0306549072265625,
0.01322174072265625,
-0.0194549560546875,
0.047149658203125,
0.007038116455078125,
-0.01079559326171875,
0.01291656494140625,
0.0157318115234375,
0.032867431640625,
0.0098724365234375,
0.01386260986328125,
-0.00565338134765625,
0.016510009765625,
-0.0227508544921875,
0.01190948486328125,
-0.00033092498779296875,
-0.013397216796875,
-0.044769287109375,
0.018218994140625,
-0.0157318115234375,
0.023895263671875,
-0.00482940673828125,
0.022247314453125,
0.03955078125,
-0.01216888427734375,
-0.0007910728454589844,
0.007717132568359375,
0.03143310546875,
-0.004497528076171875,
0.00885772705078125,
0.016632080078125,
-0.017486572265625,
-0.034698486328125,
-0.045379638671875,
0.01244354248046875,
-0.027008056640625,
-0.023040771484375,
0.0264892578125,
-0.0139312744140625,
0.01427459716796875,
-0.0134735107421875,
-0.0293426513671875,
-0.019134521484375,
-0.009674072265625,
0.007259368896484375,
0.003376007080078125,
0.0108642578125,
-0.00890350341796875,
0.01776123046875,
-0.01470184326171875,
0.00479888916015625,
-0.0256500244140625,
-0.0260772705078125,
-0.0009918212890625,
-0.00820159912109375,
0.01287078857421875,
-0.052764892578125,
-0.02520751953125,
-0.0250091552734375,
0.00733184814453125,
0.0212860107421875,
0.004665374755859375,
0.01238250732421875,
-0.0236358642578125,
-0.0226287841796875,
-0.002544403076171875,
0.0278167724609375,
0.0043792724609375,
-0.014129638671875,
-0.0013675689697265625,
-0.01861572265625,
0.01458740234375,
-0.000035643577575683594,
0.02069091796875,
-0.0033550262451171875,
-0.004608154296875,
-0.0199737548828125,
-0.0182952880859375,
0.01357269287109375,
-0.0092620849609375,
-0.05340576171875,
-0.005748748779296875,
-0.019927978515625,
0.006839752197265625,
-0.0157318115234375,
-0.00679779052734375,
0.0161285400390625,
-0.06512451171875,
0.00473785400390625,
0.016845703125,
-0.00011134147644042969,
-0.0020961761474609375,
0.007640838623046875,
0.0034923553466796875,
-0.0269622802734375,
0.004299163818359375,
-0.0125579833984375,
0.01050567626953125,
0.0260009765625,
-0.00884246826171875,
-0.043914794921875,
0.047607421875,
0.0216827392578125,
0.026458740234375,
-0.0219879150390625,
0.006999969482421875,
0.0018672943115234375,
0.02130126953125,
-0.01349639892578125,
-0.00818634033203125,
-0.004241943359375,
-0.055145263671875,
-0.015716552734375,
0.01519775390625,
-0.01190948486328125,
0.011138916015625,
0.016448974609375,
0.00827789306640625,
0.0025386810302734375,
0.00311279296875,
-0.002994537353515625,
0.01134490966796875,
0.005764007568359375,
0.0043182373046875,
0.0197296142578125,
0.035308837890625,
0.03955078125
] |
ours_514
|
Let \( r \) be the inradius of \( \triangle ABC \). We have:
\[
\sum \frac{r^2}{r_A^2} = \sum \left(\frac{s-a}{s}\right)^2
\]
where \( s \) is the semiperimeter of \( \triangle ABC \). The area of the hexagon formed by segments parallel to the sides of \( \triangle ABC \) and tangent to the incircle is:
\[
2r^2 \sum \tan \frac{A}{2}
\]
The area of \( \triangle ABC \), denoted \( K \), is given by:
\[
K = \frac{2r^2 \sum \tan \frac{A}{2}}{1 - \sum \left(\frac{s-a}{s}\right)^2}
\]
Substituting the given values:
\[
K = \frac{4.038}{1 - \frac{19}{20}} = \frac{2019}{25}
\]
Thus, \( m = 2019 \) and \( n = 25 \), leading to \( 100m + n = 201925 \).
\(\boxed{201925}\)
|
201925
|
{
"competition": "us_comps",
"dataset": "Ours",
"posts": null,
"source": "OMOFall19Solns.md"
}
|
Let \( \triangle ABC \) be a scalene triangle with inradius \( r = 1 \) and exradii \( r_A, r_B, \) and \( r_C \) such that
\[
20\left(r_B^2 r_C^2 + r_C^2 r_A^2 + r_A^2 r_B^2\right) = 19\left(r_A r_B r_C\right)^2
\]
If
\[
\tan \frac{A}{2} + \tan \frac{B}{2} + \tan \frac{C}{2} = 2.019
\]
then the area of \( \triangle ABC \) can be expressed as \( \frac{m}{n} \) for relatively prime positive integers \( m \) and \( n \). Compute \( 100m + n \).
|
[
"/Mathematics/Geometry/GeneralGeometry/EuclideanGeometry",
"/Mathematics/Geometry/GeneralGeometry/Geometry",
"/Mathematics/Geometry/PlaneGeometry/MiscellaneousPlaneGeometry/Area",
"/Mathematics/Geometry/PlaneGeometry/MiscellaneousPlaneGeometry/PlaneGeometry",
"/Mathematics/Geometry/PlaneGeometry/Polygons/ConvexPolygon",
"/Mathematics/Geometry/PlaneGeometry/Polygons/Polygon",
"/Mathematics/Geometry/PlaneGeometry/Polygons/SimplePolygon",
"/Mathematics/Geometry/PlaneGeometry/Polygons/TangentialPolygon",
"/Mathematics/Geometry/PlaneGeometry/Triangles/TriangleCircles",
"/Mathematics/Geometry/PlaneGeometry/Triangles/TriangleProperties",
"/Mathematics/Geometry/Trigonometry/Angles/Angle",
"/Mathematics/Geometry/Trigonometry/GeneralTrigonometry/Trigonometry",
"/Mathematics/Geometry/Trigonometry/TrigonometricFunctions/Tangent"
] |
Translate the exradius condition into the sum (s‑a)^2/s^2 = 19/20 and use K = 2r^2·∑tan(A/2) / (1‑∑(s‑a)^2/s^2) to find the area.
|
[
-0.00007712841033935547,
0.009765625,
0.021728515625,
0.019287109375,
-0.00013768672943115234,
0.0384521484375,
-0.00897216796875,
0.040374755859375,
0.00472259521484375,
-0.0267486572265625,
0.00011545419692993164,
-0.0010700225830078125,
-0.002872467041015625,
0.0088348388671875,
-0.019775390625,
-0.00653839111328125,
0.010101318359375,
-0.003673553466796875,
0.01110076904296875,
-0.00030040740966796875,
-0.013702392578125,
0.0142059326171875,
-0.055877685546875,
-0.01247406005859375,
-0.01113128662109375,
-0.0095367431640625,
-0.011260986328125,
-0.0021820068359375,
0.047821044921875,
-0.01273345947265625,
-0.01047515869140625,
-0.0195465087890625,
-0.01340484619140625,
0.0240936279296875,
0.00234222412109375,
0.01061248779296875,
0.001857757568359375,
-0.0037746429443359375,
-0.047332763671875,
-0.062744140625,
-0.0202789306640625,
0.044769287109375,
-0.0244293212890625,
-0.0095977783203125,
0.0032787322998046875,
-0.004558563232421875,
-0.00492095947265625,
-0.00269317626953125,
-0.01274871826171875,
0.017974853515625,
0.01082611083984375,
0.0243988037109375,
-0.034393310546875,
-0.0082550048828125,
-0.028656005859375,
-0.052215576171875,
-0.004146575927734375,
-0.005893707275390625,
-0.0013532638549804688,
-0.007793426513671875,
-0.0013990402221679688,
0.0028324127197265625,
-0.0112152099609375,
-0.034576416015625,
0.0028858184814453125,
-0.00027060508728027344,
-0.00791168212890625,
-0.0015211105346679688,
-0.005279541015625,
0.0184326171875,
0.0389404296875,
-0.009521484375,
0.003002166748046875,
0.032318115234375,
0.0579833984375,
-0.0154571533203125,
-0.00858306884765625,
0.00820159912109375,
-0.00894927978515625,
0.00032973289489746094,
0.0017452239990234375,
0.0223388671875,
0.0146636962890625,
-0.0302581787109375,
0.004119873046875,
-0.00496673583984375,
-0.004405975341796875,
0.013519287109375,
0.0170135498046875,
-0.0022296905517578125,
-0.005001068115234375,
0.049346923828125,
-0.021026611328125,
0.01169586181640625,
0.00984954833984375,
0.01462554931640625,
0.0086517333984375,
-0.007843017578125,
-0.017059326171875,
0.005279541015625,
-0.01264190673828125,
0.0024509429931640625,
-0.0042572021484375,
-0.0240936279296875,
0.00891876220703125,
-0.0096893310546875,
0.007320404052734375,
0.036865234375,
-0.01149749755859375,
-0.005992889404296875,
-0.001476287841796875,
0.003360748291015625,
0.0004093647003173828,
0.0005946159362792969,
-0.00196075439453125,
-0.003414154052734375,
0.039825439453125,
0.00864410400390625,
-0.0104217529296875,
-0.01165771484375,
-0.0055694580078125,
0.0130615234375,
-0.01483154296875,
0.026947021484375,
0.0199432373046875,
0.00560760498046875,
0.0123443603515625,
-0.019256591796875,
0.005222320556640625,
0.000017464160919189453,
0.02227783203125,
0.0200042724609375,
-0.01763916015625,
-0.0133056640625,
-0.053497314453125,
0.0180511474609375,
-0.01436614990234375,
-0.0013704299926757812,
-0.010101318359375,
-0.017852783203125,
-0.00022077560424804688,
0.0038738250732421875,
0.00485992431640625,
-0.041015625,
0.002948760986328125,
-0.04302978515625,
0.003078460693359375,
0.00334930419921875,
0.0183258056640625,
-0.006603240966796875,
-0.0073394775390625,
-0.0236053466796875,
0.01024627685546875,
0.007587432861328125,
-0.00429534912109375,
-0.002079010009765625,
0.005817413330078125,
0.0239105224609375,
0.01322174072265625,
-0.0066375732421875,
0.0111541748046875,
0.0004069805145263672,
-0.0012760162353515625,
0.0179290771484375,
0.0015106201171875,
-0.02764892578125,
0.007419586181640625,
0.00775909423828125,
-0.015716552734375,
-0.006717681884765625,
-0.00701904296875,
0.029541015625,
-0.005313873291015625,
0.0023822784423828125,
0.0008897781372070312,
-0.004093170166015625,
-0.0289459228515625,
0.0267181396484375,
-0.0231170654296875,
0.0005960464477539062,
0.003978729248046875,
-0.00974273681640625,
-0.0107879638671875,
-0.0004551410675048828,
0.01381683349609375,
0.004169464111328125,
0.01416778564453125,
0.0006699562072753906,
0.0221405029296875,
0.01477813720703125,
-0.0064239501953125,
0.0031337738037109375,
0.01079559326171875,
-0.00917816162109375,
0.01221466064453125,
-0.01555633544921875,
-0.0308074951171875,
0.005191802978515625,
0.0197601318359375,
-0.0014886856079101562,
-0.002315521240234375,
-0.0190582275390625,
0.02630615234375,
-0.0015392303466796875,
-0.0100250244140625,
0.01371002197265625,
0.016326904296875,
-0.006534576416015625,
-0.027923583984375,
0.015869140625,
-0.00815582275390625,
0.027587890625,
0.005573272705078125,
-0.0233612060546875,
-0.0081634521484375,
-0.0164031982421875,
-0.012664794921875,
0.00859832763671875,
-0.0150299072265625,
0.00902557373046875,
0.0031147003173828125,
0.002216339111328125,
0.01122283935546875,
-0.03466796875,
-0.003551483154296875,
0.0170135498046875,
0.006885528564453125,
-0.009124755859375,
-0.00789642333984375,
-0.006603240966796875,
-0.006000518798828125,
-0.0013151168823242188,
-0.006458282470703125,
0.0062408447265625,
-0.014495849609375,
0.00931549072265625,
-0.035400390625,
-0.0206298828125,
0.026885986328125,
-0.01226043701171875,
0.02630615234375,
-0.0159149169921875,
0.0094146728515625,
0.008209228515625,
0.0087738037109375,
0.002819061279296875,
0.00725555419921875,
0.0009584426879882812,
-0.00943756103515625,
-0.0163726806640625,
-0.004840850830078125,
0.0101776123046875,
0.00374603271484375,
-0.00762176513671875,
-0.00565338134765625,
0.01142120361328125,
0.016632080078125,
-0.012786865234375,
-0.01358795166015625,
0.0364990234375,
-0.003387451171875,
-0.00008106231689453125,
-0.00359344482421875,
-0.01306915283203125,
-0.00943756103515625,
0.01334381103515625,
-0.0133056640625,
0.00443267822265625,
0.001972198486328125,
0.005680084228515625,
0.0238494873046875,
-0.0256805419921875,
-0.0023326873779296875,
0.01119232177734375,
-0.01904296875,
-0.016845703125,
-0.00434112548828125,
0.003353118896484375,
0.0063018798828125,
0.01207733154296875,
0.01171875,
-0.0274810791015625,
-0.0301513671875,
0.0111083984375,
0.01036834716796875,
-0.015625,
0.01222991943359375,
-0.0258026123046875,
-0.0124969482421875,
-0.0009212493896484375,
-0.0063018798828125,
0.0037975311279296875,
-0.00897979736328125,
0.003856658935546875,
0.07037353515625,
-0.0040740966796875,
-0.007427215576171875,
0.02374267578125,
0.0178070068359375,
0.01320648193359375,
0.04534912109375,
-0.01318359375,
0.0010433197021484375,
0.006866455078125,
-0.0004146099090576172,
0.004810333251953125,
0.00890350341796875,
-0.00768280029296875,
-0.016448974609375,
0.018890380859375,
0.0011072158813476562,
0.008209228515625,
-0.00946044921875,
0.01042938232421875,
-0.038787841796875,
-0.03912353515625,
0.02325439453125,
0.018341064453125,
-0.006740570068359375,
0.006938934326171875,
0.005535125732421875,
0.043121337890625,
0.0104827880859375,
0.01276397705078125,
0.01178741455078125,
-0.03314208984375,
-0.0024738311767578125,
0.0160675048828125,
0.02935791015625,
0.0226898193359375,
-0.02716064453125,
0.01004791259765625,
0.0209503173828125,
-0.00041174888610839844,
0.00930023193359375,
-0.023223876953125,
-0.0146484375,
0.0268707275390625,
-0.0009284019470214844,
-0.01548004150390625,
0.01383209228515625,
-0.007511138916015625,
0.017181396484375,
-0.06536865234375,
-0.004711151123046875,
0.030609130859375,
0.007480621337890625,
0.004001617431640625,
0.0164031982421875,
-0.0509033203125,
0.007015228271484375,
0.0114593505859375,
0.0253753662109375,
-0.00012362003326416016,
-0.0033111572265625,
-0.00611114501953125,
-0.006275177001953125,
0.005573272705078125,
-0.0078582763671875,
0.0150146484375,
0.006397247314453125,
-0.004032135009765625,
-0.00653076171875,
0.017822265625,
-0.037261962890625,
0.0120391845703125,
-0.0260162353515625,
0.004062652587890625,
-0.0243377685546875,
0.00936126708984375,
-0.00896453857421875,
-0.025421142578125,
0.02227783203125,
-0.020843505859375,
0.0196533203125,
-0.0109710693359375,
0.00032520294189453125,
0.0258636474609375,
-0.004116058349609375,
-0.0086517333984375,
0.00038051605224609375,
0.0030574798583984375,
-0.007045745849609375,
0.02734375,
-0.00957489013671875,
-0.01216888427734375,
0.0280303955078125,
-0.04693603515625,
-0.0310516357421875,
-0.00800323486328125,
0.01934814453125,
-0.00826263427734375,
0.0034923553466796875,
-0.0020503997802734375,
-0.037841796875,
-0.044097900390625,
-0.00484466552734375,
-0.006732940673828125,
0.01406097412109375,
-0.0443115234375,
-0.060943603515625,
-0.0023288726806640625,
-0.0108642578125,
-0.005878448486328125,
-0.0042877197265625,
-0.0122833251953125,
-0.039886474609375,
0.0159149169921875,
0.00691986083984375,
-0.0072479248046875,
0.026153564453125,
-0.0007576942443847656,
0.0035400390625,
-0.01300811767578125,
0.0037994384765625,
-0.003459930419921875,
0.01071929931640625,
0.01116180419921875,
0.0039520263671875,
-0.01221466064453125,
0.0211181640625,
-0.015655517578125,
0.05218505859375,
-0.0186767578125,
0.017303466796875,
0.014556884765625,
-0.00336456298828125,
0.0223846435546875,
-0.0215911865234375,
-0.016265869140625,
0.0159149169921875,
0.006984710693359375,
-0.0340576171875,
-0.01116180419921875,
-0.0294036865234375,
0.00015997886657714844,
-0.004146575927734375,
-0.01800537109375,
0.00843048095703125,
-0.0027484893798828125,
-0.0197296142578125,
-0.01206207275390625,
-0.0170135498046875,
0.004581451416015625,
-0.0181732177734375,
-0.0224609375,
-0.01410675048828125,
-0.0096588134765625,
-0.016693115234375,
0.0009088516235351562,
-0.0056610107421875,
0.00792694091796875,
0.01081085205078125,
-0.016143798828125,
-0.003284454345703125,
0.0238037109375,
0.033355712890625,
-0.0211181640625,
-0.0298919677734375,
0.0132904052734375,
0.007068634033203125,
-0.004276275634765625,
0.007190704345703125,
0.00952911376953125,
-0.0214080810546875,
-0.0179290771484375,
-0.030059814453125,
0.052886962890625,
-0.01024627685546875,
0.00667572021484375,
0.0084991455078125,
-0.0130462646484375,
0.012298583984375,
-0.0280914306640625,
-0.021820068359375,
0.0258026123046875,
-0.0016117095947265625,
0.0190887451171875,
-0.020172119140625,
0.0234527587890625,
0.0149993896484375,
-0.00153350830078125,
-0.01302337646484375,
-0.009368896484375,
0.00481414794921875,
0.0268096923828125,
0.032745361328125,
-0.01535797119140625,
-0.017669677734375,
-0.042388916015625,
-0.01407623291015625,
0.01288604736328125,
0.01465606689453125,
-0.00795745849609375,
-0.0243988037109375,
-0.03851318359375,
0.007785797119140625,
0.008270263671875,
0.004772186279296875,
0.01380157470703125,
0.004302978515625,
-0.046783447265625,
0.00499725341796875,
0.0178680419921875,
0.012237548828125,
-0.0272064208984375,
0.063720703125,
-0.013824462890625,
0.0009412765502929688,
0.0157318115234375,
0.02740478515625,
0.00792694091796875,
0.036041259765625,
-0.0260467529296875,
-0.0023937225341796875,
-0.0017023086547851562,
0.014312744140625,
-0.0189056396484375,
0.00634002685546875,
0.05535888671875,
-0.0277557373046875,
0.00007778406143188477,
0.0155029296875,
0.0024929046630859375,
0.0015277862548828125,
0.01412200927734375,
-0.01605224609375,
0.024627685546875,
0.0033168792724609375,
0.01190948486328125,
-0.0024261474609375,
-0.019073486328125,
-0.0341796875,
0.03668212890625,
-0.04248046875,
0.0022182464599609375,
-0.0169830322265625,
-0.0219879150390625,
0.020050048828125,
-0.0027751922607421875,
-0.032318115234375,
0.002704620361328125,
0.01325225830078125,
-0.0247039794921875,
0.002933502197265625,
-0.01812744140625,
0.006938934326171875,
0.0080413818359375,
-0.0126495361328125,
0.0283203125,
0.0295562744140625,
0.017333984375,
-0.0196533203125,
-0.004482269287109375,
-0.04638671875,
-0.0008997917175292969,
-0.024017333984375,
0.02166748046875,
0.0022373199462890625,
0.0148162841796875,
0.0215301513671875,
0.004276275634765625,
0.054779052734375,
0.0014505386352539062,
-0.003749847412109375,
0.0009250640869140625,
0.005718231201171875,
-0.0192718505859375,
-0.01495361328125,
0.009490966796875,
0.0012407302856445312,
-0.0019006729125976562,
-0.00994110107421875,
0.017913818359375,
0.026275634765625,
-0.0306396484375,
0.0044403076171875,
-0.0299835205078125,
0.03802490234375,
-0.006366729736328125,
0.0322265625,
-0.002666473388671875,
-0.00501251220703125,
-0.003559112548828125,
0.006519317626953125,
0.0015420913696289062,
0.0091705322265625,
-0.00841522216796875,
-0.002964019775390625,
-0.0259857177734375,
-0.031646728515625,
0.0187530517578125,
0.009613037109375,
-0.0221710205078125,
-0.00464630126953125,
-0.0148468017578125,
0.02520751953125,
-0.0184478759765625,
0.0435791015625,
-0.00856781005859375,
0.00496673583984375,
-0.0009965896606445312,
-0.041412353515625,
0.00885772705078125,
-0.017669677734375,
-0.0101470947265625,
-0.02984619140625,
-0.00951385498046875,
0.00820159912109375,
0.0269775390625,
-0.01419830322265625,
0.0004343986511230469,
-0.01021575927734375,
0.003993988037109375,
-0.017578125,
0.006725311279296875,
-0.01690673828125,
0.0136566162109375,
0.023834228515625,
-0.045684814453125,
0.0126800537109375,
-0.0093231201171875,
0.00484466552734375,
0.044403076171875,
-0.002796173095703125,
-0.01441192626953125,
0.00738525390625,
-0.023345947265625,
0.033599853515625,
-0.039886474609375,
-0.012115478515625,
-0.0027923583984375,
-0.0285797119140625,
-0.013336181640625,
-0.035736083984375,
-0.0131683349609375,
-0.0009107589721679688,
0.0261688232421875,
0.003314971923828125,
-0.0207977294921875,
0.036376953125,
-0.0128936767578125,
-0.0007429122924804688,
-0.06524658203125,
-0.036163330078125,
-0.016204833984375,
-0.0167999267578125,
-0.0010232925415039062,
-0.004817962646484375,
0.0101470947265625,
-0.0006890296936035156,
-0.00615692138671875,
0.0092926025390625,
0.0188140869140625,
0.0205230712890625,
-0.00279998779296875,
-0.032684326171875,
-0.031707763671875,
0.03680419921875,
0.01378631591796875,
0.0323486328125,
-0.031219482421875,
0.007747650146484375,
-0.00203704833984375,
-0.004306793212890625,
-0.0098876953125,
-0.051483154296875,
-0.0423583984375,
0.0210418701171875,
0.0151214599609375,
-0.0408935546875,
-0.0233154296875,
-0.0048675537109375,
0.0086212158203125,
-0.035552978515625,
0.03485107421875,
-0.03961181640625,
-0.0157318115234375,
0.01153564453125,
0.02203369140625,
0.01959228515625,
0.031402587890625,
0.03741455078125,
-0.0256195068359375,
0.0157318115234375,
0.030853271484375,
0.01393890380859375,
0.00787353515625,
0.0030155181884765625,
-0.029296875,
-0.0088958740234375,
0.0030460357666015625,
-0.01555633544921875,
-0.0034198760986328125,
-0.0167694091796875,
0.006000518798828125,
0.02532958984375,
-0.0335693359375,
0.0102386474609375,
-0.0131683349609375,
0.0157470703125,
-0.01568603515625,
0.0206146240234375,
-0.028411865234375,
-0.0161895751953125,
-0.00698089599609375,
-0.0002574920654296875,
0.0023975372314453125,
-0.0513916015625,
0.023406982421875,
-0.043060302734375,
-0.0122528076171875,
-0.0248565673828125,
0.020782470703125,
-0.02874755859375,
-0.016632080078125,
-0.015960693359375,
-0.0178680419921875,
-0.00910186767578125,
0.01568603515625,
0.00035572052001953125,
0.0170745849609375,
-0.007640838623046875,
-0.0015392303466796875,
0.022918701171875,
-0.0008263587951660156,
0.0065155029296875,
-0.031494140625,
-0.0142822265625,
0.0243377685546875,
0.00275421142578125,
0.00548553466796875,
0.0369873046875,
0.0279388427734375,
-0.01806640625,
-0.02545166015625,
-0.0192718505859375,
-0.04150390625,
-0.0196533203125,
0.032745361328125,
0.03875732421875,
-0.0166778564453125,
0.0167999267578125,
0.022186279296875,
-0.0255279541015625,
-0.0182037353515625,
0.00003993511199951172,
-0.029052734375,
0.010650634765625,
0.00222015380859375,
0.0017175674438476562,
0.00868988037109375,
-0.0280303955078125,
-0.0312347412109375,
-0.00698089599609375,
-0.0023403167724609375,
-0.020660400390625,
0.01372528076171875,
0.014434814453125,
0.0236358642578125,
-0.006511688232421875,
-0.033294677734375,
0.01971435546875,
-0.01959228515625,
-0.00830078125,
-0.0374755859375,
-0.031097412109375,
-0.02374267578125,
-0.007526397705078125,
0.01274871826171875,
0.027862548828125,
-0.0119171142578125,
0.00882720947265625,
-0.01039886474609375,
0.0147705078125,
0.01322174072265625,
-0.033538818359375,
0.0005559921264648438,
0.025054931640625,
0.0090484619140625,
0.023773193359375,
-0.002376556396484375,
-0.012542724609375,
0.0197296142578125,
-0.02703857421875,
0.004154205322265625,
0.0038356781005859375,
0.01200103759765625,
0.041412353515625,
-0.01220703125,
0.01290130615234375,
-0.01800537109375,
0.04522705078125,
0.015838623046875,
-0.005718231201171875,
-0.0183258056640625,
-0.0241546630859375,
-0.0265655517578125,
0.0016317367553710938,
-0.0036106109619140625,
0.0184783935546875,
-0.02093505859375,
-0.0028705596923828125,
0.0290679931640625,
0.03863525390625,
0.0034389495849609375,
0.005817413330078125,
-0.0038738250732421875,
-0.020721435546875,
0.0254058837890625,
0.004150390625,
-0.0114898681640625,
0.029327392578125,
0.005985260009765625,
0.00382232666015625,
-0.045867919921875,
-0.01178741455078125,
-0.0106353759765625,
0.023468017578125,
0.01337432861328125,
-0.015838623046875,
0.022552490234375,
0.00012981891632080078,
-0.0202484130859375,
-0.023956298828125,
-0.0031261444091796875,
-0.00997161865234375,
0.0207061767578125,
0.0171356201171875,
0.0088958740234375,
0.022674560546875,
-0.016937255859375,
-0.039215087890625,
-0.0008144378662109375,
-0.019012451171875,
0.022705078125,
-0.00015413761138916016,
-0.015777587890625,
0.0004627704620361328,
-0.03460693359375,
0.016876220703125,
-0.00479888916015625,
0.0264892578125,
0.031585693359375,
0.00885772705078125,
-0.01212310791015625,
0.001392364501953125,
0.045379638671875,
0.03131103515625,
-0.003444671630859375,
-0.0115203857421875,
0.02606201171875,
-0.0312042236328125,
0.0198822021484375,
-0.016082763671875,
-0.00019240379333496094,
0.0287628173828125,
-0.0150299072265625,
0.0028133392333984375,
-0.014617919921875,
0.00164794921875,
0.0037631988525390625,
0.0131988525390625,
0.020233154296875,
-0.0003516674041748047,
0.00859832763671875,
0.005298614501953125,
0.0091552734375,
0.05780029296875,
-0.00827789306640625,
0.0184326171875,
-0.036529541015625,
0.0213623046875,
-0.0006380081176757812,
0.031951904296875,
0.033355712890625,
0.005535125732421875,
0.024444580078125,
0.025054931640625,
-0.0103912353515625,
0.01313018798828125,
-0.01227569580078125,
-0.01526641845703125,
-0.002010345458984375,
0.0163421630859375,
-0.001979827880859375,
0.00441741943359375,
-0.006053924560546875,
-0.00417327880859375,
-0.019622802734375,
-0.00836181640625,
-0.0098419189453125,
0.0163421630859375,
-0.005641937255859375,
0.0239410400390625,
0.00537109375,
0.01222991943359375,
-0.01320648193359375,
-0.0038890838623046875,
-0.021270751953125,
0.0157012939453125,
0.01488494873046875,
0.021484375,
-0.02532958984375,
0.006072998046875,
-0.039459228515625,
-0.01309967041015625,
0.00844573974609375,
-0.0179443359375,
0.0157318115234375,
0.017333984375,
0.007114410400390625,
0.0204925537109375,
0.036895751953125,
0.010345458984375,
0.02801513671875,
-0.00832366943359375,
0.005096435546875,
-0.013885498046875,
0.01235198974609375,
0.00812530517578125,
0.019622802734375,
-0.0104217529296875,
-0.002315521240234375,
-0.01139068603515625,
-0.0274810791015625,
0.01285552978515625,
-0.00762176513671875,
-0.0157012939453125,
0.032867431640625,
-0.0014867782592773438,
0.0202178955078125,
-0.0142669677734375,
-0.0233154296875,
-0.04052734375,
-0.0028171539306640625,
-0.0034542083740234375,
-0.0316162109375,
0.0013322830200195312,
-0.0290985107421875,
0.002044677734375,
0.0255126953125,
0.0209503173828125,
0.0002199411392211914,
0.01288604736328125,
0.0180206298828125,
-0.0192413330078125,
0.0159149169921875,
0.041595458984375,
-0.0201263427734375,
0.0002117156982421875,
-0.010345458984375,
0.01065826416015625,
0.0237274169921875,
-0.0178070068359375,
0.004638671875,
0.0172119140625,
0.01190948486328125,
0.004276275634765625,
0.00833892822265625,
0.028564453125,
-0.0003905296325683594,
-0.00415802001953125,
-0.023101806640625,
-0.011199951171875,
0.013641357421875,
0.0322265625,
0.03839111328125,
0.0068511962890625,
0.01605224609375,
0.0276031494140625,
-0.0222320556640625,
-0.00799560546875,
-0.015716552734375,
-0.003032684326171875,
0.00665283203125,
-0.0059967041015625,
0.01800537109375,
0.0173492431640625,
0.0015954971313476562,
-0.06634521484375,
0.0109710693359375,
-0.0017452239990234375,
-0.01511383056640625,
0.0003848075866699219,
0.01039886474609375,
0.020660400390625,
-0.02313232421875,
0.05511474609375,
0.011138916015625,
0.005298614501953125,
0.0399169921875,
-0.011810302734375,
0.0321044921875,
-0.005229949951171875,
0.03564453125,
0.0157318115234375,
-0.020111083984375,
0.01219940185546875,
-0.0178985595703125,
-0.0277862548828125,
0.0210723876953125,
0.036376953125,
-0.0040740966796875,
0.0106964111328125,
-0.015869140625,
-0.01117706298828125,
0.0258636474609375,
0.0111846923828125,
0.01464080810546875,
-0.01519012451171875,
0.0241851806640625,
-0.0011615753173828125,
0.016998291015625,
-0.0171661376953125,
0.023529052734375,
0.003936767578125,
-0.0029468536376953125,
-0.0178070068359375,
0.027587890625,
0.0114288330078125,
-0.001613616943359375,
-0.0101470947265625,
-0.022613525390625,
-0.00787353515625,
-0.0142669677734375,
-0.0298919677734375,
-0.0135650634765625,
0.02276611328125,
0.004405975341796875,
-0.00925445556640625,
0.0169525146484375,
-0.005496978759765625,
-0.048370361328125,
0.0032253265380859375,
-0.0239105224609375,
0.0095977783203125,
-0.030517578125,
0.017730712890625,
0.0196380615234375,
-0.01373291015625,
-0.00812530517578125,
-0.00640869140625,
-0.0132293701171875,
-0.04595947265625,
0.01055908203125,
-0.00630950927734375,
-0.007442474365234375,
-0.00007611513137817383,
0.0014495849609375,
0.007167816162109375,
-0.006931304931640625,
0.0090484619140625,
-0.0006442070007324219,
0.020263671875,
0.047271728515625,
0.001873016357421875,
0.01201629638671875,
0.0014066696166992188,
-0.005664825439453125,
0.02557373046875,
-0.045013427734375,
0.0038433074951171875,
-0.0255279541015625,
0.018707275390625,
-0.0082855224609375,
-0.0182952880859375,
-0.003894805908203125,
0.017822265625,
0.015838623046875,
-0.055755615234375,
-0.00231170654296875,
-0.008331298828125,
-0.0113677978515625,
0.0025424957275390625,
-0.027557373046875,
0.007190704345703125,
-0.024078369140625,
-0.0014982223510742188,
0.0167999267578125,
-0.004230499267578125,
0.0208282470703125,
-0.046661376953125,
0.030242919921875,
0.00904083251953125,
0.017181396484375,
-0.0191497802734375,
-0.051971435546875,
0.009674072265625,
-0.015960693359375,
-0.031036376953125,
-0.033721923828125,
-0.0189971923828125,
0.00737762451171875,
0.0170745849609375,
-0.009368896484375,
0.0256195068359375,
0.01117706298828125,
0.0202178955078125,
-0.003932952880859375,
0.0030879974365234375,
0.039459228515625,
0.01024627685546875,
0.002559661865234375,
0.01519775390625,
-0.01091766357421875,
-0.020904541015625,
-0.0201873779296875,
0.01256561279296875,
0.0105133056640625,
0.0131378173828125,
0.0200653076171875,
0.02667236328125,
0.00543975830078125,
-0.0186767578125,
0.0039520263671875,
-0.011810302734375,
-0.0124053955078125,
0.0198822021484375,
-0.043182373046875,
-0.0006647109985351562,
-0.0001277923583984375,
0.021240234375,
0.0012340545654296875,
0.012908935546875,
-0.0026302337646484375,
0.01090240478515625,
-0.018280029296875,
-0.00888824462890625,
-0.0012493133544921875,
0.035736083984375,
-0.0021266937255859375,
-0.0157470703125,
-0.0163726806640625,
-0.01220703125,
0.00921630859375,
0.006702423095703125,
-0.0252685546875,
0.007350921630859375,
-0.026641845703125,
0.0018482208251953125,
0.01013946533203125,
0.01502227783203125,
-0.0386962890625,
0.0068359375,
0.003910064697265625,
-0.01157379150390625,
-0.007633209228515625,
0.018646240234375,
0.0135650634765625,
-0.007293701171875,
0.0008854866027832031,
0.04888916015625,
0.012725830078125,
-0.0295867919921875,
0.00302886962890625,
-0.028106689453125,
-0.01052093505859375,
0.024932861328125,
-0.0205078125,
-0.0182342529296875,
0.0142669677734375,
0.027313232421875,
0.033447265625,
0.00028324127197265625,
0.013031005859375,
0.0018758773803710938,
0.01372528076171875,
0.0006451606750488281,
0.040191650390625,
0.0009002685546875,
-0.0003426074981689453,
0.02716064453125,
-0.004138946533203125,
-0.0308837890625,
-0.007537841796875,
-0.0242767333984375,
-0.0294647216796875,
-0.022735595703125,
0.004192352294921875,
-0.051055908203125,
0.002330780029296875,
0.0146636962890625,
-0.01453399658203125,
0.002277374267578125,
-0.0215301513671875,
-0.032989501953125,
0.004695892333984375,
-0.0207061767578125,
0.01284027099609375,
0.005100250244140625,
-0.017333984375,
-0.0210113525390625,
0.0124664306640625,
0.006549835205078125,
0.0187530517578125,
-0.0146942138671875,
-0.0169677734375,
-0.029937744140625,
-0.002941131591796875,
-0.0000947713851928711,
0.01493072509765625,
-0.041290283203125,
-0.00850677490234375,
0.03009033203125,
0.0213623046875,
-0.0176849365234375,
0.004375457763671875,
-0.02197265625,
0.0247344970703125,
0.0005297660827636719,
-0.0213165283203125,
0.0108489990234375,
-0.004642486572265625,
0.040435791015625,
-0.0257415771484375,
-0.0205535888671875,
0.0014591217041015625,
-0.03314208984375,
-0.005413055419921875,
0.015045166015625,
0.023834228515625,
0.01488494873046875,
0.005764007568359375,
-0.0012874603271484375,
-0.00617218017578125,
-0.003620147705078125,
0.021453857421875,
0.0004074573516845703,
-0.004497528076171875,
0.01959228515625,
0.044677734375,
-0.00807952880859375,
0.0282745361328125,
-0.0165557861328125,
-0.039398193359375,
-0.00441741943359375,
0.0152435302734375,
-0.03179931640625,
-0.0083770751953125,
-0.00531768798828125,
0.01085662841796875,
-0.004360198974609375,
-0.004791259765625,
0.0198211669921875,
-0.01078033447265625,
-0.032135009765625,
-0.01049041748046875,
-0.049560546875,
0.0523681640625,
-0.0027370452880859375,
0.006969451904296875,
-0.01422119140625,
-0.015960693359375,
0.006031036376953125,
0.00977325439453125,
0.00836944580078125,
0.01399993896484375,
0.0190582275390625,
-0.020172119140625,
-0.022308349609375,
0.02191162109375,
0.0020046234130859375,
-0.05389404296875,
0.003757476806640625,
-0.0010652542114257812,
0.0142059326171875,
0.034576416015625,
0.037872314453125,
0.0126953125,
0.034515380859375,
-0.00635528564453125,
0.016143798828125,
0.03759765625,
0.0345458984375,
0.00923919677734375,
0.01629638671875,
-0.0223541259765625,
0.0015735626220703125,
0.013336181640625,
-0.00347900390625,
-0.01788330078125,
0.045501708984375,
0.021636962890625,
-0.0037994384765625,
0.00464630126953125,
0.00731658935546875,
0.0234375,
-0.0116729736328125,
0.028289794921875,
0.0264434814453125,
0.0280303955078125,
-0.01467132568359375,
0.032806396484375,
0.0191650390625,
-0.030914306640625,
-0.0038242340087890625,
0.032806396484375,
0.0252838134765625,
0.004955291748046875,
-0.005191802978515625,
-0.0214080810546875,
0.0190582275390625,
0.006366729736328125,
-0.021636962890625,
0.01503753662109375,
-0.00902557373046875,
0.0016756057739257812,
0.003643035888671875,
0.0010976791381835938,
-0.0284271240234375,
0.0197601318359375,
0.0058746337890625,
-0.00809478759765625,
0.044677734375,
-0.022430419921875,
0.01493072509765625,
-0.00965118408203125,
-0.007717132568359375,
0.0027484893798828125,
-0.00992584228515625,
0.0225067138671875,
-0.040740966796875,
-0.03350830078125,
-0.01557159423828125,
-0.034423828125,
-0.026580810546875,
-0.0377197265625,
-0.0325927734375,
-0.0028362274169921875,
-0.006366729736328125,
0.03094482421875,
-0.031890869140625,
-0.003719329833984375,
0.022796630859375,
0.004711151123046875,
0.019256591796875,
0.033935546875,
0.01129913330078125,
-0.00031375885009765625,
-0.01189422607421875,
0.027587890625,
-0.041259765625,
0.0038394927978515625,
-0.01381683349609375,
-0.0102996826171875,
-0.046661376953125,
-0.0124664306640625,
0.006137847900390625,
-0.0123748779296875,
-0.0011453628540039062,
0.0081939697265625,
0.0224456787109375,
0.03802490234375,
-0.048492431640625,
-0.0107879638671875,
0.01421356201171875,
0.0296478271484375,
-0.01136016845703125,
0.01152801513671875,
0.01107025146484375,
-0.007114410400390625,
0.0064544677734375,
0.01212310791015625,
0.047698974609375,
-0.0035305023193359375,
0.00408172607421875,
-0.0222625732421875,
-0.047698974609375,
-0.004180908203125,
-0.01441192626953125,
-0.007335662841796875,
-0.0030364990234375,
-0.027008056640625,
0.00876617431640625,
-0.03240966796875,
-0.01181793212890625,
-0.027130126953125,
-0.00475311279296875,
0.01470947265625,
0.01073455810546875,
0.00021588802337646484,
-0.01052093505859375,
-0.048675537109375,
-0.00004851818084716797,
0.00357818603515625,
-0.0036563873291015625,
-0.01348876953125,
0.01406097412109375,
-0.005519866943359375,
0.0096588134765625,
0.007762908935546875,
-0.010040283203125,
0.012664794921875,
0.038421630859375,
-0.005584716796875,
0.0005383491516113281,
0.0024929046630859375,
-0.0290679931640625,
0.0177154541015625,
-0.004627227783203125,
-0.0195465087890625,
0.0033740997314453125,
0.02545166015625,
0.01132965087890625,
-0.01568603515625,
-0.00513458251953125,
0.0045318603515625,
0.0006866455078125,
-0.007755279541015625,
0.00385284423828125,
-0.007801055908203125,
0.00484466552734375,
-0.033905029296875,
0.0258941650390625,
-0.03125,
0.011810302734375,
-0.0299835205078125,
-0.0230712890625,
0.0229339599609375,
0.0158843994140625,
0.02227783203125,
-0.001949310302734375,
-0.0258636474609375,
-0.0139312744140625,
-0.0142822265625,
0.00527191162109375,
-0.0033206939697265625,
-0.0036773681640625,
-0.0099029541015625,
-0.0143585205078125,
0.017669677734375,
-0.01666259765625,
0.0014600753784179688,
-0.009796142578125,
0.00536346435546875,
0.0208892822265625,
0.024810791015625,
0.04931640625,
-0.023345947265625,
-0.00905609130859375,
-0.0136260986328125,
0.01479339599609375,
0.00638580322265625,
-0.0190277099609375,
-0.0207366943359375,
0.0236358642578125,
0.00939178466796875,
0.0132293701171875,
-0.0301513671875,
-0.0021610260009765625,
-0.0283660888671875,
-0.0157318115234375,
-0.0154266357421875,
0.0112762451171875,
-0.018890380859375,
0.0240020751953125,
0.0023441314697265625,
-0.003269195556640625,
-0.01276397705078125,
-0.02288818359375,
-0.0263671875,
0.0189056396484375,
0.02398681640625,
0.0295562744140625,
0.0200958251953125,
0.0153961181640625,
0.026611328125,
0.00418853759765625,
-0.01302337646484375,
0.00882720947265625,
0.008026123046875,
-0.01137542724609375,
0.01837158203125,
-0.0095367431640625,
0.0018033981323242188,
0.03607177734375,
0.005840301513671875,
0.01039886474609375,
-0.0032634735107421875,
0.004581451416015625,
0.0209808349609375,
0.0164031982421875,
0.0179595947265625,
-0.01285552978515625,
0.0037784576416015625,
0.0249786376953125,
-0.020294189453125,
-0.0004870891571044922,
-0.037872314453125,
-0.0008664131164550781,
-0.02490234375,
0.0208587646484375,
0.004749298095703125,
0.0286102294921875,
-0.00897979736328125,
0.0139923095703125,
-0.020050048828125,
0.00555419921875,
-0.030975341796875,
0.041229248046875,
0.0167083740234375,
0.0099029541015625,
0.003162384033203125,
0.050750732421875,
-0.037261962890625,
-0.05780029296875,
0.013275146484375,
0.0030193328857421875,
0.001247406005859375,
0.016387939453125,
-0.02679443359375,
0.001346588134765625,
0.0173492431640625,
-0.034698486328125,
0.00815582275390625,
0.0007839202880859375,
0.0090484619140625,
-0.01197052001953125,
0.004337310791015625,
0.035736083984375,
-0.00930023193359375,
0.0260162353515625,
0.0164642333984375,
0.041595458984375,
-0.010345458984375,
0.0243988037109375,
-0.01041412353515625,
-0.0238800048828125,
0.0106048583984375,
-0.01346588134765625,
0.0181732177734375,
0.0279388427734375,
0.016448974609375,
-0.015960693359375,
-0.0223388671875,
0.004756927490234375,
-0.0007414817810058594,
0.005001068115234375,
0.004886627197265625,
0.018951416015625,
-0.0135955810546875,
-0.01215362548828125,
-0.0009732246398925781,
-0.0256805419921875,
0.0291595458984375,
-0.0038127899169921875,
0.0372314453125,
0.044342041015625,
-0.027618408203125,
0.045562744140625,
0.01275634765625,
0.0176849365234375,
0.00923919677734375,
0.0162353515625,
0.01247406005859375,
0.004352569580078125,
0.0211639404296875,
0.0244293212890625,
-0.01293182373046875,
0.0175018310546875,
0.0350341796875,
-0.006824493408203125,
-0.00429534912109375,
-0.0182342529296875,
-0.0234222412109375,
-0.01500701904296875,
0.0016679763793945312,
0.0022716522216796875,
-0.0235595703125,
-0.009765625,
0.00959014892578125,
-0.01262664794921875,
0.00286102294921875,
0.00485992431640625,
0.0049591064453125,
0.00775909423828125,
-0.015838623046875,
0.0080413818359375,
0.01486968994140625,
-0.0212249755859375,
-0.0180816650390625,
0.00734710693359375,
0.0231475830078125,
-0.006572723388671875,
0.0187225341796875,
-0.006000518798828125,
0.01026153564453125,
0.005191802978515625,
0.0024852752685546875,
0.0100555419921875,
0.0028839111328125,
0.0247650146484375,
-0.02410888671875,
0.0123138427734375,
-0.029632568359375,
0.00489044189453125,
0.0037593841552734375,
0.0311737060546875,
0.0218963623046875,
-0.018463134765625,
0.0190887451171875,
-0.0010833740234375,
0.01338958740234375,
-0.0117034912109375,
0.0017070770263671875,
0.0067291259765625,
0.01934814453125,
-0.00894927978515625,
0.0190887451171875,
-0.01123809814453125,
0.006450653076171875,
-0.025146484375,
-0.00384521484375,
0.0182037353515625,
0.0269622802734375,
-0.0093231201171875,
0.043670654296875,
-0.016876220703125,
0.041259765625,
0.012054443359375,
-0.0034427642822265625,
0.01508331298828125,
0.0252838134765625,
-0.0080718994140625,
0.01418304443359375,
-0.0108489990234375,
0.0025157928466796875,
0.0186767578125,
-0.004852294921875,
0.0097808837890625,
0.00022971630096435547,
0.022918701171875,
0.0278472900390625,
-0.0201873779296875,
0.01512908935546875,
-0.0004601478576660156,
0.022125244140625,
-0.002040863037109375,
0.00811004638671875,
-0.00362396240234375,
-0.016937255859375,
0.02777099609375,
-0.015472412109375,
-0.0009169578552246094,
-0.0243072509765625,
-0.03240966796875,
-0.001064300537109375,
0.00506591796875,
-0.0180511474609375,
0.018280029296875,
-0.0094451904296875,
0.0015649795532226562,
0.01129913330078125,
-0.00887298583984375,
-0.0258026123046875,
0.017974853515625,
-0.03533935546875,
0.0008883476257324219,
0.005260467529296875,
-0.01194000244140625,
0.0184783935546875,
0.006893157958984375,
0.01378631591796875,
-0.0252838134765625,
-0.0009555816650390625,
-0.01629638671875,
-0.01262664794921875,
-0.020751953125,
0.0141143798828125,
0.017425537109375,
-0.007354736328125,
0.004970550537109375,
-0.00896453857421875,
-0.0051422119140625,
-0.01531982421875,
-0.0039825439453125,
-0.0073394775390625,
-0.01146697998046875,
-0.010711669921875,
-0.0109100341796875,
-0.0184478759765625,
-0.0181732177734375,
0.01226043701171875,
0.0144805908203125,
-0.022613525390625,
-0.0015077590942382812,
0.013275146484375,
0.01605224609375,
0.004909515380859375,
0.03265380859375,
0.009002685546875,
-0.030059814453125,
0.033843994140625,
0.0308380126953125,
0.01611328125,
0.01361846923828125,
0.00787353515625,
-0.01751708984375,
0.0131072998046875,
-0.02099609375,
-0.0099945068359375,
0.0035247802734375,
-0.01073455810546875,
0.0182647705078125,
0.0253448486328125,
-0.017425537109375,
0.006744384765625,
-0.03839111328125,
0.009429931640625,
0.0011720657348632812,
-0.0282135009765625,
-0.0028095245361328125,
-0.006542205810546875,
-0.0000998377799987793,
-0.01335906982421875,
0.0345458984375,
0.0104827880859375,
-0.043914794921875,
-0.041107177734375,
-0.007350921630859375,
0.00018131732940673828,
-0.008880615234375,
0.004596710205078125,
-0.007335662841796875,
-0.00021755695343017578,
-0.00455474853515625,
-0.00464630126953125,
0.01102447509765625,
0.01433563232421875,
-0.0153656005859375,
-0.006664276123046875,
-0.0226898193359375,
0.0225830078125,
0.0030670166015625,
-0.0193023681640625,
0.00533294677734375,
0.00437164306640625,
-0.00682830810546875,
-0.00969696044921875,
0.01442718505859375,
0.005893707275390625,
0.0245513916015625,
-0.00804901123046875,
-0.0016965866088867188,
0.00803375244140625,
0.01416015625,
-0.0030727386474609375,
0.0208282470703125,
0.020538330078125,
-0.01027679443359375,
0.0041961669921875,
0.01294708251953125,
-0.00022745132446289062,
-0.0098419189453125,
-0.0035114288330078125,
-0.0238189697265625,
-0.0158843994140625,
-0.02349853515625,
-0.01105499267578125,
0.021392822265625,
-0.00033092498779296875,
0.0228729248046875,
0.0005788803100585938,
-0.0207061767578125,
0.01593017578125,
-0.003448486328125,
-0.0269317626953125,
0.00839996337890625,
0.004955291748046875,
0.0250244140625,
0.036163330078125,
0.00794219970703125,
0.0027713775634765625,
0.0124664306640625,
-0.02142333984375,
0.03277587890625,
0.0237579345703125,
-0.0140533447265625,
-0.020294189453125,
-0.00797271728515625,
0.00864410400390625,
-0.005123138427734375,
0.0278778076171875,
-0.0287322998046875,
-0.0064544677734375,
-0.00533294677734375,
0.0013179779052734375,
-0.0391845703125,
-0.035919189453125,
-0.032745361328125,
0.0182952880859375,
-0.0266876220703125,
-0.034912109375,
-0.014007568359375,
0.0100555419921875,
0.01435089111328125,
0.0190582275390625,
0.01190185546875,
0.0038776397705078125,
-0.035552978515625,
0.0187225341796875,
-0.014251708984375,
-0.0275115966796875,
0.017364501953125,
-0.029327392578125,
-0.0197906494140625,
0.00789642333984375,
0.03350830078125,
-0.023834228515625,
0.005107879638671875,
0.04693603515625,
-0.0017576217651367188,
0.006862640380859375,
-0.0183258056640625,
-0.01090240478515625,
0.00623321533203125,
0.00531768798828125,
-0.018035888671875,
0.01113128662109375,
-0.0033111572265625,
0.0053558349609375,
-0.0100555419921875,
-0.020233154296875,
-0.00907135009765625,
-0.034881591796875,
0.01010894775390625,
-0.01158905029296875,
-0.01206207275390625,
0.0438232421875,
0.016510009765625,
-0.012603759765625,
-0.035552978515625,
-0.006458282470703125,
0.03033447265625,
0.005161285400390625,
-0.003204345703125,
-0.0107269287109375,
-0.0099029541015625,
-0.01494598388671875,
-0.0251007080078125,
0.031036376953125,
-0.01165771484375,
0.00800323486328125,
0.0133514404296875,
-0.0386962890625,
0.00911712646484375,
0.011993408203125,
0.009613037109375,
-0.007904052734375,
-0.0087127685546875,
-0.0345458984375,
0.0172271728515625,
0.018310546875,
0.0184326171875,
0.0150604248046875,
0.019012451171875,
0.00647735595703125,
-0.04583740234375,
0.0247039794921875,
0.03826904296875,
-0.0204315185546875,
-0.01168060302734375,
0.029449462890625,
0.0130157470703125,
-0.01493072509765625,
-0.004180908203125,
-0.01422119140625,
0.001102447509765625,
-0.018798828125,
0.0083465576171875,
-0.0298004150390625,
-0.01027679443359375,
0.00818634033203125,
0.00004684925079345703,
-0.0179443359375,
-0.041290283203125,
0.0013942718505859375,
0.00897979736328125,
0.03326416015625,
-0.00763702392578125,
-0.0008015632629394531,
0.009368896484375,
0.0037441253662109375,
0.003726959228515625,
0.0024662017822265625,
0.01398468017578125,
0.0306243896484375,
0.018280029296875,
0.00655364990234375,
-0.0131072998046875,
0.033203125,
0.01070404052734375,
-0.0002570152282714844,
0.0070343017578125,
-0.017333984375,
0.01081085205078125,
-0.01103973388671875,
-0.0035533905029296875,
0.031402587890625,
-0.02532958984375,
0.0171966552734375,
-0.0282440185546875,
0.005115509033203125,
-0.01308441162109375,
0.01373291015625,
0.01522064208984375,
-0.01088714599609375,
-0.037200927734375,
-0.0006651878356933594,
0.01253509521484375,
-0.0264739990234375,
0.014739990234375,
-0.0274810791015625,
-0.036224365234375,
0.039398193359375,
-0.0037746429443359375,
0.033447265625,
-0.001834869384765625,
0.01099395751953125,
-0.01204681396484375,
0.017059326171875,
0.0226898193359375,
-0.0007710456848144531,
0.007442474365234375,
-0.008087158203125,
0.01009368896484375,
-0.0084991455078125,
0.034423828125,
-0.002674102783203125,
-0.0011730194091796875,
0.0011854171752929688,
0.0147247314453125,
-0.0135498046875,
-0.006458282470703125,
-0.0026760101318359375,
-0.0419921875,
0.00878143310546875,
-0.01274871826171875,
-0.01702880859375,
0.0033130645751953125,
0.01348876953125,
0.00801849365234375,
-0.036773681640625,
-0.00888824462890625,
-0.01244354248046875,
-0.0106658935546875,
-0.0164642333984375,
-0.01445770263671875,
-0.0229949951171875,
0.018585205078125,
-0.0245208740234375,
-0.016571044921875,
0.0236663818359375,
0.01141357421875,
0.0021762847900390625,
0.0269927978515625,
0.0152587890625,
0.01064300537109375,
0.00603485107421875,
-0.004825592041015625,
-0.027679443359375,
-0.0350341796875,
-0.0220794677734375,
0.01690673828125,
0.020782470703125,
-0.00222015380859375,
-0.0289764404296875,
0.00815582275390625,
-0.0262451171875,
0.003704071044921875,
0.02105712890625,
0.0005278587341308594,
0.0158233642578125,
0.0143280029296875,
-0.013397216796875,
-0.0015211105346679688,
0.0108795166015625,
0.0125732421875,
-0.037200927734375,
-0.00420379638671875,
0.0003733634948730469,
-0.0299072265625,
0.0109405517578125,
0.00841522216796875,
-0.0309295654296875,
0.019561767578125,
-0.0208740234375,
-0.01279449462890625,
0.005001068115234375,
0.0178375244140625,
-0.030731201171875,
-0.007617950439453125,
-0.01110076904296875,
0.003376007080078125,
-0.007232666015625,
0.0005125999450683594,
0.037384033203125,
-0.0007901191711425781,
-0.00634765625,
0.0162506103515625,
0.042694091796875,
0.0028324127197265625,
-0.00902557373046875,
0.0233306884765625,
0.022979736328125,
-0.0279388427734375,
0.0299224853515625,
0.0015497207641601562,
-0.013702392578125,
0.031341552734375,
-0.002044677734375,
0.0277557373046875,
-0.00905609130859375,
-0.00598907470703125,
0.0531005859375,
-0.00008106231689453125,
-0.0274658203125,
0.0303192138671875,
0.0172271728515625,
-0.0228729248046875,
-0.045867919921875,
-0.0162353515625,
-0.00507354736328125,
-0.0023899078369140625,
-0.024444580078125,
-0.0377197265625,
0.01399993896484375,
0.008270263671875,
0.01152801513671875,
-0.01497650146484375,
-0.01434326171875,
0.053985595703125,
-0.001934051513671875,
-0.003803253173828125,
-0.0012273788452148438,
-0.0006213188171386719,
0.0185089111328125,
-0.00823211669921875,
-0.005733489990234375,
0.0090789794921875,
-0.007343292236328125,
-0.007244110107421875,
0.01580810546875,
0.01212310791015625,
-0.00911712646484375,
-0.0025424957275390625,
0.029296875,
-0.027801513671875,
0.001262664794921875,
0.01142120361328125,
0.00989532470703125,
-0.00821685791015625,
0.0103759765625,
-0.030731201171875,
0.00850677490234375,
0.005100250244140625,
-0.01155853271484375,
0.00209808349609375,
0.0010824203491210938,
-0.00797271728515625,
0.0205841064453125,
0.0178070068359375,
0.01416778564453125,
-0.0038394927978515625,
0.018402099609375,
-0.0134124755859375,
0.005298614501953125,
0.0195159912109375,
0.005306243896484375,
-0.005695343017578125,
0.037506103515625,
0.0068511962890625,
-0.0159759521484375,
0.01275634765625,
0.0024566650390625,
-0.01291656494140625,
0.03558349609375,
-0.00626373291015625,
0.0285797119140625,
-0.0101318359375,
0.01171112060546875,
0.00836181640625,
0.006534576416015625,
-0.00492095947265625,
-0.02886962890625,
-0.03631591796875,
0.0028858184814453125,
0.0189971923828125,
-0.003696441650390625,
-0.0239105224609375,
-0.0171356201171875,
0.0076904296875,
-0.0156097412109375,
-0.004932403564453125,
-0.0066986083984375,
0.0309600830078125,
-0.01287078857421875,
-0.0158843994140625,
-0.055572509765625,
0.01316070556640625,
0.0380859375,
0.02142333984375,
-0.0188751220703125,
-0.0017557144165039062,
0.0201873779296875,
0.006290435791015625,
-0.02569580078125,
-0.0211639404296875,
0.02813720703125,
0.0269317626953125,
-0.01111602783203125,
0.01520538330078125,
-0.01192474365234375,
0.01404571533203125,
-0.000789642333984375,
0.00887298583984375,
-0.0015850067138671875,
0.018890380859375,
0.0007991790771484375,
-0.02972412109375,
0.0163116455078125,
0.016937255859375,
0.01641845703125,
-0.01194000244140625,
0.029205322265625,
-0.005077362060546875,
-0.0026264190673828125,
0.00408935546875,
0.00911712646484375,
-0.023284912109375,
-0.0057830810546875,
0.01251983642578125,
-0.02362060546875,
-0.0163421630859375,
0.0032958984375,
0.0171051025390625,
-0.0100860595703125,
-0.050384521484375,
-0.0174560546875,
-0.0012760162353515625,
-0.00022649765014648438,
0.002544403076171875,
0.01409912109375,
0.004974365234375,
0.0226593017578125,
0.01457977294921875,
0.0264129638671875,
0.0361328125,
-0.025177001953125,
0.005130767822265625,
0.0296630859375,
-0.0217437744140625,
-0.0006189346313476562,
0.02191162109375,
-0.0266571044921875,
0.0025997161865234375,
-0.039886474609375,
0.007701873779296875,
0.0172119140625,
0.0164031982421875,
0.01031494140625,
-0.03326416015625,
-0.0120086669921875,
-0.0025768280029296875,
-0.034332275390625,
-0.01001739501953125,
-0.0082855224609375,
0.0206146240234375,
-0.006092071533203125,
-0.00467681884765625,
0.007167816162109375,
-0.006465911865234375,
-0.021728515625,
-0.003856658935546875,
-0.01727294921875,
0.01013946533203125,
0.0355224609375,
-0.021697998046875,
0.0007152557373046875,
0.0162811279296875,
-0.00151824951171875,
-0.00963592529296875,
-0.0160369873046875,
-0.003612518310546875,
0.028411865234375,
-0.006259918212890625,
0.021759033203125,
0.02020263671875,
-0.0196380615234375,
0.0097808837890625,
-0.0240478515625,
0.0117340087890625,
0.0289154052734375,
-0.00481414794921875,
-0.00783538818359375,
0.0262908935546875,
0.002803802490234375,
0.0282135009765625,
-0.01305389404296875,
0.02459716796875,
0.017059326171875,
-0.01441192626953125,
0.00250244140625,
0.0088043212890625,
-0.00848388671875,
-0.00943756103515625,
-0.009918212890625,
0.007205963134765625,
0.004486083984375,
-0.031951904296875,
0.02581787109375,
-0.006793975830078125,
-0.0006566047668457031,
-0.0102691650390625,
-0.0287017822265625,
0.01483154296875,
0.005645751953125,
0.003997802734375,
-0.00530242919921875,
-0.0260467529296875,
-0.02459716796875,
0.0159149169921875,
-0.02197265625,
0.050018310546875,
0.001415252685546875,
0.00968170166015625,
-0.00757598876953125,
0.01064300537109375,
-0.0124053955078125,
-0.031494140625,
-0.0031032562255859375,
0.030364990234375,
0.006328582763671875,
-0.0037384033203125,
0.034942626953125,
-0.0266265869140625,
-0.00750732421875,
-0.0369873046875,
0.029327392578125,
-0.0252685546875,
0.01050567626953125,
-0.002079010009765625,
0.030364990234375,
-0.0175323486328125,
-0.01351165771484375,
0.0033092498779296875,
-0.0316162109375,
0.023681640625,
0.00431060791015625,
-0.00333404541015625,
0.00313568115234375,
-0.0209197998046875,
-0.0183258056640625,
0.007411956787109375,
0.0010967254638671875,
0.0004680156707763672,
-0.01285552978515625,
-0.004428863525390625,
-0.01030731201171875,
0.0044403076171875,
0.0215301513671875,
-0.011627197265625,
0.002155303955078125,
-0.03851318359375,
-0.01416778564453125,
-0.020843505859375,
0.026336669921875,
-0.01654052734375,
-0.00807952880859375,
-0.00838470458984375,
0.0169830322265625,
-0.01442718505859375,
-0.00010657310485839844,
0.0230255126953125,
0.0008769035339355469,
0.018280029296875,
-0.009796142578125,
0.026702880859375,
0.00021159648895263672,
0.00004684925079345703,
-0.019256591796875,
-0.0078887939453125,
0.01177215576171875,
0.025390625,
0.0115203857421875,
-0.02264404296875,
0.0036182403564453125,
0.00958251953125,
-0.0123443603515625,
-0.003635406494140625,
-0.0213775634765625,
0.0014562606811523438,
0.026153564453125,
0.01206207275390625,
0.0157470703125,
0.04534912109375,
0.013885498046875,
-0.01165771484375,
0.019195556640625,
0.053009033203125,
0.00913238525390625,
0.028076171875,
-0.0229644775390625,
-0.0115814208984375,
-0.006282806396484375,
0.01318359375,
-0.042999267578125,
-0.0426025390625,
0.003631591796875,
0.03594970703125,
-0.0152130126953125,
0.0145416259765625,
-0.0264739990234375,
-0.009613037109375,
-0.0109710693359375,
-0.00887298583984375,
0.0170745849609375,
0.000484466552734375,
-0.00051116943359375,
-0.042083740234375,
-0.0164794921875,
0.00701141357421875,
-0.0198211669921875,
-0.020263671875,
0.00293731689453125,
0.0155792236328125,
0.0028705596923828125,
0.03369140625,
-0.01165008544921875,
-0.0203704833984375,
0.00362396240234375,
-0.035491943359375,
0.0245361328125,
-0.013641357421875,
0.002094268798828125,
0.01218414306640625,
0.03216552734375,
-0.00046634674072265625,
0.0286865234375,
-0.00980377197265625,
-0.0134429931640625,
0.0013475418090820312,
-0.001949310302734375,
0.0004162788391113281,
-0.00408935546875,
0.0231781005859375,
-0.033538818359375,
-0.0023822784423828125,
0.0088958740234375,
-0.02117919921875,
-0.0128631591796875,
0.0256195068359375,
0.008392333984375,
-0.0117034912109375,
-0.030181884765625,
-0.040283203125,
0.002834320068359375,
-0.0021514892578125,
0.0016565322875976562,
-0.00894927978515625,
0.01099395751953125,
-0.0219268798828125,
-0.0105743408203125,
-0.0118560791015625,
-0.0014257431030273438,
-0.00849151611328125,
-0.00791168212890625,
0.0350341796875,
0.02484130859375,
0.04779052734375,
0.009002685546875,
-0.0093841552734375,
-0.005687713623046875,
-0.0087127685546875,
0.04425048828125,
0.01320648193359375,
-0.0163421630859375,
0.033935546875,
-0.009796142578125,
0.00717926025390625,
0.021728515625,
-0.033050537109375,
0.01331329345703125,
0.00907135009765625,
-0.001941680908203125,
0.02557373046875,
-0.05413818359375,
0.0133819580078125,
0.0226593017578125,
0.01125335693359375,
0.0195159912109375,
0.019073486328125,
0.01519775390625,
0.0298614501953125,
-0.003093719482421875,
0.00681304931640625,
0.0216522216796875,
0.017822265625,
0.02166748046875,
0.0450439453125,
-0.0028667449951171875,
0.002696990966796875,
-0.039642333984375,
-0.02203369140625,
0.0057220458984375,
0.0015382766723632812,
0.01617431640625,
-0.0086517333984375,
-0.0213775634765625,
0.00691986083984375,
-0.005985260009765625,
-0.027862548828125,
0.0247344970703125,
-0.043975830078125,
-0.0097808837890625,
0.019287109375,
-0.0005602836608886719,
-0.0073394775390625,
-0.0160980224609375,
0.0160064697265625,
-0.016357421875,
0.0249481201171875,
-0.00762939453125,
0.0284881591796875,
0.0139007568359375,
0.007720947265625,
0.001323699951171875,
0.0036373138427734375,
0.002506256103515625,
0.026336669921875,
0.0009088516235351562,
0.028045654296875,
-0.012176513671875,
-0.0240631103515625,
-0.01898193359375,
0.040374755859375,
0.004627227783203125,
-0.027191162109375,
0.01153564453125,
0.03424072265625,
0.0266571044921875,
0.00982666015625,
-0.006763458251953125,
0.006011962890625,
0.044708251953125,
-0.03173828125,
-0.0035266876220703125,
-0.01232147216796875,
0.004238128662109375,
-0.043060302734375,
-0.0010290145874023438,
-0.01019287109375,
0.025726318359375,
0.016021728515625,
-0.034393310546875,
0.023406982421875,
-0.0091705322265625,
-0.004947662353515625,
-0.0210113525390625,
-0.0176239013671875,
0.0195770263671875,
0.0259552001953125,
-0.00403594970703125,
0.01629638671875,
-0.0213775634765625,
0.0045318603515625,
0.022430419921875,
0.0296783447265625,
-0.01511383056640625,
-0.0021495819091796875,
0.0093841552734375,
-0.0152435302734375,
-0.0386962890625,
-0.04217529296875,
-0.03753662109375,
0.004261016845703125,
-0.0214385986328125,
-0.0018100738525390625,
0.0219268798828125,
-0.01531219482421875,
-0.006778717041015625,
0.0155792236328125,
-0.0278778076171875,
-0.0195465087890625,
0.0112457275390625,
-0.0206298828125,
0.006381988525390625,
0.0188751220703125,
-0.06024169921875,
-0.0236358642578125,
-0.05731201171875,
0.00843048095703125,
0.002429962158203125,
0.0074462890625,
0.031768798828125,
-0.027557373046875,
0.00006985664367675781,
-0.01059722900390625,
0.0246429443359375,
-0.004680633544921875,
-0.0194549560546875,
-0.0298004150390625,
-0.0277557373046875,
0.00616455078125,
0.0089263916015625,
0.01568603515625,
-0.05230712890625,
-0.0202178955078125,
0.0205230712890625,
0.0098724365234375,
0.0125274658203125,
-0.0028591156005859375,
-0.035675048828125,
-0.033721923828125,
0.0224456787109375,
0.04461669921875,
-0.00727081298828125,
-0.01348114013671875,
-0.018096923828125,
-0.048736572265625,
0.002681732177734375,
0.0079803466796875,
0.00778961181640625,
-0.0148468017578125,
-0.00934600830078125,
0.03436279296875,
0.01416778564453125,
-0.024749755859375,
-0.0242462158203125,
-0.00345611572265625,
0.00226593017578125,
-0.01239776611328125,
0.01018524169921875,
0.00772857666015625,
0.00569915771484375,
0.007389068603515625,
-0.01148223876953125,
0.00591278076171875,
0.02105712890625,
-0.0002493858337402344,
0.0087890625,
0.0188751220703125,
-0.004367828369140625,
0.0019969940185546875,
-0.01036834716796875,
0.00275421142578125,
0.00220489501953125,
0.012939453125,
-0.004329681396484375,
0.00688934326171875,
0.023956298828125,
-0.01702880859375,
-0.0194549560546875,
0.0054168701171875,
-0.000888824462890625,
0.0236663818359375,
-0.0155792236328125,
-0.00669097900390625,
-0.007747650146484375
] |
ours_515
|
Note that the given equation rewrites as \(f^{m}(x)-x=y-f^{n}(y)-y\). Fixing \(y\) and varying \(x\) yields \(f^{m}(x)-x=c\) for a constant \(c\), and fixing \(x\) while varying \(y\) yields \(f^{n}(y)-y=-c\) for a constant \(c\). Combining these equations yields \(f^{m+n}(x)=x\) for all \(x\). But now note \(0=f^{m(m+n)}(x)-x=c(m+n)\), hence \(c=0\), so \(f^{m}(x)=f^{n}(x)=x\). Thus \(f^{\operatorname{gcd}(m, n)}(x)=x\) as well, so for \(f\) to be primitive it follows that \(\{m, n\}=\{\operatorname{gcd}(m, n), 2 \operatorname{gcd}(m, n)\}\), from which we get \((m, n)=(d, 2d),(2d, d)\).
Now, we need to count the number of such pairs \((m, n)\) with \(m < n < 10000\). For each \(d\), the pairs are \((d, 2d)\) and \((2d, d)\). The maximum value for \(d\) such that \(2d < 10000\) is \(4999\). Therefore, there are \(4999\) pairs \((d, 2d)\) and \(4999\) pairs \((2d, d)\), totaling \(9998\) pairs.
Thus, the number of ordered pairs \((m, n)\) is \(\boxed{9998}\).
|
9998
|
{
"competition": "us_comps",
"dataset": "Ours",
"posts": null,
"source": "OMOFall19Solns.md"
}
|
For an ordered pair \((m, n)\) of distinct positive integers, suppose, for some nonempty subset \(S\) of \(\mathbb{R}\), that a function \(f: S \rightarrow S\) satisfies the property that \(f^{m}(x)+f^{n}(y)=x+y\) for all \(x, y \in S\). (Here \(f^{k}(z)\) means the result when \(f\) is applied \(k\) times to \(z\); for example, \(f^{1}(z)=f(z)\) and \(f^{3}(z)=f(f(f(z)))\).) Then \(f\) is called \((m, n)\)-splendid. Furthermore, \(f\) is called \((m, n)\)-primitive if \(f\) is \((m, n)\)-splendid and there do not exist positive integers \(a \leq m\) and \(b \leq n\) with \((a, b) \neq(m, n)\) and \(a \neq b\) such that \(f\) is also \((a, b)\)-splendid. Compute the number of ordered pairs \((m, n)\) of distinct positive integers less than \(10000\) such that there exists a nonempty subset \(S\) of \(\mathbb{R}\) such that there exists an \((m, n)\)-primitive function \(f: S \rightarrow S\).
|
[
"/Mathematics/DiscreteMathematics/Combinatorics/Enumeration",
"/Mathematics/DiscreteMathematics/Combinatorics/GeneralCombinatorics",
"/Mathematics/DiscreteMathematics/GeneralDiscreteMathematics/DiscreteMath",
"/Mathematics/DiscreteMathematics/GeneralDiscreteMathematics/DiscreteMathematics",
"/Mathematics/NumberTheory/GeneralNumberTheory/ElementaryMethods",
"/Mathematics/NumberTheory/GeneralNumberTheory/ElementaryNumberTheory",
"/Mathematics/NumberTheory/GeneralNumberTheory/HigherArithmetic",
"/Mathematics/NumberTheory/GeneralNumberTheory/NumberTheory",
"/Mathematics/NumberTheory/Integers/Integer",
"/Mathematics/NumberTheory/Integers/N",
"/Mathematics/NumberTheory/Integers/PositiveInteger",
"/Mathematics/NumberTheory/Integers/RationalInteger",
"/Mathematics/NumberTheory/Integers/WholeNumber",
"/Mathematics/NumberTheory/Integers/Z",
"/Mathematics/NumberTheory/Integers/Z-Plus"
] |
Separate the variables to show f⁽ᵐ⁾(x)-x is constant, forcing the constant to be zero and thus f⁽ᵐ⁾=f⁽ⁿ⁾=identity, which makes m and n be gcd and twice gcd.
|
[
0.000026524066925048828,
-0.01419830322265625,
0.01013946533203125,
-0.00594329833984375,
0.0003552436828613281,
0.00897979736328125,
-0.0171966552734375,
-0.012237548828125,
0.002414703369140625,
-0.00553131103515625,
0.007480621337890625,
-0.028350830078125,
-0.0038738250732421875,
-0.0021915435791015625,
-0.03143310546875,
0.0030460357666015625,
0.023284912109375,
-0.01312255859375,
-0.028564453125,
-0.004474639892578125,
-0.00775909423828125,
-0.00225830078125,
-0.036285400390625,
0.06622314453125,
0.0026874542236328125,
-0.0135345458984375,
-0.0237274169921875,
0.0152587890625,
-0.012115478515625,
0.0220947265625,
0.02459716796875,
-0.0103302001953125,
-0.0028896331787109375,
-0.037078857421875,
0.0019741058349609375,
-0.00930023193359375,
0.001247406005859375,
0.0009417533874511719,
-0.0308990478515625,
-0.025543212890625,
-0.0212860107421875,
0.0209503173828125,
0.006732940673828125,
0.008697509765625,
-0.026702880859375,
-0.0022106170654296875,
0.0064849853515625,
0.00870513916015625,
-0.005802154541015625,
0.01470184326171875,
-0.007610321044921875,
0.0133514404296875,
0.00357818603515625,
-0.01160430908203125,
-0.05426025390625,
-0.04095458984375,
0.0184783935546875,
0.00763702392578125,
-0.0161590576171875,
-0.0146484375,
-0.0006113052368164062,
-0.042083740234375,
-0.016876220703125,
-0.00514984130859375,
-0.00025844573974609375,
-0.00916290283203125,
-0.00203704833984375,
-0.000024557113647460938,
0.01427459716796875,
-0.0173187255859375,
0.039337158203125,
-0.01491546630859375,
0.0009455680847167969,
0.032684326171875,
0.016326904296875,
-0.009918212890625,
0.0034999847412109375,
0.02227783203125,
-0.0020046234130859375,
0.006580352783203125,
0.0202178955078125,
0.016387939453125,
0.0156707763671875,
0.0020751953125,
0.00934600830078125,
0.00914764404296875,
-0.0003745555877685547,
0.0006146430969238281,
0.01465606689453125,
-0.006786346435546875,
0.00362396240234375,
0.042816162109375,
0.01312255859375,
0.01398468017578125,
-0.005359649658203125,
0.00447845458984375,
-0.00023758411407470703,
-0.00020205974578857422,
-0.007701873779296875,
0.00605010986328125,
-0.00464630126953125,
-0.0084381103515625,
0.0172576904296875,
-0.003124237060546875,
-0.067138671875,
-0.012969970703125,
-0.01273345947265625,
0.00067901611328125,
-0.020751953125,
0.004764556884765625,
0.017730712890625,
0.01412200927734375,
0.044403076171875,
0.0255126953125,
0.02264404296875,
-0.007266998291015625,
0.0259552001953125,
0.01496124267578125,
0.001041412353515625,
-0.00966644287109375,
-0.00220489501953125,
-0.00582122802734375,
-0.0032596588134765625,
0.0014524459838867188,
-0.00482940673828125,
-0.0196990966796875,
0.0011072158813476562,
-0.043182373046875,
-0.0233612060546875,
0.002040863037109375,
0.00510406494140625,
0.020172119140625,
-0.0216064453125,
-0.022735595703125,
-0.05279541015625,
0.0162506103515625,
-0.01458740234375,
-0.016937255859375,
0.006923675537109375,
-0.01116180419921875,
-0.0015382766723632812,
-0.0254364013671875,
-0.00927734375,
0.016998291015625,
0.0006756782531738281,
0.0078887939453125,
-0.004131317138671875,
-0.0305938720703125,
0.005405426025390625,
0.001491546630859375,
0.0014390945434570312,
-0.0012197494506835938,
0.007228851318359375,
-0.0087432861328125,
-0.0190582275390625,
0.01113128662109375,
0.0082244873046875,
0.01264190673828125,
-0.003482818603515625,
-0.002033233642578125,
0.0032978057861328125,
-0.0032939910888671875,
0.0149688720703125,
0.00872039794921875,
-0.0035247802734375,
-0.004360198974609375,
0.005290985107421875,
-0.005290985107421875,
-0.01110076904296875,
-0.0382080078125,
0.0178680419921875,
0.0214691162109375,
-0.004894256591796875,
-0.026580810546875,
0.0010976791381835938,
0.0071258544921875,
-0.001964569091796875,
-0.0177001953125,
-0.001659393310546875,
0.02020263671875,
0.01558685302734375,
-0.03424072265625,
-0.026580810546875,
0.017120361328125,
0.007801055908203125,
-0.01265716552734375,
-0.00640106201171875,
0.027679443359375,
0.0170745849609375,
-0.0024127960205078125,
0.0196380615234375,
-0.01947021484375,
-0.038726806640625,
0.0277557373046875,
-0.0222930908203125,
-0.0202789306640625,
0.002185821533203125,
0.0197906494140625,
0.023895263671875,
0.01309967041015625,
-0.0012865066528320312,
-0.0143890380859375,
-0.01239013671875,
-0.0014486312866210938,
0.034576416015625,
-0.0018510818481445312,
-0.0013723373413085938,
-0.0015430450439453125,
-0.007965087890625,
0.01265716552734375,
0.014251708984375,
-0.029998779296875,
-0.0066375732421875,
-0.0203399658203125,
-0.00659942626953125,
-0.00827789306640625,
-0.007427215576171875,
-0.001537322998046875,
0.0008544921875,
-0.0914306640625,
-0.01390838623046875,
0.0015087127685546875,
-0.0018644332885742188,
-0.020904541015625,
-0.0115966796875,
-0.0059967041015625,
0.01033782958984375,
-0.01849365234375,
-0.01132965087890625,
0.005039215087890625,
0.0301666259765625,
0.03143310546875,
-0.008331298828125,
0.005889892578125,
0.01224517822265625,
-0.01702880859375,
0.0296630859375,
-0.0243072509765625,
0.0182037353515625,
0.006893157958984375,
0.015838623046875,
0.00963592529296875,
0.002208709716796875,
0.01366424560546875,
-0.01214599609375,
0.00606536865234375,
0.011383056640625,
-0.005161285400390625,
0.01467132568359375,
-0.016632080078125,
-0.0006198883056640625,
-0.0095062255859375,
-0.0229034423828125,
-0.007724761962890625,
0.032135009765625,
-0.002544403076171875,
-0.008514404296875,
-0.0009984970092773438,
-0.024566650390625,
-0.020233154296875,
0.00775146484375,
-0.029449462890625,
-0.0025806427001953125,
-0.01084136962890625,
0.002811431884765625,
0.01285552978515625,
-0.00511932373046875,
0.006801605224609375,
-0.01003265380859375,
-0.00922393798828125,
0.033843994140625,
-0.0230560302734375,
-0.013214111328125,
0.0013179779052734375,
0.0290985107421875,
-0.0208892822265625,
-0.011627197265625,
-0.0033721923828125,
0.0267181396484375,
-0.02081298828125,
0.0182647705078125,
-0.01284027099609375,
-0.01381683349609375,
0.0038909912109375,
-0.01207733154296875,
-0.01221466064453125,
-0.0092010498046875,
-0.017791748046875,
-0.0173797607421875,
-0.0182342529296875,
-0.006336212158203125,
-0.030975341796875,
-0.0185394287109375,
0.009490966796875,
0.04180908203125,
-0.048736572265625,
0.01666259765625,
-0.001659393310546875,
0.002208709716796875,
-0.0142059326171875,
0.01776123046875,
-0.003936767578125,
-0.01242828369140625,
0.0115814208984375,
0.007419586181640625,
0.01509857177734375,
-0.000021576881408691406,
0.004730224609375,
-0.018402099609375,
-0.011016845703125,
0.00664520263671875,
-0.0208587646484375,
0.005634307861328125,
0.0045318603515625,
-0.021331787109375,
-0.0153656005859375,
-0.0312347412109375,
-0.0104217529296875,
-0.0311126708984375,
0.022857666015625,
0.00835418701171875,
0.00829315185546875,
0.003326416015625,
-0.00962066650390625,
0.01345062255859375,
-0.00173187255859375,
-0.01053619384765625,
0.012359619140625,
-0.06988525390625,
0.018341064453125,
-0.03668212890625,
0.003986358642578125,
0.005779266357421875,
-0.02484130859375,
-0.01134490966796875,
0.0075836181640625,
-0.006473541259765625,
-0.00634765625,
-0.005863189697265625,
-0.01535797119140625,
0.01544952392578125,
-0.03204345703125,
-0.0011129379272460938,
-0.00247955322265625,
-0.002986907958984375,
0.024749755859375,
-0.0252227783203125,
-0.0127105712890625,
-0.0081787109375,
-0.0237884521484375,
0.039703369140625,
0.03533935546875,
-0.00995635986328125,
0.00047779083251953125,
-0.031494140625,
0.005245208740234375,
-0.0067291259765625,
-0.0157470703125,
0.006053924560546875,
0.01397705078125,
-0.01035308837890625,
-0.008544921875,
0.010986328125,
0.018310546875,
0.014801025390625,
-0.027099609375,
0.0026092529296875,
0.005619049072265625,
-0.023956298828125,
0.0134735107421875,
-0.0179443359375,
-0.0114288330078125,
0.005222320556640625,
-0.0184478759765625,
-0.0081787109375,
0.0079193115234375,
0.02325439453125,
-0.0074920654296875,
0.00811767578125,
0.01105499267578125,
0.00531005859375,
0.00615692138671875,
-0.00420379638671875,
0.0263519287109375,
-0.003154754638671875,
-0.01513671875,
0.00719451904296875,
-0.042877197265625,
-0.01904296875,
0.01580810546875,
-0.00962066650390625,
-0.01500701904296875,
-0.018157958984375,
0.033935546875,
-0.0243072509765625,
-0.007534027099609375,
-0.002399444580078125,
0.024444580078125,
0.0240631103515625,
-0.0214385986328125,
-0.021331787109375,
0.011749267578125,
-0.0236053466796875,
-0.0024929046630859375,
0.0055389404296875,
0.01110076904296875,
-0.0177154541015625,
-0.00470733642578125,
-0.00046253204345703125,
0.004901885986328125,
0.006832122802734375,
0.00870513916015625,
-0.0291900634765625,
-0.0123138427734375,
0.0279998779296875,
-0.01384735107421875,
0.01953125,
-0.029205322265625,
-0.064453125,
0.0013360977172851562,
-0.0258026123046875,
-0.0198822021484375,
0.005832672119140625,
0.0016345977783203125,
0.0102081298828125,
0.01629638671875,
0.0008435249328613281,
0.01145172119140625,
0.0017118453979492188,
0.01824951171875,
-0.005359649658203125,
-0.0187225341796875,
0.0239410400390625,
0.0271148681640625,
0.0041656494140625,
-0.0211639404296875,
0.06317138671875,
0.01117706298828125,
0.0004863739013671875,
0.006145477294921875,
-0.0225982666015625,
-0.0038013458251953125,
0.0038909912109375,
0.01207733154296875,
0.0010623931884765625,
0.00925445556640625,
0.014739990234375,
0.0205230712890625,
-0.0244903564453125,
0.0207061767578125,
-0.0245208740234375,
-0.01922607421875,
-0.03631591796875,
-0.00879669189453125,
0.0185089111328125,
0.009124755859375,
0.00449371337890625,
0.0303955078125,
-0.0166473388671875,
-0.01218414306640625,
0.0107421875,
-0.006061553955078125,
-0.031585693359375,
0.00374603271484375,
-0.02972412109375,
0.020965576171875,
0.01629638671875,
-0.004329681396484375,
0.027740478515625,
-0.017608642578125,
-0.01361846923828125,
-0.00951385498046875,
-0.002849578857421875,
0.01300811767578125,
-0.061004638671875,
-0.0023059844970703125,
0.010528564453125,
0.022369384765625,
-0.027618408203125,
-0.016204833984375,
0.03729248046875,
-0.00899505615234375,
0.01418304443359375,
0.0106201171875,
-0.0022296905517578125,
0.01432037353515625,
0.037200927734375,
0.0168914794921875,
0.0031986236572265625,
-0.00643157958984375,
0.0234832763671875,
0.0260467529296875,
-0.030242919921875,
-0.02923583984375,
-0.037353515625,
-0.029632568359375,
-0.01245880126953125,
-0.01611328125,
-0.00977325439453125,
0.00005334615707397461,
0.004955291748046875,
-0.0308380126953125,
0.0018663406372070312,
0.03173828125,
-0.00481414794921875,
-0.023101806640625,
0.00592041015625,
-0.0247955322265625,
-0.01412200927734375,
-0.031280517578125,
-0.02593994140625,
0.0123748779296875,
0.007579803466796875,
-0.0290679931640625,
0.0352783203125,
-0.0038280487060546875,
-0.0162506103515625,
0.00850677490234375,
0.00933837890625,
0.0037059783935546875,
-0.0254364013671875,
-0.0157012939453125,
0.037994384765625,
0.014434814453125,
0.0177459716796875,
0.01067352294921875,
0.0021991729736328125,
-0.04132080078125,
0.00229644775390625,
-0.0252685546875,
-0.01024627685546875,
-0.00978851318359375,
0.01189422607421875,
-0.0218505859375,
-0.0206298828125,
0.01093292236328125,
0.0007839202880859375,
-0.01349639892578125,
0.046539306640625,
0.025299072265625,
0.008819580078125,
0.0117034912109375,
0.02239990234375,
-0.0238037109375,
-0.0239715576171875,
0.0033397674560546875,
0.0033702850341796875,
0.007587432861328125,
0.00963592529296875,
0.0275726318359375,
0.0014324188232421875,
0.0093841552734375,
-0.00919342041015625,
0.03643798828125,
-0.0285491943359375,
-0.004169464111328125,
-0.005451202392578125,
0.0016841888427734375,
-0.0036716461181640625,
-0.029876708984375,
0.0216064453125,
0.0231781005859375,
0.021575927734375,
0.0080108642578125,
0.00783538818359375,
-0.032073974609375,
-0.0022907257080078125,
-0.0130157470703125,
0.0211639404296875,
-0.04095458984375,
0.0079803466796875,
-0.0177001953125,
-0.004116058349609375,
-0.0185699462890625,
0.01361083984375,
0.01509857177734375,
-0.020751953125,
-0.01409912109375,
-0.0005068778991699219,
0.0006704330444335938,
0.019927978515625,
0.009246826171875,
-0.01324462890625,
-0.0170745849609375,
0.01358795166015625,
0.0303955078125,
0.0181732177734375,
0.00022161006927490234,
0.0352783203125,
0.0042266845703125,
-0.005146026611328125,
-0.0087127685546875,
0.0030460357666015625,
0.0157623291015625,
0.0105438232421875,
0.016998291015625,
0.060150146484375,
-0.0031795501708984375,
-0.0130767822265625,
0.0073394775390625,
0.02764892578125,
-0.026611328125,
-0.0272674560546875,
-0.00829315185546875,
-0.0316162109375,
-0.00685882568359375,
0.035858154296875,
-0.0030803680419921875,
0.0041351318359375,
-0.00278472900390625,
0.00782012939453125,
-0.01690673828125,
0.038482666015625,
0.0006661415100097656,
0.012908935546875,
0.01184844970703125,
-0.00020682811737060547,
-0.02880859375,
0.000005424022674560547,
-0.017333984375,
0.0208587646484375,
-0.0025234222412109375,
0.0048370361328125,
0.0162811279296875,
0.00930023193359375,
0.0100860595703125,
0.03070068359375,
-0.0151214599609375,
-0.00316619873046875,
0.0225677490234375,
-0.0180206298828125,
-0.01396942138671875,
0.02239990234375,
-0.00823211669921875,
-0.0010595321655273438,
0.00746917724609375,
-0.024749755859375,
0.0229339599609375,
0.03155517578125,
0.0018787384033203125,
0.003902435302734375,
0.0284423828125,
0.0307769775390625,
-0.04620361328125,
-0.0145263671875,
0.0106048583984375,
-0.0007452964782714844,
-0.023223876953125,
-0.028076171875,
-0.00823974609375,
-0.0229034423828125,
-0.017822265625,
-0.00806427001953125,
0.0171966552734375,
0.023101806640625,
0.023162841796875,
0.02581787109375,
-0.0172576904296875,
0.0174407958984375,
-0.0260009765625,
0.002559661865234375,
-0.004749298095703125,
-0.016693115234375,
-0.007320404052734375,
-0.0194244384765625,
0.0281982421875,
0.0211334228515625,
0.001445770263671875,
0.01531219482421875,
-0.039031982421875,
0.007213592529296875,
-0.026336669921875,
0.0011339187622070312,
0.0022430419921875,
-0.01361846923828125,
-0.0181121826171875,
0.0128936767578125,
0.004802703857421875,
-0.006061553955078125,
0.04766845703125,
0.0130462646484375,
0.0301666259765625,
0.029571533203125,
-0.0198974609375,
0.04052734375,
0.017974853515625,
-0.01380157470703125,
0.00870513916015625,
-0.03765869140625,
0.0015468597412109375,
-0.00003892183303833008,
0.04150390625,
-0.0379638671875,
0.006927490234375,
0.002685546875,
-0.005733489990234375,
0.007686614990234375,
-0.0177154541015625,
-0.0190277099609375,
-0.0012006759643554688,
-0.0088348388671875,
-0.03662109375,
-0.01325225830078125,
0.0094146728515625,
-0.01214599609375,
-0.043670654296875,
-0.00494384765625,
-0.01385498046875,
-0.0202178955078125,
-0.002788543701171875,
-0.00931549072265625,
0.01549530029296875,
-0.005123138427734375,
0.0036373138427734375,
-0.01041412353515625,
0.02203369140625,
0.026763916015625,
0.0236968994140625,
-0.0215301513671875,
-0.00937652587890625,
-0.0188751220703125,
-0.00965118408203125,
-0.0149383544921875,
-0.01407623291015625,
0.0279388427734375,
0.00334930419921875,
0.02325439453125,
-0.0408935546875,
-0.032867431640625,
-0.004108428955078125,
-0.032745361328125,
0.0028629302978515625,
0.0007205009460449219,
-0.0210723876953125,
-0.04364013671875,
-0.0177154541015625,
0.0241851806640625,
0.005191802978515625,
-0.0022335052490234375,
0.00904083251953125,
0.042510986328125,
0.015594482421875,
0.0183258056640625,
0.00946044921875,
0.0035228729248046875,
-0.0175323486328125,
0.01515960693359375,
0.016571044921875,
-0.0079345703125,
0.0013208389282226562,
0.0308837890625,
-0.037994384765625,
-0.0264434814453125,
-0.055908203125,
-0.0100860595703125,
0.0101318359375,
0.031829833984375,
-0.024261474609375,
0.003444671630859375,
-0.0285491943359375,
-0.039459228515625,
0.01202392578125,
-0.0275421142578125,
-0.00400543212890625,
-0.011199951171875,
-0.00472259521484375,
-0.003376007080078125,
-0.03521728515625,
-0.06268310546875,
0.0316162109375,
-0.02447509765625,
0.0160675048828125,
0.02691650390625,
0.0023040771484375,
0.01387786865234375,
0.0184783935546875,
-0.047515869140625,
-0.01419830322265625,
0.0258331298828125,
-0.0162200927734375,
-0.004180908203125,
-0.0186614990234375,
0.007358551025390625,
0.0008339881896972656,
-0.0260467529296875,
0.00007832050323486328,
-0.0075531005859375,
0.015716552734375,
-0.007537841796875,
0.0070953369140625,
0.0276336669921875,
0.0028285980224609375,
-0.00016117095947265625,
0.0105133056640625,
-0.0022983551025390625,
-0.0055084228515625,
-0.032135009765625,
0.00330352783203125,
-0.0278472900390625,
0.016815185546875,
-0.0022068023681640625,
-0.0006895065307617188,
0.00951385498046875,
-0.01261138916015625,
0.01690673828125,
-0.008514404296875,
0.05328369140625,
-0.01450347900390625,
0.01268768310546875,
0.01532745361328125,
0.021087646484375,
-0.00167083740234375,
0.008575439453125,
-0.01544189453125,
0.0141143798828125,
-0.0025157928466796875,
-0.00885772705078125,
0.04217529296875,
0.0117034912109375,
0.004795074462890625,
-0.0206298828125,
0.0035648345947265625,
-0.01132965087890625,
-0.0042877197265625,
-0.0031223297119140625,
0.012969970703125,
-0.0064849853515625,
-0.00550079345703125,
-0.0055389404296875,
0.02764892578125,
0.01386260986328125,
0.017822265625,
0.0018930435180664062,
0.036346435546875,
0.02197265625,
0.0197601318359375,
-0.0041046142578125,
0.03326416015625,
-0.01300811767578125,
-0.0031719207763671875,
-0.0174713134765625,
0.017120361328125,
0.01236724853515625,
-0.0123748779296875,
0.01922607421875,
0.006755828857421875,
-0.01641845703125,
0.0052490234375,
-0.003925323486328125,
-0.00624847412109375,
0.0277557373046875,
-0.0204010009765625,
0.01139068603515625,
-0.006885528564453125,
0.0044403076171875,
0.033355712890625,
-0.00910186767578125,
0.0197296142578125,
-0.0166168212890625,
-0.004116058349609375,
-0.006275177001953125,
-0.0439453125,
0.0172271728515625,
0.01232147216796875,
-0.006053924560546875,
0.0279693603515625,
-0.002185821533203125,
-0.037261962890625,
-0.0002646446228027344,
-0.004978179931640625,
0.0170440673828125,
-0.004680633544921875,
0.018768310546875,
0.01082611083984375,
0.053558349609375,
0.0067138671875,
0.00833892822265625,
0.0171966552734375,
0.00986480712890625,
0.0267486572265625,
0.0025577545166015625,
-0.0286407470703125,
-0.055511474609375,
0.002788543701171875,
-0.00945281982421875,
-0.0289459228515625,
-0.002368927001953125,
0.01007843017578125,
-0.026519775390625,
-0.024383544921875,
-0.019317626953125,
0.0189361572265625,
0.02850341796875,
-0.0299530029296875,
0.041748046875,
0.0101318359375,
-0.00756072998046875,
-0.0227203369140625,
-0.007167816162109375,
-0.0285797119140625,
0.002643585205078125,
-0.026824951171875,
0.0247344970703125,
0.01123046875,
-0.01157379150390625,
-0.013580322265625,
0.01056671142578125,
0.0007123947143554688,
-0.0130615234375,
0.0015201568603515625,
-0.0067596435546875,
-0.005107879638671875,
0.0017881393432617188,
0.0186767578125,
-0.04345703125,
-0.022430419921875,
-0.012786865234375,
-0.005519866943359375,
0.03216552734375,
0.017181396484375,
0.034454345703125,
-0.002452850341796875,
0.01087188720703125,
-0.0017862319946289062,
0.0124053955078125,
0.007724761962890625,
-0.0247650146484375,
0.01190185546875,
-0.027587890625,
0.0037136077880859375,
0.007732391357421875,
0.01042938232421875,
0.00795745849609375,
0.0187530517578125,
-0.00449371337890625,
0.0089111328125,
-0.0264434814453125,
-0.018646240234375,
-0.006526947021484375,
0.01485443115234375,
-0.0245513916015625,
-0.004810333251953125,
0.01287841796875,
0.03277587890625,
-0.01302337646484375,
0.00589752197265625,
0.00640869140625,
0.00562286376953125,
-0.035919189453125,
-0.03045654296875,
-0.01629638671875,
-0.001331329345703125,
-0.0163421630859375,
0.016998291015625,
0.012237548828125,
-0.00461578369140625,
0.03961181640625,
-0.00835418701171875,
-0.0097503662109375,
-0.028045654296875,
-0.0214996337890625,
0.01375579833984375,
-0.04931640625,
-0.0005240440368652344,
-0.0026950836181640625,
0.04937744140625,
0.004222869873046875,
-0.0033359527587890625,
0.00835418701171875,
-0.00647735595703125,
-0.0165252685546875,
-0.02447509765625,
0.00948333740234375,
-0.0215911865234375,
-0.0194091796875,
0.0247039794921875,
-0.0268707275390625,
-0.004947662353515625,
0.004314422607421875,
0.021942138671875,
0.00908660888671875,
0.028564453125,
-0.01849365234375,
-0.01415252685546875,
-0.022857666015625,
0.0244293212890625,
0.0182952880859375,
0.0138702392578125,
-0.00656890869140625,
-0.0022602081298828125,
-0.044036865234375,
-0.0026264190673828125,
0.0079498291015625,
0.050689697265625,
-0.005413055419921875,
0.0198822021484375,
0.0012683868408203125,
0.009490966796875,
0.01438140869140625,
0.032073974609375,
-0.029754638671875,
-0.006687164306640625,
-0.00223541259765625,
0.0242919921875,
0.035400390625,
-0.004497528076171875,
0.017181396484375,
-0.024932861328125,
-0.02716064453125,
0.0288848876953125,
-0.00632476806640625,
0.0008869171142578125,
-0.04388427734375,
-0.0026988983154296875,
-0.00836181640625,
0.00626373291015625,
0.0232696533203125,
0.0248565673828125,
-0.0116729736328125,
0.004611968994140625,
-0.0204925537109375,
0.01910400390625,
-0.00923919677734375,
-0.037017822265625,
-0.03436279296875,
-0.00296783447265625,
0.01029205322265625,
0.01064300537109375,
0.049285888671875,
0.029144287109375,
-0.004573822021484375,
-0.0027179718017578125,
0.01018524169921875,
-0.0265045166015625,
-0.0186004638671875,
-0.0018930435180664062,
-0.021270751953125,
-0.0290069580078125,
0.0033092498779296875,
0.00945281982421875,
0.005054473876953125,
0.006649017333984375,
-0.005268096923828125,
-0.002777099609375,
0.0230255126953125,
0.0064849853515625,
0.018096923828125,
-0.00550079345703125,
-0.022064208984375,
-0.0005865097045898438,
0.0077362060546875,
0.001926422119140625,
-0.021209716796875,
0.0217437744140625,
-0.0191802978515625,
0.0181884765625,
0.022613525390625,
-0.0159759521484375,
0.026885986328125,
0.0004076957702636719,
0.004581451416015625,
-0.007068634033203125,
-0.0007734298706054688,
-0.019134521484375,
-0.00174713134765625,
-0.00859832763671875,
-0.03790283203125,
-0.03155517578125,
-0.015899658203125,
0.044281005859375,
-0.03582763671875,
-0.002834320068359375,
0.017608642578125,
-0.00966644287109375,
0.021514892578125,
0.0107421875,
-0.00812530517578125,
0.00628662109375,
-0.01544952392578125,
-0.010223388671875,
0.0081634521484375,
0.024261474609375,
-0.0509033203125,
0.0224456787109375,
0.00766754150390625,
0.01094818115234375,
0.004375457763671875,
0.0008835792541503906,
-0.01496124267578125,
0.00777435302734375,
-0.003208160400390625,
-0.0244903564453125,
-0.040191650390625,
0.00586700439453125,
-0.0316162109375,
0.03216552734375,
0.031219482421875,
0.01145172119140625,
0.0200653076171875,
0.0100250244140625,
-0.007099151611328125,
0.0283660888671875,
-0.00691986083984375,
0.031524658203125,
0.0015630722045898438,
0.032928466796875,
0.037384033203125,
-0.006725311279296875,
0.00136566162109375,
0.01256561279296875,
-0.0223236083984375,
0.016357421875,
0.00931549072265625,
-0.019073486328125,
-0.00894927978515625,
0.004596710205078125,
-0.0474853515625,
-0.043792724609375,
-0.0088348388671875,
-0.0187835693359375,
0.0279693603515625,
0.0234375,
-0.019561767578125,
0.00948333740234375,
0.007045745849609375,
0.04302978515625,
-0.0003139972686767578,
-0.0222015380859375,
0.01023101806640625,
0.0175018310546875,
0.0108489990234375,
0.0052032470703125,
0.01763916015625,
0.01184844970703125,
0.0018062591552734375,
0.035858154296875,
0.0008287429809570312,
0.0198211669921875,
0.02947998046875,
-0.039031982421875,
0.00002002716064453125,
0.00604248046875,
-0.0234527587890625,
-0.01019287109375,
-0.0062255859375,
-0.01035308837890625,
0.0131988525390625,
-0.025634765625,
0.012847900390625,
0.0245819091796875,
-0.0162506103515625,
-0.00019431114196777344,
-0.037322998046875,
-0.02825927734375,
0.0012111663818359375,
0.00809478759765625,
-0.01073455810546875,
-0.0350341796875,
0.037933349609375,
-0.007427215576171875,
0.01444244384765625,
-0.0210723876953125,
0.0088043212890625,
0.033294677734375,
-0.0640869140625,
-0.006866455078125,
0.0100555419921875,
0.036041259765625,
-0.031951904296875,
-0.0242156982421875,
-0.0178375244140625,
-0.009979248046875,
-0.0006351470947265625,
-0.0111083984375,
-0.0169525146484375,
0.00905609130859375,
0.018218994140625,
0.00799560546875,
-0.01593017578125,
0.000911712646484375,
-0.026336669921875,
0.0118408203125,
0.0007171630859375,
-0.0006189346313476562,
-0.0023021697998046875,
0.012054443359375,
-0.0189971923828125,
-0.01540374755859375,
-0.005725860595703125,
0.01401519775390625,
-0.01605224609375,
0.01241302490234375,
0.0012531280517578125,
0.00923919677734375,
0.005344390869140625,
0.00707244873046875,
0.009552001953125,
-0.0215911865234375,
-0.017791748046875,
-0.007259368896484375,
-0.00965118408203125,
0.0325927734375,
-0.039154052734375,
-0.0277252197265625,
0.0177001953125,
0.00847625732421875,
-0.010223388671875,
0.00852203369140625,
0.0127105712890625,
-0.0177154541015625,
-0.007709503173828125,
0.0126190185546875,
-0.00795745849609375,
-0.035247802734375,
0.00537872314453125,
0.0275421142578125,
0.0050201416015625,
-0.0250396728515625,
0.0020427703857421875,
-0.006816864013671875,
0.021240234375,
0.0020904541015625,
-0.005527496337890625,
-0.002838134765625,
-0.016937255859375,
-0.00930023193359375,
-0.040802001953125,
0.0218048095703125,
0.0005154609680175781,
-0.00734710693359375,
0.0343017578125,
-0.00791168212890625,
-0.001987457275390625,
-0.00009316205978393555,
-0.015106201171875,
-0.0218505859375,
-0.026824951171875,
0.023956298828125,
-0.001617431640625,
0.02362060546875,
-0.0183563232421875,
0.036834716796875,
0.0167083740234375,
-0.014923095703125,
0.018707275390625,
0.01824951171875,
-0.0240020751953125,
-0.0146026611328125,
0.01525115966796875,
0.026123046875,
0.0245361328125,
0.0200958251953125,
-0.008636474609375,
0.0225372314453125,
0.0003046989440917969,
-0.0209503173828125,
0.016876220703125,
-0.0100860595703125,
-0.01050567626953125,
0.0264129638671875,
0.016998291015625,
0.0217742919921875,
-0.005344390869140625,
-0.004913330078125,
-0.01529693603515625,
0.006633758544921875,
-0.0050048828125,
-0.006336212158203125,
-0.0262908935546875,
-0.0158843994140625,
0.0135650634765625,
0.01152801513671875,
-0.0149993896484375,
0.0059356689453125,
0.006046295166015625,
-0.0200042724609375,
-0.015228271484375,
-0.03125,
-0.005466461181640625,
-0.007457733154296875,
-0.0299835205078125,
0.0382080078125,
0.022674560546875,
0.00365447998046875,
-0.03070068359375,
-0.0010271072387695312,
-0.00888824462890625,
0.013275146484375,
-0.01000213623046875,
0.0002033710479736328,
-0.037322998046875,
0.0241241455078125,
-0.0173492431640625,
-0.0032482147216796875,
-0.005229949951171875,
-0.0038242340087890625,
-0.01070404052734375,
0.0210723876953125,
-0.00864410400390625,
-0.00801849365234375,
0.021026611328125,
-0.0214691162109375,
-0.01219940185546875,
-0.022857666015625,
-0.0162200927734375,
0.01088714599609375,
0.02386474609375,
0.00756072998046875,
0.01080322265625,
-0.0231781005859375,
0.00389862060546875,
0.0509033203125,
0.0245819091796875,
-0.003932952880859375,
0.0240020751953125,
0.01428985595703125,
-0.0120086669921875,
0.0118560791015625,
-0.054046630859375,
-0.0218505859375,
0.00038504600524902344,
0.01824951171875,
0.0096893310546875,
0.0113983154296875,
0.03106689453125,
0.003223419189453125,
-0.01393890380859375,
-0.004467010498046875,
0.0037517547607421875,
-0.0177764892578125,
0.00250244140625,
0.00794219970703125,
-0.04449462890625,
-0.00360107421875,
-0.00823211669921875,
0.0316162109375,
-0.0159454345703125,
0.03643798828125,
0.006839752197265625,
-0.0283966064453125,
0.00019049644470214844,
0.052581787109375,
-0.00853729248046875,
-0.029937744140625,
-0.0113067626953125,
0.0264434814453125,
-0.03680419921875,
0.0177459716796875,
0.0131683349609375,
-0.018341064453125,
0.04205322265625,
0.0018749237060546875,
-0.005878448486328125,
0.0264434814453125,
-0.0201263427734375,
0.002826690673828125,
-0.0048828125,
-0.0018663406372070312,
0.0129241943359375,
-0.006099700927734375,
0.0173492431640625,
-0.0165557861328125,
0.0223541259765625,
-0.0234222412109375,
0.01508331298828125,
0.02301025390625,
-0.01482391357421875,
-0.00539398193359375,
0.0150604248046875,
0.0008344650268554688,
0.006740570068359375,
0.0004978179931640625,
-0.033203125,
0.01122283935546875,
0.020233154296875,
-0.036529541015625,
0.024200439453125,
0.01446533203125,
0.01178741455078125,
0.01446533203125,
0.00286102294921875,
-0.01727294921875,
-0.0131683349609375,
-0.008941650390625,
0.0015459060668945312,
0.01204681396484375,
-0.01132965087890625,
0.01323699951171875,
0.031219482421875,
-0.0002143383026123047,
0.0433349609375,
0.0005822181701660156,
-0.0205230712890625,
-0.0088043212890625,
-0.019134521484375,
-0.020843505859375,
-0.0011119842529296875,
-0.012664794921875,
-0.00243377685546875,
0.00484466552734375,
0.0194549560546875,
-0.01399993896484375,
0.004940032958984375,
0.00994873046875,
0.01824951171875,
-0.0176849365234375,
0.014068603515625,
-0.0048980712890625,
0.0248870849609375,
0.0231781005859375,
-0.0151214599609375,
0.00870513916015625,
-0.018585205078125,
-0.032379150390625,
-0.032745361328125,
-0.0201263427734375,
-0.0240325927734375,
-0.01116180419921875,
0.005588531494140625,
-0.0020236968994140625,
0.006107330322265625,
0.011077880859375,
-0.0156097412109375,
0.01538848876953125,
0.0027103424072265625,
-0.00688934326171875,
0.007183074951171875,
0.00026035308837890625,
-0.027191162109375,
-0.0161895751953125,
-0.00136566162109375,
-0.034027099609375,
-0.0065765380859375,
-0.0021457672119140625,
0.013671875,
-0.0009493827819824219,
0.01500701904296875,
-0.00879669189453125,
0.047149658203125,
0.0027141571044921875,
-0.0055084228515625,
-0.0208740234375,
0.0233612060546875,
-0.000007152557373046875,
-0.0027713775634765625,
-0.035247802734375,
0.021484375,
0.032928466796875,
-0.04193115234375,
0.007427215576171875,
-0.0219573974609375,
-0.0262451171875,
-0.00478363037109375,
0.016632080078125,
0.04095458984375,
0.003993988037109375,
0.006359100341796875,
-0.00531005859375,
-0.01763916015625,
-0.0129547119140625,
-0.040313720703125,
-0.0204010009765625,
-0.004199981689453125,
0.0297698974609375,
0.00904083251953125,
0.00588226318359375,
-0.020355224609375,
0.04443359375,
0.004940032958984375,
-0.0254364013671875,
0.00200653076171875,
-0.0288238525390625,
0.008209228515625,
0.0215301513671875,
-0.031707763671875,
-0.0009236335754394531,
0.0209808349609375,
-0.00388336181640625,
0.0043487548828125,
0.00618743896484375,
-0.01068115234375,
-0.01386260986328125,
0.0264129638671875,
0.0028820037841796875,
-0.00948333740234375,
-0.0214691162109375,
0.02520751953125,
-0.036834716796875,
-0.0263214111328125,
-0.00731658935546875,
-0.04132080078125,
0.0013093948364257812,
0.0015115737915039062,
-0.004711151123046875,
0.0181121826171875,
0.0212860107421875,
-0.001918792724609375,
-0.0285186767578125,
-0.005321502685546875,
0.004467010498046875,
-0.027618408203125,
0.00873565673828125,
-0.0005965232849121094,
-0.019775390625,
-0.015045166015625,
-0.020111083984375,
-0.0032711029052734375,
-0.003925323486328125,
-0.033843994140625,
-0.0024547576904296875,
-0.0042877197265625,
-0.0219573974609375,
0.0270843505859375,
0.010467529296875,
-0.051513671875,
0.0089874267578125,
-0.011138916015625,
-0.0214385986328125,
-0.006847381591796875,
-0.01078033447265625,
0.0221405029296875,
0.0467529296875,
-0.0260772705078125,
0.0006041526794433594,
-0.01032257080078125,
-0.045654296875,
-0.01084136962890625,
0.005702972412109375,
-0.0033550262451171875,
0.0191497802734375,
-0.0011243820190429688,
-0.0308380126953125,
0.026641845703125,
-0.00286102294921875,
0.0267333984375,
-0.01078033447265625,
0.006683349609375,
0.021759033203125,
-0.0038909912109375,
0.00624847412109375,
-0.0003516674041748047,
-0.00994873046875,
0.0159454345703125,
0.03173828125,
-0.01137542724609375,
0.003582000732421875,
0.0015764236450195312,
-0.0162811279296875,
0.01184844970703125,
0.0173492431640625,
0.0293731689453125,
0.005420684814453125,
0.01230621337890625,
-0.0191802978515625,
-0.0182037353515625,
0.0070953369140625,
0.005107879638671875,
-0.00798797607421875,
-0.0011730194091796875,
-0.0191650390625,
0.013763427734375,
0.006198883056640625,
0.0093231201171875,
0.01371002197265625,
-0.02288818359375,
0.045745849609375,
-0.00804901123046875,
-0.00690460205078125,
0.0304718017578125,
0.008880615234375,
0.01517486572265625,
0.0220794677734375,
-0.008544921875,
0.0019893646240234375,
0.01482391357421875,
-0.01214599609375,
0.0222625732421875,
-0.004955291748046875,
0.0196380615234375,
0.002452850341796875,
0.0292205810546875,
0.0053558349609375,
0.031951904296875,
0.00891876220703125,
-0.0175018310546875,
-0.03265380859375,
-0.0214385986328125,
0.032806396484375,
-0.060272216796875,
-0.017181396484375,
-0.007110595703125,
-0.0146331787109375,
0.01079559326171875,
0.037322998046875,
0.0032806396484375,
-0.01029205322265625,
0.024261474609375,
-0.0155487060546875,
0.0131378173828125,
0.01261138916015625,
0.0151824951171875,
-0.017059326171875,
0.02178955078125,
0.0015249252319335938,
0.0194549560546875,
-0.007328033447265625,
-0.00919342041015625,
-0.006923675537109375,
-0.0169219970703125,
0.01293182373046875,
-0.00662994384765625,
0.0243377685546875,
0.01059722900390625,
-0.01180267333984375,
0.03289794921875,
0.005611419677734375,
0.003894805908203125,
0.03607177734375,
-0.017333984375,
0.0208740234375,
0.0190887451171875,
-0.0010776519775390625,
0.0301971435546875,
-0.02850341796875,
0.02874755859375,
-0.00009834766387939453,
-0.013885498046875,
-0.0083160400390625,
-0.0213623046875,
0.0027008056640625,
-0.00022518634796142578,
-0.00894927978515625,
-0.0421142578125,
0.00365447998046875,
-0.0023937225341796875,
0.00519561767578125,
-0.0012254714965820312,
-0.01580810546875,
-0.027374267578125,
0.0027370452880859375,
-0.004482269287109375,
-0.0280303955078125,
-0.0172576904296875,
-0.0273590087890625,
0.01316070556640625,
-0.0158233642578125,
-0.00789642333984375,
0.0112762451171875,
0.004482269287109375,
-0.013885498046875,
0.0020427703857421875,
0.027679443359375,
0.0115966796875,
-0.01142120361328125,
0.043975830078125,
-0.0129241943359375,
-0.02239990234375,
0.007305145263671875,
0.00510406494140625,
0.010498046875,
0.0209503173828125,
0.0201416015625,
-0.01325225830078125,
0.01554107666015625,
-0.0227508544921875,
0.0149383544921875,
0.01104736328125,
0.0286712646484375,
-0.027374267578125,
0.0175933837890625,
-0.034393310546875,
-0.039276123046875,
0.0169677734375,
0.020965576171875,
-0.0015115737915039062,
-0.0013532638549804688,
0.021728515625,
-0.0235137939453125,
-0.0198516845703125,
-0.0251312255859375,
0.031982421875,
-0.0263824462890625,
-0.004413604736328125,
-0.0078125,
-0.019775390625,
0.024169921875,
-0.004978179931640625,
-0.01275634765625,
0.018341064453125,
0.006038665771484375,
0.059356689453125,
-0.0157470703125,
-0.0233306884765625,
0.01103973388671875,
0.01116180419921875,
0.011260986328125,
0.031890869140625,
-0.01204681396484375,
0.004375457763671875,
0.053375244140625,
-0.001758575439453125,
-0.0026149749755859375,
0.0011434555053710938,
-0.01517486572265625,
-0.0023212432861328125,
0.0245513916015625,
-0.03955078125,
-0.0255584716796875,
-0.05096435546875,
0.0264434814453125,
0.0310821533203125,
-0.042816162109375,
-0.0036792755126953125,
-0.015045166015625,
-0.00740814208984375,
-0.035186767578125,
0.0211944580078125,
-0.002590179443359375,
0.021240234375,
-0.005767822265625,
0.019195556640625,
0.02667236328125,
0.03314208984375,
-0.01812744140625,
0.0004429817199707031,
-0.0008106231689453125,
0.0460205078125,
0.002132415771484375,
0.0181121826171875,
0.017852783203125,
-0.0051727294921875,
0.04193115234375,
-0.019073486328125,
0.005889892578125,
0.0165557861328125,
0.00542449951171875,
0.018035888671875,
-0.032440185546875,
-0.054351806640625,
0.0117034912109375,
0.039306640625,
0.032470703125,
0.01136016845703125,
0.0027065277099609375,
-0.007160186767578125,
0.01319122314453125,
-0.0235443115234375,
0.006687164306640625,
0.0258941650390625,
0.0105133056640625,
0.0152587890625,
-0.031585693359375,
0.0229339599609375,
-0.0162811279296875,
-0.00965118408203125,
0.003143310546875,
-0.02569580078125,
-0.018890380859375,
-0.0249786376953125,
0.00423431396484375,
-0.01024627685546875,
0.004657745361328125,
-0.005222320556640625,
-0.01288604736328125,
0.0191192626953125,
0.0005674362182617188,
-0.0148468017578125,
-0.0011148452758789062,
-0.0150909423828125,
-0.0140380859375,
0.0010900497436523438,
0.01468658447265625,
0.006687164306640625,
-0.007579803466796875,
-0.007404327392578125,
0.0027751922607421875,
0.0083465576171875,
-0.013580322265625,
-0.0214080810546875,
0.033905029296875,
0.01139068603515625,
0.003448486328125,
0.03546142578125,
0.00470733642578125,
-0.01265716552734375,
-0.006748199462890625,
0.00824737548828125,
-0.005214691162109375,
0.0067596435546875,
0.00467681884765625,
-0.0072174072265625,
0.0028514862060546875,
-0.019805908203125,
-0.011627197265625,
0.027740478515625,
0.0033702850341796875,
0.020294189453125,
-0.01088714599609375,
0.000942230224609375,
0.03448486328125,
-0.023193359375,
0.04705810546875,
0.021942138671875,
-0.02191162109375,
0.0286865234375,
0.0242156982421875,
-0.0155792236328125,
-0.0210113525390625,
0.0347900390625,
-0.018951416015625,
-0.020904541015625,
-0.037689208984375,
-0.0265655517578125,
-0.00939178466796875,
-0.02740478515625,
-0.0330810546875,
0.004772186279296875,
0.0120697021484375,
-0.022796630859375,
-0.01343536376953125,
-0.02783203125,
-0.0093841552734375,
-0.0006852149963378906,
-0.036712646484375,
0.03594970703125,
0.0274658203125,
-0.00843048095703125,
-0.0240478515625,
0.0044097900390625,
0.042755126953125,
-0.015869140625,
0.0269927978515625,
-0.01532745361328125,
-0.044769287109375,
-0.016815185546875,
0.005245208740234375,
-0.03265380859375,
0.0288543701171875,
0.0184783935546875,
0.006084442138671875,
-0.007678985595703125,
0.006046295166015625,
-0.008636474609375,
0.0120849609375,
0.048431396484375,
-0.005290985107421875,
0.022613525390625,
0.007701873779296875,
0.0049591064453125,
0.003753662109375,
0.0109710693359375,
0.01117706298828125,
-0.00506591796875,
-0.01715087890625,
0.0211639404296875,
-0.008270263671875,
-0.0018167495727539062,
-0.01027679443359375,
0.004730224609375,
-0.03131103515625,
0.021881103515625,
-0.0033435821533203125,
0.033782958984375,
-0.0139007568359375,
-0.01161956787109375,
0.04833984375,
0.00008577108383178711,
-0.002758026123046875,
0.004962921142578125,
-0.0094451904296875,
0.0183563232421875,
-0.007335662841796875,
-0.049591064453125,
0.03546142578125,
0.0174560546875,
-0.007701873779296875,
-0.009063720703125,
0.0114593505859375,
0.03753662109375,
-0.0142364501953125,
-0.0222015380859375,
0.044342041015625,
0.023284912109375,
-0.0223846435546875,
-0.0202484130859375,
0.0159912109375,
-0.0027027130126953125,
0.02777099609375,
0.00927734375,
-0.0012483596801757812,
-0.0124359130859375,
0.0076141357421875,
-0.003421783447265625,
0.00836181640625,
-0.005401611328125,
0.00457763671875,
0.0037326812744140625,
-0.00429534912109375,
-0.0018377304077148438,
-0.0204620361328125,
0.01556396484375,
-0.01255035400390625,
-0.002071380615234375,
-0.00199127197265625,
-0.0168304443359375,
0.0184173583984375,
-0.039703369140625,
0.00656890869140625,
0.009674072265625,
-0.025909423828125,
-0.0007686614990234375,
-0.01253509521484375,
-0.04559326171875,
-0.00777435302734375,
-0.04949951171875,
0.0133819580078125,
0.0007314682006835938,
0.019622802734375,
-0.0237579345703125,
-0.001827239990234375,
-0.0027866363525390625,
0.00328826904296875,
0.022918701171875,
-0.004852294921875,
0.051177978515625,
0.015777587890625,
-0.0170135498046875,
0.01342010498046875,
-0.048126220703125,
-0.014556884765625,
0.034637451171875,
0.006381988525390625,
-0.00577545166015625,
-0.00038909912109375,
-0.006000518798828125,
-0.0142669677734375,
-0.003482818603515625,
0.0083770751953125,
-0.0183563232421875,
-0.006221771240234375,
0.0072021484375,
0.003231048583984375,
0.0201263427734375,
-0.01079559326171875,
0.002956390380859375,
0.0100555419921875,
0.00600433349609375,
0.02447509765625,
0.0034160614013671875,
-0.0097808837890625,
-0.035003662109375,
-0.02685546875,
-0.039031982421875,
-0.0267486572265625,
-0.0126495361328125,
0.0271148681640625,
0.0160369873046875,
-0.0182952880859375,
-0.000850677490234375,
0.016754150390625,
-0.00860595703125,
-0.016326904296875,
-0.0210418701171875,
-0.0135650634765625,
-0.044097900390625,
-0.01097869873046875,
0.00026607513427734375,
-0.00975799560546875,
-0.035858154296875,
-0.0159912109375,
0.0037841796875,
-0.0321044921875,
0.005123138427734375,
0.01300048828125,
0.02264404296875,
-0.0189361572265625,
0.04510498046875,
0.022552490234375,
0.01212310791015625,
-0.00943756103515625,
-0.022918701171875,
-0.0006427764892578125,
-0.0235595703125,
0.00318145751953125,
0.060516357421875,
-0.040069580078125,
-0.019287109375,
-0.018646240234375,
-0.0007958412170410156,
-0.007183074951171875,
0.008056640625,
-0.040924072265625,
0.00794219970703125,
0.0157318115234375,
-0.01629638671875,
0.004825592041015625,
0.027496337890625,
-0.0108642578125,
0.009124755859375,
0.0002758502960205078,
0.015960693359375,
-0.032745361328125,
0.0114593505859375,
0.0180511474609375,
-0.006946563720703125,
0.00536346435546875,
-0.0181121826171875,
0.005199432373046875,
-0.005756378173828125,
-0.0176849365234375,
0.007457733154296875,
-0.02392578125,
-0.0030345916748046875,
0.020050048828125,
-0.0399169921875,
0.017425537109375,
-0.037109375,
-0.00519561767578125,
-0.0111541748046875,
0.01110076904296875,
-0.008575439453125,
-0.00994110107421875,
-0.022613525390625,
-0.0255279541015625,
-0.035858154296875,
0.043487548828125,
0.0019216537475585938,
-0.011627197265625,
-0.01000213623046875,
0.0022754669189453125,
0.020721435546875,
-0.01317596435546875,
0.0140533447265625,
0.0352783203125,
0.003795623779296875,
-0.0196533203125,
0.0016994476318359375,
0.0010471343994140625,
0.00827789306640625,
-0.0194091796875,
0.03271484375,
-0.01117706298828125,
-0.019500732421875,
0.0021839141845703125,
0.01007080078125,
-0.00679779052734375,
-0.01160430908203125,
0.017730712890625,
0.0157623291015625,
0.01065826416015625,
-0.006622314453125,
-0.0017862319946289062,
0.0287017822265625,
0.0018663406372070312,
-0.004726409912109375,
-0.0098419189453125,
0.020538330078125,
-0.0075836181640625,
0.0194549560546875,
0.01277923583984375,
0.00579071044921875,
0.012664794921875,
-0.01329803466796875,
-0.00922393798828125,
-0.0106201171875,
0.0044097900390625,
-0.01355743408203125,
-0.00714874267578125,
-0.0109405517578125,
0.00024580955505371094,
0.011749267578125,
0.023406982421875,
-0.026275634765625,
-0.01059722900390625,
0.013824462890625,
-0.00713348388671875,
-0.020660400390625,
0.039398193359375,
-0.01654052734375,
-0.0229339599609375,
-0.04205322265625,
-0.004665374755859375,
0.006336212158203125,
0.006801605224609375,
-0.0179290771484375,
-0.01337432861328125,
-0.0236358642578125,
-0.017730712890625,
0.050994873046875,
-0.0078277587890625,
0.0084228515625,
-0.043975830078125,
-0.0235137939453125,
0.01312255859375,
0.01873779296875,
-0.000125885009765625,
-0.007419586181640625,
-0.0106964111328125,
0.025115966796875,
-0.001636505126953125,
-0.021392822265625,
0.00548553466796875,
-0.000009357929229736328,
-0.00501251220703125,
0.0222625732421875,
0.01763916015625,
-0.0128326416015625,
-0.025177001953125,
-0.0006608963012695312,
-0.027191162109375,
0.01407623291015625,
-0.0018568038940429688,
0.01849365234375,
-0.00926971435546875,
0.02313232421875,
0.012847900390625,
0.01837158203125,
0.0172271728515625,
0.0145416259765625,
-0.01113128662109375,
0.0265655517578125,
0.039642333984375,
0.0017642974853515625,
0.005794525146484375,
0.026275634765625,
0.0274200439453125,
-0.040802001953125,
0.0276336669921875,
0.00445556640625,
0.0289459228515625,
-0.01763916015625,
-0.0110321044921875,
0.0163116455078125,
-0.017730712890625,
-0.01366424560546875,
-0.00966644287109375,
0.0012865066528320312,
-0.0073394775390625,
-0.011871337890625,
0.0221710205078125,
0.0232391357421875,
0.006473541259765625,
-0.0155487060546875,
0.00262451171875,
0.0278778076171875,
0.01508331298828125,
-0.0158233642578125,
0.034698486328125,
0.0210723876953125,
-0.0029697418212890625,
-0.005283355712890625,
-0.01143646240234375,
-0.00933074951171875,
-0.0012664794921875,
0.0179595947265625,
0.01385498046875,
-0.0222625732421875,
0.00913238525390625,
0.00274658203125,
0.00897979736328125,
0.0030841827392578125,
-0.007724761962890625,
-0.014495849609375,
-0.0160369873046875,
-0.005523681640625,
-0.00621795654296875,
-0.03436279296875,
-0.00722503662109375,
-0.004192352294921875,
-0.0202178955078125,
-0.0160980224609375,
0.0057830810546875,
-0.005138397216796875,
-0.0048980712890625,
0.00841522216796875,
0.0232391357421875,
0.00206756591796875,
0.04205322265625,
0.02703857421875,
-0.01409149169921875,
-0.0279693603515625,
0.00945281982421875,
0.0031337738037109375,
0.01186370849609375,
0.045806884765625,
0.0008940696716308594,
-0.0291748046875,
0.01131439208984375,
0.01371002197265625,
-0.023284912109375,
0.02801513671875,
-0.0235137939453125,
0.036956787109375,
0.011932373046875,
-0.005584716796875,
-0.0206451416015625,
-0.00772857666015625,
-0.01345062255859375,
0.004032135009765625,
-0.02056884765625,
0.00974273681640625,
-0.0236053466796875,
-0.0203857421875,
-0.0156097412109375,
-0.008392333984375,
-0.01378631591796875,
-0.0164794921875,
-0.0041351318359375,
-0.01250457763671875,
-0.004398345947265625,
-0.0248565673828125,
0.0124969482421875,
-0.0004525184631347656,
0.012542724609375,
0.01317596435546875,
0.0027713775634765625,
0.0139312744140625,
-0.01025390625,
0.0164337158203125,
0.00406646728515625,
0.00885772705078125,
-0.01251983642578125,
0.01119232177734375,
0.01442718505859375,
0.02764892578125,
-0.0142822265625,
0.0097808837890625,
-0.037872314453125,
0.03057861328125,
0.01335906982421875,
-0.00959014892578125,
0.0357666015625,
0.037933349609375,
-0.0024852752685546875,
0.0259246826171875,
-0.02545166015625,
-0.0236968994140625,
0.032012939453125,
0.01544189453125,
0.0204925537109375,
-0.036651611328125,
0.03033447265625,
-0.0202789306640625,
0.00795745849609375,
-0.01041412353515625,
-0.0195159912109375,
0.01214599609375,
-0.01108551025390625,
0.01058197021484375,
0.004329681396484375,
0.004352569580078125,
-0.006870269775390625,
0.003570556640625,
0.01134490966796875,
-0.0006074905395507812,
0.0025615692138671875,
0.0018491744995117188,
0.0214080810546875,
-0.00955963134765625,
0.0082550048828125,
0.035430908203125,
0.0377197265625,
0.0283050537109375,
0.0006432533264160156,
0.00792694091796875,
0.0300140380859375,
0.0034275054931640625,
-0.0211639404296875,
-0.0008630752563476562,
0.0111083984375,
-0.0251617431640625,
-0.037322998046875,
-0.00009739398956298828,
0.00804901123046875,
-0.0360107421875,
0.0037784576416015625,
0.00972747802734375,
0.0242156982421875,
-0.0147552490234375,
0.01488494873046875,
-0.0020809173583984375,
-0.005748748779296875,
-0.0111083984375,
-0.0157623291015625,
0.02374267578125,
-0.00017201900482177734,
-0.0096435546875,
0.0104217529296875,
0.022003173828125,
-0.00677490234375,
-0.0180206298828125,
-0.021087646484375,
-0.02264404296875,
-0.0013151168823242188,
0.00482177734375,
-0.0037899017333984375,
0.0275421142578125,
-0.0126800537109375,
0.0091094970703125,
0.016998291015625,
0.01105499267578125,
-0.019561767578125,
0.002071380615234375,
-0.002849578857421875,
-0.01433563232421875,
0.016326904296875,
0.01007843017578125,
0.01245880126953125,
0.0113983154296875,
-0.002471923828125,
0.0035457611083984375,
-0.0253448486328125,
-0.002101898193359375,
-0.020843505859375,
-0.0160369873046875,
0.020782470703125,
-0.014129638671875,
0.006511688232421875,
0.01544952392578125,
0.007602691650390625,
-0.01312255859375,
0.0113372802734375,
0.00653076171875,
0.0294036865234375,
-0.0166168212890625,
-0.01183319091796875,
-0.0131072998046875,
0.0226593017578125,
0.01116943359375,
-0.0007715225219726562,
0.01528167724609375,
-0.01560211181640625,
0.03729248046875,
0.0155181884765625,
0.004180908203125,
0.0219268798828125,
-0.0094757080078125,
-0.00396728515625,
-0.0131378173828125,
0.0104522705078125,
-0.002391815185546875,
-0.018890380859375,
-0.0056915283203125,
0.0121307373046875,
0.009490966796875,
0.01392364501953125,
0.01306915283203125,
-0.031768798828125,
-0.0214080810546875,
-0.00920867919921875,
0.003688812255859375,
-0.006092071533203125,
-0.00582122802734375,
-0.0248260498046875,
-0.0181732177734375,
0.0012731552124023438,
0.001590728759765625,
-0.0211029052734375,
0.004596710205078125,
-0.01055145263671875,
-0.017303466796875,
-0.005458831787109375,
0.0036373138427734375,
-0.0016984939575195312,
-0.0203857421875,
0.0341796875,
-0.0008068084716796875,
0.0064697265625,
-0.00312042236328125,
-0.0213623046875,
-0.0154571533203125,
-0.003437042236328125,
-0.0195159912109375,
-0.0297393798828125,
-0.0115814208984375,
0.0265655517578125,
0.05224609375,
-0.01561737060546875,
0.027374267578125,
0.0089569091796875,
0.022430419921875,
0.026031494140625,
-0.04473876953125,
0.01617431640625,
0.0147247314453125,
0.01483154296875,
0.037750244140625,
-0.02947998046875,
0.0286102294921875,
-0.004909515380859375,
-0.0008082389831542969,
0.0005292892456054688,
-0.01131439208984375,
0.0060577392578125,
-0.0123291015625,
0.0236663818359375,
-0.0309295654296875,
0.00891876220703125,
-0.00843048095703125,
-0.01097869873046875,
0.0252685546875,
-0.01087188720703125,
0.0006923675537109375,
-0.001277923583984375,
-0.0008416175842285156,
0.0230255126953125,
-0.029541015625,
0.0173797607421875,
0.0161895751953125,
-0.026519775390625,
0.0006747245788574219,
0.0288543701171875,
-0.0231475830078125,
0.038787841796875,
-0.0202789306640625,
0.003559112548828125,
-0.0297698974609375,
0.015869140625,
-0.033416748046875,
0.006591796875,
0.044036865234375,
-0.0198974609375,
0.0009489059448242188,
-0.0094757080078125,
0.000957489013671875,
-0.039642333984375,
-0.004634857177734375,
0.027008056640625,
-0.01202392578125,
0.004077911376953125,
0.00502777099609375,
-0.0090789794921875,
0.02337646484375,
-0.0192413330078125,
0.007251739501953125,
-0.0102996826171875,
0.045135498046875,
0.00592803955078125,
-0.037322998046875,
-0.00991058349609375,
-0.03369140625,
0.01132965087890625,
0.045501708984375,
0.030914306640625,
-0.0019664764404296875,
0.005458831787109375,
-0.0222320556640625,
0.0283660888671875,
-0.03985595703125,
0.0099029541015625,
-0.00583648681640625,
-0.006298065185546875,
-0.02899169921875,
-0.00811004638671875,
0.0211639404296875,
-0.01110076904296875,
-0.001613616943359375,
-0.0037059783935546875,
0.00011223554611206055,
0.002742767333984375,
-0.0219573974609375,
-0.0178070068359375,
0.060638427734375,
-0.00827789306640625,
-0.032012939453125,
-0.03302001953125,
-0.078125,
0.013458251953125,
-0.0491943359375,
0.000301361083984375,
0.01261138916015625,
0.01055145263671875,
0.019073486328125,
-0.01324462890625,
0.00047135353088378906,
0.01007843017578125,
0.015960693359375,
0.0223236083984375,
-0.0241851806640625,
-0.0206298828125,
0.0105133056640625,
0.00598907470703125,
-0.0003838539123535156,
-0.0114898681640625,
-0.035491943359375,
-0.017333984375,
0.02362060546875,
-0.01522064208984375,
0.004924774169921875,
-0.0189056396484375,
-0.023101806640625,
-0.043304443359375,
0.0069732666015625,
-0.0012121200561523438,
0.0155792236328125,
-0.0183563232421875,
0.023345947265625,
0.00359344482421875,
0.007778167724609375,
-0.00982666015625,
-0.00385284423828125,
-0.040557861328125,
0.00670623779296875,
0.0026302337646484375,
0.0247650146484375,
-0.0201568603515625,
-0.01435089111328125,
-0.019622802734375,
0.005084991455078125,
-0.0236358642578125,
0.0080108642578125,
0.01020050048828125,
-0.01068115234375,
-0.0382080078125,
0.002925872802734375,
0.0024776458740234375,
0.0276947021484375,
0.0101165771484375,
0.024993896484375,
0.032928466796875,
-0.00475311279296875,
0.029083251953125,
0.0142822265625,
-0.02191162109375,
0.0147705078125,
-0.032470703125,
0.0238800048828125,
0.00966644287109375,
0.02203369140625,
0.00963592529296875,
-0.0221710205078125,
0.01611328125,
-0.018890380859375,
0.0076141357421875,
0.01361846923828125,
-0.00318145751953125,
0.017242431640625,
-0.019287109375,
0.000492095947265625,
0.03729248046875,
0.0295257568359375,
0.000044465065002441406,
0.005031585693359375,
0.0086212158203125,
0.016082763671875,
-0.0282135009765625,
-0.007610321044921875,
0.0003457069396972656,
-0.0074462890625,
-0.03350830078125,
0.0006818771362304688,
-0.02447509765625,
-0.02728271484375,
-0.007442474365234375,
0.00957489013671875,
-0.007724761962890625,
0.01148223876953125,
-0.0034198760986328125,
0.01849365234375,
0.0308990478515625
] |
ours_516
|
Define \(g^{\prime}(n)\) as follows: \(g^{\prime}(1)=1\), \(g^{\prime}(2)=2\), \(g^{\prime}(3)=3\), \(g^{\prime}(4)=3\), \(g^{\prime}(5)=3\), and \(g^{\prime}(n)=4\) for all positive integers \(n \geq 6\). We claim \(g(n)=g^{\prime}(n)\) for all positive integers \(n\).
We first show \(g(n) \geq g^{\prime}(n)\) for all positive integers \(n\). The diagrams below are examples that can be used to prove that \(g(1) \geq 1\), \(g(2) \geq 2\), \(g(3) \geq 3\), and \(g(6) \geq 4\). (The details are left as an exercise to the reader.)
The sum \(g(1) + g(2) + \cdots + g(2019)\) can be computed using the values of \(g^{\prime}(n)\):
- For \(n = 1\), \(g(1) = 1\).
- For \(n = 2\), \(g(2) = 2\).
- For \(n = 3\), \(g(3) = 3\).
- For \(n = 4\), \(g(4) = 3\).
- For \(n = 5\), \(g(5) = 3\).
- For \(n \geq 6\), \(g(n) = 4\).
Thus, the sum is:
\[
g(1) + g(2) + g(3) + g(4) + g(5) + \sum_{n=6}^{2019} g(n) = 1 + 2 + 3 + 3 + 3 + 4 \times (2019 - 5)
\]
Calculating the sum:
\[
1 + 2 + 3 + 3 + 3 + 4 \times 2014 = 12 + 8056 = 8068
\]
Therefore, the answer is \(\boxed{8068}\).
|
8068
|
{
"competition": "us_comps",
"dataset": "Ours",
"posts": null,
"source": "OMOFall19Solns.md"
}
|
Define a modern artwork to be a nonempty finite set of rectangles in the Cartesian coordinate plane with positive areas, pairwise disjoint interiors, and sides parallel to the coordinate axes. For a modern artwork \(S\), define its price to be the minimum number of colors with which Sean could paint the interiors of rectangles in \(S\) such that every rectangle's interior is painted in exactly one color and every two distinct touching rectangles have distinct colors, where two rectangles are touching if they share infinitely many points. For a positive integer \(n\), let \(g(n)\) denote the maximum price of any modern artwork with exactly \(n\) rectangles. Compute \(g(1)+g(2)+\cdots+g(2019)\).
|
[
"/Mathematics/DiscreteMathematics/Combinatorics/CombinatorialOptimization",
"/Mathematics/DiscreteMathematics/Combinatorics/Configurations",
"/Mathematics/DiscreteMathematics/Combinatorics/GeneralCombinatorics",
"/Mathematics/DiscreteMathematics/GraphTheory/GeneralGraphTheory",
"/Mathematics/DiscreteMathematics/GraphTheory/GraphColoring",
"/Mathematics/Geometry/CombinatorialGeometry",
"/Mathematics/Geometry/CoordinateGeometry/Cartesian",
"/Mathematics/Geometry/CoordinateGeometry/CartesianCoordinateSystem",
"/Mathematics/Geometry/CoordinateGeometry/CartesianCoordinates",
"/Mathematics/Geometry/CoordinateGeometry/CartesianGeometry",
"/Mathematics/Geometry/CoordinateGeometry/CartesianPlane",
"/Mathematics/Geometry/CoordinateGeometry/CoordinatePlane",
"/Mathematics/Geometry/CoordinateGeometry/CoordinateSystem",
"/Mathematics/Geometry/CoordinateGeometry/Coordinates",
"/Mathematics/Geometry/PlaneGeometry/Rectangles/Rectangle"
] |
Interpret the touching relation among rectangles as a planar graph and use the four‑color theorem to bound the needed colors, while constructing a six‑rectangle example that actually requires four colors.
|
[
0.0001062154769897461,
-0.0305328369140625,
0.03515625,
0.00489044189453125,
0.0005469322204589844,
-0.00795745849609375,
0.005275726318359375,
-0.0223236083984375,
0.00643157958984375,
-0.01285552978515625,
0.01194000244140625,
-0.017578125,
-0.002635955810546875,
0.01788330078125,
-0.0149993896484375,
-0.044219970703125,
-0.0074615478515625,
-0.0256195068359375,
-0.01110076904296875,
-0.00438690185546875,
-0.017120361328125,
0.045074462890625,
-0.044342041015625,
0.02587890625,
-0.0017681121826171875,
-0.059539794921875,
-0.0162811279296875,
0.00925445556640625,
0.0236663818359375,
-0.006866455078125,
-0.0264434814453125,
-0.0307159423828125,
0.042388916015625,
0.00792694091796875,
0.002414703369140625,
0.01122283935546875,
0.0380859375,
0.001873016357421875,
-0.04669189453125,
-0.0064697265625,
-0.01519012451171875,
0.0018138885498046875,
0.005222320556640625,
0.006038665771484375,
0.030548095703125,
0.00015556812286376953,
0.00771331787109375,
0.0310516357421875,
-0.0438232421875,
0.00763702392578125,
0.00312042236328125,
0.01251983642578125,
-0.000046372413635253906,
0.0044708251953125,
-0.0177001953125,
-0.0219268798828125,
-0.0112152099609375,
0.0068206787109375,
0.0247650146484375,
-0.01313018798828125,
-0.012451171875,
-0.006412506103515625,
0.01171112060546875,
-0.00978851318359375,
-0.0011167526245117188,
0.004070281982421875,
0.0153350830078125,
-0.01605224609375,
0.0180206298828125,
-0.025665283203125,
-0.008148193359375,
-0.0208587646484375,
-0.020782470703125,
0.038665771484375,
0.036651611328125,
-0.0250396728515625,
-0.0015172958374023438,
0.01052093505859375,
0.00402069091796875,
0.0067138671875,
0.0177001953125,
0.02362060546875,
-0.0003540515899658203,
-0.040374755859375,
0.009979248046875,
0.0004620552062988281,
0.0213775634765625,
-0.00016176700592041016,
0.0325927734375,
0.003040313720703125,
0.01393890380859375,
0.0253753662109375,
0.007389068603515625,
-0.0148162841796875,
0.007350921630859375,
0.004512786865234375,
-0.0040435791015625,
-0.00530242919921875,
-0.0166473388671875,
-0.00916290283203125,
-0.011505126953125,
-0.003505706787109375,
0.017059326171875,
-0.017974853515625,
-0.032684326171875,
-0.025390625,
-0.006793975830078125,
0.006595611572265625,
-0.005214691162109375,
0.0067291259765625,
0.0179290771484375,
-0.0138397216796875,
0.0179901123046875,
-0.01288604736328125,
0.029296875,
-0.00214385986328125,
-0.014312744140625,
0.00948333740234375,
0.0048980712890625,
-0.0055694580078125,
0.00775146484375,
0.012359619140625,
0.004146575927734375,
0.017822265625,
0.01258087158203125,
-0.06402587890625,
0.007587432861328125,
-0.0227813720703125,
0.0015573501586914062,
0.005748748779296875,
-0.00640869140625,
0.0021305084228515625,
-0.010498046875,
0.0167694091796875,
-0.0171661376953125,
0.0185699462890625,
-0.01526641845703125,
0.0013484954833984375,
0.003513336181640625,
0.007137298583984375,
0.0011129379272460938,
0.00836944580078125,
-0.0105133056640625,
0.006160736083984375,
-0.0222930908203125,
0.0312347412109375,
0.000036656856536865234,
-0.0321044921875,
0.01534271240234375,
-0.0033779144287109375,
0.0003266334533691406,
-0.0194549560546875,
0.01345062255859375,
0.004856109619140625,
0.0114593505859375,
0.017822265625,
0.00013899803161621094,
0.0035228729248046875,
-0.0175018310546875,
-0.01064300537109375,
0.00047278404235839844,
0.00408172607421875,
0.00743865966796875,
0.040771484375,
-0.005550384521484375,
-0.003448486328125,
0.007328033447265625,
0.01953125,
-0.01102447509765625,
0.0200653076171875,
0.005130767822265625,
-0.0301513671875,
0.0208892822265625,
-0.0219573974609375,
0.0027256011962890625,
0.0032863616943359375,
-0.01004791259765625,
0.013092041015625,
-0.002933502197265625,
-0.00841522216796875,
0.0038089752197265625,
-0.00508880615234375,
0.038055419921875,
-0.002758026123046875,
0.010986328125,
-0.0120849609375,
0.01081085205078125,
-0.00255584716796875,
0.03314208984375,
0.0227813720703125,
0.01477813720703125,
0.01873779296875,
-0.0160675048828125,
-0.0040130615234375,
-0.021209716796875,
0.0170440673828125,
0.00501251220703125,
0.01513671875,
0.020263671875,
0.00038051605224609375,
0.0011844635009765625,
-0.00955963134765625,
0.0252685546875,
-0.0005254745483398438,
0.01384735107421875,
-0.0088653564453125,
0.020477294921875,
-0.0140228271484375,
-0.01255035400390625,
-0.00012540817260742188,
0.01082611083984375,
-0.048828125,
-0.0206298828125,
0.01320648193359375,
-0.015777587890625,
-0.0030231475830078125,
-0.01128387451171875,
0.0036563873291015625,
0.00569915771484375,
-0.051544189453125,
-0.0013380050659179688,
0.00860595703125,
-0.0192413330078125,
-0.01380157470703125,
-0.0275726318359375,
-0.0005898475646972656,
0.0287017822265625,
0.01678466796875,
0.022674560546875,
-0.0144805908203125,
0.01418304443359375,
0.0192108154296875,
-0.0276336669921875,
-0.021942138671875,
-0.0094757080078125,
0.0057525634765625,
-0.00399017333984375,
-0.0013532638549804688,
0.0130767822265625,
0.0084686279296875,
0.027862548828125,
-0.0014400482177734375,
0.014801025390625,
0.0016613006591796875,
-0.00787353515625,
0.011444091796875,
-0.01261138916015625,
-0.0245361328125,
-0.01294708251953125,
-0.02105712890625,
-0.00702667236328125,
0.003631591796875,
-0.01358795166015625,
-0.010528564453125,
-0.03179931640625,
-0.0200958251953125,
0.0050811767578125,
-0.0026416778564453125,
-0.016937255859375,
-0.0416259765625,
-0.0218048095703125,
0.0035953521728515625,
0.006618499755859375,
0.00926971435546875,
0.00901031494140625,
0.004138946533203125,
-0.0122833251953125,
0.0020809173583984375,
-0.0101776123046875,
-0.008148193359375,
0.03533935546875,
-0.00872039794921875,
-0.005153656005859375,
0.0013170242309570312,
0.02447509765625,
-0.0433349609375,
-0.00597381591796875,
0.0092315673828125,
0.007778167724609375,
-0.00250244140625,
0.00847625732421875,
-0.024261474609375,
0.00775146484375,
0.0237274169921875,
-0.0051422119140625,
0.01462554931640625,
-0.00875091552734375,
-0.01611328125,
0.008544921875,
0.012969970703125,
-0.0019817352294921875,
0.0036220550537109375,
-0.0006084442138671875,
0.0025482177734375,
0.04473876953125,
-0.06134033203125,
-0.0012569427490234375,
0.013671875,
-0.0095672607421875,
-0.0171661376953125,
0.0011205673217773438,
-0.00525665283203125,
-0.01259613037109375,
0.06396484375,
0.042144775390625,
0.05279541015625,
0.00598907470703125,
0.0090789794921875,
-0.042999267578125,
-0.00438690185546875,
0.0076904296875,
-0.0026950836181640625,
-0.0033550262451171875,
0.00795745849609375,
-0.0263519287109375,
-0.01971435546875,
0.01078033447265625,
0.00897216796875,
-0.002849578857421875,
-0.03399658203125,
0.0171356201171875,
0.043548583984375,
0.007965087890625,
-0.0021343231201171875,
-0.0060882568359375,
0.0017404556274414062,
0.0133056640625,
0.0104522705078125,
-0.0200042724609375,
0.022125244140625,
-0.0179290771484375,
0.013580322265625,
0.0135650634765625,
-0.0083465576171875,
-0.0279693603515625,
0.0171051025390625,
-0.003894805908203125,
0.005695343017578125,
0.006679534912109375,
-0.013580322265625,
-0.0002446174621582031,
0.0159149169921875,
-0.005321502685546875,
-0.020660400390625,
-0.0119476318359375,
0.022674560546875,
0.005916595458984375,
-0.01239013671875,
-0.019989013671875,
-0.01410675048828125,
-0.0118560791015625,
0.01277923583984375,
-0.0271148681640625,
0.0289459228515625,
-0.018280029296875,
0.024505615234375,
-0.04266357421875,
-0.0084381103515625,
-0.0019178390502929688,
0.02581787109375,
-0.01177978515625,
0.00766754150390625,
0.0097808837890625,
-0.0014476776123046875,
0.0260009765625,
-0.01458740234375,
-0.01148223876953125,
0.0091705322265625,
-0.01270294189453125,
-0.01517486572265625,
0.0204315185546875,
0.00882720947265625,
0.00983428955078125,
-0.0357666015625,
-0.0142822265625,
-0.0217437744140625,
0.015167236328125,
-0.00157928466796875,
-0.010589599609375,
-0.01136016845703125,
-0.0032978057861328125,
0.01702880859375,
0.01201629638671875,
0.0491943359375,
-0.022369384765625,
0.01232147216796875,
0.0018911361694335938,
-0.026763916015625,
-0.038970947265625,
0.00917816162109375,
0.00677490234375,
-0.0355224609375,
-0.0128173828125,
0.03289794921875,
0.0002856254577636719,
-0.037384033203125,
0.00344085693359375,
-0.00507354736328125,
0.032623291015625,
-0.0111541748046875,
-0.029388427734375,
-0.00909423828125,
-0.02093505859375,
0.03143310546875,
0.0017271041870117188,
-0.0142822265625,
-0.0167388916015625,
-0.00540924072265625,
0.004543304443359375,
-0.023834228515625,
0.014984130859375,
0.0102386474609375,
0.018798828125,
-0.00628662109375,
0.041412353515625,
-0.02740478515625,
0.03448486328125,
0.0150146484375,
-0.0292510986328125,
-0.0026187896728515625,
0.0120697021484375,
-0.032806396484375,
-0.0167083740234375,
0.010345458984375,
0.0017995834350585938,
0.01708984375,
0.005458831787109375,
0.0310516357421875,
-0.0013856887817382812,
0.027099609375,
0.0323486328125,
-0.01027679443359375,
0.021820068359375,
0.0062713623046875,
0.00897216796875,
0.0302734375,
0.0171356201171875,
-0.005519866943359375,
0.005023956298828125,
-0.019195556640625,
-0.020721435546875,
-0.0181884765625,
0.037322998046875,
-0.0244293212890625,
-0.01788330078125,
-0.0092010498046875,
0.02203369140625,
0.023284912109375,
0.0223236083984375,
0.00977325439453125,
-0.034637451171875,
0.01873779296875,
-0.01116943359375,
-0.003147125244140625,
-0.0214080810546875,
0.04180908203125,
-0.0026721954345703125,
-0.0352783203125,
0.003971099853515625,
-0.053009033203125,
-0.00617218017578125,
0.004978179931640625,
0.0014781951904296875,
-0.0044403076171875,
-0.0198822021484375,
-0.01247406005859375,
-0.0005960464477539062,
0.003997802734375,
0.0268707275390625,
0.01047515869140625,
0.0012531280517578125,
-0.0265655517578125,
0.0212860107421875,
-0.0038604736328125,
-0.0261383056640625,
0.0002963542938232422,
0.008819580078125,
0.014495849609375,
-0.0186004638671875,
-0.00569915771484375,
-0.019378662109375,
-0.00396728515625,
0.0200653076171875,
0.0291595458984375,
0.033599853515625,
0.0010347366333007812,
0.0266265869140625,
0.01251983642578125,
-0.0124969482421875,
-0.005115509033203125,
0.0036640167236328125,
0.059051513671875,
-0.006511688232421875,
-0.0193634033203125,
-0.003429412841796875,
-0.0149078369140625,
-0.01392364501953125,
0.0148468017578125,
0.01161956787109375,
-0.01328277587890625,
-0.0123291015625,
0.00200653076171875,
0.0057830810546875,
0.032196044921875,
0.004638671875,
0.0302886962890625,
0.043701171875,
-0.0283355712890625,
0.0012426376342773438,
0.00037741661071777344,
-0.0201416015625,
0.005138397216796875,
0.0224456787109375,
-0.0287017822265625,
0.0146331787109375,
-0.0236663818359375,
-0.0060577392578125,
-0.020233154296875,
0.007659912109375,
0.0250244140625,
0.001262664794921875,
0.0024394989013671875,
0.0298004150390625,
0.022369384765625,
-0.00836944580078125,
0.00226593017578125,
0.01806640625,
-0.0386962890625,
0.045745849609375,
0.0205078125,
0.00902557373046875,
-0.019989013671875,
-0.00852203369140625,
0.01042938232421875,
-0.0238800048828125,
0.01528167724609375,
0.0093841552734375,
0.0150146484375,
-0.006927490234375,
-0.0159454345703125,
0.0111083984375,
0.0179595947265625,
0.01776123046875,
0.01184844970703125,
-0.0231781005859375,
-0.00931549072265625,
0.004352569580078125,
0.0145416259765625,
0.016815185546875,
-0.0081787109375,
0.00910186767578125,
0.01270294189453125,
-0.027069091796875,
-0.005252838134765625,
-0.028656005859375,
0.017547607421875,
0.01325225830078125,
0.0148162841796875,
0.004261016845703125,
0.0158843994140625,
0.0036487579345703125,
0.046142578125,
0.00519561767578125,
0.01305389404296875,
0.016845703125,
-0.021820068359375,
0.0204010009765625,
0.00798797607421875,
-0.0026645660400390625,
-0.025421142578125,
-0.00010579824447631836,
-0.0029296875,
0.0268096923828125,
-0.043182373046875,
0.00014281272888183594,
0.0006999969482421875,
0.0010919570922851562,
0.019134521484375,
0.003055572509765625,
-0.021820068359375,
0.007843017578125,
-0.0086669921875,
0.0022106170654296875,
-0.012237548828125,
0.0263671875,
-0.006816864013671875,
0.0036945343017578125,
0.011932373046875,
0.01371002197265625,
-0.0016040802001953125,
0.0091705322265625,
0.03631591796875,
0.041900634765625,
-0.02728271484375,
0.00881195068359375,
-0.01464080810546875,
0.0005974769592285156,
0.02728271484375,
0.0093994140625,
-0.00945281982421875,
-0.0115203857421875,
-0.01381683349609375,
-0.0187225341796875,
0.049774169921875,
-0.01155853271484375,
0.0114593505859375,
0.038421630859375,
0.01303863525390625,
-0.0289154052734375,
-0.0032978057861328125,
0.024658203125,
-0.0249481201171875,
0.0238800048828125,
-0.017242431640625,
0.0218048095703125,
-0.00620269775390625,
0.00482940673828125,
-0.03369140625,
-0.007904052734375,
0.032745361328125,
0.0078582763671875,
-0.00788116455078125,
0.0005488395690917969,
0.004177093505859375,
-0.009918212890625,
0.02337646484375,
0.01232147216796875,
-0.0184326171875,
0.0052032470703125,
0.02166748046875,
0.001552581787109375,
-0.03546142578125,
-0.00782012939453125,
-0.0347900390625,
-0.0146484375,
-0.0267791748046875,
-0.01557159423828125,
-0.001682281494140625,
-0.025054931640625,
-0.0078125,
0.019287109375,
0.00946044921875,
0.01093292236328125,
-0.036956787109375,
0.01099395751953125,
0.0176544189453125,
0.006801605224609375,
-0.016143798828125,
0.024566650390625,
0.0157318115234375,
-0.0214691162109375,
-0.006397247314453125,
-0.036712646484375,
-0.03497314453125,
-0.01058197021484375,
-0.01403045654296875,
0.0230712890625,
0.002777099609375,
0.02276611328125,
0.004665374755859375,
0.0228271484375,
0.002368927001953125,
0.01141357421875,
0.00678253173828125,
-0.0172882080078125,
0.0193023681640625,
-0.0151214599609375,
0.0011548995971679688,
0.004230499267578125,
0.006916046142578125,
-0.026214599609375,
0.01297760009765625,
-0.050018310546875,
-0.0076141357421875,
-0.001552581787109375,
0.003681182861328125,
-0.0199127197265625,
-0.0019130706787109375,
-0.01139068603515625,
-0.00007218122482299805,
0.00997161865234375,
0.0298309326171875,
0.045074462890625,
-0.01320648193359375,
0.02923583984375,
-0.01055145263671875,
0.01702880859375,
0.013397216796875,
0.0220794677734375,
-0.0008912086486816406,
0.00872802734375,
0.004169464111328125,
-0.004070281982421875,
0.0150146484375,
0.0008792877197265625,
-0.003963470458984375,
0.00713348388671875,
-0.010711669921875,
-0.01263427734375,
-0.01493072509765625,
-0.0025081634521484375,
-0.01207733154296875,
0.0328369140625,
0.00765228271484375,
-0.0021533966064453125,
-0.03009033203125,
-0.007617950439453125,
-0.00942230224609375,
-0.0272369384765625,
0.0325927734375,
-0.016754150390625,
0.0028228759765625,
-0.03668212890625,
0.021759033203125,
0.021453857421875,
-0.053558349609375,
0.016632080078125,
-0.00012505054473876953,
-0.0146026611328125,
-0.01363372802734375,
0.00672149658203125,
0.02435302734375,
0.0065460205078125,
-0.03375244140625,
0.0033435821533203125,
0.055450439453125,
-0.018096923828125,
-0.0272674560546875,
-0.023651123046875,
0.0019073486328125,
0.00855255126953125,
-0.020721435546875,
0.0135650634765625,
-0.016845703125,
-0.02899169921875,
-0.0357666015625,
0.0098724365234375,
-0.006763458251953125,
0.0008025169372558594,
-0.00974273681640625,
0.03741455078125,
0.00930023193359375,
-0.01239776611328125,
0.0096282958984375,
-0.02911376953125,
-0.020965576171875,
-0.0269622802734375,
-0.01180267333984375,
-0.0079498291015625,
0.01275634765625,
0.037445068359375,
0.02001953125,
0.0230255126953125,
-0.056854248046875,
-0.0253143310546875,
0.00756072998046875,
0.015777587890625,
-0.0147247314453125,
-0.0185089111328125,
0.0161895751953125,
-0.031494140625,
0.0045318603515625,
-0.005847930908203125,
-0.01386260986328125,
-0.0247650146484375,
-0.044586181640625,
0.0203857421875,
-0.0296478271484375,
-0.0311737060546875,
0.0017108917236328125,
0.01415252685546875,
-0.01445770263671875,
0.00949859619140625,
-0.0054931640625,
0.0293121337890625,
-0.0034160614013671875,
-0.03558349609375,
0.006256103515625,
0.0286407470703125,
-0.0299835205078125,
-0.033203125,
-0.014312744140625,
0.0026187896728515625,
0.029052734375,
-0.046417236328125,
-0.0020885467529296875,
0.031951904296875,
0.009521484375,
0.0016164779663085938,
0.01308441162109375,
0.034942626953125,
0.004192352294921875,
-0.0011310577392578125,
-0.0026149749755859375,
-0.0011739730834960938,
-0.00547027587890625,
0.030059814453125,
0.00632476806640625,
0.023040771484375,
0.0178070068359375,
0.0239105224609375,
0.00501251220703125,
-0.01160430908203125,
0.039520263671875,
0.005832672119140625,
0.004856109619140625,
-0.0008697509765625,
0.00934600830078125,
-0.00911712646484375,
0.0015611648559570312,
-0.00033926963806152344,
-0.01093292236328125,
0.0305938720703125,
-0.02679443359375,
-0.021453857421875,
0.0036182403564453125,
0.00684356689453125,
-0.01285552978515625,
-0.0008664131164550781,
0.050872802734375,
-0.0116729736328125,
0.047393798828125,
-0.014129638671875,
0.0057220458984375,
-0.0194854736328125,
0.01503753662109375,
0.0060577392578125,
0.0031261444091796875,
0.0163421630859375,
0.01116943359375,
-0.0221405029296875,
-0.00487518310546875,
-0.01346588134765625,
0.0197601318359375,
0.00589752197265625,
-0.005611419677734375,
0.00955963134765625,
-0.0022945404052734375,
0.0032596588134765625,
-0.0248260498046875,
0.01409149169921875,
0.020477294921875,
-0.0036602020263671875,
-0.036041259765625,
-0.024017333984375,
-0.0194854736328125,
-0.01467132568359375,
0.0206298828125,
0.0224151611328125,
0.0192108154296875,
0.0027446746826171875,
0.0096893310546875,
-0.050445556640625,
-0.028350830078125,
0.00989532470703125,
0.019378662109375,
0.01421356201171875,
0.007022857666015625,
0.00286102294921875,
-0.044097900390625,
-0.003780364990234375,
-0.01016998291015625,
0.01012420654296875,
-0.0032062530517578125,
-0.018798828125,
-0.00978851318359375,
-0.0124359130859375,
-0.0289764404296875,
0.0229644775390625,
-0.00821685791015625,
0.01508331298828125,
-0.0072479248046875,
0.01271820068359375,
-0.00311279296875,
0.018310546875,
-0.0019197463989257812,
-0.029296875,
0.016937255859375,
0.00719451904296875,
-0.0199432373046875,
0.00008934736251831055,
-0.02532958984375,
-0.0252685546875,
0.00763702392578125,
-0.01055145263671875,
-0.06610107421875,
-0.018402099609375,
0.0052490234375,
0.0240478515625,
-0.01325225830078125,
0.0178680419921875,
-0.01129913330078125,
-0.002307891845703125,
0.004421234130859375,
0.0013446807861328125,
-0.006763458251953125,
0.01036834716796875,
-0.026580810546875,
0.0002040863037109375,
0.00860595703125,
-0.0236663818359375,
-0.01995849609375,
0.01328277587890625,
0.0265655517578125,
0.022613525390625,
-0.025970458984375,
0.003643035888671875,
-0.0002880096435546875,
-0.021759033203125,
0.023468017578125,
0.005512237548828125,
0.00424957275390625,
0.0100250244140625,
0.032073974609375,
-0.044921875,
-0.00943756103515625,
0.014862060546875,
0.041534423828125,
0.01102447509765625,
-0.0083770751953125,
-0.001956939697265625,
0.004871368408203125,
0.023956298828125,
-0.04180908203125,
0.007350921630859375,
-0.024932861328125,
-0.0108795166015625,
0.0028438568115234375,
-0.003139495849609375,
0.00321197509765625,
-0.004711151123046875,
0.0369873046875,
0.0009899139404296875,
0.004131317138671875,
-0.0266265869140625,
0.01056671142578125,
0.0009064674377441406,
-0.0181121826171875,
0.00494384765625,
-0.0224151611328125,
-0.007030487060546875,
0.01432037353515625,
-0.01096343994140625,
0.013336181640625,
0.017486572265625,
-0.0021266937255859375,
0.0182342529296875,
-0.03009033203125,
-0.0161285400390625,
-0.040130615234375,
0.0001329183578491211,
-0.0285186767578125,
0.00015878677368164062,
0.01235198974609375,
-0.04254150390625,
0.001026153564453125,
0.00260162353515625,
-0.0004782676696777344,
-0.00868988037109375,
-0.009521484375,
0.00585174560546875,
0.01189422607421875,
-0.0244598388671875,
0.0185089111328125,
0.039520263671875,
0.0214996337890625,
-0.01157379150390625,
-0.00797271728515625,
0.020172119140625,
0.00847625732421875,
0.007007598876953125,
-0.005390167236328125,
0.0006852149963378906,
-0.0164947509765625,
-0.0299530029296875,
-0.0162200927734375,
-0.021392822265625,
0.0016040802001953125,
-0.001285552978515625,
-0.01373291015625,
-0.01580810546875,
0.0034694671630859375,
0.004608154296875,
0.0198974609375,
-0.0174560546875,
-0.00720977783203125,
-0.01161956787109375,
-0.0364990234375,
-0.01032257080078125,
-0.0156402587890625,
-0.0284271240234375,
0.041900634765625,
0.0240325927734375,
0.0028362274169921875,
-0.028839111328125,
0.01050567626953125,
0.006671905517578125,
0.01373291015625,
0.031524658203125,
0.01145172119140625,
-0.0207366943359375,
0.016632080078125,
0.0098724365234375,
-0.014007568359375,
0.03302001953125,
-0.0186309814453125,
0.01364898681640625,
0.00799560546875,
0.01531219482421875,
0.004421234130859375,
-0.006298065185546875,
0.0050201416015625,
-0.0126190185546875,
-0.01490020751953125,
0.005092620849609375,
0.004512786865234375,
-0.008453369140625,
-0.006534576416015625,
-0.02825927734375,
0.0297088623046875,
-0.007755279541015625,
0.0285797119140625,
-0.008819580078125,
-0.02313232421875,
-0.00940704345703125,
-0.00849151611328125,
-0.0308380126953125,
0.01824951171875,
0.0268402099609375,
0.00952911376953125,
0.0025272369384765625,
0.0135955810546875,
0.033782958984375,
0.00907135009765625,
-0.0001533031463623047,
0.0003345012664794922,
0.0279388427734375,
-0.0240936279296875,
-0.007450103759765625,
0.0333251953125,
-0.021575927734375,
0.001911163330078125,
0.052947998046875,
-0.001987457275390625,
0.0204315185546875,
-0.026519775390625,
0.0024318695068359375,
-0.0248870849609375,
-0.0255889892578125,
0.01360321044921875,
-0.001949310302734375,
0.0226593017578125,
-0.01324462890625,
0.004791259765625,
0.01236724853515625,
0.007755279541015625,
0.028656005859375,
-0.01385498046875,
-0.00695037841796875,
0.0123291015625,
0.029327392578125,
-0.01393890380859375,
-0.006488800048828125,
-0.0160980224609375,
-0.004253387451171875,
-0.00836944580078125,
-0.033782958984375,
0.0191650390625,
0.0247039794921875,
0.02996826171875,
-0.01052093505859375,
0.01006317138671875,
0.0143890380859375,
-0.038482666015625,
0.01146697998046875,
-0.0245208740234375,
0.0160369873046875,
0.002010345458984375,
-0.007965087890625,
0.0011262893676757812,
-0.0279083251953125,
-0.008819580078125,
-0.0638427734375,
0.00667572021484375,
0.0095062255859375,
0.01291656494140625,
-0.0194244384765625,
0.013641357421875,
0.00666046142578125,
0.0186004638671875,
-0.012115478515625,
0.0040283203125,
0.0013532638549804688,
0.0308990478515625,
0.006412506103515625,
0.0072021484375,
0.0158843994140625,
0.0027313232421875,
-0.0023021697998046875,
0.001827239990234375,
-0.0012845993041992188,
0.039154052734375,
-0.002567291259765625,
-0.0081634521484375,
-0.0025653839111328125,
-0.001964569091796875,
-0.00640869140625,
0.0181884765625,
-0.0118560791015625,
-0.007335662841796875,
-0.01238250732421875,
0.004428863525390625,
0.0188140869140625,
0.0179595947265625,
0.0019664764404296875,
-0.004421234130859375,
-0.038360595703125,
-0.069091796875,
-0.031646728515625,
-0.0015401840209960938,
-0.01337432861328125,
0.03155517578125,
0.0165557861328125,
0.0018444061279296875,
0.0121917724609375,
0.0020618438720703125,
0.00969696044921875,
-0.013946533203125,
-0.03509521484375,
-0.004650115966796875,
-0.0291748046875,
0.021392822265625,
0.00742340087890625,
-0.0235443115234375,
-0.016937255859375,
0.00394439697265625,
-0.005306243896484375,
-0.0005636215209960938,
0.056304931640625,
-0.0272369384765625,
-0.006893157958984375,
-0.00875091552734375,
-0.035247802734375,
-0.0236053466796875,
0.01104736328125,
-0.0108184814453125,
-0.0231781005859375,
-0.007335662841796875,
0.0220489501953125,
0.00711822509765625,
-0.03253173828125,
0.0301055908203125,
-0.0301361083984375,
-0.01177215576171875,
-0.0013341903686523438,
0.01282501220703125,
-0.01561737060546875,
-0.01061248779296875,
0.02325439453125,
-0.0211334228515625,
-0.007701873779296875,
-0.0248260498046875,
0.0109100341796875,
0.0244140625,
0.00096893310546875,
-0.002391815185546875,
-0.007022857666015625,
0.00640869140625,
-0.007137298583984375,
0.030242919921875,
-0.0172882080078125,
-0.0218505859375,
-0.0038928985595703125,
0.0233154296875,
-0.035797119140625,
0.0265350341796875,
0.0057525634765625,
0.01358795166015625,
-0.003948211669921875,
0.0211334228515625,
-0.0135040283203125,
0.03118896484375,
-0.0295562744140625,
0.0010395050048828125,
0.0079193115234375,
-0.034423828125,
0.016021728515625,
0.00028586387634277344,
-0.022552490234375,
0.0367431640625,
0.00974273681640625,
-0.0150299072265625,
0.04644775390625,
0.00740814208984375,
-0.010650634765625,
-0.0229644775390625,
-0.0184173583984375,
-0.01305389404296875,
0.0094146728515625,
-0.01360321044921875,
-0.00191497802734375,
-0.001743316650390625,
-0.023040771484375,
-0.006320953369140625,
0.01465606689453125,
-0.00244140625,
-0.013397216796875,
0.0252685546875,
-0.004032135009765625,
-0.01006317138671875,
-0.0277252197265625,
-0.00505828857421875,
0.04315185546875,
-0.002796173095703125,
0.01678466796875,
0.00595855712890625,
0.00417327880859375,
0.00279998779296875,
-0.002414703369140625,
-0.01508331298828125,
0.01299285888671875,
-0.03375244140625,
-0.0233306884765625,
-0.0113677978515625,
0.006984710693359375,
0.02105712890625,
-0.03485107421875,
0.035400390625,
0.0222625732421875,
0.01218414306640625,
0.07318115234375,
0.023040771484375,
-0.006351470947265625,
0.00923919677734375,
-0.03680419921875,
-0.03167724609375,
-0.00969696044921875,
0.032135009765625,
-0.0006580352783203125,
-0.005077362060546875,
-0.036773681640625,
0.0192718505859375,
-0.011260986328125,
0.015625,
0.0225372314453125,
-0.01493072509765625,
-0.028717041015625,
-0.0116729736328125,
-0.037811279296875,
0.02056884765625,
-0.024932861328125,
-0.0017824172973632812,
-0.0321044921875,
0.003925323486328125,
-0.005321502685546875,
-0.0181884765625,
0.0038967132568359375,
-0.01132965087890625,
-0.00955963134765625,
-0.0220947265625,
0.0221405029296875,
0.004192352294921875,
-0.0021514892578125,
-0.0036296844482421875,
-0.00907135009765625,
0.0189208984375,
0.0007739067077636719,
0.014068603515625,
0.0034122467041015625,
-0.004688262939453125,
-0.0058135986328125,
-0.0238494873046875,
0.0178985595703125,
0.01410675048828125,
0.02862548828125,
0.00798797607421875,
-0.00388336181640625,
-0.00702667236328125,
-0.00283050537109375,
0.036834716796875,
-0.0264892578125,
0.016754150390625,
-0.0017652511596679688,
-0.00246429443359375,
-0.01187896728515625,
0.0017871856689453125,
-0.03558349609375,
-0.01029205322265625,
-0.01058197021484375,
0.02423095703125,
-0.0168914794921875,
-0.00007653236389160156,
-0.016357421875,
0.01276397705078125,
0.0067596435546875,
-0.0200958251953125,
0.0035076141357421875,
0.0171356201171875,
0.01690673828125,
0.04156494140625,
0.001190185546875,
0.00959014892578125,
0.0008511543273925781,
0.01343536376953125,
0.0018243789672851562,
-0.0094757080078125,
-0.00616455078125,
-0.0036334991455078125,
-0.0218658447265625,
-0.02349853515625,
0.0097198486328125,
0.00737762451171875,
0.036529541015625,
-0.041259765625,
0.051361083984375,
0.00608062744140625,
-0.00698089599609375,
0.003398895263671875,
-0.00797271728515625,
0.0305023193359375,
-0.004878997802734375,
-0.004360198974609375,
-0.0225372314453125,
0.00472259521484375,
0.013671875,
-0.0089111328125,
-0.02923583984375,
0.006359100341796875,
-0.03680419921875,
0.0131988525390625,
-0.0068817138671875,
0.005584716796875,
0.00521087646484375,
-0.006366729736328125,
-0.01287841796875,
0.032928466796875,
-0.003635406494140625,
0.0174713134765625,
0.0007557868957519531,
-0.005352020263671875,
-0.005157470703125,
0.025177001953125,
-0.02374267578125,
0.00942230224609375,
0.000518798828125,
0.0033206939697265625,
-0.033782958984375,
0.01885986328125,
0.048980712890625,
-0.0257568359375,
0.0208892822265625,
0.011444091796875,
0.005878448486328125,
0.024322509765625,
-0.02703857421875,
-0.011322021484375,
0.0003819465637207031,
0.024200439453125,
0.057342529296875,
-0.0103302001953125,
0.0394287109375,
-0.0237884521484375,
-0.00873565673828125,
0.0018396377563476562,
0.03668212890625,
0.009674072265625,
0.0170135498046875,
-0.0223541259765625,
0.01258087158203125,
-0.0003235340118408203,
-0.0328369140625,
-0.0158843994140625,
0.0013561248779296875,
-0.02325439453125,
0.01548004150390625,
-0.041046142578125,
-0.00702667236328125,
0.016510009765625,
-0.005130767822265625,
-0.007747650146484375,
-0.03326416015625,
0.00315093994140625,
-0.031097412109375,
-0.057281494140625,
-0.040740966796875,
0.038665771484375,
-0.0131683349609375,
0.0169830322265625,
0.034027099609375,
-0.0283355712890625,
-0.0162506103515625,
-0.0043182373046875,
-0.021759033203125,
0.0005793571472167969,
0.006488800048828125,
-0.02081298828125,
-0.0309600830078125,
-0.01153564453125,
-0.041046142578125,
0.0012798309326171875,
-0.00007712841033935547,
-0.0087738037109375,
-0.0313720703125,
0.01425933837890625,
-0.0007805824279785156,
-0.017181396484375,
0.0156402587890625,
-0.00305938720703125,
0.028839111328125,
-0.01515960693359375,
0.0119171142578125,
0.00025391578674316406,
-0.007476806640625,
-0.058807373046875,
-0.022552490234375,
-0.016845703125,
0.01458740234375,
0.0012760162353515625,
-0.0152587890625,
-0.0009684562683105469,
-0.003475189208984375,
0.01013946533203125,
0.01506805419921875,
0.001079559326171875,
0.0369873046875,
0.0121612548828125,
-0.024932861328125,
-0.0026187896728515625,
-0.0211639404296875,
-0.003704071044921875,
-0.006134033203125,
-0.033416748046875,
-0.0011034011840820312,
-0.0006279945373535156,
-0.0128173828125,
-0.006870269775390625,
0.0232086181640625,
0.009674072265625,
0.0452880859375,
0.0268096923828125,
0.004150390625,
-0.0026912689208984375,
0.01128387451171875,
0.0241851806640625,
-0.01413726806640625,
-0.0131988525390625,
0.0208892822265625,
0.01023101806640625,
0.012542724609375,
0.0097503662109375,
-0.01142120361328125,
0.0003960132598876953,
-0.0014858245849609375,
0.0172576904296875,
0.028472900390625,
0.00661468505859375,
-0.006256103515625,
0.0309600830078125,
-0.0015010833740234375,
0.0245513916015625,
-0.00037169456481933594,
0.0186767578125,
0.029937744140625,
0.006389617919921875,
0.0200042724609375,
-0.00620269775390625,
-0.057830810546875,
0.01357269287109375,
0.01126861572265625,
-0.040374755859375,
0.01314544677734375,
-0.003139495849609375,
0.03515625,
0.0272064208984375,
-0.0333251953125,
-0.0233917236328125,
-0.0201568603515625,
0.00054931640625,
0.00328826904296875,
-0.025177001953125,
-0.021270751953125,
0.004138946533203125,
0.0185699462890625,
-0.002002716064453125,
-0.0279083251953125,
-0.0016231536865234375,
-0.01129150390625,
0.01103973388671875,
-0.006275177001953125,
-0.006744384765625,
-0.033599853515625,
-0.0231475830078125,
0.01067352294921875,
0.007778167724609375,
0.0310516357421875,
-0.019805908203125,
-0.00890350341796875,
-0.0038394927978515625,
-0.0263214111328125,
-0.0142669677734375,
-0.0189056396484375,
-0.029571533203125,
0.0195465087890625,
-0.0173187255859375,
0.0136871337890625,
-0.046600341796875,
-0.045013427734375,
0.005146026611328125,
0.0002994537353515625,
-0.0008873939514160156,
0.0028839111328125,
-0.00041675567626953125,
0.0044403076171875,
-0.0135040283203125,
-0.031097412109375,
-0.023651123046875,
-0.0236663818359375,
-0.0002894401550292969,
0.00461578369140625,
-0.011566162109375,
0.0306396484375,
0.0096893310546875,
0.00879669189453125,
0.00324249267578125,
0.00923919677734375,
-0.00017976760864257812,
0.033355712890625,
-0.0023326873779296875,
-0.034698486328125,
0.0008821487426757812,
0.00030541419982910156,
-0.0023937225341796875,
0.03167724609375,
-0.002407073974609375,
0.00823211669921875,
-0.0294036865234375,
0.03326416015625,
-0.009979248046875,
0.0176239013671875,
0.009490966796875,
-0.014862060546875,
0.004474639892578125,
-0.0206756591796875,
0.029266357421875,
0.0186309814453125,
0.042449951171875,
0.0199737548828125,
0.0183258056640625,
0.0179595947265625,
-0.0005655288696289062,
0.0096893310546875,
-0.010589599609375,
-0.007045745849609375,
-0.004947662353515625,
-0.01540374755859375,
-0.01502227783203125,
0.0142822265625,
0.0352783203125,
-0.01470947265625,
-0.00988006591796875,
0.0193939208984375,
0.022613525390625,
-0.01108551025390625,
0.006275177001953125,
-0.015625,
0.027679443359375,
-0.004108428955078125,
0.00689697265625,
0.00984954833984375,
-0.005458831787109375,
0.00733184814453125,
-0.010589599609375,
-0.01088714599609375,
0.0020084381103515625,
0.0208282470703125,
-0.007175445556640625,
0.0234375,
0.0090484619140625,
-0.00384521484375,
0.0004940032958984375,
-0.0255584716796875,
-0.0204925537109375,
0.00691986083984375,
0.02520751953125,
0.0153350830078125,
-0.029083251953125,
0.010467529296875,
0.044097900390625,
-0.0172271728515625,
-0.0301971435546875,
0.003360748291015625,
0.017547607421875,
0.00997161865234375,
0.0085601806640625,
0.0051422119140625,
0.0018281936645507812,
-0.00021088123321533203,
-0.00449371337890625,
-0.0066986083984375,
0.016387939453125,
-0.03009033203125,
-0.005237579345703125,
-0.0183563232421875,
0.009552001953125,
0.01499176025390625,
-0.01198577880859375,
0.0007061958312988281,
-0.0171966552734375,
0.00936126708984375,
0.01296234130859375,
0.033477783203125,
-0.00049591064453125,
0.0272216796875,
-0.01348876953125,
0.0206756591796875,
0.0126800537109375,
-0.0186004638671875,
0.058197021484375,
0.0007309913635253906,
0.03851318359375,
0.0012226104736328125,
-0.0021686553955078125,
-0.00283050537109375,
-0.007358551025390625,
0.038421630859375,
0.00902557373046875,
-0.000017344951629638672,
-0.01235198974609375,
0.012054443359375,
-0.032501220703125,
0.0256805419921875,
0.016265869140625,
0.00896453857421875,
0.03729248046875,
-0.0245513916015625,
-0.028411865234375,
-0.005340576171875,
0.0186614990234375,
-0.019866943359375,
0.00897979736328125,
0.0035858154296875,
0.0201263427734375,
-0.006526947021484375,
-0.061004638671875,
-0.005725860595703125,
0.0037326812744140625,
-0.0228424072265625,
0.0194549560546875,
-0.005908966064453125,
0.01139068603515625,
0.0095062255859375,
0.012725830078125,
-0.00794219970703125,
-0.01910400390625,
0.00835418701171875,
-0.0303955078125,
-0.024749755859375,
0.006832122802734375,
0.0036258697509765625,
-0.01171875,
0.03692626953125,
0.0227508544921875,
0.00334930419921875,
0.0273895263671875,
-0.02862548828125,
0.007167816162109375,
0.0052947998046875,
0.0046234130859375,
0.0015544891357421875,
0.02227783203125,
-0.0022716522216796875,
-0.0146636962890625,
-0.0107421875,
0.01448822021484375,
-0.0341796875,
0.00890350341796875,
0.0023555755615234375,
-0.002475738525390625,
-0.0032596588134765625,
-0.01340484619140625,
0.027099609375,
-0.0007719993591308594,
-0.000028967857360839844,
0.0210723876953125,
0.01352691650390625,
-0.032135009765625,
0.028533935546875,
-0.006488800048828125,
0.0018558502197265625,
-0.03741455078125,
0.05194091796875,
-0.0228424072265625,
-0.0106964111328125,
-0.0028705596923828125,
0.020751953125,
0.002899169921875,
0.02874755859375,
-0.008270263671875,
-0.0124969482421875,
0.042510986328125,
-0.00720977783203125,
0.045135498046875,
-0.00472259521484375,
0.027984619140625,
0.0243988037109375,
0.015716552734375,
-0.007183074951171875,
0.0018796920776367188,
-0.060943603515625,
-0.009521484375,
0.004726409912109375,
-0.0128326416015625,
-0.0169677734375,
0.032379150390625,
0.017852783203125,
-0.0264129638671875,
0.041534423828125,
-0.0013799667358398438,
-0.0105133056640625,
-0.039825439453125,
0.033416748046875,
-0.0067901611328125,
0.018829345703125,
0.00988006591796875,
0.02392578125,
-0.0191192626953125,
0.01474761962890625,
-0.0086517333984375,
0.00356292724609375,
-0.01085662841796875,
-0.00493621826171875,
0.02850341796875,
0.007659912109375,
0.00897216796875,
0.007709503173828125,
-0.0176239013671875,
0.018646240234375,
-0.0168304443359375,
-0.02081298828125,
0.010528564453125,
0.020721435546875,
0.00077056884765625,
0.0087432861328125,
-0.0240020751953125,
-0.0131683349609375,
-0.0023899078369140625,
0.00290679931640625,
0.02081298828125,
0.01197052001953125,
0.02667236328125,
-0.0009207725524902344,
0.0002238750457763672,
0.0138092041015625,
-0.01079559326171875,
0.00406646728515625,
0.0105438232421875,
0.00839996337890625,
-0.003238677978515625,
-0.03009033203125,
-0.0008978843688964844,
0.00240325927734375,
-0.0277862548828125,
-0.0128021240234375,
-0.0007710456848144531,
-0.0105438232421875,
0.005992889404296875,
-0.01346588134765625,
0.006092071533203125,
0.0018720626831054688,
0.01464080810546875,
0.0216522216796875,
0.01800537109375,
0.0188140869140625,
0.0138702392578125,
-0.0194091796875,
0.0070648193359375,
0.0203704833984375,
0.0117645263671875,
-0.046417236328125,
-0.006122589111328125,
-0.01165771484375,
-0.01102447509765625,
0.01392364501953125,
0.003490447998046875,
0.007678985595703125,
-0.0003566741943359375,
-0.003086090087890625,
0.0074310302734375,
-0.02191162109375,
-0.0005397796630859375,
-0.00749969482421875,
-0.01384735107421875,
-0.00579071044921875,
0.0158538818359375,
-0.0137786865234375,
0.0009465217590332031,
0.01201629638671875,
0.00443267822265625,
0.00489044189453125,
0.00940704345703125,
-0.011566162109375,
0.0156402587890625,
-0.0252685546875,
-0.0006823539733886719,
0.016204833984375,
-0.007213592529296875,
-0.007793426513671875,
0.013397216796875,
0.0087890625,
-0.0263519287109375,
0.0157928466796875,
0.01006317138671875,
0.003604888916015625,
-0.003231048583984375,
-0.043487548828125,
-0.007778167724609375,
0.00623321533203125,
0.00695037841796875,
-0.037078857421875,
0.004093170166015625,
-0.00862884521484375,
-0.026123046875,
-0.00879669189453125,
-0.01824951171875,
0.0233612060546875,
0.0027294158935546875,
0.01262664794921875,
-0.0105438232421875,
-0.0142364501953125,
0.032440185546875,
0.0169525146484375,
0.01305389404296875,
-0.01495361328125,
-0.0244598388671875,
0.0059051513671875,
0.0210113525390625,
-0.020599365234375,
-0.03240966796875,
-0.0010557174682617188,
0.01093292236328125,
0.03802490234375,
-0.0132293701171875,
-0.02142333984375,
-0.0016870498657226562,
-0.0004591941833496094,
-0.02545166015625,
0.01459503173828125,
0.016571044921875,
0.0019969940185546875,
-0.0195159912109375,
0.00551605224609375,
-0.0316162109375,
0.00794219970703125,
-0.0179595947265625,
-0.0169677734375,
-0.0090179443359375,
0.0252227783203125,
-0.00910186767578125,
-0.01180267333984375,
-0.0070648193359375,
0.013641357421875,
-0.0213623046875,
0.036956787109375,
-0.0270538330078125,
0.0152130126953125,
-0.00870513916015625,
0.01541900634765625,
-0.015960693359375,
0.0020656585693359375,
-0.01300811767578125,
0.0210418701171875,
-0.0260009765625,
-0.00638580322265625,
0.029144287109375,
0.006710052490234375,
0.00011545419692993164,
-0.033477783203125,
-0.008270263671875,
0.0251922607421875,
0.01812744140625,
0.007843017578125,
0.00617218017578125,
0.007274627685546875,
0.0024166107177734375,
-0.027801513671875,
-0.0005655288696289062,
-0.001827239990234375,
0.038818359375,
-0.0005583763122558594,
-0.02447509765625,
-0.010711669921875,
0.004764556884765625,
0.0015344619750976562,
-0.00501251220703125,
0.0229644775390625,
-0.0094451904296875,
-0.01299285888671875,
0.013580322265625,
-0.02862548828125,
-0.0012226104736328125,
-0.02484130859375,
0.0099639892578125,
-0.006244659423828125,
0.03741455078125,
-0.036590576171875,
0.01198577880859375,
-0.0002715587615966797,
-0.0099334716796875,
-0.012359619140625,
0.00884246826171875,
0.01320648193359375,
0.0004589557647705078,
-0.034423828125,
-0.006870269775390625,
-0.00789642333984375,
0.0213623046875,
0.0054779052734375,
0.041473388671875,
0.004299163818359375,
0.00865936279296875,
-0.014373779296875,
-0.00836181640625,
0.033538818359375,
0.03448486328125,
-0.0082550048828125,
0.01413726806640625,
-0.0019779205322265625,
0.007541656494140625,
-0.0033130645751953125,
-0.0216064453125,
-0.01593017578125,
0.01284027099609375,
-0.00395965576171875,
-0.028289794921875,
-0.0280609130859375,
0.0003921985626220703,
-0.041412353515625,
0.0111236572265625,
-0.0151519775390625,
-0.01277923583984375,
0.0002422332763671875,
-0.0186767578125,
-0.00539398193359375,
-0.016265869140625,
-0.01004791259765625,
-0.0027256011962890625,
-0.007793426513671875,
0.0157012939453125,
0.00901031494140625,
-0.01293182373046875,
-0.0112457275390625,
-0.016510009765625,
-0.024169921875,
-0.00608062744140625,
-0.0111236572265625,
0.0022029876708984375,
0.01068115234375,
-0.017822265625,
0.032196044921875,
-0.0277252197265625,
-0.007205963134765625,
-0.0076751708984375,
-0.032379150390625,
-0.019439697265625,
-0.0216217041015625,
0.013824462890625,
0.03485107421875,
-0.04095458984375,
-0.0208587646484375,
0.0029354095458984375,
0.0224761962890625,
-0.0086517333984375,
0.01496124267578125,
-0.0114898681640625,
0.0304107666015625,
0.0188751220703125,
-0.01092529296875,
-0.0012845993041992188,
0.00931549072265625,
-0.020355224609375,
0.00661468505859375,
-0.0202484130859375,
-0.02471923828125,
-0.0003864765167236328,
0.03955078125,
-0.06732177734375,
0.0215301513671875,
-0.0246734619140625,
-0.01412200927734375,
-0.008087158203125,
0.0029277801513671875,
-0.032562255859375,
0.020263671875,
-0.0191802978515625,
-0.0100860595703125,
-0.004405975341796875,
0.01110076904296875,
-0.020660400390625,
-0.0002815723419189453,
-0.0195159912109375,
0.00637054443359375,
0.03564453125,
0.015655517578125,
0.014801025390625,
0.0062713623046875,
-0.004421234130859375,
-0.005199432373046875,
-0.006809234619140625,
-0.0038700103759765625,
0.01654052734375,
0.004032135009765625,
-0.0697021484375,
0.026885986328125,
-0.00177001953125,
-0.034393310546875,
0.0204925537109375,
-0.0074462890625,
-0.029754638671875,
-0.00948333740234375,
0.03326416015625,
-0.01055145263671875,
-0.0283203125,
0.006244659423828125,
0.01105499267578125,
-0.02734375,
0.004734039306640625,
-0.01329803466796875,
0.0092620849609375,
-0.0252685546875,
0.005084991455078125,
0.00666046142578125,
-0.006542205810546875,
0.034576416015625,
0.0250701904296875,
-0.0037841796875,
-0.01947021484375,
-0.02569580078125,
0.0018720626831054688,
0.01039886474609375,
-0.00439453125,
0.01279449462890625,
0.01099395751953125,
0.0189361572265625,
-0.00279998779296875,
0.003459930419921875,
0.0175018310546875,
-0.0059814453125,
0.020294189453125,
0.0012531280517578125,
-0.0079345703125,
0.021636962890625,
0.0112762451171875,
0.0158233642578125,
0.0136566162109375,
-0.0098724365234375,
-0.010284423828125,
0.034942626953125,
0.007251739501953125,
-0.00928497314453125,
-0.0098114013671875,
-0.004215240478515625,
0.02191162109375,
0.020111083984375,
-0.008392333984375,
0.0050811767578125,
0.038177490234375,
-0.0212249755859375,
0.0029296875,
0.0250091552734375,
-0.005603790283203125,
0.040802001953125,
0.0250091552734375,
-0.01450347900390625,
0.007549285888671875,
0.01204681396484375,
0.01806640625,
-0.0186767578125,
0.0438232421875,
0.01076507568359375,
-0.034698486328125,
-0.05072021484375,
-0.004573822021484375,
0.020477294921875,
0.043182373046875,
-0.01904296875,
-0.027191162109375,
-0.01528167724609375,
0.01456451416015625,
0.018280029296875,
-0.00940704345703125,
-0.0186767578125,
0.01025390625,
-0.001758575439453125,
0.042449951171875,
0.01407623291015625,
0.0014371871948242188,
0.0174560546875,
0.0004763603210449219,
0.028594970703125,
-0.02557373046875,
-0.0007686614990234375,
0.0006117820739746094,
0.007526397705078125,
-0.0005140304565429688,
-0.0053863525390625,
0.01372528076171875,
-0.03253173828125,
-0.0228271484375,
0.01227569580078125,
0.0008616447448730469,
0.01000213623046875,
-0.01206207275390625,
0.0271453857421875,
0.01129150390625,
0.0614013671875,
-0.00994873046875,
-0.02130126953125,
0.0028324127197265625,
0.0014133453369140625,
-0.006366729736328125,
-0.0241546630859375,
-0.001010894775390625,
-0.004505157470703125,
0.0190277099609375,
0.01306915283203125,
0.034454345703125,
-0.0163116455078125,
0.0268096923828125,
-0.0200347900390625,
-0.01010894775390625,
-0.0260772705078125,
-0.01788330078125,
0.0133819580078125,
-0.01096343994140625,
0.0090789794921875,
-0.0196533203125,
-0.0010528564453125,
0.0117034912109375,
-0.038543701171875,
0.005275726318359375,
-0.0007038116455078125,
0.0182952880859375,
0.01531982421875,
0.0167236328125,
-0.00029659271240234375,
0.0304718017578125,
0.01690673828125,
0.0003066062927246094,
-0.0413818359375,
0.003017425537109375,
-0.014617919921875,
-0.01296234130859375,
0.0038661956787109375,
-0.0256195068359375,
0.01450347900390625,
0.050445556640625,
-0.02508544921875,
-0.044891357421875,
0.003032684326171875,
0.035980224609375,
0.021575927734375,
-0.0027675628662109375,
0.00308990478515625,
-0.034393310546875,
-0.029052734375,
-0.011810302734375,
-0.01010894775390625,
-0.03570556640625,
-0.013824462890625,
-0.0174102783203125,
-0.00327301025390625,
0.004222869873046875,
-0.033111572265625,
0.00350189208984375,
0.046051025390625,
-0.006954193115234375,
-0.0194854736328125,
0.031951904296875,
0.0017328262329101562,
-0.01120758056640625,
-0.0198211669921875,
0.010040283203125,
-0.047210693359375,
0.013427734375,
0.0482177734375,
0.003810882568359375,
0.016204833984375,
0.035888671875,
0.0131378173828125,
-0.002346038818359375,
0.01358795166015625,
-0.0015993118286132812,
0.018341064453125,
0.024566650390625,
-0.0043182373046875,
-0.0011301040649414062,
0.0059814453125,
-0.00782012939453125,
0.0173492431640625,
0.0036258697509765625,
0.0438232421875,
-0.031707763671875,
-0.0306549072265625,
0.0254364013671875,
0.0091552734375,
-0.00272369384765625,
0.019256591796875,
-0.0009813308715820312,
0.0272979736328125,
-0.008880615234375,
0.00241851806640625,
0.024688720703125,
-0.0200958251953125,
-0.0017995834350585938,
-0.00943756103515625,
0.01287078857421875,
0.00893402099609375,
-0.049407958984375,
-0.0017490386962890625,
0.00689697265625,
-0.0095367431640625,
0.004581451416015625,
0.019744873046875,
-0.014404296875,
0.0208740234375,
-0.006862640380859375,
-0.0106353759765625,
-0.044158935546875,
0.008819580078125,
0.0166473388671875,
-0.017913818359375,
0.01216888427734375,
0.05084228515625,
0.0008459091186523438,
-0.036346435546875,
0.010162353515625,
0.03192138671875,
0.004810333251953125,
-0.007579803466796875,
0.0269775390625,
-0.0264434814453125,
0.0107574462890625,
-0.021148681640625,
-0.00411224365234375,
-0.03253173828125,
-0.0096435546875,
0.02874755859375,
0.0030002593994140625,
0.0159454345703125,
0.02301025390625,
-0.0247039794921875,
-0.004665374755859375,
-0.00689697265625,
0.00417327880859375,
0.00592803955078125,
0.002735137939453125,
-0.00437164306640625,
0.011505126953125,
-0.0145721435546875,
0.0093841552734375,
0.00394439697265625,
0.032562255859375,
0.01934814453125,
-0.00782012939453125,
0.00771331787109375,
0.027587890625,
0.0287933349609375,
0.01015472412109375,
-0.029205322265625,
0.0025730133056640625,
-0.00362396240234375,
-0.002017974853515625,
0.0307769775390625,
0.0081634521484375,
0.0229949951171875,
-0.0088653564453125,
0.00040459632873535156,
0.0022220611572265625,
-0.01593017578125,
-0.006328582763671875,
-0.002010345458984375,
0.00885772705078125,
-0.0033931732177734375,
-0.01219940185546875,
0.00838470458984375,
-0.00009310245513916016,
-0.0258636474609375,
-0.01168060302734375,
0.018157958984375,
0.0269622802734375,
-0.0158538818359375,
0.0222320556640625,
0.0347900390625,
0.0157623291015625,
0.004451751708984375,
0.0157470703125,
0.018585205078125,
-0.0192108154296875,
-0.0220947265625,
0.007213592529296875,
-0.00992584228515625,
0.0045166015625,
0.0069732666015625,
-0.0119781494140625,
-0.00508880615234375,
-0.0247802734375,
-0.00809478759765625,
-0.0399169921875,
-0.0208282470703125,
-0.0217132568359375,
0.005069732666015625,
0.0177154541015625,
-0.01210784912109375,
-0.01264190673828125,
-0.038238525390625,
-0.0019550323486328125,
-0.02557373046875,
0.04962158203125,
0.01345062255859375,
-0.0061798095703125,
-0.014068603515625,
0.0033092498779296875,
-0.011749267578125,
0.02783203125,
-0.0172119140625,
0.01020050048828125,
0.0032501220703125,
0.005970001220703125,
0.01568603515625,
-0.0101470947265625,
-0.005023956298828125,
-0.0218963623046875,
0.01334381103515625,
0.0274505615234375,
-0.0134429931640625,
-0.027069091796875,
0.004222869873046875,
0.0130462646484375,
-0.00797271728515625,
-0.00177001953125,
-0.0175323486328125,
0.0026416778564453125,
0.0004055500030517578,
0.018280029296875,
-0.0224761962890625,
-0.002140045166015625,
0.01983642578125,
-0.006702423095703125,
-0.0142974853515625,
-0.03997802734375,
-0.0167388916015625,
-0.009368896484375,
0.02001953125,
-0.01415252685546875,
-0.03778076171875,
-0.0364990234375,
-0.004726409912109375,
-0.004329681396484375,
0.0182342529296875,
-0.00833892822265625,
0.0224456787109375,
0.0081939697265625,
0.024993896484375,
-0.006313323974609375,
-0.03533935546875,
0.032470703125,
-0.0249481201171875,
0.005645751953125,
-0.0184173583984375,
-0.0185699462890625,
-0.017791748046875,
-0.000030159950256347656,
-0.0124053955078125,
0.01476287841796875,
-0.0191802978515625,
0.01039886474609375,
0.0014333724975585938,
-0.0309906005859375,
0.0535888671875,
0.0131378173828125,
-0.00036215782165527344,
-0.0005440711975097656,
-0.030609130859375,
0.0122528076171875,
-0.050201416015625,
0.0009365081787109375,
0.0279998779296875,
-0.018035888671875,
0.028106689453125,
0.01373291015625,
0.032623291015625,
0.03167724609375,
0.014495849609375,
0.01354217529296875,
0.0222930908203125,
0.0189208984375,
-0.0178070068359375,
0.0167236328125,
-0.003509521484375,
-0.00884246826171875,
0.0247650146484375,
-0.0010700225830078125,
0.0166168212890625,
-0.051361083984375,
-0.0178985595703125,
-0.011199951171875,
0.002849578857421875,
0.046173095703125,
-0.007720947265625,
-0.0285491943359375,
0.0025730133056640625,
0.0135498046875,
-0.0084991455078125,
0.018463134765625,
-0.010223388671875,
0.0014972686767578125,
-0.045074462890625,
-0.034820556640625,
-0.00980377197265625,
0.01473236083984375,
0.00785064697265625,
-0.031402587890625,
0.033843994140625,
-0.0010013580322265625,
0.01404571533203125,
-0.01528167724609375,
0.02911376953125,
-0.031158447265625,
0.001316070556640625,
-0.005489349365234375,
0.004459381103515625,
-0.00914764404296875,
0.05987548828125,
-0.022003173828125,
-0.00467681884765625,
-0.01153564453125,
0.0301361083984375,
-0.00518798828125,
-0.0287628173828125,
0.009521484375,
-0.00876617431640625,
-0.01448822021484375,
0.00974273681640625,
-0.005596160888671875,
-0.01474761962890625,
0.016632080078125,
-0.006526947021484375,
-0.06396484375,
-0.018035888671875,
0.0285491943359375,
-0.0171966552734375,
-0.01067352294921875,
-0.00247955322265625,
-0.00856781005859375,
-0.01419830322265625,
-0.021331787109375,
0.01445770263671875,
-0.023040771484375,
-0.01483917236328125,
0.007213592529296875,
-0.016845703125,
0.00640106201171875,
0.048553466796875,
0.00835418701171875,
-0.019195556640625,
-0.0109405517578125,
-0.02960205078125,
0.017791748046875,
-0.007564544677734375,
0.00400543212890625,
0.0255889892578125,
-0.005039215087890625,
0.00371551513671875,
0.01300811767578125,
-0.031982421875,
-0.0192108154296875,
-0.01043701171875,
0.01611328125,
0.01251983642578125,
0.0201263427734375,
-0.003421783447265625,
0.00014543533325195312,
-0.0138702392578125,
0.006893157958984375,
-0.0024547576904296875,
-0.0340576171875,
-0.0221405029296875,
-0.022430419921875,
0.00037789344787597656,
-0.04998779296875,
-0.054931640625,
-0.01097869873046875,
0.00008481740951538086,
-0.0301666259765625,
0.0174560546875,
-0.04254150390625,
-0.0265960693359375,
0.0023746490478515625,
-0.02178955078125,
0.01678466796875,
-0.004779815673828125,
-0.0304107666015625,
-0.020355224609375,
-0.004001617431640625,
0.0133819580078125,
0.02166748046875,
0.0092315673828125,
-0.0253753662109375,
0.01470184326171875,
-0.0010166168212890625,
0.03033447265625,
-0.020050048828125,
0.0124664306640625,
-0.0386962890625,
-0.017578125,
-0.00013339519500732422,
0.00421905517578125,
0.00452423095703125,
-0.0010557174682617188,
0.026031494140625,
-0.031707763671875,
-0.03131103515625,
0.021331787109375,
-0.0013113021850585938,
-0.0243377685546875,
-0.019378662109375,
0.006053924560546875,
0.0018978118896484375,
0.00826263427734375,
0.003932952880859375,
0.0024890899658203125,
-0.01068878173828125,
-0.0279388427734375,
-0.0127410888671875,
0.0133819580078125,
0.0194091796875,
-0.00992584228515625,
-0.017822265625,
-0.002696990966796875,
-0.0081024169921875,
0.0174713134765625,
-0.004787445068359375,
0.0029392242431640625,
0.01097869873046875,
0.0063934326171875,
-0.00336456298828125,
0.036224365234375,
0.01093292236328125,
0.01806640625,
-0.0016832351684570312,
-0.01055908203125,
-0.01287078857421875,
-0.01137542724609375,
-0.0143890380859375,
0.0290679931640625,
0.004634857177734375,
-0.01216888427734375,
0.00926971435546875,
0.00896453857421875,
-0.0026912689208984375
] |
ours_517
|
By Ceva's theorem,
\[
\frac{BE}{EA} \cdot \frac{AD}{DC} \cdot \frac{CF}{FB} = 1
\]
By the angle bisector theorem,
\[
\frac{BE}{EA} \cdot \frac{AD}{DC} = \frac{BP}{PC}
\]
Thus, \(\angle FPC = \frac{\angle BPC}{2} = 45^\circ\). Since \(\triangle BPC\) is right, \(\angle MPC = \angle MCP = 90^\circ - \angle PBF = 20^\circ\). Therefore, \(\angle MPF = \angle FPC - \angle MPC = 25^\circ\).
\(\boxed{25}\)
|
25
|
{
"competition": "us_comps",
"dataset": "Ours",
"posts": null,
"source": "OMOSoln2-2.md"
}
|
In triangle \(ABC\), \(AB=1\) and \(AC=2\). Suppose there exists a point \(P\) in the interior of triangle \(ABC\) such that \(\angle PBC=70^\circ\), and that there are points \(E\) and \(D\) on segments \(AB\) and \(AC\), such that \(\angle BPE=\angle EPA=75^\circ\) and \(\angle APD=\angle DPC=60^\circ\). Let \(BD\) meet \(CE\) at \(Q\), and let \(AQ\) meet \(BC\) at \(F\). If \(M\) is the midpoint of \(BC\), compute the degree measure of \(\angle MPF\).
|
[
"/Mathematics/Geometry/GeneralGeometry/Bisector",
"/Mathematics/Geometry/GeneralGeometry/EuclideanGeometry",
"/Mathematics/Geometry/GeneralGeometry/Geometry",
"/Mathematics/Geometry/PlaneGeometry/Triangles/Cevians",
"/Mathematics/Geometry/Trigonometry/Angles/Angle",
"/Mathematics/Geometry/Trigonometry/Angles/AngleBisector",
"/Mathematics/Geometry/Trigonometry/Angles/AngleBisectorTheorem",
"/Mathematics/Geometry/Trigonometry/Angles/InternalAngleBisector"
] |
Show that PF bisects angle BPC using Ceva and the angle bisector theorem, yielding a 45° sub-angle.
|
[
-0.00028252601623535156,
-0.0012407302856445312,
0.01776123046875,
0.00855255126953125,
-0.0008640289306640625,
0.029327392578125,
0.03753662109375,
0.01186370849609375,
-0.004505157470703125,
-0.0212249755859375,
-0.0267486572265625,
0.00783538818359375,
-0.002544403076171875,
0.0274658203125,
-0.0162811279296875,
-0.033111572265625,
-0.0147247314453125,
-0.01007843017578125,
0.0231475830078125,
-0.000827789306640625,
-0.006664276123046875,
-0.01529693603515625,
-0.034271240234375,
0.0021076202392578125,
-0.004871368408203125,
0.00901031494140625,
-0.0179901123046875,
0.0156402587890625,
-0.0318603515625,
-0.016845703125,
0.0325927734375,
-0.0021686553955078125,
-0.01042938232421875,
-0.0289154052734375,
0.0015878677368164062,
-0.0190582275390625,
-0.039886474609375,
-0.004970550537109375,
-0.015350341796875,
-0.0322265625,
-0.0010042190551757812,
-0.0207672119140625,
0.0029296875,
0.023712158203125,
-0.01458740234375,
0.01050567626953125,
-0.0012941360473632812,
-0.0182037353515625,
0.00849151611328125,
-0.0153350830078125,
0.007595062255859375,
0.00727081298828125,
-0.048248291015625,
-0.01605224609375,
-0.00536346435546875,
-0.054779052734375,
-0.01546478271484375,
0.0027828216552734375,
-0.035888671875,
-0.037261962890625,
-0.0009984970092773438,
0.003162384033203125,
-0.0003490447998046875,
-0.0187530517578125,
-0.0016031265258789062,
-0.0201416015625,
-0.038665771484375,
0.00464630126953125,
0.005374908447265625,
-0.01201629638671875,
0.042266845703125,
-0.02984619140625,
0.0311737060546875,
0.0303497314453125,
0.038330078125,
-0.0147857666015625,
-0.005645751953125,
0.01342010498046875,
-0.0272369384765625,
0.01313018798828125,
-0.006439208984375,
-0.01007843017578125,
0.0121917724609375,
-0.019256591796875,
0.0374755859375,
-0.005878448486328125,
0.00041675567626953125,
0.011199951171875,
0.0281829833984375,
-0.01270294189453125,
0.0079193115234375,
-0.034912109375,
-0.0127410888671875,
-0.0158843994140625,
-0.00426483154296875,
0.0017805099487304688,
0.02130126953125,
-0.011932373046875,
-0.01534271240234375,
0.004718780517578125,
-0.0196380615234375,
-0.00605010986328125,
0.0011014938354492188,
-0.01177215576171875,
0.01412200927734375,
-0.00571441650390625,
-0.0191192626953125,
0.01029205322265625,
-0.01080322265625,
0.016082763671875,
0.00995635986328125,
0.00653076171875,
0.033599853515625,
0.0138092041015625,
0.0115966796875,
-0.01439666748046875,
0.03436279296875,
-0.001407623291015625,
0.00806427001953125,
0.01250457763671875,
-0.005214691162109375,
0.01593017578125,
-0.021087646484375,
0.018798828125,
-0.00890350341796875,
-0.0164794921875,
-0.01366424560546875,
-0.017852783203125,
-0.0240020751953125,
0.0171661376953125,
-0.0078125,
0.0001062154769897461,
-0.01812744140625,
-0.04547119140625,
-0.0175323486328125,
0.0178680419921875,
0.00780487060546875,
-0.007904052734375,
-0.0260009765625,
0.0053863525390625,
0.0021209716796875,
-0.0037288665771484375,
-0.004009246826171875,
-0.0391845703125,
0.0180511474609375,
-0.032806396484375,
0.0127105712890625,
-0.0011873245239257812,
-0.002197265625,
-0.005290985107421875,
-0.01316070556640625,
-0.01020050048828125,
0.0169219970703125,
0.0088043212890625,
-0.00531768798828125,
-0.012786865234375,
-0.005687713623046875,
0.0296173095703125,
0.022216796875,
0.0086517333984375,
-0.007724761962890625,
-0.01399993896484375,
-0.00983428955078125,
0.01006317138671875,
-0.0034236907958984375,
-0.01087188720703125,
-0.00047326087951660156,
0.0306854248046875,
-0.0250396728515625,
0.01287841796875,
-0.002899169921875,
0.0000743865966796875,
-0.004024505615234375,
-0.013458251953125,
-0.0174407958984375,
0.01264190673828125,
-0.003887176513671875,
0.00795745849609375,
-0.0153961181640625,
0.026214599609375,
0.01239013671875,
-0.032684326171875,
0.018463134765625,
0.0257110595703125,
0.01319122314453125,
-0.0028839111328125,
-0.00690460205078125,
0.030364990234375,
-0.00800323486328125,
0.0067901611328125,
-0.01390838623046875,
-0.0017061233520507812,
-0.005229949951171875,
0.02362060546875,
0.0071868896484375,
-0.022613525390625,
-0.04217529296875,
0.006038665771484375,
0.004215240478515625,
0.024383544921875,
-0.01517486572265625,
0.03399658203125,
0.0301055908203125,
-0.001705169677734375,
-0.0167083740234375,
-0.01459503173828125,
-0.0024013519287109375,
0.00021755695343017578,
-0.01024627685546875,
-0.0028533935546875,
0.0238494873046875,
-0.006023406982421875,
-0.0190277099609375,
-0.0235137939453125,
-0.0120849609375,
-0.0210113525390625,
-0.028167724609375,
0.00481414794921875,
0.00399017333984375,
0.0046539306640625,
0.00545501708984375,
-0.0137176513671875,
0.014190673828125,
-0.009918212890625,
-0.00902557373046875,
0.006870269775390625,
-0.0087127685546875,
-0.0325927734375,
-0.0032558441162109375,
-0.0074310302734375,
0.0111541748046875,
0.0152740478515625,
-0.027801513671875,
-0.003086090087890625,
-0.024871826171875,
-0.00995635986328125,
-0.00875091552734375,
-0.00569915771484375,
0.00044846534729003906,
-0.007568359375,
0.0243072509765625,
-0.0357666015625,
0.006687164306640625,
0.0122833251953125,
-0.0177154541015625,
-0.00215911865234375,
0.019378662109375,
0.006992340087890625,
0.00823211669921875,
0.01084136962890625,
-0.01055908203125,
0.01006317138671875,
-0.004718780517578125,
-0.00029969215393066406,
-0.0008001327514648438,
0.00180816650390625,
0.0045166015625,
-0.004314422607421875,
-0.008941650390625,
-0.003856658935546875,
0.0037708282470703125,
0.00501251220703125,
0.0035495758056640625,
-0.0153350830078125,
-0.021636962890625,
0.0482177734375,
0.0107879638671875,
0.005893707275390625,
0.01593017578125,
-0.0072479248046875,
0.025054931640625,
-0.031768798828125,
-0.00891876220703125,
0.0020542144775390625,
0.02093505859375,
-0.015899658203125,
-0.002544403076171875,
0.01340484619140625,
-0.0018024444580078125,
-0.0005640983581542969,
0.01361846923828125,
0.00794219970703125,
-0.03656005859375,
0.00391387939453125,
-0.0197906494140625,
-0.0231781005859375,
-0.00555419921875,
-0.03131103515625,
-0.004375457763671875,
-0.005107879638671875,
0.006999969482421875,
0.00122833251953125,
0.004543304443359375,
-0.0204010009765625,
0.04986572265625,
0.0222320556640625,
-0.00476837158203125,
0.0010986328125,
-0.0037097930908203125,
0.0021514892578125,
0.02093505859375,
-0.017822265625,
0.00792694091796875,
0.008697509765625,
0.0140533447265625,
0.00949859619140625,
0.017059326171875,
0.0240936279296875,
-0.0191192626953125,
-0.015777587890625,
0.013702392578125,
-0.00782012939453125,
-0.021392822265625,
-0.01222991943359375,
-0.00829315185546875,
-0.0206756591796875,
0.006542205810546875,
0.007358551025390625,
-0.011138916015625,
0.005767822265625,
0.0035915374755859375,
-0.003345489501953125,
0.021820068359375,
-0.0083770751953125,
0.038116455078125,
-0.033447265625,
0.01505279541015625,
0.015380859375,
0.02685546875,
0.01158905029296875,
0.0033054351806640625,
-0.012542724609375,
-0.01025390625,
0.0014181137084960938,
0.0106048583984375,
0.004238128662109375,
-0.01239776611328125,
0.013153076171875,
-0.0199127197265625,
-0.00879669189453125,
0.0037860870361328125,
0.00019276142120361328,
0.04132080078125,
-0.06304931640625,
-0.040496826171875,
0.02105712890625,
-0.0245819091796875,
0.0088348388671875,
-0.034912109375,
-0.0450439453125,
0.020233154296875,
0.00852203369140625,
0.006664276123046875,
-0.004833221435546875,
-0.0276641845703125,
-0.01226043701171875,
0.01041412353515625,
0.0113067626953125,
-0.026702880859375,
0.0377197265625,
0.01666259765625,
-0.01369476318359375,
-0.01268768310546875,
0.0014085769653320312,
-0.0311737060546875,
0.004108428955078125,
-0.020263671875,
0.0284423828125,
-0.015869140625,
0.01340484619140625,
-0.01406097412109375,
-0.016357421875,
0.028106689453125,
-0.004604339599609375,
0.02447509765625,
0.00702667236328125,
0.008392333984375,
0.0299224853515625,
-0.012237548828125,
-0.007465362548828125,
-0.0182037353515625,
-0.0235595703125,
-0.00775909423828125,
0.0231475830078125,
-0.018341064453125,
0.01922607421875,
0.0091705322265625,
-0.01678466796875,
0.00431060791015625,
0.010711669921875,
-0.0248870849609375,
0.03326416015625,
-0.0022430419921875,
-0.0251312255859375,
-0.0217437744140625,
0.005306243896484375,
0.000008046627044677734,
0.02459716796875,
0.039703369140625,
-0.0130462646484375,
-0.005809783935546875,
-0.010101318359375,
-0.001392364501953125,
-0.0237884521484375,
0.0182952880859375,
0.001605987548828125,
0.0079345703125,
0.01251220703125,
0.0024127960205078125,
-0.0030078887939453125,
0.0184783935546875,
0.00960540771484375,
0.00632476806640625,
-0.0230560302734375,
-0.0269927978515625,
0.00678253173828125,
0.003566741943359375,
-0.00717926025390625,
-0.000873565673828125,
0.0009107589721679688,
0.01313018798828125,
-0.01511383056640625,
0.01373291015625,
-0.007404327392578125,
0.01068115234375,
0.035430908203125,
-0.0073699951171875,
0.0242462158203125,
-0.0181884765625,
-0.007843017578125,
0.00768280029296875,
-0.0238037109375,
-0.00986480712890625,
0.0215911865234375,
0.004703521728515625,
-0.009857177734375,
0.047271728515625,
-0.0142974853515625,
-0.006465911865234375,
0.0231170654296875,
0.002689361572265625,
-0.0201873779296875,
-0.015380859375,
-0.0201873779296875,
0.0154876708984375,
0.0110015869140625,
0.007167816162109375,
0.0233154296875,
0.0167388916015625,
0.00022614002227783203,
-0.00148773193359375,
-0.014251708984375,
-0.0005779266357421875,
-0.037261962890625,
0.0186614990234375,
-0.0218658447265625,
0.0254058837890625,
-0.01160430908203125,
-0.0243377685546875,
0.01387786865234375,
-0.03546142578125,
0.0009326934814453125,
-0.0223236083984375,
-0.01486968994140625,
-0.005779266357421875,
-0.0093231201171875,
-0.0177154541015625,
-0.0015077590942382812,
0.00980377197265625,
-0.002227783203125,
-0.01336669921875,
-0.039215087890625,
-0.0382080078125,
-0.01727294921875,
-0.01849365234375,
0.01456451416015625,
0.0179290771484375,
0.0104522705078125,
-0.004398345947265625,
0.037384033203125,
-0.0232086181640625,
-0.01070404052734375,
0.006893157958984375,
-0.0088348388671875,
-0.018890380859375,
0.025848388671875,
0.0185089111328125,
-0.00673675537109375,
0.004673004150390625,
-0.0172576904296875,
0.0219268798828125,
0.058563232421875,
-0.01329803466796875,
-0.014190673828125,
-0.052337646484375,
-0.03497314453125,
0.018035888671875,
-0.00684356689453125,
-0.000324249267578125,
0.005847930908203125,
0.0084075927734375,
-0.0253143310546875,
-0.0010118484497070312,
0.0124359130859375,
-0.00634002685546875,
-0.034454345703125,
0.024566650390625,
-0.0276641845703125,
0.01122283935546875,
0.0052947998046875,
-0.0002880096435546875,
0.00862884521484375,
-0.00791168212890625,
-0.01104736328125,
0.01556396484375,
0.01995849609375,
0.00467681884765625,
-0.01335906982421875,
0.0264434814453125,
0.05419921875,
-0.00611114501953125,
0.03961181640625,
0.00856781005859375,
0.02069091796875,
0.0162811279296875,
0.03570556640625,
-0.0288238525390625,
-0.01438140869140625,
0.0135650634765625,
-0.0091705322265625,
0.02252197265625,
0.01617431640625,
-0.02447509765625,
0.01154327392578125,
-0.023681640625,
0.00894927978515625,
-0.0023403167724609375,
-0.0024890899658203125,
0.0284576416015625,
0.008026123046875,
-0.0146026611328125,
0.0011444091796875,
-0.00675201416015625,
-0.001155853271484375,
-0.0295257568359375,
-0.005523681640625,
-0.0308837890625,
0.0012760162353515625,
0.0230865478515625,
0.01366424560546875,
0.022003173828125,
0.0230865478515625,
-0.02728271484375,
0.0005397796630859375,
-0.0276336669921875,
0.00713348388671875,
-0.003971099853515625,
0.0207672119140625,
0.0253143310546875,
0.037994384765625,
0.01183319091796875,
0.003231048583984375,
0.03717041015625,
0.0088653564453125,
-0.0101776123046875,
-0.005886077880859375,
0.0268096923828125,
0.006793975830078125,
-0.0160064697265625,
-0.047607421875,
-0.01171875,
0.00030994415283203125,
-0.032806396484375,
-0.01219940185546875,
0.03936767578125,
-0.01123809814453125,
-0.0028629302978515625,
0.0059814453125,
0.0340576171875,
-0.039703369140625,
0.0218658447265625,
0.04937744140625,
0.0032405853271484375,
-0.035247802734375,
0.017303466796875,
0.001918792724609375,
-0.0181427001953125,
0.0088958740234375,
-0.01383209228515625,
-0.0153045654296875,
-0.00408172607421875,
-0.0021915435791015625,
-0.0061187744140625,
-0.0206451416015625,
-0.0027828216552734375,
-0.024566650390625,
0.004062652587890625,
0.021148681640625,
0.024078369140625,
0.01242828369140625,
0.0028076171875,
0.0085906982421875,
0.0015172958374023438,
0.04473876953125,
-0.00501251220703125,
0.016876220703125,
-0.013671875,
0.0189666748046875,
0.0209808349609375,
0.0207061767578125,
-0.02117919921875,
0.015655517578125,
-0.0246124267578125,
-0.00565338134765625,
-0.0175628662109375,
0.006031036376953125,
-0.0265960693359375,
0.004932403564453125,
0.004772186279296875,
0.0028018951416015625,
0.004085540771484375,
0.030029296875,
0.0011510848999023438,
0.035308837890625,
-0.0341796875,
-0.0255126953125,
-0.0113983154296875,
-0.0352783203125,
-0.005268096923828125,
-0.027374267578125,
0.00934600830078125,
0.00742340087890625,
-0.0175018310546875,
0.0157928466796875,
-0.0186004638671875,
-0.00823211669921875,
0.003231048583984375,
0.0140838623046875,
-0.00972747802734375,
0.005558013916015625,
0.0311126708984375,
0.0247344970703125,
0.01078033447265625,
-0.06353759765625,
0.0029087066650390625,
0.0035495758056640625,
-0.0163421630859375,
0.00920867919921875,
0.0186309814453125,
-0.0029468536376953125,
0.0029850006103515625,
-0.00391387939453125,
0.0169525146484375,
0.00771331787109375,
0.041412353515625,
-0.01340484619140625,
-0.03228759765625,
0.00661468505859375,
0.0088958740234375,
-0.007068634033203125,
0.013946533203125,
-0.027496337890625,
0.0004703998565673828,
0.0028095245361328125,
-0.0217742919921875,
0.0122833251953125,
-0.028045654296875,
-0.04107666015625,
-0.018524169921875,
0.0139312744140625,
0.0146484375,
-0.0168914794921875,
0.008514404296875,
-0.01910400390625,
0.0004818439483642578,
0.0120697021484375,
-0.01123809814453125,
0.035491943359375,
-0.03924560546875,
0.016815185546875,
0.00302886962890625,
0.0116424560546875,
0.051727294921875,
0.01024627685546875,
-0.0186767578125,
0.0526123046875,
0.034027099609375,
-0.0208740234375,
0.0287017822265625,
-0.033905029296875,
0.023895263671875,
0.0175018310546875,
-0.01210784912109375,
0.005001068115234375,
-0.0145111083984375,
-0.006320953369140625,
-0.00795745849609375,
-0.00394439697265625,
-0.01534271240234375,
-0.01470947265625,
0.01100921630859375,
-0.020965576171875,
0.0009927749633789062,
-0.01079559326171875,
-0.00955963134765625,
-0.00994110107421875,
0.01763916015625,
0.0305633544921875,
-0.0364990234375,
-0.0008463859558105469,
-0.045196533203125,
-0.0272064208984375,
0.01076507568359375,
-0.00414276123046875,
-0.017364501953125,
-0.0105438232421875,
-0.0005750656127929688,
-0.0013685226440429688,
-0.01641845703125,
0.005397796630859375,
-0.022796630859375,
0.00418853759765625,
-0.0162200927734375,
-0.01332855224609375,
0.035797119140625,
0.0236663818359375,
-0.0223236083984375,
-0.0116119384765625,
-0.0173187255859375,
0.0033397674560546875,
0.0325927734375,
-0.020538330078125,
0.0081634521484375,
0.00733184814453125,
-0.01161956787109375,
-0.0031909942626953125,
-0.02166748046875,
-0.05267333984375,
-0.00962066650390625,
-0.0152435302734375,
0.0296783447265625,
-0.006526947021484375,
0.00048661231994628906,
0.00684356689453125,
0.0009708404541015625,
-0.00040602684020996094,
-0.0545654296875,
-0.021636962890625,
0.00457763671875,
0.006481170654296875,
0.01202392578125,
-0.0241546630859375,
0.0023956298828125,
-0.0281982421875,
-0.048431396484375,
0.006153106689453125,
-0.01082611083984375,
-0.01334381103515625,
-0.0003802776336669922,
0.0096588134765625,
-0.0258331298828125,
0.0172119140625,
-0.00753021240234375,
-0.010498046875,
-0.00937652587890625,
-0.0328369140625,
-0.01477813720703125,
0.001094818115234375,
-0.0215606689453125,
0.004451751708984375,
0.004909515380859375,
-0.005115509033203125,
0.0187225341796875,
0.0128173828125,
0.002452850341796875,
-0.00775909423828125,
-0.039276123046875,
-0.0003752708435058594,
0.0089874267578125,
0.007843017578125,
0.0015506744384765625,
0.0204315185546875,
-0.007480621337890625,
0.03155517578125,
-0.039337158203125,
0.0072021484375,
-0.0265655517578125,
-0.008209228515625,
0.018157958984375,
-0.0102386474609375,
0.01003265380859375,
0.0189056396484375,
0.0106201171875,
0.01024627685546875,
0.0018205642700195312,
-0.00839996337890625,
-0.01280975341796875,
-0.0212860107421875,
-0.00760650634765625,
0.005275726318359375,
-0.00490570068359375,
-0.0198974609375,
0.00867462158203125,
0.00627899169921875,
0.035369873046875,
-0.0188751220703125,
0.0297393798828125,
0.01375579833984375,
-0.0255279541015625,
0.048309326171875,
-0.015960693359375,
-0.032928466796875,
0.0299224853515625,
0.0292205810546875,
-0.006259918212890625,
-0.0203094482421875,
-0.02032470703125,
-0.00945281982421875,
0.00592041015625,
-0.0160980224609375,
-0.0207366943359375,
0.0181427001953125,
-0.01910400390625,
-0.01465606689453125,
-0.01190185546875,
0.0004830360412597656,
0.038116455078125,
-0.0004000663757324219,
0.01111602783203125,
0.0217132568359375,
0.0121307373046875,
-0.0280303955078125,
-0.00986480712890625,
-0.0202178955078125,
-0.037078857421875,
-0.00785064697265625,
-0.0172882080078125,
0.0038280487060546875,
-0.0565185546875,
-0.007511138916015625,
-0.00823974609375,
-0.0007476806640625,
0.045196533203125,
0.00833892822265625,
0.036041259765625,
-0.0007982254028320312,
-0.01041412353515625,
0.00033783912658691406,
-0.00972747802734375,
0.0311279296875,
0.031951904296875,
0.053680419921875,
-0.0303192138671875,
0.0247955322265625,
-0.015960693359375,
-0.01329803466796875,
0.00807952880859375,
0.0401611328125,
0.015625,
-0.00986480712890625,
0.0019893646240234375,
-0.0167694091796875,
-0.00189971923828125,
0.0172271728515625,
-0.0198974609375,
-0.01123809814453125,
-0.01160430908203125,
-0.01396942138671875,
0.01214599609375,
0.01332855224609375,
0.01218414306640625,
-0.016265869140625,
-0.00439453125,
0.006366729736328125,
0.01404571533203125,
0.03289794921875,
0.0163726806640625,
0.0172882080078125,
0.050384521484375,
0.032928466796875,
-0.0103912353515625,
-0.0146026611328125,
-0.01336669921875,
0.0164794921875,
-0.029754638671875,
0.0036869049072265625,
0.002964019775390625,
-0.00020360946655273438,
-0.01215362548828125,
0.0167236328125,
-0.0161590576171875,
-0.0277862548828125,
-0.015045166015625,
-0.0191650390625,
0.036590576171875,
0.000827789306640625,
-0.00405120849609375,
0.00879669189453125,
0.0220947265625,
-0.015716552734375,
0.017333984375,
0.0261993408203125,
0.007495880126953125,
-0.02069091796875,
-0.0288238525390625,
-0.0261688232421875,
0.0052642822265625,
-0.01198577880859375,
0.006855010986328125,
-0.004116058349609375,
0.005413055419921875,
0.0017442703247070312,
-0.01142120361328125,
-0.0010175704956054688,
-0.0110626220703125,
-0.0134429931640625,
-0.0237884521484375,
0.013885498046875,
-0.009735107421875,
-0.01499176025390625,
0.0028820037841796875,
0.0008082389831542969,
-0.015655517578125,
0.007274627685546875,
0.005062103271484375,
-0.0264892578125,
0.02630615234375,
0.006946563720703125,
-0.0399169921875,
-0.00341796875,
-0.01296234130859375,
0.020751953125,
-0.01202392578125,
-0.0435791015625,
-0.02191162109375,
-0.005603790283203125,
-0.002349853515625,
-0.01198577880859375,
-0.00339508056640625,
-0.0121917724609375,
-0.01306915283203125,
0.00821685791015625,
0.012908935546875,
0.0280914306640625,
0.016265869140625,
-0.0099945068359375,
-0.005924224853515625,
0.009552001953125,
-0.006778717041015625,
-0.01406097412109375,
-0.01294708251953125,
-0.0244293212890625,
0.015777587890625,
0.02020263671875,
-0.01323699951171875,
-0.017913818359375,
-0.0189208984375,
-0.0120849609375,
-0.013671875,
-0.038177490234375,
0.01000213623046875,
0.0212860107421875,
0.01293182373046875,
0.01654052734375,
-0.0157012939453125,
0.0086822509765625,
0.032928466796875,
0.01519012451171875,
0.00902557373046875,
0.022186279296875,
0.0162811279296875,
0.01513671875,
0.016693115234375,
-0.01290130615234375,
0.0083465576171875,
0.011749267578125,
0.01552581787109375,
0.0222930908203125,
0.0293121337890625,
0.0113983154296875,
-0.036651611328125,
-0.0125885009765625,
-0.0111846923828125,
-0.015228271484375,
0.003795623779296875,
0.01010894775390625,
0.016082763671875,
0.005725860595703125,
0.048187255859375,
0.016845703125,
-0.0055389404296875,
0.03173828125,
-0.00012814998626708984,
0.01617431640625,
-0.0150299072265625,
0.0173797607421875,
-0.0030059814453125,
-0.042083740234375,
0.008392333984375,
0.002559661865234375,
-0.0399169921875,
0.00984954833984375,
0.0097808837890625,
0.007171630859375,
-0.0175628662109375,
-0.034698486328125,
-0.008514404296875,
0.0122833251953125,
-0.003269195556640625,
0.00916290283203125,
-0.017425537109375,
-0.0054931640625,
0.018646240234375,
0.01654052734375,
-0.009490966796875,
0.005718231201171875,
-0.00469207763671875,
0.00807952880859375,
-0.032958984375,
-0.009979248046875,
0.0294189453125,
-0.01320648193359375,
-0.052520751953125,
-0.054473876953125,
0.01267242431640625,
-0.014923095703125,
-0.0196990966796875,
-0.016998291015625,
0.0020847320556640625,
0.0015497207641601562,
-0.0181427001953125,
-0.00366973876953125,
-0.022125244140625,
-0.017913818359375,
0.004268646240234375,
-0.005641937255859375,
-0.0107574462890625,
-0.0301361083984375,
0.03509521484375,
0.0190887451171875,
-0.0157318115234375,
0.0157012939453125,
-0.0027637481689453125,
-0.033935546875,
-0.0171051025390625,
0.0203399658203125,
-0.01309967041015625,
0.0101470947265625,
-0.004669189453125,
0.0113525390625,
0.03515625,
0.0160064697265625,
0.012237548828125,
-0.0000026226043701171875,
0.02374267578125,
-0.015411376953125,
-0.01238250732421875,
-0.024566650390625,
0.00655364990234375,
0.036102294921875,
0.020263671875,
-0.04156494140625,
-0.01149749755859375,
-0.005245208740234375,
0.00919342041015625,
-0.01406097412109375,
0.003475189208984375,
0.030609130859375,
-0.0075836181640625,
0.00824737548828125,
-0.043304443359375,
-0.0086669921875,
-0.002017974853515625,
-0.0270233154296875,
0.006015777587890625,
-0.015716552734375,
-0.020416259765625,
-0.003643035888671875,
-0.001354217529296875,
0.01316070556640625,
0.00911712646484375,
0.01216888427734375,
-0.00542449951171875,
-0.0013246536254882812,
0.0116424560546875,
-0.01605224609375,
-0.0020046234130859375,
-0.0131378173828125,
0.0056610107421875,
0.01323699951171875,
0.0298309326171875,
0.0010471343994140625,
-0.0012884140014648438,
0.0007562637329101562,
-0.003643035888671875,
-0.0006718635559082031,
-0.01065826416015625,
0.0219573974609375,
0.035247802734375,
0.003574371337890625,
-0.002498626708984375,
0.031036376953125,
0.04095458984375,
0.00007778406143188477,
-0.0109100341796875,
-0.023712158203125,
-0.043426513671875,
0.03131103515625,
-0.025177001953125,
-0.01904296875,
0.0035953521728515625,
0.033905029296875,
-0.01114654541015625,
0.00902557373046875,
-0.0140533447265625,
-0.034423828125,
-0.016082763671875,
-0.025543212890625,
0.0295867919921875,
-0.006256103515625,
0.0066680908203125,
0.014007568359375,
0.01346588134765625,
0.06549072265625,
0.01406097412109375,
-0.0009436607360839844,
0.000244140625,
-0.00689697265625,
-0.0400390625,
0.01224517822265625,
-0.060211181640625,
0.0050201416015625,
-0.0205078125,
-0.00673675537109375,
0.0026073455810546875,
0.0169525146484375,
0.0157470703125,
-0.0011873245239257812,
-0.0032100677490234375,
0.026123046875,
-0.017913818359375,
-0.0070953369140625,
-0.0070037841796875,
-0.04144287109375,
-0.04595947265625,
-0.0258026123046875,
0.01078033447265625,
-0.004734039306640625,
0.0136260986328125,
-0.0045013427734375,
-0.0157318115234375,
-0.0012798309326171875,
-0.0001747608184814453,
0.01788330078125,
-0.022918701171875,
-0.00698089599609375,
-0.033111572265625,
-0.00933074951171875,
-0.00928497314453125,
-0.022491455078125,
-0.00489044189453125,
-0.01690673828125,
0.0394287109375,
-0.00069427490234375,
-0.007152557373046875,
-0.0015802383422851562,
0.0214996337890625,
0.029998779296875,
-0.02679443359375,
0.003520965576171875,
-0.0033721923828125,
-0.0033321380615234375,
0.0271759033203125,
0.0016260147094726562,
-0.0192718505859375,
0.0265045166015625,
-0.002685546875,
-0.034515380859375,
-0.01971435546875,
-0.0072021484375,
-0.019134521484375,
0.0255279541015625,
0.0081634521484375,
-0.02020263671875,
-0.00247955322265625,
0.0213775634765625,
-0.0223541259765625,
-0.015380859375,
-0.04022216796875,
-0.0201263427734375,
0.00281524658203125,
0.01125335693359375,
-0.005126953125,
0.0372314453125,
0.0126800537109375,
0.017852783203125,
-0.030059814453125,
-0.0177459716796875,
-0.042510986328125,
-0.0085296630859375,
0.0010929107666015625,
-0.0311737060546875,
-0.034423828125,
-0.04241943359375,
0.0008883476257324219,
0.006725311279296875,
-0.026214599609375,
0.0264739990234375,
0.014190673828125,
0.0010366439819335938,
-0.0095977783203125,
0.014068603515625,
0.0103302001953125,
-0.036407470703125,
0.0279083251953125,
-0.01123046875,
-0.0197906494140625,
-0.0138092041015625,
0.004680633544921875,
-0.00102996826171875,
-0.00414276123046875,
0.01153564453125,
-0.01012420654296875,
-0.024444580078125,
-0.01120758056640625,
0.00021004676818847656,
-0.0050201416015625,
0.0311126708984375,
0.0311431884765625,
0.01849365234375,
0.0239410400390625,
0.01116180419921875,
-0.005268096923828125,
0.0276947021484375,
-0.007228851318359375,
-0.006805419921875,
-0.00376129150390625,
0.00699615478515625,
-0.002117156982421875,
0.01093292236328125,
0.0016908645629882812,
-0.0118408203125,
0.0008745193481445312,
-0.033721923828125,
0.01062774658203125,
-0.03961181640625,
-0.036407470703125,
-0.00974273681640625,
-0.0233917236328125,
0.006008148193359375,
0.0277099609375,
0.0318603515625,
-0.03253173828125,
-0.0048065185546875,
-0.010009765625,
0.0149078369140625,
0.01435089111328125,
0.014190673828125,
0.010772705078125,
0.004497528076171875,
-0.0248565673828125,
0.024261474609375,
-0.01371002197265625,
0.017120361328125,
-0.007793426513671875,
0.01006317138671875,
-0.00592803955078125,
0.01453399658203125,
0.0207061767578125,
0.0155181884765625,
-0.005016326904296875,
0.0018138885498046875,
0.0298309326171875,
0.0187835693359375,
-0.0152435302734375,
-0.0230255126953125,
-0.032928466796875,
-0.005474090576171875,
0.005786895751953125,
0.016815185546875,
0.00484466552734375,
-0.0164642333984375,
0.037994384765625,
0.019439697265625,
-0.017364501953125,
-0.0274505615234375,
-0.02001953125,
0.00986480712890625,
0.034637451171875,
0.0112457275390625,
-0.0168914794921875,
0.020477294921875,
0.0090179443359375,
0.00382232666015625,
0.0018148422241210938,
-0.0141754150390625,
0.0168609619140625,
0.008056640625,
0.0306396484375,
-0.00904083251953125,
0.0143585205078125,
0.0027370452880859375,
0.0293426513671875,
-0.005802154541015625,
-0.01168060302734375,
-0.020355224609375,
0.0006723403930664062,
0.0027942657470703125,
-0.0018835067749023438,
-0.015960693359375,
0.0219268798828125,
0.005641937255859375,
-0.0237579345703125,
0.0190887451171875,
0.036651611328125,
0.0028972625732421875,
0.0162353515625,
0.00010210275650024414,
-0.0360107421875,
0.0052337646484375,
-0.004512786865234375,
-0.0069427490234375,
-0.041412353515625,
-0.0269927978515625,
-0.031097412109375,
0.0014486312866210938,
-0.0215606689453125,
-0.01102447509765625,
0.01447296142578125,
-0.04473876953125,
0.00276947021484375,
0.00833892822265625,
-0.04296875,
0.0018520355224609375,
0.0221099853515625,
0.01485443115234375,
0.0277862548828125,
-0.0274200439453125,
0.0105743408203125,
-0.01270294189453125,
0.0006546974182128906,
0.004547119140625,
0.00199127197265625,
0.004150390625,
0.022430419921875,
0.0023822784423828125,
-0.0517578125,
0.042205810546875,
-0.00286102294921875,
0.0008111000061035156,
0.02215576171875,
0.021270751953125,
-0.006786346435546875,
0.01561737060546875,
-0.044769287109375,
0.0124359130859375,
-0.01329803466796875,
0.00360107421875,
-0.0123291015625,
-0.01537322998046875,
0.042572021484375,
-0.0215301513671875,
0.0191650390625,
-0.001094818115234375,
0.0283050537109375,
-0.0080108642578125,
0.005016326904296875,
-0.036529541015625,
-0.0129852294921875,
-0.020843505859375,
-0.0208892822265625,
0.02783203125,
-0.0021343231201171875,
0.014984130859375,
0.0377197265625,
-0.0020732879638671875,
-0.020904541015625,
-0.004150390625,
0.0016012191772460938,
0.0198211669921875,
0.01044464111328125,
0.0032749176025390625,
-0.019317626953125,
-0.012054443359375,
-0.0033588409423828125,
0.0192718505859375,
-0.018035888671875,
0.00937652587890625,
0.0004343986511230469,
-0.0004887580871582031,
0.0118560791015625,
0.0209503173828125,
-0.00647735595703125,
0.027862548828125,
-0.01383209228515625,
-0.01971435546875,
0.024078369140625,
-0.00792694091796875,
-0.005626678466796875,
0.01306915283203125,
0.00966644287109375,
-0.024139404296875,
-0.0014057159423828125,
0.027618408203125,
0.0087127685546875,
-0.01473236083984375,
0.0142364501953125,
-0.0010595321655273438,
0.0030364990234375,
0.011016845703125,
-0.01513671875,
0.00019872188568115234,
-0.0030994415283203125,
-0.0247344970703125,
-0.019439697265625,
0.00614166259765625,
-0.005100250244140625,
-0.03851318359375,
-0.007904052734375,
-0.029998779296875,
0.035430908203125,
0.029998779296875,
-0.026123046875,
-0.0031032562255859375,
0.004650115966796875,
-0.0207977294921875,
0.016815185546875,
-0.0177154541015625,
0.0157470703125,
0.0018949508666992188,
0.007343292236328125,
-0.00366973876953125,
-0.016021728515625,
0.00604248046875,
0.0254364013671875,
0.0172576904296875,
0.045379638671875,
0.0263671875,
0.0229644775390625,
0.01306915283203125,
0.0020923614501953125,
-0.01168060302734375,
0.01227569580078125,
-0.00830841064453125,
-0.0246124267578125,
-0.020172119140625,
0.0164794921875,
0.0313720703125,
-0.019805908203125,
0.006488800048828125,
0.0196685791015625,
-0.03314208984375,
-0.0130615234375,
0.0260009765625,
0.02081298828125,
0.01141357421875,
0.0182342529296875,
-0.0012197494506835938,
0.0200653076171875,
-0.01360321044921875,
-0.024688720703125,
0.020904541015625,
-0.0033111572265625,
0.021514892578125,
-0.0045166015625,
0.007144927978515625,
0.00641632080078125,
0.052337646484375,
0.006313323974609375,
-0.0284423828125,
-0.00007277727127075195,
0.0149383544921875,
-0.0191650390625,
-0.0249176025390625,
0.01160430908203125,
0.0013408660888671875,
0.036224365234375,
-0.0156097412109375,
0.004077911376953125,
-0.034637451171875,
0.0173492431640625,
0.01274871826171875,
0.0172271728515625,
0.0102996826171875,
-0.00922393798828125,
-0.018402099609375,
-0.002468109130859375,
0.03656005859375,
0.0147705078125,
-0.030059814453125,
0.00511932373046875,
-0.031280517578125,
0.0230560302734375,
0.0279693603515625,
0.00907135009765625,
0.01399993896484375,
-0.003635406494140625,
-0.01226806640625,
-0.021575927734375,
-0.01641845703125,
-0.0059814453125,
0.01415252685546875,
0.0236663818359375,
0.019775390625,
0.03265380859375,
-0.0411376953125,
-0.00405120849609375,
-0.0039825439453125,
0.0170135498046875,
0.00522613525390625,
-0.0161285400390625,
0.0121612548828125,
-0.0133056640625,
0.005268096923828125,
-0.024444580078125,
0.03753662109375,
-0.0111846923828125,
-0.00653076171875,
-0.00774383544921875,
0.01024627685546875,
0.004970550537109375,
0.0016336441040039062,
-0.00934600830078125,
0.016082763671875,
0.03570556640625,
-0.004970550537109375,
-0.00079345703125,
-0.027618408203125,
-0.00588226318359375,
0.0170135498046875,
-0.0207366943359375,
-0.017333984375,
0.033111572265625,
0.01392364501953125,
0.0125579833984375,
0.0238189697265625,
-0.02899169921875,
0.0230712890625,
0.0011491775512695312,
-0.01009368896484375,
0.006778717041015625,
0.003025054931640625,
0.003345489501953125,
0.016998291015625,
-0.005252838134765625,
-0.01537322998046875,
0.0138702392578125,
0.0204315185546875,
0.03509521484375,
0.0098876953125,
-0.0014190673828125,
0.0009202957153320312,
0.0012054443359375,
-0.00884246826171875,
0.00714874267578125,
-0.00003886222839355469,
0.0222320556640625,
0.048614501953125,
-0.017181396484375,
-0.00940704345703125,
-0.007843017578125,
0.0205078125,
-0.015228271484375,
-0.0170745849609375,
-0.00904083251953125,
-0.0241851806640625,
0.0044097900390625,
0.019622802734375,
-0.00521087646484375,
0.004791259765625,
0.0252532958984375,
0.0081939697265625,
0.01788330078125,
-0.001583099365234375,
-0.0020847320556640625,
0.00611114501953125,
0.01849365234375,
0.0133819580078125,
-0.0007457733154296875,
0.025848388671875,
0.01812744140625,
-0.01361083984375,
0.01473236083984375,
-0.0029735565185546875,
0.0247650146484375,
0.0126800537109375,
-0.040130615234375,
0.0132904052734375,
-0.0218505859375,
0.0216064453125,
0.022125244140625,
0.0136566162109375,
0.0119476318359375,
-0.010528564453125,
-0.01155853271484375,
-0.0182037353515625,
0.0055999755859375,
0.029571533203125,
0.054779052734375,
0.035186767578125,
-0.031463623046875,
0.036163330078125,
-0.006214141845703125,
0.0227508544921875,
-0.0223846435546875,
0.0140533447265625,
-0.010406494140625,
-0.01198577880859375,
-0.01093292236328125,
0.0055084228515625,
-0.00566864013671875,
-0.01055908203125,
0.0031070709228515625,
0.05633544921875,
0.00656890869140625,
0.02337646484375,
-0.0081634521484375,
0.058135986328125,
-0.005859375,
-0.032806396484375,
0.0197296142578125,
0.007366180419921875,
-0.00490570068359375,
0.033538818359375,
0.017578125,
0.01004791259765625,
-0.02923583984375,
0.00560760498046875,
-0.019989013671875,
-0.01290130615234375,
0.0142669677734375,
0.0142822265625,
-0.005222320556640625,
0.025299072265625,
-0.024322509765625,
0.00029277801513671875,
-0.0017843246459960938,
-0.015472412109375,
-0.0198974609375,
0.009613037109375,
0.0223236083984375,
-0.0218963623046875,
0.033721923828125,
-0.02374267578125,
-0.0086212158203125,
0.0194549560546875,
0.0177154541015625,
0.00754547119140625,
0.004230499267578125,
-0.0556640625,
0.0044097900390625,
0.0238037109375,
0.03399658203125,
0.0038661956787109375,
-0.035614013671875,
-0.00775909423828125,
-0.0148468017578125,
0.01227569580078125,
0.01020050048828125,
0.0120697021484375,
-0.0115814208984375,
-0.00553131103515625,
0.0145111083984375,
0.031341552734375,
0.01241302490234375,
0.019775390625,
-0.004734039306640625,
-0.018035888671875,
-0.01396942138671875,
-0.011749267578125,
-0.0008063316345214844,
-0.0117034912109375,
0.017486572265625,
0.0054779052734375,
-0.04168701171875,
0.01226043701171875,
-0.026153564453125,
-0.0102081298828125,
-0.0213623046875,
-0.037445068359375,
-0.0156707763671875,
-0.0183563232421875,
-0.020111083984375,
0.0272369384765625,
-0.006793975830078125,
-0.0040435791015625,
0.016571044921875,
-0.01396942138671875,
0.01030731201171875,
0.02880859375,
0.0386962890625,
0.030914306640625,
-0.0249481201171875,
0.0546875,
-0.006866455078125,
0.046051025390625,
0.0088348388671875,
-0.032623291015625,
-0.00513458251953125,
0.0283355712890625,
-0.0102081298828125,
-0.0069732666015625,
0.019683837890625,
-0.048583984375,
-0.004146575927734375,
0.0275115966796875,
-0.020721435546875,
0.00572967529296875,
-0.035003662109375,
-0.0299224853515625,
0.04217529296875,
-0.01678466796875,
-0.019622802734375,
0.01110076904296875,
-0.01052093505859375,
0.00856781005859375,
0.0367431640625,
-0.0183258056640625,
0.005321502685546875,
0.000058710575103759766,
-0.003131866455078125,
0.01531219482421875,
0.00965118408203125,
-0.003482818603515625,
-0.0014705657958984375,
-0.01739501953125,
0.01068115234375,
-0.02447509765625,
-0.004302978515625,
-0.0003495216369628906,
0.007617950439453125,
-0.0013990402221679688,
-0.02471923828125,
-0.00861358642578125,
-0.0222930908203125,
-0.01004791259765625,
0.036285400390625,
-0.03912353515625,
0.002475738525390625,
0.01126861572265625,
0.0027904510498046875,
0.01204681396484375,
-0.002979278564453125,
0.02886962890625,
0.0177001953125,
0.0031032562255859375,
0.01039886474609375,
0.03179931640625,
-0.0005316734313964844,
0.0091094970703125,
0.005542755126953125,
0.005985260009765625,
-0.0089874267578125,
-0.01251220703125,
-0.0189666748046875,
0.0038433074951171875,
-0.0010204315185546875,
-0.00576019287109375,
0.022552490234375,
-0.01326751708984375,
0.00168609619140625,
-0.032867431640625,
0.0494384765625,
0.01415252685546875,
-0.012725830078125,
-0.0170440673828125,
-0.035430908203125,
0.00585174560546875,
-0.0210723876953125,
0.0316162109375,
0.01244354248046875,
0.0214691162109375,
0.012969970703125,
0.031951904296875,
0.01349639892578125,
-0.0099639892578125,
-0.0178375244140625,
-0.0191650390625,
-0.029296875,
0.023040771484375,
0.0116729736328125,
0.0121307373046875,
-0.01348114013671875,
0.037811279296875,
0.0338134765625,
-0.003108978271484375,
-0.019775390625,
0.0158538818359375,
0.0026340484619140625,
-0.0025310516357421875,
0.01377105712890625,
-0.002269744873046875,
-0.0031147003173828125,
-0.0171966552734375,
-0.006458282470703125,
0.01308441162109375,
-0.0025959014892578125,
-0.0220489501953125,
-0.04547119140625,
0.01947021484375,
-0.01207733154296875,
-0.0005903244018554688,
-0.0229644775390625,
0.002399444580078125,
0.034820556640625,
0.0121612548828125,
0.0044403076171875,
-0.027099609375,
0.020263671875,
-0.040252685546875,
-0.0036792755126953125,
-0.01300048828125,
0.02239990234375,
0.0258026123046875,
-0.01204681396484375,
0.008392333984375,
-0.00978851318359375,
0.01390838623046875,
-0.035064697265625,
0.0225830078125,
0.0209503173828125,
0.005126953125,
-0.00972747802734375,
0.016510009765625,
-0.006748199462890625,
-0.0160369873046875,
-0.0157928466796875,
-0.0206146240234375,
-0.007450103759765625,
-0.020782470703125,
0.039581298828125,
0.005279541015625,
-0.0369873046875,
-0.012115478515625,
0.032073974609375,
-0.01142120361328125,
0.0192718505859375,
-0.04058837890625,
0.036865234375,
-0.01279449462890625,
-0.007007598876953125,
-0.0135345458984375,
-0.0224761962890625,
0.0589599609375,
0.022003173828125,
0.00571441650390625,
-0.0099945068359375,
0.03515625,
0.004550933837890625,
0.0204925537109375,
0.004611968994140625,
-0.00441741943359375,
0.00640106201171875,
0.0296478271484375,
0.0083160400390625,
-0.01131439208984375,
0.00421905517578125,
-0.033660888671875,
-0.00487518310546875,
-0.004913330078125,
0.007476806640625,
-0.037200927734375,
-0.0037364959716796875,
-0.0007252693176269531,
-0.001216888427734375,
0.03717041015625,
-0.0248260498046875,
0.00911712646484375,
-0.0152130126953125,
0.006816864013671875,
0.004673004150390625,
-0.0305633544921875,
0.0107879638671875,
-0.0097503662109375,
-0.0120086669921875,
0.0248870849609375,
0.01641845703125,
0.018585205078125,
0.0106964111328125,
0.0240020751953125,
-0.007488250732421875,
0.0225830078125,
0.0269775390625,
0.0024242401123046875,
-0.00372314453125,
-0.0255889892578125,
0.0236053466796875,
0.018280029296875,
0.038421630859375,
0.0134124755859375,
0.006809234619140625,
0.01053619384765625,
-0.0004355907440185547,
0.01654052734375,
-0.00815582275390625,
0.010162353515625,
0.00225830078125,
0.0198516845703125,
-0.00970458984375,
-0.00556182861328125,
-0.01319122314453125,
0.002117156982421875,
-0.0230712890625,
0.0186309814453125,
0.0138092041015625,
0.02044677734375,
-0.0240478515625,
-0.015655517578125,
0.0011968612670898438,
-0.034698486328125,
0.004405975341796875,
-0.0254669189453125,
0.0052032470703125,
-0.0098876953125,
-0.0201568603515625,
0.012725830078125,
-0.002410888671875,
0.041717529296875,
-0.023681640625,
0.0166473388671875,
-0.021697998046875,
-0.0134124755859375,
0.0014944076538085938,
0.003162384033203125,
0.0148468017578125,
0.0181427001953125,
-0.0212249755859375,
-0.001659393310546875,
0.01348114013671875,
-0.004734039306640625,
0.02935791015625,
-0.002964019775390625,
0.038909912109375,
-0.025054931640625,
0.008026123046875,
-0.0016965866088867188,
0.01470947265625,
0.00455474853515625,
0.0008654594421386719,
-0.005802154541015625,
0.01255035400390625,
-0.0027904510498046875,
0.0009379386901855469,
-0.021942138671875,
0.01763916015625,
-0.0303192138671875,
-0.00408172607421875,
-0.035858154296875,
-0.031341552734375,
-0.0145416259765625,
0.005126953125,
-0.00330352783203125,
0.015960693359375,
-0.01123046875,
-0.0198516845703125,
0.01885986328125,
0.01236724853515625,
-0.005092620849609375,
0.023956298828125,
0.03271484375,
0.023040771484375,
0.023223876953125,
-0.019012451171875,
-0.039825439453125,
-0.0299224853515625,
0.013946533203125,
-0.0625,
-0.0196990966796875,
-0.0173797607421875,
-0.01557159423828125,
0.00003522634506225586,
-0.0171051025390625,
-0.0232696533203125,
0.0037212371826171875,
0.00446319580078125,
-0.0003268718719482422,
-0.0091552734375,
0.024017333984375,
0.00844573974609375,
-0.06134033203125,
-0.00870513916015625,
0.001270294189453125,
-0.0253143310546875,
-0.0080413818359375,
0.02032470703125,
-0.018310546875,
0.033172607421875,
0.01413726806640625,
-0.00708770751953125,
0.0124969482421875,
0.0132293701171875,
-0.01529693603515625,
0.0104522705078125,
0.054046630859375,
-0.0188751220703125,
0.0014238357543945312,
0.0185089111328125,
0.01517486572265625,
-0.003314971923828125,
0.0146942138671875,
-0.01151275634765625,
-0.0244903564453125,
0.036285400390625,
-0.018798828125,
0.01470184326171875,
0.0139617919921875,
-0.004390716552734375,
-0.00014925003051757812,
0.013946533203125,
-0.01328277587890625,
0.0129547119140625,
0.01287078857421875,
0.021240234375,
0.00785064697265625,
-0.035797119140625,
0.0098114013671875,
-0.018707275390625,
-0.0164337158203125,
0.0066986083984375,
0.03302001953125,
-0.00829315185546875,
-0.0271148681640625,
-0.02386474609375,
0.00302886962890625,
-0.032440185546875,
-0.0341796875,
-0.0145263671875,
0.04144287109375,
-0.008331298828125,
-0.033905029296875,
0.0011930465698242188,
-0.0294647216796875,
0.0177001953125,
-0.0172271728515625,
0.0406494140625,
-0.01064300537109375,
-0.0006966590881347656,
0.004337310791015625,
-0.00152587890625,
-0.0261993408203125,
0.0307769775390625,
-0.02606201171875,
0.0137786865234375,
0.0223541259765625,
-0.0022430419921875,
0.01934814453125,
0.01324462890625,
0.00290679931640625,
0.004825592041015625,
0.011322021484375,
0.00531005859375,
-0.006275177001953125,
-0.0179595947265625,
-0.002094268798828125,
-0.031585693359375,
0.01230621337890625,
0.01519775390625,
-0.007755279541015625,
-0.0006265640258789062,
-0.04150390625,
0.004688262939453125,
0.006237030029296875,
0.0005807876586914062,
-0.03125,
-0.008575439453125,
0.001155853271484375,
-0.0022220611572265625,
0.0126495361328125,
-0.01113128662109375,
-0.0020198822021484375,
0.01519012451171875,
0.0030574798583984375,
-0.0177154541015625,
-0.004241943359375,
0.0014801025390625,
0.0279388427734375,
-0.0033664703369140625,
-0.009002685546875,
-0.0031795501708984375,
0.0194091796875,
-0.0280914306640625,
0.003978729248046875,
0.0166168212890625,
0.0267486572265625,
0.0196990966796875,
-0.0243377685546875,
-0.0084991455078125,
-0.000043392181396484375,
-0.006160736083984375,
-0.0222015380859375,
-0.0178680419921875,
-0.024078369140625,
0.0037288665771484375,
0.0086517333984375,
0.024383544921875,
0.01030731201171875,
0.024932861328125,
0.002941131591796875,
0.01461029052734375,
-0.0113372802734375,
0.024871826171875,
0.0117645263671875,
-0.005279541015625,
-0.0193634033203125,
-0.0220184326171875,
0.0007781982421875,
-0.03338623046875,
0.00873565673828125,
-0.0260772705078125,
0.0153656005859375,
-0.0200042724609375,
-0.042083740234375,
0.0011310577392578125,
0.004878997802734375,
0.0303192138671875,
0.036224365234375,
0.028656005859375,
-0.0570068359375,
0.0236663818359375,
0.04058837890625,
0.021392822265625,
0.01052093505859375,
-0.0023708343505859375,
0.004482269287109375,
-0.0202484130859375,
0.0278778076171875,
0.0272064208984375,
0.0132293701171875,
0.01323699951171875,
0.006252288818359375,
-0.007480621337890625,
0.0167083740234375,
-0.0240631103515625,
-0.0118865966796875,
-0.00910186767578125,
-0.0270843505859375,
0.04534912109375,
-0.021453857421875,
0.018310546875,
0.0377197265625,
0.0009937286376953125,
-0.0276336669921875,
0.0028591156005859375,
0.0141754150390625,
-0.01342010498046875,
-0.007110595703125,
0.02679443359375,
0.023681640625,
0.039215087890625,
-0.0321044921875,
-0.0219879150390625,
0.062347412109375,
-0.0238189697265625,
0.0211029052734375,
0.025665283203125,
-0.0224456787109375,
0.006366729736328125,
-0.04437255859375,
0.0058441162109375,
-0.0171051025390625,
0.042144775390625,
0.0028934478759765625,
-0.0243377685546875,
0.0007185935974121094,
-0.0037384033203125,
-0.0462646484375,
0.01509857177734375,
0.0211334228515625,
0.00582122802734375,
0.03399658203125,
0.003154754638671875,
-0.01326751708984375,
0.01163482666015625,
-0.02655029296875,
-0.0182342529296875,
0.006557464599609375,
0.0307769775390625,
0.005950927734375,
0.0173492431640625,
-0.006969451904296875,
0.0192718505859375,
-0.00580596923828125,
-0.0265350341796875,
0.0248870849609375,
0.0156707763671875,
0.026397705078125,
-0.01505279541015625,
-0.01508331298828125,
0.03961181640625,
0.0270233154296875,
0.0295562744140625,
0.0036411285400390625,
0.0042724609375,
0.040679931640625,
0.005718231201171875,
0.032318115234375,
0.011688232421875,
-0.02197265625,
-0.0160980224609375,
-0.0020046234130859375,
0.01145172119140625,
0.0207366943359375,
-0.0015287399291992188,
-0.003631591796875,
-0.0163421630859375,
-0.0200653076171875,
0.032073974609375,
-0.019927978515625,
-0.0254974365234375,
-0.01032257080078125,
0.01360321044921875,
-0.0016689300537109375,
-0.00884246826171875,
0.01403045654296875,
-0.0081787109375,
-0.0240325927734375,
0.034088134765625,
-0.00115203857421875,
0.0086212158203125,
0.004276275634765625,
-0.022216796875,
0.004001617431640625,
0.045135498046875,
-0.0247955322265625,
0.0053863525390625,
0.0015592575073242188,
0.004364013671875,
0.01529693603515625,
0.006900787353515625,
-0.0151824951171875,
-0.0030422210693359375,
0.01020050048828125,
-0.0038127899169921875,
0.00428009033203125,
0.00931549072265625,
0.00798797607421875,
-0.0180816650390625,
0.02911376953125,
-0.0160064697265625,
0.0186004638671875,
-0.004070281982421875,
0.008270263671875,
-0.029052734375,
0.0223236083984375,
0.00025534629821777344,
-0.0182342529296875,
0.030120849609375,
-0.0017900466918945312,
0.0445556640625,
0.00791168212890625,
-0.022491455078125,
0.004711151123046875,
-0.01122283935546875,
-0.00980377197265625,
-0.0007119178771972656,
-0.00574493408203125,
-0.033538818359375,
0.0172576904296875,
-0.00952911376953125,
0.0004456043243408203,
0.0244903564453125,
0.032073974609375,
-0.0202484130859375,
0.029083251953125,
-0.044921875,
-0.015350341796875,
-0.01209259033203125,
-0.0072174072265625,
-0.020050048828125,
-0.0298004150390625,
0.0088348388671875,
0.0003516674041748047,
0.01392364501953125,
-0.0116729736328125,
0.0189666748046875,
0.0309600830078125,
0.032989501953125,
0.0149383544921875,
-0.00876617431640625,
0.02020263671875,
0.0199737548828125,
0.02081298828125,
-0.0166778564453125,
-0.0296173095703125,
0.005130767822265625,
0.01502227783203125,
-0.0019483566284179688,
0.0105743408203125,
0.0280914306640625,
0.01219940185546875,
0.01556396484375,
0.025146484375,
0.00975799560546875,
0.0312347412109375,
0.004673004150390625,
0.040069580078125,
-0.0008950233459472656,
0.01372528076171875,
0.0304412841796875,
0.027740478515625,
0.00275421142578125,
0.0011272430419921875,
0.02557373046875,
-0.007801055908203125,
-0.01375579833984375,
0.00565338134765625,
0.00244140625,
0.0004401206970214844,
-0.025543212890625,
0.0191650390625,
0.0017871856689453125,
-0.046966552734375,
0.038818359375,
0.0054931640625,
-0.02728271484375,
0.0203094482421875,
-0.043914794921875,
0.01428985595703125,
0.015869140625,
-0.01103973388671875,
-0.0004715919494628906,
-0.0117950439453125,
0.0087890625,
0.01392364501953125,
-0.019775390625,
0.0014400482177734375,
-0.01001739501953125,
-0.00727081298828125,
-0.016693115234375,
0.0040740966796875,
0.0167999267578125,
-0.03656005859375,
-0.0067596435546875,
0.01471710205078125,
-0.0122222900390625,
0.005542755126953125,
0.011871337890625,
0.0019321441650390625,
-0.0213470458984375,
0.02838134765625,
-0.021759033203125,
-0.02008056640625,
0.0223236083984375,
0.0162353515625,
-0.0008058547973632812,
0.02734375,
-0.02239990234375,
0.023651123046875,
0.0160980224609375,
-0.0099334716796875,
-0.028076171875,
0.01079559326171875,
-0.026763916015625,
0.0136566162109375,
-0.033233642578125,
-0.021331787109375,
-0.032257080078125,
0.001354217529296875,
-0.0100555419921875,
-0.007602691650390625,
-0.0167083740234375,
0.0269317626953125,
0.00676727294921875,
0.004688262939453125,
-0.0038127899169921875,
-0.000020682811737060547,
0.005466461181640625,
-0.0166015625,
-0.0014896392822265625,
0.026031494140625,
0.008056640625,
0.0253143310546875,
-0.045989990234375,
0.0006761550903320312,
0.0228729248046875,
0.00848388671875,
0.01540374755859375,
-0.0018367767333984375,
-0.009490966796875,
0.039794921875,
0.03936767578125,
0.0238189697265625,
-0.015472412109375,
0.0001329183578491211,
0.017059326171875,
0.006130218505859375,
-0.0006933212280273438,
-0.0489501953125,
0.00824737548828125,
0.01294708251953125,
-0.004810333251953125,
0.0171661376953125,
0.01837158203125,
0.01038360595703125,
-0.011474609375,
-0.0083770751953125,
-0.0002796649932861328,
-0.002208709716796875,
-0.01708984375,
0.01421356201171875,
0.03814697265625,
-0.00859832763671875,
0.0188446044921875,
-0.004512786865234375,
-0.019500732421875,
0.01824951171875,
-0.01145172119140625,
0.0209197998046875,
-0.0025882720947265625,
-0.013214111328125,
0.0360107421875,
-0.0145416259765625,
-0.040557861328125,
-0.016845703125,
-0.00579833984375,
-0.0118560791015625,
0.004215240478515625,
-0.00392913818359375,
-0.0286712646484375,
-0.01485443115234375,
-0.0009918212890625,
-0.038330078125,
-0.00911712646484375,
0.0191497802734375,
0.01020050048828125,
-0.0093536376953125,
-0.012451171875,
0.02899169921875,
-0.01261138916015625,
0.003665924072265625,
0.0024585723876953125,
-0.01230621337890625,
0.0013246536254882812,
-0.00799560546875,
-0.01102447509765625,
0.004245758056640625,
0.0173797607421875,
0.0159759521484375,
-0.0205535888671875,
0.007781982421875,
0.022857666015625,
0.00368499755859375,
0.0248565673828125,
0.0058441162109375,
0.0168304443359375,
0.035675048828125,
-0.0181732177734375,
0.022430419921875,
-0.003948211669921875,
-0.0033702850341796875,
-0.037200927734375,
-0.0036144256591796875,
-0.00215911865234375,
0.01629638671875,
0.0043182373046875,
-0.00345611572265625,
-0.002445220947265625,
-0.007167816162109375,
0.027191162109375,
0.010772705078125,
0.00908660888671875,
-0.0141754150390625,
-0.0136260986328125,
0.009063720703125,
-0.0089111328125,
-0.0226898193359375,
-0.020599365234375,
0.0130615234375,
-0.00428009033203125,
0.00009083747863769531,
0.0181121826171875,
-0.00628662109375,
0.00962066650390625,
-0.049285888671875,
-0.0306396484375,
-0.032012939453125,
0.021026611328125,
-0.0294342041015625,
-0.01326751708984375,
0.00868988037109375,
0.0041656494140625,
0.01099395751953125,
-0.002227783203125,
-0.01059722900390625,
-0.0190887451171875,
-0.0172271728515625,
-0.007785797119140625,
-0.005672454833984375,
-0.0013742446899414062,
-0.0050201416015625,
-0.031097412109375,
-0.052642822265625,
0.01947021484375,
0.00917816162109375,
-0.0245819091796875,
0.004058837890625,
-0.003185272216796875,
-0.001316070556640625,
-0.0016155242919921875,
0.005687713623046875,
-0.01052093505859375,
-0.03485107421875,
0.005756378173828125,
-0.0265350341796875,
0.0084381103515625,
-0.0278472900390625,
0.0165252685546875,
-0.00392913818359375,
-0.0114593505859375,
-0.01015472412109375,
-0.0177001953125,
0.0047760009765625,
0.002811431884765625,
-0.0021762847900390625,
-0.0269775390625,
0.01751708984375,
0.0288238525390625,
-0.0357666015625,
-0.01366424560546875,
0.0114593505859375,
-0.0278167724609375,
0.006496429443359375,
0.00847625732421875,
0.01100921630859375,
0.0143280029296875,
-0.034454345703125,
0.01410675048828125,
-0.034149169921875,
0.0247955322265625,
-0.020050048828125,
-0.0179443359375,
0.006984710693359375,
-0.0101318359375,
-0.0330810546875,
0.01392364501953125,
-0.0005631446838378906,
0.03631591796875,
0.0027313232421875,
-0.025299072265625,
0.005718231201171875,
0.003795623779296875,
0.01015472412109375,
-0.0025997161865234375,
-0.0276947021484375,
-0.01512908935546875,
0.002780914306640625,
-0.0114593505859375,
-0.01337432861328125,
-0.0159454345703125,
-0.007755279541015625,
0.0233001708984375,
0.03778076171875,
0.023834228515625,
0.0259246826171875,
-0.0017213821411132812,
-0.0283050537109375,
-0.0177001953125,
-0.0170440673828125,
0.020965576171875,
0.01953125
] |
ours_518
|
The answer is \( 2018 \).
Let \( P(x) = a_n x^n + a_{n-1} x^{n-1} + \cdots + a_0 \). Newton's sums tell us:
\[
\begin{aligned}
a_n S_1 + a_{n-1} &= 0, \\
a_n S_2 + a_{n-1} S_1 + 2a_{n-2} &= 0, \\
&\vdots \\
a_n S_n + \cdots + a_1 S_1 + n a_0 &= 0,
\end{aligned}
\]
where \( S_k \) is the sum of the \( k \)-th powers of the roots.
Now, suppose we subtract 1 from \( a_0 \). The first \( (n-1) \) sums do not change, as they are not dependent on \( a_0 \). The last \( S_n \) must increase by \( n / a_n \).
Application to this problem: The sum of the 2011th powers of the roots is now \( 1 + 2^{2011} + 2^{4022} + \cdots + 2^{2010 \cdot 2011} + 2011 \).
The binary representation of 2012 is \( 11111011100_2 \), which has 8 ones. The sum of the remaining terms in binary is a sequence of ones followed by zeros, with 2010 ones. Therefore, the total number of ones in the binary expansion of \( S \) is \( 2010 + 8 = 2018 \).
\(\boxed{2018}\)
|
2018
|
{
"competition": "us_comps",
"dataset": "Ours",
"posts": null,
"source": "OMOSoln2-2.md"
}
|
Let \( S \) denote the sum of the 2011th powers of the roots of the polynomial \((x-2^0)(x-2^1)\cdots(x-2^{2010}) - 1\). How many 1's are in the binary expansion of \( S \)?
|
[
"/Mathematics/Algebra/NumberTheory/BinarySequences",
"/Mathematics/Algebra/NumberTheory/GeneralNumberTheory/ElementaryNumberTheory",
"/Mathematics/Algebra/NumberTheory/GeneralNumberTheory/NumberTheory",
"/Mathematics/Algebra/NumberTheory/Integers/Integer",
"/Mathematics/Algebra/NumberTheory/Integers/N",
"/Mathematics/Algebra/NumberTheory/Integers/NonnegativeInteger",
"/Mathematics/Algebra/NumberTheory/Integers/PositiveInteger",
"/Mathematics/Algebra/NumberTheory/Integers/RationalInteger",
"/Mathematics/Algebra/NumberTheory/Integers/Z",
"/Mathematics/Algebra/NumberTheory/Integers/Z-Plus",
"/Mathematics/Algebra/Polynomials/Newton-GirardFormulas",
"/Mathematics/Algebra/Polynomials/Polynomial",
"/Mathematics/Algebra/Polynomials/PolynomialRoots",
"/Mathematics/Algebra/Sums/PowerSum",
"/Mathematics/Algebra/Sums/Sum",
"/Mathematics/NumberTheory/BinarySequences",
"/Mathematics/NumberTheory/GeneralNumberTheory/ElementaryNumberTheory",
"/Mathematics/NumberTheory/GeneralNumberTheory/HigherArithmetic",
"/Mathematics/NumberTheory/GeneralNumberTheory/NumberTheory",
"/Mathematics/NumberTheory/Integers/Integer",
"/Mathematics/NumberTheory/Integers/PositiveInteger",
"/Mathematics/NumberTheory/Integers/RationalInteger",
"/Mathematics/NumberTheory/Integers/Z",
"/Mathematics/NumberTheory/Integers/Z-Plus"
] |
Use Newton's sums to show that lowering the constant term by 1 adds exactly 2011 to the sum of the 2011‑th powers of the roots.
|
[
-0.0001671314239501953,
0.00450897216796875,
0.0305023193359375,
0.020477294921875,
-0.0008134841918945312,
0.037841796875,
0.0200958251953125,
-0.03240966796875,
0.014373779296875,
-0.0067901611328125,
0.025787353515625,
-0.0712890625,
-0.0006079673767089844,
0.000446319580078125,
-0.04608154296875,
-0.00862884521484375,
0.046905517578125,
0.006591796875,
-0.004955291748046875,
-0.007171630859375,
-0.01253509521484375,
-0.004108428955078125,
-0.034942626953125,
0.03619384765625,
-0.02642822265625,
-0.007640838623046875,
-0.019683837890625,
-0.0162200927734375,
0.034454345703125,
0.0172119140625,
-0.0011243820190429688,
-0.04034423828125,
-0.00099945068359375,
-0.03240966796875,
0.0026378631591796875,
-0.0134735107421875,
0.029083251953125,
-0.00688934326171875,
0.005992889404296875,
-0.03472900390625,
0.002899169921875,
-0.0105438232421875,
-0.00466156005859375,
0.00341796875,
0.019134521484375,
-0.0135955810546875,
-0.00775146484375,
-0.0013446807861328125,
-0.0012941360473632812,
-0.0261383056640625,
0.003826141357421875,
0.00464630126953125,
-0.0173492431640625,
-0.0183563232421875,
-0.049102783203125,
-0.05157470703125,
-0.0386962890625,
-0.0025424957275390625,
-0.03167724609375,
-0.0165863037109375,
0.0006093978881835938,
-0.01003265380859375,
-0.01708984375,
-0.03167724609375,
-0.0030956268310546875,
-0.0133514404296875,
0.0185699462890625,
-0.005268096923828125,
-0.004344940185546875,
-0.002246856689453125,
0.031829833984375,
0.005672454833984375,
-0.0189361572265625,
0.034027099609375,
0.0262451171875,
-0.0212860107421875,
-0.01027679443359375,
0.007785797119140625,
0.0278472900390625,
0.01084136962890625,
0.0079803466796875,
0.00988006591796875,
0.01490020751953125,
-0.00923919677734375,
-0.005069732666015625,
-0.001445770263671875,
-0.0190582275390625,
0.00949859619140625,
0.0182037353515625,
-0.0256500244140625,
0.004268646240234375,
0.0269012451171875,
0.026580810546875,
-0.004367828369140625,
-0.007358551025390625,
-0.00824737548828125,
-0.002162933349609375,
-0.026214599609375,
-0.0201568603515625,
0.004192352294921875,
-0.00919342041015625,
-0.01201629638671875,
0.00589752197265625,
-0.01395416259765625,
-0.051971435546875,
-0.0204925537109375,
-0.0225830078125,
0.0218658447265625,
-0.00217437744140625,
0.0082855224609375,
0.00408172607421875,
0.0063934326171875,
-0.0028514862060546875,
-0.002044677734375,
-0.03887939453125,
0.035858154296875,
-0.0159149169921875,
0.0087127685546875,
-0.01129913330078125,
-0.00687408447265625,
-0.0014677047729492188,
0.010101318359375,
-0.0084228515625,
0.00730133056640625,
0.022003173828125,
0.0008292198181152344,
-0.0139007568359375,
-0.0005431175231933594,
0.019012451171875,
0.00959014892578125,
0.01552581787109375,
-0.0025997161865234375,
-0.04046630859375,
-0.026275634765625,
-0.06048583984375,
-0.005252838134765625,
0.007472991943359375,
-0.01537322998046875,
0.00047898292541503906,
-0.0306854248046875,
0.01174163818359375,
-0.0042266845703125,
0.00620269775390625,
-0.01216888427734375,
-0.01020050048828125,
0.0118560791015625,
-0.007205963134765625,
-0.0014257431030273438,
0.015716552734375,
0.003597259521484375,
0.0180511474609375,
0.006526947021484375,
0.0180206298828125,
0.01110076904296875,
-0.00927734375,
0.0066375732421875,
0.0031414031982421875,
0.0012865066528320312,
-0.0018072128295898438,
0.0027408599853515625,
-0.0013284683227539062,
0.0035305023193359375,
-0.0269775390625,
0.027801513671875,
-0.0124969482421875,
-0.01071929931640625,
-0.01708984375,
-0.0214385986328125,
-0.0118865966796875,
-0.0014867782592773438,
-0.0087890625,
0.0065460205078125,
0.0003998279571533203,
-0.023590087890625,
-0.0182037353515625,
0.017425537109375,
-0.0201416015625,
0.01245880126953125,
0.0027904510498046875,
0.0212554931640625,
-0.00504302978515625,
-0.07000732421875,
0.0030651092529296875,
-0.017486572265625,
0.0081329345703125,
-0.01239776611328125,
-0.0003142356872558594,
0.029632568359375,
0.025360107421875,
0.0194549560546875,
-0.0114288330078125,
0.0042572021484375,
0.007640838623046875,
0.0090484619140625,
-0.006404876708984375,
-0.00839996337890625,
-0.012969970703125,
-0.0015020370483398438,
0.0072479248046875,
0.0018281936645507812,
0.004985809326171875,
0.009521484375,
0.0112152099609375,
0.0201873779296875,
0.00803375244140625,
-0.011993408203125,
0.0145416259765625,
-0.01318359375,
0.0121917724609375,
-0.0020923614501953125,
0.004474639892578125,
-0.0230560302734375,
-0.0082855224609375,
-0.046722412109375,
-0.0090179443359375,
-0.006671905517578125,
-0.032196044921875,
0.0001443624496459961,
0.004657745361328125,
-0.0212249755859375,
-0.005779266357421875,
0.0159759521484375,
-0.00778961181640625,
-0.01458740234375,
-0.033050537109375,
-0.00556182861328125,
-0.0029315948486328125,
-0.00405120849609375,
-0.0083465576171875,
0.016265869140625,
0.031402587890625,
0.00970458984375,
-0.02630615234375,
-0.0162506103515625,
0.02020263671875,
0.01218414306640625,
-0.002643585205078125,
-0.0038814544677734375,
0.01360321044921875,
-0.0171051025390625,
-0.0271453857421875,
-0.0194244384765625,
0.0194549560546875,
0.0028076171875,
-0.0007472038269042969,
-0.01143646240234375,
-0.004608154296875,
-0.00494384765625,
0.00870513916015625,
-0.0107574462890625,
-0.0186920166015625,
-0.005153656005859375,
-0.00995635986328125,
-0.000934600830078125,
-0.01343536376953125,
-0.0108184814453125,
0.0009627342224121094,
-0.01537322998046875,
-0.0191497802734375,
-0.0026645660400390625,
0.0017023086547851562,
-0.0184783935546875,
-0.0012083053588867188,
-0.0025043487548828125,
-0.0204010009765625,
-0.00408172607421875,
0.006740570068359375,
-0.01264190673828125,
0.0245513916015625,
0.002109527587890625,
0.033172607421875,
-0.0117950439453125,
-0.023529052734375,
0.00473785400390625,
-0.0059967041015625,
-0.0071563720703125,
0.002140045166015625,
-0.005008697509765625,
0.01171112060546875,
-0.004138946533203125,
0.0052490234375,
0.016082763671875,
-0.0071258544921875,
0.0148773193359375,
0.0020961761474609375,
-0.0145111083984375,
0.011260986328125,
-0.0182037353515625,
0.00039577484130859375,
0.01090240478515625,
0.0178985595703125,
-0.008636474609375,
-0.0123291015625,
-0.0303955078125,
0.041351318359375,
-0.0154266357421875,
0.026885986328125,
0.0135650634765625,
-0.0023193359375,
-0.0196533203125,
0.017425537109375,
-0.014495849609375,
0.01143646240234375,
0.0011653900146484375,
-0.015838623046875,
0.0037631988525390625,
-0.0018367767333984375,
0.01190185546875,
-0.0197296142578125,
-0.00901031494140625,
0.005954742431640625,
0.00937652587890625,
-0.02294921875,
-0.00005328655242919922,
-0.0181732177734375,
-0.042938232421875,
0.01486968994140625,
0.0022983551025390625,
-0.028289794921875,
-0.00428009033203125,
0.010223388671875,
0.018951416015625,
-0.0016794204711914062,
-0.0087738037109375,
-0.01105499267578125,
-0.00920867919921875,
0.02825927734375,
-0.0004801750183105469,
-0.028106689453125,
0.01306915283203125,
-0.0538330078125,
0.01259613037109375,
0.00551605224609375,
-0.0222320556640625,
-0.003070831298828125,
-0.005767822265625,
-0.016937255859375,
0.0258636474609375,
0.01348876953125,
0.0013408660888671875,
-0.009429931640625,
0.0016689300537109375,
0.0266571044921875,
0.0176849365234375,
-0.0187225341796875,
0.0094451904296875,
-0.0196075439453125,
-0.0133209228515625,
-0.031982421875,
-0.01468658447265625,
0.01513671875,
0.01320648193359375,
0.01319122314453125,
-0.0265960693359375,
-0.040863037109375,
0.0270233154296875,
-0.019561767578125,
0.0148773193359375,
-0.0011644363403320312,
0.03143310546875,
0.0038547515869140625,
-0.005970001220703125,
0.0156402587890625,
0.00817108154296875,
-0.017730712890625,
-0.0036258697509765625,
-0.03863525390625,
0.03448486328125,
-0.039642333984375,
-0.0130615234375,
-0.0144195556640625,
-0.03155517578125,
-0.00797271728515625,
-0.0261077880859375,
-0.033935546875,
0.0123138427734375,
0.00347137451171875,
-0.006069183349609375,
-0.00042557716369628906,
0.0102691650390625,
0.01480865478515625,
0.0308074951171875,
-0.0178985595703125,
0.0171966552734375,
0.01406097412109375,
-0.0104827880859375,
-0.0011339187622070312,
-0.029083251953125,
-0.036041259765625,
0.01531982421875,
-0.016357421875,
-0.01056671142578125,
-0.00690460205078125,
0.0252685546875,
-0.0159454345703125,
-0.0206756591796875,
-0.0001920461654663086,
0.01107025146484375,
0.01224517822265625,
-0.01244354248046875,
0.0235137939453125,
-0.036376953125,
-0.020721435546875,
0.0190887451171875,
0.007656097412109375,
-0.0147705078125,
-0.01128387451171875,
-0.0192108154296875,
-0.0006456375122070312,
-0.0030879974365234375,
0.0274200439453125,
0.0201263427734375,
0.01849365234375,
-0.024658203125,
0.00804901123046875,
-0.0179901123046875,
0.04278564453125,
-0.007659912109375,
-0.014434814453125,
-0.00438690185546875,
-0.00795745849609375,
-0.00705718994140625,
0.0279693603515625,
0.009521484375,
0.0179290771484375,
0.0270538330078125,
-0.043182373046875,
0.01383209228515625,
0.004924774169921875,
0.0011892318725585938,
0.0214385986328125,
-0.04193115234375,
0.038543701171875,
0.0081787109375,
-0.0005664825439453125,
0.0423583984375,
0.0333251953125,
0.007617950439453125,
-0.015869140625,
0.0108795166015625,
0.02008056640625,
0.007801055908203125,
-0.011260986328125,
0.005558013916015625,
-0.038543701171875,
-0.006153106689453125,
-0.0001405477523803711,
0.035919189453125,
-0.040924072265625,
0.0028476715087890625,
-0.0227813720703125,
0.005466461181640625,
-0.00771331787109375,
-0.004398345947265625,
-0.034332275390625,
0.01352691650390625,
0.0289459228515625,
0.0008602142333984375,
-0.004302978515625,
-0.026824951171875,
-0.02105712890625,
-0.001323699951171875,
0.0020656585693359375,
0.00617218017578125,
-0.0369873046875,
-0.005031585693359375,
-0.03521728515625,
-0.00539398193359375,
0.03997802734375,
-0.005954742431640625,
-0.02777099609375,
-0.0176849365234375,
0.026947021484375,
-0.0211181640625,
-0.0491943359375,
0.0269622802734375,
0.027984619140625,
0.02960205078125,
-0.00913238525390625,
-0.024688720703125,
0.0271759033203125,
0.009796142578125,
-0.0226898193359375,
0.053619384765625,
-0.0030803680419921875,
0.0266265869140625,
0.03167724609375,
0.0091400146484375,
-0.01041412353515625,
0.00896453857421875,
0.020172119140625,
0.0240936279296875,
-0.01215362548828125,
-0.026092529296875,
-0.007049560546875,
-0.0191650390625,
0.01537322998046875,
0.004673004150390625,
-0.0140228271484375,
0.0201568603515625,
-0.00591278076171875,
-0.04852294921875,
0.0182647705078125,
0.01438140869140625,
0.0204620361328125,
-0.01139068603515625,
0.041168212890625,
0.0024089813232421875,
0.0203857421875,
0.0263519287109375,
0.026611328125,
-0.004425048828125,
-0.0016078948974609375,
-0.039031982421875,
0.0211181640625,
0.0025386810302734375,
0.040283203125,
-0.014556884765625,
-0.00858306884765625,
-0.0098419189453125,
-0.017425537109375,
0.011993408203125,
0.0223846435546875,
-0.0134124755859375,
0.0002646446228027344,
0.01491546630859375,
0.0218048095703125,
-0.00787353515625,
0.0006465911865234375,
0.00547027587890625,
-0.0218963623046875,
-0.0242462158203125,
-0.0224456787109375,
0.0016231536865234375,
-0.0487060546875,
0.004863739013671875,
0.00022709369659423828,
-0.0022869110107421875,
0.00994873046875,
-0.0008378028869628906,
-0.0269775390625,
0.01413726806640625,
0.007732391357421875,
-0.01837158203125,
-0.0073699951171875,
-0.0268402099609375,
-0.0214080810546875,
0.0297698974609375,
-0.056640625,
0.004718780517578125,
0.01097869873046875,
-0.0238037109375,
0.03631591796875,
0.006481170654296875,
-0.0299835205078125,
0.0242156982421875,
0.0195159912109375,
0.01548004150390625,
-0.008880615234375,
-0.0023956298828125,
-0.0011014938354492188,
-0.0070343017578125,
0.0182952880859375,
0.0103912353515625,
0.013702392578125,
-0.005908966064453125,
-0.00473785400390625,
0.001483917236328125,
-0.01065826416015625,
-0.042724609375,
0.0033721923828125,
0.018829345703125,
0.00502777099609375,
0.0307464599609375,
-0.0224456787109375,
-0.0244293212890625,
-0.0258026123046875,
0.01812744140625,
-0.006252288818359375,
-0.0213470458984375,
0.01544189453125,
0.003185272216796875,
-0.01441192626953125,
0.0039005279541015625,
0.00940704345703125,
-0.0188446044921875,
0.0270233154296875,
-0.0020122528076171875,
-0.00232696533203125,
0.0034275054931640625,
-0.0207672119140625,
0.00010436773300170898,
-0.037841796875,
0.018951416015625,
-0.0005040168762207031,
-0.026824951171875,
0.0247955322265625,
-0.0149993896484375,
-0.0109100341796875,
-0.00675201416015625,
0.03399658203125,
-0.0118408203125,
-0.003345489501953125,
0.0347900390625,
-0.004657745361328125,
-0.0018291473388671875,
-0.01441192626953125,
0.01399993896484375,
-0.002613067626953125,
0.006923675537109375,
-0.0224151611328125,
-0.0223236083984375,
0.031494140625,
0.01387786865234375,
0.017486572265625,
-0.0180511474609375,
-0.0246734619140625,
0.005779266357421875,
0.03515625,
-0.029541015625,
-0.006008148193359375,
0.00742340087890625,
-0.0198516845703125,
-0.0008921623229980469,
-0.0037136077880859375,
-0.037017822265625,
-0.0025882720947265625,
0.00861358642578125,
0.01444244384765625,
-0.00925445556640625,
-0.007793426513671875,
-0.0006780624389648438,
0.0279541015625,
-0.000995635986328125,
0.0218505859375,
0.0047760009765625,
-0.02398681640625,
0.006450653076171875,
0.02008056640625,
0.01158905029296875,
0.0189056396484375,
0.015228271484375,
0.01375579833984375,
-0.047027587890625,
0.0087432861328125,
0.0205078125,
-0.030548095703125,
0.00628662109375,
0.01194000244140625,
0.0310211181640625,
-0.004299163818359375,
0.01324462890625,
-0.0247344970703125,
0.0007495880126953125,
0.0028553009033203125,
0.027313232421875,
0.00899505615234375,
-0.02294921875,
0.00458526611328125,
-0.00928497314453125,
0.0228424072265625,
-0.00803375244140625,
0.0133514404296875,
0.02545166015625,
-0.01009368896484375,
-0.0189056396484375,
0.0069427490234375,
-0.01480865478515625,
0.05584716796875,
0.0005998611450195312,
0.049072265625,
-0.0113525390625,
0.0196990966796875,
-0.0184478759765625,
0.01097869873046875,
-0.0202178955078125,
-0.0287322998046875,
-0.01154327392578125,
0.034088134765625,
0.029205322265625,
0.006473541259765625,
0.00220489501953125,
0.018646240234375,
-0.0191497802734375,
0.0244293212890625,
-0.0124969482421875,
-0.01160430908203125,
0.0192108154296875,
0.021728515625,
-0.00981903076171875,
-0.0004684925079345703,
-0.02960205078125,
-0.0214691162109375,
-0.006511688232421875,
-0.003742218017578125,
-0.021728515625,
0.0103759765625,
0.007053375244140625,
-0.006500244140625,
-0.0222625732421875,
0.016021728515625,
-0.00864410400390625,
0.038665771484375,
0.00601959228515625,
-0.004032135009765625,
-0.019989013671875,
0.0006732940673828125,
-0.005279541015625,
-0.01465606689453125,
0.00627899169921875,
-0.02435302734375,
0.01031494140625,
-0.03460693359375,
-0.01024627685546875,
-0.0213470458984375,
0.02130126953125,
0.007678985595703125,
0.00699615478515625,
0.00406646728515625,
-0.024871826171875,
-0.0275726318359375,
-0.017730712890625,
-0.04119873046875,
0.007221221923828125,
0.00841522216796875,
0.0247344970703125,
-0.001239776611328125,
-0.0195770263671875,
-0.0171966552734375,
-0.0027866363525390625,
0.0167236328125,
-0.0103759765625,
0.020904541015625,
0.004779815673828125,
0.00901031494140625,
-0.03167724609375,
-0.0023326873779296875,
-0.036376953125,
-0.00923919677734375,
-0.011383056640625,
0.0181427001953125,
0.004444122314453125,
0.0160980224609375,
0.0136260986328125,
-0.0004336833953857422,
-0.01256561279296875,
-0.004383087158203125,
-0.0176849365234375,
-0.00588226318359375,
0.002468109130859375,
0.01103973388671875,
0.055694580078125,
0.0011777877807617188,
-0.038482666015625,
-0.0242156982421875,
-0.0114593505859375,
0.005901336669921875,
-0.0223236083984375,
-0.0002186298370361328,
0.006282806396484375,
-0.061920166015625,
-0.0120849609375,
-0.0016851425170898438,
0.004253387451171875,
0.00601959228515625,
-0.0008883476257324219,
-0.001617431640625,
-0.0050506591796875,
-0.00957489013671875,
0.061431884765625,
-0.0030975341796875,
0.0044708251953125,
0.01019287109375,
-0.005512237548828125,
0.0311279296875,
-0.02178955078125,
-0.015899658203125,
-0.01123809814453125,
0.040374755859375,
-0.0000851750373840332,
-0.0020599365234375,
0.0070037841796875,
-0.0117950439453125,
0.01265716552734375,
-0.0124359130859375,
-0.01280975341796875,
0.01136016845703125,
-0.03839111328125,
0.0265655517578125,
-0.0238189697265625,
0.0035552978515625,
0.0169677734375,
0.003467559814453125,
0.01198577880859375,
-0.004497528076171875,
0.027557373046875,
0.00115203857421875,
-0.041839599609375,
0.003795623779296875,
0.004398345947265625,
0.002376556396484375,
-0.0296783447265625,
-0.0233154296875,
0.02783203125,
0.0001850128173828125,
0.001220703125,
-0.00139617919921875,
0.01375579833984375,
0.0004038810729980469,
0.033111572265625,
0.01548004150390625,
0.0035800933837890625,
-0.004425048828125,
-0.0299224853515625,
0.02813720703125,
-0.032073974609375,
-0.01422882080078125,
-0.0127716064453125,
0.0012674331665039062,
0.0283203125,
-0.017547607421875,
0.0226593017578125,
0.0225982666015625,
-0.004547119140625,
-0.0236358642578125,
-0.01108551025390625,
0.0253753662109375,
0.01428985595703125,
0.0308685302734375,
-0.0030078887939453125,
-0.0136566162109375,
-0.0300140380859375,
-0.0025806427001953125,
0.0270233154296875,
-0.018524169921875,
0.0159454345703125,
-0.004192352294921875,
0.00426483154296875,
-0.0008678436279296875,
-0.02685546875,
0.026092529296875,
0.037322998046875,
0.035003662109375,
-0.0328369140625,
0.03033447265625,
-0.00174713134765625,
-0.039337158203125,
0.034027099609375,
-0.006023406982421875,
0.00014460086822509766,
-0.012115478515625,
0.0230560302734375,
-0.01029205322265625,
0.0214691162109375,
-0.01038360595703125,
0.0283660888671875,
-0.0011129379272460938,
-0.00984954833984375,
-0.00124359130859375,
-0.0258331298828125,
-0.018341064453125,
-0.0252838134765625,
0.0029506683349609375,
-0.0004076957702636719,
0.0005750656127929688,
0.021575927734375,
0.00045490264892578125,
0.006587982177734375,
0.0124053955078125,
-0.0163726806640625,
0.0230255126953125,
-0.0140380859375,
0.005794525146484375,
0.0017709732055664062,
0.004245758056640625,
0.0224151611328125,
-0.0225067138671875,
-0.0197601318359375,
0.032318115234375,
0.035186767578125,
0.0290069580078125,
-0.051361083984375,
0.004001617431640625,
0.0208282470703125,
0.00447845458984375,
0.02972412109375,
0.0047149658203125,
0.01157379150390625,
-0.024993896484375,
-0.020904541015625,
-0.020477294921875,
0.0011472702026367188,
0.018341064453125,
0.0301666259765625,
0.023590087890625,
0.0168609619140625,
0.0005044937133789062,
-0.0081024169921875,
0.003810882568359375,
-0.062469482421875,
0.01311492919921875,
0.006320953369140625,
0.016571044921875,
-0.002712249755859375,
-0.0272216796875,
-0.006214141845703125,
-0.01055908203125,
0.002292633056640625,
0.0218505859375,
0.0288848876953125,
0.0006537437438964844,
0.0084228515625,
0.00791168212890625,
0.0197296142578125,
-0.057159423828125,
-7.152557373046875e-7,
-0.0223236083984375,
0.0195770263671875,
0.005260467529296875,
0.01141357421875,
0.00868988037109375,
0.003978729248046875,
-0.05712890625,
-0.003108978271484375,
0.01561737060546875,
-0.018218994140625,
-0.013580322265625,
0.01163482666015625,
-0.03302001953125,
0.002300262451171875,
-0.02667236328125,
0.0175628662109375,
-0.0242767333984375,
-0.0458984375,
-0.0013494491577148438,
0.028228759765625,
0.012298583984375,
-0.0005884170532226562,
0.00262451171875,
0.0026950836181640625,
-0.023193359375,
0.006855010986328125,
-0.00319671630859375,
0.0044097900390625,
0.028564453125,
0.00820159912109375,
0.019439697265625,
0.03900146484375,
0.005176544189453125,
-0.0074310302734375,
-0.0199432373046875,
-0.0034923553466796875,
-0.031646728515625,
0.045989990234375,
-0.026885986328125,
-0.0048370361328125,
-0.0276947021484375,
-0.01934814453125,
0.031402587890625,
-0.0249176025390625,
0.00106048583984375,
0.01084136962890625,
-0.043487548828125,
0.0118560791015625,
-0.01800537109375,
0.018402099609375,
-0.01123809814453125,
0.01088714599609375,
0.015625,
0.0063323974609375,
-0.03985595703125,
-0.005588531494140625,
-0.004375457763671875,
-0.00719451904296875,
-0.0040283203125,
-0.0016775131225585938,
0.0112152099609375,
0.01386260986328125,
0.017059326171875,
0.0188446044921875,
-0.0252685546875,
0.00038504600524902344,
0.01049041748046875,
-0.01499176025390625,
-0.0176849365234375,
0.0188751220703125,
0.02154541015625,
-0.033538818359375,
0.039306640625,
-0.007537841796875,
0.000438690185546875,
0.04022216796875,
-0.01181793212890625,
0.0262908935546875,
-0.0031299591064453125,
0.0105133056640625,
-0.01934814453125,
-0.0131378173828125,
0.0159454345703125,
0.00818634033203125,
-0.0278472900390625,
0.014556884765625,
0.0008625984191894531,
-0.0025730133056640625,
-0.007778167724609375,
-0.0112457275390625,
-0.00441741943359375,
0.02490234375,
0.0244293212890625,
0.01473236083984375,
-0.019012451171875,
-0.01004791259765625,
-0.004058837890625,
-0.018951416015625,
-0.036895751953125,
0.017730712890625,
-0.001312255859375,
-0.020965576171875,
-0.021636962890625,
-0.001983642578125,
0.042327880859375,
-0.00476837158203125,
-0.0235137939453125,
-0.0285491943359375,
0.021575927734375,
0.0137481689453125,
-0.02130126953125,
0.043701171875,
0.0122833251953125,
0.0226593017578125,
-0.008575439453125,
-0.0227508544921875,
0.033050537109375,
-0.03173828125,
-0.005725860595703125,
0.0102081298828125,
-0.0372314453125,
-0.0218963623046875,
0.0308380126953125,
-0.005153656005859375,
0.0131072998046875,
0.0047760009765625,
0.0218963623046875,
-0.005916595458984375,
-0.01934814453125,
-0.0283355712890625,
0.0028591156005859375,
0.007537841796875,
0.004547119140625,
-0.006359100341796875,
-0.01517486572265625,
0.01482391357421875,
-0.0147857666015625,
-0.020355224609375,
-0.007717132568359375,
-0.0002034902572631836,
0.0130157470703125,
-0.02008056640625,
0.0017881393432617188,
0.03204345703125,
0.00569915771484375,
-0.007678985595703125,
-0.007537841796875,
-0.050384521484375,
-0.00004220008850097656,
0.00719451904296875,
-0.033111572265625,
0.00449371337890625,
-0.015899658203125,
0.01392364501953125,
-0.01446533203125,
0.0280609130859375,
0.0100555419921875,
-0.041717529296875,
0.006847381591796875,
-0.0264892578125,
0.008697509765625,
-0.0215606689453125,
-0.00740814208984375,
-0.0003566741943359375,
-0.0096435546875,
-0.005611419677734375,
-0.04022216796875,
0.007038116455078125,
0.040496826171875,
-0.0193634033203125,
0.01035308837890625,
0.004489898681640625,
0.0013113021850585938,
-0.0177764892578125,
0.006244659423828125,
-0.007068634033203125,
-0.0035419464111328125,
-0.016815185546875,
0.0195770263671875,
-0.0214996337890625,
0.0023651123046875,
-0.01555633544921875,
0.00891876220703125,
0.0086822509765625,
0.0086669921875,
0.026885986328125,
-0.0169525146484375,
-0.01263427734375,
-0.004077911376953125,
-0.0004968643188476562,
-0.01258087158203125,
0.0185394287109375,
-0.00916290283203125,
-0.01349639892578125,
-0.012451171875,
0.02484130859375,
0.01094818115234375,
0.02459716796875,
0.0071258544921875,
0.005401611328125,
-0.02984619140625,
-0.00020170211791992188,
-0.0008907318115234375,
-0.029266357421875,
-0.004619598388671875,
0.02056884765625,
0.01389312744140625,
-0.0157928466796875,
0.007373809814453125,
0.0093536376953125,
0.018524169921875,
-0.00516510009765625,
-0.0282440185546875,
0.005329132080078125,
-0.0230560302734375,
0.0237579345703125,
-0.00913238525390625,
-0.01279449462890625,
-0.00588226318359375,
-0.00780487060546875,
-0.0155029296875,
0.028594970703125,
0.0198822021484375,
-0.0114288330078125,
0.01206207275390625,
-0.002201080322265625,
-0.0357666015625,
-0.0232086181640625,
-0.002117156982421875,
0.016387939453125,
-0.0140838623046875,
0.002899169921875,
-0.005489349365234375,
0.0266265869140625,
0.0014696121215820312,
0.0210418701171875,
-0.01227569580078125,
-0.03515625,
-0.0098419189453125,
0.0094451904296875,
-0.014495849609375,
0.0159759521484375,
0.00855255126953125,
-0.014617919921875,
0.01488494873046875,
-0.01739501953125,
0.02716064453125,
0.02130126953125,
-0.0231781005859375,
0.011688232421875,
-0.039154052734375,
0.043701171875,
-0.01255035400390625,
-0.00027871131896972656,
-0.031219482421875,
-0.0218963623046875,
0.007762908935546875,
-0.00525665283203125,
-0.0019330978393554688,
-0.006313323974609375,
0.0284881591796875,
-0.0305023193359375,
-0.0227813720703125,
0.006313323974609375,
-0.008941650390625,
0.01039886474609375,
0.0102996826171875,
-0.01229095458984375,
-0.0189361572265625,
-0.01035308837890625,
-0.02191162109375,
0.0016126632690429688,
-0.0011358261108398438,
0.00047850608825683594,
0.00605010986328125,
0.01409149169921875,
-0.0204315185546875,
-0.0011653900146484375,
-0.00301361083984375,
-0.003055572509765625,
-0.011444091796875,
-0.01178741455078125,
0.0013599395751953125,
-0.0015554428100585938,
0.002834320068359375,
-0.0240936279296875,
-0.033843994140625,
-0.0171661376953125,
0.00008606910705566406,
0.005641937255859375,
-0.0250244140625,
0.019622802734375,
-0.0146636962890625,
0.038665771484375,
-0.046539306640625,
-0.01502227783203125,
-0.0208892822265625,
-0.0185699462890625,
0.006381988525390625,
-0.017120361328125,
0.04534912109375,
0.0135498046875,
-0.02801513671875,
-0.02276611328125,
0.0059356689453125,
0.0002777576446533203,
0.0037555694580078125,
0.03033447265625,
-0.006885528564453125,
0.0088653564453125,
-0.00872039794921875,
0.0273895263671875,
-0.0093231201171875,
0.01629638671875,
-0.002208709716796875,
0.02154541015625,
-0.002407073974609375,
0.040924072265625,
-0.0119171142578125,
-0.0158843994140625,
0.004947662353515625,
0.0144195556640625,
-0.006641387939453125,
0.0372314453125,
-0.003536224365234375,
0.022796630859375,
0.004932403564453125,
0.01291656494140625,
0.0400390625,
-0.035552978515625,
-0.035247802734375,
0.02435302734375,
-0.0235595703125,
-0.0032138824462890625,
-0.00646209716796875,
0.009002685546875,
-0.0021839141845703125,
-0.006145477294921875,
-0.0172119140625,
-0.01326751708984375,
0.0221099853515625,
-0.013275146484375,
0.0119781494140625,
0.0130615234375,
-0.02777099609375,
-0.0025348663330078125,
-0.00949859619140625,
-0.00994873046875,
0.010528564453125,
0.012664794921875,
0.01247406005859375,
0.0245208740234375,
-0.0004906654357910156,
0.022979736328125,
0.017059326171875,
0.031951904296875,
0.00266265869140625,
0.04736328125,
-0.005298614501953125,
0.0098114013671875,
-0.012115478515625,
-0.021514892578125,
0.014068603515625,
-0.01934814453125,
-0.01151275634765625,
0.0426025390625,
0.01528167724609375,
-0.01528167724609375,
-0.01197052001953125,
-0.018798828125,
-0.0161285400390625,
0.005168914794921875,
-0.0190887451171875,
-0.004787445068359375,
0.00391387939453125,
-0.01091766357421875,
-0.00968170166015625,
0.023956298828125,
0.02166748046875,
0.01416015625,
0.005771636962890625,
-0.0176544189453125,
0.0164794921875,
-0.0079803466796875,
-0.0010499954223632812,
-0.036712646484375,
0.0258026123046875,
-0.0078887939453125,
-0.0204620361328125,
-0.031524658203125,
0.0311431884765625,
-0.0079193115234375,
-0.028656005859375,
-0.022796630859375,
0.01543426513671875,
0.01849365234375,
0.0105438232421875,
0.0096435546875,
0.0229949951171875,
-0.01546478271484375,
-0.021392822265625,
-0.001918792724609375,
-0.0222930908203125,
-0.0188751220703125,
-0.0005741119384765625,
-0.0090789794921875,
-0.00215911865234375,
-0.006793975830078125,
-0.024749755859375,
0.0164947509765625,
-0.0194549560546875,
0.006168365478515625,
-0.023468017578125,
-0.01554107666015625,
-0.005008697509765625,
0.01534271240234375,
-0.033111572265625,
-0.01233673095703125,
0.012664794921875,
0.0088653564453125,
-0.0084075927734375,
0.00707244873046875,
0.01297760009765625,
-0.0172882080078125,
-0.010650634765625,
0.028472900390625,
-0.028656005859375,
-0.0027675628662109375,
-0.007419586181640625,
-0.0026683807373046875,
-0.0218963623046875,
0.01462554931640625,
0.0413818359375,
0.000019669532775878906,
-0.0207672119140625,
0.0161285400390625,
0.01470184326171875,
0.00881195068359375,
-0.01702880859375,
-0.01129913330078125,
0.016571044921875,
-0.009552001953125,
0.005825042724609375,
0.01064300537109375,
0.03387451171875,
-0.01309967041015625,
0.00140380859375,
-0.0054931640625,
0.004913330078125,
0.0227813720703125,
0.0030918121337890625,
-0.0164642333984375,
-0.01361083984375,
0.0047454833984375,
0.0004596710205078125,
-0.0118560791015625,
-0.01042938232421875,
-0.0022983551025390625,
-0.00473785400390625,
0.005016326904296875,
-0.060089111328125,
-0.00217437744140625,
-0.028411865234375,
-0.003528594970703125,
-0.033111572265625,
-0.004413604736328125,
0.0035800933837890625,
-0.01419830322265625,
0.031097412109375,
0.045440673828125,
-0.00934600830078125,
0.016815185546875,
0.0042877197265625,
-0.019012451171875,
0.0221099853515625,
-0.032379150390625,
-0.024169921875,
0.0135040283203125,
-0.00775909423828125,
-0.027252197265625,
0.02435302734375,
-0.027099609375,
-0.01409912109375,
0.02801513671875,
0.0272979736328125,
-0.00896453857421875,
-0.0017824172973632812,
0.00481414794921875,
0.02178955078125,
-0.04559326171875,
0.00969696044921875,
-0.027099609375,
-0.01226806640625,
-0.0250091552734375,
-0.00994110107421875,
0.0015707015991210938,
-0.00577545166015625,
-0.0168914794921875,
0.004100799560546875,
-0.0110626220703125,
0.006313323974609375,
-0.0307769775390625,
-0.0270538330078125,
-0.0153350830078125,
0.02166748046875,
0.0302734375,
-0.0269012451171875,
0.005107879638671875,
-0.007083892822265625,
-0.0228424072265625,
0.0258331298828125,
-0.00823211669921875,
0.00215911865234375,
-0.025177001953125,
-0.01186370849609375,
-0.0211181640625,
-0.0296173095703125,
-0.0080413818359375,
-0.0164947509765625,
-0.0008106231689453125,
0.0280914306640625,
0.0159912109375,
0.0286865234375,
-0.025604248046875,
0.007335662841796875,
-0.006320953369140625,
-0.005146026611328125,
-0.0194244384765625,
-0.0433349609375,
-0.00154876708984375,
0.0252532958984375,
0.0025501251220703125,
-0.0127716064453125,
-0.0190887451171875,
-0.0178680419921875,
-0.02386474609375,
0.007305145263671875,
-0.0017919540405273438,
0.035888671875,
-0.01568603515625,
-0.014251708984375,
0.0055999755859375,
0.01519012451171875,
-0.00458526611328125,
-0.04046630859375,
0.0004978179931640625,
-0.00545501708984375,
0.0066070556640625,
0.046661376953125,
-0.021270751953125,
-0.01546478271484375,
0.0163726806640625,
0.025115966796875,
-0.01605224609375,
0.010009765625,
-0.019805908203125,
-0.011260986328125,
-0.0235595703125,
-0.0126190185546875,
-0.01238250732421875,
0.026702880859375,
-0.02783203125,
0.00907135009765625,
-0.0438232421875,
0.014373779296875,
0.00859832763671875,
0.049957275390625,
0.0251007080078125,
-0.0209503173828125,
0.005573272705078125,
0.012359619140625,
0.004608154296875,
0.01201629638671875,
0.00980377197265625,
-0.00543212890625,
-0.037017822265625,
0.008148193359375,
0.0185546875,
0.024078369140625,
0.0036296844482421875,
-0.0186767578125,
-0.01153564453125,
-0.010467529296875,
0.0105743408203125,
0.0157318115234375,
0.0149688720703125,
0.057464599609375,
0.00439453125,
0.034698486328125,
-0.00968170166015625,
0.001644134521484375,
0.0286712646484375,
-0.00650787353515625,
-0.0227508544921875,
0.0006361007690429688,
-0.010589599609375,
0.0003101825714111328,
0.00870513916015625,
-0.023651123046875,
-0.0272674560546875,
-0.0200653076171875,
-0.007419586181640625,
-0.041290283203125,
-0.032379150390625,
0.01528167724609375,
-0.01076507568359375,
-0.01268768310546875,
0.0196075439453125,
0.025665283203125,
-0.020477294921875,
0.01155853271484375,
0.0086822509765625,
-0.0142669677734375,
0.01035308837890625,
0.002201080322265625,
-0.0210723876953125,
-0.0255279541015625,
-0.0108642578125,
0.0204620361328125,
-0.01299285888671875,
0.0228118896484375,
0.0178375244140625,
0.0170440673828125,
0.00800323486328125,
-0.006816864013671875,
0.00667572021484375,
-0.0162353515625,
-0.003437042236328125,
0.00749969482421875,
-0.00893402099609375,
0.0246734619140625,
0.033233642578125,
0.0178985595703125,
-0.0182952880859375,
0.0318603515625,
0.0184478759765625,
0.00798797607421875,
-0.009979248046875,
-0.04351806640625,
0.004215240478515625,
-0.0068359375,
0.0009317398071289062,
-0.0134735107421875,
-0.0167236328125,
-0.004848480224609375,
-0.00015234947204589844,
-0.0244140625,
0.002147674560546875,
-0.011566162109375,
-0.0306396484375,
0.0131988525390625,
0.046417236328125,
-0.01251983642578125,
-0.023040771484375,
0.003795623779296875,
0.0125732421875,
-0.01212310791015625,
0.035400390625,
-0.01056671142578125,
-0.0141448974609375,
-0.019256591796875,
-0.006591796875,
0.01153564453125,
0.016387939453125,
0.017364501953125,
-0.01690673828125,
-0.0192108154296875,
0.015838623046875,
0.022064208984375,
-0.007076263427734375,
-0.006343841552734375,
0.01611328125,
-0.0244140625,
-0.0213775634765625,
0.0174560546875,
-0.01409912109375,
0.0175933837890625,
-0.01148223876953125,
-0.019805908203125,
-0.007480621337890625,
0.01953125,
-0.02008056640625,
0.055450439453125,
0.0295562744140625,
-0.004360198974609375,
0.015777587890625,
-0.0027370452880859375,
-0.006290435791015625,
-0.0113372802734375,
0.030242919921875,
0.004688262939453125,
-0.023529052734375,
0.0006203651428222656,
0.02496337890625,
-0.0070953369140625,
-0.01220703125,
0.0020599365234375,
0.0059814453125,
0.011260986328125,
0.00008487701416015625,
0.004047393798828125,
-0.0184478759765625,
0.005313873291015625,
0.0034160614013671875,
0.0235748291015625,
-0.00537872314453125,
-0.011444091796875,
-0.026763916015625,
-0.0060577392578125,
0.0445556640625,
-0.02191162109375,
0.0126800537109375,
-0.01462554931640625,
-0.048065185546875,
0.0201873779296875,
-0.0011129379272460938,
-0.03228759765625,
0.01224517822265625,
-0.0294342041015625,
-0.0052947998046875,
-0.00748443603515625,
0.013427734375,
-0.0362548828125,
0.01113128662109375,
-0.022430419921875,
-0.038543701171875,
0.01947021484375,
-0.05474853515625,
-0.0278167724609375,
0.003932952880859375,
-0.005413055419921875,
0.03179931640625,
-0.005401611328125,
0.010345458984375,
-0.0009455680847167969,
-0.0144500732421875,
0.022613525390625,
0.002521514892578125,
0.0006227493286132812,
-0.01462554931640625,
0.023223876953125,
0.01103973388671875,
-0.003269195556640625,
-0.0050811767578125,
-0.0019311904907226562,
-0.017242431640625,
0.034698486328125,
-0.00647735595703125,
-0.024871826171875,
0.019683837890625,
0.0013322830200195312,
0.00634765625,
-0.0194854736328125,
-0.003948211669921875,
-0.041351318359375,
-0.0200347900390625,
-0.0002617835998535156,
0.01239013671875,
-0.0189208984375,
-0.006591796875,
-0.00545501708984375,
-0.00008273124694824219,
-0.0050201416015625,
-0.0192718505859375,
0.0163116455078125,
-0.0157470703125,
-0.01235198974609375,
0.0204010009765625,
-0.006725311279296875,
-0.010162353515625,
0.01971435546875,
-0.004756927490234375,
-0.019683837890625,
-0.008453369140625,
0.0379638671875,
0.006252288818359375,
0.00911712646484375,
0.041534423828125,
0.036041259765625,
0.01384735107421875,
0.0021266937255859375,
-0.01224517822265625,
0.01056671142578125,
-0.015716552734375,
0.0005674362182617188,
0.0030612945556640625,
0.0266876220703125,
-0.0269622802734375,
0.0179443359375,
0.0273590087890625,
-0.038665771484375,
-0.0005412101745605469,
-0.0237274169921875,
0.0105743408203125,
0.007205963134765625,
-0.020782470703125,
-0.006229400634765625,
0.00098419189453125,
0.00899505615234375,
0.0189208984375,
0.04864501953125,
-0.0114593505859375,
-0.00913238525390625,
-0.0069580078125,
0.0130462646484375,
0.00623321533203125,
0.0017213821411132812,
-0.03924560546875,
0.021881103515625,
0.0040283203125,
0.0031185150146484375,
0.0088653564453125,
-0.004245758056640625,
0.0178375244140625,
-0.0156097412109375,
-0.005435943603515625,
-0.01033782958984375,
-0.02288818359375,
0.0041656494140625,
-0.0265045166015625,
-0.0018606185913085938,
-0.035980224609375,
-0.0169219970703125,
-0.0104827880859375,
0.02264404296875,
0.021820068359375,
-0.00946807861328125,
-0.03192138671875,
-0.01062774658203125,
-0.0197296142578125,
-0.0023174285888671875,
0.03167724609375,
0.0149688720703125,
0.002475738525390625,
-0.01049041748046875,
-0.023712158203125,
-0.01953125,
-0.0012979507446289062,
-0.0083465576171875,
-0.01166534423828125,
-0.0010051727294921875,
-0.02337646484375,
-0.0116424560546875,
-0.002445220947265625,
0.0243377685546875,
-0.047607421875,
-0.0106201171875,
-0.01263427734375,
-0.01224517822265625,
0.0013151168823242188,
0.01174163818359375,
-0.0306243896484375,
-0.011322021484375,
-0.006603240966796875,
0.0016794204711914062,
0.01181793212890625,
0.01000213623046875,
0.01471710205078125,
0.0212249755859375,
-0.025360107421875,
0.024871826171875,
0.004123687744140625,
-0.00733184814453125,
0.0087890625,
0.0029315948486328125,
-0.01488494873046875,
0.032012939453125,
-0.01065826416015625,
-0.0240020751953125,
0.008544921875,
0.0181121826171875,
0.01537322998046875,
0.00984954833984375,
-0.0209808349609375,
-0.027862548828125,
0.01629638671875,
0.0159759521484375,
0.0027904510498046875,
0.00006961822509765625,
0.001110076904296875,
-0.00426483154296875,
0.030609130859375,
0.00133514404296875,
0.0159912109375,
-0.031341552734375,
-0.006160736083984375,
0.01386260986328125,
0.01200103759765625,
0.039459228515625,
0.0034313201904296875,
-0.037750244140625,
0.01605224609375,
0.0155792236328125,
-0.005413055419921875,
0.0038204193115234375,
0.0257720947265625,
-0.010040283203125,
0.0255126953125,
-0.0163421630859375,
-0.005706787109375,
-0.01261138916015625,
0.0165863037109375,
-0.017242431640625,
0.0098419189453125,
-0.00074005126953125,
0.0197601318359375,
-0.025848388671875,
0.00145721435546875,
-0.0164794921875,
-0.01183319091796875,
-0.019439697265625,
0.004428863525390625,
-0.0149078369140625,
0.0362548828125,
-0.0148773193359375,
0.00688934326171875,
-0.034454345703125,
-0.0030002593994140625,
0.005764007568359375,
-0.0028285980224609375,
0.01219940185546875,
-0.0202484130859375,
-0.022491455078125,
0.01052093505859375,
0.0238037109375,
0.04498291015625,
-0.040252685546875,
0.0086669921875,
-0.0020122528076171875,
-0.032196044921875,
-0.0140838623046875,
0.00949859619140625,
-0.041473388671875,
0.0222015380859375,
-0.00311279296875,
-0.0186004638671875,
-0.00408172607421875,
0.0140228271484375,
-0.0034770965576171875,
-0.0023059844970703125,
-0.0053863525390625,
-0.01494598388671875,
0.01134490966796875,
0.02587890625,
-0.003368377685546875,
-0.01021575927734375,
-0.01012420654296875,
-0.00019347667694091797,
-0.01424407958984375,
0.0036907196044921875,
-0.0186767578125,
-0.0038814544677734375,
-0.0120697021484375,
0.0170745849609375,
0.0092926025390625,
0.0022945404052734375,
-0.032623291015625,
-0.01000213623046875,
0.0060577392578125,
0.032379150390625,
-0.029144287109375,
0.025054931640625,
0.01739501953125,
0.0154266357421875,
0.002513885498046875,
0.03167724609375,
0.01229095458984375,
0.0247650146484375,
0.0008654594421386719,
0.00830841064453125,
0.038818359375,
0.036163330078125,
-0.018280029296875,
0.0038604736328125,
-0.03619384765625,
0.00008618831634521484,
0.0255584716796875,
-0.015777587890625,
-0.0169830322265625,
-0.0053863525390625,
-0.01617431640625,
-0.0015497207641601562,
-0.04156494140625,
0.047576904296875,
-0.0024929046630859375,
0.016571044921875,
-0.0060577392578125,
0.005916595458984375,
0.004039764404296875,
0.000446319580078125,
-0.021881103515625,
-0.032073974609375,
0.0188446044921875,
0.006805419921875,
0.0305633544921875,
-0.02197265625,
-0.0362548828125,
0.004119873046875,
-0.0000018477439880371094,
0.072021484375,
0.00666046142578125,
0.0270843505859375,
0.005847930908203125,
0.019866943359375,
-0.0014133453369140625,
-0.01105499267578125,
0.030792236328125,
0.01097869873046875,
0.00931549072265625,
0.0028228759765625,
0.0012874603271484375,
-0.0187530517578125,
0.0092926025390625,
-0.0041961669921875,
0.0217437744140625,
-0.0198211669921875,
0.012603759765625,
-0.005764007568359375,
0.0031566619873046875,
0.0041351318359375,
-0.01531219482421875,
0.001682281494140625,
0.017059326171875,
0.031463623046875,
0.004364013671875,
-0.01198577880859375,
0.009002685546875,
-0.0123138427734375,
-0.00982666015625,
-0.007465362548828125,
0.0005698204040527344,
-0.014923095703125,
0.03411865234375,
0.0011348724365234375,
0.01493072509765625,
-0.00860595703125,
-0.005889892578125,
-0.00247955322265625,
0.00959014892578125,
0.033203125,
0.006805419921875,
0.0008301734924316406,
0.0283050537109375,
-0.0025882720947265625,
-0.01197052001953125,
-0.033233642578125,
-0.00792694091796875,
-0.042327880859375,
-0.0179290771484375,
0.00380706787109375,
0.0239410400390625,
-0.067138671875,
-0.003635406494140625,
-0.03240966796875,
0.00045180320739746094,
0.0155181884765625,
0.033203125,
0.0179443359375,
0.01264190673828125,
0.0063018798828125,
-0.0304718017578125,
0.0132904052734375,
0.0154876708984375,
-0.0006256103515625,
-0.01322174072265625,
-0.029632568359375,
-0.023345947265625,
-0.02691650390625,
0.01038360595703125,
-0.02630615234375,
0.0250244140625,
-0.009429931640625,
-0.01540374755859375,
0.047088623046875,
0.001110076904296875,
-0.0176544189453125,
-0.01904296875,
0.001201629638671875,
0.01136016845703125,
-0.0003974437713623047,
0.0254058837890625,
0.020843505859375,
0.007843017578125,
-0.01555633544921875,
-0.00821685791015625,
0.007259368896484375,
0.0292510986328125,
-0.005123138427734375,
-0.01197052001953125,
0.004650115966796875,
0.002971649169921875,
0.035491943359375,
-0.020538330078125,
-0.00818634033203125,
-0.0007457733154296875,
-0.041229248046875,
0.0110015869140625,
0.0007834434509277344,
-0.07366943359375,
0.054168701171875,
-0.0278167724609375,
0.01357269287109375,
0.00661468505859375,
0.01471710205078125,
-0.01947021484375,
-0.0286865234375,
-0.0006775856018066406,
0.0029449462890625,
0.015106201171875,
0.033355712890625,
0.0009984970092773438,
-0.0031452178955078125,
-0.020599365234375,
0.002567291259765625,
-0.005107879638671875,
0.0018634796142578125,
0.01027679443359375,
0.041412353515625,
0.01392364501953125,
0.0036869049072265625,
0.0181427001953125,
0.001373291015625,
0.002857208251953125,
-0.00927734375,
-0.03515625,
0.007228851318359375,
-0.0160369873046875,
0.042083740234375,
0.00665283203125,
-0.043609619140625,
0.03314208984375,
0.0005846023559570312,
-0.037841796875,
0.0227813720703125,
0.005168914794921875,
0.014434814453125,
0.006786346435546875,
0.0135040283203125,
-0.0005698204040527344,
0.00473785400390625,
0.034088134765625,
-0.0126190185546875,
-0.0006365776062011719,
0.0257415771484375,
-0.01065826416015625,
0.02215576171875,
0.00286102294921875,
-0.007419586181640625,
-0.0157928466796875,
0.04473876953125,
-0.031280517578125,
0.003345489501953125,
-0.0304412841796875,
0.01401519775390625,
-0.0015249252319335938,
-0.01018524169921875,
-0.0235137939453125,
0.005596160888671875,
0.03582763671875,
-0.00266265869140625,
-0.0219879150390625,
0.0252532958984375,
0.0112152099609375,
-0.000008106231689453125,
-0.01018524169921875,
0.0095367431640625,
0.01050567626953125,
0.03619384765625,
-0.001422882080078125,
-0.005260467529296875,
-0.0286865234375,
-0.005634307861328125,
0.0206146240234375,
-0.0300750732421875,
-0.040618896484375,
0.01934814453125,
-0.0288238525390625,
-0.004444122314453125,
0.018310546875,
0.0191650390625,
-0.01065826416015625,
-0.0024051666259765625,
0.0301666259765625,
-0.052215576171875,
-0.0160675048828125,
0.00896453857421875,
-0.01727294921875,
-0.01092529296875,
-0.0005660057067871094,
0.01727294921875,
0.0048370361328125,
-0.032745361328125,
-0.01248931884765625,
0.0062255859375,
-0.01348114013671875,
-0.0124664306640625,
0.0345458984375,
0.01055908203125,
0.0269622802734375,
0.014190673828125,
0.01953125,
-0.039337158203125,
0.01947021484375,
-0.0037899017333984375,
-0.0010004043579101562,
0.00875091552734375,
-0.02618408203125,
0.00765228271484375,
-0.0178680419921875,
0.0306549072265625,
0.0242462158203125,
0.006290435791015625,
0.0033588409423828125,
-0.00383758544921875,
-0.00897216796875,
0.0190582275390625,
0.00832366943359375,
-0.0238800048828125,
-0.0234222412109375,
-0.003818511962890625,
0.0292816162109375,
-0.018218994140625,
0.0022144317626953125,
-0.005767822265625,
-0.006977081298828125,
0.00518798828125,
0.0150146484375,
0.0172119140625,
0.009063720703125,
-0.006343841552734375,
0.01232147216796875,
0.01428985595703125,
0.01407623291015625,
0.032562255859375,
-0.00844573974609375,
0.0204620361328125,
-0.0206451416015625,
0.00891876220703125,
0.032562255859375,
-0.008056640625,
-0.005588531494140625,
-0.001827239990234375,
-0.035736083984375,
0.0236968994140625,
0.0235137939453125,
-0.036224365234375,
-0.0155792236328125,
-0.013153076171875,
-0.01012420654296875,
-0.03778076171875,
0.007625579833984375,
-0.0059051513671875,
-0.00952911376953125,
-0.0025310516357421875,
0.0146942138671875,
-0.0155181884765625,
0.0061187744140625,
0.016082763671875,
-0.01380157470703125,
-0.006671905517578125,
-0.0360107421875,
0.0137939453125,
-0.01904296875,
-0.0107879638671875,
0.0125274658203125,
0.01155853271484375,
-0.03656005859375,
0.0179443359375,
0.033447265625,
-0.0087432861328125,
-0.0143585205078125,
0.0277099609375,
0.01424407958984375,
0.01837158203125,
0.00484466552734375,
-0.0248870849609375,
0.041290283203125,
0.029510498046875,
-0.01209259033203125,
0.009735107421875,
-0.0007915496826171875,
0.031646728515625,
-0.035064697265625,
-0.01093292236328125,
0.00669097900390625,
0.0265655517578125,
-0.032012939453125,
0.00678253173828125,
0.005527496337890625,
0.0023670196533203125,
-0.0016107559204101562,
-0.03350830078125,
-0.0011701583862304688,
0.0016317367553710938,
-0.026397705078125,
0.0294036865234375,
-0.0305023193359375,
0.0214385986328125,
-0.0100860595703125,
-0.011962890625,
-0.0029449462890625,
0.0001283884048461914,
-0.00284576416015625,
0.0210418701171875,
0.0016841888427734375,
0.00589752197265625,
0.0189971923828125,
-0.005748748779296875,
0.03631591796875,
0.012939453125,
0.0129852294921875,
0.0259246826171875,
-0.004302978515625,
-0.0207366943359375,
0.007354736328125,
-0.0036182403564453125,
0.01541900634765625,
0.006046295166015625,
0.001880645751953125,
0.035675048828125,
-0.0176239013671875,
0.0090789794921875,
-0.0120086669921875,
0.033538818359375,
-0.033905029296875,
-0.0184173583984375,
-0.04498291015625,
-0.01348876953125,
-0.01070404052734375,
-0.0194854736328125,
0.03973388671875,
-0.004673004150390625,
0.015869140625,
0.0013141632080078125,
-0.0211334228515625,
0.015472412109375,
-0.01319122314453125,
0.000949859619140625,
0.024322509765625,
-0.03497314453125,
0.01317596435546875,
-0.00921630859375,
-0.0150299072265625,
-0.03216552734375,
0.0028247833251953125,
0.03546142578125,
-0.00039958953857421875,
0.0292205810546875,
0.00734710693359375,
0.02447509765625,
-0.004245758056640625,
-0.01078033447265625,
0.0035610198974609375,
-0.0010805130004882812,
-0.004241943359375,
-0.02008056640625,
0.00666046142578125,
0.01561737060546875,
0.03961181640625,
0.03302001953125,
-0.0218048095703125,
-0.00885772705078125,
-0.026885986328125,
0.025360107421875,
0.0119476318359375,
-0.0167236328125,
-0.03216552734375,
-0.031768798828125,
0.026702880859375,
-0.0052490234375,
-0.0228118896484375,
-0.00868988037109375,
0.0107879638671875,
0.003582000732421875,
0.0013866424560546875,
-0.0032100677490234375,
0.035858154296875,
0.02972412109375,
0.03704833984375,
0.00511932373046875,
0.060699462890625,
0.002902984619140625,
-0.0017852783203125,
0.005817413330078125,
0.0243988037109375,
0.021697998046875,
0.01355743408203125,
-0.003887176513671875,
-0.01334381103515625,
0.00026702880859375,
-0.0004010200500488281,
-0.01522064208984375,
-0.0248260498046875,
0.0180511474609375,
0.0279388427734375,
-0.0165557861328125,
-0.0190277099609375,
0.002788543701171875,
-0.01445770263671875,
-0.03424072265625,
-0.035491943359375,
0.0287628173828125,
0.00673675537109375,
-0.0364990234375,
-0.0367431640625,
-0.0173797607421875,
0.009552001953125,
-0.0003459453582763672,
-0.01041412353515625,
0.0241851806640625,
0.006580352783203125,
0.0124053955078125,
-0.0010776519775390625,
0.01433563232421875,
-0.0126190185546875,
-0.02655029296875,
-0.002262115478515625,
0.0276947021484375,
-0.010467529296875,
0.00044655799865722656,
-0.0198974609375,
0.00785064697265625,
-0.0090179443359375,
0.0182647705078125,
-0.01019287109375,
0.0178070068359375,
-0.002063751220703125,
-0.00647735595703125,
-0.002811431884765625,
0.0203094482421875,
-0.0079193115234375,
-0.0187835693359375,
-0.0290069580078125,
-0.00490570068359375,
-0.022674560546875,
-0.01100921630859375,
0.00475311279296875,
-0.0093231201171875,
-0.03118896484375,
-0.01213836669921875,
-0.0256500244140625,
-0.0203704833984375,
0.01019287109375,
-0.031829833984375,
-0.020111083984375,
0.0084381103515625,
0.0253753662109375,
-0.006839752197265625,
-0.036712646484375,
-0.004695892333984375,
0.0086669921875,
-0.02081298828125,
0.00001150369644165039,
-0.0233001708984375,
0.013885498046875,
0.020263671875,
-0.007965087890625,
-0.0006384849548339844,
-0.04156494140625,
0.0178375244140625,
0.01551055908203125,
-0.04986572265625,
0.0306854248046875,
0.0151214599609375,
0.04718017578125,
0.05975341796875,
-0.007472991943359375,
-0.007617950439453125,
-0.00890350341796875,
-0.0035915374755859375,
-0.006923675537109375,
-0.006008148193359375,
-0.0208587646484375,
0.03289794921875,
0.0070648193359375,
-0.00539398193359375,
-0.032958984375,
0.018310546875,
0.0196533203125,
0.0166015625,
0.01580810546875,
-0.01398468017578125,
-0.0018529891967773438,
-0.00957489013671875,
0.0333251953125,
0.007358551025390625,
-0.004390716552734375,
-0.02325439453125,
-0.0301971435546875,
0.007602691650390625,
-0.0020847320556640625,
0.0299224853515625,
-0.004329681396484375,
-0.0184326171875,
0.002811431884765625,
-0.0018157958984375,
-0.0229339599609375,
0.0194244384765625,
0.00014781951904296875,
-0.0031490325927734375,
0.027435302734375,
0.00225830078125,
-0.01465606689453125,
0.028961181640625,
-0.006839752197265625,
-0.00220489501953125,
0.015411376953125,
0.0057220458984375,
0.005706787109375,
-0.048004150390625,
-0.007228851318359375,
0.02569580078125,
-0.0034389495849609375,
-0.012481689453125,
0.017608642578125,
-0.007904052734375,
0.03839111328125,
-0.0372314453125,
-0.00958251953125,
0.01186370849609375,
0.00995635986328125,
-0.0389404296875,
-0.0206298828125,
0.00701904296875,
0.020965576171875,
-0.0161285400390625,
0.004703521728515625,
-0.00914764404296875,
0.0010766983032226562,
-0.012237548828125,
0.0191192626953125,
-0.00017130374908447266,
0.01605224609375,
0.0294342041015625,
-0.026702880859375,
-0.0062255859375,
0.006732940673828125,
0.0360107421875,
0.03277587890625,
-0.01953125,
0.006378173828125,
0.0066375732421875,
0.007152557373046875,
0.0101776123046875,
-0.01520538330078125,
-0.002292633056640625,
0.0292510986328125,
-0.006465911865234375,
-0.0270538330078125,
-0.01202392578125,
0.021026611328125,
0.035003662109375,
0.0020008087158203125,
0.01617431640625,
0.0182037353515625,
0.0009489059448242188,
-0.033111572265625,
-0.006229400634765625,
-0.06341552734375,
-0.0338134765625,
0.0108795166015625,
-0.043365478515625,
-0.00997161865234375,
0.0186920166015625,
-0.01197052001953125,
0.009552001953125,
0.0018253326416015625,
0.000919342041015625,
-0.01708984375,
-0.02154541015625,
0.004261016845703125,
-0.006603240966796875,
0.044677734375,
-0.030517578125,
0.007663726806640625,
-0.0193328857421875,
0.00930023193359375,
0.00891876220703125,
0.01479339599609375,
-0.024505615234375,
-0.031829833984375,
-0.0130157470703125,
-0.0050048828125,
0.0244903564453125,
-0.0210113525390625,
-0.0027446746826171875,
0.004329681396484375,
-0.0173187255859375,
0.0010766983032226562,
-0.01145172119140625,
-0.00246429443359375,
-0.003643035888671875,
-0.0287628173828125,
-0.0221710205078125,
0.005138397216796875,
0.004405975341796875,
-0.028167724609375,
-0.0027446746826171875,
-0.02789306640625,
0.0256805419921875,
0.024261474609375,
-0.033782958984375,
0.0018281936645507812,
0.018218994140625,
-0.0155487060546875,
0.0031299591064453125,
-0.0167999267578125,
-0.0038051605224609375,
0.0112152099609375,
-0.01134490966796875,
0.00226593017578125,
0.01104736328125,
0.0013475418090820312,
-0.001216888427734375,
0.009857177734375,
-0.00368499755859375,
-0.0379638671875,
0.00008618831634521484,
-0.004085540771484375,
0.01316070556640625,
0.02911376953125,
0.0084075927734375,
-0.0247802734375,
-0.017120361328125,
-0.022308349609375,
0.0221405029296875,
0.00579071044921875,
-0.006191253662109375,
-0.0204315185546875,
-0.00914764404296875,
0.0026493072509765625,
0.0008001327514648438,
-0.01593017578125,
-0.035430908203125,
-0.003643035888671875,
0.0009002685546875,
-0.033447265625,
-0.01064300537109375,
0.008758544921875,
0.022308349609375,
-0.05718994140625,
-0.00458526611328125,
0.0102386474609375,
0.0159454345703125
] |
ours_519
|
The answer is \( 6859000 \).
In general, for \( n \geq 0 \), let \( s_{n} \) denote the number of subsets of \(\{1,2, \ldots, 3^{n}\}\) such that \( 2 \mid \nu_{3}(a-b) \) for any distinct \( a, b \in S \), and \( t_{n} \) the number of subsets with \( 2 \nmid \nu_{3}(a-b) \) for any distinct \( a, b \in S \). Clearly, \( s_{0} = t_{0} = 2 \), and for \( n \geq 2 \), \( s_{n} = t_{n-1}^{3} \) while \( t_{n} = 3 s_{n-1} - 2 \).
Thus,
\[
s_{4} = t_{3}^{3} = \left(3 s_{2} - 2\right)^{3} = \left(3\left(3 s_{0} - 2\right)^{3} - 2\right)^{3} = 190^{3} = 6859000
\]
is the desired answer.
\(\boxed{6859000}\)
|
6859000
|
{
"competition": "us_comps",
"dataset": "Ours",
"posts": null,
"source": "OMOSoln2-2.md"
}
|
For positive integers \( n \), let \(\nu_{3}(n)\) denote the largest integer \( k \) such that \( 3^{k} \) divides \( n \). Find the number of subsets \( S \) (possibly containing 0 or 1 elements) of \(\{1,2, \ldots, 81\}\) such that for any distinct \( a, b \in S \) with \( a > b \), \(\nu_{3}(a-b)\) is even.
|
[
"/Mathematics/DiscreteMathematics/Combinatorics/Enumeration",
"/Mathematics/DiscreteMathematics/Combinatorics/GeneralCombinatorics",
"/Mathematics/DiscreteMathematics/DivisionProblems/NumberPartitioningProblem",
"/Mathematics/DiscreteMathematics/GeneralDiscreteMathematics/DiscreteMath",
"/Mathematics/DiscreteMathematics/GeneralDiscreteMathematics/DiscreteMathematics",
"/Mathematics/DiscreteMathematics/GeneralDiscreteMathematics/FiniteMathematics",
"/Mathematics/DiscreteMathematics/RecurrenceEquations/RecurrenceEquation",
"/Mathematics/DiscreteMathematics/RecurrenceEquations/RecurrenceRelation",
"/Mathematics/NumberTheory/GeneralNumberTheory/AdditiveNumberTheory",
"/Mathematics/NumberTheory/GeneralNumberTheory/ElementaryMethods",
"/Mathematics/NumberTheory/GeneralNumberTheory/ElementaryNumberTheory",
"/Mathematics/NumberTheory/GeneralNumberTheory/HigherArithmetic",
"/Mathematics/NumberTheory/GeneralNumberTheory/NumberTheory",
"/Mathematics/NumberTheory/NumberTheoreticFunctions/GeneralNumberTheoreticFunctions",
"/Mathematics/NumberTheory/NumberTheoreticFunctions/IntegerFunctions",
"/Mathematics/NumberTheory/Parity",
"/Mathematics/NumberTheory/p-adicNumbers/p-adicNumber"
] |
Exploit the self‑similar block structure of {1,…,3^n} to separate cases by even/odd ν₃ differences and obtain recurrences sₙ = t_{n‑1}³, tₙ = 3·s_{n‑1} – 2.
|
[
-0.00004184246063232422,
-0.0164337158203125,
0.01947021484375,
-0.0163421630859375,
-0.00022017955780029297,
0.00588226318359375,
-0.012939453125,
-0.00881195068359375,
0.005245208740234375,
-0.030120849609375,
0.03424072265625,
-0.035675048828125,
-0.000865936279296875,
-0.0323486328125,
-0.022857666015625,
-0.01435089111328125,
0.043792724609375,
0.03631591796875,
-0.03472900390625,
-0.0031261444091796875,
-0.0095977783203125,
-0.0223236083984375,
-0.00867462158203125,
0.061309814453125,
-0.01352691650390625,
-0.026397705078125,
-0.017333984375,
0.039459228515625,
0.0289459228515625,
0.021270751953125,
-0.00946044921875,
-0.034454345703125,
0.0106658935546875,
-0.015350341796875,
0.006145477294921875,
0.00583648681640625,
0.0191192626953125,
-0.004245758056640625,
0.040802001953125,
-0.0238494873046875,
-0.00028324127197265625,
0.01788330078125,
-0.013702392578125,
0.00446319580078125,
0.035125732421875,
0.00746917724609375,
-0.0029659271240234375,
-0.0008959770202636719,
0.00629425048828125,
-0.004955291748046875,
-0.003231048583984375,
0.0081787109375,
-0.0237274169921875,
-0.0174713134765625,
-0.00104522705078125,
-0.05059814453125,
0.01605224609375,
0.0024814605712890625,
-0.019317626953125,
0.0022411346435546875,
0.003795623779296875,
-0.005950927734375,
-0.01311492919921875,
-0.026275634765625,
-0.004444122314453125,
-0.015899658203125,
-0.00864410400390625,
0.0154266357421875,
0.0098114013671875,
0.0001817941665649414,
0.0161285400390625,
0.00896453857421875,
-0.01422882080078125,
0.031646728515625,
0.01313018798828125,
-0.0039520263671875,
-0.00400543212890625,
0.021514892578125,
0.006137847900390625,
0.0233306884765625,
0.027374267578125,
0.0012531280517578125,
-0.0097503662109375,
0.0019474029541015625,
0.0131072998046875,
0.01055145263671875,
-0.0213165283203125,
-0.0014801025390625,
-0.0026226043701171875,
-0.01447296142578125,
-0.01299285888671875,
0.020599365234375,
0.0097808837890625,
0.023345947265625,
-0.00849151611328125,
-0.0009403228759765625,
0.02105712890625,
-0.007099151611328125,
-0.00860595703125,
0.002872467041015625,
0.00505828857421875,
0.009185791015625,
0.0259552001953125,
-0.0221405029296875,
-0.0318603515625,
-0.01922607421875,
-0.0151214599609375,
-0.0030670166015625,
-0.001949310302734375,
-0.00933837890625,
0.00699615478515625,
-0.024383544921875,
0.0159454345703125,
0.0233001708984375,
-0.01369476318359375,
0.01125335693359375,
0.01641845703125,
-0.0309295654296875,
-0.00905609130859375,
-0.0435791015625,
0.00539398193359375,
0.0042724609375,
0.00855255126953125,
-0.0081787109375,
-0.0037403106689453125,
0.01430511474609375,
-0.0174713134765625,
-0.0076446533203125,
0.0023059844970703125,
0.000026404857635498047,
0.024383544921875,
0.0115966796875,
-0.0201873779296875,
-0.0254974365234375,
-0.035797119140625,
-0.020111083984375,
0.0184478759765625,
-0.0196380615234375,
-0.0025844573974609375,
-0.006015777587890625,
0.0247039794921875,
-0.005828857421875,
0.0083770751953125,
0.0213623046875,
-0.0147705078125,
0.035919189453125,
-0.006572723388671875,
-0.03863525390625,
-0.003337860107421875,
0.010406494140625,
-0.015960693359375,
-0.0005278587341308594,
-0.017730712890625,
-0.019683837890625,
-0.00881195068359375,
-0.0085906982421875,
0.00911712646484375,
0.01276397705078125,
-0.028778076171875,
-0.0016002655029296875,
-0.030059814453125,
0.0005707740783691406,
-0.012664794921875,
0.051116943359375,
-0.004917144775390625,
-0.002532958984375,
0.020751953125,
-0.01476287841796875,
0.0095367431640625,
0.003887176513671875,
0.016326904296875,
-0.0121002197265625,
-0.0004050731658935547,
-0.01439666748046875,
0.004154205322265625,
0.006313323974609375,
0.006519317626953125,
0.0034275054931640625,
-0.01168060302734375,
0.02923583984375,
0.004108428955078125,
-0.02532958984375,
0.0256805419921875,
0.004489898681640625,
0.0010957717895507812,
-0.0202178955078125,
-0.0063018798828125,
0.025360107421875,
0.035736083984375,
0.00917816162109375,
-0.032379150390625,
-0.00994873046875,
-0.0121002197265625,
0.0174407958984375,
-0.00392913818359375,
-0.01470184326171875,
-0.022918701171875,
-0.0013628005981445312,
0.0193634033203125,
0.00792694091796875,
0.0007963180541992188,
-0.0057373046875,
-0.014495849609375,
-0.006664276123046875,
0.00628662109375,
0.0010633468627929688,
0.00885009765625,
-0.01218414306640625,
0.008819580078125,
-0.008270263671875,
-0.0130462646484375,
0.0032520294189453125,
0.003978729248046875,
-0.0169525146484375,
0.002597808837890625,
-0.006366729736328125,
-0.02825927734375,
-0.00562286376953125,
0.00007092952728271484,
-0.04705810546875,
0.00469207763671875,
0.01404571533203125,
-0.0031681060791015625,
-0.00199127197265625,
-0.023345947265625,
0.008544921875,
0.00675201416015625,
0.01226806640625,
0.0173187255859375,
0.016143798828125,
-0.00016760826110839844,
0.01092529296875,
-0.0013608932495117188,
-0.0012035369873046875,
0.0029125213623046875,
-0.007110595703125,
-0.0268096923828125,
-0.01177978515625,
-0.0076141357421875,
-0.006549835205078125,
0.053619384765625,
0.0010328292846679688,
0.00972747802734375,
-0.01806640625,
-0.0021533966064453125,
0.01152801513671875,
0.0016021728515625,
0.007266998291015625,
-0.00043487548828125,
-0.00811767578125,
-0.0229339599609375,
0.0084381103515625,
-0.00814056396484375,
-0.0212249755859375,
-0.00011283159255981445,
-0.0048065185546875,
-0.0015935897827148438,
0.047607421875,
-0.0185089111328125,
-0.04046630859375,
0.005908966064453125,
0.00025153160095214844,
-0.0057373046875,
-0.007808685302734375,
0.00958251953125,
-0.0000209808349609375,
0.04583740234375,
-0.0162353515625,
0.00927734375,
0.0100250244140625,
0.01348876953125,
0.00885772705078125,
-0.01158905029296875,
0.01480865478515625,
0.0016345977783203125,
-0.01508331298828125,
-0.00249481201171875,
0.001739501953125,
0.01751708984375,
-0.0177459716796875,
0.01462554931640625,
-0.00669097900390625,
0.03265380859375,
-0.0029582977294921875,
0.00722503662109375,
-0.039337158203125,
-0.0016469955444335938,
0.005123138427734375,
-0.007099151611328125,
0.024871826171875,
0.0089569091796875,
0.018646240234375,
-0.0121612548828125,
-0.00428009033203125,
0.034027099609375,
-0.05560302734375,
-0.00957489013671875,
0.0105743408203125,
0.0205230712890625,
0.00909423828125,
0.00658416748046875,
-0.005001068115234375,
0.023681640625,
0.0093231201171875,
-0.01169586181640625,
0.0070343017578125,
-0.00429534912109375,
-0.0037403106689453125,
-0.0287017822265625,
-0.0142822265625,
-0.0013208389282226562,
0.0031642913818359375,
-0.0085601806640625,
-0.0035343170166015625,
0.00252532958984375,
-0.038970947265625,
0.0015649795532226562,
0.0177764892578125,
0.007266998291015625,
-0.002597808837890625,
0.009735107421875,
-0.01104736328125,
-0.002918243408203125,
0.01094818115234375,
0.0194091796875,
-0.00963592529296875,
0.0019588470458984375,
0.01384735107421875,
-0.0335693359375,
0.0237579345703125,
-0.039886474609375,
0.0168304443359375,
-0.015228271484375,
-0.0220947265625,
-0.0110321044921875,
0.0284271240234375,
-0.0132904052734375,
0.0295562744140625,
-0.0041046142578125,
-0.01522064208984375,
-0.0042724609375,
0.01227569580078125,
0.01317596435546875,
-0.000041484832763671875,
-0.041412353515625,
-0.00682830810546875,
-0.0165557861328125,
0.00344085693359375,
-0.0110931396484375,
-0.00971221923828125,
0.01105499267578125,
-0.010406494140625,
-0.0113372802734375,
0.01161956787109375,
-0.0499267578125,
0.0022220611572265625,
-0.050384521484375,
-0.017181396484375,
-0.0004811286926269531,
-0.00290679931640625,
0.005153656005859375,
0.01145172119140625,
-0.006832122802734375,
0.0117034912109375,
0.0084228515625,
-0.0233154296875,
-0.029022216796875,
-0.00470733642578125,
-0.0151214599609375,
-0.037689208984375,
0.0153656005859375,
-0.04010009765625,
-0.01277923583984375,
-0.042877197265625,
-0.047515869140625,
0.0156402587890625,
-0.004451751708984375,
-0.02435302734375,
-0.004901885986328125,
0.01410675048828125,
-0.00860595703125,
0.0121307373046875,
0.0035858154296875,
0.03961181640625,
0.0171966552734375,
-0.01255035400390625,
-0.01372528076171875,
-0.08343505859375,
-0.0188140869140625,
0.01153564453125,
-0.01264190673828125,
0.0242919921875,
0.0045318603515625,
0.0323486328125,
0.03900146484375,
-0.032958984375,
0.0019588470458984375,
-0.0140228271484375,
0.040496826171875,
-0.0194854736328125,
0.011962890625,
-0.0171356201171875,
-0.007534027099609375,
0.01947021484375,
-0.004878997802734375,
-0.0038280487060546875,
-0.0026721954345703125,
0.0159912109375,
-0.0088348388671875,
0.0124053955078125,
0.04144287109375,
-0.003204345703125,
-0.01184844970703125,
-0.005558013916015625,
0.03594970703125,
-0.004730224609375,
0.0266876220703125,
0.0059356689453125,
-0.053253173828125,
-0.0052490234375,
-0.0010042190551757812,
-0.01328277587890625,
0.001220703125,
0.0008697509765625,
0.0207672119140625,
0.01088714599609375,
-0.0235443115234375,
0.03570556640625,
0.00928497314453125,
0.0164337158203125,
0.021820068359375,
-0.02789306640625,
0.0187530517578125,
0.0233154296875,
0.0165252685546875,
0.0221710205078125,
0.0111541748046875,
0.005825042724609375,
-0.02099609375,
0.01512908935546875,
0.00434112548828125,
-0.004741668701171875,
-0.0078277587890625,
-0.00698089599609375,
0.041900634765625,
0.0214385986328125,
-0.0010166168212890625,
0.0240020751953125,
-0.05047607421875,
0.017669677734375,
-0.011871337890625,
-0.07513427734375,
-0.031707763671875,
0.01256561279296875,
-0.0115509033203125,
0.0175323486328125,
0.01458740234375,
-0.0269927978515625,
-0.014678955078125,
-0.057281494140625,
0.00862884521484375,
0.0214385986328125,
0.0264739990234375,
0.03302001953125,
-0.0006213188171386719,
0.01074981689453125,
-0.01473236083984375,
0.0079803466796875,
0.01070404052734375,
-0.0233306884765625,
-0.005191802978515625,
-0.0205841064453125,
-0.006793975830078125,
-0.0016851425170898438,
-0.0474853515625,
0.01313018798828125,
-0.01374053955078125,
0.0207672119140625,
-0.0126495361328125,
-0.0020923614501953125,
0.005649566650390625,
0.01055908203125,
-0.00670623779296875,
0.07073974609375,
-0.00623321533203125,
0.013031005859375,
-0.0035343170166015625,
0.0242156982421875,
0.00771331787109375,
0.0034465789794921875,
0.0208282470703125,
0.0224151611328125,
-0.05120849609375,
-0.02191162109375,
-0.016143798828125,
-0.0092010498046875,
0.02001953125,
0.01543426513671875,
-0.01494598388671875,
-0.00533294677734375,
0.00872039794921875,
-0.0257568359375,
0.0041351318359375,
0.010101318359375,
-0.0037994384765625,
0.01505279541015625,
0.0189208984375,
-0.01016998291015625,
0.0095977783203125,
-0.00531768798828125,
0.00396728515625,
0.0198974609375,
0.014892578125,
-0.00975799560546875,
-0.01369476318359375,
-0.0181732177734375,
0.00931549072265625,
0.00048828125,
-0.009185791015625,
-0.0233917236328125,
-0.0213775634765625,
0.01457977294921875,
0.01184844970703125,
0.017303466796875,
-0.01438140869140625,
0.00353240966796875,
0.0115814208984375,
-0.0247039794921875,
0.0172576904296875,
0.0022487640380859375,
0.0189361572265625,
-0.00644683837890625,
0.03326416015625,
-0.035430908203125,
0.0031890869140625,
-0.0034160614013671875,
0.0272979736328125,
-0.02587890625,
0.031890869140625,
0.041046142578125,
-0.0035343170166015625,
-0.009735107421875,
-0.006984710693359375,
-0.0016965866088867188,
0.006328582763671875,
-0.0240936279296875,
0.0014619827270507812,
0.00414276123046875,
-0.0251617431640625,
-0.0009698867797851562,
-0.00591278076171875,
-0.0074920654296875,
-0.01531219482421875,
0.01458740234375,
-0.040283203125,
0.0313720703125,
-0.028350830078125,
0.005168914794921875,
0.007659912109375,
-0.0089569091796875,
-0.0022792816162109375,
0.017059326171875,
0.01261138916015625,
0.0201263427734375,
0.0090484619140625,
0.0025272369384765625,
-0.0145111083984375,
-0.0010986328125,
-0.00785064697265625,
-0.02508544921875,
0.00457763671875,
-0.01129913330078125,
0.0150146484375,
0.01520538330078125,
-0.0084686279296875,
-0.01322174072265625,
-0.00798797607421875,
0.002384185791015625,
0.0137939453125,
-0.042022705078125,
0.0225830078125,
-0.01129913330078125,
0.006244659423828125,
0.041656494140625,
0.0217742919921875,
-0.00853729248046875,
0.0023365020751953125,
0.042755126953125,
0.011993408203125,
0.012237548828125,
-0.01091766357421875,
0.0233917236328125,
0.001422882080078125,
0.0305938720703125,
-0.0261688232421875,
-0.036895751953125,
0.036041259765625,
0.019378662109375,
-0.021484375,
-0.0137786865234375,
-0.01132965087890625,
-0.0042877197265625,
-0.01055908203125,
0.018798828125,
0.00591278076171875,
-0.02813720703125,
0.0189208984375,
0.0028057098388671875,
0.0029888153076171875,
-0.005290985107421875,
-0.0169677734375,
0.0160675048828125,
-0.011383056640625,
-0.005786895751953125,
0.0205230712890625,
0.013641357421875,
-0.021575927734375,
0.0111083984375,
0.00888824462890625,
-0.0154571533203125,
-0.007648468017578125,
0.02288818359375,
0.019195556640625,
-0.0189666748046875,
-0.006336212158203125,
0.02459716796875,
0.0123748779296875,
-0.0364990234375,
0.007671356201171875,
-0.0267181396484375,
0.0023288726806640625,
0.0247344970703125,
0.014373779296875,
-0.032867431640625,
0.004863739013671875,
0.0088958740234375,
-0.0161895751953125,
0.0019178390502929688,
-0.026153564453125,
-0.015655517578125,
-0.002658843994140625,
0.01496124267578125,
0.0030765533447265625,
-0.04931640625,
-0.00789642333984375,
0.01898193359375,
-0.0011425018310546875,
0.0016632080078125,
-0.0285797119140625,
0.003925323486328125,
-0.018280029296875,
0.0123748779296875,
-0.00855255126953125,
0.004825592041015625,
-0.006710052490234375,
0.007080078125,
-0.016845703125,
-0.0240631103515625,
0.017730712890625,
-0.00254058837890625,
0.014190673828125,
-0.02911376953125,
0.01446533203125,
0.0031375885009765625,
-0.01371002197265625,
-0.01898193359375,
0.0285797119140625,
-0.0003223419189453125,
0.00640106201171875,
-0.0160369873046875,
0.0236358642578125,
-0.0184326171875,
0.0081939697265625,
-0.03680419921875,
-0.0021266937255859375,
-0.0216217041015625,
0.005855560302734375,
-0.0102691650390625,
0.00255584716796875,
0.036163330078125,
0.0184326171875,
0.0171661376953125,
0.0113983154296875,
-0.0133514404296875,
0.031341552734375,
0.020782470703125,
-0.0036449432373046875,
0.004535675048828125,
-0.03082275390625,
-0.0232086181640625,
0.0040740966796875,
0.00759124755859375,
0.015289306640625,
0.0164794921875,
0.0125274658203125,
-0.0207061767578125,
-0.004825592041015625,
-0.0180511474609375,
-0.02142333984375,
-0.0070953369140625,
0.003627777099609375,
0.007472991943359375,
0.0059814453125,
0.022308349609375,
0.00801849365234375,
-0.0158843994140625,
-0.0304412841796875,
-0.006866455078125,
-0.0107421875,
0.006725311279296875,
-0.004673004150390625,
-0.0273590087890625,
-0.049896240234375,
0.02325439453125,
-0.0195770263671875,
0.02252197265625,
-0.00902557373046875,
0.01485443115234375,
0.001556396484375,
-0.00948333740234375,
-0.0401611328125,
-0.0250244140625,
-0.01348876953125,
-0.004596710205078125,
0.004024505615234375,
0.0163421630859375,
-0.013519287109375,
-0.01103973388671875,
-0.031402587890625,
-0.01235198974609375,
-0.0037708282470703125,
-0.024505615234375,
-0.010162353515625,
-0.00498199462890625,
-0.005283355712890625,
-0.0211181640625,
0.008880615234375,
-0.031097412109375,
0.00007891654968261719,
-0.0125579833984375,
0.037750244140625,
-0.0093231201171875,
-0.0033721923828125,
-0.016448974609375,
0.001598358154296875,
0.0097198486328125,
-0.00814056396484375,
-0.01224517822265625,
-0.004993438720703125,
-0.01189422607421875,
0.01302337646484375,
-0.001949310302734375,
0.018035888671875,
-0.06414794921875,
0.0128936767578125,
-0.01236724853515625,
-0.021942138671875,
-0.0024280548095703125,
-0.0174560546875,
0.01739501953125,
-0.0131072998046875,
0.00569915771484375,
-0.010498046875,
-0.01177978515625,
0.0306549072265625,
-0.01702880859375,
-0.008453369140625,
-0.0165252685546875,
-0.023101806640625,
0.040557861328125,
-0.01483154296875,
0.0113067626953125,
0.0225067138671875,
0.0222015380859375,
0.0021820068359375,
-0.0104827880859375,
-0.0186004638671875,
0.017669677734375,
0.07818603515625,
-0.0251922607421875,
-0.01197052001953125,
-0.0256500244140625,
0.00998687744140625,
0.0156402587890625,
0.01151275634765625,
-0.01438140869140625,
-0.031951904296875,
-0.0146331787109375,
0.012420654296875,
-0.00629425048828125,
0.0005574226379394531,
-0.0018262863159179688,
-0.005405426025390625,
-0.021759033203125,
0.018157958984375,
0.00502777099609375,
0.0095672607421875,
-0.0157928466796875,
-0.0296478271484375,
0.018585205078125,
0.00933837890625,
-0.024505615234375,
-0.006374359130859375,
0.0159759521484375,
-0.0045013427734375,
-0.00762176513671875,
0.0284271240234375,
-0.005767822265625,
0.0036945343017578125,
-0.01180267333984375,
0.005176544189453125,
0.0161285400390625,
-0.02264404296875,
-0.030853271484375,
-0.0002918243408203125,
0.0040435791015625,
0.0045318603515625,
0.0240020751953125,
-0.00937652587890625,
0.033843994140625,
-0.01654052734375,
0.0184326171875,
-0.0091094970703125,
-0.016265869140625,
-0.0110626220703125,
0.005184173583984375,
0.00897979736328125,
0.005939483642578125,
0.0025787353515625,
-0.0047149658203125,
-0.01480865478515625,
0.00409698486328125,
0.00615692138671875,
-0.005741119384765625,
0.0183258056640625,
0.0196380615234375,
0.016326904296875,
0.0025882720947265625,
0.0166168212890625,
-0.049041748046875,
-0.02734375,
0.0222625732421875,
0.0161590576171875,
-0.012451171875,
-0.0126495361328125,
-0.022613525390625,
-0.033843994140625,
-0.028564453125,
0.0063018798828125,
-0.014251708984375,
-0.002960205078125,
-0.0011034011840820312,
-0.0163726806640625,
0.006946563720703125,
0.01345062255859375,
-0.0126190185546875,
0.0002765655517578125,
0.0280609130859375,
-0.0156402587890625,
0.0089111328125,
-0.016632080078125,
-0.0148468017578125,
-0.00551605224609375,
-0.0009255409240722656,
0.01123046875,
0.01021575927734375,
-0.026275634765625,
-0.0160064697265625,
-0.01397705078125,
0.0236663818359375,
0.0310821533203125,
0.00977325439453125,
0.0055084228515625,
0.00450897216796875,
0.0178680419921875,
0.0111083984375,
-0.00502777099609375,
-0.0208740234375,
0.00685882568359375,
0.021148681640625,
0.0302734375,
-0.05938720703125,
-0.0023822784423828125,
0.006893157958984375,
0.007198333740234375,
-0.00238800048828125,
0.033721923828125,
0.018096923828125,
-0.035919189453125,
-0.01192474365234375,
0.0102996826171875,
0.0235748291015625,
-0.007656097412109375,
-0.0196380615234375,
0.0129852294921875,
-0.0297698974609375,
0.00921630859375,
0.01861572265625,
-0.00495147705078125,
-0.038238525390625,
0.0046844482421875,
0.022705078125,
0.00963592529296875,
-0.0008702278137207031,
-0.023712158203125,
-0.00820159912109375,
-0.0266876220703125,
0.0017786026000976562,
0.03204345703125,
0.028778076171875,
-0.01076507568359375,
0.0048675537109375,
0.0184326171875,
0.0110321044921875,
-0.027740478515625,
0.01837158203125,
-0.02117919921875,
0.01629638671875,
0.01044464111328125,
0.036712646484375,
0.0016260147094726562,
0.0228118896484375,
-0.007205963134765625,
0.0145263671875,
-0.00989532470703125,
-0.0144195556640625,
-0.01519775390625,
-0.0146636962890625,
0.00525665283203125,
-0.01666259765625,
0.00726318359375,
0.055938720703125,
-0.0059356689453125,
0.022247314453125,
-0.0298004150390625,
-0.01132965087890625,
-0.008544921875,
-0.0013341903686523438,
-0.00815582275390625,
0.0310211181640625,
-0.01995849609375,
-0.01352691650390625,
0.0011892318725585938,
0.0159149169921875,
0.0289306640625,
0.005008697509765625,
-0.007099151611328125,
0.0158538818359375,
-0.0254669189453125,
-0.0189208984375,
-0.005001068115234375,
-0.0017452239990234375,
0.00208282470703125,
-0.00460052490234375,
0.0360107421875,
0.041290283203125,
0.005218505859375,
-0.023712158203125,
-0.012603759765625,
-0.0364990234375,
0.0260162353515625,
0.021881103515625,
-0.0408935546875,
0.0220947265625,
-0.01031494140625,
0.004627227783203125,
-0.01541900634765625,
-0.00988006591796875,
-0.001483917236328125,
0.00897216796875,
-0.0228729248046875,
-0.005702972412109375,
0.00843048095703125,
-0.0222930908203125,
0.007007598876953125,
0.02490234375,
-0.0209503173828125,
0.026123046875,
0.0277557373046875,
0.05029296875,
-0.01114654541015625,
-0.0177001953125,
-0.0196990966796875,
-0.01311492919921875,
-0.0290985107421875,
-0.0126800537109375,
0.0261688232421875,
-0.04180908203125,
0.026397705078125,
-0.0295867919921875,
-0.0128021240234375,
0.031707763671875,
0.011322021484375,
0.04473876953125,
-0.00823211669921875,
-0.01561737060546875,
-0.01611328125,
-0.0045928955078125,
0.031585693359375,
0.0032482147216796875,
-0.0201568603515625,
-0.01253509521484375,
0.002349853515625,
-0.03460693359375,
0.0428466796875,
-0.00322723388671875,
-0.0021991729736328125,
-0.0206756591796875,
0.0184478759765625,
0.040252685546875,
-0.018280029296875,
-0.0146636962890625,
0.0243988037109375,
0.00786590576171875,
0.005359649658203125,
0.025604248046875,
0.03076171875,
0.0181121826171875,
-0.00862884521484375,
0.032073974609375,
-0.0218963623046875,
0.00432586669921875,
-0.028350830078125,
-0.0168914794921875,
-0.00457000732421875,
-0.02606201171875,
0.00006002187728881836,
-0.00402069091796875,
0.037384033203125,
-0.0010128021240234375,
0.012481689453125,
-0.00128936767578125,
-0.04449462890625,
0.001247406005859375,
-0.0252532958984375,
-0.0174102783203125,
0.0101165771484375,
-0.0343017578125,
0.006877899169921875,
-0.004123687744140625,
0.00839996337890625,
0.005584716796875,
0.01070404052734375,
0.01031494140625,
-0.0112457275390625,
-0.037567138671875,
0.0166473388671875,
0.0137481689453125,
-0.00823211669921875,
-0.00989532470703125,
-0.01010894775390625,
0.02301025390625,
-0.0079498291015625,
0.0153045654296875,
0.0220947265625,
-0.0083465576171875,
-0.00992584228515625,
-0.01373291015625,
0.02947998046875,
0.01397705078125,
-0.0126953125,
-0.0167388916015625,
0.00859832763671875,
-0.01983642578125,
0.0196380615234375,
0.0183563232421875,
-0.02435302734375,
-0.0038661956787109375,
0.022552490234375,
0.0161895751953125,
-0.0184478759765625,
0.021820068359375,
0.045074462890625,
-0.0148468017578125,
0.040985107421875,
-0.0052490234375,
0.004749298095703125,
0.00785064697265625,
-0.01348114013671875,
0.0015954971313476562,
0.006839752197265625,
0.03228759765625,
-0.037017822265625,
-0.00885009765625,
0.0157928466796875,
0.02117919921875,
0.003360748291015625,
-0.0192718505859375,
-0.010284423828125,
0.027130126953125,
-0.0012493133544921875,
0.02545166015625,
-0.016632080078125,
0.00348663330078125,
0.0120849609375,
-0.0219879150390625,
0.003582000732421875,
0.01262664794921875,
-0.0073394775390625,
-0.00643157958984375,
0.004192352294921875,
-0.0011157989501953125,
0.0208892822265625,
0.003631591796875,
0.024810791015625,
0.0162200927734375,
0.020477294921875,
0.0254364013671875,
-0.0026493072509765625,
0.01641845703125,
-0.0015382766723632812,
0.0091705322265625,
0.0251312255859375,
-0.0001888275146484375,
-0.0010080337524414062,
-0.0287322998046875,
-0.031982421875,
-0.0123291015625,
-0.02679443359375,
0.000560760498046875,
-0.01522064208984375,
0.0394287109375,
-0.0213775634765625,
0.0237274169921875,
-0.015777587890625,
0.00978851318359375,
0.007534027099609375,
-0.0003743171691894531,
-0.03375244140625,
0.022186279296875,
0.002368927001953125,
0.00286102294921875,
-0.0029125213623046875,
-0.0215911865234375,
0.005229949951171875,
0.01171875,
-0.0038089752197265625,
-0.0012454986572265625,
0.00373077392578125,
-0.0239410400390625,
0.006259918212890625,
0.0208892822265625,
-0.01280975341796875,
-0.0244903564453125,
-0.03131103515625,
0.0153961181640625,
-0.023651123046875,
0.003459930419921875,
-0.0160980224609375,
0.0109100341796875,
0.009124755859375,
0.03436279296875,
-0.03326416015625,
0.01427459716796875,
-0.005428314208984375,
-0.01255035400390625,
0.00283050537109375,
-0.0229339599609375,
-0.0023479461669921875,
-0.00015103816986083984,
0.01275634765625,
0.0085296630859375,
0.039215087890625,
0.0193634033203125,
-0.01349639892578125,
-0.006805419921875,
-0.004425048828125,
0.031829833984375,
-0.021209716796875,
-0.00026702880859375,
-0.022979736328125,
-0.057830810546875,
0.0259857177734375,
0.0263519287109375,
-0.01111602783203125,
-0.01079559326171875,
-0.0015840530395507812,
0.0017604827880859375,
-0.012176513671875,
0.00641632080078125,
-0.0079193115234375,
0.00666046142578125,
0.031097412109375,
-0.0036334991455078125,
-0.0029430389404296875,
0.0067291259765625,
-0.00597381591796875,
0.010833740234375,
0.00278472900390625,
-0.01351165771484375,
-0.01038360595703125,
-0.00559234619140625,
-0.043365478515625,
0.00986480712890625,
-0.0101318359375,
0.0206298828125,
-0.0229034423828125,
0.0247344970703125,
-0.0059051513671875,
-0.005748748779296875,
-0.029388427734375,
0.00678253173828125,
-0.00836181640625,
-0.0340576171875,
-0.00695037841796875,
0.000048100948333740234,
0.0206451416015625,
0.007419586181640625,
-0.022369384765625,
0.01551055908203125,
-0.0169525146484375,
-0.050933837890625,
-0.0033626556396484375,
-0.00824737548828125,
0.0068206787109375,
0.021240234375,
0.030487060546875,
0.00263214111328125,
-0.00954437255859375,
-0.0007548332214355469,
-0.0008120536804199219,
-0.00110626220703125,
0.0022907257080078125,
-0.004817962646484375,
-0.00971221923828125,
-0.021881103515625,
-0.01145172119140625,
-0.01300811767578125,
-0.007755279541015625,
0.0114898681640625,
0.0021381378173828125,
0.002483367919921875,
-0.021331787109375,
-0.01119232177734375,
-0.0128631591796875,
-0.0159454345703125,
-0.01036834716796875,
0.01483154296875,
0.003803253173828125,
0.0174560546875,
-0.00272369384765625,
0.01517486572265625,
0.01160430908203125,
0.0309295654296875,
0.0113677978515625,
-0.020751953125,
-0.0153045654296875,
0.01593017578125,
0.00418853759765625,
0.0198211669921875,
-0.0040283203125,
0.01751708984375,
0.0082550048828125,
0.005161285400390625,
0.022705078125,
-0.003490447998046875,
0.01898193359375,
-0.01523590087890625,
0.010162353515625,
-0.015899658203125,
0.037109375,
0.005817413330078125,
-0.0165863037109375,
0.004360198974609375,
-0.019866943359375,
-0.0032196044921875,
0.04345703125,
0.006591796875,
-0.03363037109375,
0.0487060546875,
0.01136016845703125,
0.006587982177734375,
-0.026092529296875,
0.04669189453125,
0.03436279296875,
-0.0125579833984375,
-0.0006732940673828125,
-0.0435791015625,
-0.01175689697265625,
-0.00476837158203125,
-0.0169830322265625,
0.020477294921875,
0.0015621185302734375,
-0.0026645660400390625,
0.0050201416015625,
-0.0196533203125,
-0.0180816650390625,
-0.029632568359375,
0.02435302734375,
0.0305938720703125,
-0.00728607177734375,
-0.00449371337890625,
0.0100250244140625,
0.031890869140625,
-0.029754638671875,
0.0306854248046875,
-0.0212554931640625,
-0.004611968994140625,
-0.0018033981323242188,
0.035552978515625,
-0.03485107421875,
0.0089263916015625,
-0.0084991455078125,
-0.0158538818359375,
0.005153656005859375,
-0.04925537109375,
0.0111236572265625,
0.0039043426513671875,
0.0008420944213867188,
-0.0211181640625,
-0.0038394927978515625,
0.034576416015625,
0.02392578125,
-0.0031147003173828125,
0.0109405517578125,
0.002803802490234375,
-0.0152435302734375,
0.005344390869140625,
-0.005329132080078125,
-0.025634765625,
-0.03399658203125,
0.0203399658203125,
-0.0008821487426757812,
0.051300048828125,
0.0019445419311523438,
0.007556915283203125,
-0.006969451904296875,
0.0124664306640625,
-0.01213836669921875,
-0.0076904296875,
0.0038471221923828125,
-0.004322052001953125,
-0.04443359375,
-0.01983642578125,
-0.005123138427734375,
0.02642822265625,
0.010833740234375,
0.026214599609375,
0.001926422119140625,
-0.01290130615234375,
-0.0098724365234375,
0.0197296142578125,
-0.034332275390625,
0.00833892822265625,
-0.016693115234375,
0.039886474609375,
-0.014129638671875,
-0.0036716461181640625,
0.026824951171875,
-0.0304412841796875,
-0.007236480712890625,
0.01605224609375,
-0.0098419189453125,
0.03369140625,
0.0021915435791015625,
-0.032257080078125,
0.0148468017578125,
0.01690673828125,
0.00583648681640625,
-0.0172882080078125,
-0.00917816162109375,
-0.0244140625,
0.00933837890625,
-0.0204620361328125,
0.02044677734375,
0.03741455078125,
0.006542205810546875,
0.00824737548828125,
0.03924560546875,
0.0002799034118652344,
-0.0220489501953125,
0.00199127197265625,
0.01114654541015625,
0.0191802978515625,
0.05780029296875,
0.030548095703125,
-0.01568603515625,
-0.011505126953125,
-0.01251220703125,
0.005767822265625,
-0.0111083984375,
-0.004913330078125,
-0.0036220550537109375,
-0.0196685791015625,
0.01554107666015625,
0.0068817138671875,
0.007320404052734375,
0.032135009765625,
-0.00939178466796875,
0.049041748046875,
0.0272979736328125,
-0.0217437744140625,
-0.037384033203125,
0.00958251953125,
-0.0029582977294921875,
-0.0002340078353881836,
-0.01171112060546875,
0.010345458984375,
-0.039764404296875,
0.017242431640625,
0.0126495361328125,
-0.0029621124267578125,
-0.0158538818359375,
-0.0020313262939453125,
0.015167236328125,
-0.0218963623046875,
-0.00402069091796875,
0.0012559890747070312,
0.00267791748046875,
0.00801849365234375,
0.0027065277099609375,
0.014801025390625,
0.0243988037109375,
-0.01788330078125,
-0.0130615234375,
-0.0120697021484375,
0.00794219970703125,
-0.0296173095703125,
-0.00455474853515625,
0.00826263427734375,
0.0008206367492675781,
-0.00010418891906738281,
-0.01995849609375,
0.0025844573974609375,
-0.0091552734375,
-0.01068878173828125,
0.0215606689453125,
-0.00835418701171875,
-0.0272674560546875,
-0.0125885009765625,
0.007724761962890625,
-0.043701171875,
-0.02203369140625,
-0.0175018310546875,
-0.00039505958557128906,
-0.002685546875,
-0.00201416015625,
0.0025234222412109375,
0.01708984375,
0.0024623870849609375,
-0.005680084228515625,
-0.004840850830078125,
-0.00748443603515625,
0.02850341796875,
-0.0157928466796875,
-0.0161590576171875,
-0.00536346435546875,
0.0084991455078125,
-0.0521240234375,
-0.004268646240234375,
-0.0189666748046875,
-0.01641845703125,
0.009063720703125,
-0.0026378631591796875,
0.04534912109375,
0.011871337890625,
-0.0154571533203125,
-0.00988006591796875,
-0.0170440673828125,
-0.0250244140625,
-0.033477783203125,
-0.01021575927734375,
0.0225982666015625,
0.023651123046875,
0.036163330078125,
-0.0086822509765625,
0.002742767333984375,
0.01506805419921875,
-0.0022144317626953125,
-0.00566864013671875,
-0.01180267333984375,
-0.014556884765625,
-0.016204833984375,
0.0161285400390625,
0.0179901123046875,
0.01470947265625,
0.011810302734375,
0.00457763671875,
0.0107421875,
-0.025421142578125,
-0.00005835294723510742,
0.01082611083984375,
0.04638671875,
-0.0177001953125,
0.001621246337890625,
-0.039794921875,
0.0012340545654296875,
0.0175628662109375,
0.00568389892578125,
-0.0230712890625,
-0.0133056640625,
0.0197601318359375,
0.01235198974609375,
0.034576416015625,
0.03363037109375,
-0.00572967529296875,
-0.005550384521484375,
-0.039459228515625,
-0.02392578125,
0.00559234619140625,
-0.0185394287109375,
0.03399658203125,
0.01335906982421875,
-0.0282440185546875,
-0.027740478515625,
-0.0082550048828125,
-0.007198333740234375,
-0.002544403076171875,
-0.0341796875,
0.0002810955047607422,
0.0178680419921875,
-0.00540924072265625,
0.039764404296875,
0.006214141845703125,
-0.0259246826171875,
0.025726318359375,
-0.0193328857421875,
-0.0262603759765625,
-0.01812744140625,
0.0008931159973144531,
0.0152435302734375,
0.00750732421875,
-0.006618499755859375,
-0.0086669921875,
0.01476287841796875,
-0.024139404296875,
-0.031402587890625,
0.0093231201171875,
0.004993438720703125,
0.0104827880859375,
-0.01042938232421875,
0.011932373046875,
0.004039764404296875,
0.00940704345703125,
-0.01080322265625,
-0.03143310546875,
-0.005237579345703125,
-0.0028972625732421875,
0.0103302001953125,
0.0271759033203125,
-0.0039215087890625,
0.0080718994140625,
0.01062774658203125,
0.0265350341796875,
0.006015777587890625,
-0.01415252685546875,
0.023681640625,
0.01074981689453125,
0.0128326416015625,
0.002780914306640625,
0.0255584716796875,
-0.0062255859375,
-0.0241241455078125,
-0.005268096923828125,
-0.0152587890625,
0.005466461181640625,
-0.004230499267578125,
-0.012939453125,
-0.003662109375,
-0.0156097412109375,
0.0217742919921875,
0.00921630859375,
-0.0131988525390625,
0.0311737060546875,
-0.0006728172302246094,
0.00220489501953125,
0.0177459716796875,
0.004669189453125,
-0.0258636474609375,
0.013275146484375,
0.01165008544921875,
0.011871337890625,
-0.0111083984375,
-0.032073974609375,
0.0309600830078125,
-0.0018892288208007812,
0.017822265625,
-0.0305023193359375,
0.0176544189453125,
-0.006862640380859375,
0.02362060546875,
-0.02203369140625,
0.01244354248046875,
0.0164794921875,
0.012939453125,
-0.0139923095703125,
-0.024322509765625,
-0.00634765625,
-0.0179901123046875,
-0.006725311279296875,
-0.0026111602783203125,
0.050567626953125,
0.0244140625,
0.002223968505859375,
0.0026073455810546875,
0.0030879974365234375,
0.006420135498046875,
-0.0102386474609375,
0.01262664794921875,
-0.0126190185546875,
0.00115203857421875,
0.0193023681640625,
0.02032470703125,
0.00643157958984375,
0.01265716552734375,
0.007503509521484375,
0.006366729736328125,
-0.0126953125,
-0.0023136138916015625,
0.04168701171875,
0.0189208984375,
0.0207061767578125,
0.004047393798828125,
-0.00916290283203125,
-0.01067352294921875,
0.00843048095703125,
0.033294677734375,
0.0130767822265625,
0.010345458984375,
0.01012420654296875,
0.0201873779296875,
-0.0037670135498046875,
0.039093017578125,
-0.0216827392578125,
0.02703857421875,
-0.01275634765625,
-0.0301666259765625,
-0.01910400390625,
0.006168365478515625,
-0.005279541015625,
0.018646240234375,
0.002277374267578125,
0.00928497314453125,
0.0260009765625,
-0.0014448165893554688,
-0.045257568359375,
0.0183868408203125,
0.007114410400390625,
-0.0106048583984375,
0.0101776123046875,
0.006954193115234375,
-0.00400543212890625,
0.006500244140625,
-0.047607421875,
0.0008559226989746094,
0.01139068603515625,
0.04180908203125,
0.01273345947265625,
0.00817108154296875,
-0.028350830078125,
-0.007049560546875,
-0.00926971435546875,
0.0004749298095703125,
-0.0022125244140625,
0.01543426513671875,
0.01271820068359375,
0.0142059326171875,
0.006046295166015625,
0.031585693359375,
-0.0239410400390625,
0.0290374755859375,
0.017730712890625,
0.0108642578125,
0.052764892578125,
-0.01222991943359375,
0.0203704833984375,
0.005718231201171875,
-0.00826263427734375,
-0.008544921875,
-0.00019860267639160156,
0.001422882080078125,
-0.026092529296875,
-0.02557373046875,
0.0382080078125,
0.0127105712890625,
-0.0003459453582763672,
-0.00118255615234375,
0.006473541259765625,
0.0078125,
0.01433563232421875,
-0.0011959075927734375,
-0.039306640625,
0.011749267578125,
0.017242431640625,
-0.0196380615234375,
-0.000705718994140625,
-0.00970458984375,
-0.005970001220703125,
0.01186370849609375,
-0.0271759033203125,
0.01549530029296875,
0.0257110595703125,
-0.00023221969604492188,
-0.01445770263671875,
0.038421630859375,
0.0153961181640625,
0.023101806640625,
0.003498077392578125,
-0.00614166259765625,
0.0322265625,
-0.004505157470703125,
0.005977630615234375,
0.0191650390625,
0.0089874267578125,
0.03851318359375,
0.0274505615234375,
0.0005545616149902344,
-0.064453125,
0.0003070831298828125,
0.0141754150390625,
0.005626678466796875,
-0.032928466796875,
-0.06768798828125,
0.0241241455078125,
0.0003426074981689453,
0.035675048828125,
-0.0069427490234375,
-0.017059326171875,
0.005523681640625,
0.01165771484375,
0.032318115234375,
-0.0294189453125,
0.0328369140625,
-0.04327392578125,
0.038818359375,
-0.02056884765625,
0.003597259521484375,
-0.03192138671875,
-0.02618408203125,
0.00832366943359375,
0.00804901123046875,
0.026763916015625,
0.00777435302734375,
-0.0014047622680664062,
0.017303466796875,
0.0094146728515625,
0.0015392303466796875,
-0.0201873779296875,
-0.019256591796875,
0.033416748046875,
0.00006687641143798828,
0.005313873291015625,
-0.0241546630859375,
-0.0014505386352539062,
0.00717926025390625,
0.0018405914306640625,
-0.001979827880859375,
0.028472900390625,
0.0181427001953125,
0.0014791488647460938,
-0.018096923828125,
-0.0107574462890625,
0.009521484375,
-0.019195556640625,
-0.005401611328125,
-0.0035114288330078125,
-0.01551055908203125,
0.01120758056640625,
0.0010995864868164062,
-0.006732940673828125,
0.047271728515625,
-0.0518798828125,
0.0090789794921875,
-0.02447509765625,
0.0159454345703125,
0.021697998046875,
-0.0219879150390625,
-0.02508544921875,
-0.02496337890625,
-0.0133056640625,
-0.0223388671875,
0.01088714599609375,
0.018310546875,
0.0217437744140625,
0.005687713623046875,
-0.0266571044921875,
0.026580810546875,
-0.0006289482116699219,
-0.0295867919921875,
0.005260467529296875,
0.0034008026123046875,
-0.0039215087890625,
0.029876708984375,
-0.0150909423828125,
-0.004856109619140625,
-0.0021839141845703125,
-0.0034580230712890625,
-0.004344940185546875,
0.0052642822265625,
-0.0287017822265625,
-0.00759124755859375,
0.0203704833984375,
0.0016632080078125,
-0.01081085205078125,
-0.01531982421875,
0.00013756752014160156,
0.0165863037109375,
0.0159149169921875,
0.01514434814453125,
0.006549835205078125,
-0.01380157470703125,
0.003406524658203125,
-0.005916595458984375,
-0.0189361572265625,
0.01403045654296875,
-0.0022487640380859375,
-0.021087646484375,
-0.00215911865234375,
0.00872039794921875,
-0.00991058349609375,
-0.00565338134765625,
-0.0267181396484375,
-0.0169525146484375,
0.000743865966796875,
-0.032562255859375,
-0.0019741058349609375,
0.03155517578125,
0.00794219970703125,
-0.0140838623046875,
-0.017822265625,
-0.023101806640625,
0.0186309814453125,
-0.0172271728515625,
-0.0293426513671875,
-0.00214385986328125,
-0.01306915283203125,
0.058929443359375,
0.00833892822265625,
0.004032135009765625,
0.0257568359375,
0.0198822021484375,
0.0118255615234375,
-0.01364898681640625,
-0.031005859375,
0.01788330078125,
-0.003070831298828125,
-0.005603790283203125,
-0.02447509765625,
-0.0022411346435546875,
0.0036029815673828125,
0.01528167724609375,
0.049774169921875,
-0.018829345703125,
0.010040283203125,
-0.006664276123046875,
-0.027130126953125,
0.006175994873046875,
0.007785797119140625,
-0.0028076171875,
0.0222930908203125,
0.0092620849609375,
-0.0237274169921875,
-0.032745361328125,
-0.019744873046875,
-0.0193328857421875,
-0.000713348388671875,
0.0115509033203125,
-0.00887298583984375,
-0.01001739501953125,
0.023651123046875,
0.0018644332885742188,
-0.051361083984375,
0.033355712890625,
-0.0181884765625,
-0.043304443359375,
-0.0091552734375,
-0.005138397216796875,
-0.0162353515625,
0.00424957275390625,
-0.017486572265625,
0.0233154296875,
-0.021331787109375,
-0.03936767578125,
-0.0279541015625,
0.03363037109375,
0.01251220703125,
0.0009531974792480469,
0.036895751953125,
0.0282745361328125,
-0.016387939453125,
0.00804901123046875,
-0.044525146484375,
-0.006710052490234375,
-0.0022258758544921875,
0.00177764892578125,
0.0110931396484375,
0.0184478759765625,
0.0438232421875,
-0.0158538818359375,
-0.0160675048828125,
-0.0232391357421875,
-0.0271453857421875,
0.0173797607421875,
0.037078857421875,
0.01141357421875,
-0.014373779296875,
0.023681640625,
-0.0016460418701171875,
-0.00030994415283203125,
0.0311737060546875,
-0.0170440673828125,
-0.0024261474609375,
-0.016448974609375,
0.0111083984375,
0.00902557373046875,
0.035919189453125,
-0.03155517578125,
-0.0238800048828125,
0.003665924072265625,
0.0298919677734375,
0.01593017578125,
0.003147125244140625,
-0.0465087890625,
-0.0085296630859375,
-0.033447265625,
-0.0029544830322265625,
0.02923583984375,
0.0260009765625,
0.03143310546875,
-0.01316070556640625,
0.0272064208984375,
0.00457763671875,
0.0279693603515625,
0.0001895427703857422,
-0.00848388671875,
-0.0208282470703125,
-0.015655517578125,
0.029815673828125,
-0.005191802978515625,
-0.006877899169921875,
-0.0117645263671875,
-0.0225982666015625,
-0.006816864013671875,
0.007053375244140625,
0.0003097057342529297,
0.00656890869140625,
-0.033294677734375,
-0.013153076171875,
0.017425537109375,
0.0280303955078125,
-0.019744873046875,
-0.01062774658203125,
-0.025299072265625,
0.0034637451171875,
-0.00441741943359375,
-0.033935546875,
0.0227203369140625,
-0.0203399658203125,
-0.01526641845703125,
-0.01126861572265625,
-0.0173797607421875,
-0.01273345947265625,
-0.031768798828125,
0.0012655258178710938,
-0.020751953125,
0.01302337646484375,
0.006916046142578125,
0.00971221923828125,
0.01023101806640625,
0.0181427001953125,
0.02081298828125,
-0.0192413330078125,
-0.00707244873046875,
-0.00597381591796875,
-0.026153564453125,
-0.020660400390625,
0.0168304443359375,
-0.043853759765625,
-0.0421142578125,
0.0173187255859375,
-0.0100555419921875,
-0.01438140869140625,
0.031341552734375,
-0.00225067138671875,
0.008697509765625,
0.0102691650390625,
0.01806640625,
0.020263671875,
-0.00548553466796875,
0.005870819091796875,
-0.01279449462890625,
-0.007843017578125,
-0.036224365234375,
0.00444793701171875,
-0.0016918182373046875,
-0.01268768310546875,
0.006591796875,
0.0042877197265625,
-0.0011959075927734375,
0.0032939910888671875,
-0.016510009765625,
-0.040679931640625,
-0.0110931396484375,
-0.018035888671875,
0.0288848876953125,
0.006000518798828125,
0.01268768310546875,
0.0194244384765625,
-0.02606201171875,
-0.0032672882080078125,
-0.0282745361328125,
0.01070404052734375,
0.01551055908203125,
0.0174407958984375,
-0.024810791015625,
0.004573822021484375,
-0.0019664764404296875,
-0.01016998291015625,
-0.006793975830078125,
-0.02423095703125,
0.0164031982421875,
-0.018890380859375,
0.00698089599609375,
0.0238189697265625,
-0.0248260498046875,
-0.0021877288818359375,
-0.059661865234375,
-0.010650634765625,
0.00914764404296875,
0.002544403076171875,
0.015411376953125,
-0.001796722412109375,
-0.024749755859375,
-0.010833740234375,
-0.009765625,
0.02862548828125,
-0.006595611572265625,
0.0006575584411621094,
-0.008056640625,
-0.0089263916015625,
0.038543701171875,
-0.01152801513671875,
0.039459228515625,
0.0051422119140625,
-0.004299163818359375,
0.014923095703125,
0.01346588134765625,
0.0007958412170410156,
0.005558013916015625,
-0.00551605224609375,
-0.01251983642578125,
-0.0072021484375,
-0.020355224609375,
0.0304412841796875,
-0.0270843505859375,
-0.02496337890625,
0.0012025833129882812,
-0.0116424560546875,
-0.0040740966796875,
0.032073974609375,
-0.0037136077880859375,
0.037689208984375,
0.0291748046875,
-0.006435394287109375,
0.0063323974609375,
0.007259368896484375,
0.0029964447021484375,
-0.0438232421875,
-0.01300811767578125,
0.037933349609375,
-0.0097808837890625,
0.0220184326171875,
-0.0190887451171875,
0.0033168792724609375,
0.003963470458984375,
0.037872314453125,
-0.07470703125,
-0.01078033447265625,
-0.0143890380859375,
-0.0009093284606933594,
-0.00998687744140625,
0.0188446044921875,
-0.0182952880859375,
-0.0092010498046875,
0.0146636962890625,
-0.0227813720703125,
-0.04510498046875,
0.030609130859375,
0.00884246826171875,
0.0218353271484375,
-0.0167083740234375,
-0.0127105712890625,
0.01220703125,
0.00884246826171875,
-0.00676727294921875,
-0.0244903564453125,
-0.0379638671875,
0.017791748046875,
0.0157623291015625,
-0.024078369140625,
0.0196533203125,
0.006137847900390625,
-0.021636962890625,
-0.01568603515625,
0.005001068115234375,
-0.017974853515625,
-0.027496337890625,
-0.0303802490234375,
0.050567626953125,
-0.0034923553466796875,
-0.032073974609375,
0.022491455078125,
0.00911712646484375,
-0.0161590576171875,
0.0004467964172363281,
-0.006336212158203125,
0.01139068603515625,
-0.030029296875,
0.00492095947265625,
0.00217437744140625,
-0.0081634521484375,
-0.038116455078125,
0.038299560546875,
-0.007740020751953125,
0.05389404296875,
0.0025691986083984375,
0.036285400390625,
0.01168060302734375,
0.00738525390625,
0.00821685791015625,
-0.005859375,
0.0298919677734375,
-0.0159149169921875,
-0.016143798828125,
0.00884246826171875,
0.0111083984375,
0.023773193359375,
0.0020503997802734375,
0.0283966064453125,
0.03662109375,
-0.033477783203125,
0.0121307373046875,
0.0267486572265625,
0.01568603515625,
0.0023059844970703125,
0.031341552734375,
0.00414276123046875,
0.003978729248046875,
0.0086822509765625,
0.0083160400390625,
0.0220184326171875,
-0.026702880859375,
0.0277557373046875,
-0.01373291015625,
0.01025390625,
0.01047515869140625,
-0.0232391357421875,
0.01204681396484375,
0.01026153564453125,
-0.01436614990234375,
0.00385284423828125,
-0.002002716064453125,
-0.0145721435546875,
-0.0130615234375,
0.0193939208984375,
-0.00830841064453125,
-0.033721923828125,
0.0168609619140625,
0.00555419921875,
0.001544952392578125,
0.0211334228515625,
-0.031341552734375,
0.01271820068359375,
-0.0157012939453125,
0.01074981689453125,
-0.0082550048828125,
-0.050201416015625,
0.0024127960205078125,
0.035552978515625,
-0.032257080078125,
-0.00832366943359375,
-0.01192474365234375,
0.00013756752014160156,
0.038116455078125,
0.0122833251953125,
-0.005657196044921875,
0.004978179931640625,
-0.0129852294921875,
-0.0031871795654296875,
0.0217437744140625,
-0.01320648193359375,
0.01348114013671875,
-0.017486572265625,
0.02838134765625,
0.0259552001953125,
0.0287628173828125,
-0.0198974609375,
0.0261383056640625,
0.030487060546875,
-0.01239013671875,
0.01029205322265625,
0.005596160888671875,
0.051055908203125,
-0.00589752197265625,
-0.0223388671875,
-0.0007824897766113281,
-0.02056884765625,
-0.002719879150390625,
-0.01556396484375,
-0.0206298828125,
0.026947021484375,
0.0036334991455078125,
-0.019866943359375,
-0.0066070556640625,
0.0208282470703125,
0.0267181396484375,
0.0189208984375,
-0.01229095458984375,
0.006748199462890625,
-0.003337860107421875,
0.00749969482421875,
0.0102691650390625,
-0.0235443115234375,
0.0089263916015625,
-0.00019228458404541016,
0.002040863037109375,
0.00737762451171875,
-0.029693603515625,
-0.00228118896484375,
0.01548004150390625,
-0.0257720947265625,
0.01218414306640625,
0.00008612871170043945,
-0.024810791015625,
0.016448974609375,
-0.0106048583984375,
0.0177459716796875,
-0.01282501220703125,
0.041290283203125,
0.01049041748046875,
0.012847900390625,
-0.0050506591796875,
0.01262664794921875,
0.006687164306640625,
-0.0013265609741210938,
0.002536773681640625,
-0.01007080078125,
0.0163726806640625,
-0.0271148681640625,
0.0169830322265625,
-0.031494140625,
-0.001461029052734375,
-0.055908203125,
-0.029205322265625,
0.0032253265380859375,
-0.045257568359375,
0.004169464111328125,
-0.004161834716796875,
0.0511474609375,
0.00684356689453125,
-0.01434326171875,
-0.03009033203125,
-0.00331878662109375,
-0.0032253265380859375,
0.004329681396484375,
-0.00897216796875,
-0.0146026611328125,
-0.0022430419921875,
-0.033966064453125,
-0.0186004638671875,
-0.01702880859375,
-0.01078033447265625,
0.01068115234375,
0.003566741943359375,
-0.0021114349365234375,
0.0180511474609375,
0.01203155517578125,
-0.0248565673828125,
0.00457763671875,
-0.035247802734375,
0.0041351318359375,
-0.00699615478515625,
0.0216217041015625,
0.0104217529296875,
0.0178680419921875,
-0.0187225341796875,
-0.02166748046875,
-0.0362548828125,
-0.004047393798828125,
-0.0119171142578125,
0.0345458984375,
0.0255126953125,
0.01033782958984375,
-0.034576416015625,
0.035491943359375,
0.00429534912109375,
0.009307861328125,
0.0020904541015625,
0.0177001953125,
-0.03125,
-0.05474853515625,
-0.00760650634765625,
0.02044677734375,
-0.01459503173828125,
0.004734039306640625,
0.005527496337890625,
-0.009979248046875,
0.049530029296875,
0.0135955810546875,
-0.0005617141723632812,
-0.016326904296875,
0.01424407958984375,
0.01334381103515625,
-0.01364898681640625,
-0.0179443359375,
-0.0131988525390625,
0.0303497314453125,
-0.029937744140625,
0.009307861328125,
0.007904052734375,
0.01207733154296875,
-0.0139312744140625,
-0.0014495849609375,
-0.00047659873962402344,
0.0131988525390625,
-0.0303192138671875,
0.0227813720703125,
0.03839111328125,
0.017852783203125,
-0.0025005340576171875,
-0.0161590576171875,
0.0005869865417480469,
0.004901885986328125,
0.022552490234375,
0.0022373199462890625,
-0.0111846923828125,
0.008819580078125,
-0.01023101806640625,
0.00966644287109375,
0.001583099365234375,
0.021240234375,
-0.018585205078125,
0.0020122528076171875,
-0.002765655517578125,
-0.0224609375,
0.00708770751953125,
-0.02203369140625,
-0.0024242401123046875,
0.0160675048828125,
0.00858306884765625,
-0.024627685546875,
0.0158233642578125,
-0.024993896484375,
-0.0004105567932128906,
-0.0037975311279296875,
0.00777435302734375,
0.026336669921875,
-0.011749267578125,
0.00006276369094848633,
-0.018310546875,
0.0035552978515625,
0.0084686279296875,
-0.015838623046875,
-0.0016431808471679688,
-0.005992889404296875,
-0.027130126953125,
0.0216827392578125,
-0.006259918212890625,
0.01108551025390625,
0.0164947509765625,
-0.00502777099609375,
0.01800537109375,
0.014007568359375,
0.009368896484375,
-0.0059661865234375,
-0.0007777214050292969,
-0.00522613525390625,
-0.01023101806640625,
0.01465606689453125,
-0.0048065185546875,
0.024658203125,
-0.0006084442138671875,
0.0015430450439453125,
-0.01273345947265625,
0.00039649009704589844,
-0.0086822509765625,
0.040924072265625,
-0.0263519287109375,
0.025634765625,
0.021270751953125,
0.01259613037109375,
0.0156097412109375,
-0.039276123046875,
0.039794921875,
-0.004970550537109375,
-0.0167236328125,
0.0103759765625,
0.004055023193359375,
0.0113067626953125,
0.0068511962890625,
0.00804901123046875,
0.003665924072265625,
-0.034271240234375,
0.0211181640625,
0.023468017578125,
0.0127410888671875,
-0.033172607421875,
0.01277923583984375,
-0.0268707275390625,
0.006946563720703125,
0.0401611328125,
-0.019683837890625,
0.028778076171875,
0.0025730133056640625,
-0.026702880859375,
0.005001068115234375,
0.0218048095703125,
0.02001953125,
0.029205322265625,
-0.0026493072509765625,
-0.04937744140625,
0.025054931640625,
-0.0426025390625,
0.0108795166015625,
0.00445556640625,
-0.01849365234375,
0.0138092041015625,
0.0237274169921875,
-0.0245208740234375,
-0.00850677490234375,
0.0132293701171875,
-0.009002685546875,
0.0199127197265625,
0.0194854736328125,
0.00409698486328125,
-0.003246307373046875,
0.0230255126953125,
0.0199432373046875,
-0.048919677734375,
0.0260009765625,
-0.00670623779296875,
-0.0035190582275390625,
0.054779052734375,
-0.044708251953125,
0.00679779052734375,
-0.00968170166015625,
0.0096435546875,
-0.018096923828125,
-0.01502227783203125,
0.0189208984375,
0.014862060546875,
-0.00632476806640625,
-0.003589630126953125,
0.02618408203125,
-0.01509857177734375,
0.019287109375,
-0.003368377685546875,
0.005283355712890625,
0.00797271728515625,
0.038238525390625,
-0.0100250244140625,
-0.01548004150390625,
0.0111083984375,
0.02264404296875,
0.00930023193359375,
-0.0222015380859375,
0.029571533203125,
0.0016145706176757812,
-0.0160064697265625,
-0.01230621337890625,
-0.0027790069580078125,
-0.0156402587890625,
0.038421630859375,
0.0171356201171875,
-0.031524658203125,
-0.00215911865234375,
-0.051910400390625,
0.0182037353515625,
-0.0308837890625,
0.006374359130859375,
0.049652099609375,
0.005817413330078125,
-0.005634307861328125,
-0.005146026611328125,
-0.0298309326171875,
0.015380859375,
0.01319122314453125,
-0.007415771484375,
-0.003131866455078125,
0.007793426513671875,
0.016082763671875,
-0.00424957275390625,
0.014739990234375,
0.005023956298828125,
-0.0181121826171875,
-0.0316162109375,
-0.00644683837890625,
-0.01419830322265625,
0.01526641845703125,
-0.0169219970703125,
-0.020263671875,
-0.0207366943359375,
0.01139068603515625,
-0.0209808349609375,
0.0018434524536132812,
-0.027374267578125,
-0.035980224609375,
0.0110321044921875,
0.0162506103515625,
0.02899169921875,
0.01395416259765625,
0.00524139404296875,
-0.00994873046875,
-0.03448486328125,
0.0157012939453125,
-0.01409912109375,
0.005237579345703125,
-0.02093505859375,
-0.0156707763671875,
-0.004505157470703125,
-0.0041961669921875,
-0.0264129638671875,
-0.01148223876953125,
-0.026214599609375,
0.005748748779296875,
-0.0015954971313476562,
-0.026763916015625,
-0.020782470703125,
0.0128936767578125,
0.00652313232421875,
-0.02587890625,
0.028167724609375,
0.0194091796875,
-0.037139892578125,
-0.0106201171875,
-0.0163726806640625,
-0.0195159912109375,
0.031219482421875,
-0.004955291748046875,
-0.01390838623046875,
0.039398193359375,
0.001056671142578125,
-0.032958984375,
0.0034427642822265625,
0.000579833984375,
-0.0017518997192382812,
-0.0129852294921875,
-0.038726806640625,
0.03387451171875,
0.0027332305908203125,
0.0146636962890625,
0.01168060302734375,
0.0027599334716796875,
0.0206298828125,
-0.002803802490234375,
-0.0143890380859375,
-0.020355224609375,
0.006465911865234375,
-0.0197296142578125,
-0.041473388671875,
-0.0399169921875,
-0.007373809814453125,
0.0261077880859375,
0.000240325927734375,
-0.01983642578125,
0.01137542724609375,
-0.005527496337890625,
0.003673553466796875,
0.0187225341796875,
0.01531982421875
] |
ours_520
|
Consider a quadrilateral \(ABCD\), with \(AB=w, BC=x, CD=y, DA=z\), and \(AC=6\). By the law of cosines, the first two equations imply that \(\cos B=\frac{1}{4}\) and \(\cos D=-\frac{1}{4}\), so \(ABCD\) must be cyclic. By Ptolemy's theorem, \(BD \cdot AC=wy+xz=30\), so \(BD=5\).
Note that \(\sin B=\sin D=\sqrt{1-\cos^2 B}=\frac{\sqrt{15}}{4}\), so
\[
[ABCD]=[ABC]+[CDA]=\frac{wx \sin B}{2}+\frac{yz \sin D}{2}=\frac{\sqrt{15}}{8}(wx+yz)
\]
Let \(\theta\) be the angle formed by diagonals \(BD\) and \(AC\). It is well-known that \([ABCD]=\frac{BD \cdot AC}{2} \sin \theta \leq \frac{BD \cdot AC}{2}=15\), with equality holding exactly when \(\theta=90^\circ\). It follows that
\[
(wx+yz)^{2} \leq \frac{64}{15} \cdot 15^{2}=960
\]
Equality holds when \(BD \perp AC\); we can ensure that such a configuration exists by holding \(AC\) fixed in the circumcircle of \(ABCD\), and varying chord \(BD\) of length \(5\) until it is perpendicular to chord \(AC\).
Thus, the largest possible value of \((xy+wz)^{2}\) is \(\boxed{960}\).
|
960
|
{
"competition": "us_comps",
"dataset": "Ours",
"posts": null,
"source": "OMOSoln2-2.md"
}
|
Suppose \(x, y, z\), and \(w\) are positive reals such that
\[
x^{2}+y^{2}-\frac{x y}{2}=w^{2}+z^{2}+\frac{w z}{2}=36
\]
and
\[
x z+y w=30
\]
Find the largest possible value of \((x y+w z)^{2}\).
|
[
"/Mathematics/Geometry/GeneralGeometry/EuclideanGeometry",
"/Mathematics/Geometry/GeneralGeometry/Geometry",
"/Mathematics/Geometry/PlaneGeometry/Quadrangles/OrthodiagonalQuadrangle",
"/Mathematics/Geometry/PlaneGeometry/Quadrilaterals/CyclicQuadrangle",
"/Mathematics/Geometry/PlaneGeometry/Quadrilaterals/CyclicQuadrilateral",
"/Mathematics/Geometry/PlaneGeometry/Quadrilaterals/PtolemysTheorem",
"/Mathematics/Geometry/Trigonometry/Angles/Angle",
"/Mathematics/Geometry/Trigonometry/GeneralTrigonometry/Trigonometry",
"/Mathematics/Geometry/Trigonometry/TrigonometricFunctions/Cosine",
"/Mathematics/Geometry/Trigonometry/TrigonometricFunctions/LawofCosines"
] |
Model the variables as sides of a cyclic quadrilateral and apply Ptolemy’s theorem plus the diagonal‑area inequality to bound the expression.
|
[
-0.00008469820022583008,
-0.005825042724609375,
0.042877197265625,
0.01032257080078125,
-0.0000972747802734375,
-0.0045166015625,
0.0174713134765625,
0.0156097412109375,
0.00701904296875,
-0.00931549072265625,
0.01488494873046875,
0.0048980712890625,
-0.005023956298828125,
-0.00508880615234375,
-0.0206298828125,
0.0034694671630859375,
0.00020873546600341797,
-0.01306915283203125,
0.05059814453125,
-0.0024280548095703125,
-0.00860595703125,
-0.0033245086669921875,
-0.058380126953125,
0.01432037353515625,
-0.030120849609375,
-0.0096893310546875,
-0.01690673828125,
-0.0194091796875,
0.0172271728515625,
0.04400634765625,
-0.0125885009765625,
-0.011566162109375,
0.0004851818084716797,
-0.025299072265625,
-0.0012044906616210938,
0.026580810546875,
0.0265960693359375,
-0.00696563720703125,
-0.0199127197265625,
-0.041961669921875,
0.0043182373046875,
-0.0193939208984375,
-0.0024051666259765625,
-0.0021514892578125,
0.00384521484375,
0.0136260986328125,
-0.00307464599609375,
0.00006449222564697266,
-0.01322174072265625,
0.01180267333984375,
-0.00036644935607910156,
0.00833892822265625,
0.015960693359375,
0.0026073455810546875,
0.0019989013671875,
-0.01326751708984375,
0.01561737060546875,
-0.0008091926574707031,
-0.0022716522216796875,
-0.00015676021575927734,
0.0010404586791992188,
-0.006496429443359375,
0.00597381591796875,
-0.00920867919921875,
-0.003589630126953125,
-0.01369476318359375,
-0.01806640625,
-0.06658935546875,
0.01171112060546875,
-0.00859832763671875,
-0.00933074951171875,
-0.04180908203125,
0.006572723388671875,
0.0130767822265625,
0.01114654541015625,
-0.0005578994750976562,
-0.01132965087890625,
0.00827789306640625,
0.00431060791015625,
0.021484375,
0.044189453125,
0.028839111328125,
0.00226593017578125,
-0.060302734375,
0.00556182861328125,
-0.0178680419921875,
-0.032135009765625,
0.0037078857421875,
-0.0115966796875,
-0.0330810546875,
-0.0023288726806640625,
0.009857177734375,
-0.02899169921875,
-0.0254974365234375,
0.0077972412109375,
-0.006763458251953125,
-0.01495361328125,
0.0091705322265625,
-0.0185699462890625,
0.01096343994140625,
0.01114654541015625,
-0.00829315185546875,
-0.006244659423828125,
-0.0230255126953125,
-0.03717041015625,
-0.007564544677734375,
-0.018646240234375,
-0.00933074951171875,
-0.003597259521484375,
0.0015506744384765625,
0.0121917724609375,
-0.0040283203125,
0.0245819091796875,
0.02105712890625,
0.0004723072052001953,
0.003276824951171875,
0.0157012939453125,
0.00931549072265625,
-0.01271820068359375,
0.0141754150390625,
-0.003143310546875,
0.0159912109375,
0.0003185272216796875,
0.0269775390625,
-0.0091552734375,
0.00508880615234375,
-0.000919342041015625,
-0.0289306640625,
-0.01824951171875,
-0.005458831787109375,
0.00039958953857421875,
-0.00559234619140625,
-0.0355224609375,
-0.02423095703125,
-0.06793212890625,
0.00850677490234375,
-0.0084991455078125,
0.018829345703125,
-0.01084136962890625,
-0.0032444000244140625,
0.0023059844970703125,
-0.0075225830078125,
0.0102386474609375,
-0.0269317626953125,
-0.0245819091796875,
0.0021114349365234375,
-0.005096435546875,
-0.0019893646240234375,
0.01392364501953125,
-0.0008387565612792969,
0.00274658203125,
0.0017328262329101562,
0.0068359375,
-0.0037517547607421875,
0.01210784912109375,
0.0124969482421875,
0.00736236572265625,
0.00010669231414794922,
-0.005352020263671875,
-0.0020809173583984375,
0.0010251998901367188,
-0.00801849365234375,
0.01190185546875,
0.01148223876953125,
0.00792694091796875,
-0.0184326171875,
-0.005283355712890625,
0.00052642822265625,
-0.0109710693359375,
0.00807952880859375,
0.0033283233642578125,
-0.00482177734375,
0.010162353515625,
-0.008636474609375,
-0.0120697021484375,
0.01904296875,
-0.00563812255859375,
0.032562255859375,
-0.0169525146484375,
0.00843048095703125,
0.007038116455078125,
-0.03173828125,
-0.005222320556640625,
0.0008454322814941406,
0.01543426513671875,
-0.0266876220703125,
-0.0014829635620117188,
0.00579833984375,
0.0186614990234375,
0.0084075927734375,
-0.01312255859375,
-0.024658203125,
0.0011043548583984375,
-0.01282501220703125,
-0.010650634765625,
0.00809478759765625,
-0.02838134765625,
-0.016815185546875,
0.01056671142578125,
0.01355743408203125,
-0.00013816356658935547,
-0.008697509765625,
0.049957275390625,
0.0017518997192382812,
0.0008502006530761719,
-0.0029296875,
0.0051422119140625,
-0.008941650390625,
-0.0115966796875,
0.01349639892578125,
0.0032978057861328125,
0.0009560585021972656,
-0.00298309326171875,
-0.004001617431640625,
-0.0119171142578125,
-0.01038360595703125,
-0.0192718505859375,
-0.00418853759765625,
0.0190582275390625,
0.0026454925537109375,
0.01371002197265625,
0.006946563720703125,
0.0118408203125,
0.0007486343383789062,
-0.01070404052734375,
0.0237579345703125,
0.00234222412109375,
-0.00626373291015625,
0.0223846435546875,
-0.006206512451171875,
0.004856109619140625,
-0.008575439453125,
-0.0083160400390625,
0.01433563232421875,
-0.0166015625,
0.0003151893615722656,
-0.04638671875,
-0.0002777576446533203,
0.0045166015625,
-0.0202484130859375,
0.024749755859375,
-0.038177490234375,
-0.010650634765625,
-0.004547119140625,
0.0057373046875,
0.004726409912109375,
0.004299163818359375,
-0.035186767578125,
0.0245361328125,
-0.00972747802734375,
-0.008209228515625,
0.01258087158203125,
-0.0062255859375,
-0.0190277099609375,
-0.02337646484375,
-0.006351470947265625,
0.03240966796875,
0.006999969482421875,
-0.0032501220703125,
0.01493072509765625,
-0.00917816162109375,
-0.03118896484375,
-0.0010709762573242188,
-0.002277374267578125,
-0.006229400634765625,
0.01474761962890625,
0.0278167724609375,
0.001346588134765625,
0.01239776611328125,
-0.00653076171875,
0.0491943359375,
0.0099945068359375,
-0.004154205322265625,
0.01031494140625,
-0.022674560546875,
0.0014753341674804688,
0.005970001220703125,
0.0006222724914550781,
0.0043487548828125,
0.0087127685546875,
0.0028896331787109375,
0.0132293701171875,
-0.01141357421875,
-0.00003975629806518555,
0.01258087158203125,
-0.01265716552734375,
0.032958984375,
0.009674072265625,
0.01360321044921875,
0.0267791748046875,
-0.005863189697265625,
-0.018035888671875,
-0.006389617919921875,
-0.0141448974609375,
0.076904296875,
-0.0069427490234375,
0.0104217529296875,
0.019134521484375,
0.0226593017578125,
-0.006351470947265625,
0.0285186767578125,
-0.01416778564453125,
0.0070037841796875,
0.003414154052734375,
0.040435791015625,
0.030120849609375,
0.0008406639099121094,
-0.004550933837890625,
-0.0146026611328125,
0.024383544921875,
0.0139617919921875,
-0.0036945343017578125,
0.0027332305908203125,
-0.028045654296875,
-0.0166778564453125,
-0.036895751953125,
0.0080413818359375,
0.00098419189453125,
-0.004344940185546875,
0.0210113525390625,
0.012115478515625,
0.0192413330078125,
0.037750244140625,
0.020263671875,
0.0203704833984375,
-0.0169219970703125,
0.0098419189453125,
0.0078887939453125,
-0.01514434814453125,
0.043548583984375,
-0.038665771484375,
0.019500732421875,
0.00010782480239868164,
-0.020782470703125,
-0.0224609375,
-0.0087127685546875,
-0.02001953125,
0.00507354736328125,
-0.004486083984375,
0.0029315948486328125,
0.00536346435546875,
-0.01739501953125,
-0.005138397216796875,
-0.01375579833984375,
-0.009185791015625,
0.01480865478515625,
-0.006351470947265625,
-0.0056610107421875,
0.0017156600952148438,
0.0023632049560546875,
-0.0041961669921875,
-0.0096435546875,
0.0092010498046875,
-0.0130157470703125,
-0.037567138671875,
0.01513671875,
-0.01494598388671875,
0.00873565673828125,
-0.0135955810546875,
0.00836944580078125,
0.00800323486328125,
-0.00988006591796875,
0.00646209716796875,
0.002727508544921875,
-0.0051727294921875,
0.007266998291015625,
-0.022735595703125,
0.0209503173828125,
-0.0254364013671875,
0.0145111083984375,
-0.0141448974609375,
0.0223388671875,
0.010833740234375,
-0.00021517276763916016,
0.01082611083984375,
0.0122222900390625,
0.0035648345947265625,
-0.0198974609375,
0.02581787109375,
-0.0024929046630859375,
0.0298004150390625,
0.024688720703125,
-0.00908660888671875,
-0.003871917724609375,
-0.00083160400390625,
-0.00927734375,
-0.0147857666015625,
0.00980377197265625,
-0.03900146484375,
0.0180816650390625,
0.00322723388671875,
0.01383209228515625,
-0.0145263671875,
0.0165252685546875,
-0.004852294921875,
-0.03680419921875,
0.0058441162109375,
0.0216827392578125,
0.0110321044921875,
-0.00867462158203125,
-0.06390380859375,
0.0036182403564453125,
-0.0134735107421875,
-0.050262451171875,
-0.0114898681640625,
-0.024139404296875,
-0.0065765380859375,
0.01290130615234375,
-0.0129547119140625,
0.0009126663208007812,
-0.0010232925415039062,
-0.007297515869140625,
0.01641845703125,
-0.01280975341796875,
-0.026214599609375,
0.004268646240234375,
-0.0038299560546875,
-0.00792694091796875,
0.0296630859375,
-0.0216064453125,
0.0009732246398925781,
-0.020599365234375,
-0.0009236335754394531,
-0.01010894775390625,
0.021026611328125,
0.028961181640625,
-0.0281524658203125,
0.03558349609375,
0.0165863037109375,
-0.032501220703125,
0.01177978515625,
-0.0042877197265625,
-0.0216064453125,
-0.0036258697509765625,
0.005809783935546875,
0.028533935546875,
0.0231475830078125,
0.0013942718505859375,
0.0174407958984375,
0.0155487060546875,
-0.03759765625,
0.01346588134765625,
0.00482940673828125,
-0.01047515869140625,
0.035064697265625,
-0.017486572265625,
0.0104522705078125,
0.0220184326171875,
0.0347900390625,
-0.0181884765625,
-0.01390838623046875,
0.0263214111328125,
0.0019855499267578125,
-0.03778076171875,
-0.021240234375,
0.0243072509765625,
0.04241943359375,
0.0036067962646484375,
-0.0246734619140625,
0.006069183349609375,
0.00013947486877441406,
-0.0225677490234375,
0.019622802734375,
0.00954437255859375,
-0.01406097412109375,
-0.0172576904296875,
-0.0166778564453125,
0.0169830322265625,
0.038665771484375,
0.036102294921875,
0.015869140625,
-0.0162200927734375,
0.00351715087890625,
-0.0087738037109375,
-0.055389404296875,
0.013580322265625,
0.01000213623046875,
0.01605224609375,
-0.0187835693359375,
-0.00133514404296875,
0.0113372802734375,
-0.0156707763671875,
-0.048431396484375,
-0.01357269287109375,
-0.006832122802734375,
0.010162353515625,
0.0224151611328125,
-0.005523681640625,
-0.0265960693359375,
-0.0189056396484375,
0.02880859375,
0.0675048828125,
-0.02496337890625,
-0.03515625,
-0.0030193328857421875,
-0.005199432373046875,
0.0288848876953125,
-0.0020198822021484375,
-0.00418853759765625,
-0.0114288330078125,
0.034576416015625,
-0.0192108154296875,
-0.0084075927734375,
-0.0224761962890625,
0.0191192626953125,
0.0217742919921875,
0.0166473388671875,
0.023223876953125,
0.005626678466796875,
0.02386474609375,
0.0369873046875,
0.005954742431640625,
0.0234527587890625,
-0.032958984375,
0.01381683349609375,
-0.023040771484375,
0.0210113525390625,
-0.02587890625,
0.01001739501953125,
0.0016317367553710938,
-0.033782958984375,
0.0242462158203125,
0.043304443359375,
-0.019073486328125,
-0.019500732421875,
0.0382080078125,
-0.01300048828125,
-0.01323699951171875,
0.04290771484375,
0.0036411285400390625,
0.006008148193359375,
-0.0110015869140625,
-0.0116424560546875,
0.0202484130859375,
-0.031707763671875,
-0.0020046234130859375,
0.00165557861328125,
-0.023681640625,
0.0192718505859375,
0.026031494140625,
0.015411376953125,
-0.0152435302734375,
-0.0163116455078125,
-0.01031494140625,
-0.011138916015625,
0.0230712890625,
-0.0214691162109375,
0.02142333984375,
-0.0197601318359375,
0.0032825469970703125,
0.036590576171875,
0.0005474090576171875,
-0.007289886474609375,
0.002765655517578125,
0.005035400390625,
-0.00504302978515625,
0.00252532958984375,
0.0020122528076171875,
-0.027618408203125,
0.0272216796875,
0.0164031982421875,
-0.014801025390625,
0.046051025390625,
0.030853271484375,
0.036041259765625,
-0.019195556640625,
0.0197601318359375,
-0.06195068359375,
0.0107269287109375,
-0.01551055908203125,
-0.01361846923828125,
-0.020721435546875,
-0.0009341239929199219,
0.0173797607421875,
0.000804901123046875,
-0.00832366943359375,
-0.01470947265625,
-0.01331329345703125,
0.0015773773193359375,
-0.0223541259765625,
0.018310546875,
0.011199951171875,
-0.005367279052734375,
-0.00788116455078125,
0.005756378173828125,
-0.0098114013671875,
-0.0256195068359375,
0.045379638671875,
-0.0232391357421875,
-0.0121307373046875,
-0.01132965087890625,
0.045928955078125,
0.004421234130859375,
-0.0133056640625,
0.0102996826171875,
-0.01263427734375,
0.005214691162109375,
-0.01216888427734375,
0.0306549072265625,
0.006809234619140625,
0.046142578125,
0.037353515625,
-0.0166778564453125,
0.005706787109375,
-0.002201080322265625,
0.01395416259765625,
-0.0268096923828125,
0.0004341602325439453,
0.0026416778564453125,
0.006015777587890625,
-0.01468658447265625,
0.006511688232421875,
-0.043701171875,
0.031402587890625,
0.007167816162109375,
0.012664794921875,
-0.0237884521484375,
-0.0169219970703125,
0.037872314453125,
-0.0145111083984375,
-0.03375244140625,
-0.01483154296875,
-0.0018148422241210938,
0.016143798828125,
-0.04302978515625,
-0.0154571533203125,
-0.0011167526245117188,
-0.0206146240234375,
0.005130767822265625,
0.003116607666015625,
-0.00583648681640625,
0.01031494140625,
0.032257080078125,
-0.006526947021484375,
0.00508880615234375,
0.0254058837890625,
-0.00829315185546875,
0.019989013671875,
-0.021728515625,
0.00878143310546875,
0.021820068359375,
-0.01385498046875,
0.00037288665771484375,
-0.022796630859375,
0.005550384521484375,
0.0002384185791015625,
-0.0167083740234375,
-0.0242767333984375,
-0.06890869140625,
-0.007717132568359375,
-0.0220947265625,
-0.036651611328125,
-0.0221099853515625,
0.023345947265625,
0.00435638427734375,
-0.00533294677734375,
0.00457763671875,
0.005283355712890625,
0.0166015625,
0.0261688232421875,
0.0235137939453125,
-0.0250244140625,
-0.00977325439453125,
0.0119476318359375,
-0.049774169921875,
-0.007617950439453125,
-0.005054473876953125,
-0.004283905029296875,
0.015380859375,
0.0303802490234375,
0.022369384765625,
-0.000518798828125,
0.0230560302734375,
-0.0034236907958984375,
-0.00922393798828125,
0.005615234375,
-0.016845703125,
-0.0293731689453125,
0.0255126953125,
-0.0111083984375,
-0.0108795166015625,
0.0188751220703125,
0.0167236328125,
0.005702972412109375,
0.0008463859558105469,
-0.0117645263671875,
0.0111236572265625,
-0.00930023193359375,
0.014739990234375,
-0.0014829635620117188,
0.004962921142578125,
0.0012340545654296875,
-0.0205230712890625,
0.025054931640625,
-0.006664276123046875,
-0.00830841064453125,
0.01776123046875,
0.01329803466796875,
-0.0007224082946777344,
-0.00997161865234375,
0.006191253662109375,
-0.016754150390625,
0.0225372314453125,
-0.01137542724609375,
-0.008819580078125,
-0.019927978515625,
0.00714874267578125,
0.00543975830078125,
-0.03131103515625,
0.052032470703125,
-0.01050567626953125,
0.021331787109375,
0.0049591064453125,
-0.009918212890625,
-0.00748443603515625,
-0.0037841796875,
-0.006134033203125,
-0.01007843017578125,
0.0209808349609375,
-0.005252838134765625,
0.026763916015625,
0.006374359130859375,
-0.017059326171875,
-0.003284454345703125,
0.039642333984375,
0.0271453857421875,
0.0010309219360351562,
-0.019317626953125,
0.007266998291015625,
0.03656005859375,
-0.003582000732421875,
-0.014373779296875,
-0.0018138885498046875,
0.02972412109375,
0.0022335052490234375,
-0.01407623291015625,
0.004917144775390625,
-0.03924560546875,
-0.026641845703125,
0.0208587646484375,
0.026458740234375,
-0.0249176025390625,
-0.03167724609375,
0.00847625732421875,
-0.00975799560546875,
-0.028717041015625,
-0.01171112060546875,
0.00875091552734375,
-0.0196990966796875,
-0.0096282958984375,
0.0223236083984375,
0.0172576904296875,
0.01261138916015625,
-0.053802490234375,
-0.032470703125,
-0.01348114013671875,
-0.0174713134765625,
-0.025238037109375,
-0.0016031265258789062,
0.0215606689453125,
-0.006153106689453125,
0.005146026611328125,
-0.00428009033203125,
0.043731689453125,
0.0193023681640625,
-0.00910186767578125,
-0.0087890625,
-0.018157958984375,
-0.037750244140625,
-0.0030612945556640625,
-0.0105743408203125,
0.007747650146484375,
-0.00960540771484375,
0.010986328125,
0.0162200927734375,
0.0171051025390625,
-0.031829833984375,
-0.0000355839729309082,
0.0455322265625,
-0.0170745849609375,
0.01532745361328125,
-0.0042266845703125,
0.009124755859375,
0.0208587646484375,
-0.0204315185546875,
0.00045180320739746094,
-0.0131988525390625,
-0.01122283935546875,
0.0192108154296875,
-0.0157012939453125,
0.049713134765625,
-0.018157958984375,
0.0222930908203125,
-0.0103759765625,
0.00473785400390625,
-0.0355224609375,
-0.0292510986328125,
-0.037322998046875,
-0.018310546875,
0.0273284912109375,
-0.006534576416015625,
0.00441741943359375,
-0.01389312744140625,
0.008331298828125,
0.027435302734375,
-0.0178375244140625,
0.0215911865234375,
0.0207366943359375,
-0.0211639404296875,
0.01043701171875,
0.00539398193359375,
-0.03497314453125,
-0.0101470947265625,
-0.0195770263671875,
0.021026611328125,
-0.00652313232421875,
0.019134521484375,
0.0118560791015625,
-0.004878997802734375,
0.0124664306640625,
0.01116943359375,
0.01593017578125,
-0.00836181640625,
0.0054931640625,
-0.0330810546875,
0.0140838623046875,
-0.053436279296875,
0.013885498046875,
0.046417236328125,
0.037811279296875,
-0.007175445556640625,
-0.0164947509765625,
-0.01593017578125,
-0.00550079345703125,
-0.01739501953125,
0.001132965087890625,
-0.0013284683227539062,
-0.004608154296875,
-0.020416259765625,
0.00725555419921875,
-0.0110931396484375,
-0.0019369125366210938,
-0.003421783447265625,
-0.01287078857421875,
-0.0187530517578125,
-0.0019121170043945312,
-0.0152740478515625,
0.0265045166015625,
0.022369384765625,
0.0069580078125,
0.0105438232421875,
0.0170745849609375,
-0.01430511474609375,
0.017730712890625,
-0.047882080078125,
0.00934600830078125,
0.027618408203125,
0.028564453125,
-0.030548095703125,
0.01073455810546875,
0.0206451416015625,
-0.004268646240234375,
-0.002552032470703125,
-0.00281524658203125,
-0.00865936279296875,
-0.03729248046875,
0.009307861328125,
-0.0208892822265625,
0.03521728515625,
0.0019464492797851562,
0.007724761962890625,
-0.0119171142578125,
-0.0011053085327148438,
-0.02069091796875,
0.049560546875,
0.005107879638671875,
-0.00799560546875,
0.01537322998046875,
0.03948974609375,
-0.0199127197265625,
0.0029048919677734375,
-0.0237579345703125,
0.024383544921875,
-0.016387939453125,
0.0122833251953125,
-0.031097412109375,
0.013671875,
0.0029659271240234375,
0.0029010772705078125,
-0.0158233642578125,
-0.0159454345703125,
-0.0161285400390625,
-0.004001617431640625,
0.0002644062042236328,
0.0068206787109375,
0.004909515380859375,
-0.05584716796875,
-0.00878143310546875,
0.018798828125,
-0.0130615234375,
-0.040283203125,
0.004505157470703125,
0.004520416259765625,
0.0198211669921875,
-0.0024662017822265625,
0.016448974609375,
0.00024437904357910156,
0.005001068115234375,
-0.0220794677734375,
0.050994873046875,
-0.038665771484375,
-0.0186004638671875,
-0.01171875,
-0.0142364501953125,
0.029937744140625,
-0.0172882080078125,
-0.02593994140625,
-0.0007152557373046875,
-0.0299072265625,
0.01338958740234375,
-0.0018463134765625,
-0.041412353515625,
-0.0007410049438476562,
-0.0014562606811523438,
0.004901885986328125,
-0.01157379150390625,
0.001262664794921875,
0.005886077880859375,
-0.04656982421875,
0.01482391357421875,
0.00959014892578125,
0.00885009765625,
0.0193328857421875,
0.0225372314453125,
0.00516510009765625,
-0.0009245872497558594,
0.004489898681640625,
-0.021087646484375,
0.01898193359375,
-0.007904052734375,
0.00624847412109375,
0.00792694091796875,
0.038787841796875,
0.0313720703125,
-0.029022216796875,
-0.008148193359375,
0.0034732818603515625,
-0.0000807642936706543,
-0.004589080810546875,
-0.031341552734375,
0.0020885467529296875,
0.0018014907836914062,
0.01214599609375,
0.044097900390625,
-0.0111541748046875,
-0.00740814208984375,
0.02313232421875,
0.004993438720703125,
0.0008616447448730469,
-0.004077911376953125,
-0.01442718505859375,
0.004703521728515625,
-0.03985595703125,
-0.005771636962890625,
0.01508331298828125,
0.01397705078125,
0.011199951171875,
0.0230712890625,
-0.00160980224609375,
-0.0010232925415039062,
0.00884246826171875,
-0.0149993896484375,
-0.0287322998046875,
-0.0377197265625,
0.004871368408203125,
0.0247650146484375,
-0.006931304931640625,
0.02105712890625,
0.00806427001953125,
0.01512908935546875,
-0.0274505615234375,
-0.027557373046875,
0.0205078125,
-0.0157470703125,
-0.004619598388671875,
-0.0169219970703125,
0.00983428955078125,
-0.01041412353515625,
0.0213165283203125,
-0.006778717041015625,
-0.0214385986328125,
0.023468017578125,
-0.02386474609375,
-0.0113067626953125,
0.005016326904296875,
0.02301025390625,
-0.016815185546875,
-0.0108795166015625,
0.00315093994140625,
-0.0151214599609375,
-0.038909912109375,
-0.0034008026123046875,
0.0224151611328125,
-0.019317626953125,
-0.0036468505859375,
-0.0171661376953125,
-0.01038360595703125,
0.01210784912109375,
-0.01288604736328125,
0.0201416015625,
-0.01055145263671875,
-0.00701141357421875,
-0.0225982666015625,
0.021270751953125,
-0.019195556640625,
0.01241302490234375,
-0.0017032623291015625,
0.0011548995971679688,
-0.060516357421875,
0.0308074951171875,
0.0141754150390625,
-0.0158538818359375,
-0.01273345947265625,
-0.01018524169921875,
0.0037288665771484375,
-0.0034732818603515625,
0.0034122467041015625,
0.011871337890625,
0.0088653564453125,
-0.0010824203491210938,
-0.039520263671875,
-0.0158538818359375,
0.00875091552734375,
-0.00997161865234375,
-0.01383209228515625,
-0.005115509033203125,
-0.01123809814453125,
-0.0033283233642578125,
-0.0103302001953125,
0.03460693359375,
0.0155029296875,
0.0248565673828125,
0.052734375,
-0.0082244873046875,
-0.007556915283203125,
-0.0282440185546875,
0.0003399848937988281,
0.03717041015625,
0.0017538070678710938,
0.0040740966796875,
0.01134490966796875,
-0.0115814208984375,
0.0015411376953125,
0.00708770751953125,
-0.00298309326171875,
0.004276275634765625,
0.0237274169921875,
0.0012216567993164062,
-0.0021686553955078125,
0.043609619140625,
0.01522064208984375,
-0.0009593963623046875,
-0.025970458984375,
-0.0157623291015625,
0.01549530029296875,
0.00634765625,
-0.0171966552734375,
-0.03204345703125,
-0.018768310546875,
0.02313232421875,
-0.04241943359375,
-0.031768798828125,
-0.0026378631591796875,
-0.01406097412109375,
0.01568603515625,
-0.01415252685546875,
0.018798828125,
0.003711700439453125,
0.018707275390625,
0.0235137939453125,
0.00043201446533203125,
-0.01422119140625,
-0.04345703125,
0.017669677734375,
0.034393310546875,
0.024993896484375,
-0.0187835693359375,
0.004344940185546875,
-0.00914764404296875,
-0.0031566619873046875,
-0.005741119384765625,
0.0173492431640625,
-0.0007195472717285156,
-0.00800323486328125,
0.01161956787109375,
0.0223541259765625,
0.033294677734375,
0.0171051025390625,
0.00616455078125,
-0.025543212890625,
0.0175628662109375,
0.04327392578125,
-0.003871917724609375,
-0.028839111328125,
-0.012451171875,
-0.0012121200561523438,
0.0247039794921875,
-0.00855255126953125,
-0.027740478515625,
-0.007564544677734375,
-0.04461669921875,
0.004856109619140625,
0.0210418701171875,
0.0537109375,
0.0164947509765625,
-0.003997802734375,
-0.0518798828125,
-0.0264129638671875,
0.001026153564453125,
0.00902557373046875,
0.01910400390625,
0.0345458984375,
0.00038814544677734375,
0.00894927978515625,
0.00348663330078125,
-0.02386474609375,
0.05657958984375,
0.01003265380859375,
-0.0223388671875,
0.035064697265625,
-0.01220703125,
0.01177215576171875,
-0.01010894775390625,
-0.025726318359375,
0.01123046875,
0.0147705078125,
-0.0021686553955078125,
-0.02459716796875,
0.0135498046875,
0.021697998046875,
-0.01395416259765625,
0.01070404052734375,
0.01335906982421875,
-0.002681732177734375,
-0.0103912353515625,
-0.0158233642578125,
0.0007734298706054688,
-0.0003514289855957031,
0.01457977294921875,
0.007778167724609375,
-0.032958984375,
0.0255279541015625,
-0.02227783203125,
0.02349853515625,
0.0026607513427734375,
0.005382537841796875,
-0.007221221923828125,
-0.0141448974609375,
0.0022983551025390625,
-0.0196685791015625,
-0.0030078887939453125,
-0.023773193359375,
-0.023712158203125,
0.01206207275390625,
-0.0237274169921875,
-0.0038089752197265625,
-0.025604248046875,
-0.00447845458984375,
-0.040252685546875,
0.035675048828125,
0.0102081298828125,
-0.0245208740234375,
0.00415802001953125,
0.01459503173828125,
-0.03289794921875,
0.047027587890625,
-0.0009427070617675781,
0.010589599609375,
-0.0031871795654296875,
-0.007049560546875,
-0.023681640625,
0.0186614990234375,
0.00433349609375,
-0.0159759521484375,
-0.005023956298828125,
-0.004413604736328125,
0.014617919921875,
-0.0209503173828125,
-0.0129852294921875,
0.013336181640625,
-0.00878143310546875,
0.0026187896728515625,
-0.04498291015625,
-0.0149688720703125,
-0.001903533935546875,
-0.0008044242858886719,
-0.0119476318359375,
0.0032672882080078125,
-0.01192474365234375,
0.007053375244140625,
-0.0085906982421875,
-0.0027561187744140625,
-0.016204833984375,
0.0017147064208984375,
0.02276611328125,
0.037353515625,
0.02374267578125,
0.046966552734375,
0.003810882568359375,
0.005237579345703125,
-0.0000030994415283203125,
-0.0248870849609375,
0.051544189453125,
-0.003643035888671875,
0.01148223876953125,
-0.00016450881958007812,
0.04290771484375,
0.0321044921875,
-0.00013828277587890625,
-0.002742767333984375,
-0.0213165283203125,
-0.006786346435546875,
0.0184326171875,
-0.0089263916015625,
-0.0013151168823242188,
0.0222625732421875,
0.0011320114135742188,
0.038421630859375,
-0.0137176513671875,
-0.01654052734375,
0.0010080337524414062,
0.0007176399230957031,
0.0159759521484375,
0.029510498046875,
-0.02227783203125,
0.02545166015625,
-0.012054443359375,
0.040496826171875,
0.00762939453125,
0.0248870849609375,
-0.0029811859130859375,
0.0189971923828125,
-0.01444244384765625,
-0.01100921630859375,
0.048004150390625,
-0.0024013519287109375,
-0.0179901123046875,
-0.0117034912109375,
-0.03778076171875,
-0.020233154296875,
-0.0008611679077148438,
0.049102783203125,
0.00012314319610595703,
0.00701141357421875,
-0.005100250244140625,
-0.036712646484375,
-0.01389312744140625,
-0.002338409423828125,
-0.0092010498046875,
-0.0218353271484375,
-0.0018215179443359375,
0.0287933349609375,
-0.01062774658203125,
-0.00124359130859375,
0.017822265625,
0.007488250732421875,
0.00933837890625,
0.02783203125,
0.0198211669921875,
0.01183319091796875,
0.0101776123046875,
-0.001552581787109375,
0.007289886474609375,
0.0172119140625,
0.007717132568359375,
0.0195465087890625,
0.00617218017578125,
-0.04803466796875,
-0.0136871337890625,
-0.00677490234375,
-0.0186309814453125,
-0.00787353515625,
0.01396942138671875,
-0.0236663818359375,
-0.02117919921875,
0.00720977783203125,
-0.03277587890625,
0.016632080078125,
0.00637054443359375,
-0.018646240234375,
0.042236328125,
-0.0073394775390625,
-0.0000030994415283203125,
0.01194000244140625,
-0.037933349609375,
-0.010955810546875,
-0.0181427001953125,
-0.041778564453125,
0.03387451171875,
-0.01334381103515625,
-0.0006341934204101562,
-0.024322509765625,
-0.00897216796875,
-0.0131378173828125,
-0.00632476806640625,
0.0137176513671875,
0.01145172119140625,
-0.00995635986328125,
-0.005367279052734375,
0.0018205642700195312,
-0.0074310302734375,
0.0059661865234375,
-0.0041656494140625,
0.0025882720947265625,
0.047027587890625,
0.00452423095703125,
0.03350830078125,
-0.00373077392578125,
0.0083770751953125,
0.00238800048828125,
0.004566192626953125,
0.03717041015625,
-0.00435638427734375,
-0.004878997802734375,
0.0002923011779785156,
0.00936126708984375,
-0.0190887451171875,
0.00037479400634765625,
-0.0303497314453125,
-0.00839996337890625,
-0.03082275390625,
0.0111083984375,
-0.00008046627044677734,
0.0185699462890625,
-0.0399169921875,
0.021331787109375,
0.00775146484375,
0.0216217041015625,
-0.01337432861328125,
-0.0113067626953125,
-0.023773193359375,
0.0289154052734375,
-0.0265655517578125,
-0.044830322265625,
0.0235748291015625,
0.0155792236328125,
-0.04534912109375,
0.006664276123046875,
0.0002155303955078125,
-0.014190673828125,
0.006649017333984375,
-0.004413604736328125,
-0.01273345947265625,
-0.0234832763671875,
-0.03955078125,
0.01401519775390625,
0.022003173828125,
0.006290435791015625,
0.0184173583984375,
-0.0066986083984375,
0.0121002197265625,
-0.0037975311279296875,
0.00893402099609375,
0.01605224609375,
0.0163726806640625,
0.0240478515625,
-0.0168304443359375,
-0.010101318359375,
-0.0198211669921875,
-0.020233154296875,
-0.0147857666015625,
0.00774383544921875,
-0.021087646484375,
-0.002803802490234375,
-0.01079559326171875,
-0.001659393310546875,
-0.0151824951171875,
-0.004352569580078125,
-0.013458251953125,
0.004459381103515625,
0.006458282470703125,
-0.044830322265625,
-0.01505279541015625,
-0.0537109375,
0.00794219970703125,
0.01038360595703125,
0.0126800537109375,
0.0121002197265625,
0.0212860107421875,
-0.0053558349609375,
-0.030731201171875,
-0.0264739990234375,
-0.0236968994140625,
0.020477294921875,
0.0225677490234375,
0.00716400146484375,
0.02496337890625,
-0.004428863525390625,
-0.0228424072265625,
0.0009617805480957031,
0.029327392578125,
0.017303466796875,
0.00411224365234375,
-0.0015058517456054688,
0.01031494140625,
0.0159454345703125,
-0.00850677490234375,
0.002162933349609375,
0.004062652587890625,
-0.0271453857421875,
0.0024280548095703125,
0.020263671875,
-0.00833892822265625,
0.0011205673217773438,
0.04278564453125,
-0.040374755859375,
0.020263671875,
0.015472412109375,
0.01001739501953125,
0.0362548828125,
0.0198516845703125,
0.05224609375,
-0.0235443115234375,
0.0106353759765625,
-0.0036983489990234375,
0.01007080078125,
0.007965087890625,
-0.01678466796875,
-0.03106689453125,
-0.0005350112915039062,
0.0252685546875,
-0.00829315185546875,
-0.01227569580078125,
-0.0196075439453125,
0.00771331787109375,
0.01268768310546875,
-0.01494598388671875,
0.00563812255859375,
0.023590087890625,
0.02386474609375,
-0.0265350341796875,
0.0038928985595703125,
0.0236968994140625,
0.0187225341796875,
-0.0266876220703125,
0.0037479400634765625,
-0.0161590576171875,
0.029998779296875,
-0.024322509765625,
0.00942230224609375,
-0.029815673828125,
0.01297760009765625,
-0.01149749755859375,
0.0035991668701171875,
0.0190582275390625,
-0.0021343231201171875,
-0.0004420280456542969,
0.017730712890625,
0.0009288787841796875,
-0.0147705078125,
-0.019744873046875,
0.012176513671875,
0.005382537841796875,
0.04107666015625,
0.024505615234375,
-0.012664794921875,
0.006557464599609375,
0.016326904296875,
0.023834228515625,
-0.007434844970703125,
-0.0167083740234375,
-0.037384033203125,
0.005031585693359375,
-0.0082550048828125,
0.034820556640625,
-0.0050201416015625,
-0.0089874267578125,
-0.056640625,
0.023834228515625,
-0.006748199462890625,
-0.00914764404296875,
-0.013336181640625,
0.00775909423828125,
-0.00006026029586791992,
-0.0144500732421875,
-0.01227569580078125,
0.0008344650268554688,
0.0242462158203125,
0.0148162841796875,
-0.0149078369140625,
-0.0183258056640625,
-0.004802703857421875,
0.017852783203125,
-0.01157379150390625,
0.016143798828125,
0.0210113525390625,
-0.010986328125,
0.00078582763671875,
-0.003475189208984375,
-0.0122528076171875,
0.0240325927734375,
0.005767822265625,
0.0258331298828125,
-0.0343017578125,
0.013092041015625,
-0.024169921875,
-0.0175628662109375,
-0.00799560546875,
0.00751495361328125,
-0.04388427734375,
-0.01082611083984375,
-0.0265350341796875,
0.005130767822265625,
0.0177001953125,
-0.0198516845703125,
-0.0195159912109375,
-0.0169219970703125,
0.013885498046875,
0.002655029296875,
-0.0269317626953125,
0.0131683349609375,
-0.033538818359375,
0.0189971923828125,
0.02447509765625,
0.0132598876953125,
-0.0123443603515625,
0.00377655029296875,
-0.0196533203125,
-0.01336669921875,
0.004108428955078125,
0.0049896240234375,
-0.00795745849609375,
-0.00882720947265625,
0.041473388671875,
0.0027790069580078125,
-0.0107574462890625,
0.0211944580078125,
-0.006572723388671875,
0.0080718994140625,
0.01806640625,
0.03240966796875,
-0.006622314453125,
-0.01483917236328125,
0.0008630752563476562,
-0.0016260147094726562,
0.005313873291015625,
0.0024662017822265625,
0.002735137939453125,
0.043304443359375,
0.004756927490234375,
0.02593994140625,
-0.003559112548828125,
0.00347137451171875,
-0.01739501953125,
-0.0029354095458984375,
0.016754150390625,
0.0273895263671875,
0.052581787109375,
-0.0214385986328125,
-0.0172882080078125,
0.026580810546875,
-0.00156402587890625,
-0.0259857177734375,
0.01702880859375,
0.03192138671875,
-0.002452850341796875,
-0.005451202392578125,
0.0216217041015625,
-0.0011453628540039062,
-0.0117950439453125,
-0.005428314208984375,
0.0184326171875,
-0.0160369873046875,
-0.0136871337890625,
-0.004150390625,
0.0152130126953125,
0.0215911865234375,
0.026611328125,
0.03900146484375,
0.0023651123046875,
-0.0212249755859375,
-0.0186767578125,
-0.0035915374755859375,
-0.008148193359375,
-0.01119232177734375,
0.0206298828125,
0.01531219482421875,
0.0391845703125,
-0.0236663818359375,
0.0061187744140625,
-0.00403594970703125,
0.011962890625,
-0.0011081695556640625,
0.00909423828125,
0.00756072998046875,
-0.0428466796875,
0.0290069580078125,
-0.00211334228515625,
0.00841522216796875,
0.0218963623046875,
0.0002810955047607422,
0.0017995834350585938,
-0.010101318359375,
0.03900146484375,
-0.00472259521484375,
-0.01546478271484375,
0.002918243408203125,
0.01010894775390625,
0.0280303955078125,
0.031494140625,
0.01215362548828125,
-0.01922607421875,
-0.01401519775390625,
0.01922607421875,
0.01183319091796875,
0.0310821533203125,
0.00012046098709106445,
0.0249481201171875,
0.02838134765625,
0.0146331787109375,
0.02581787109375,
-0.0016374588012695312,
0.00870513916015625,
-0.01517486572265625,
0.0333251953125,
0.01509857177734375,
0.0213470458984375,
-0.0098114013671875,
-0.031768798828125,
-0.0012025833129882812,
0.013275146484375,
-0.03179931640625,
0.0206451416015625,
-0.00202178955078125,
-0.0162353515625,
-0.01214599609375,
-0.015716552734375,
0.00852203369140625,
-0.0323486328125,
0.01898193359375,
0.0005168914794921875,
-0.00626373291015625,
0.01062774658203125,
-0.00725555419921875,
0.0202178955078125,
0.0147552490234375,
-0.035736083984375,
0.01450347900390625,
0.018646240234375,
-0.014251708984375,
-0.00963592529296875,
0.025360107421875,
0.03619384765625,
0.0009007453918457031,
-0.007122039794921875,
-0.0200042724609375,
-0.0123443603515625,
-0.0199432373046875,
0.01268768310546875,
-0.005207061767578125,
-0.0238037109375,
0.058013916015625,
-0.002086639404296875,
0.0340576171875,
-0.0238494873046875,
-0.005344390869140625,
-0.003154754638671875,
0.0082550048828125,
0.00820159912109375,
0.00799560546875,
0.0171051025390625,
-0.01197052001953125,
-0.0035381317138671875,
-0.01666259765625,
-0.01358795166015625,
-0.03271484375,
-0.0069580078125,
-0.00263214111328125,
-0.040557861328125,
0.02362060546875,
0.00379180908203125,
-0.0311126708984375,
0.012664794921875,
0.0105438232421875,
-0.01471710205078125,
-0.04241943359375,
-0.0225677490234375,
0.03143310546875,
0.0189666748046875,
-0.0012845993041992188,
0.01519012451171875,
0.0166168212890625,
-0.0116119384765625,
0.0137176513671875,
-0.01029205322265625,
0.0152130126953125,
0.01229095458984375,
-0.0181884765625,
-0.0241241455078125,
0.024139404296875,
-0.003124237060546875,
-0.0033054351806640625,
-0.0164642333984375,
0.005275726318359375,
0.005741119384765625,
0.00559234619140625,
-0.008941650390625,
0.01515960693359375,
-0.031402587890625,
0.0003199577331542969,
0.018951416015625,
-0.0166778564453125,
-0.00017964839935302734,
0.021392822265625,
0.01094818115234375,
0.0255889892578125,
0.01263427734375,
0.033935546875,
-0.0121307373046875,
-0.01470184326171875,
0.0001118779182434082,
-0.0066375732421875,
-0.0181427001953125,
-0.0266265869140625,
0.010833740234375,
0.0000699758529663086,
0.020355224609375,
0.01247406005859375,
-0.0256805419921875,
0.0217437744140625,
-0.004100799560546875,
0.023406982421875,
0.0095367431640625,
0.0018281936645507812,
0.0033435821533203125,
0.002162933349609375,
0.026275634765625,
-0.03985595703125,
0.015380859375,
0.0194854736328125,
-0.0239410400390625,
0.0185394287109375,
0.0035991668701171875,
0.01116180419921875,
-0.00411224365234375,
-0.0183563232421875,
-0.010284423828125,
0.020904541015625,
0.01358795166015625,
-0.00847625732421875,
0.00582122802734375,
-0.0357666015625,
0.01140594482421875,
0.006267547607421875,
-0.03607177734375,
0.0269012451171875,
0.03125,
0.0087890625,
-0.023834228515625,
-0.0008721351623535156,
-0.0112152099609375,
-0.033599853515625,
0.005588531494140625,
-0.0175933837890625,
-0.0286407470703125,
0.023406982421875,
0.00745391845703125,
0.0015802383422851562,
0.00304412841796875,
-0.0248565673828125,
-0.0005068778991699219,
0.02899169921875,
0.03973388671875,
-0.01064300537109375,
0.00274658203125,
-0.0196075439453125,
0.017059326171875,
0.0158538818359375,
-0.03692626953125,
-0.00502777099609375,
0.004608154296875,
0.01287078857421875,
0.0236358642578125,
-0.00713348388671875,
-0.00742340087890625,
-0.0095367431640625,
-0.032989501953125,
-0.004833221435546875,
-0.0192718505859375,
0.01192474365234375,
-0.0184326171875,
-0.007770538330078125,
0.004474639892578125,
-0.01666259765625,
-0.0194091796875,
-0.007404327392578125,
-0.01529693603515625,
0.02777099609375,
0.004314422607421875,
0.029571533203125,
-0.00205230712890625,
-0.020751953125,
-0.0167999267578125,
0.0302734375,
0.02239990234375,
0.0025234222412109375,
-0.02581787109375,
0.0433349609375,
0.0171966552734375,
0.01035308837890625,
0.008514404296875,
0.0469970703125,
-0.01788330078125,
0.0046539306640625,
-0.020233154296875,
0.008148193359375,
-0.0002758502960205078,
0.01175689697265625,
-0.01210784912109375,
0.016082763671875,
-0.0114593505859375,
0.0021190643310546875,
-0.01422882080078125,
-0.0228271484375,
-0.003894805908203125,
0.0020160675048828125,
0.02801513671875,
-0.0183563232421875,
-0.0160980224609375,
0.036041259765625,
0.0024261474609375,
-0.0010929107666015625,
0.0008096694946289062,
-0.0184326171875,
0.03680419921875,
0.0167083740234375,
-0.014373779296875,
-0.033538818359375,
-0.015716552734375,
-0.0032749176025390625,
0.00843048095703125,
-0.00739288330078125,
-0.00010883808135986328,
0.0293426513671875,
0.02960205078125,
-0.0039825439453125,
-0.0156707763671875,
0.0201873779296875,
-0.00783538818359375,
0.00518035888671875,
-0.005397796630859375,
-0.0197296142578125,
-0.020477294921875,
-0.0308990478515625,
-0.0036945343017578125,
-0.0009794235229492188,
-0.028045654296875,
-0.001018524169921875,
0.00499725341796875,
0.008941650390625,
0.00926971435546875,
-0.0047607421875,
0.0004837512969970703,
-0.032501220703125,
-0.0048828125,
-0.0024356842041015625,
-0.00789642333984375,
0.01241302490234375,
0.0182342529296875,
0.015411376953125,
0.0084228515625,
-0.0284271240234375,
-0.018157958984375,
-0.00028061866760253906,
-0.00901031494140625,
0.021148681640625,
0.007549285888671875,
-0.01580810546875,
0.057952880859375,
0.00904083251953125,
0.01458740234375,
0.01312255859375,
0.0301513671875,
0.01076507568359375,
-0.03265380859375,
-0.014495849609375,
0.021331787109375,
0.0401611328125,
0.03155517578125,
0.004253387451171875,
0.0187225341796875,
-0.006130218505859375,
0.0197906494140625,
-0.01605224609375,
0.032989501953125,
-0.0162200927734375,
-0.018798828125,
-0.0078277587890625,
-0.01617431640625,
0.01468658447265625,
-0.043243408203125,
-0.01641845703125,
-0.0126495361328125,
0.01104736328125,
-0.0178985595703125,
0.024810791015625,
0.0038738250732421875,
-0.00719451904296875,
-0.034423828125,
0.00926971435546875,
-0.03753662109375,
-0.029296875,
-0.002960205078125,
-0.031646728515625,
-0.034149169921875,
0.04913330078125,
0.0228424072265625,
0.02105712890625,
-0.0258636474609375,
-0.019927978515625,
0.01250457763671875,
-0.01959228515625,
0.0274505615234375,
0.00301361083984375,
0.005275726318359375,
0.0191802978515625,
-0.0235595703125,
-0.0307769775390625,
0.0164794921875,
-0.0012121200561523438,
-0.007678985595703125,
-0.0114898681640625,
0.006526947021484375,
-0.018768310546875,
0.0005211830139160156,
0.01361083984375,
0.00060272216796875,
0.0233306884765625,
0.03009033203125,
0.0291595458984375,
-0.00904083251953125,
-0.038421630859375,
0.0020732879638671875,
0.0209197998046875,
0.00867462158203125,
-0.0166473388671875,
0.0038299560546875,
-0.014984130859375,
-0.01232147216796875,
-0.027099609375,
-0.0008473396301269531,
-0.01580810546875,
0.013580322265625,
-0.0242919921875,
-0.0194549560546875,
0.042755126953125,
-0.0224609375,
-0.0159759521484375,
-0.01396942138671875,
-0.01026153564453125,
0.004669189453125,
-0.002651214599609375,
-0.0138092041015625,
-0.0264434814453125,
-0.0187225341796875,
0.005252838134765625,
0.0012493133544921875,
-0.0357666015625,
-0.00605010986328125,
-0.0136871337890625,
-0.008880615234375,
0.042694091796875,
-0.00897979736328125,
0.0223541259765625,
0.031463623046875,
-0.004123687744140625,
0.019134521484375,
0.04168701171875,
-0.00917816162109375,
-0.024139404296875,
0.03369140625,
0.00018787384033203125,
-0.0280914306640625,
0.00446319580078125,
-0.00188446044921875,
-0.03778076171875,
0.0161590576171875,
-0.034698486328125,
-0.0034999847412109375,
0.005611419677734375,
0.0175323486328125,
0.00909423828125,
0.01568603515625,
-0.00962066650390625,
0.01203155517578125,
-0.0132293701171875,
0.00669097900390625,
0.0168609619140625,
-0.00937652587890625,
-0.005771636962890625,
0.01090240478515625,
0.037322998046875,
0.0180206298828125,
0.00830078125,
-0.006458282470703125,
-0.0091552734375,
-0.00453948974609375,
0.007488250732421875,
-0.0029144287109375,
-0.02203369140625,
0.00484466552734375,
-0.03485107421875,
0.0028095245361328125,
-0.01424407958984375,
0.0014438629150390625,
0.01751708984375,
-0.034698486328125,
0.0009937286376953125,
-0.0298004150390625,
-0.0036029815673828125,
-0.020538330078125,
0.00867462158203125,
-0.004894256591796875,
-0.0207366943359375,
-0.0029659271240234375,
0.0127105712890625,
-0.0183563232421875,
0.0037822723388671875,
0.01126861572265625,
0.0211639404296875,
-0.013214111328125,
0.0103912353515625,
0.03424072265625,
0.0189666748046875,
0.0205230712890625,
-0.00733184814453125,
0.01447296142578125,
-0.01369476318359375,
0.0237579345703125,
-0.00920867919921875,
-0.02685546875,
-0.015411376953125,
-0.0048065185546875,
0.02337646484375,
-0.00023031234741210938,
0.0048675537109375,
0.034454345703125,
0.03985595703125,
-0.017059326171875,
-0.01477813720703125,
0.0030670166015625,
0.00836181640625,
0.0220947265625,
-0.0001156926155090332,
-0.007312774658203125,
-0.0233001708984375,
0.007720947265625,
-0.006359100341796875,
0.0006575584411621094,
-0.034637451171875,
0.00005602836608886719,
0.01386260986328125,
0.0308380126953125,
-0.025299072265625,
0.0018854141235351562,
0.00203704833984375,
-0.00405120849609375,
0.0203857421875,
0.0120086669921875,
-0.052490234375,
0.0014562606811523438,
0.01319122314453125,
-0.02734375,
0.023956298828125,
0.01357269287109375,
-0.001056671142578125,
-0.0106048583984375,
0.004962921142578125,
-0.00743865966796875,
0.0164031982421875,
-0.034881591796875,
0.01544952392578125,
0.0247650146484375,
0.00447845458984375,
0.0614013671875,
-0.032989501953125,
-0.001865386962890625,
-0.0164337158203125,
0.019134521484375,
0.009735107421875,
-0.016937255859375,
0.01074981689453125,
0.029388427734375,
0.0118865966796875,
0.0260009765625,
0.007251739501953125,
-0.0308685302734375,
-0.0009512901306152344,
0.033599853515625,
-0.035247802734375,
0.0014400482177734375,
0.00476837158203125,
-0.0087890625,
-0.02508544921875,
-0.003559112548828125,
0.0200653076171875,
0.01067352294921875,
-0.0198822021484375,
-0.017913818359375,
-0.00302886962890625,
-0.01800537109375,
-0.00937652587890625,
-0.01432037353515625,
0.00580596923828125,
0.005817413330078125,
0.035369873046875,
0.031829833984375,
0.00823974609375,
0.01552581787109375,
-0.0389404296875,
-0.000675201416015625,
-0.0235748291015625,
-0.030792236328125,
0.005893707275390625,
0.01415252685546875,
0.0206146240234375,
0.01091766357421875,
-0.0129547119140625,
-0.0213623046875,
-0.0087890625,
0.0169830322265625,
-0.02337646484375,
-0.0224761962890625,
-0.0202789306640625,
-0.013671875,
-0.019287109375,
0.01209259033203125,
0.00791168212890625,
-0.005695343017578125,
0.0110626220703125,
0.011077880859375,
0.00901031494140625,
0.0106048583984375,
0.011016845703125,
0.016571044921875,
-0.0174102783203125,
0.0124664306640625,
0.0140380859375,
0.0027980804443359375,
-0.02716064453125,
-0.00695037841796875,
0.0056304931640625,
-0.01045989990234375,
-0.02117919921875,
0.0260009765625,
0.023284912109375,
0.0307464599609375,
-0.00919342041015625,
0.006618499755859375,
0.036651611328125,
0.0002791881561279297,
-0.0219879150390625,
-0.005352020263671875,
-0.01328277587890625,
-0.0048675537109375,
-0.0225372314453125,
0.02020263671875,
-0.028594970703125,
-0.01171875,
0.01529693603515625,
-0.00782012939453125,
-0.0308837890625,
0.025054931640625,
-0.01226806640625,
0.006389617919921875,
0.0124359130859375,
0.00383758544921875,
0.0139312744140625,
0.0106201171875,
-0.0142059326171875,
-0.033538818359375,
0.046356201171875,
-0.0225982666015625,
0.041839599609375,
0.01030731201171875,
0.006023406982421875,
-0.0296173095703125,
0.0285186767578125,
0.00815582275390625,
-0.0159912109375,
0.0104522705078125,
0.024627685546875,
0.0202178955078125,
0.0239105224609375,
0.005645751953125,
0.00836181640625,
0.0162200927734375,
0.01374053955078125,
-0.00421905517578125,
0.0192108154296875,
-0.00467681884765625,
0.0007801055908203125,
-0.0021343231201171875,
-0.0190582275390625,
-0.01404571533203125,
-0.031402587890625,
-0.031402587890625,
-0.00281524658203125,
0.0218658447265625,
-0.01678466796875,
-0.0183868408203125,
0.01291656494140625,
-0.03118896484375,
0.0056610107421875,
-0.00623321533203125,
-0.0018815994262695312,
0.0015802383422851562,
-0.042724609375,
0.0236053466796875,
0.0309600830078125,
-0.009429931640625,
-0.0238800048828125,
0.0262298583984375,
-0.009796142578125,
0.01384735107421875,
0.02044677734375,
0.0322265625,
0.016357421875,
0.0188751220703125,
-0.015411376953125,
0.00958251953125,
0.01108551025390625,
-0.00312042236328125,
-0.0019435882568359375,
-0.033538818359375,
0.037506103515625,
-0.010894775390625,
0.01300048828125,
-0.03350830078125,
-0.008544921875,
-0.028961181640625,
0.0218048095703125,
-0.039825439453125,
0.01064300537109375,
-0.0276336669921875,
-0.00695037841796875,
0.00311279296875,
0.0084381103515625,
0.0007252693176269531,
0.004489898681640625,
-0.0068206787109375,
0.00362396240234375,
-0.01885986328125,
0.0174713134765625,
0.001071929931640625,
-0.0286712646484375,
-0.0065155029296875,
0.00016117095947265625,
-0.0247039794921875,
-0.0148773193359375,
0.0010881423950195312,
-0.01235198974609375,
-0.007720947265625,
-0.012786865234375,
0.02001953125,
0.009735107421875,
-0.01934814453125,
0.045654296875,
-0.007350921630859375,
-0.0186920166015625,
-0.0143585205078125,
0.0166778564453125,
-0.01296234130859375,
-0.030670166015625,
0.0099639892578125,
0.0252838134765625,
-0.031280517578125,
0.0175933837890625,
0.0255889892578125,
0.005474090576171875,
0.00344085693359375,
-0.0100860595703125,
-0.036468505859375,
-0.02618408203125,
0.0151824951171875,
-0.028167724609375,
-0.046142578125,
0.0119171142578125,
0.00502777099609375,
0.01277923583984375,
-0.01531982421875,
-0.01309967041015625,
-0.01201629638671875,
0.005435943603515625,
-0.004108428955078125,
0.002544403076171875,
0.053802490234375,
0.0184478759765625,
0.001476287841796875,
0.00815582275390625,
0.03778076171875,
-0.0187225341796875,
-0.0006046295166015625,
-0.028350830078125,
-0.030609130859375,
-0.001461029052734375,
-0.0230712890625,
-0.0033626556396484375,
0.006198883056640625,
0.020660400390625,
0.0190277099609375,
0.0172576904296875,
-0.0085906982421875,
0.0206756591796875,
-0.0178985595703125,
-0.004482269287109375,
0.0164031982421875,
0.0182342529296875,
-0.01316070556640625,
0.0164031982421875,
-0.00873565673828125,
-0.030487060546875,
-0.005062103271484375,
0.004131317138671875,
-0.0042877197265625,
0.0166015625,
0.004467010498046875,
-0.0008640289306640625,
0.0360107421875,
-0.0245819091796875,
-0.021331787109375,
0.0173797607421875,
-0.0216827392578125,
0.035491943359375,
-0.038665771484375,
-0.0105438232421875,
0.023529052734375,
-0.016082763671875,
0.01526641845703125,
0.019317626953125,
-0.01348876953125,
-0.00714111328125,
0.0078277587890625,
-0.006801605224609375,
-0.0084381103515625,
-0.021453857421875,
0.039031982421875,
0.01514434814453125,
0.0283660888671875,
0.0209808349609375,
-0.03179931640625,
-0.0033054351806640625,
-0.00246429443359375,
0.0191802978515625,
-0.0161895751953125,
-0.005489349365234375,
-0.0017786026000976562,
-0.0106353759765625,
-0.006748199462890625,
-0.04510498046875,
0.0069732666015625,
0.01690673828125,
0.01447296142578125,
0.035675048828125,
-0.01410675048828125,
0.01131439208984375,
0.016510009765625,
0.002422332763671875,
0.018463134765625,
-0.005519866943359375,
0.0081939697265625,
0.012603759765625,
0.03582763671875,
-0.011993408203125,
-0.0118408203125,
-0.0006546974182128906,
0.0127716064453125,
-0.019775390625,
0.032470703125,
0.0186004638671875,
-0.016876220703125,
0.023468017578125,
-0.0128936767578125,
0.016265869140625,
0.004222869873046875,
0.013519287109375,
0.00249481201171875,
-0.059967041015625,
0.0120849609375,
-0.029754638671875,
-0.007770538330078125,
0.03887939453125,
-0.01324462890625,
0.007732391357421875,
-0.01873779296875,
0.0129547119140625,
0.009002685546875,
0.01284027099609375,
0.00661468505859375,
0.023040771484375,
0.018157958984375,
0.01050567626953125,
-0.005664825439453125,
-0.017913818359375,
-0.0333251953125,
0.024993896484375,
0.0015592575073242188,
0.0219573974609375,
-0.004711151123046875,
0.0006465911865234375,
-0.005878448486328125,
-0.009979248046875,
-0.041839599609375,
0.0017786026000976562,
-0.0120849609375,
0.007251739501953125,
0.0269775390625,
-0.032867431640625,
-0.015716552734375,
-0.00975799560546875,
0.0173187255859375,
-0.021636962890625,
0.011962890625,
-0.0266265869140625,
-0.004474639892578125,
-0.0214080810546875,
-0.00418853759765625,
-0.00774383544921875,
-0.01180267333984375,
-0.01033782958984375,
0.0005841255187988281,
-0.01479339599609375,
0.05157470703125,
-0.0325927734375,
0.006435394287109375,
-0.0194244384765625,
0.031402587890625,
0.00307464599609375,
-0.03790283203125,
0.0255889892578125,
-0.0037670135498046875,
-0.01103973388671875,
0.01042938232421875,
-0.0162200927734375,
-0.0069732666015625,
0.03924560546875,
-0.021026611328125,
-0.0006532669067382812,
-0.0042724609375,
-0.0211181640625,
-0.0249176025390625,
0.005405426025390625,
-0.0181884765625,
0.0180511474609375,
0.0183563232421875,
-0.020111083984375,
0.0245208740234375,
-0.038177490234375,
-0.0258941650390625,
0.0010175704956054688,
0.006435394287109375,
0.01363372802734375,
0.046875,
0.0169677734375,
-0.006626129150390625,
-0.01158905029296875,
0.01776123046875,
0.01380157470703125,
-0.01020050048828125,
0.0090789794921875,
0.0222930908203125,
0.004241943359375,
-0.004306793212890625,
-0.0086212158203125,
-0.051605224609375,
-0.031524658203125,
0.001598358154296875,
-0.02294921875,
0.0226593017578125,
0.0196990966796875,
0.00913238525390625,
0.0101776123046875,
-0.00009435415267944336,
0.00482940673828125,
-0.0177001953125,
0.00136566162109375,
-0.006526947021484375,
-0.0081329345703125,
0.0014524459838867188,
-0.052459716796875,
-0.0007939338684082031,
-0.036224365234375,
0.00330352783203125,
0.0227508544921875,
0.0054931640625,
0.0276641845703125,
-0.03375244140625,
-0.002666473388671875,
0.01438140869140625,
0.032440185546875,
-0.0033397674560546875,
-0.01324462890625,
-0.00937652587890625,
-0.03704833984375,
-0.0037441253662109375,
-0.016021728515625,
0.01326751708984375,
-0.01123046875,
-0.032440185546875,
-0.01261138916015625,
-0.0157928466796875,
0.0291595458984375,
0.007305145263671875,
-0.040740966796875,
0.0026073455810546875,
-0.005290985107421875,
0.0027065277099609375,
-0.00965118408203125,
-0.00014150142669677734,
0.010986328125,
-0.038238525390625,
0.0159454345703125,
-0.01904296875,
0.03106689453125,
-0.01078033447265625,
0.033966064453125,
-0.00897979736328125,
-0.0010652542114257812,
0.0016384124755859375,
0.01490020751953125,
0.020538330078125,
-0.00933837890625,
-0.03045654296875,
-0.027099609375,
-0.01617431640625,
0.029754638671875,
0.0259246826171875,
-0.002414703369140625,
0.045257568359375,
-0.0146484375,
0.0308380126953125,
-0.00748443603515625,
0.0035572052001953125,
-0.03375244140625,
0.00199127197265625,
-0.00740814208984375,
-0.004238128662109375,
-0.0070648193359375,
0.0030517578125,
0.0174407958984375,
-0.005092620849609375,
0.0034961700439453125,
-0.0213623046875,
-0.00836944580078125,
0.00037932395935058594,
0.03546142578125,
-0.0224761962890625,
-0.02288818359375,
0.0081329345703125,
0.0157470703125
] |
ours_521
|
Solution.
Solution 1: It is known for odd \(n\) and odd \(k\) that \(1+2+\cdots+n \mid 1^{k}+2^{k}+\cdots+n^{k}\). To see this, note that
$$
1^{k}+2^{k}+\cdots+n^{k}=\left(1^{k}+(n-1)^{k}\right)+\left(2^{k}+(n-2)^{k}\right)+\cdots+\left(\left(\frac{n-1}{2}\right)^{k}+\left(\frac{n+1}{2}\right)^{k}+n^{k}\right.
$$
and that each summand is a multiple of \(n\), and that
$$
1^{k}+2^{k}+\cdots+n^{k}=\left(1^{k}+n^{k}\right)+\left(2^{k}+(n-1)^{k}\right)+\cdots+\left(\left(\frac{n-1}{2}\right)^{k}+\left(\frac{n+3}{2}\right)^{k}\right)+\left(\frac{n+1}{2}\right)^{k},
$$
and that each summand is a multiple of \(\frac{n+1}{2}\), so \(1^{k}+2^{k}+\cdots+n^{k}\) must be a multiple of \(\frac{n(n+1)}{2}\). Consequently, \(1^{k}+2^{k}+\cdots+63^{k} \equiv 0 \pmod{2016}\) for all odd \(k\).
Solution 2: Let \(P(i)=\frac{i^{2011}-i}{i^{2}-1}\) after dividing out. Note that \(P(1)=1005\) (l'Hôpital's rule makes this easy). Let \(S\) be the sum we want. Note that \(P(i)\) is an odd function, so \(P(i)+P(63-i) \equiv 0 \pmod{63}\) and we easily get \(P(1)+S \equiv P(63) \equiv 0 \pmod{63}\). Similarly, \(P(1)+S \equiv 0 \pmod{64}\). So \(S \equiv -1005 \pmod{2016}\) and the answer is \(1011\).
\(\boxed{1011}\)
|
1011
|
{
"competition": "us_comps",
"dataset": "Ours",
"posts": null,
"source": "OMOSoln2-2.md"
}
|
Find the remainder when
$$
\sum_{i=2}^{63} \frac{i^{2011}-i}{i^{2}-1}
$$
is divided by \(2016\).
|
[
"/Mathematics/DiscreteMathematics/DivisionProblems",
"/Mathematics/DiscreteMathematics/GeneralDiscreteMathematics/DiscreteMath",
"/Mathematics/DiscreteMathematics/GeneralDiscreteMathematics/DiscreteMathematics",
"/Mathematics/DiscreteMathematics/GeneralDiscreteMathematics/FiniteMathematics",
"/Mathematics/NumberTheory/Arithmetic/GeneralArithmetic",
"/Mathematics/NumberTheory/Congruences/ChineseRemainderTheorem",
"/Mathematics/NumberTheory/Congruences/Congruence",
"/Mathematics/NumberTheory/Congruences/CongruenceEquation",
"/Mathematics/NumberTheory/Congruences/Congruent",
"/Mathematics/NumberTheory/Congruences/Mod",
"/Mathematics/NumberTheory/Congruences/ModularArithmetic",
"/Mathematics/NumberTheory/Congruences/Modulus",
"/Mathematics/NumberTheory/GeneralNumberTheory/ElementaryMethods",
"/Mathematics/NumberTheory/GeneralNumberTheory/ElementaryNumberTheory",
"/Mathematics/NumberTheory/GeneralNumberTheory/HigherArithmetic",
"/Mathematics/NumberTheory/GeneralNumberTheory/NumberTheory",
"/Mathematics/NumberTheory/Integers/Integer",
"/Mathematics/NumberTheory/Integers/N",
"/Mathematics/NumberTheory/Integers/PositiveInteger",
"/Mathematics/NumberTheory/Integers/WholeNumber",
"/Mathematics/NumberTheory/Integers/Z",
"/Mathematics/NumberTheory/Integers/Z-Plus"
] |
Pair the terms i and 63−i to obtain cancellations modulo 63 and modulo 64, then use the value at i=1 and CRT to find the remainder.
|
[
-0.00009638071060180664,
-0.0238189697265625,
0.03863525390625,
0.0183868408203125,
-0.000400543212890625,
0.04083251953125,
0.0009222030639648438,
-0.044158935546875,
0.00640106201171875,
-0.01404571533203125,
0.036651611328125,
-0.058319091796875,
-0.0008063316345214844,
0.0252532958984375,
-0.04083251953125,
-0.040985107421875,
0.01375579833984375,
-0.0010690689086914062,
0.0095977783203125,
-0.001125335693359375,
-0.00978851318359375,
0.00608062744140625,
-0.01407623291015625,
0.017608642578125,
-0.0275115966796875,
-0.0014486312866210938,
-0.017120361328125,
0.01418304443359375,
0.0221710205078125,
0.0294036865234375,
-0.035003662109375,
-0.025390625,
-0.02520751953125,
-0.00942230224609375,
-0.003017425537109375,
-0.00830841064453125,
0.01268768310546875,
-0.00213623046875,
0.00432586669921875,
-0.0203094482421875,
-0.007350921630859375,
0.03485107421875,
0.0004782676696777344,
-0.00634765625,
-0.0123291015625,
0.009033203125,
-0.0026073455810546875,
0.00389862060546875,
-0.007282257080078125,
-0.0007271766662597656,
-0.00484466552734375,
0.01268768310546875,
0.007526397705078125,
-0.005199432373046875,
-0.0217742919921875,
-0.0706787109375,
0.0123748779296875,
-0.007091522216796875,
-0.01161956787109375,
-0.045135498046875,
0.00791168212890625,
0.0197296142578125,
-0.01451873779296875,
-0.0131988525390625,
-0.0013437271118164062,
-0.016510009765625,
0.0256195068359375,
-0.0277252197265625,
-0.00466156005859375,
0.0029659271240234375,
0.00856781005859375,
-0.016204833984375,
-0.01371002197265625,
0.022247314453125,
0.025482177734375,
-0.014404296875,
-0.0177001953125,
0.0153961181640625,
0.0021266937255859375,
-0.00238800048828125,
0.01558685302734375,
0.02215576171875,
-0.008270263671875,
0.035247802734375,
-0.004024505615234375,
0.01299285888671875,
-0.01898193359375,
-0.0031757354736328125,
0.0261383056640625,
-0.004894256591796875,
-0.00016319751739501953,
-0.003269195556640625,
0.0175018310546875,
-0.029998779296875,
0.011566162109375,
-0.0179443359375,
0.006923675537109375,
-0.006900787353515625,
-0.0184173583984375,
0.0169525146484375,
-0.00705718994140625,
-0.018310546875,
-0.0177764892578125,
0.0025005340576171875,
-0.06304931640625,
-0.00963592529296875,
-0.02105712890625,
0.0023212432861328125,
-0.005588531494140625,
0.02398681640625,
0.0059967041015625,
0.004550933837890625,
0.040313720703125,
0.0216827392578125,
-0.014129638671875,
-0.009124755859375,
0.01226043701171875,
-0.0005040168762207031,
-0.006381988525390625,
0.004413604736328125,
-0.0028018951416015625,
-0.003910064697265625,
-0.003841400146484375,
-0.013427734375,
0.01297760009765625,
-0.01035308837890625,
-0.00623321533203125,
-0.01001739501953125,
0.02362060546875,
0.0250396728515625,
0.0149993896484375,
0.01068115234375,
-0.036651611328125,
-0.0280609130859375,
-0.0543212890625,
-0.0023441314697265625,
-0.00878143310546875,
-0.01052093505859375,
-0.01458740234375,
-0.0081024169921875,
0.022003173828125,
-0.0081024169921875,
0.014495849609375,
-0.007297515869140625,
-0.0086822509765625,
0.0296630859375,
-0.007801055908203125,
-0.0282745361328125,
-0.00042557716369628906,
-0.004077911376953125,
-0.0028362274169921875,
0.008941650390625,
0.00966644287109375,
-0.01641845703125,
-0.00319671630859375,
0.0182952880859375,
0.0035247802734375,
-0.01251983642578125,
-0.029449462890625,
0.00772857666015625,
-0.007659912109375,
-0.0021572113037109375,
-0.05804443359375,
0.037445068359375,
-0.0034084320068359375,
-0.0029430389404296875,
0.0025615692138671875,
-0.0176544189453125,
-0.009613037109375,
-0.00894927978515625,
0.01055908203125,
-0.01300048828125,
0.0086669921875,
-0.00142669677734375,
0.0027294158935546875,
0.01268768310546875,
-0.00995635986328125,
0.03826904296875,
-0.01149749755859375,
-0.017852783203125,
0.01513671875,
-0.0304107666015625,
-0.032318115234375,
-0.00458526611328125,
0.040679931640625,
-0.004848480224609375,
-0.0001996755599975586,
-0.01091766357421875,
0.027496337890625,
0.0034503936767578125,
-0.006412506103515625,
0.024688720703125,
0.006771087646484375,
0.00835418701171875,
-0.0143585205078125,
-0.01226806640625,
0.01047515869140625,
0.002208709716796875,
0.0058441162109375,
0.0115509033203125,
-0.0050811767578125,
0.0019073486328125,
0.00942230224609375,
0.0145263671875,
0.01184844970703125,
-0.0114288330078125,
0.025146484375,
0.00885772705078125,
0.004863739013671875,
-0.00799560546875,
0.00586700439453125,
0.0204010009765625,
-0.002414703369140625,
-0.07659912109375,
-0.01146697998046875,
-0.0015716552734375,
-0.007659912109375,
0.010955810546875,
0.023345947265625,
-0.0005464553833007812,
0.0151214599609375,
0.01515960693359375,
0.00476837158203125,
-0.0213623046875,
-0.023193359375,
-0.002788543701171875,
0.0157012939453125,
0.007579803466796875,
-0.0057373046875,
0.0087738037109375,
0.028778076171875,
0.0152435302734375,
-0.0230865478515625,
0.00179290771484375,
0.0093231201171875,
0.01105499267578125,
-0.0202178955078125,
-0.00604248046875,
0.0026569366455078125,
-0.0120391845703125,
0.00803375244140625,
-0.003498077392578125,
0.0171356201171875,
0.006282806396484375,
0.0154876708984375,
0.0050506591796875,
0.00835418701171875,
-0.005950927734375,
-0.019195556640625,
-0.0022258758544921875,
0.00911712646484375,
-0.0080718994140625,
-0.006839752197265625,
0.0034503936767578125,
0.01312255859375,
0.0008292198181152344,
0.0082244873046875,
-0.0090789794921875,
-0.0291748046875,
0.00960540771484375,
-0.0039825439453125,
-0.005138397216796875,
-0.01277923583984375,
0.0027561187744140625,
-0.004199981689453125,
-0.01763916015625,
-0.015655517578125,
-0.0022945404052734375,
0.023162841796875,
0.0175933837890625,
0.044525146484375,
-0.0092315673828125,
-0.02569580078125,
0.0024166107177734375,
-0.01097869873046875,
-0.003475189208984375,
0.0101318359375,
0.01395416259765625,
-0.0010395050048828125,
-0.01195526123046875,
0.0102081298828125,
-0.0240478515625,
0.0090484619140625,
0.0103912353515625,
0.0155181884765625,
-0.005096435546875,
0.0296630859375,
0.0009002685546875,
0.006015777587890625,
0.0083770751953125,
0.007640838623046875,
-0.0057373046875,
-0.0072479248046875,
0.01763916015625,
0.05303955078125,
-0.0439453125,
0.0249176025390625,
0.00988006591796875,
0.0033931732177734375,
-0.0230712890625,
0.0295562744140625,
0.00466156005859375,
-0.027618408203125,
-0.0095062255859375,
0.0098419189453125,
-0.0033435821533203125,
-0.0025119781494140625,
0.0031719207763671875,
0.00899505615234375,
-0.005298614501953125,
0.016845703125,
-0.002445220947265625,
0.00341033935546875,
-0.01241302490234375,
-0.02459716796875,
-0.0269317626953125,
0.00847625732421875,
0.023651123046875,
-0.02496337890625,
-0.006622314453125,
0.01068878173828125,
0.060333251953125,
0.004657745361328125,
0.0115966796875,
-0.031707763671875,
0.00969696044921875,
0.0390625,
0.01139068603515625,
-0.034088134765625,
0.01374053955078125,
-0.07537841796875,
0.01788330078125,
0.002819061279296875,
-0.00269317626953125,
-0.0279998779296875,
0.0016994476318359375,
0.00640869140625,
0.017333984375,
0.02490234375,
-0.0037631988525390625,
-0.01117706298828125,
-0.012298583984375,
0.0185699462890625,
0.0220489501953125,
-0.0147552490234375,
-0.0034313201904296875,
0.007518768310546875,
-0.00901031494140625,
0.01052093505859375,
0.00921630859375,
0.0184478759765625,
-0.00029158592224121094,
0.020477294921875,
-0.0034503936767578125,
-0.0283050537109375,
0.0015630722045898438,
-0.02471923828125,
-0.002605438232421875,
-0.044647216796875,
0.030609130859375,
0.0117950439453125,
0.00391387939453125,
-0.0133209228515625,
0.0106048583984375,
-0.00986480712890625,
-0.004482269287109375,
-0.026397705078125,
0.0030879974365234375,
-0.033905029296875,
0.00823974609375,
-0.00246429443359375,
-0.0280609130859375,
0.02569580078125,
-0.00394439697265625,
-0.04888916015625,
0.0016145706176757812,
0.0183868408203125,
0.0020046234130859375,
0.0240325927734375,
0.009002685546875,
0.03076171875,
0.04205322265625,
-0.029449462890625,
0.02459716796875,
0.0088958740234375,
-0.00827789306640625,
-0.0196075439453125,
-0.026702880859375,
-0.03607177734375,
0.0019588470458984375,
-0.00803375244140625,
-0.017822265625,
-0.0092620849609375,
-0.0108642578125,
-0.0157623291015625,
0.00783538818359375,
-0.00308990478515625,
0.0051422119140625,
0.033782958984375,
-0.03643798828125,
-0.0055084228515625,
-0.018829345703125,
-0.006252288818359375,
0.0032196044921875,
0.013031005859375,
0.01059722900390625,
-0.004245758056640625,
0.0013275146484375,
-0.0238494873046875,
0.03021240234375,
0.022369384765625,
0.02423095703125,
0.01629638671875,
-0.01215362548828125,
0.009674072265625,
-0.0242462158203125,
0.01148223876953125,
-0.00035643577575683594,
-0.01241302490234375,
0.0003833770751953125,
-0.01084136962890625,
-0.019256591796875,
0.038421630859375,
0.01470184326171875,
0.006656646728515625,
0.01119232177734375,
-0.030914306640625,
0.007843017578125,
0.024383544921875,
-0.01238250732421875,
0.001979827880859375,
-0.03326416015625,
0.04437255859375,
-0.015594482421875,
-0.0074615478515625,
0.005733489990234375,
0.00046944618225097656,
0.016448974609375,
-0.01274871826171875,
0.01001739501953125,
0.005870819091796875,
0.017120361328125,
-0.021026611328125,
0.0155029296875,
-0.04620361328125,
0.01503753662109375,
0.033355712890625,
0.01558685302734375,
-0.03814697265625,
0.004558563232421875,
-0.0191650390625,
-0.00463104248046875,
-0.00787353515625,
0.01538848876953125,
-0.006988525390625,
0.02972412109375,
-0.003276824951171875,
-0.0027408599853515625,
-0.006744384765625,
0.0007328987121582031,
-0.006595611572265625,
0.021453857421875,
0.00559234619140625,
-0.01557159423828125,
-0.038330078125,
-0.004695892333984375,
-0.03607177734375,
-0.002948760986328125,
0.0010890960693359375,
0.0012054443359375,
0.0007405281066894531,
-0.0004215240478515625,
0.0377197265625,
-0.0242767333984375,
-0.06036376953125,
0.032745361328125,
-0.00814056396484375,
0.020904541015625,
-0.00826263427734375,
-0.030792236328125,
0.0241546630859375,
0.00720977783203125,
-0.0164337158203125,
0.05810546875,
0.0033664703369140625,
0.0252838134765625,
0.035247802734375,
0.01317596435546875,
-0.0036067962646484375,
0.01678466796875,
0.019744873046875,
0.05950927734375,
-0.005352020263671875,
-0.004962921142578125,
-0.0293731689453125,
-0.0260772705078125,
-0.02685546875,
-0.00231170654296875,
-0.0265350341796875,
0.01187896728515625,
-0.0109100341796875,
-0.025634765625,
-0.0202484130859375,
0.0206451416015625,
0.007526397705078125,
-0.016571044921875,
0.0279998779296875,
-0.02874755859375,
0.0399169921875,
-0.01641845703125,
-0.0025157928466796875,
0.01336669921875,
0.0421142578125,
-0.0217437744140625,
-0.005931854248046875,
0.03729248046875,
0.00212860107421875,
-0.0051116943359375,
0.00676727294921875,
-0.00212860107421875,
-0.01171112060546875,
0.038360595703125,
0.03118896484375,
-0.01175689697265625,
-0.0087432861328125,
-0.01248931884765625,
-0.004726409912109375,
-0.005298614501953125,
0.01265716552734375,
-0.0051727294921875,
-0.0009083747863769531,
-0.0272216796875,
0.045562744140625,
0.0082550048828125,
-0.048553466796875,
-0.002529144287109375,
0.0173187255859375,
-0.0200958251953125,
0.0130767822265625,
0.00768280029296875,
0.0213165283203125,
-0.01407623291015625,
-0.0294342041015625,
-0.03253173828125,
-0.01139068603515625,
-0.037384033203125,
-0.0164031982421875,
0.0028209686279296875,
-0.020233154296875,
0.0143280029296875,
0.0301666259765625,
-0.02191162109375,
0.0195770263671875,
-0.0181732177734375,
-0.0211181640625,
0.006130218505859375,
0.02825927734375,
-0.0015439987182617188,
-0.0162200927734375,
-0.0008053779602050781,
-0.0034313201904296875,
0.0054931640625,
0.037811279296875,
0.0287933349609375,
0.01406097412109375,
-0.005115509033203125,
-0.0257720947265625,
0.0229949951171875,
0.0017852783203125,
-0.004764556884765625,
0.002796173095703125,
-0.00164031982421875,
0.005794525146484375,
-0.0004258155822753906,
-0.0241546630859375,
-0.033538818359375,
-0.011199951171875,
-0.00757598876953125,
0.0294342041015625,
-0.0296173095703125,
0.027313232421875,
0.0081329345703125,
0.00011211633682250977,
0.001445770263671875,
0.0235595703125,
0.0079498291015625,
0.0297393798828125,
-0.00502777099609375,
-0.0004830360412597656,
0.01788330078125,
-0.0157928466796875,
0.006931304931640625,
-0.026123046875,
0.001689910888671875,
-0.0236663818359375,
-0.0010919570922851562,
0.0292510986328125,
0.01085662841796875,
-0.033599853515625,
-0.00658416748046875,
-0.01512908935546875,
0.0289764404296875,
-0.0175628662109375,
0.0268707275390625,
0.015899658203125,
-0.01494598388671875,
0.0149078369140625,
0.01555633544921875,
-0.00424957275390625,
-0.01151275634765625,
0.00007987022399902344,
0.007297515869140625,
0.035003662109375,
0.0189208984375,
0.019683837890625,
0.0004639625549316406,
-0.0078125,
-0.00049591064453125,
-0.0021648406982421875,
-0.01439666748046875,
0.0038661956787109375,
0.0050048828125,
-0.01451873779296875,
-0.006023406982421875,
-0.0213470458984375,
-0.01708984375,
0.0211181640625,
-0.0242919921875,
-0.004840850830078125,
0.0015773773193359375,
-0.0244903564453125,
0.0067596435546875,
0.0328369140625,
-0.0012769699096679688,
0.0268402099609375,
0.021087646484375,
-0.0191497802734375,
0.0018663406372070312,
0.01306915283203125,
-0.016845703125,
-0.00017714500427246094,
-0.004657745361328125,
-0.02587890625,
-0.042694091796875,
0.01177978515625,
0.003528594970703125,
-0.0256805419921875,
0.010009765625,
-0.01303863525390625,
0.0164337158203125,
-0.02545166015625,
-0.0160369873046875,
-0.013458251953125,
0.00042247772216796875,
-0.00203704833984375,
-0.01418304443359375,
0.01119232177734375,
-0.007568359375,
0.02392578125,
-0.003173828125,
0.0169219970703125,
-0.006122589111328125,
-0.011383056640625,
-0.0026264190673828125,
-0.046630859375,
-0.004886627197265625,
-0.0003368854522705078,
-0.01262664794921875,
0.03167724609375,
-0.0179443359375,
0.0146636962890625,
-0.0183868408203125,
0.0357666015625,
-0.007659912109375,
-0.0180816650390625,
-0.0071563720703125,
0.01021575927734375,
-0.00923919677734375,
0.01415252685546875,
0.027557373046875,
0.00771331787109375,
0.036041259765625,
0.0291290283203125,
0.02288818359375,
0.0291900634765625,
0.0004546642303466797,
-0.0203399658203125,
0.0090484619140625,
0.0125274658203125,
-0.0306854248046875,
0.01959228515625,
0.00913238525390625,
0.0196685791015625,
0.0242919921875,
-0.0044097900390625,
-0.038421630859375,
0.027679443359375,
-0.013519287109375,
-0.0184173583984375,
0.005584716796875,
-0.0017042160034179688,
-0.0117034912109375,
0.03546142578125,
0.00037217140197753906,
-0.0013055801391601562,
-0.00539398193359375,
-0.01971435546875,
-0.020721435546875,
-0.03948974609375,
0.00212860107421875,
-0.023590087890625,
0.005039215087890625,
-0.01458740234375,
-0.03302001953125,
0.003322601318359375,
0.00447845458984375,
0.0150146484375,
0.010955810546875,
0.0016069412231445312,
-0.024566650390625,
-0.0200347900390625,
0.026702880859375,
-0.0465087890625,
0.011260986328125,
0.0272369384765625,
-0.0013227462768554688,
-0.00441741943359375,
-0.0281219482421875,
-0.0355224609375,
0.0113067626953125,
-0.0285797119140625,
0.018951416015625,
-0.00609588623046875,
0.0257720947265625,
0.00910186767578125,
-0.00890350341796875,
0.004985809326171875,
-0.035980224609375,
0.0233001708984375,
-0.0114593505859375,
0.028656005859375,
-0.000690460205078125,
0.021270751953125,
-0.01052093505859375,
-0.0018491744995117188,
-0.01163482666015625,
-0.016265869140625,
-0.011932373046875,
0.00800323486328125,
-0.023956298828125,
0.0416259765625,
0.03546142578125,
0.0051116943359375,
-0.045501708984375,
-0.00940704345703125,
0.01309967041015625,
0.021759033203125,
-0.016571044921875,
-0.003307342529296875,
-0.011566162109375,
-0.03668212890625,
-0.0222930908203125,
0.0018177032470703125,
-0.0002073049545288086,
0.0039043426513671875,
-0.01273345947265625,
0.0007829666137695312,
0.0027313232421875,
-0.004291534423828125,
0.0280914306640625,
-0.0053863525390625,
0.0174713134765625,
0.032196044921875,
-0.0263519287109375,
0.0012912750244140625,
-0.0267181396484375,
-0.031524658203125,
-0.0031833648681640625,
0.0308380126953125,
0.00039649009704589844,
0.0282440185546875,
-0.01201629638671875,
0.0114288330078125,
-0.01229095458984375,
-0.0294647216796875,
-0.021881103515625,
0.0019817352294921875,
-0.0178070068359375,
0.0025634765625,
-0.01230621337890625,
0.042205810546875,
0.005321502685546875,
0.02484130859375,
-0.01384735107421875,
0.01166534423828125,
0.01873779296875,
0.03515625,
-0.056182861328125,
-0.00567626953125,
0.01166534423828125,
0.0287322998046875,
-0.0297088623046875,
0.0112762451171875,
0.020721435546875,
0.0156402587890625,
-0.033050537109375,
0.01424407958984375,
0.0020599365234375,
-0.0233612060546875,
0.0224609375,
-0.0095062255859375,
-0.0025463104248046875,
0.015899658203125,
0.010589599609375,
0.0132904052734375,
0.00431060791015625,
-0.0018243789672851562,
0.00815582275390625,
0.005580902099609375,
0.0277252197265625,
-0.00835418701171875,
-0.002193450927734375,
-0.0189361572265625,
-0.010711669921875,
-0.00905609130859375,
0.0078582763671875,
0.01207733154296875,
0.028472900390625,
0.019500732421875,
0.034088134765625,
-0.0174102783203125,
-0.0162200927734375,
0.0033740997314453125,
0.0017147064208984375,
0.0004298686981201172,
-0.00754547119140625,
-0.004924774169921875,
-0.006439208984375,
-0.016754150390625,
0.0149078369140625,
0.018951416015625,
0.03955078125,
0.004894256591796875,
-0.042816162109375,
0.0239105224609375,
-0.0228729248046875,
-0.00917816162109375,
0.0100555419921875,
0.007843017578125,
-0.0162200927734375,
0.0009083747863769531,
-0.0030078887939453125,
-0.00390625,
0.026336669921875,
-0.00783538818359375,
0.026519775390625,
0.005641937255859375,
0.00315093994140625,
-0.030914306640625,
-0.004611968994140625,
0.0193939208984375,
-0.0396728515625,
-0.01116180419921875,
0.0241241455078125,
-0.007129669189453125,
0.03253173828125,
-0.0076751708984375,
-0.007183074951171875,
0.025634765625,
-0.004047393798828125,
0.004241943359375,
0.0323486328125,
0.0031147003173828125,
-0.0230255126953125,
-0.0212554931640625,
-0.0219879150390625,
-0.00012791156768798828,
0.005580902099609375,
-0.007572174072265625,
0.00824737548828125,
0.006500244140625,
-0.035980224609375,
0.02459716796875,
0.00428009033203125,
0.0035228729248046875,
0.0153961181640625,
0.00589752197265625,
0.033172607421875,
-0.03668212890625,
-0.026519775390625,
-0.01197052001953125,
0.007251739501953125,
0.005359649658203125,
0.0008978843688964844,
0.0118865966796875,
0.01314544677734375,
0.01064300537109375,
0.0006403923034667969,
-0.0035877227783203125,
-0.061431884765625,
0.0271148681640625,
0.01494598388671875,
0.0252227783203125,
0.0112762451171875,
-0.025543212890625,
-0.0270538330078125,
-0.034820556640625,
0.0090789794921875,
0.002941131591796875,
0.01343536376953125,
0.0173187255859375,
0.01399993896484375,
-0.006961822509765625,
0.0185546875,
-0.0133514404296875,
-0.01165771484375,
0.01241302490234375,
-0.0063323974609375,
-0.01296234130859375,
0.011016845703125,
-0.032135009765625,
0.031341552734375,
0.00501251220703125,
-0.01161956787109375,
0.0030231475830078125,
0.0153656005859375,
-0.027801513671875,
0.001949310302734375,
0.01259613037109375,
0.0115203857421875,
-0.0303802490234375,
0.01546478271484375,
-0.01383209228515625,
-0.0038909912109375,
0.0285186767578125,
0.0257415771484375,
0.031280517578125,
0.007610321044921875,
0.0091400146484375,
-0.004138946533203125,
-0.032257080078125,
-0.0225982666015625,
0.04351806640625,
0.00981903076171875,
0.01873779296875,
0.03033447265625,
-0.00981903076171875,
0.02056884765625,
-0.0306396484375,
-0.007030487060546875,
-0.00821685791015625,
0.01052093505859375,
-0.0024089813232421875,
0.05426025390625,
-0.00917816162109375,
0.0011472702026367188,
-0.0019588470458984375,
-0.0150604248046875,
-0.019989013671875,
-0.0192718505859375,
-0.00023162364959716797,
0.0048980712890625,
-0.073486328125,
0.0243988037109375,
-0.0036144256591796875,
0.0007214546203613281,
0.03253173828125,
0.018341064453125,
0.042755126953125,
0.00989532470703125,
-0.0465087890625,
-0.0143280029296875,
-0.041168212890625,
-0.0218048095703125,
0.029052734375,
-0.0082855224609375,
-0.003963470458984375,
-0.006938934326171875,
0.0362548828125,
0.035247802734375,
-0.040740966796875,
0.01509857177734375,
-0.00658416748046875,
-0.0002541542053222656,
-0.028472900390625,
0.005962371826171875,
0.020751953125,
-0.0218353271484375,
0.0213165283203125,
-0.0023250579833984375,
-0.01081085205078125,
0.0189361572265625,
-0.003955841064453125,
-0.01349639892578125,
0.0291595458984375,
0.007171630859375,
-0.032318115234375,
-0.0015478134155273438,
0.03240966796875,
-0.0014734268188476562,
-0.0207366943359375,
-0.004657745361328125,
-0.01332855224609375,
-0.00432586669921875,
0.0013418197631835938,
0.01214599609375,
0.0253448486328125,
-0.0081024169921875,
0.00536346435546875,
-0.0030498504638671875,
-0.0207061767578125,
0.00530242919921875,
-0.007171630859375,
0.01165771484375,
-0.041229248046875,
0.0103302001953125,
0.004261016845703125,
-0.0012979507446289062,
-0.045806884765625,
-0.004055023193359375,
0.00949859619140625,
0.0302276611328125,
-0.0305023193359375,
-0.0219268798828125,
0.01161956787109375,
0.0161590576171875,
-0.0185394287109375,
0.02313232421875,
0.040618896484375,
0.01142120361328125,
-0.0011644363403320312,
-0.03009033203125,
-0.0029754638671875,
-0.01119232177734375,
-0.01537322998046875,
0.004245758056640625,
-0.002933502197265625,
-0.006282806396484375,
0.0007333755493164062,
-0.00322723388671875,
0.002254486083984375,
-0.0001329183578491211,
0.033782958984375,
0.0096588134765625,
-0.0107421875,
0.00015544891357421875,
-0.00711822509765625,
0.0176849365234375,
-0.036834716796875,
-0.020050048828125,
-0.037841796875,
0.0283660888671875,
-0.043487548828125,
-0.00458526611328125,
0.02264404296875,
0.005126953125,
0.04608154296875,
-0.0081634521484375,
0.005908966064453125,
0.02178955078125,
0.033843994140625,
-0.03350830078125,
-0.00926971435546875,
-0.05462646484375,
-0.015472412109375,
0.01256561279296875,
-0.0286865234375,
0.0033702850341796875,
-0.0030975341796875,
0.045806884765625,
-0.028656005859375,
0.036865234375,
0.00626373291015625,
0.00101470947265625,
0.01776123046875,
-0.00202178955078125,
0.0154266357421875,
-0.0531005859375,
-0.018463134765625,
0.01496124267578125,
-0.01251983642578125,
-0.00009953975677490234,
-0.0360107421875,
0.01412200927734375,
0.0096435546875,
-0.01043701171875,
-0.026214599609375,
-0.0361328125,
0.0004940032958984375,
-0.02752685546875,
-0.00315093994140625,
0.0269775390625,
0.01288604736328125,
-0.010528564453125,
0.0377197265625,
0.006534576416015625,
-0.0086822509765625,
0.0146484375,
-0.006305694580078125,
0.002063751220703125,
0.00447845458984375,
0.026275634765625,
-0.005733489990234375,
-0.0025501251220703125,
-0.0165252685546875,
-0.01355743408203125,
-0.025115966796875,
0.0190582275390625,
-0.0167083740234375,
-0.0127410888671875,
0.002933502197265625,
0.00807952880859375,
0.022613525390625,
0.01018524169921875,
0.0033130645751953125,
0.00823974609375,
-0.0223388671875,
-0.00852203369140625,
-0.02734375,
-0.005603790283203125,
0.00928497314453125,
0.0352783203125,
-0.0029392242431640625,
0.0009732246398925781,
0.0209503173828125,
0.0092010498046875,
-0.0233154296875,
-0.00852203369140625,
-0.015899658203125,
0.00010526180267333984,
0.021087646484375,
0.023956298828125,
-0.0158538818359375,
-0.0238189697265625,
0.0033931732177734375,
-0.0009441375732421875,
0.004161834716796875,
-0.0218048095703125,
0.023773193359375,
-0.00803375244140625,
-0.0024776458740234375,
-0.0248260498046875,
-0.00728607177734375,
-0.0229949951171875,
-0.01953125,
0.0162200927734375,
0.01024627685546875,
0.0036830902099609375,
0.01177215576171875,
-0.02001953125,
-0.0018377304077148438,
0.0129547119140625,
-0.0266265869140625,
-0.0172882080078125,
0.0107879638671875,
0.004543304443359375,
-0.027008056640625,
-0.003398895263671875,
0.005096435546875,
-0.030303955078125,
0.0246734619140625,
-0.0163116455078125,
0.01116180419921875,
-0.0087890625,
-0.0123138427734375,
-0.00833892822265625,
0.0028438568115234375,
0.03106689453125,
-0.0247650146484375,
-0.0106964111328125,
-0.0212249755859375,
-0.03253173828125,
-0.001399993896484375,
0.009124755859375,
-0.0233917236328125,
0.016571044921875,
0.0156402587890625,
0.0005950927734375,
-0.0302886962890625,
-0.00691986083984375,
-0.01219940185546875,
0.0037136077880859375,
0.005626678466796875,
-0.0067596435546875,
0.01168060302734375,
-0.007091522216796875,
0.002819061279296875,
-0.022705078125,
0.01439666748046875,
0.0197906494140625,
-0.0125732421875,
0.0236358642578125,
0.00464630126953125,
-0.0016021728515625,
0.00347900390625,
-0.00797271728515625,
-0.0301361083984375,
0.0183868408203125,
0.0262908935546875,
-0.009918212890625,
-0.0003650188446044922,
0.0008363723754882812,
0.006366729736328125,
0.000949859619140625,
-0.003276824951171875,
0.00849151611328125,
-0.01108551025390625,
0.029052734375,
-0.01407623291015625,
0.025665283203125,
-0.01334381103515625,
-0.0226593017578125,
0.006031036376953125,
-0.0129241943359375,
0.015228271484375,
0.004604339599609375,
0.04327392578125,
0.01190185546875,
0.002349853515625,
-0.01910400390625,
0.01013946533203125,
0.0165863037109375,
0.0028324127197265625,
-0.0078582763671875,
-0.0125732421875,
-0.0159149169921875,
-0.004184722900390625,
0.027923583984375,
-0.0183868408203125,
0.0113067626953125,
-0.0196533203125,
0.0023288726806640625,
0.0200958251953125,
0.04779052734375,
-0.0105438232421875,
-0.0104827880859375,
0.00807952880859375,
0.01233673095703125,
-0.0080718994140625,
0.034423828125,
0.00576019287109375,
0.035064697265625,
0.013580322265625,
0.00853729248046875,
0.01107025146484375,
-0.0203704833984375,
-0.0357666015625,
-0.023040771484375,
-0.010528564453125,
-0.0166778564453125,
-0.0185394287109375,
0.00852203369140625,
-0.036529541015625,
0.014801025390625,
-0.0171051025390625,
-0.016204833984375,
0.0194854736328125,
-0.0190887451171875,
-0.00524139404296875,
-0.0133209228515625,
-0.051422119140625,
0.00014722347259521484,
-0.0101776123046875,
0.01343536376953125,
-0.0027751922607421875,
-0.0209808349609375,
0.0147552490234375,
0.00920867919921875,
0.0032901763916015625,
0.0261993408203125,
0.0185089111328125,
-0.0211181640625,
-0.01568603515625,
0.03643798828125,
-0.0027484893798828125,
-0.0037631988525390625,
-0.0139007568359375,
-0.005107879638671875,
0.03912353515625,
0.0189208984375,
-0.004001617431640625,
0.03167724609375,
0.04290771484375,
-0.0030803680419921875,
-0.01114654541015625,
-0.036346435546875,
-0.045379638671875,
-0.01055145263671875,
-0.0080108642578125,
0.020721435546875,
0.0078125,
-0.00897216796875,
-0.023406982421875,
0.0172882080078125,
-0.008880615234375,
-0.0103607177734375,
-0.0036716461181640625,
0.028228759765625,
0.0191497802734375,
0.004993438720703125,
-0.02923583984375,
-0.01360321044921875,
-0.012847900390625,
-0.0001615285873413086,
-0.02801513671875,
-0.009429931640625,
0.051116943359375,
-0.01275634765625,
-0.0178985595703125,
0.004352569580078125,
0.002658843994140625,
0.01959228515625,
0.03582763671875,
0.020965576171875,
0.04083251953125,
0.0002696514129638672,
-0.005859375,
-0.0037746429443359375,
-0.03564453125,
0.01055145263671875,
-0.023101806640625,
0.00978851318359375,
-0.0159454345703125,
0.041595458984375,
-0.007236480712890625,
0.0164031982421875,
-0.018035888671875,
-0.005329132080078125,
-0.041412353515625,
-0.00815582275390625,
-0.00644683837890625,
-0.0272064208984375,
-0.029266357421875,
-0.006191253662109375,
-0.017333984375,
0.05133056640625,
-0.01071929931640625,
0.024078369140625,
0.02142333984375,
-0.033782958984375,
-0.0010652542114257812,
0.0269775390625,
-0.0157318115234375,
0.01216888427734375,
-0.0235595703125,
-0.0018110275268554688,
-0.035247802734375,
0.0022144317626953125,
0.022064208984375,
0.0015478134155273438,
-0.01464080810546875,
0.015716552734375,
0.007488250732421875,
0.039947509765625,
-0.0038242340087890625,
-0.0028743743896484375,
0.005550384521484375,
0.00406646728515625,
0.005764007568359375,
0.019775390625,
0.0003235340118408203,
0.00787353515625,
0.0131378173828125,
-0.001007080078125,
0.0111541748046875,
0.00603485107421875,
-0.0099334716796875,
0.00299835205078125,
0.009796142578125,
-0.0143280029296875,
-0.0129241943359375,
-0.01104736328125,
-0.0146331787109375,
0.01303863525390625,
0.00868988037109375,
0.019195556640625,
-0.05450439453125,
-0.0095062255859375,
-0.01375579833984375,
0.0233001708984375,
-0.0161895751953125,
-0.036834716796875,
-0.0017042160034179688,
-0.033782958984375,
0.005390167236328125,
0.0445556640625,
-0.004108428955078125,
0.028350830078125,
0.0249176025390625,
-0.0203399658203125,
0.0172882080078125,
-0.018310546875,
0.0103759765625,
0.009002685546875,
-0.0024852752685546875,
-0.0209197998046875,
0.038055419921875,
-0.0191650390625,
-0.038543701171875,
0.019989013671875,
0.0301666259765625,
0.01303863525390625,
-0.005252838134765625,
0.041229248046875,
-0.0222930908203125,
-0.03643798828125,
-0.004787445068359375,
0.0005173683166503906,
-0.00943756103515625,
-0.0007410049438476562,
0.0089263916015625,
0.00510406494140625,
0.0219879150390625,
-0.0038166046142578125,
0.01085662841796875,
-0.039459228515625,
-0.01165008544921875,
-0.0234832763671875,
0.0173187255859375,
0.03216552734375,
0.00478363037109375,
-0.01303863525390625,
-0.0106201171875,
0.001728057861328125,
-0.0037288665771484375,
-0.0164794921875,
0.0144195556640625,
-0.006298065185546875,
-0.0291748046875,
-0.0170440673828125,
-0.034088134765625,
-0.0270843505859375,
-0.0015821456909179688,
0.00711822509765625,
-0.0225677490234375,
-0.00218963623046875,
0.031402587890625,
-0.0022983551025390625,
0.0296173095703125,
0.01580810546875,
0.00238800048828125,
0.00682830810546875,
-0.0139923095703125,
0.00826263427734375,
-0.00907135009765625,
-0.01139068603515625,
0.004566192626953125,
0.00710296630859375,
-0.00397491455078125,
-0.01430511474609375,
-0.0047454833984375,
-0.046051025390625,
-0.0146484375,
0.03656005859375,
0.03387451171875,
0.01369476318359375,
-0.03558349609375,
0.0195465087890625,
0.02642822265625,
-0.002685546875,
-0.0284881591796875,
-0.01471710205078125,
0.017364501953125,
0.022796630859375,
0.0292205810546875,
-0.005153656005859375,
-0.056640625,
0.00801849365234375,
-0.01139068603515625,
-0.002147674560546875,
0.0281982421875,
-0.025970458984375,
0.0197296142578125,
-0.007541656494140625,
-0.011199951171875,
-0.01093292236328125,
0.0127716064453125,
0.005634307861328125,
0.020477294921875,
-0.002643585205078125,
-0.0228118896484375,
0.0228729248046875,
0.01666259765625,
0.0017175674438476562,
-0.01739501953125,
-0.01251220703125,
0.0272064208984375,
-0.01494598388671875,
-0.0174102783203125,
0.00797271728515625,
-0.0099029541015625,
-0.0189666748046875,
-0.0021305084228515625,
0.00933074951171875,
0.036712646484375,
-0.018310546875,
-0.00959014892578125,
-0.0219879150390625,
-0.00925445556640625,
0.0077972412109375,
-0.0104522705078125,
0.013671875,
0.04571533203125,
-0.031829833984375,
-0.004474639892578125,
-0.00970458984375,
-0.02490234375,
0.04638671875,
-0.0157623291015625,
-0.0254058837890625,
-0.00531768798828125,
-0.02484130859375,
-0.0141754150390625,
-0.006504058837890625,
-0.0322265625,
-0.023345947265625,
0.007205963134765625,
-0.032928466796875,
-0.0191192626953125,
-0.0281524658203125,
0.004974365234375,
0.00951385498046875,
0.011688232421875,
-0.00984954833984375,
0.009002685546875,
-0.0361328125,
-0.01172637939453125,
-0.01947021484375,
-0.0149383544921875,
0.0140380859375,
0.02435302734375,
-0.008819580078125,
-0.007358551025390625,
0.0177001953125,
0.0163116455078125,
0.0246734619140625,
0.0193023681640625,
0.020751953125,
0.003559112548828125,
0.0207366943359375,
0.01435089111328125,
0.00461578369140625,
-0.01201629638671875,
0.009124755859375,
0.01499176025390625,
-0.0251312255859375,
0.01143646240234375,
0.0162811279296875,
-0.00833892822265625,
0.009368896484375,
0.0285797119140625,
-0.006610870361328125,
0.0082550048828125,
0.0033397674560546875,
-0.035064697265625,
-0.000881195068359375,
-0.0174713134765625,
0.033447265625,
0.006702423095703125,
-0.0297393798828125,
-0.00836944580078125,
0.0202178955078125,
-0.022857666015625,
0.0175323486328125,
0.02911376953125,
0.0162811279296875,
0.018402099609375,
0.01055145263671875,
-0.0160369873046875,
-0.00579071044921875,
-0.000629425048828125,
0.0298004150390625,
0.0232391357421875,
0.0292510986328125,
-0.004795074462890625,
-0.012969970703125,
0.008148193359375,
-0.0185394287109375,
-0.01285552978515625,
0.01375579833984375,
-0.00623321533203125,
0.004241943359375,
0.00013566017150878906,
0.0018863677978515625,
-0.01312255859375,
-0.0065155029296875,
-0.025177001953125,
0.026397705078125,
0.0026569366455078125,
-0.00797271728515625,
0.060516357421875,
-0.00579071044921875,
-0.002964019775390625,
0.016571044921875,
-0.014923095703125,
-0.0110015869140625,
0.020233154296875,
-0.02374267578125,
0.0016078948974609375,
0.0308685302734375,
-0.030548095703125,
-0.0219879150390625,
-0.01161956787109375,
0.0247650146484375,
-0.007404327392578125,
0.018280029296875,
-0.002414703369140625,
-0.0203399658203125,
0.00997161865234375,
-0.00614166259765625,
0.0214385986328125,
-0.01476287841796875,
0.0184783935546875,
0.0006861686706542969,
0.01169586181640625,
0.0261688232421875,
-0.0120391845703125,
0.0083160400390625,
-0.0026493072509765625,
0.00984954833984375,
-0.00040411949157714844,
0.007335662841796875,
0.0194854736328125,
0.0010166168212890625,
0.035980224609375,
-0.0010690689086914062,
-0.0262451171875,
-0.020263671875,
-0.022216796875,
-0.0195770263671875,
0.0355224609375,
-0.022857666015625,
0.001819610595703125,
0.0239105224609375,
-0.01306915283203125,
0.0188446044921875,
-0.01312255859375,
0.032440185546875,
-0.012969970703125,
0.022979736328125,
-0.0173187255859375,
-0.016754150390625,
0.0190277099609375,
-0.0634765625,
-0.0301513671875,
0.033843994140625,
0.0218963623046875,
0.01953125,
0.016754150390625,
0.01497650146484375,
-0.0054168701171875,
0.0156402587890625,
0.0070648193359375,
0.017059326171875,
-0.00826263427734375,
-0.015411376953125,
-0.01337432861328125,
0.0183258056640625,
0.0090179443359375,
-0.006103515625,
-0.0236358642578125,
0.02081298828125,
0.037109375,
-0.00013518333435058594,
-0.00991058349609375,
-0.01067352294921875,
-0.0104827880859375,
0.01540374755859375,
-0.01342010498046875,
0.0021839141845703125,
-0.031707763671875,
-0.0125579833984375,
-0.00021028518676757812,
0.00934600830078125,
-0.0215911865234375,
0.01910400390625,
-0.0130767822265625,
0.029632568359375,
-0.0178070068359375,
-0.00803375244140625,
-0.0132293701171875,
-0.0189361572265625,
0.0092620849609375,
0.0263214111328125,
-0.021514892578125,
0.00955963134765625,
-0.00800323486328125,
0.0159454345703125,
0.006458282470703125,
0.032806396484375,
0.052703857421875,
-0.0011415481567382812,
0.008697509765625,
0.017913818359375,
0.052337646484375,
0.013763427734375,
0.0178680419921875,
0.00737762451171875,
-0.02545166015625,
0.0310516357421875,
-0.00897979736328125,
0.01290130615234375,
0.015625,
-0.0408935546875,
0.0022754669189453125,
0.0157470703125,
-0.02081298828125,
0.029510498046875,
-0.0203857421875,
0.00582122802734375,
-0.005886077880859375,
-0.0005154609680175781,
-0.051971435546875,
0.021453857421875,
-0.0135955810546875,
0.017852783203125,
0.04071044921875,
0.0169219970703125,
0.01047515869140625,
-0.04766845703125,
-0.0098419189453125,
-0.006610870361328125,
0.0218048095703125,
-0.0135650634765625,
0.02728271484375,
0.01535797119140625,
0.01149749755859375,
0.00946044921875,
0.005542755126953125,
-0.00009340047836303711,
0.0022678375244140625,
0.015625,
0.017181396484375,
-0.00501251220703125,
0.0225067138671875,
-0.006496429443359375,
0.0258941650390625,
-0.00913238525390625,
-0.00860595703125,
-0.0189056396484375,
0.00006633996963500977,
0.0006089210510253906,
0.01461029052734375,
0.0174102783203125,
-0.0023441314697265625,
-0.00811767578125,
-0.03509521484375,
0.0144805908203125,
0.0204315185546875,
-0.0156402587890625,
-0.0252838134765625,
-0.03759765625,
0.006313323974609375,
-0.01300048828125,
-0.03253173828125,
0.0219573974609375,
-0.01287841796875,
-0.0152435302734375,
0.0122833251953125,
-0.006885528564453125,
-0.005725860595703125,
-0.04718017578125,
0.00390625,
0.0024890899658203125,
-0.01424407958984375,
-0.004192352294921875,
0.014862060546875,
-0.00006115436553955078,
-0.03955078125,
-0.0042724609375,
-0.007595062255859375,
0.00637054443359375,
0.00609588623046875,
0.01134490966796875,
-0.005603790283203125,
-0.01349639892578125,
0.0197296142578125,
0.0177154541015625,
-0.0229949951171875,
-0.007793426513671875,
0.00994873046875,
0.022918701171875,
0.033111572265625,
0.00501251220703125,
0.033294677734375,
0.02642822265625,
0.009033203125,
-0.007038116455078125,
0.0024509429931640625,
-0.010986328125,
-0.023651123046875,
0.01508331298828125,
0.0159454345703125,
0.005977630615234375,
0.00042724609375,
0.0120391845703125,
-0.01434326171875,
-0.0174102783203125,
-0.00502777099609375,
0.01213836669921875,
0.0047607421875,
0.01194000244140625,
-0.0028076171875,
0.0225982666015625,
0.00885772705078125,
-0.02081298828125,
-0.043670654296875,
0.0443115234375,
0.01316070556640625,
0.0032958984375,
0.00611114501953125,
0.0217742919921875,
0.0144805908203125,
0.0239715576171875,
-0.006504058837890625,
-0.0282440185546875,
-0.022125244140625,
0.0303497314453125,
-0.00484466552734375,
-0.01531219482421875,
-0.01010894775390625,
0.01110076904296875,
-0.0229034423828125,
-0.0022754669189453125,
0.00492095947265625,
0.0011491775512695312,
0.0017061233520507812,
0.0151824951171875,
-0.0103607177734375,
0.038665771484375,
-0.01177215576171875,
0.025299072265625,
-0.0135040283203125,
-0.0221099853515625,
0.032135009765625,
-0.003894805908203125,
-0.01235198974609375,
-0.0275421142578125,
-0.0048980712890625,
0.0228271484375,
0.00574493408203125,
0.023284912109375,
0.008880615234375,
-0.0084228515625,
0.0261993408203125,
-0.01180267333984375,
-0.01007080078125,
-0.004360198974609375,
-0.00989532470703125,
0.0316162109375,
-0.0002770423889160156,
-0.027069091796875,
-0.00479888916015625,
0.0318603515625,
-0.01433563232421875,
0.00521087646484375,
-0.006877899169921875,
0.0029735565185546875,
0.006866455078125,
-0.006000518798828125,
0.0298309326171875,
-0.0267333984375,
0.005054473876953125,
-0.005245208740234375,
0.0199432373046875,
-0.0151519775390625,
0.020721435546875,
0.0010156631469726562,
0.006023406982421875,
0.01502227783203125,
-0.0051727294921875,
0.0140228271484375,
-0.01485443115234375,
-0.0399169921875,
0.00930023193359375,
-0.0014171600341796875,
0.0004088878631591797,
0.0168914794921875,
-0.016448974609375,
0.0191497802734375,
0.006927490234375,
0.00579071044921875,
-0.018585205078125,
0.01036834716796875,
0.004085540771484375,
0.0024089813232421875,
0.049957275390625,
0.033233642578125,
0.0167083740234375,
-0.0220947265625,
0.006504058837890625,
-0.0007543563842773438,
0.053070068359375,
-0.0156707763671875,
-0.01641845703125,
-0.033111572265625,
0.01300811767578125,
0.009429931640625,
-0.00930023193359375,
0.0047760009765625,
-0.0213775634765625,
-0.0066986083984375,
-0.0079345703125,
-0.00699615478515625,
-0.028533935546875,
0.00237274169921875,
-0.0072479248046875,
-0.030181884765625,
0.01056671142578125,
-0.003543853759765625,
0.02294921875,
-0.0099334716796875,
-0.036376953125,
-0.01178741455078125,
0.00540924072265625,
0.04022216796875,
0.0266571044921875,
0.0027828216552734375,
-0.004192352294921875,
0.01532745361328125,
0.0009760856628417969,
-0.0225677490234375,
0.01430511474609375,
0.0104827880859375,
0.0023784637451171875,
-0.01326751708984375,
-0.00047707557678222656,
0.00791168212890625,
0.005146026611328125,
-0.011993408203125,
-0.027252197265625,
-0.00449371337890625,
0.006526947021484375,
-0.00569915771484375,
-0.01552581787109375,
0.009918212890625,
-0.0347900390625,
-0.0012712478637695312,
0.0199432373046875,
-0.01136016845703125,
-0.0196990966796875,
-0.0110626220703125,
0.024627685546875,
0.00742340087890625,
0.0084228515625,
-0.02490234375,
0.004001617431640625,
-0.00513458251953125,
0.01480865478515625,
-0.034942626953125,
-0.01194000244140625,
-0.0216217041015625,
-0.0106964111328125,
-0.01041412353515625,
0.01275634765625,
0.0144195556640625,
0.02874755859375,
0.00798797607421875,
0.0020904541015625,
-0.005321502685546875,
0.01088714599609375,
-0.0176544189453125,
-0.017303466796875,
-0.03411865234375,
-0.00713348388671875,
0.007297515869140625,
0.0287933349609375,
-0.040924072265625,
-0.014892578125,
-0.00958251953125,
-0.01398468017578125,
-0.01299285888671875,
-0.00519561767578125,
0.007350921630859375,
0.061309814453125,
0.0025577545166015625,
-0.016326904296875,
0.0123138427734375,
0.0205535888671875,
-0.009429931640625,
-0.0025310516357421875,
-0.0237579345703125,
-0.0034236907958984375,
-0.0060577392578125,
0.0169219970703125,
-0.029693603515625,
0.0223388671875,
-0.0164794921875,
-0.02398681640625,
0.01296234130859375,
0.001995086669921875,
-0.02642822265625,
0.014404296875,
-0.00360107421875,
0.03216552734375,
0.01446533203125,
0.0264434814453125,
0.01474761962890625,
-0.0128173828125,
-0.016204833984375,
0.0096282958984375,
0.01611328125,
0.0186920166015625,
-0.01206207275390625,
0.020263671875,
0.011444091796875,
-0.007160186767578125,
0.0070648193359375,
-0.0019702911376953125,
-0.005100250244140625,
0.002964019775390625,
-0.030029296875,
-0.0146484375,
0.0010967254638671875,
-0.0238800048828125,
0.0193634033203125,
-0.027099609375,
0.0190887451171875,
0.036712646484375,
0.0208282470703125,
0.003055572509765625,
-0.01007843017578125,
0.0202789306640625,
-0.00814056396484375,
0.009613037109375,
0.0241851806640625,
0.0013561248779296875,
-0.02435302734375,
-0.024993896484375,
0.006877899169921875,
0.0112152099609375,
-0.0138397216796875,
0.01409912109375,
0.018646240234375,
0.00737762451171875,
0.03399658203125,
-0.0038433074951171875,
0.01507568359375,
0.002750396728515625,
-0.0212249755859375,
-0.0171661376953125,
0.02001953125,
-0.003795623779296875,
-0.006122589111328125,
-0.0079498291015625,
-0.015777587890625,
0.009674072265625,
-0.0107574462890625,
-0.00611114501953125,
0.01540374755859375,
0.0160980224609375,
0.027252197265625,
-0.0228271484375,
0.00888824462890625,
-0.0004470348358154297,
-0.006206512451171875,
0.050445556640625,
-0.0030517578125,
-0.0219573974609375,
0.03802490234375,
-0.0065460205078125,
0.03924560546875,
0.022735595703125,
-0.02099609375,
0.020782470703125,
0.04559326171875,
-0.03729248046875,
0.00107574462890625,
-0.0226287841796875,
-0.0007572174072265625,
-0.0233001708984375,
0.01007843017578125,
0.00676727294921875,
0.01111602783203125,
0.00015783309936523438,
-0.02117919921875,
0.01000213623046875,
0.031829833984375,
0.0010938644409179688,
-0.01485443115234375,
-0.01277923583984375,
0.02667236328125,
0.029296875,
0.0374755859375,
-0.0016965866088867188,
-0.0023441314697265625,
-0.03509521484375,
0.00238037109375,
-0.003376007080078125,
-0.0281982421875,
-0.054595947265625,
0.0029735565185546875,
-0.00603485107421875,
0.0369873046875,
0.006103515625,
-0.0001461505889892578,
-0.00640869140625,
-0.0223846435546875,
0.031585693359375,
-0.028228759765625,
0.0226898193359375,
0.0142669677734375,
0.0017452239990234375,
-0.01424407958984375,
-0.002803802490234375,
0.0003426074981689453,
0.005779266357421875,
-0.033447265625,
-0.005977630615234375,
-0.005748748779296875,
-0.04486083984375,
-0.0108184814453125,
0.0298919677734375,
0.0300445556640625,
0.03704833984375,
0.0117034912109375,
0.0048675537109375,
-0.0465087890625,
0.004444122314453125,
-0.01165008544921875,
0.02642822265625,
0.0134429931640625,
-0.04644775390625,
-0.00833892822265625,
0.0021724700927734375,
-0.00774383544921875,
0.0024204254150390625,
0.01018524169921875,
-0.0232696533203125,
0.0274200439453125,
-0.0042572021484375,
0.0243377685546875,
0.01299285888671875,
0.0111846923828125,
-0.00848388671875,
-0.0218505859375,
0.0259552001953125,
-0.044464111328125,
-0.0115509033203125,
0.00829315185546875,
-0.0202789306640625,
0.01349639892578125,
0.04119873046875,
-0.0156707763671875,
-0.01117706298828125,
-0.005889892578125,
-0.0023479461669921875,
-0.00946807861328125,
0.043304443359375,
-0.003566741943359375,
0.021209716796875,
0.01186370849609375,
-0.037109375,
-0.022674560546875,
0.0084228515625,
0.01544189453125,
0.0035381317138671875,
-0.0006518363952636719,
-0.0038661956787109375,
0.016937255859375,
-0.00749969482421875,
-0.028717041015625,
-0.030731201171875,
-0.007724761962890625,
-0.00261688232421875,
-0.032928466796875,
0.005462646484375,
-0.02569580078125,
-0.0090789794921875,
-0.005962371826171875,
-0.0179901123046875,
-0.0158843994140625,
-0.01366424560546875,
0.011688232421875,
-0.005428314208984375,
-0.0245208740234375,
-0.027130126953125,
0.02081298828125,
0.00020503997802734375,
-0.02484130859375,
-0.02227783203125,
0.0247344970703125,
-0.04351806640625,
-0.003787994384765625,
0.05059814453125,
-0.010162353515625,
0.0092315673828125,
0.007038116455078125,
0.026580810546875,
-0.00846099853515625,
-0.0021209716796875,
0.00691986083984375,
0.015899658203125,
-0.012603759765625,
-0.010040283203125,
-0.0237274169921875,
-0.00608062744140625,
0.00270843505859375,
-0.021270751953125,
0.0090789794921875,
0.0167083740234375,
0.005950927734375,
-0.004329681396484375,
0.0164642333984375,
-0.01236724853515625,
-0.0017061233520507812,
-0.007633209228515625,
-0.046112060546875,
0.021697998046875,
0.0038127899169921875,
-0.0218658447265625,
0.01479339599609375,
-0.01898193359375,
0.007144927978515625,
-0.01001739501953125,
-0.0061798095703125,
-0.0079803466796875,
0.0053863525390625,
0.006557464599609375,
-0.0161895751953125,
-0.0005803108215332031,
-0.0263519287109375,
0.0171966552734375,
-0.01549530029296875,
-0.015167236328125,
-0.0166168212890625,
0.00693511962890625,
0.0115203857421875,
-0.0002930164337158203,
-0.01549530029296875,
-0.005878448486328125,
-0.007354736328125,
0.0254058837890625,
-0.0197906494140625,
0.00513458251953125,
0.01763916015625,
-0.00994110107421875,
0.01544952392578125,
-0.0007519721984863281,
0.0002760887145996094,
-0.029052734375,
0.0016660690307617188,
-0.025238037109375,
-0.01029205322265625,
0.0124359130859375,
-0.0036563873291015625,
0.0086669921875,
-0.0275726318359375,
0.032684326171875,
-0.0227203369140625,
-0.043914794921875,
-0.01335906982421875,
-0.00030422210693359375,
-0.016082763671875,
0.006061553955078125,
-0.01947021484375,
-0.003162384033203125,
-0.0002694129943847656,
0.0026798248291015625,
-0.010406494140625,
-0.0010194778442382812,
0.00835418701171875,
0.0019025802612304688,
0.01201629638671875,
-0.024444580078125,
0.00943756103515625,
-0.0213775634765625,
-0.0110321044921875,
0.034515380859375,
0.00559234619140625,
-0.025360107421875,
-0.0023250579833984375,
0.033050537109375,
-0.0056915283203125,
0.0224609375,
0.01377105712890625,
-0.0095367431640625,
-0.01885986328125,
-0.0252838134765625,
0.027099609375,
0.028472900390625,
0.0107421875,
-0.0195770263671875,
-0.0269775390625,
0.016937255859375,
-0.00357818603515625,
0.0095367431640625,
-0.002716064453125,
0.01532745361328125,
0.00760650634765625,
0.0099029541015625,
-0.0155181884765625,
0.01422119140625,
0.026641845703125,
-0.01514434814453125,
0.0290679931640625,
0.0310821533203125,
0.0110321044921875,
-0.005931854248046875,
0.037445068359375,
0.039947509765625,
-0.01605224609375,
0.024169921875,
-0.039031982421875,
-0.00885772705078125,
-0.033203125,
-0.031646728515625,
-0.016510009765625,
0.00829315185546875,
0.026641845703125,
0.027557373046875,
0.0020542144775390625,
0.0166015625,
-0.0031719207763671875,
-0.029693603515625,
-0.01047515869140625,
0.00568389892578125,
0.0152130126953125,
0.0106964111328125,
-0.0076446533203125,
-0.02850341796875,
-0.02203369140625,
0.0168914794921875,
-0.0174560546875,
-0.00737762451171875,
0.01702880859375,
0.00769805908203125,
-0.031402587890625,
0.010467529296875,
-0.022064208984375,
0.02532958984375,
-0.00519561767578125,
-0.01763916015625,
0.02288818359375,
-0.0360107421875,
0.005306243896484375,
0.001811981201171875,
0.005146026611328125,
0.01190185546875,
0.0006666183471679688,
-0.034027099609375,
-0.00774383544921875,
0.016082763671875,
-0.01345062255859375,
-0.0182952880859375,
0.017425537109375,
0.0011873245239257812,
-0.0095367431640625,
0.00841522216796875,
-0.01271820068359375,
-0.021240234375,
-0.01267242431640625,
0.004726409912109375,
0.0012979507446289062,
-0.0189666748046875,
-0.01081085205078125,
-0.020599365234375,
-0.0158843994140625,
-0.0007529258728027344,
-0.0199737548828125,
-0.0042266845703125,
0.0279541015625,
0.023590087890625,
0.0008111000061035156,
-0.01445770263671875,
0.007167816162109375,
0.00576019287109375,
0.0028839111328125,
0.01336669921875,
-0.0036602020263671875,
-0.01041412353515625,
0.0003027915954589844,
-0.0047454833984375,
-0.0182647705078125,
0.01111602783203125,
0.0007081031799316406,
0.0272216796875,
-0.0240631103515625,
0.03912353515625,
0.0265655517578125,
0.042236328125,
0.032073974609375,
-0.01776123046875,
-0.007144927978515625,
-0.014617919921875,
0.0271148681640625,
-0.0199737548828125,
0.01483154296875,
0.004032135009765625,
-0.0173492431640625,
0.019744873046875,
0.023223876953125,
-0.02264404296875,
0.00763702392578125,
0.0204620361328125,
0.04144287109375,
-0.0178070068359375,
0.00506591796875,
-0.032470703125,
-0.0177764892578125,
0.02166748046875,
-0.025390625,
-0.003185272216796875,
-0.007541656494140625,
-0.028289794921875,
0.00528717041015625,
-0.005153656005859375,
0.0394287109375,
0.0174560546875,
-0.02984619140625,
-0.01290130615234375,
0.0139312744140625,
-0.0219268798828125,
-0.015533447265625,
-0.002044677734375,
-0.00809478759765625,
0.0021457672119140625,
-0.00042891502380371094,
-0.039642333984375,
0.0167083740234375,
0.0172576904296875,
-0.007080078125,
0.0096588134765625,
0.014404296875,
-0.0062408447265625,
-0.026702880859375,
-0.0100860595703125,
0.0131988525390625,
-0.01326751708984375,
0.0004458427429199219,
-0.00811004638671875,
0.0250396728515625,
0.035247802734375,
-0.039947509765625,
0.0207061767578125,
0.01067352294921875,
0.022979736328125,
-0.0279998779296875,
-0.000012516975402832031,
0.01166534423828125,
0.007053375244140625,
-0.034454345703125,
0.0263671875,
0.026947021484375,
-0.00811004638671875,
0.0200958251953125,
0.009979248046875,
-0.0028667449951171875,
0.003936767578125,
0.0228271484375,
0.00872039794921875,
-0.00769805908203125,
-0.01256561279296875,
0.009765625,
0.0015439987182617188,
-0.05889892578125,
-0.0018720626831054688,
-0.0017490386962890625,
0.005588531494140625,
0.01401519775390625,
-0.01338958740234375,
-0.035888671875,
0.00047135353088378906,
-0.01406097412109375,
-0.002147674560546875,
-0.0237579345703125,
0.0185394287109375,
0.0266876220703125,
-0.029296875,
-0.0011663436889648438,
0.04437255859375,
0.005275726318359375,
-0.0250091552734375,
0.004756927490234375,
-0.04864501953125,
-0.015960693359375,
0.0212860107421875,
0.0211334228515625,
0.005916595458984375,
0.0174713134765625,
0.0090484619140625,
-0.007602691650390625,
-0.00019228458404541016,
0.0170135498046875,
-0.03167724609375,
-0.00194549560546875,
0.0070953369140625,
0.020111083984375,
0.0036449432373046875,
-0.043609619140625,
0.01157379150390625,
-0.02801513671875,
0.01389312744140625,
0.0158233642578125,
0.0100555419921875,
-0.01256561279296875,
-0.04241943359375,
-0.004512786865234375,
-0.0046234130859375,
-0.0230712890625,
0.0187835693359375,
-0.01611328125,
-0.01233673095703125,
0.0325927734375,
0.01000213623046875,
0.0010080337524414062,
0.0209503173828125,
0.0175933837890625,
-0.01291656494140625,
-0.01207733154296875,
-0.03204345703125,
-0.032958984375,
-0.017242431640625,
-0.04779052734375,
-0.0106353759765625,
-0.0154876708984375,
0.004344940185546875,
-0.0130767822265625,
-0.00524139404296875,
0.0411376953125,
-0.0217437744140625,
0.01216888427734375,
-0.0261077880859375,
-0.00848388671875,
-0.00919342041015625,
-0.0250091552734375,
-0.01172637939453125,
-0.0015764236450195312,
-0.0027523040771484375,
-0.001857757568359375,
0.00635528564453125,
0.00548553466796875,
-0.0318603515625,
-0.01062774658203125,
0.0140380859375,
-0.00827789306640625,
0.0141143798828125,
-0.00528717041015625,
0.0232696533203125,
0.0203094482421875,
0.0011758804321289062,
0.01361083984375,
0.00717926025390625,
-0.004955291748046875,
-0.01280975341796875,
-0.019195556640625,
0.0126800537109375,
-0.002788543701171875,
0.0251312255859375,
0.004894256591796875,
0.01995849609375,
-0.03460693359375,
-0.041290283203125,
-0.0003952980041503906,
0.00615692138671875,
0.01326751708984375,
-0.03271484375,
-0.037872314453125,
0.020111083984375,
0.022369384765625
] |
ours_522
|
Let \(A = (0, 0)\) and \(D = (1, 0)\). Then let vectors \(DB\) and \(DC\) be \([-3a, 3b]\) and \([-2b, -2a]\). Now, \(B = (1 - 3a, 3b)\) and \(C = (1 - 2b, -2a)\). We know \(\tan \frac{A}{2} = \frac{1}{2}\) by the half-angle formula, so \(\frac{3b}{1 - 3a} = \frac{1}{2}\) and \(\frac{-2a}{1 - 2b} = \frac{-1}{2}\). Solving this linear system of equations, we find \(a = \frac{2}{9}\) and \(b = \frac{1}{18}\). Thus, \(B = \left(\frac{1}{3}, \frac{1}{6}\right)\) and \(C = \left(\frac{8}{9}, \frac{-4}{9}\right)\). Using the distance formula, we find \(AB + AC = \frac{\sqrt{5}}{6} + \frac{4\sqrt{5}}{9} = \frac{11\sqrt{5}}{18}\), giving an answer of \(11 + 5 + 18 = 34\).
\(\boxed{34}\)
|
34
|
{
"competition": "us_comps",
"dataset": "Ours",
"posts": null,
"source": "OMOSoln2-2.md"
}
|
In triangle \(ABC\), \(\sin \angle A = \frac{4}{5}\) and \(\angle A < 90^\circ\). Let \(D\) be a point outside triangle \(ABC\) such that \(\angle BAD = \angle DAC\) and \(\angle BDC = 90^\circ\). Suppose that \(AD = 1\) and that \(\frac{BD}{CD} = \frac{3}{2}\). If \(AB + AC\) can be expressed in the form \(\frac{a \sqrt{b}}{c}\) where \(a, b, c\) are pairwise relatively prime integers, find \(a + b + c\).
|
[
"/Mathematics/Geometry/CoordinateGeometry/AnalyticGeometry",
"/Mathematics/Geometry/CoordinateGeometry/Cartesian",
"/Mathematics/Geometry/CoordinateGeometry/CartesianCoordinateSystem",
"/Mathematics/Geometry/CoordinateGeometry/CartesianCoordinates",
"/Mathematics/Geometry/Distance/Point-PointDistance2-Dimensional",
"/Mathematics/Geometry/GeneralGeometry/Bisector",
"/Mathematics/Geometry/GeneralGeometry/CartesianPattern",
"/Mathematics/Geometry/GeneralGeometry/EuclideanGeometry",
"/Mathematics/Geometry/PlaneGeometry/Triangles/TriangleProperties",
"/Mathematics/Geometry/Trigonometry/Angles/Angle",
"/Mathematics/Geometry/Trigonometry/Angles/AngleBisector",
"/Mathematics/Geometry/Trigonometry/Angles/InternalAngleBisector",
"/Mathematics/Geometry/Trigonometry/GeneralTrigonometry/Trigonometry",
"/Mathematics/Geometry/Trigonometry/TrigonometricFunctions/Sine",
"/Mathematics/Geometry/Trigonometry/TrigonometricFunctions/Tangent"
] |
Compute tan(A/2) from sin A and use it to express the angle bisector condition as a simple slope ratio in coordinates.
|
[
-0.00016558170318603516,
-0.01629638671875,
0.036712646484375,
-0.0148468017578125,
-0.0003440380096435547,
-0.0019235610961914062,
0.0063323974609375,
0.035980224609375,
0.0018901824951171875,
-0.0032138824462890625,
0.00423431396484375,
0.0404052734375,
0.0022525787353515625,
0.00765228271484375,
0.0012187957763671875,
-0.037872314453125,
-0.00818634033203125,
-0.017852783203125,
0.0633544921875,
-0.001506805419921875,
-0.0148773193359375,
0.0033550262451171875,
-0.032989501953125,
-0.0055389404296875,
-0.0303802490234375,
0.010955810546875,
-0.0170440673828125,
-0.0113525390625,
-0.00731658935546875,
0.00002562999725341797,
0.0120849609375,
0.01551055908203125,
-0.006725311279296875,
-0.020477294921875,
0.0005617141723632812,
0.0003418922424316406,
0.0011396408081054688,
0.0004286766052246094,
-0.0209503173828125,
-0.004673004150390625,
0.0168304443359375,
0.021575927734375,
-0.0304412841796875,
0.0020618438720703125,
0.01519775390625,
-0.0015974044799804688,
-0.01507568359375,
-0.0008816719055175781,
-0.01007080078125,
-0.0169830322265625,
0.001552581787109375,
0.0162200927734375,
-0.043304443359375,
-0.0010433197021484375,
-0.005023956298828125,
-0.03375244140625,
0.00013971328735351562,
0.0033817291259765625,
-0.02386474609375,
-0.001522064208984375,
0.00023663043975830078,
0.01236724853515625,
0.0178985595703125,
-0.01513671875,
-0.0024356842041015625,
0.007129669189453125,
-0.025115966796875,
-0.01019287109375,
0.0040283203125,
0.00193023681640625,
0.0227508544921875,
-0.016448974609375,
0.00799560546875,
0.040313720703125,
-0.015625,
-0.005649566650390625,
-0.0130615234375,
0.00958251953125,
-0.0259246826171875,
0.0284423828125,
0.01398468017578125,
-0.0084075927734375,
0.01372528076171875,
-0.039459228515625,
0.01122283935546875,
-0.00008720159530639648,
-0.04608154296875,
0.01739501953125,
0.05047607421875,
0.001903533935546875,
-0.00811004638671875,
-0.01425933837890625,
-0.027862548828125,
-0.0120086669921875,
0.00983428955078125,
0.007843017578125,
0.00418853759765625,
-0.00665283203125,
-0.00588226318359375,
0.0029544830322265625,
-0.00275421142578125,
-0.018707275390625,
-0.0029449462890625,
-0.0227813720703125,
0.022430419921875,
0.0011873245239257812,
-0.01093292236328125,
-0.007579803466796875,
-0.01558685302734375,
0.010101318359375,
0.0118255615234375,
0.0115203857421875,
0.04107666015625,
0.00974273681640625,
0.0211639404296875,
0.00437164306640625,
0.04937744140625,
0.0148468017578125,
-0.0004849433898925781,
-0.00957489013671875,
-0.0011959075927734375,
0.00823211669921875,
-0.0295257568359375,
0.03692626953125,
-0.00228118896484375,
0.00739288330078125,
0.0024471282958984375,
-0.020965576171875,
-0.0302734375,
0.01383209228515625,
0.0250091552734375,
0.0029697418212890625,
-0.01473236083984375,
-0.0129547119140625,
-0.02490234375,
0.0303802490234375,
-0.0112152099609375,
-0.0001518726348876953,
-0.00243377685546875,
-0.0237884521484375,
-0.0029735565185546875,
-0.004512786865234375,
0.00775146484375,
-0.05889892578125,
-0.0076751708984375,
-0.05438232421875,
0.0185546875,
0.017730712890625,
0.0012903213500976562,
0.01552581787109375,
0.01447296142578125,
-0.007579803466796875,
0.011260986328125,
0.01174163818359375,
0.02001953125,
-0.004138946533203125,
0.01110076904296875,
0.0197906494140625,
0.024078369140625,
-0.002948760986328125,
0.0006093978881835938,
-0.004352569580078125,
-0.0086517333984375,
0.0239715576171875,
-0.0016946792602539062,
-0.0207672119140625,
0.01284027099609375,
0.0167083740234375,
-0.0207366943359375,
0.00005739927291870117,
-0.0059967041015625,
0.0012073516845703125,
-0.0018301010131835938,
-0.005588531494140625,
-0.006557464599609375,
0.016632080078125,
-0.00421142578125,
0.01036834716796875,
-0.015533447265625,
0.054046630859375,
-0.0005779266357421875,
-0.01678466796875,
0.002960205078125,
0.011688232421875,
0.00843048095703125,
0.005939483642578125,
-0.0011625289916992188,
-0.0023956298828125,
0.002101898193359375,
0.0229644775390625,
-0.018951416015625,
-0.0155792236328125,
-0.008392333984375,
-0.02471923828125,
0.00626373291015625,
-0.037353515625,
-0.031097412109375,
0.0023822784423828125,
0.01168060302734375,
0.0062713623046875,
-0.02001953125,
-0.004581451416015625,
0.0277099609375,
0.006256103515625,
-0.01172637939453125,
-0.004486083984375,
-0.0263824462890625,
-0.01525115966796875,
-0.0216522216796875,
0.01474761962890625,
-0.003650665283203125,
0.052978515625,
-0.0017957687377929688,
-0.02435302734375,
-0.003108978271484375,
-0.003940582275390625,
-0.021575927734375,
-0.00473785400390625,
-0.0139007568359375,
0.02325439453125,
-0.0025844573974609375,
-0.009857177734375,
0.010467529296875,
-0.0119781494140625,
-0.006130218505859375,
0.0019388198852539062,
-0.01421356201171875,
-0.01690673828125,
-0.0216522216796875,
-0.0116729736328125,
0.0004630088806152344,
-0.0006680488586425781,
-0.0072784423828125,
0.0011663436889648438,
-0.028533935546875,
0.013092041015625,
-0.0426025390625,
-0.009002685546875,
0.0031833648681640625,
0.0023784637451171875,
0.01090240478515625,
-0.0295867919921875,
0.0031414031982421875,
0.005767822265625,
0.0038890838623046875,
0.0099945068359375,
0.01065826416015625,
-0.0172882080078125,
-0.00695037841796875,
-0.01004791259765625,
-0.00681304931640625,
0.01342010498046875,
0.0006966590881347656,
-0.005283355712890625,
-0.01395416259765625,
0.01361846923828125,
0.01282501220703125,
0.040374755859375,
0.00026607513427734375,
0.014007568359375,
0.0011014938354492188,
-0.006397247314453125,
0.006801605224609375,
-0.007808685302734375,
0.0066680908203125,
0.0260467529296875,
0.019073486328125,
0.025634765625,
0.02728271484375,
-0.005046844482421875,
0.0247802734375,
-0.0290679931640625,
0.01611328125,
0.013214111328125,
-0.0167388916015625,
-0.0038700103759765625,
0.00565338134765625,
0.017913818359375,
-0.006561279296875,
0.01346588134765625,
-0.016448974609375,
-0.006923675537109375,
-0.09124755859375,
0.0005345344543457031,
-0.005008697509765625,
-0.0181732177734375,
0.0225067138671875,
-0.03399658203125,
-0.00479888916015625,
0.028961181640625,
-0.0080718994140625,
-0.007904052734375,
-0.015655517578125,
-0.023956298828125,
0.0570068359375,
0.0098876953125,
0.01617431640625,
-0.018035888671875,
-0.0098114013671875,
-0.0103302001953125,
0.032684326171875,
-0.0144195556640625,
-0.0027313232421875,
0.0066070556640625,
0.0291595458984375,
0.0282745361328125,
0.0193023681640625,
0.01354217529296875,
0.0018157958984375,
0.0167694091796875,
0.017425537109375,
-0.00965118408203125,
-0.0146636962890625,
-0.004100799560546875,
-0.02392578125,
-0.043121337890625,
0.010650634765625,
-0.006237030029296875,
-0.025299072265625,
0.0200347900390625,
0.0026798248291015625,
0.0169677734375,
0.042083740234375,
0.004634857177734375,
0.0251007080078125,
-0.01446533203125,
0.002948760986328125,
-0.0035305023193359375,
0.010406494140625,
0.037689208984375,
0.0025730133056640625,
0.00962066650390625,
0.0203857421875,
-0.006168365478515625,
0.03106689453125,
-0.0006017684936523438,
-0.0176544189453125,
0.0116424560546875,
-0.0196533203125,
-0.0029926300048828125,
0.0173797607421875,
0.007503509521484375,
0.01018524169921875,
-0.0738525390625,
-0.0308685302734375,
0.005596160888671875,
0.00362396240234375,
-0.02276611328125,
-0.00921630859375,
-0.0361328125,
-0.01136016845703125,
-0.0026912689208984375,
0.0129547119140625,
-0.00452423095703125,
-0.0031986236572265625,
-0.0157928466796875,
0.0090484619140625,
0.01352691650390625,
-0.0189208984375,
-0.0017757415771484375,
0.0023860931396484375,
-0.0252685546875,
-0.0093231201171875,
0.01605224609375,
0.003955841064453125,
0.007404327392578125,
0.006931304931640625,
0.01067352294921875,
-0.0220184326171875,
0.0178375244140625,
-0.0142974853515625,
-0.00728607177734375,
0.01041412353515625,
0.00649261474609375,
0.02593994140625,
0.0083465576171875,
-0.004444122314453125,
-0.003620147705078125,
0.001125335693359375,
-0.0178070068359375,
-0.00936126708984375,
-0.0145416259765625,
-0.0004787445068359375,
0.0362548828125,
-0.0175018310546875,
-0.00390625,
-0.0002636909484863281,
-0.0157012939453125,
-0.0118255615234375,
-0.018035888671875,
-0.013702392578125,
-0.01058197021484375,
0.00476837158203125,
-0.0273895263671875,
-0.046234130859375,
-0.020416259765625,
0.00213623046875,
0.00414276123046875,
0.0499267578125,
-0.0087738037109375,
-0.049346923828125,
-0.00390625,
-0.0136260986328125,
-0.0013637542724609375,
0.02960205078125,
-0.003673553466796875,
-0.037017822265625,
0.0295867919921875,
0.008392333984375,
-0.0455322265625,
0.030792236328125,
-0.0112152099609375,
0.00528717041015625,
0.0145111083984375,
-0.049774169921875,
0.015716552734375,
0.0262451171875,
-0.01580810546875,
0.0232696533203125,
-0.0142974853515625,
0.01165771484375,
-0.01158905029296875,
0.03424072265625,
-0.00826263427734375,
0.0200347900390625,
0.01026153564453125,
-0.0086669921875,
0.024017333984375,
-0.0123443603515625,
-0.006557464599609375,
0.0202484130859375,
0.020751953125,
0.004123687744140625,
-0.008697509765625,
-0.01276397705078125,
-0.023162841796875,
0.03857421875,
-0.013031005859375,
0.01004791259765625,
0.015625,
-0.00605010986328125,
-0.0291290283203125,
-0.022430419921875,
-0.004581451416015625,
0.0019168853759765625,
-0.0036678314208984375,
-0.0276947021484375,
-0.00267791748046875,
0.001621246337890625,
0.00995635986328125,
-0.0123748779296875,
-0.01381683349609375,
0.02349853515625,
-0.04644775390625,
-0.0225830078125,
0.00835418701171875,
0.0164642333984375,
-0.00897979736328125,
-0.02850341796875,
0.0185546875,
-0.0167388916015625,
0.00556182861328125,
0.0189971923828125,
0.03460693359375,
-0.00965118408203125,
-0.006626129150390625,
0.004680633544921875,
0.021636962890625,
-0.019073486328125,
0.025146484375,
0.0010156631469726562,
-0.0316162109375,
0.0077362060546875,
-0.0279998779296875,
-0.014801025390625,
0.0306243896484375,
0.00809478759765625,
0.031280517578125,
-0.0247955322265625,
0.0280303955078125,
0.006038665771484375,
-0.01558685302734375,
0.010467529296875,
-0.021514892578125,
-0.0164947509765625,
0.038360595703125,
0.01239776611328125,
-0.0241241455078125,
-0.0005908012390136719,
-0.03460693359375,
-0.0015306472778320312,
0.0287322998046875,
-0.0298004150390625,
-0.0164031982421875,
-0.035980224609375,
-0.028656005859375,
0.0127410888671875,
-0.00881195068359375,
-0.01861572265625,
-0.01081085205078125,
0.036376953125,
-0.0258941650390625,
0.0145721435546875,
0.017608642578125,
0.0094146728515625,
-0.0457763671875,
0.0506591796875,
-0.016937255859375,
-0.01251220703125,
0.0139617919921875,
0.0299835205078125,
-0.0105743408203125,
0.00687408447265625,
-0.005832672119140625,
0.038360595703125,
0.003322601318359375,
0.00856781005859375,
-0.019012451171875,
0.017730712890625,
0.03912353515625,
0.0127716064453125,
-0.0021800994873046875,
-0.001407623291015625,
0.01360321044921875,
0.0389404296875,
0.011322021484375,
0.004924774169921875,
-0.0032958984375,
0.008209228515625,
-0.00836944580078125,
0.01038360595703125,
-0.03521728515625,
-0.03759765625,
0.005970001220703125,
-0.0200958251953125,
-0.001983642578125,
-0.00020396709442138672,
-0.006641387939453125,
0.0177154541015625,
-0.00043511390686035156,
-0.0242767333984375,
-0.0025920867919921875,
0.0012388229370117188,
-0.0187530517578125,
0.009368896484375,
0.0007758140563964844,
0.01178741455078125,
0.0249786376953125,
0.007205963134765625,
0.0301666259765625,
0.0131683349609375,
-0.0032062530517578125,
-0.037384033203125,
-0.0032291412353515625,
-0.0159454345703125,
0.00592803955078125,
-0.032440185546875,
0.004673004150390625,
0.0136871337890625,
0.0240936279296875,
0.041290283203125,
-0.0010633468627929688,
0.020050048828125,
-0.01045989990234375,
-0.01345062255859375,
-0.01230621337890625,
0.0015716552734375,
-0.00450897216796875,
0.0149993896484375,
-0.029876708984375,
-0.0182647705078125,
-0.0233917236328125,
-0.00908660888671875,
0.0238189697265625,
0.0283203125,
-0.03582763671875,
0.014923095703125,
-0.0030059814453125,
0.022613525390625,
-0.000274658203125,
0.043701171875,
0.0132293701171875,
-0.0166015625,
-0.01274871826171875,
-0.0230712890625,
-0.04290771484375,
-0.000843048095703125,
0.00904083251953125,
0.003253936767578125,
-0.0194549560546875,
-0.01236724853515625,
0.027862548828125,
0.0008745193481445312,
-0.0249481201171875,
-0.0052337646484375,
-0.0161285400390625,
-0.018585205078125,
0.00415802001953125,
0.03363037109375,
0.0062713623046875,
-0.015045166015625,
-0.0129852294921875,
-0.0184478759765625,
-0.0004711151123046875,
-0.006183624267578125,
0.01132965087890625,
-0.045806884765625,
-0.009246826171875,
0.0335693359375,
-0.00969696044921875,
0.006191253662109375,
-0.0299530029296875,
-0.02276611328125,
0.005962371826171875,
0.00991058349609375,
0.0263214111328125,
-0.00954437255859375,
0.0095672607421875,
-0.01543426513671875,
0.007312774658203125,
-0.00348663330078125,
-0.005901336669921875,
-0.0010557174682617188,
0.0206451416015625,
-0.0281219482421875,
-0.0189056396484375,
-0.043609619140625,
-0.0270233154296875,
0.006229400634765625,
0.00007015466690063477,
-0.045867919921875,
-0.0110321044921875,
0.01580810546875,
0.03955078125,
-0.007617950439453125,
-0.02325439453125,
-0.0185546875,
0.0201568603515625,
0.01019287109375,
-0.0260467529296875,
-0.00005751848220825195,
0.01311492919921875,
-0.0008296966552734375,
-0.04144287109375,
-0.00244903564453125,
-0.0450439453125,
-0.01001739501953125,
0.0010242462158203125,
-0.0151214599609375,
0.0019092559814453125,
0.0000960230827331543,
0.001041412353515625,
0.031768798828125,
0.02362060546875,
0.03375244140625,
-0.0007338523864746094,
-0.00531768798828125,
-0.036407470703125,
0.03839111328125,
0.027984619140625,
-0.005413055419921875,
0.0004839897155761719,
-0.013580322265625,
-0.0081024169921875,
-0.0138092041015625,
-0.012420654296875,
-0.03680419921875,
-0.029510498046875,
0.0196533203125,
0.023345947265625,
-0.0169830322265625,
-0.02008056640625,
0.01171875,
-0.028228759765625,
-0.0254974365234375,
0.0306854248046875,
-0.0223388671875,
0.0246124267578125,
-0.025848388671875,
0.020599365234375,
0.01119232177734375,
-0.006542205810546875,
0.0340576171875,
0.01230621337890625,
0.0069427490234375,
0.04107666015625,
0.022003173828125,
-0.020111083984375,
0.00379180908203125,
0.00960540771484375,
-0.0003516674041748047,
0.0244140625,
-0.01837158203125,
0.022308349609375,
-0.01251983642578125,
-0.003204345703125,
0.0305633544921875,
0.0037288665771484375,
0.00787353515625,
-0.04241943359375,
-0.01074981689453125,
-0.0157928466796875,
0.01438140869140625,
-0.029449462890625,
-0.0222625732421875,
-0.01422119140625,
0.0009341239929199219,
0.0159454345703125,
-0.020721435546875,
0.0007696151733398438,
-0.0189666748046875,
-0.0143585205078125,
0.01824951171875,
0.00965118408203125,
0.0003612041473388672,
-0.03851318359375,
-0.0286712646484375,
-0.0117340087890625,
-0.0032825469970703125,
0.025360107421875,
0.00582122802734375,
-0.0196685791015625,
-0.013671875,
-0.0261688232421875,
0.0268402099609375,
0.018768310546875,
-0.0288238525390625,
-0.0168304443359375,
-0.00992584228515625,
0.01690673828125,
0.0034236907958984375,
-0.0066070556640625,
-0.0010166168212890625,
-0.0104522705078125,
-0.0408935546875,
0.012786865234375,
-0.005451202392578125,
-0.045806884765625,
-0.00469207763671875,
0.00811767578125,
0.035552978515625,
-0.006404876708984375,
0.0113372802734375,
-0.0037822723388671875,
0.0017156600952148438,
-0.0162200927734375,
-0.0005922317504882812,
-0.00841522216796875,
0.013397216796875,
0.00865936279296875,
0.0018224716186523438,
-0.0233001708984375,
0.004405975341796875,
-0.040252685546875,
0.0035495758056640625,
0.03271484375,
-0.018798828125,
-0.048187255859375,
-0.00910186767578125,
-0.006580352783203125,
0.0010623931884765625,
0.00646209716796875,
-0.0140380859375,
-0.01558685302734375,
0.0202178955078125,
0.0186309814453125,
-0.037750244140625,
0.007358551025390625,
-0.037139892578125,
-0.0159454345703125,
0.0300140380859375,
-0.0010366439819335938,
0.01617431640625,
0.01021575927734375,
0.0156402587890625,
0.028076171875,
-0.01715087890625,
0.004543304443359375,
0.020538330078125,
-0.00876617431640625,
-0.005031585693359375,
0.0148162841796875,
-0.0018091201782226562,
0.02008056640625,
-0.01087188720703125,
0.00782012939453125,
-0.047882080078125,
-0.0156707763671875,
0.035308837890625,
-0.0032901763916015625,
0.040679931640625,
-0.02288818359375,
0.0240478515625,
-0.028594970703125,
0.00025177001953125,
-0.0269775390625,
-0.01407623291015625,
-0.002788543701171875,
-0.00936126708984375,
0.017608642578125,
-0.0049591064453125,
-0.01210784912109375,
0.01383209228515625,
0.008087158203125,
0.04388427734375,
-0.003284454345703125,
0.0168609619140625,
-0.005397796630859375,
-0.015777587890625,
0.0004191398620605469,
-0.018341064453125,
0.0068206787109375,
0.008758544921875,
-0.007476806640625,
-0.01849365234375,
-0.027191162109375,
-0.0220947265625,
-0.0404052734375,
-0.004520416259765625,
0.01129913330078125,
-0.055419921875,
0.0200042724609375,
-0.030609130859375,
-0.01220703125,
-0.043853759765625,
-0.024749755859375,
-0.0007429122924804688,
-0.022186279296875,
0.0007171630859375,
0.004802703857421875,
0.020782470703125,
-0.008270263671875,
-0.0418701171875,
0.0081024169921875,
-0.0266571044921875,
0.0209197998046875,
-0.0008273124694824219,
0.011383056640625,
-0.044097900390625,
-0.0236053466796875,
0.02191162109375,
0.0012369155883789062,
0.032135009765625,
0.0022602081298828125,
-0.01192474365234375,
0.00678253173828125,
-0.01248931884765625,
-0.0095367431640625,
-0.0016908645629882812,
0.00212860107421875,
-0.0027065277099609375,
0.03466796875,
-0.03472900390625,
0.017974853515625,
-0.0286102294921875,
0.0121307373046875,
0.0293426513671875,
-0.0033702850341796875,
-0.01366424560546875,
0.0078125,
0.00701141357421875,
0.00555419921875,
0.029327392578125,
-0.002872467041015625,
0.00839996337890625,
-0.00981903076171875,
0.0131378173828125,
0.005207061767578125,
0.04815673828125,
-0.006191253662109375,
0.048614501953125,
-0.00417327880859375,
-0.008392333984375,
0.006397247314453125,
0.0389404296875,
0.027740478515625,
-0.005252838134765625,
0.01203155517578125,
0.022003173828125,
0.01041412353515625,
0.0034084320068359375,
-0.00672149658203125,
-0.0267486572265625,
0.0195465087890625,
-0.006046295166015625,
0.00762939453125,
-0.0223846435546875,
0.0292816162109375,
0.0188751220703125,
0.00843048095703125,
-0.01091766357421875,
-0.01493072509765625,
0.0037384033203125,
0.0047149658203125,
0.0303497314453125,
0.01114654541015625,
-0.00484466552734375,
-0.01181793212890625,
-0.0018968582153320312,
0.0111083984375,
-0.00522613525390625,
0.0183563232421875,
0.00434112548828125,
0.004039764404296875,
-0.006298065185546875,
-0.004825592041015625,
-0.0193328857421875,
0.023651123046875,
0.031707763671875,
0.019622802734375,
-0.004032135009765625,
0.0224609375,
0.0036716461181640625,
0.03143310546875,
0.033172607421875,
0.005462646484375,
-0.0189666748046875,
0.00699615478515625,
-0.026031494140625,
-0.006992340087890625,
-0.00033664703369140625,
-0.006603240966796875,
-0.004161834716796875,
-0.0029144287109375,
-0.01428985595703125,
0.0015325546264648438,
-0.00942230224609375,
-0.016693115234375,
-0.043304443359375,
-0.004741668701171875,
-0.0267181396484375,
0.00971221923828125,
-0.00855255126953125,
-0.009765625,
-0.007610321044921875,
0.019805908203125,
0.011016845703125,
-0.01554107666015625,
0.01317596435546875,
-0.01275634765625,
0.0156707763671875,
0.006145477294921875,
-0.00923919677734375,
0.004207611083984375,
-0.032684326171875,
-0.00563812255859375,
-0.0083770751953125,
0.0036945343017578125,
0.0382080078125,
-0.00713348388671875,
0.0181121826171875,
0.0012874603271484375,
0.01480865478515625,
0.008392333984375,
0.0038013458251953125,
-0.044921875,
0.006988525390625,
0.001789093017578125,
-0.0029087066650390625,
-0.0182952880859375,
0.0054931640625,
0.01287841796875,
-0.018035888671875,
-0.016448974609375,
-0.018798828125,
0.0036525726318359375,
0.0278778076171875,
0.006168365478515625,
-0.0028858184814453125,
0.04693603515625,
0.03106689453125,
-0.0228424072265625,
0.0057830810546875,
-0.01300048828125,
-0.01126861572265625,
-0.0203704833984375,
0.00782012939453125,
0.04632568359375,
0.0258636474609375,
0.0044403076171875,
-0.044464111328125,
0.017486572265625,
0.010101318359375,
-0.0250396728515625,
-0.015960693359375,
0.007137298583984375,
0.0235595703125,
-0.00807952880859375,
0.03277587890625,
-0.0172576904296875,
0.0098419189453125,
0.033599853515625,
-0.006977081298828125,
0.047576904296875,
-0.004001617431640625,
0.000522613525390625,
0.0035686492919921875,
-0.022216796875,
0.015960693359375,
-0.025238037109375,
-0.039825439453125,
-0.0237274169921875,
0.02459716796875,
0.02972412109375,
0.0177459716796875,
-0.02569580078125,
0.0017194747924804688,
0.0257110595703125,
0.0074615478515625,
0.0181732177734375,
-0.0227203369140625,
0.003284454345703125,
0.01215362548828125,
0.005462646484375,
-0.0152587890625,
0.037445068359375,
-0.003253936767578125,
0.0267333984375,
-0.0238800048828125,
0.01329803466796875,
0.01251220703125,
-0.040283203125,
-0.038360595703125,
-0.0474853515625,
-0.0009312629699707031,
-0.060821533203125,
0.01448822021484375,
-0.0184326171875,
0.016754150390625,
0.0472412109375,
-0.03741455078125,
0.00484466552734375,
-0.0516357421875,
0.004924774169921875,
0.004253387451171875,
-0.03692626953125,
0.00002872943878173828,
-0.0277099609375,
0.01258087158203125,
-0.0030117034912109375,
-0.00664520263671875,
-0.005649566650390625,
-0.0018596649169921875,
-0.0255279541015625,
-0.01445770263671875,
0.01390838623046875,
0.0003695487976074219,
-0.005184173583984375,
-0.01556396484375,
0.0087890625,
0.05792236328125,
0.0068817138671875,
-0.0144195556640625,
0.0030193328857421875,
-0.0158233642578125,
0.0067596435546875,
0.0009698867797851562,
-0.0034637451171875,
0.0174407958984375,
0.0445556640625,
0.0012311935424804688,
-0.0210723876953125,
-0.03936767578125,
-0.01349639892578125,
0.017181396484375,
0.0175018310546875,
-0.0077667236328125,
0.0123138427734375,
0.0008754730224609375,
0.0130615234375,
-0.046600341796875,
-0.0289764404296875,
0.00200653076171875,
0.01360321044921875,
-0.01070404052734375,
-0.0098114013671875,
0.005252838134765625,
-0.002895355224609375,
0.0175018310546875,
-0.01291656494140625,
0.0015516281127929688,
-0.01068878173828125,
-0.037322998046875,
0.0333251953125,
0.02215576171875,
-0.0025691986083984375,
-0.005786895751953125,
0.00653839111328125,
0.006683349609375,
0.0006003379821777344,
-0.0048828125,
-0.0008549690246582031,
-0.0015716552734375,
0.020904541015625,
0.0074310302734375,
-0.01544952392578125,
0.010223388671875,
0.0158538818359375,
0.00568389892578125,
0.00006401538848876953,
0.0146331787109375,
0.024139404296875,
0.0154876708984375,
0.0152587890625,
0.00971221923828125,
-0.01345062255859375,
-0.0140380859375,
0.01143646240234375,
-0.0005125999450683594,
0.004116058349609375,
0.00203704833984375,
0.03857421875,
0.0291595458984375,
0.037933349609375,
-0.0002384185791015625,
-0.02325439453125,
-0.0240936279296875,
-0.048187255859375,
-0.01617431640625,
-0.014801025390625,
-0.0026912689208984375,
-0.0174560546875,
0.00933074951171875,
0.0078125,
-0.004299163818359375,
0.00399017333984375,
0.0119476318359375,
-0.0291900634765625,
-0.0360107421875,
0.022125244140625,
-0.0024547576904296875,
0.01238250732421875,
-0.006053924560546875,
-0.006618499755859375,
-0.008758544921875,
0.0164794921875,
0.01458740234375,
0.002994537353515625,
-0.020599365234375,
-0.0036487579345703125,
-0.006214141845703125,
0.0135345458984375,
0.02557373046875,
-0.032562255859375,
-0.043670654296875,
0.0197296142578125,
0.0026302337646484375,
-0.0035419464111328125,
0.03741455078125,
-0.002346038818359375,
-0.0399169921875,
0.0000972747802734375,
0.0013885498046875,
0.024658203125,
0.003459930419921875,
-0.03369140625,
0.00295257568359375,
-0.01358795166015625,
0.00372314453125,
0.00202178955078125,
0.01800537109375,
-0.0101318359375,
-0.0053863525390625,
0.0054473876953125,
-0.0031108856201171875,
0.029571533203125,
-0.0227203369140625,
0.0038890838623046875,
-0.00202178955078125,
0.01788330078125,
0.031463623046875,
-0.00957489013671875,
0.04766845703125,
-0.0190887451171875,
-0.00711822509765625,
0.011199951171875,
0.02044677734375,
-0.06256103515625,
-0.0292816162109375,
0.00023186206817626953,
-0.0182952880859375,
0.031768798828125,
-0.00009250640869140625,
0.01094818115234375,
0.00757598876953125,
0.01145172119140625,
0.00371551513671875,
-0.03753662109375,
-0.0396728515625,
-0.0241851806640625,
-0.01995849609375,
-0.0012111663818359375,
-0.03240966796875,
0.0328369140625,
-0.004528045654296875,
0.0292816162109375,
-0.025604248046875,
-0.00832366943359375,
-0.029998779296875,
-0.003936767578125,
-0.0153961181640625,
-0.01410675048828125,
-0.033599853515625,
-0.01007080078125,
0.0044403076171875,
0.0219879150390625,
0.02008056640625,
0.00812530517578125,
-0.03509521484375,
-0.0097503662109375,
0.011474609375,
0.0217742919921875,
0.0016078948974609375,
-0.026611328125,
-0.0025272369384765625,
-0.04364013671875,
-0.01213836669921875,
-0.005100250244140625,
-0.006046295166015625,
0.001995086669921875,
0.005588531494140625,
-0.00688934326171875,
0.012054443359375,
-0.002597808837890625,
-0.0159149169921875,
0.01322174072265625,
-0.007137298583984375,
0.0174713134765625,
0.018524169921875,
0.0226287841796875,
0.023284912109375,
0.001605987548828125,
-0.025543212890625,
0.01227569580078125,
-0.02978515625,
0.010009765625,
-0.032958984375,
0.022674560546875,
-0.0297393798828125,
0.029937744140625,
0.00714874267578125,
0.0178985595703125,
-0.0160675048828125,
-0.0219268798828125,
0.018280029296875,
-0.03363037109375,
-0.054168701171875,
0.01690673828125,
-0.039764404296875,
0.024627685546875,
0.0009102821350097656,
0.01319122314453125,
0.00023353099822998047,
-0.01552581787109375,
-0.007450103759765625,
0.00323486328125,
0.00035762786865234375,
0.0139312744140625,
-0.0027332305908203125,
-0.026763916015625,
-0.00917816162109375,
0.006031036376953125,
-0.006809234619140625,
-0.0129241943359375,
0.004337310791015625,
-0.00750732421875,
-0.019866943359375,
0.0216217041015625,
0.01230621337890625,
0.0147247314453125,
-0.00931549072265625,
-0.00176239013671875,
-0.011962890625,
0.046966552734375,
0.0240936279296875,
-0.0028705596923828125,
0.0005645751953125,
-0.0296478271484375,
-0.005298614501953125,
0.02362060546875,
-0.0178070068359375,
0.005321502685546875,
0.0091552734375,
-0.0029544830322265625,
-0.004009246826171875,
-0.018402099609375,
-0.01041412353515625,
0.0198516845703125,
0.034820556640625,
-0.0089569091796875,
-0.00020897388458251953,
0.026824951171875,
0.001708984375,
0.026031494140625,
-0.0300140380859375,
0.01806640625,
-0.003070831298828125,
0.006740570068359375,
0.0269927978515625,
-0.009796142578125,
0.0216064453125,
-0.002155303955078125,
0.01380157470703125,
-0.042083740234375,
-0.01143646240234375,
-0.015869140625,
0.029937744140625,
0.017303466796875,
-0.0025959014892578125,
-0.01885986328125,
-0.0010356903076171875,
-0.0013170242309570312,
0.00650787353515625,
-0.004634857177734375,
0.03741455078125,
-0.0007596015930175781,
0.02947998046875,
-0.0119171142578125,
-0.01461029052734375,
0.0019893646240234375,
-0.01178741455078125,
0.02203369140625,
-0.00646209716796875,
-0.0264434814453125,
0.01108551025390625,
-0.01885986328125,
-0.01074981689453125,
-0.017852783203125,
-0.0007395744323730469,
-0.019989013671875,
0.00853729248046875,
-0.00036716461181640625,
-0.00424957275390625,
0.0004744529724121094,
0.004940032958984375,
0.0280303955078125,
0.01053619384765625,
-0.00928497314453125,
0.009307861328125,
0.00211334228515625,
-0.0160980224609375,
0.0372314453125,
-0.00543212890625,
-0.0031642913818359375,
0.019927978515625,
-0.0019626617431640625,
-0.048858642578125,
0.0033168792724609375,
0.00830078125,
-0.017730712890625,
0.0250091552734375,
-0.0184478759765625,
-0.01285552978515625,
0.0484619140625,
-0.04052734375,
-0.0106658935546875,
0.0185546875,
0.0248870849609375,
0.0017843246459960938,
-0.00859832763671875,
0.02325439453125,
-0.0110626220703125,
0.007770538330078125,
-0.00791168212890625,
0.006221771240234375,
0.0207672119140625,
0.0023403167724609375,
-0.02642822265625,
-0.027374267578125,
0.01045989990234375,
-0.0185089111328125,
0.0202178955078125,
0.0028400421142578125,
-0.031890869140625,
0.0050048828125,
-0.013519287109375,
0.0011663436889648438,
-0.015045166015625,
-0.01117706298828125,
-0.0084381103515625,
-0.00420379638671875,
-0.020294189453125,
-0.0252227783203125,
-0.0211944580078125,
0.0170745849609375,
0.0100555419921875,
-0.01983642578125,
-0.004398345947265625,
0.005626678466796875,
0.010406494140625,
0.033935546875,
0.011077880859375,
-0.0225677490234375,
0.0301666259765625,
0.0207366943359375,
0.00368499755859375,
0.0142974853515625,
-0.00949859619140625,
-0.02691650390625,
0.01297760009765625,
0.01465606689453125,
0.0178985595703125,
-0.00710296630859375,
0.00958251953125,
0.029388427734375,
0.004116058349609375,
0.005855560302734375,
-0.00328826904296875,
0.006256103515625,
0.0121917724609375,
-0.00884246826171875,
0.01111602783203125,
-0.029998779296875,
-0.057281494140625,
0.01128387451171875,
-0.0072174072265625,
-0.0022373199462890625,
-0.0021877288818359375,
0.0001125335693359375,
0.028228759765625,
0.0264129638671875,
0.0292205810546875,
-0.0276031494140625,
-0.0147247314453125,
-0.010498046875,
-0.018157958984375,
-0.0027332305908203125,
-0.036956787109375,
0.01085662841796875,
0.0191497802734375,
0.005802154541015625,
-0.016143798828125,
-0.01397705078125,
0.0038242340087890625,
-0.009674072265625,
-0.0220794677734375,
0.01528167724609375,
0.0294952392578125,
-0.00981903076171875,
0.0005311965942382812,
-0.0109710693359375,
0.03387451171875,
-0.0017023086547851562,
0.0297088623046875,
-0.0024967193603515625,
0.0231170654296875,
0.007640838623046875,
-0.0006308555603027344,
0.0152740478515625,
0.0128021240234375,
0.0025691986083984375,
-0.05120849609375,
0.0002906322479248047,
-0.0253448486328125,
0.01384735107421875,
-0.0007905960083007812,
0.00226593017578125,
0.0009918212890625,
0.0240631103515625,
-0.0204925537109375,
-0.04364013671875,
0.00008779764175415039,
0.0034942626953125,
0.020843505859375,
0.0149078369140625,
-0.00423431396484375,
0.0028743743896484375,
0.03875732421875,
0.00897216796875,
-0.01605224609375,
-0.0142822265625,
0.041656494140625,
0.01026153564453125,
-0.002216339111328125,
0.019775390625,
-0.006893157958984375,
0.038848876953125,
-0.0016679763793945312,
-0.0019273757934570312,
-0.00090789794921875,
-0.01385498046875,
-0.020050048828125,
0.0124969482421875,
-0.005039215087890625,
-0.0034618377685546875,
-0.042510986328125,
0.0301361083984375,
0.0269012451171875,
0.00366973876953125,
-0.037841796875,
-0.006809234619140625,
-0.00933074951171875,
0.007415771484375,
0.0001004338264465332,
0.039215087890625,
0.0264129638671875,
-0.038543701171875,
-0.01526641845703125,
0.00112152099609375,
-0.04180908203125,
0.03863525390625,
0.025177001953125,
0.0193634033203125,
-0.000026285648345947266,
0.015167236328125,
-0.0323486328125,
-0.02459716796875,
-0.017608642578125,
0.0175018310546875,
-0.0019931793212890625,
0.0042877197265625,
-0.00974273681640625,
-0.005840301513671875,
0.041900634765625,
-0.056976318359375,
0.00870513916015625,
0.0100860595703125,
-0.01061248779296875,
-0.02716064453125,
-0.0196990966796875,
0.0182647705078125,
-0.0291900634765625,
-0.0263214111328125,
0.043304443359375,
0.01605224609375,
-0.01544189453125,
0.017608642578125,
0.01068878173828125,
-0.029327392578125,
0.0084991455078125,
-0.016815185546875,
-0.01464080810546875,
0.053619384765625,
0.0108489990234375,
-0.0016260147094726562,
-0.00887298583984375,
-0.03875732421875,
0.003692626953125,
0.0081939697265625,
-0.01013946533203125,
-0.0077972412109375,
0.006183624267578125,
-0.02447509765625,
0.0281829833984375,
0.004695892333984375,
0.0028247833251953125,
0.005016326904296875,
0.01424407958984375,
0.033416748046875,
-0.009002685546875,
0.00711822509765625,
0.004779815673828125,
0.0265350341796875,
0.005603790283203125,
0.0142059326171875,
-0.0017900466918945312,
-0.005603790283203125,
0.0173492431640625,
-0.004482269287109375,
-0.01898193359375,
-0.004192352294921875,
0.0482177734375,
-0.022979736328125,
0.0131988525390625,
-0.01055908203125,
0.0135040283203125,
0.0172119140625,
-0.0007901191711425781,
0.007373809814453125,
-0.0206298828125,
0.00315093994140625,
0.037017822265625,
-0.0095977783203125,
-0.00902557373046875,
0.00928497314453125,
0.0308380126953125,
0.008209228515625,
-0.0247039794921875,
0.001434326171875,
0.006931304931640625,
-0.0193328857421875,
-0.01416778564453125,
0.005733489990234375,
0.0309906005859375,
0.0123138427734375,
0.00719451904296875,
-0.021942138671875,
0.02117919921875,
-0.0138702392578125,
-0.014373779296875,
0.0018758773803710938,
0.004039764404296875,
-0.007038116455078125,
-0.0142669677734375,
-0.0092315673828125,
-0.021484375,
-0.00458526611328125,
0.006023406982421875,
0.0300445556640625,
0.0111846923828125,
-0.000011801719665527344,
0.048980712890625,
-0.011138916015625,
-0.0016164779663085938,
-0.0278167724609375,
0.007904052734375,
0.001697540283203125,
-0.01284027099609375,
-0.0030956268310546875,
0.0244598388671875,
-0.00897979736328125,
-0.0005955696105957031,
0.021759033203125,
0.016845703125,
-0.02099609375,
-0.01025390625,
0.025543212890625,
0.058013916015625,
0.00988006591796875,
-0.0247039794921875,
0.041656494140625,
-0.01345062255859375,
0.01100921630859375,
0.005615234375,
0.0005059242248535156,
0.01239013671875,
0.01678466796875,
0.00899505615234375,
0.01535797119140625,
-0.0164031982421875,
-0.0007295608520507812,
-0.0016918182373046875,
-0.007396697998046875,
0.021820068359375,
-0.0295257568359375,
-0.0012273788452148438,
0.0025424957275390625,
-0.0003216266632080078,
0.00530242919921875,
0.0235443115234375,
-0.0155181884765625,
-0.045074462890625,
0.0362548828125,
-0.029510498046875,
-0.031463623046875,
0.031280517578125,
0.0026187896728515625,
0.00411224365234375,
0.037200927734375,
-0.01788330078125,
-0.0077972412109375,
0.0280609130859375,
0.0161895751953125,
0.005382537841796875,
0.002529144287109375,
0.005641937255859375,
0.006046295166015625,
-0.01654052734375,
-0.02545166015625,
-0.0010433197021484375,
-0.0036449432373046875,
0.0218505859375,
-0.006610870361328125,
0.0035991668701171875,
-0.0008611679077148438,
0.007686614990234375,
0.0120391845703125,
-0.012054443359375,
-0.0013570785522460938,
-0.0005340576171875,
0.0168304443359375,
-0.0168304443359375,
0.0232391357421875,
0.0135650634765625,
-0.00981903076171875,
0.0016088485717773438,
0.02178955078125,
-0.0269622802734375,
-0.002689361572265625,
-0.015655517578125,
0.00925445556640625,
-0.0297088623046875,
-0.01137542724609375,
0.04052734375,
-0.014617919921875,
-0.025726318359375,
-0.00438690185546875,
0.01055145263671875,
0.03033447265625,
0.0187835693359375,
0.02691650390625,
-0.0133056640625,
-0.0237884521484375,
0.0267181396484375,
0.0154571533203125,
0.030731201171875,
0.0166778564453125,
-0.0012416839599609375,
-0.016448974609375,
-0.005451202392578125,
-0.00589752197265625,
-0.0089569091796875,
0.03167724609375,
-0.031585693359375,
-0.005741119384765625,
0.00537109375,
-0.0133209228515625,
0.0030841827392578125,
-0.01325225830078125,
-0.0008983612060546875,
0.0029430389404296875,
-0.01702880859375,
-0.0179443359375,
-0.0000794529914855957,
0.0017242431640625,
0.00820159912109375,
0.046417236328125,
0.005565643310546875,
-0.00933837890625,
-0.0560302734375,
-0.01329803466796875,
0.0009250640869140625,
0.0017385482788085938,
-0.0156402587890625,
0.00601959228515625,
-0.007747650146484375,
0.0198822021484375,
-0.0215911865234375,
-0.0019006729125976562,
0.0021457672119140625,
0.0092620849609375,
0.007251739501953125,
-0.0179290771484375,
-0.003322601318359375,
-0.01082611083984375,
-0.0081939697265625,
0.0059814453125,
-0.01515960693359375,
0.00861358642578125,
-0.0033702850341796875,
-0.040008544921875,
0.0445556640625,
-0.004779815673828125,
-0.007404327392578125,
-0.018402099609375,
-0.00443267822265625,
0.028167724609375,
-0.0004949569702148438,
0.038299560546875,
0.020904541015625,
0.0243682861328125,
-0.0250701904296875,
0.033966064453125,
0.0188751220703125,
0.00214385986328125,
0.006656646728515625,
-0.01045989990234375,
0.004787445068359375,
-0.0035648345947265625,
-0.034393310546875,
-0.0028705596923828125,
-0.00643157958984375,
-0.01849365234375,
-0.0257568359375,
0.010406494140625,
-0.00875091552734375,
-0.0196685791015625,
-0.02020263671875,
0.0208282470703125,
0.01248931884765625,
0.0112152099609375,
0.01708984375,
0.02642822265625,
0.01026153564453125,
0.0242919921875,
0.01099395751953125,
0.037353515625,
0.003040313720703125,
-0.003856658935546875,
0.0034160614013671875,
0.0019063949584960938,
0.00004756450653076172,
0.0157012939453125,
0.0112457275390625,
-0.016693115234375,
-0.032745361328125,
0.008514404296875,
-0.0133514404296875,
-0.025238037109375,
-0.0210418701171875,
-0.015289306640625,
-0.00858306884765625,
-0.004817962646484375,
-0.03692626953125,
-0.0131378173828125,
0.0020580291748046875,
-0.0284423828125,
-0.0259857177734375,
0.0023784637451171875,
0.00870513916015625,
-0.0007576942443847656,
0.001277923583984375,
-0.04925537109375,
0.005847930908203125,
0.01042938232421875,
-0.020050048828125,
0.0030727386474609375,
-0.0029087066650390625,
0.03387451171875,
-0.0169219970703125,
0.0119171142578125,
-0.00884246826171875,
0.007110595703125,
-0.01239776611328125,
-0.00827789306640625,
-0.0155181884765625,
0.00140380859375,
-0.0167999267578125,
-0.0498046875,
0.01543426513671875,
-0.022125244140625,
0.003246307373046875,
-0.0197601318359375,
-0.025726318359375,
-0.0009374618530273438,
-0.0203094482421875,
0.0200958251953125,
-0.031768798828125,
-0.02294921875,
-0.005222320556640625,
0.0347900390625,
0.0030078887939453125,
-0.0027217864990234375,
-0.00812530517578125,
0.03497314453125,
-0.0205841064453125,
-0.03668212890625,
-0.01654052734375,
-0.004207611083984375,
-0.036468505859375,
0.005588531494140625,
0.017974853515625,
-0.004528045654296875,
0.022369384765625,
0.01043701171875,
0.017974853515625,
0.0017681121826171875,
0.01617431640625,
-0.0032176971435546875,
0.0188751220703125,
0.001956939697265625,
-0.0197906494140625,
0.00945281982421875,
0.0028667449951171875,
-0.00722503662109375,
-0.0019016265869140625,
0.0167999267578125,
0.00704193115234375,
-0.0131683349609375,
0.01082611083984375,
-0.0005941390991210938,
-0.022003173828125,
0.006290435791015625,
0.01479339599609375,
-0.0194091796875,
0.0102691650390625,
-0.018035888671875,
-0.0132904052734375,
0.00672149658203125,
-0.0118865966796875,
-0.012939453125,
-0.013336181640625,
-0.0118865966796875,
-0.0269317626953125,
0.007488250732421875,
0.00494384765625,
-0.006587982177734375,
0.021331787109375,
0.02459716796875,
0.0178375244140625,
0.00829315185546875,
-0.01183319091796875,
0.008209228515625,
0.00629425048828125,
-0.00794219970703125,
0.020111083984375,
-0.0091094970703125,
0.017242431640625,
0.0303192138671875,
0.029266357421875,
0.01168060302734375,
0.01222991943359375,
-0.001041412353515625,
0.0034275054931640625,
0.003856658935546875,
-0.0011854171752929688,
-0.0164947509765625,
0.01041412353515625,
-0.0177459716796875,
-0.002231597900390625,
-0.0269012451171875,
0.003063201904296875,
-0.01580810546875,
0.020965576171875,
-0.009552001953125,
0.007579803466796875,
0.00315093994140625,
0.006351470947265625,
-0.009918212890625,
0.003448486328125,
-0.016754150390625,
-0.02777099609375,
-0.01666259765625,
0.00057220458984375,
-0.023101806640625,
0.037811279296875,
-0.02203369140625,
0.0017528533935546875,
-0.0276336669921875,
-0.00205230712890625,
-0.0274505615234375,
-0.0047760009765625,
-0.002437591552734375,
-0.004802703857421875,
-0.018310546875,
-0.0043487548828125,
-0.0181732177734375,
-0.0203857421875,
0.0108795166015625,
-0.027099609375,
0.032562255859375,
-0.040679931640625,
0.01079559326171875,
-0.0149993896484375,
-0.013427734375,
0.003997802734375,
-0.020416259765625,
0.0018758773803710938,
0.00605010986328125,
-0.023956298828125,
-0.022705078125,
-0.002696990966796875,
0.014190673828125,
-0.00608062744140625,
0.011138916015625,
0.020263671875,
-0.0273590087890625,
-0.02923583984375,
-0.01506805419921875,
0.005718231201171875,
-0.00554656982421875,
-0.0084381103515625,
0.006702423095703125,
-0.001995086669921875,
0.0015382766723632812,
-0.0160064697265625,
-0.002410888671875,
0.024200439453125,
0.00289154052734375,
0.0010118484497070312,
0.0023212432861328125,
-0.007724761962890625,
-0.01244354248046875,
-0.03521728515625,
0.00018095970153808594,
-0.00991058349609375,
0.0009455680847167969,
0.0018157958984375,
-0.0018377304077148438,
-0.045745849609375,
-0.0088043212890625,
0.0318603515625,
0.0104522705078125,
0.01363372802734375,
-0.002109527587890625,
-0.013946533203125,
0.01251220703125,
0.00527191162109375,
-0.0221710205078125,
-0.0272674560546875,
0.0257110595703125,
0.00742340087890625,
-0.038330078125,
0.0018396377563476562,
0.01812744140625,
-0.0191497802734375,
0.01094818115234375,
0.0178375244140625,
0.0001825094223022461,
0.0007109642028808594,
0.0211181640625,
-0.0118255615234375,
0.006305694580078125,
0.04498291015625,
0.007389068603515625,
-0.01947021484375,
0.00800323486328125,
0.03076171875,
0.00769805908203125,
-0.0235748291015625,
-0.0304718017578125,
0.0165863037109375,
0.034637451171875,
0.0074920654296875,
-0.005802154541015625,
-0.0199432373046875,
-0.0254364013671875,
-0.0142059326171875,
0.00919342041015625,
-0.042266845703125,
-0.01045989990234375,
-0.0092315673828125,
0.03460693359375,
-0.001209259033203125,
-0.035675048828125,
0.03546142578125,
0.0009579658508300781,
0.00853729248046875,
-0.00010514259338378906,
-0.016021728515625,
-0.019775390625,
0.0218505859375,
0.005462646484375,
-0.006061553955078125,
0.008453369140625,
-0.0118408203125,
-0.0201263427734375,
0.03619384765625,
-0.00921630859375,
0.0087890625,
-0.003143310546875,
-0.029327392578125,
-0.007129669189453125,
0.026031494140625,
0.0252838134765625,
0.048980712890625,
-0.0039215087890625,
0.0087738037109375,
-0.005008697509765625,
-0.0238494873046875,
0.02001953125,
-0.016021728515625,
0.0229339599609375,
0.021728515625,
0.03125,
-0.016143798828125,
0.017486572265625,
-0.00836181640625,
-0.0210418701171875,
-0.0031452178955078125,
0.006694793701171875,
-0.01132965087890625,
0.01140594482421875,
-0.01129913330078125,
-0.0268096923828125,
0.00405120849609375,
-0.008148193359375,
-0.0146484375,
0.020965576171875,
0.021759033203125,
0.00611114501953125,
0.0018167495727539062,
0.019317626953125,
-0.01210784912109375,
-0.018646240234375,
-0.0003132820129394531,
-0.006580352783203125,
0.0014028549194335938,
-0.010711669921875,
-0.01849365234375,
0.006328582763671875,
0.00974273681640625,
-0.0161895751953125,
-0.029388427734375,
0.0092620849609375,
0.045379638671875,
-0.004703521728515625,
0.00984954833984375,
-0.01352691650390625,
0.0122528076171875,
-0.01068115234375,
-0.0032749176025390625,
0.022064208984375,
0.0171356201171875,
0.03204345703125,
-0.0283050537109375,
-0.0122833251953125,
-0.00669097900390625,
-0.019927978515625,
0.00612640380859375,
-0.0274505615234375,
-0.006404876708984375,
-0.00824737548828125,
0.00797271728515625,
0.0189361572265625,
0.011505126953125,
0.0267181396484375,
0.006099700927734375,
0.01004791259765625,
-0.0002830028533935547,
-0.00992584228515625,
0.0007314682006835938,
0.0226898193359375,
-0.01201629638671875,
0.00475311279296875,
-0.0124359130859375,
0.00640106201171875,
-0.025177001953125,
-0.02752685546875,
0.0123748779296875,
0.042755126953125,
0.01042938232421875,
0.01226806640625,
-0.01137542724609375,
0.023834228515625,
0.01477813720703125,
0.0227203369140625,
-0.0267181396484375,
0.034576416015625,
0.0228424072265625,
-0.0014963150024414062,
0.004802703857421875,
0.0266876220703125,
0.01158905029296875,
-0.00696563720703125,
0.0323486328125,
0.044708251953125,
0.0137786865234375,
0.030731201171875,
0.00861358642578125,
-0.0122833251953125,
-0.002391815185546875,
0.0185394287109375,
-0.030487060546875,
0.00281524658203125,
-0.005664825439453125,
0.012054443359375,
0.0109405517578125,
-0.004993438720703125,
0.013671875,
0.0198974609375,
-0.01058197021484375,
0.0292205810546875,
0.042083740234375,
0.00591278076171875,
-0.0035419464111328125,
0.0223236083984375,
0.0131683349609375,
0.01436614990234375,
-0.00698089599609375,
-0.00989532470703125,
0.01064300537109375,
-0.0137481689453125,
0.0015344619750976562,
0.0670166015625,
-0.022308349609375,
0.025115966796875,
-0.0190277099609375,
-0.01044464111328125,
-0.03131103515625,
-0.01433563232421875,
0.006748199462890625,
-0.0289154052734375,
-0.00222015380859375,
-0.00933837890625,
-0.034820556640625,
-0.006839752197265625,
0.01910400390625,
0.03594970703125,
0.0159454345703125,
0.006710052490234375,
-0.017364501953125,
0.0150909423828125,
-0.0183563232421875,
0.00864410400390625,
-0.0083160400390625,
0.005313873291015625,
0.00579071044921875,
-0.0179595947265625,
-0.024871826171875,
0.00402069091796875,
0.036834716796875,
-0.01102447509765625,
-0.0033130645751953125,
0.020782470703125,
0.01508331298828125,
-0.00521087646484375,
0.009979248046875,
0.005222320556640625,
-0.02593994140625,
0.004108428955078125,
-0.035064697265625,
0.00797271728515625,
0.0049591064453125,
-0.0059356689453125,
0.0286865234375,
0.021209716796875,
0.01210784912109375,
-0.01294708251953125,
-0.0208892822265625,
-0.0185089111328125,
0.00839996337890625,
-0.0008625984191894531,
-0.025634765625,
-0.004436492919921875,
-0.00992584228515625,
-0.01395416259765625,
-0.00774383544921875,
0.008758544921875,
-0.0288543701171875,
-0.034912109375,
0.007068634033203125,
-0.01004791259765625,
0.01324462890625,
0.0178070068359375,
-0.0162353515625,
0.0214385986328125,
0.0016498565673828125,
0.0019969940185546875,
-0.0013103485107421875,
-0.0570068359375,
-0.0216522216796875,
-0.0012693405151367188,
0.003204345703125,
0.00130462646484375,
-0.023468017578125,
-0.00007814168930053711,
0.00015056133270263672,
-0.0163726806640625,
-0.00921630859375,
-0.004486083984375,
0.025726318359375,
0.0126495361328125,
-0.00748443603515625,
-0.0172271728515625,
0.0164031982421875,
-0.036956787109375,
0.006549835205078125,
-0.045623779296875,
0.006244659423828125,
-0.045623779296875,
0.0189666748046875,
-0.03753662109375,
0.0241241455078125,
0.0026035308837890625,
-0.033111572265625,
-0.01349639892578125,
-0.044830322265625,
0.001201629638671875,
0.01334381103515625,
-0.0132904052734375,
0.00438690185546875,
0.006526947021484375,
-0.0008306503295898438,
-0.01456451416015625,
-0.004962921142578125,
-0.0080413818359375,
-0.0237579345703125,
-0.033721923828125,
0.037841796875,
-0.004238128662109375,
0.0035305023193359375,
-0.011627197265625,
0.01255035400390625,
-0.0249176025390625,
-0.0070648193359375,
0.0020904541015625,
-0.01515960693359375,
-0.0462646484375,
-0.005828857421875,
-0.01337432861328125,
0.0290069580078125,
-0.00872039794921875,
-0.005672454833984375,
-0.01490020751953125,
0.024627685546875,
0.0238189697265625,
-0.00524139404296875,
-0.009368896484375,
-0.0012607574462890625,
0.008941650390625,
-0.01497650146484375,
-0.029937744140625,
-0.0323486328125,
0.0193328857421875,
0.007617950439453125,
-0.006809234619140625,
0.006687164306640625,
0.02801513671875,
-0.00894927978515625,
0.0254364013671875,
0.0243377685546875,
-0.0000010132789611816406,
0.0025463104248046875,
0.00710296630859375,
0.0374755859375,
0.022064208984375,
0.018280029296875,
0.0193328857421875,
0.01837158203125,
0.02349853515625,
-0.018707275390625,
0.02105712890625,
-0.004673004150390625,
-0.01479339599609375,
-0.003635406494140625,
0.005588531494140625,
-0.0108184814453125,
-0.0257110595703125,
-0.0035686492919921875,
0.01898193359375,
-0.04791259765625,
0.032440185546875,
-0.026824951171875,
-0.01302337646484375,
-0.00757598876953125,
0.016143798828125,
0.01409149169921875,
0.00720977783203125,
0.013641357421875,
-0.0153656005859375,
-0.015625,
-0.0171661376953125,
-0.01202392578125,
-0.0300750732421875,
-0.0181884765625,
0.022216796875,
0.01308441162109375,
-0.01230621337890625,
-0.0312347412109375,
0.006198883056640625,
-0.006549835205078125,
0.0006189346313476562,
0.02020263671875,
-0.0172882080078125,
0.0284576416015625,
0.01158905029296875,
0.0002065896987915039,
-0.0017938613891601562,
0.00121307373046875,
-0.0234527587890625,
-0.043792724609375,
-0.003841400146484375,
0.007720947265625,
-0.00783538818359375,
0.0291748046875,
-0.03802490234375,
0.019989013671875,
0.0116729736328125,
0.0306549072265625,
-0.0308837890625,
0.0203704833984375,
-0.0030193328857421875,
0.0113677978515625,
-0.0289154052734375,
-0.005687713623046875,
-0.0567626953125,
-0.014984130859375,
-0.0239410400390625,
-0.0238494873046875,
0.0033206939697265625,
0.0246124267578125,
-0.00921630859375,
0.0165863037109375,
-0.01486968994140625,
0.004669189453125,
-0.0222930908203125,
0.01096343994140625,
0.03533935546875,
0.018768310546875,
0.055511474609375,
0.007320404052734375,
-0.03216552734375,
-0.002750396728515625,
-0.0014705657958984375,
0.03350830078125,
0.0170745849609375,
-0.0083465576171875,
0.022674560546875,
0.01800537109375,
0.0173492431640625,
0.00566864013671875,
-0.0221710205078125,
0.00438690185546875,
0.0191192626953125,
0.00507354736328125,
0.006458282470703125,
-0.0135040283203125,
0.023681640625,
-0.00021851062774658203,
0.01776123046875,
0.0306854248046875,
0.0174407958984375,
0.0073699951171875,
-0.00920867919921875,
0.0007648468017578125,
0.016876220703125,
-0.00507354736328125,
0.0180511474609375,
0.0172119140625,
0.045074462890625,
0.00909423828125,
0.007564544677734375,
-0.005474090576171875,
-0.014984130859375,
0.031707763671875,
0.004489898681640625,
0.01123809814453125,
-0.004680633544921875,
-0.0084686279296875,
0.020599365234375,
-0.0074462890625,
-0.0657958984375,
0.006664276123046875,
-0.0146942138671875,
-0.0283355712890625,
0.02337646484375,
0.005756378173828125,
-0.007579803466796875,
-0.0131988525390625,
0.0275115966796875,
-0.020782470703125,
0.0101165771484375,
0.0100250244140625,
0.0133056640625,
-0.03155517578125,
0.014678955078125,
0.018524169921875,
-0.026885986328125,
0.0089874267578125,
0.006031036376953125,
0.003963470458984375,
0.0428466796875,
0.00902557373046875,
-0.01436614990234375,
0.019866943359375,
0.022705078125,
0.0172119140625,
-0.029266357421875,
0.02520751953125,
0.0198974609375,
0.026580810546875,
-0.003631591796875,
0.0167999267578125,
0.01189422607421875,
0.03826904296875,
-0.0295867919921875,
0.012908935546875,
-0.01129913330078125,
-0.009033203125,
-0.05462646484375,
0.0023040771484375,
-0.0186614990234375,
0.01297760009765625,
-0.0108489990234375,
0.011016845703125,
0.0126800537109375,
0.041229248046875,
-0.006992340087890625,
-0.0038318634033203125,
0.0103759765625,
-0.01128387451171875,
0.0220489501953125,
0.00989532470703125,
-0.00035572052001953125,
-0.006313323974609375,
-0.0298309326171875,
0.03662109375,
-0.0011739730834960938,
-0.0261993408203125,
-0.006374359130859375,
0.0053253173828125,
-0.0205841064453125,
-0.01047515869140625,
-0.0162353515625,
-0.0321044921875,
0.014190673828125,
-0.0203399658203125,
-0.01763916015625,
-0.006069183349609375,
0.0188446044921875,
-0.0078582763671875,
0.01157379150390625,
-0.0033092498779296875,
-0.023681640625,
0.0159759521484375,
-0.023895263671875,
0.00830078125,
0.0007085800170898438,
-0.042266845703125,
-0.0423583984375,
-0.03668212890625,
0.011932373046875,
0.000873565673828125,
0.002529144287109375,
0.002140045166015625,
0.0162353515625,
-0.0019989013671875,
0.0029850006103515625,
-0.00046372413635253906,
-0.003658294677734375,
-0.017578125,
-0.0228729248046875,
-0.017822265625,
0.01285552978515625,
-0.0308074951171875,
0.015716552734375,
-0.044097900390625,
0.026336669921875,
-0.00347900390625,
-0.021087646484375,
0.01349639892578125,
-0.0194854736328125,
-0.0202178955078125,
-0.01033782958984375,
0.0093231201171875,
0.045806884765625,
-0.01120758056640625,
-0.0377197265625,
-0.0149688720703125,
-0.0423583984375,
-0.018280029296875,
0.00035452842712402344,
0.003429412841796875,
-0.0173492431640625,
-0.00946807861328125,
0.004413604736328125,
0.0069122314453125,
-0.0246124267578125,
-0.0108489990234375,
0.007350921630859375,
0.0235443115234375,
-0.0201873779296875,
-0.037109375,
-0.0017004013061523438,
0.0018587112426757812,
0.0198974609375,
0.0018177032470703125,
-0.0113372802734375,
0.01364898681640625,
-0.0206756591796875,
0.007717132568359375,
0.02490234375,
-0.05401611328125,
-0.01215362548828125,
-0.0149993896484375,
-0.006198883056640625,
-0.010833740234375,
0.00405120849609375,
-0.0043792724609375,
0.00945281982421875,
0.0063629150390625,
0.0267791748046875,
0.0039825439453125,
-0.00809478759765625,
-0.014495849609375,
-0.0068359375,
-0.00539398193359375,
-0.0075225830078125,
0.0179443359375
] |
ours_523
|
Let \( p = 2011 \) (which is prime), and for \( k = 1, 2, \ldots, p \), let \( S_k = \{ x \in [1, 2011!] \mid x \equiv k \pmod{p} \} \) and \( T_k = \{ x \in S_k \mid p \mid x^x - 1 \} \). As \(|S_1| = \cdots = |S_p| = \frac{1}{p} \cdot p! \), the desired probability is \(\frac{1}{p} \sum_{k=1}^{p} \frac{|T_k|}{|S_k|}\).
Now we observe that for \( x \in S_k \), \( p \mid x^x - 1 \) if and only if \( k \neq 0 \) and \(\operatorname{ord}_p(k) \mid x\). But \(\operatorname{ord}_p(k) \mid p-1\) by Fermat's Little Theorem and \(\gcd(p, p-1) = 1\). Therefore, using the Chinese Remainder Theorem and the fact that \( S_k = k + p\{0, 1, \ldots, (p-1)! - 1\} \), we have \(\frac{|T_k|}{|S_k|} = \frac{1}{\operatorname{ord}_p(k)}\).
Thus, the probability is:
\[
\frac{1}{p} \sum_{k=1}^{p-1} \frac{1}{\operatorname{ord}_p(k)}
\]
For every positive divisor \( d \) of \( p-1 \), there are exactly \(\phi(d)\) (where \(\phi\) denotes Euler's totient function) residues \( k \) with \(\operatorname{ord}_p(k) = d\). Therefore, our answer is:
\[
\frac{1}{p} \sum_{d \mid p-1} \frac{\phi(d)}{d} = \frac{1}{2011} \sum_{d \mid 2010} \frac{\phi(d)}{d}
\]
This evaluates to:
\[
\frac{1}{2011} \left(1 + \left(1 - \frac{1}{2}\right)\right)\left(1 + \left(1 - \frac{1}{3}\right)\right)\left(1 + \left(1 - \frac{1}{5}\right)\right)\left(1 + \left(1 - \frac{1}{67}\right)\right)
\]
which simplifies to \(\frac{1197}{269474}\). Therefore, the value of \( m \) is \(\boxed{1197}\).
|
1197
|
{
"competition": "us_comps",
"dataset": "Ours",
"posts": null,
"source": "OMOSoln2-2.md"
}
|
An integer \( x \) is selected at random between \( 1 \) and \( 2011! \) inclusive. The probability that \( x^x - 1 \) is divisible by \( 2011 \) can be expressed in the form \(\frac{m}{n}\), where \( m \) and \( n \) are relatively prime positive integers. Find \( m \).
|
[
"/Mathematics/NumberTheory/Congruences/ChineseRemainderTheorem",
"/Mathematics/NumberTheory/Congruences/ModuloOrder",
"/Mathematics/NumberTheory/Congruences/MultiplicativeOrder",
"/Mathematics/NumberTheory/GeneralNumberTheory/ElementaryNumberTheory",
"/Mathematics/NumberTheory/GeneralNumberTheory/HigherArithmetic",
"/Mathematics/NumberTheory/GeneralNumberTheory/NumberTheory",
"/Mathematics/NumberTheory/PrimeNumbers/PrimeNumberProperties",
"/Mathematics/ProbabilityandStatistics/Probability/ProbabilitySpace",
"/Mathematics/ProbabilityandStatistics/Probability/SampleSpace"
] |
Translate the condition p | xᵡ − 1 into “the multiplicative order of x mod p divides x” and average over residue classes using the distribution of orders.
|
[
-0.00013196468353271484,
-0.0205078125,
0.007411956787109375,
0.022308349609375,
-0.00048089027404785156,
0.0496826171875,
0.0007085800170898438,
-0.0232086181640625,
-0.004863739013671875,
0.009918212890625,
0.046295166015625,
-0.0675048828125,
-0.0023326873779296875,
-0.045166015625,
-0.04461669921875,
-0.031585693359375,
0.061309814453125,
0.0028228759765625,
-0.0116119384765625,
0.0012187957763671875,
-0.006999969482421875,
-0.049102783203125,
-0.004108428955078125,
0.030517578125,
-0.01140594482421875,
-0.0196990966796875,
-0.00937652587890625,
0.012542724609375,
0.024810791015625,
0.00542449951171875,
-0.033172607421875,
-0.0006504058837890625,
0.0278472900390625,
-0.041107177734375,
-0.0009584426879882812,
-0.0050201416015625,
-0.0005135536193847656,
-0.00522613525390625,
0.00396728515625,
-0.0133056640625,
0.01043701171875,
0.033477783203125,
0.0023097991943359375,
0.0067901611328125,
0.00833892822265625,
-0.037322998046875,
-0.006832122802734375,
0.0213165283203125,
0.00440216064453125,
-0.00505828857421875,
-0.0014524459838867188,
-0.007232666015625,
0.01267242431640625,
-0.013458251953125,
-0.034454345703125,
-0.055877685546875,
0.024169921875,
0.0020847320556640625,
0.002597808837890625,
-0.00785064697265625,
0.0009322166442871094,
-0.01465606689453125,
0.0041961669921875,
-0.00792694091796875,
-0.000016570091247558594,
-0.017608642578125,
0.0110626220703125,
0.00733184814453125,
0.0080718994140625,
-0.012420654296875,
0.0190277099609375,
-0.011932373046875,
-0.021148681640625,
0.046875,
0.032073974609375,
-0.0157470703125,
-0.0028247833251953125,
0.0013055801391601562,
0.02459716796875,
-0.00531005859375,
0.0230865478515625,
0.01519012451171875,
0.0008993148803710938,
0.0213775634765625,
0.0148468017578125,
0.0253753662109375,
-0.0292205810546875,
0.0022068023681640625,
0.029815673828125,
-0.009613037109375,
-0.01073455810546875,
0.0679931640625,
0.00016617774963378906,
-0.0126800537109375,
-0.0052032470703125,
-0.006938934326171875,
0.021575927734375,
-0.018310546875,
-0.0213165283203125,
0.0101776123046875,
-0.00441741943359375,
-0.01172637939453125,
0.0193939208984375,
-0.0006480216979980469,
-0.07110595703125,
-0.00014841556549072266,
-0.0279998779296875,
0.0015707015991210938,
0.00910186767578125,
0.0013856887817382812,
-0.0036563873291015625,
0.0030803680419921875,
0.0263519287109375,
0.01171112060546875,
-0.00803375244140625,
0.0207977294921875,
0.018310546875,
0.01300811767578125,
-0.0104827880859375,
-0.0016765594482421875,
0.005481719970703125,
0.004222869873046875,
-0.00962066650390625,
0.01328277587890625,
-0.0020751953125,
0.01519012451171875,
-0.004791259765625,
0.0099029541015625,
-0.01041412353515625,
0.007740020751953125,
0.0198516845703125,
0.0246429443359375,
-0.054718017578125,
-0.0193634033203125,
-0.0712890625,
0.0081024169921875,
0.01229095458984375,
-0.024169921875,
0.004795074462890625,
-0.03265380859375,
0.00989532470703125,
-0.008697509765625,
-0.0011301040649414062,
-0.030364990234375,
-0.0015115737915039062,
0.00365447998046875,
-0.017425537109375,
-0.042877197265625,
-0.01120758056640625,
0.00438690185546875,
0.01142120361328125,
0.001430511474609375,
0.0032253265380859375,
-0.0124664306640625,
-0.0024394989013671875,
0.00884246826171875,
0.0068206787109375,
-0.0066070556640625,
-0.00836944580078125,
-0.002010345458984375,
0.0059356689453125,
-0.00844573974609375,
-0.0390625,
0.0103302001953125,
-0.00016748905181884766,
-0.0002231597900390625,
-0.0002892017364501953,
-0.03631591796875,
-0.0002810955047607422,
-0.0269622802734375,
0.020782470703125,
0.01525115966796875,
0.012420654296875,
-0.013397216796875,
-0.006805419921875,
0.00547027587890625,
-0.007465362548828125,
0.01393890380859375,
0.008148193359375,
0.00878143310546875,
0.002471923828125,
-0.02545166015625,
0.0054931640625,
-0.0088653564453125,
0.0178375244140625,
-0.012359619140625,
-0.00798797607421875,
0.0014200210571289062,
0.02362060546875,
-0.0042724609375,
0.00014388561248779297,
0.0007290840148925781,
0.006771087646484375,
-0.0031871795654296875,
-0.01438140869140625,
-0.013671875,
-0.0031490325927734375,
-0.00411224365234375,
0.036865234375,
0.0213775634765625,
-0.0098876953125,
0.00030803680419921875,
0.00296783447265625,
0.0181732177734375,
-0.006927490234375,
0.00927734375,
0.016754150390625,
-0.00502777099609375,
0.00665283203125,
-0.000579833984375,
0.01264190673828125,
-0.00025534629821777344,
-0.00627899169921875,
-0.042724609375,
-0.01174163818359375,
0.00241851806640625,
-0.00970458984375,
0.004062652587890625,
0.01404571533203125,
-0.053680419921875,
-0.00756072998046875,
0.0190582275390625,
-0.00699615478515625,
-0.019287109375,
-0.006778717041015625,
-0.0079803466796875,
-0.00016021728515625,
0.0068511962890625,
-0.01306915283203125,
0.00811004638671875,
0.0035114288330078125,
0.0133056640625,
-0.0125885009765625,
-0.00019073486328125,
0.0321044921875,
0.01171112060546875,
0.00839996337890625,
-0.005275726318359375,
-0.0014934539794921875,
-0.014373779296875,
0.00897216796875,
-0.00617218017578125,
0.00527191162109375,
0.0005698204040527344,
-0.0049285888671875,
-0.014312744140625,
0.0081634521484375,
-0.004932403564453125,
-0.0014314651489257812,
-0.0094146728515625,
0.0090179443359375,
-0.0019407272338867188,
0.00616455078125,
0.00891876220703125,
0.0265350341796875,
-0.00872039794921875,
0.0129547119140625,
-0.0364990234375,
-0.00946807861328125,
0.0007152557373046875,
-0.008880615234375,
-0.01079559326171875,
-0.0124053955078125,
-0.01131439208984375,
-0.01111602783203125,
-0.01502227783203125,
-0.0184478759765625,
-0.01273345947265625,
0.01009368896484375,
0.00656890869140625,
0.0300140380859375,
-0.032440185546875,
-0.007167816162109375,
0.0007333755493164062,
0.00402069091796875,
-0.0107879638671875,
-0.0009007453918457031,
0.00508880615234375,
-0.01380157470703125,
-0.01282501220703125,
0.0008630752563476562,
-0.0174713134765625,
0.004932403564453125,
-0.0038051605224609375,
0.0271453857421875,
-0.021331787109375,
-0.0134124755859375,
-0.0194091796875,
-0.0255889892578125,
-0.00856781005859375,
0.0029468536376953125,
0.01342010498046875,
-0.023681640625,
0.007476806640625,
0.020050048828125,
-0.04559326171875,
-0.00382232666015625,
0.020172119140625,
0.006954193115234375,
-0.00689697265625,
0.0321044921875,
0.00624847412109375,
-0.009613037109375,
-0.004520416259765625,
-0.00460052490234375,
0.001842498779296875,
0.0012149810791015625,
0.007415771484375,
-0.004650115966796875,
-0.034942626953125,
-0.0020198822021484375,
0.0062408447265625,
0.01493072509765625,
0.01166534423828125,
-0.0281219482421875,
-0.042694091796875,
-0.0047760009765625,
0.007022857666015625,
-0.012115478515625,
0.020294189453125,
0.01174163818359375,
0.0236053466796875,
-0.01502227783203125,
-0.01279449462890625,
0.0033721923828125,
0.00717926025390625,
0.005680084228515625,
0.021270751953125,
-0.022308349609375,
0.00897216796875,
-0.040557861328125,
0.0128326416015625,
0.0209197998046875,
-0.025665283203125,
0.004360198974609375,
0.0131072998046875,
-0.004306793212890625,
0.0340576171875,
0.021087646484375,
-0.00170135498046875,
-0.00218963623046875,
-0.02117919921875,
0.03204345703125,
0.034454345703125,
0.0002067089080810547,
0.0228424072265625,
0.0142974853515625,
-0.025238037109375,
0.007480621337890625,
-0.00986480712890625,
0.0090179443359375,
-0.0012645721435546875,
-0.0232391357421875,
-0.00262451171875,
-0.0292510986328125,
0.0081024169921875,
-0.001117706298828125,
0.004894256591796875,
-0.0301055908203125,
0.0220184326171875,
0.01200103759765625,
-0.00035953521728515625,
0.0189361572265625,
0.0176239013671875,
0.033843994140625,
-0.0149383544921875,
-0.008880615234375,
0.00461578369140625,
-0.023590087890625,
-0.004428863525390625,
-0.0228271484375,
-0.03759765625,
0.0062713623046875,
-0.00360870361328125,
-0.0355224609375,
-0.0194091796875,
0.020599365234375,
-0.016448974609375,
0.00811004638671875,
0.01355743408203125,
0.031036376953125,
0.048248291015625,
-0.0019140243530273438,
0.05010986328125,
-0.0248260498046875,
-0.0174713134765625,
0.0159454345703125,
-0.031280517578125,
-0.007755279541015625,
0.00411224365234375,
-0.0080108642578125,
-0.01143646240234375,
-0.01629638671875,
0.006664276123046875,
0.010650634765625,
-0.0257568359375,
-0.004100799560546875,
0.005443572998046875,
0.0207977294921875,
-0.008544921875,
0.038726806640625,
-0.01366424560546875,
-0.0158538818359375,
0.004520416259765625,
0.0118408203125,
-0.005420684814453125,
-0.00884246826171875,
-0.019317626953125,
-0.012420654296875,
0.01415252685546875,
0.0009050369262695312,
0.01204681396484375,
0.005367279052734375,
-0.004009246826171875,
0.045074462890625,
-0.00904083251953125,
0.0167694091796875,
-0.004638671875,
-0.034942626953125,
0.0010194778442382812,
-0.024261474609375,
-0.031585693359375,
0.0153961181640625,
-0.01532745361328125,
0.02783203125,
0.02740478515625,
-0.021697998046875,
0.02935791015625,
0.00962066650390625,
0.00199127197265625,
-0.014617919921875,
-0.002593994140625,
0.020782470703125,
0.03314208984375,
0.002796173095703125,
-0.00345611572265625,
0.0004410743713378906,
0.007099151611328125,
-0.018524169921875,
0.0021839141845703125,
0.00966644287109375,
-0.002460479736328125,
-0.0295867919921875,
0.01079559326171875,
-0.04638671875,
-0.0032062530517578125,
-0.0012903213500976562,
0.01322174072265625,
-0.053741455078125,
0.0096893310546875,
-0.0233154296875,
0.00803375244140625,
-0.01824951171875,
0.005016326904296875,
0.024627685546875,
0.0141143798828125,
0.02032470703125,
-0.0202178955078125,
0.0196533203125,
0.0015897750854492188,
-0.018646240234375,
-0.00563812255859375,
-0.0268402099609375,
-0.0063934326171875,
-0.034423828125,
0.0076904296875,
-0.03564453125,
-0.005340576171875,
0.019378662109375,
-0.0269775390625,
-0.0224151611328125,
-0.021697998046875,
0.03759765625,
-0.0052947998046875,
-0.0257720947265625,
0.020050048828125,
0.018646240234375,
0.032501220703125,
-0.01528167724609375,
-0.031036376953125,
0.0157928466796875,
-0.01062774658203125,
-0.023101806640625,
0.048248291015625,
0.01287841796875,
0.0221405029296875,
0.0391845703125,
0.0180816650390625,
0.00007623434066772461,
0.0178070068359375,
0.01416778564453125,
0.02777099609375,
-0.009490966796875,
-0.01374053955078125,
-0.0360107421875,
-0.00843048095703125,
-0.021514892578125,
-0.00902557373046875,
-0.022064208984375,
0.005718231201171875,
-0.018310546875,
-0.003124237060546875,
-0.020782470703125,
0.040374755859375,
-0.0167999267578125,
0.00940704345703125,
0.031280517578125,
-0.0038394927978515625,
-0.014678955078125,
-0.0261077880859375,
-0.002765655517578125,
-0.00499725341796875,
0.027984619140625,
-0.0240325927734375,
-0.0030918121337890625,
-0.0037899017333984375,
0.012603759765625,
-0.0205535888671875,
-0.004970550537109375,
0.0061492919921875,
-0.0176544189453125,
0.0250244140625,
0.020904541015625,
-0.0210723876953125,
0.0106658935546875,
-0.0122528076171875,
0.01493072509765625,
-0.00960540771484375,
-0.0145263671875,
-0.02764892578125,
-0.00638580322265625,
-0.00765228271484375,
0.004230499267578125,
-0.0097808837890625,
-0.007541656494140625,
0.019256591796875,
0.0277557373046875,
-0.00044846534729003906,
-0.01288604736328125,
-0.00859832763671875,
0.0216217041015625,
0.0003101825714111328,
0.0113677978515625,
-0.009246826171875,
0.0010433197021484375,
-0.036407470703125,
-0.01052093505859375,
0.0095977783203125,
-0.0018205642700195312,
0.0214691162109375,
0.01123046875,
0.016021728515625,
0.06695556640625,
0.0066680908203125,
-0.0242156982421875,
0.03973388671875,
-0.01505279541015625,
-0.00824737548828125,
0.00007927417755126953,
0.01543426513671875,
0.017913818359375,
0.0085906982421875,
-0.004009246826171875,
-0.0037899017333984375,
0.0028896331787109375,
0.01129913330078125,
-0.0130767822265625,
0.00913238525390625,
0.01317596435546875,
-0.048004150390625,
-0.004207611083984375,
0.00933074951171875,
0.0047454833984375,
0.03057861328125,
0.007236480712890625,
0.007625579833984375,
-0.0174713134765625,
-0.010101318359375,
0.00324249267578125,
-0.026031494140625,
-0.016448974609375,
0.026458740234375,
-0.0014629364013671875,
-0.011016845703125,
0.033843994140625,
0.022705078125,
0.02215576171875,
0.00823974609375,
0.0194244384765625,
0.0083160400390625,
-0.0166015625,
0.01203155517578125,
-0.0179290771484375,
0.031707763671875,
0.0032558441162109375,
-0.0222320556640625,
0.0416259765625,
-0.0297698974609375,
-0.0072021484375,
-0.005489349365234375,
0.00672149658203125,
0.0266265869140625,
-0.0193023681640625,
-0.00771331787109375,
-0.002307891845703125,
-0.027191162109375,
0.020111083984375,
0.038360595703125,
0.005130767822265625,
-0.0117340087890625,
0.02740478515625,
0.0037078857421875,
0.0218505859375,
0.0104827880859375,
0.049072265625,
0.012176513671875,
-0.0070037841796875,
-0.0026912689208984375,
-0.0025081634521484375,
-0.034027099609375,
-0.013519287109375,
-0.0177001953125,
-0.0198974609375,
0.01010894775390625,
-0.005222320556640625,
-0.00323486328125,
0.0162353515625,
0.0017223358154296875,
-0.034515380859375,
-0.008514404296875,
0.0028324127197265625,
0.0033111572265625,
0.0318603515625,
0.00769805908203125,
-0.01013946533203125,
0.01371002197265625,
-0.0106964111328125,
-0.0069732666015625,
-0.0038433074951171875,
-0.01425933837890625,
0.01311492919921875,
0.01422119140625,
0.01483917236328125,
-0.04876708984375,
0.00394439697265625,
0.003955841064453125,
-0.0228118896484375,
0.024200439453125,
-0.0263824462890625,
0.0124664306640625,
-0.018218994140625,
-0.01788330078125,
-0.00798797607421875,
0.01751708984375,
-0.0185699462890625,
0.03204345703125,
0.0004317760467529297,
-0.01149749755859375,
0.01123046875,
-0.0011548995971679688,
0.002166748046875,
0.015716552734375,
0.048797607421875,
-0.0241546630859375,
-0.0159912109375,
0.0204010009765625,
0.0016222000122070312,
-0.01483917236328125,
0.04541015625,
-0.0184783935546875,
0.0075836181640625,
-0.03533935546875,
0.0231781005859375,
-0.0301361083984375,
0.0179901123046875,
-0.026885986328125,
0.00615692138671875,
-0.00222015380859375,
0.0279388427734375,
0.045257568359375,
0.0035305023193359375,
-0.0015344619750976562,
-0.0005292892456054688,
-0.01235198974609375,
0.031768798828125,
0.030120849609375,
-0.0484619140625,
-0.01432037353515625,
-0.01236724853515625,
0.0011129379272460938,
0.00293731689453125,
-0.0045623779296875,
0.01092529296875,
0.00005918741226196289,
-0.004467010498046875,
-0.01837158203125,
0.01494598388671875,
0.0003495216369628906,
-0.016143798828125,
-0.0017528533935546875,
0.004108428955078125,
-0.0265045166015625,
0.004146575927734375,
0.0018911361694335938,
0.0070953369140625,
-0.0291290283203125,
-0.004657745361328125,
0.0182342529296875,
-0.03778076171875,
-0.0160064697265625,
-0.025054931640625,
0.0024662017822265625,
0.0032367706298828125,
0.0016870498657226562,
-0.01568603515625,
0.0173797607421875,
0.042205810546875,
0.0120391845703125,
-0.03369140625,
-0.0117340087890625,
-0.0290374755859375,
0.0186309814453125,
-0.029083251953125,
0.0010499954223632812,
0.0166168212890625,
-0.0088043212890625,
-0.0094757080078125,
-0.02557373046875,
-0.0286407470703125,
-0.0165557861328125,
-0.0072479248046875,
-0.0183563232421875,
0.002521514892578125,
-0.0015439987182617188,
-0.00829315185546875,
0.01380157470703125,
0.0170745849609375,
-0.0394287109375,
0.017974853515625,
-0.00183868408203125,
0.050933837890625,
-0.0104217529296875,
0.041473388671875,
-0.01259613037109375,
0.007045745849609375,
0.001430511474609375,
0.0330810546875,
-0.028533935546875,
0.0213165283203125,
0.00472259521484375,
0.0207061767578125,
0.005645751953125,
-0.034027099609375,
0.0060882568359375,
-0.00940704345703125,
-0.0032958984375,
0.0091705322265625,
-0.0245208740234375,
-0.00812530517578125,
0.0003733634948730469,
-0.0312042236328125,
0.0033054351806640625,
0.0086822509765625,
0.01299285888671875,
0.006610870361328125,
0.01204681396484375,
-0.006839752197265625,
0.0002942085266113281,
0.003482818603515625,
0.052001953125,
-0.0198974609375,
0.0197296142578125,
0.037200927734375,
-0.03289794921875,
0.009552001953125,
-0.0225830078125,
0.0002541542053222656,
0.0028209686279296875,
0.030792236328125,
-0.032928466796875,
0.0278167724609375,
-0.01175689697265625,
0.0179595947265625,
0.009124755859375,
-0.035125732421875,
-0.047698974609375,
-0.00415802001953125,
-0.04461669921875,
0.004543304443359375,
-0.0234832763671875,
0.0266265869140625,
0.0116729736328125,
0.005298614501953125,
-0.0083770751953125,
-0.0177001953125,
-0.0038509368896484375,
0.01534271240234375,
-0.0030193328857421875,
-0.0213470458984375,
0.0010194778442382812,
-0.0014295578002929688,
-0.0184783935546875,
-0.02886962890625,
0.01387786865234375,
0.004512786865234375,
0.003246307373046875,
0.0254669189453125,
-0.00568389892578125,
-0.00040435791015625,
0.0199432373046875,
-0.006954193115234375,
-0.0160369873046875,
-0.0307159423828125,
0.004268646240234375,
0.01204681396484375,
-0.03900146484375,
0.0149078369140625,
-0.019683837890625,
0.007061004638671875,
0.039581298828125,
-0.0180816650390625,
0.0213165283203125,
0.014190673828125,
-0.00724029541015625,
-0.0202178955078125,
0.01174163818359375,
0.0059051513671875,
0.024932861328125,
0.01442718505859375,
0.0218658447265625,
-0.0024738311767578125,
-0.0202789306640625,
0.035736083984375,
0.018035888671875,
0.01387786865234375,
0.01280975341796875,
-0.0301361083984375,
0.01038360595703125,
-0.024200439453125,
-0.018310546875,
0.00937652587890625,
-0.0194091796875,
-0.00553131103515625,
-0.038177490234375,
0.0213165283203125,
-0.022216796875,
-0.001010894775390625,
-0.0189208984375,
0.0020904541015625,
-0.01220703125,
0.0168609619140625,
0.003223419189453125,
-0.00572967529296875,
0.018646240234375,
-0.0250244140625,
0.041015625,
0.02630615234375,
0.01419830322265625,
0.0006318092346191406,
-0.0026397705078125,
-0.010986328125,
-0.0274200439453125,
-0.00653076171875,
-0.0245208740234375,
-0.0059814453125,
0.036529541015625,
-0.0121307373046875,
0.0199127197265625,
-0.01165008544921875,
0.00469207763671875,
-0.0302581787109375,
0.0038623809814453125,
0.0205078125,
0.0191650390625,
-0.01265716552734375,
-0.01050567626953125,
0.0154266357421875,
0.02532958984375,
0.000751495361328125,
-0.0033283233642578125,
0.00598907470703125,
-0.0419921875,
0.01201629638671875,
-0.00048661231994628906,
-0.0040740966796875,
0.0270233154296875,
0.033294677734375,
0.041107177734375,
-0.0230255126953125,
-0.00606536865234375,
-0.0004394054412841797,
0.0015325546264648438,
0.01557159423828125,
-0.0189666748046875,
0.0199127197265625,
0.0325927734375,
-0.0221099853515625,
0.00762939453125,
-0.001796722412109375,
-0.06268310546875,
0.0287628173828125,
-0.007457733154296875,
0.03875732421875,
0.007061004638671875,
-0.02850341796875,
-0.0258331298828125,
-0.0265960693359375,
-0.0276641845703125,
0.022186279296875,
0.0160064697265625,
0.004047393798828125,
0.0036258697509765625,
0.0146026611328125,
0.0276031494140625,
-0.03515625,
-0.01100921630859375,
-0.0032100677490234375,
-0.00473785400390625,
0.016632080078125,
0.0252838134765625,
-0.0020809173583984375,
0.004222869873046875,
0.0117645263671875,
-0.005840301513671875,
-0.005069732666015625,
0.01904296875,
-0.0115509033203125,
0.00428009033203125,
-0.0194549560546875,
-0.0006284713745117188,
-0.012115478515625,
0.01161956787109375,
-0.03216552734375,
0.0233306884765625,
0.0034580230712890625,
0.0218353271484375,
-0.006229400634765625,
0.01279449462890625,
0.0209808349609375,
0.008331298828125,
-0.00971221923828125,
0.01351165771484375,
-0.00786590576171875,
0.0182037353515625,
0.010955810546875,
0.004756927490234375,
0.0150604248046875,
0.03179931640625,
-0.054046630859375,
0.010009765625,
-0.053375244140625,
-0.0135955810546875,
-0.0183868408203125,
0.021087646484375,
0.002796173095703125,
0.0015401840209960938,
-0.0242767333984375,
-0.0247650146484375,
-0.02569580078125,
-0.04913330078125,
0.0022335052490234375,
0.02178955078125,
-0.05804443359375,
-0.0201416015625,
-0.01309967041015625,
0.035552978515625,
0.025115966796875,
-0.006229400634765625,
0.01465606689453125,
-0.009002685546875,
-0.021087646484375,
-0.0231781005859375,
-0.033538818359375,
-0.0299224853515625,
0.018768310546875,
-0.01421356201171875,
-0.0045623779296875,
0.016815185546875,
0.02557373046875,
0.0266265869140625,
-0.024078369140625,
0.0015239715576171875,
0.00833892822265625,
0.0012521743774414062,
-0.01546478271484375,
0.0179595947265625,
0.0290679931640625,
-0.021026611328125,
0.0117340087890625,
0.0025768280029296875,
-0.00789642333984375,
0.0130157470703125,
0.0014238357543945312,
0.0076446533203125,
0.016143798828125,
-0.002925872802734375,
-0.034759521484375,
0.0028171539306640625,
-0.01171112060546875,
0.0105438232421875,
0.002140045166015625,
0.00012004375457763672,
-0.00421142578125,
-0.0115203857421875,
0.01087188720703125,
-0.006687164306640625,
0.04498291015625,
-0.012298583984375,
-0.00955963134765625,
0.00588226318359375,
-0.004589080810546875,
-0.0090484619140625,
-0.01534271240234375,
0.00473785400390625,
-0.0179443359375,
-0.0104522705078125,
-0.0113067626953125,
-0.0183563232421875,
-0.044189453125,
-0.0139923095703125,
0.0236358642578125,
0.017608642578125,
-0.001617431640625,
-0.020263671875,
-0.0259857177734375,
0.00662994384765625,
-0.03173828125,
0.0023059844970703125,
0.0259552001953125,
0.00629425048828125,
0.0126190185546875,
-0.0240936279296875,
-0.013275146484375,
-0.010772705078125,
0.0180511474609375,
-0.006565093994140625,
-0.0018682479858398438,
-0.0191192626953125,
0.0202789306640625,
0.014617919921875,
-0.0164337158203125,
-0.003040313720703125,
0.02874755859375,
0.005435943603515625,
0.0017757415771484375,
0.0006299018859863281,
-0.0100860595703125,
-0.007843017578125,
-0.0190277099609375,
-0.0310821533203125,
0.004924774169921875,
0.031402587890625,
-0.0201873779296875,
-0.022369384765625,
0.021820068359375,
-0.00627899169921875,
0.01568603515625,
-0.0220489501953125,
-0.032196044921875,
0.0010213851928710938,
0.03887939453125,
0.005680084228515625,
-0.0053863525390625,
-0.038421630859375,
-0.0019683837890625,
0.00777435302734375,
-0.00891876220703125,
-0.00460052490234375,
-0.0088043212890625,
0.035552978515625,
-0.0306854248046875,
0.0169830322265625,
-0.01453399658203125,
-0.014434814453125,
0.006076812744140625,
-0.01290130615234375,
0.022796630859375,
-0.003299713134765625,
-0.012176513671875,
0.01090240478515625,
-0.0008630752563476562,
0.00617218017578125,
-0.04803466796875,
0.00878143310546875,
0.0244598388671875,
0.00818634033203125,
-0.01551055908203125,
-0.0305938720703125,
-0.0105438232421875,
-0.0162811279296875,
0.01035308837890625,
-0.0109710693359375,
0.0027408599853515625,
-0.005245208740234375,
0.0279541015625,
-0.0087432861328125,
-0.0208892822265625,
0.00151824951171875,
-0.007434844970703125,
-0.006519317626953125,
-0.00138092041015625,
-0.0012197494506835938,
-0.01322174072265625,
-0.0002624988555908203,
-0.007289886474609375,
0.0296783447265625,
-0.0211181640625,
0.01409912109375,
-0.01861572265625,
-0.0203857421875,
-0.00690460205078125,
0.0306549072265625,
0.010162353515625,
-0.01493072509765625,
-0.0419921875,
0.01384735107421875,
-0.05657958984375,
-0.009429931640625,
0.0027294158935546875,
-0.0128326416015625,
0.01016998291015625,
0.057464599609375,
-0.0038299560546875,
0.01024627685546875,
-0.01155853271484375,
0.00836181640625,
-0.00327301025390625,
-0.0170745849609375,
-0.03875732421875,
0.01171875,
-0.031005859375,
0.0280303955078125,
-0.04278564453125,
-0.02056884765625,
-0.010162353515625,
0.0215911865234375,
-0.01020050048828125,
0.017578125,
0.0228271484375,
0.00421142578125,
0.0174407958984375,
-0.01120758056640625,
-0.0281829833984375,
-0.0025005340576171875,
0.003993988037109375,
0.0117645263671875,
0.0013885498046875,
0.021087646484375,
-0.01432037353515625,
0.010711669921875,
-0.00675201416015625,
0.0045166015625,
-0.02410888671875,
-0.01540374755859375,
0.00592041015625,
0.03741455078125,
-0.032135009765625,
0.0084686279296875,
0.009002685546875,
0.013427734375,
-0.00182342529296875,
-0.027252197265625,
-0.0131072998046875,
0.002391815185546875,
-0.0191192626953125,
0.01202392578125,
-0.0015163421630859375,
0.021942138671875,
-0.06915283203125,
0.01477813720703125,
-0.0250244140625,
-0.0285797119140625,
-0.0014753341674804688,
-0.0029811859130859375,
-0.004947662353515625,
-0.002506256103515625,
0.00957489013671875,
-0.006412506103515625,
-0.0248870849609375,
-0.0012369155883789062,
-0.021087646484375,
0.03472900390625,
0.0220794677734375,
-0.0262451171875,
0.0008869171142578125,
-0.0201873779296875,
-0.0203857421875,
0.0149688720703125,
-0.0038280487060546875,
0.02294921875,
0.006969451904296875,
-0.002857208251953125,
-0.00791168212890625,
0.0095977783203125,
0.01812744140625,
0.036407470703125,
-0.005100250244140625,
-0.0182037353515625,
0.004039764404296875,
-0.0114898681640625,
-0.033172607421875,
0.0197906494140625,
0.00014710426330566406,
-0.00007033348083496094,
-0.01239776611328125,
0.005657196044921875,
0.0021572113037109375,
0.0244903564453125,
0.008087158203125,
-0.01361846923828125,
-0.00878143310546875,
-0.021331787109375,
-0.0018434524536132812,
-0.00007414817810058594,
0.0257568359375,
-0.001514434814453125,
0.0191802978515625,
0.0096435546875,
-0.02587890625,
-0.015594482421875,
0.00331878662109375,
0.01540374755859375,
0.00939178466796875,
0.01294708251953125,
-0.01959228515625,
-0.0309600830078125,
-0.0028095245361328125,
0.010772705078125,
0.010528564453125,
0.01535797119140625,
-0.01537322998046875,
-0.01079559326171875,
0.004772186279296875,
0.02197265625,
-0.0374755859375,
-0.0278167724609375,
0.00738525390625,
0.0235137939453125,
-0.007396697998046875,
0.0267791748046875,
-0.0261383056640625,
0.0244598388671875,
0.01166534423828125,
-0.00771331787109375,
0.0157928466796875,
-0.0112762451171875,
-0.03863525390625,
-0.0019779205322265625,
0.00373077392578125,
-0.0210418701171875,
0.009735107421875,
0.00628662109375,
-0.00795745849609375,
-0.004726409912109375,
-0.01251983642578125,
-0.01161956787109375,
0.016815185546875,
0.01025390625,
0.006572723388671875,
0.0284423828125,
-0.04547119140625,
0.006908416748046875,
-0.007305145263671875,
-0.004730224609375,
-0.0163421630859375,
-0.013702392578125,
-0.0124969482421875,
0.02178955078125,
-0.01396942138671875,
0.030914306640625,
0.002590179443359375,
0.0086212158203125,
0.0013074874877929688,
0.039306640625,
0.020233154296875,
-0.01214599609375,
-0.016571044921875,
0.007083892822265625,
0.02362060546875,
-0.010162353515625,
-0.0301971435546875,
0.00641632080078125,
0.0289154052734375,
-0.0180206298828125,
-0.0255584716796875,
-0.006595611572265625,
-0.02239990234375,
0.0144195556640625,
-0.0017910003662109375,
0.0228271484375,
0.027069091796875,
-0.0274505615234375,
-0.00437164306640625,
0.0084228515625,
0.005245208740234375,
-0.008331298828125,
-0.0002295970916748047,
0.047027587890625,
-0.0005130767822265625,
-0.00995635986328125,
0.005329132080078125,
-0.04278564453125,
0.0227508544921875,
0.004802703857421875,
-0.0237884521484375,
-0.00958251953125,
0.050872802734375,
-0.01264190673828125,
-0.006786346435546875,
-0.03314208984375,
0.020111083984375,
0.013214111328125,
0.0196533203125,
0.0160369873046875,
0.01055908203125,
-0.0257415771484375,
-0.0131378173828125,
-0.0010242462158203125,
-0.012664794921875,
-0.0235595703125,
-0.006855010986328125,
0.007465362548828125,
-0.01117706298828125,
0.046478271484375,
0.01280975341796875,
0.036865234375,
0.000012040138244628906,
-0.0020294189453125,
-0.032928466796875,
-0.0207672119140625,
0.01160430908203125,
-0.0025043487548828125,
0.00026607513427734375,
0.009765625,
0.011444091796875,
0.03521728515625,
-0.0188751220703125,
0.03265380859375,
0.0205230712890625,
-0.0247344970703125,
-0.02532958984375,
0.0226898193359375,
-0.0034637451171875,
-0.0009641647338867188,
0.00464630126953125,
0.041290283203125,
-0.042755126953125,
0.01059722900390625,
0.0188751220703125,
-0.0280609130859375,
-0.01312255859375,
0.013336181640625,
0.0283660888671875,
0.023529052734375,
0.017181396484375,
-0.0081024169921875,
0.00861358642578125,
-0.001750946044921875,
0.01471710205078125,
-0.01342010498046875,
0.0240478515625,
-0.0294647216796875,
-0.0113372802734375,
-0.014892578125,
0.004390716552734375,
0.021148681640625,
0.0051116943359375,
-0.0064544677734375,
-0.006824493408203125,
-0.0023746490478515625,
0.0205078125,
-0.010223388671875,
-0.025115966796875,
0.00910186767578125,
-0.0035247802734375,
-0.006145477294921875,
-0.005340576171875,
-0.0256195068359375,
-0.0299835205078125,
0.0247039794921875,
0.004444122314453125,
-0.02166748046875,
-0.0021953582763671875,
-0.027252197265625,
0.0143890380859375,
0.03216552734375,
0.0021839141845703125,
0.035186767578125,
0.00803375244140625,
-0.004657745361328125,
0.0217132568359375,
-0.0004296302795410156,
0.005107879638671875,
-0.024139404296875,
-0.0014944076538085938,
0.01473236083984375,
0.03448486328125,
-0.00653839111328125,
-0.01328277587890625,
0.02032470703125,
0.027587890625,
-0.0189056396484375,
-0.006595611572265625,
0.00933074951171875,
0.0172119140625,
-0.041717529296875,
0.0015001296997070312,
-0.0029468536376953125,
0.032440185546875,
0.0138092041015625,
-0.0289459228515625,
0.00843048095703125,
-0.0048980712890625,
-0.009735107421875,
0.01418304443359375,
-0.01442718505859375,
-0.0030765533447265625,
-0.039825439453125,
-0.01433563232421875,
0.00787353515625,
0.02276611328125,
-0.031036376953125,
-0.027313232421875,
-0.007358551025390625,
0.020294189453125,
-0.00197601318359375,
0.022735595703125,
-0.004314422607421875,
-0.0083160400390625,
0.0017709732055664062,
-0.022735595703125,
-0.002559661865234375,
-0.0156097412109375,
0.0019378662109375,
0.04541015625,
-0.0243072509765625,
0.03350830078125,
-0.0174407958984375,
0.0078277587890625,
0.00885009765625,
-0.0291748046875,
-0.0034809112548828125,
0.00266265869140625,
0.0007472038269042969,
-0.036590576171875,
-0.0015001296997070312,
0.014923095703125,
0.01174163818359375,
-0.0124664306640625,
-0.0015392303466796875,
-0.0113372802734375,
-0.0013980865478515625,
0.00823211669921875,
0.0176544189453125,
0.021331787109375,
-0.004467010498046875,
-0.0264129638671875,
-0.0038814544677734375,
-0.0020542144775390625,
-0.01245880126953125,
-0.039093017578125,
-0.013427734375,
-0.000576019287109375,
0.006259918212890625,
0.01763916015625,
-0.018341064453125,
-0.055328369140625,
0.014190673828125,
-0.00783538818359375,
-0.0026988983154296875,
-0.01238250732421875,
-0.01422882080078125,
-0.002307891845703125,
-0.0252838134765625,
0.0031585693359375,
-0.0225067138671875,
0.01183319091796875,
0.01482391357421875,
0.040618896484375,
-0.05548095703125,
-0.0008611679077148438,
0.0033111572265625,
0.0236663818359375,
0.0007386207580566406,
-0.00563812255859375,
-0.00574493408203125,
0.042633056640625,
-0.01360321044921875,
-0.01369476318359375,
-0.0206146240234375,
-0.0038433074951171875,
0.00968170166015625,
0.0106658935546875,
-0.0007848739624023438,
0.00751495361328125,
-0.01403045654296875,
-0.0243682861328125,
0.0125885009765625,
-0.01068878173828125,
0.00559234619140625,
0.0150604248046875,
0.02447509765625,
0.002803802490234375,
-0.0189208984375,
0.006649017333984375,
-0.00925445556640625,
-0.005725860595703125,
0.00351715087890625,
0.0167388916015625,
-0.010009765625,
0.01166534423828125,
-0.039398193359375,
-0.00897979736328125,
0.03472900390625,
-0.054168701171875,
0.00531005859375,
-0.023834228515625,
-0.004749298095703125,
-0.0027446746826171875,
-0.015472412109375,
0.0165863037109375,
0.0362548828125,
-0.0060272216796875,
-0.00934600830078125,
0.0181121826171875,
-0.01035308837890625,
-0.0041656494140625,
0.00826263427734375,
-0.0030975341796875,
-0.01311492919921875,
0.024627685546875,
-0.005756378173828125,
-0.01496124267578125,
-0.0028285980224609375,
0.00072479248046875,
-0.008880615234375,
0.030548095703125,
0.0004525184631347656,
-0.00485992431640625,
0.0128936767578125,
0.01898193359375,
0.005535125732421875,
-0.0095672607421875,
0.0113983154296875,
-0.006137847900390625,
-0.005588531494140625,
-0.0169677734375,
0.00921630859375,
0.01016998291015625,
-0.005641937255859375,
0.0240020751953125,
0.00885009765625,
0.0141448974609375,
0.004608154296875,
-0.0291900634765625,
0.00827789306640625,
-0.01345062255859375,
0.018829345703125,
0.00222015380859375,
-0.050537109375,
0.0008597373962402344,
0.021636962890625,
-0.007221221923828125,
0.006954193115234375,
-0.0198974609375,
0.0016088485717773438,
0.0205841064453125,
-0.00527191162109375,
0.001323699951171875,
-0.0137939453125,
0.01222991943359375,
-0.002223968505859375,
-0.00518798828125,
0.05072021484375,
0.034271240234375,
-0.0016374588012695312,
0.0322265625,
-0.0306854248046875,
-0.0025348663330078125,
0.01415252685546875,
0.003009796142578125,
-0.01934814453125,
-0.0247039794921875,
0.01140594482421875,
0.00004172325134277344,
0.010894775390625,
-0.028778076171875,
0.044281005859375,
-0.049468994140625,
-0.0179290771484375,
0.0265045166015625,
-0.0163726806640625,
-0.0075531005859375,
0.007781982421875,
-0.023040771484375,
0.003063201904296875,
0.054534912109375,
0.00783538818359375,
0.010955810546875,
0.00975799560546875,
-0.00748443603515625,
-0.0007739067077636719,
-0.0148162841796875,
0.0183258056640625,
-0.019683837890625,
0.00766754150390625,
0.0102996826171875,
0.007080078125,
0.0183868408203125,
0.01059722900390625,
0.032501220703125,
0.0101470947265625,
-0.0042266845703125,
-0.021575927734375,
-0.0012578964233398438,
-0.0049591064453125,
0.008819580078125,
0.01788330078125,
0.005123138427734375,
0.030242919921875,
0.01203155517578125,
-0.0091705322265625,
0.01038360595703125,
-0.0199737548828125,
0.039215087890625,
0.01186370849609375,
-0.0178985595703125,
-0.0066375732421875,
-0.04034423828125,
-0.044464111328125,
0.0307769775390625,
-0.00899505615234375,
-0.01331329345703125,
0.015899658203125,
-0.007266998291015625,
-0.0245513916015625,
-0.0014657974243164062,
0.0160675048828125,
-0.01348114013671875,
0.01158905029296875,
-0.007732391357421875,
-0.0221405029296875,
0.0173797607421875,
-0.045257568359375,
-0.0292816162109375,
0.024871826171875,
0.033843994140625,
0.006534576416015625,
-0.019805908203125,
0.0017385482788085938,
0.0005373954772949219,
0.010589599609375,
0.02325439453125,
-0.01910400390625,
0.0250396728515625,
-0.01552581787109375,
-0.0001590251922607422,
-0.0026454925537109375,
-0.025360107421875,
0.0275421142578125,
0.0211944580078125,
-0.01611328125,
0.006702423095703125,
-0.00594329833984375,
-0.00103759765625,
-0.0095367431640625,
-0.0030384063720703125,
0.016387939453125,
-0.041107177734375,
0.0160064697265625,
-0.0258331298828125,
-0.020233154296875,
-0.007518768310546875,
0.02593994140625,
-0.0015344619750976562,
0.0192718505859375,
-0.0022602081298828125,
0.019317626953125,
-0.017242431640625,
0.006664276123046875,
-0.0257568359375,
-0.02001953125,
-0.0232391357421875,
0.0018815994262695312,
-0.01800537109375,
-0.0005407333374023438,
0.017791748046875,
-0.007537841796875,
0.015838623046875,
0.0118560791015625,
0.04754638671875,
0.00003045797348022461,
-0.01447296142578125,
0.01149749755859375,
0.04534912109375,
-0.0023193359375,
0.03863525390625,
0.0016155242919921875,
0.01471710205078125,
0.0014543533325195312,
0.001007080078125,
0.02203369140625,
0.005222320556640625,
-0.01433563232421875,
0.00937652587890625,
0.007293701171875,
-0.018463134765625,
0.0260467529296875,
-0.01503753662109375,
0.01392364501953125,
0.01143646240234375,
-0.0316162109375,
-0.013641357421875,
-0.0107879638671875,
-0.01036834716796875,
-0.0173797607421875,
0.0254058837890625,
-0.0015745162963867188,
0.0108795166015625,
-0.028564453125,
0.0206756591796875,
-0.01555633544921875,
0.01404571533203125,
0.0005307197570800781,
0.0157318115234375,
0.01001739501953125,
0.0114288330078125,
0.0234832763671875,
-0.01268768310546875,
-0.0267791748046875,
-0.01361083984375,
-0.0101470947265625,
0.0182952880859375,
0.01175689697265625,
0.019256591796875,
-0.0157623291015625,
0.01219940185546875,
-0.0221405029296875,
-0.005035400390625,
-0.00699615478515625,
0.0158538818359375,
0.0253753662109375,
-0.00641632080078125,
-0.006866455078125,
0.02850341796875,
0.01062774658203125,
-0.0008306503295898438,
0.018798828125,
0.03216552734375,
-0.00800323486328125,
-0.005199432373046875,
-0.03656005859375,
-0.004913330078125,
-0.00732421875,
-0.0159149169921875,
0.0080108642578125,
-0.0183563232421875,
-0.0036067962646484375,
-0.0025005340576171875,
0.0158843994140625,
-0.0153961181640625,
-0.01580810546875,
0.036865234375,
-0.0191650390625,
-0.01332855224609375,
-0.004180908203125,
0.01947021484375,
-0.0270538330078125,
-0.0251312255859375,
-0.004978179931640625,
0.00786590576171875,
-0.0103759765625,
0.0200347900390625,
-0.0182952880859375,
0.002834320068359375,
-0.003353118896484375,
0.0285797119140625,
0.01018524169921875,
-0.0102386474609375,
-0.0079193115234375,
-0.00647735595703125,
-0.0165557861328125,
0.05364990234375,
0.0029811859130859375,
0.0350341796875,
0.0214691162109375,
0.0245361328125,
-0.004436492919921875,
-0.0068817138671875,
-0.0165863037109375,
-0.0008397102355957031,
-0.005786895751953125,
0.0080413818359375,
-0.012939453125,
0.012237548828125,
-0.0054168701171875,
0.0117340087890625,
-0.0010709762573242188,
0.02294921875,
0.017425537109375,
0.008056640625,
0.0171966552734375,
0.01458740234375,
-0.0219879150390625,
0.02398681640625,
-0.01213836669921875,
-0.0160675048828125,
0.01141357421875,
0.025238037109375,
0.00800323486328125,
-0.025634765625,
-0.00815582275390625,
0.0228729248046875,
0.006221771240234375,
-0.005458831787109375,
-0.0125274658203125,
0.0270538330078125,
0.0345458984375,
0.00696563720703125,
0.006526947021484375,
0.00864410400390625,
0.01201629638671875,
-0.01214599609375,
0.006046295166015625,
0.0110626220703125,
0.0000756978988647461,
-0.005359649658203125,
0.024566650390625,
0.01146697998046875,
0.0599365234375,
-0.01280975341796875,
0.052734375,
-0.0179901123046875,
-0.0180206298828125,
0.001605987548828125,
0.01195526123046875,
-0.0215301513671875,
-0.006439208984375,
-0.017486572265625,
0.00539398193359375,
-0.0007123947143554688,
-0.00612640380859375,
0.008880615234375,
-0.0252838134765625,
0.019927978515625,
-0.04681396484375,
0.01143646240234375,
0.0138397216796875,
-0.0024089813232421875,
-0.01019287109375,
0.044189453125,
0.004566192626953125,
0.00518035888671875,
0.024139404296875,
-0.00933074951171875,
0.0007448196411132812,
-0.0054168701171875,
0.01340484619140625,
-0.0014667510986328125,
0.0020427703857421875,
0.009918212890625,
-0.040679931640625,
-0.01198577880859375,
0.00655364990234375,
-0.005092620849609375,
0.0012769699096679688,
0.026641845703125,
0.0268402099609375,
0.003177642822265625,
0.01190185546875,
0.02252197265625,
0.0297393798828125,
-0.0030193328857421875,
0.0021648406982421875,
-0.0008893013000488281,
0.01416015625,
-0.006900787353515625,
0.0135650634765625,
-0.031494140625,
-0.01605224609375,
0.00682830810546875,
0.003570556640625,
0.0008478164672851562,
-0.00787353515625,
0.0233917236328125,
0.0293731689453125,
0.011505126953125,
0.0302581787109375,
0.0012445449829101562,
-0.002452850341796875,
0.0120391845703125,
-0.01416015625,
0.01259613037109375,
-0.00455474853515625,
0.004238128662109375,
0.0258331298828125,
0.00815582275390625,
0.013214111328125,
0.0014820098876953125,
0.0274658203125,
0.004741668701171875,
0.02398681640625,
-0.01338958740234375,
-0.0184326171875,
-0.032196044921875,
0.010894775390625,
-0.036163330078125,
-0.00830078125,
0.00891876220703125,
-0.007595062255859375,
-0.002399444580078125,
-0.01363372802734375,
-0.054840087890625,
-0.00720977783203125,
-0.0120697021484375,
0.0208587646484375,
-0.0189971923828125,
0.003082275390625,
-0.02978515625,
0.0081329345703125,
-0.01776123046875,
-0.0187225341796875,
0.055023193359375,
-0.0078887939453125,
-0.038970947265625,
-0.0125885009765625,
-0.01136016845703125,
0.0173797607421875,
0.0012969970703125,
-0.0006923675537109375,
0.005504608154296875,
0.0059051513671875,
0.0072174072265625,
-0.0238494873046875,
-0.0109100341796875,
0.0159454345703125,
-0.0199737548828125,
0.034149169921875,
0.0172119140625,
-0.0018396377563476562,
-0.01451873779296875,
-0.0175933837890625,
0.018341064453125,
-0.01190948486328125,
0.0004467964172363281,
-0.004306793212890625,
0.01216888427734375,
-0.005619049072265625,
0.02935791015625,
-0.0186004638671875,
-0.0154876708984375,
-0.017364501953125,
-0.03424072265625,
-0.0209197998046875,
-0.01187896728515625,
0.036163330078125,
0.0374755859375,
0.0210723876953125,
0.006084442138671875,
0.028839111328125,
-0.0168609619140625,
-0.031494140625,
-0.0023860931396484375,
-0.0229644775390625,
-0.0047760009765625,
0.00434112548828125,
0.04132080078125,
-0.0017747879028320312,
-0.0247802734375,
-0.00226593017578125,
-0.0170135498046875,
-0.019744873046875,
-0.00030303001403808594,
0.045318603515625,
0.033416748046875,
-0.01190948486328125,
0.004978179931640625,
0.023956298828125,
0.0249176025390625,
-0.0196990966796875,
-0.04168701171875,
-0.047149658203125,
-0.006496429443359375,
0.013275146484375,
0.0128631591796875,
-0.0008525848388671875,
0.022369384765625,
0.003387451171875,
0.017822265625,
0.0386962890625,
-0.0203857421875,
-0.036041259765625,
0.00009816884994506836,
-0.0094451904296875,
-0.0054473876953125,
0.01299285888671875,
0.0292205810546875,
-0.004741668701171875,
-0.019775390625,
0.01056671142578125,
0.0304412841796875,
-0.00936126708984375,
0.02471923828125,
-0.024658203125,
0.01328277587890625,
0.042510986328125,
0.0219573974609375,
0.0177154541015625,
0.01110076904296875,
0.0016145706176757812,
-0.007099151611328125,
-0.025543212890625,
-0.023590087890625,
-0.00728607177734375,
-0.0217132568359375,
0.0276641845703125,
-0.0022945404052734375,
0.01197052001953125,
0.00865936279296875,
0.004596710205078125,
-0.00606536865234375,
-0.0088653564453125,
0.007671356201171875,
-0.0010709762573242188,
0.0052642822265625,
0.0170440673828125,
0.0167236328125,
0.0021266937255859375,
-0.0364990234375,
-0.0011529922485351562,
-0.0023193359375,
-0.040679931640625,
0.0220794677734375,
0.0262603759765625,
-0.0132293701171875,
0.0180206298828125,
-0.01080322265625,
0.0026493072509765625,
-0.0133209228515625,
-0.01479339599609375,
0.00637054443359375,
0.006275177001953125,
-0.0261077880859375,
0.01134490966796875,
0.0059661865234375,
-0.022552490234375,
0.029388427734375,
-0.0102691650390625,
-0.00914764404296875,
0.029022216796875,
0.01153564453125,
0.03948974609375,
-0.004650115966796875,
-0.01044464111328125,
0.0139923095703125,
0.0255584716796875,
0.035369873046875,
0.0018205642700195312,
0.009979248046875,
0.036346435546875,
-0.00843048095703125,
0.03485107421875,
0.00296783447265625,
-0.004993438720703125,
0.01155853271484375,
0.033599853515625,
-0.05267333984375,
-0.005077362060546875,
-0.047637939453125,
0.0051116943359375,
-0.0079193115234375,
-0.004573822021484375,
0.0003955364227294922,
-0.01947021484375,
0.0263519287109375,
0.003314971923828125,
0.003948211669921875,
0.0271148681640625,
0.01326751708984375,
0.0005145072937011719,
-0.034423828125,
0.060028076171875,
0.006427764892578125,
0.035614013671875,
-0.004856109619140625,
0.00014507770538330078,
-0.034454345703125,
-0.002986907958984375,
0.00390625,
-0.01387786865234375,
-0.026153564453125,
-0.01776123046875,
-0.005619049072265625,
-0.0032863616943359375,
0.0012035369873046875,
-0.0257568359375,
0.0086669921875,
0.0007381439208984375,
0.033966064453125,
-0.021453857421875,
-0.03240966796875,
0.021453857421875,
0.0020542144775390625,
-0.0125732421875,
0.0146026611328125,
0.01122283935546875,
0.0152587890625,
-0.048828125,
-0.0262298583984375,
-0.029449462890625,
0.00385284423828125,
-0.01983642578125,
0.01029205322265625,
-0.0179290771484375,
0.0308380126953125,
0.01015472412109375,
0.022979736328125,
0.001068115234375,
0.01611328125,
-0.00412750244140625,
0.005218505859375,
0.017822265625,
-0.0164337158203125,
0.0164794921875,
-0.033905029296875,
-0.026458740234375,
0.0016050338745117188,
0.005817413330078125,
0.00759124755859375,
0.0151214599609375,
-0.03369140625,
-0.005489349365234375,
-0.005855560302734375,
-0.0225372314453125,
0.00428009033203125,
0.00264739990234375,
0.020416259765625,
-0.040740966796875,
-0.0093536376953125,
-0.0211181640625,
-0.0033779144287109375,
0.0307769775390625,
-0.018096923828125,
0.0131683349609375,
0.010284423828125,
-0.0180816650390625,
0.00001627206802368164,
0.011505126953125,
0.011016845703125,
0.0104827880859375,
0.01131439208984375,
0.007564544677734375,
-0.00473785400390625,
0.01493072509765625,
0.025665283203125,
-0.00287628173828125,
-0.01073455810546875,
0.02374267578125,
0.00753021240234375,
0.005718231201171875,
0.006855010986328125,
-0.015655517578125,
-0.04534912109375,
-0.01153564453125,
0.01322174072265625,
-0.01213836669921875,
-0.036956787109375,
0.00047779083251953125,
-0.032989501953125,
0.0096588134765625,
-0.027984619140625,
0.0023746490478515625,
0.0017566680908203125,
0.01407623291015625,
-0.002780914306640625,
-0.01146697998046875,
-0.0158538818359375,
0.0147247314453125,
0.00521087646484375,
0.009368896484375,
-0.0153045654296875,
-0.0086517333984375,
-0.0322265625,
-0.023651123046875,
0.03411865234375,
0.023193359375,
0.00970458984375,
0.0268707275390625,
-0.001232147216796875,
-0.00789642333984375,
-0.00429534912109375,
-0.017486572265625,
0.0279388427734375,
0.020751953125,
-0.018585205078125,
-0.00844573974609375,
0.005863189697265625,
-0.0008459091186523438,
-0.028350830078125,
-0.042572021484375,
0.043731689453125,
-0.0015697479248046875,
-0.017822265625,
-0.0018949508666992188,
0.0091094970703125,
-0.01551055908203125,
0.004070281982421875,
0.0042877197265625,
0.02313232421875,
-0.004741668701171875,
-0.0079803466796875,
0.027862548828125,
-0.033050537109375,
-0.00693511962890625,
0.0130157470703125,
-0.0091552734375,
0.021270751953125,
0.0175628662109375,
0.00775146484375,
-0.001399993896484375,
-0.0094451904296875,
-0.004581451416015625,
-0.0038013458251953125,
0.0102081298828125,
0.003002166748046875,
0.015960693359375,
-0.0020656585693359375,
0.0140533447265625,
-0.0113067626953125,
-0.004673004150390625,
-0.00476837158203125,
-0.0055389404296875,
0.01953125,
0.007724761962890625,
0.03668212890625,
-0.0234832763671875,
-0.02093505859375,
0.0242156982421875,
-0.007770538330078125,
-0.01160430908203125,
-0.03863525390625,
0.0194854736328125,
0.0030002593994140625,
-0.0201416015625,
0.004802703857421875,
-0.048980712890625,
0.0087890625,
0.00713348388671875,
0.043182373046875,
0.03228759765625,
-0.0136566162109375,
-0.009429931640625,
-0.021331787109375,
0.0146942138671875,
0.01349639892578125,
-0.0408935546875,
0.0299530029296875,
0.0167083740234375,
-0.005313873291015625,
-0.0158843994140625,
0.0118560791015625,
0.0232086181640625,
-0.01229095458984375,
0.0003819465637207031,
-0.0071258544921875,
-0.01250457763671875,
-0.0147247314453125,
-0.009124755859375,
0.025634765625,
0.006072998046875,
-0.0250396728515625,
-0.0145721435546875,
0.0235137939453125,
-0.0013980865478515625,
0.0148468017578125,
-0.0099334716796875,
0.011993408203125,
0.028472900390625,
-0.0278167724609375,
0.0207977294921875,
0.032257080078125,
-0.01458740234375,
-0.01410675048828125,
-0.01450347900390625,
0.01161956787109375,
0.008026123046875,
0.005481719970703125,
-0.0144500732421875,
0.0253753662109375,
0.02337646484375,
-0.0188751220703125,
-0.017486572265625,
0.008026123046875,
0.036529541015625,
-0.007045745849609375,
0.0123443603515625,
0.0258941650390625,
-0.01021575927734375,
0.00508880615234375,
0.0246429443359375,
0.0265350341796875,
0.0013818740844726562,
0.03704833984375,
-0.01224517822265625,
0.0079193115234375,
-0.022674560546875,
-0.039398193359375,
-0.0162506103515625,
0.004734039306640625,
0.0281219482421875,
0.01151275634765625,
-0.03076171875,
0.0016880035400390625,
0.0068511962890625,
0.01073455810546875,
-0.037017822265625,
0.0091552734375,
0.0130615234375,
0.01275634765625,
-0.0121612548828125,
-0.0145721435546875,
-0.007228851318359375,
-0.0004334449768066406,
0.03900146484375,
0.00983428955078125,
0.0170135498046875,
-0.020477294921875,
-0.0235137939453125,
0.0272369384765625,
-0.001483917236328125,
0.0134124755859375,
-0.018096923828125,
-0.00888824462890625,
0.03192138671875,
-0.012237548828125,
-0.0106201171875,
0.011260986328125,
0.004634857177734375,
-0.00936126708984375,
0.032867431640625,
-0.042236328125,
-0.006786346435546875,
0.00742340087890625,
-0.0232086181640625,
-0.00661468505859375,
0.0307464599609375,
-0.0231170654296875,
-0.01372528076171875,
-0.01056671142578125,
-0.00035309791564941406,
-0.017181396484375,
-0.01284027099609375,
-0.002994537353515625,
-0.01064300537109375,
-0.0247344970703125,
0.019256591796875,
-0.011016845703125,
-0.00676727294921875,
-0.0025997161865234375,
-0.0157318115234375,
-0.01094818115234375,
0.0232696533203125,
0.0134124755859375,
-0.0355224609375,
-0.06561279296875,
0.004520416259765625,
-0.0147705078125,
-0.004199981689453125,
0.036651611328125,
0.005702972412109375,
0.0211029052734375,
0.00955963134765625,
-0.01288604736328125,
-0.0266876220703125,
-0.0013275146484375,
0.01169586181640625,
0.0290985107421875,
-0.027587890625,
0.0299530029296875,
0.005313873291015625,
0.05926513671875,
0.0267791748046875,
-0.025146484375,
0.0137786865234375,
-0.00704193115234375,
0.020233154296875,
-0.0077667236328125,
-0.0029201507568359375,
0.0021686553955078125,
0.01995849609375,
0.0235748291015625,
0.0188140869140625,
-0.0203857421875,
-0.01438140869140625,
0.032928466796875,
0.0179443359375,
-0.02215576171875,
0.0255584716796875,
-0.033721923828125,
-0.0005688667297363281,
0.057220458984375,
-0.0178680419921875,
0.02520751953125,
-0.029205322265625,
-0.0183868408203125,
-0.0224609375,
0.041900634765625,
0.01343536376953125,
0.0136566162109375,
-0.015411376953125,
-0.0205078125,
0.041748046875,
-0.0288238525390625,
-0.001789093017578125,
-0.0174102783203125,
-0.0134124755859375,
-0.04327392578125,
0.01342010498046875,
-0.0067596435546875,
0.005840301513671875,
0.026397705078125,
-0.0201416015625,
0.02935791015625,
0.037322998046875,
-0.016937255859375,
-0.0066680908203125,
0.025115966796875,
0.032440185546875,
0.004268646240234375,
-0.0242767333984375,
0.0259246826171875,
-0.0007634162902832031,
0.01399993896484375,
0.006740570068359375,
0.0081024169921875,
-0.0267333984375,
0.01293182373046875,
-0.0222930908203125,
0.0180816650390625,
0.0239715576171875,
-0.0234375,
-0.01004791259765625,
0.0235137939453125,
0.00189971923828125,
0.003376007080078125,
-0.0018329620361328125,
0.0018415451049804688,
-0.01312255859375,
0.0181427001953125,
0.03759765625,
0.017730712890625,
0.0019245147705078125,
-0.034393310546875,
0.0271453857421875,
0.022216796875,
-0.058013916015625,
-0.032867431640625,
0.026123046875,
-0.0098724365234375,
0.01544952392578125,
-0.01204681396484375,
0.0016584396362304688,
0.038543701171875,
-0.0325927734375,
-0.025390625,
-0.0143280029296875,
-0.022674560546875,
0.02447509765625,
-0.051727294921875,
-0.01337432861328125,
0.01959228515625,
0.005207061767578125,
-0.0267181396484375,
-0.0167999267578125,
-0.0538330078125,
0.008819580078125,
0.026519775390625,
0.021575927734375,
-0.002025604248046875,
-0.017333984375,
0.01471710205078125,
0.016510009765625,
0.00841522216796875,
-0.0064849853515625,
-0.0020046234130859375,
-0.01470184326171875,
0.01373291015625,
0.01129913330078125,
0.0008225440979003906,
-0.0237884521484375,
-0.0010967254638671875,
-0.0293426513671875,
-0.000629425048828125,
0.005573272705078125,
-0.005401611328125,
-0.0199737548828125,
-0.039947509765625,
-0.0246124267578125,
-0.0099945068359375,
-0.005828857421875,
0.0052032470703125,
-0.018524169921875,
-0.003505706787109375,
0.0263214111328125,
0.00720977783203125,
-0.0271148681640625,
-0.0087127685546875,
-0.0168914794921875,
-0.02508544921875,
0.00787353515625,
-0.00910186767578125,
-0.0124053955078125,
-0.01140594482421875,
-0.025604248046875,
-0.01541900634765625,
-0.00386810302734375,
0.0155487060546875,
0.005748748779296875,
-0.0076446533203125,
0.0256805419921875,
-0.01519012451171875,
0.019927978515625,
-0.003871917724609375,
-0.00888824462890625,
0.03717041015625,
-0.0004425048828125,
0.003078460693359375,
-0.0005278587341308594,
0.00640106201171875,
0.002437591552734375,
0.0357666015625,
0.01279449462890625,
-0.01204681396484375,
-0.00922393798828125,
-0.0177001953125,
0.0150299072265625,
0.01372528076171875,
-0.01195526123046875,
-0.0023651123046875,
0.00783538818359375,
-0.00592803955078125,
0.04010009765625,
0.0250396728515625,
0.0178680419921875,
0.00853729248046875,
-0.0227813720703125,
-0.02471923828125,
0.003582000732421875,
0.00612640380859375,
-0.030059814453125,
-0.0019741058349609375,
-0.004932403564453125,
-0.012054443359375,
0.004428863525390625,
-0.0027637481689453125,
-0.01461029052734375,
-0.01308441162109375,
-0.035919189453125,
0.0061187744140625,
0.00495147705078125
] |
ours_524
|
The answer is \(1025\).
Notice that the parity of a point's coordinates does not change when it undergoes a jump. If we consider the unit 10-dimensional cube (where all coordinates are either 0 or 1), we have \(2^{10}\) points, and no two will ever coincide because that would imply their parities are the same. Thus, the answer is at least \(1025\).
To show that \(1025\) works, we use induction on the number of dimensions.
**Base Case:** Any 3 points in 1-dimensional space can be moved so that some two coincide. Proof: Jump an outer point over the middle point, and the maximum distance decreases.
**Inductive Step:** Consider any \(2^{n+1}+1\) points in \((n+1)\)-dimensional space. We will show that we can make some \(2^{n}+1\) of them lie in an \(n\)-dimensional "plane," so that we can apply the inductive step.
Project the points down onto 1-dimensional space by looking only at the first coordinate. Then any jump in \((n+1)\)-space corresponds directly to a jump of the projected points in 1-space.
Divide the points into two sets \(A\) and \(B\) based on the parity of the first coordinate. We can assume without loss of generality that both \(A\) and \(B\) are non-empty. By the pigeonhole principle, one of the sets has at least \(2^{n}+1\) elements; let that be \(A\). Choose any element \(P\) of \(B\). By manipulating the coordinates of any two elements \(a_1, a_2 \in A\) and \(P\), we can get the coordinates of \(a_1\) and \(a_2\) to coincide (by the base case and parity), and thus \(a_1\) and \(a_2\) lie in the same \(n\)-dimensional plane.
Repeat this process, treating \(a_1\) and \(a_2\) as a unit (so that they remain in the same plane whenever they jump over another point). By repeatedly manipulating the coordinates of \(P\) and two elements from \(A\), we can accumulate all the points in \(A\) into \(n\)-space, completing the proof.
Thus, the answer is \(\boxed{1025}\).
|
1025
|
{
"competition": "us_comps",
"dataset": "Ours",
"posts": null,
"source": "OMOSoln2-2.md"
}
|
Given a set of points in space, a jump consists of taking two points in the set, \(P\) and \(Q\), removing \(P\) from the set, and replacing it with the reflection of \(P\) over \(Q\). Find the smallest number \(n\) such that for any set of \(n\) lattice points in 10-dimensional space, it is possible to perform a finite number of jumps so that some two points coincide.
|
[
"/Mathematics/DiscreteMathematics/Combinatorics/GeneralCombinatorics",
"/Mathematics/DiscreteMathematics/PointLattices/CubicLattice",
"/Mathematics/DiscreteMathematics/PointLattices/IntegerLattice",
"/Mathematics/DiscreteMathematics/PointLattices/Lattice",
"/Mathematics/DiscreteMathematics/PointLattices/LatticePoint",
"/Mathematics/DiscreteMathematics/PointLattices/PointLattice",
"/Mathematics/Geometry/MultidimensionalGeometry/n-DimensionalGeometry/Hypercube",
"/Mathematics/Geometry/Points/LatticePoint"
] |
Observe that coordinate parity is preserved by jumps and apply the pigeonhole principle to force two points into the same parity class.
|
[
0.00009423494338989258,
-0.00682830810546875,
0.06500244140625,
-0.0243988037109375,
0.0006508827209472656,
-0.0140533447265625,
0.0231781005859375,
-0.04046630859375,
0.0152435302734375,
0.0189666748046875,
0.0008058547973632812,
-0.0284423828125,
-0.0023040771484375,
0.02423095703125,
-0.04937744140625,
-0.0236968994140625,
0.0135955810546875,
0.0297393798828125,
-0.012969970703125,
-0.002635955810546875,
-0.01346588134765625,
-0.0027370452880859375,
-0.044281005859375,
0.083984375,
-0.01457977294921875,
0.0006456375122070312,
-0.012664794921875,
-0.0184326171875,
0.01190948486328125,
0.029052734375,
-0.059051513671875,
-0.0205078125,
0.004940032958984375,
0.0049285888671875,
-0.0007433891296386719,
0.01806640625,
0.036529541015625,
-0.0008215904235839844,
-0.0751953125,
-0.0152740478515625,
-0.0219573974609375,
-0.0311737060546875,
-0.005283355712890625,
0.0034656524658203125,
-0.030181884765625,
0.00853729248046875,
-0.0022068023681640625,
0.005344390869140625,
0.00597381591796875,
-0.01207733154296875,
-0.0008363723754882812,
0.013458251953125,
0.0013647079467773438,
-0.01763916015625,
-0.031585693359375,
-0.0205230712890625,
-0.003078460693359375,
-0.0036907196044921875,
-0.007236480712890625,
-0.035980224609375,
-0.002056121826171875,
-0.00846099853515625,
0.01552581787109375,
0.0083160400390625,
-0.010406494140625,
-0.01389312744140625,
0.0245361328125,
-0.0131988525390625,
0.00745391845703125,
-0.001247406005859375,
-0.0198822021484375,
0.00262451171875,
0.005306243896484375,
0.022796630859375,
0.0095367431640625,
-0.00241851806640625,
-0.0177459716796875,
0.0109710693359375,
0.019989013671875,
0.01519775390625,
0.033416748046875,
0.007717132568359375,
0.006053924560546875,
-0.01213836669921875,
-0.00335693359375,
-0.01197052001953125,
-0.0004687309265136719,
-0.02154541015625,
0.04913330078125,
-0.00858306884765625,
0.0032405853271484375,
-0.0111083984375,
0.0058441162109375,
0.042327880859375,
-0.0024967193603515625,
0.0127410888671875,
0.00644683837890625,
-0.00872802734375,
-0.01849365234375,
-0.0048675537109375,
-0.006900787353515625,
-0.00598907470703125,
0.0517578125,
-0.006366729736328125,
-0.053985595703125,
-0.01453399658203125,
-0.01082611083984375,
-0.006717681884765625,
-0.01050567626953125,
-0.006072998046875,
0.012725830078125,
-0.0100555419921875,
-0.00669097900390625,
0.0215301513671875,
-0.00027441978454589844,
0.006610870361328125,
-0.02935791015625,
-0.0049285888671875,
-0.0024261474609375,
0.00653839111328125,
0.00027489662170410156,
0.0116424560546875,
-0.01050567626953125,
0.01403045654296875,
-0.003780364990234375,
-0.02252197265625,
-0.0091400146484375,
-0.010223388671875,
-0.0311737060546875,
0.01070404052734375,
-0.01209259033203125,
0.01068115234375,
-0.04718017578125,
-0.042633056640625,
-0.0142822265625,
0.00023305416107177734,
-0.00832366943359375,
-0.014404296875,
0.01200103759765625,
0.0012369155883789062,
0.01316070556640625,
-0.0134735107421875,
0.0038585662841796875,
-0.032073974609375,
-0.00023937225341796875,
-0.0093994140625,
-0.0045166015625,
-0.0197296142578125,
0.01605224609375,
0.001140594482421875,
-0.0142364501953125,
-0.00199127197265625,
0.0101470947265625,
0.0034503936767578125,
-0.01102447509765625,
0.0182342529296875,
0.001865386962890625,
-0.005031585693359375,
0.022186279296875,
0.0210723876953125,
-0.001277923583984375,
-0.0150146484375,
0.032073974609375,
0.059783935546875,
0.0007343292236328125,
0.01326751708984375,
0.00876617431640625,
-0.01052093505859375,
-0.008758544921875,
0.0239715576171875,
-0.006191253662109375,
-0.01056671142578125,
0.01209259033203125,
-0.00917816162109375,
-0.01678466796875,
0.0002703666687011719,
-0.005329132080078125,
0.0035610198974609375,
0.0005660057067871094,
0.0023517608642578125,
-0.009368896484375,
-0.04425048828125,
0.048675537109375,
0.01047515869140625,
-0.0020351409912109375,
0.00540924072265625,
-0.00469207763671875,
0.0174713134765625,
0.0029888153076171875,
0.0254058837890625,
-0.033172607421875,
-0.01129913330078125,
-0.0066680908203125,
0.003276824951171875,
-0.0106201171875,
-0.000797271728515625,
-0.01024627685546875,
-0.00121307373046875,
0.0297698974609375,
0.0249786376953125,
-0.01157379150390625,
0.001117706298828125,
-0.0018138885498046875,
0.0038013458251953125,
-0.0176849365234375,
-0.0100250244140625,
-0.00635528564453125,
-0.0196990966796875,
0.006778717041015625,
-0.00708770751953125,
0.007472991943359375,
-0.038604736328125,
-0.015411376953125,
-0.01422119140625,
0.00263214111328125,
0.00588226318359375,
-0.01171875,
-0.0012073516845703125,
0.01006317138671875,
-0.0445556640625,
0.006389617919921875,
-0.002231597900390625,
0.00035858154296875,
-0.00777435302734375,
-0.01293182373046875,
-0.01084136962890625,
-0.017059326171875,
-0.005985260009765625,
-0.005962371826171875,
-0.0134735107421875,
0.02203369140625,
0.0088348388671875,
-0.0134735107421875,
-0.00015795230865478516,
0.002899169921875,
-0.01560211181640625,
0.022369384765625,
-0.00882720947265625,
0.004283905029296875,
0.00687408447265625,
0.049896240234375,
-0.0017528533935546875,
-0.00405120849609375,
-0.01508331298828125,
-0.0067596435546875,
-0.00801849365234375,
-0.00763702392578125,
-0.01151275634765625,
-0.00024437904357910156,
-0.0250396728515625,
-0.012603759765625,
0.00879669189453125,
-0.0165863037109375,
-0.01255035400390625,
-0.0279998779296875,
0.00507354736328125,
-0.0237579345703125,
-0.01104736328125,
-0.0188751220703125,
-0.01605224609375,
-0.001041412353515625,
-0.0033054351806640625,
0.01477813720703125,
-0.004642486572265625,
-0.0000750422477722168,
-0.0075225830078125,
-0.0169677734375,
0.010772705078125,
0.002498626708984375,
0.0058135986328125,
0.0021381378173828125,
-0.0034503936767578125,
-0.01213836669921875,
0.00827789306640625,
0.0259552001953125,
-0.0129852294921875,
-0.0134429931640625,
0.0274810791015625,
0.0243988037109375,
0.00484466552734375,
0.0261077880859375,
0.002899169921875,
0.031036376953125,
0.0055694580078125,
0.006744384765625,
-0.01324462890625,
-0.020751953125,
-0.01904296875,
-0.0170135498046875,
0.009735107421875,
-0.0016622543334960938,
-0.0390625,
-0.01183319091796875,
-0.00603485107421875,
-0.01641845703125,
-0.040618896484375,
0.0145263671875,
0.01202392578125,
0.0149383544921875,
-0.0216217041015625,
0.0053863525390625,
-0.0163421630859375,
-0.009674072265625,
0.012664794921875,
-0.015625,
0.0225982666015625,
-0.00010848045349121094,
0.004848480224609375,
-0.0212554931640625,
0.01383209228515625,
-0.000629425048828125,
0.00457763671875,
-0.004467010498046875,
-0.0234527587890625,
-0.0191802978515625,
-0.03326416015625,
0.002834320068359375,
0.008209228515625,
-0.0023097991943359375,
-0.01131439208984375,
0.019683837890625,
-0.0281219482421875,
-0.00014412403106689453,
0.03253173828125,
0.0306243896484375,
-0.0007815361022949219,
0.01275634765625,
0.00901031494140625,
-0.0176239013671875,
0.005519866943359375,
-0.025909423828125,
0.0033092498779296875,
-0.016693115234375,
-0.00600433349609375,
-0.0223541259765625,
0.0189056396484375,
-0.0217437744140625,
0.0185089111328125,
0.0003819465637207031,
0.023406982421875,
-0.01751708984375,
-0.006435394287109375,
0.0150299072265625,
0.007244110107421875,
0.01142120361328125,
0.014495849609375,
0.01027679443359375,
-0.011932373046875,
0.0068511962890625,
0.00884246826171875,
0.0229339599609375,
0.01456451416015625,
-0.0126953125,
-0.0109100341796875,
-0.022430419921875,
0.005840301513671875,
0.0113067626953125,
-0.01363372802734375,
0.000583648681640625,
0.037841796875,
0.013824462890625,
-0.0278167724609375,
-0.0168914794921875,
-0.031005859375,
-0.007720947265625,
-0.00023293495178222656,
-0.0205078125,
0.0087738037109375,
-0.038421630859375,
-0.005290985107421875,
-0.00909423828125,
-0.006450653076171875,
-0.00162506103515625,
-0.00543212890625,
-0.02783203125,
0.0367431640625,
0.023651123046875,
-0.013702392578125,
-0.00860595703125,
-0.00616455078125,
0.0225677490234375,
0.0214080810546875,
0.0184173583984375,
0.0160064697265625,
0.0026988983154296875,
0.0146484375,
-0.0020580291748046875,
-0.034576416015625,
-0.005344390869140625,
0.0199127197265625,
-0.0260009765625,
-0.0198974609375,
-0.01983642578125,
-0.00995635986328125,
-0.0002522468566894531,
-0.0162200927734375,
-0.0024280548095703125,
0.021636962890625,
0.0245208740234375,
0.0008645057678222656,
0.044921875,
-0.0153656005859375,
0.00689697265625,
0.0243682861328125,
-0.0024929046630859375,
-0.038299560546875,
0.02655029296875,
0.018890380859375,
0.0037899017333984375,
-0.006061553955078125,
-0.01204681396484375,
0.0159759521484375,
0.005939483642578125,
-0.0141448974609375,
0.00067138671875,
0.01393890380859375,
0.0225067138671875,
0.01727294921875,
-0.05487060546875,
0.0063323974609375,
0.002532958984375,
-0.02484130859375,
-0.004467010498046875,
-0.0183563232421875,
0.038665771484375,
0.01531982421875,
-0.0390625,
0.034637451171875,
0.005649566650390625,
0.018035888671875,
-0.02642822265625,
-0.0008230209350585938,
0.0255279541015625,
0.0282135009765625,
0.00909423828125,
0.035797119140625,
0.035736083984375,
-0.0330810546875,
-0.03826904296875,
-0.0267486572265625,
0.0007925033569335938,
-0.0010156631469726562,
0.020263671875,
-0.0010433197021484375,
0.0303955078125,
0.0116119384765625,
0.033172607421875,
-0.0316162109375,
0.018829345703125,
-0.011199951171875,
0.0028285980224609375,
-0.032440185546875,
-0.01061248779296875,
0.006031036376953125,
-0.0235595703125,
0.037078857421875,
0.018829345703125,
0.0011539459228515625,
-0.0302581787109375,
-0.0038661956787109375,
-0.0003204345703125,
-0.013824462890625,
-0.03045654296875,
0.01326751708984375,
-0.0164947509765625,
-0.0014820098876953125,
0.0002262592315673828,
-0.01271820068359375,
0.0263519287109375,
-0.0196685791015625,
0.01207733154296875,
-0.014984130859375,
-0.0006957054138183594,
-0.00897216796875,
-0.0265045166015625,
0.021881103515625,
0.014495849609375,
0.0141448974609375,
-0.01904296875,
-0.0096435546875,
0.010650634765625,
0.0068511962890625,
0.006458282470703125,
0.036895751953125,
-0.01132965087890625,
-0.0113067626953125,
-0.0008649826049804688,
0.01043701171875,
0.041168212890625,
-0.0176239013671875,
-0.007293701171875,
-0.0011157989501953125,
0.0017461776733398438,
-0.021270751953125,
0.002750396728515625,
-0.032562255859375,
0.0208892822265625,
0.0117950439453125,
-0.0028667449951171875,
0.00836944580078125,
0.00856781005859375,
0.01499176025390625,
-0.00015354156494140625,
0.0167999267578125,
0.01490020751953125,
0.01082611083984375,
0.0176544189453125,
-0.0284423828125,
0.01198577880859375,
-0.00035572052001953125,
0.003398895263671875,
-0.00734710693359375,
-0.00424957275390625,
-0.037261962890625,
-0.0115203857421875,
0.0083465576171875,
-0.00554656982421875,
0.01027679443359375,
0.01175689697265625,
0.015594482421875,
-0.0250701904296875,
0.041107177734375,
0.0209808349609375,
0.029449462890625,
-0.003345489501953125,
0.01053619384765625,
-0.006427764892578125,
-0.01385498046875,
-0.0004858970642089844,
-0.021728515625,
0.022186279296875,
-0.04888916015625,
-0.0247955322265625,
-0.016937255859375,
-0.0018644332885742188,
0.01555633544921875,
0.01421356201171875,
-0.00460052490234375,
0.02313232421875,
-0.0082855224609375,
-0.022216796875,
-0.00183868408203125,
0.0174407958984375,
-0.02227783203125,
0.0279541015625,
0.01091766357421875,
0.01334381103515625,
-0.004901885986328125,
-0.02703857421875,
0.005176544189453125,
-0.02630615234375,
0.023345947265625,
-0.0029582977294921875,
0.024169921875,
0.0037841796875,
0.039154052734375,
-0.023590087890625,
-0.01190948486328125,
-0.01273345947265625,
0.027191162109375,
-0.00939178466796875,
-0.0016326904296875,
0.03033447265625,
-0.0105743408203125,
0.015838623046875,
-0.00016963481903076172,
-0.0086822509765625,
-0.00431060791015625,
-0.0133819580078125,
-0.032135009765625,
-0.0252532958984375,
0.006862640380859375,
0.003917694091796875,
0.01023101806640625,
-0.033050537109375,
-0.01375579833984375,
-0.0085601806640625,
0.0002930164337158203,
-0.0177154541015625,
-0.00789642333984375,
0.01812744140625,
0.0254669189453125,
-0.032806396484375,
0.0234832763671875,
-0.016204833984375,
-0.005443572998046875,
-0.0130462646484375,
0.01399993896484375,
-0.0094757080078125,
-0.01523590087890625,
-0.028350830078125,
0.040863037109375,
0.0090789794921875,
0.0225372314453125,
-0.009796142578125,
-0.0199432373046875,
0.018035888671875,
-0.00433349609375,
0.01110076904296875,
-0.0061492919921875,
0.035491943359375,
0.0014677047729492188,
0.0011005401611328125,
0.0109100341796875,
-0.007701873779296875,
0.0010471343994140625,
0.0168609619140625,
0.04803466796875,
-0.004863739013671875,
-0.025970458984375,
-0.0280609130859375,
-0.0137481689453125,
-0.005054473876953125,
-0.01050567626953125,
0.02813720703125,
-0.01084136962890625,
0.01336669921875,
0.0288543701171875,
-0.01308441162109375,
0.040313720703125,
-0.01395416259765625,
0.01922607421875,
0.000057220458984375,
0.016510009765625,
0.0212554931640625,
-0.030059814453125,
-0.024017333984375,
-0.01123046875,
0.0009508132934570312,
-0.0035839080810546875,
-0.01134490966796875,
-0.00311279296875,
0.021728515625,
-0.01458740234375,
-0.0001627206802368164,
-0.028228759765625,
-0.050811767578125,
0.007293701171875,
-0.009552001953125,
0.0418701171875,
-0.006595611572265625,
0.001720428466796875,
0.0054931640625,
-0.0171356201171875,
-0.0064239501953125,
-0.0024166107177734375,
-0.038177490234375,
0.01052093505859375,
0.01294708251953125,
-0.00223541259765625,
-0.056304931640625,
-0.0209503173828125,
-0.009002685546875,
0.01180267333984375,
0.02545166015625,
0.0023021697998046875,
-0.0086517333984375,
-0.01445770263671875,
0.001926422119140625,
-0.0177154541015625,
0.01166534423828125,
0.00365447998046875,
-0.003208160400390625,
0.01300811767578125,
0.0006213188171386719,
0.001186370849609375,
0.016204833984375,
0.0171051025390625,
-0.01340484619140625,
-0.0167083740234375,
-0.00890350341796875,
-0.0236968994140625,
-0.03265380859375,
0.0011005401611328125,
0.00673675537109375,
-0.0357666015625,
-0.00921630859375,
-0.01198577880859375,
-0.0135650634765625,
-0.0311737060546875,
0.01284027099609375,
0.008331298828125,
0.02606201171875,
0.004192352294921875,
-0.0005440711975097656,
0.0452880859375,
-0.0347900390625,
0.00881195068359375,
-0.00479888916015625,
0.003688812255859375,
0.00266265869140625,
0.00832366943359375,
-0.042205810546875,
-0.00029850006103515625,
0.0305633544921875,
-0.031402587890625,
-0.0108184814453125,
-0.0308837890625,
-0.04669189453125,
0.00388336181640625,
0.033905029296875,
-0.010711669921875,
0.0224456787109375,
0.0145721435546875,
0.00844573974609375,
-0.0154571533203125,
-0.005146026611328125,
-0.001911163330078125,
-0.02313232421875,
0.003986358642578125,
-0.00695037841796875,
-0.033050537109375,
-0.0030956268310546875,
-0.006732940673828125,
0.0110015869140625,
0.0026416778564453125,
-0.0190887451171875,
0.01934814453125,
0.044097900390625,
0.0237579345703125,
-0.007419586181640625,
-0.0157318115234375,
-0.03546142578125,
0.011871337890625,
-0.00550079345703125,
0.02154541015625,
-0.009796142578125,
-0.00848388671875,
-0.0374755859375,
-0.006591796875,
0.0204315185546875,
-0.006984710693359375,
0.029449462890625,
0.0110321044921875,
-0.032989501953125,
-0.0634765625,
0.01262664794921875,
-0.0262451171875,
0.007843017578125,
-0.015960693359375,
0.03192138671875,
0.01187896728515625,
-0.018707275390625,
0.0015325546264648438,
-0.0035228729248046875,
-0.004222869873046875,
-0.014373779296875,
0.004512786865234375,
-0.01885986328125,
-0.006252288818359375,
0.016876220703125,
0.03466796875,
0.04266357421875,
0.00439453125,
-0.01491546630859375,
0.0413818359375,
0.0251312255859375,
-0.01116180419921875,
-0.01367950439453125,
0.017181396484375,
-0.0241851806640625,
0.0155181884765625,
0.00962066650390625,
0.007709503173828125,
0.0241241455078125,
-0.033172607421875,
-0.0104217529296875,
-0.0002257823944091797,
-0.04656982421875,
0.0121917724609375,
-0.027069091796875,
0.00005131959915161133,
0.0141754150390625,
0.0090484619140625,
0.028289794921875,
-0.007350921630859375,
-0.00847625732421875,
-0.0018329620361328125,
0.0126495361328125,
-0.005275726318359375,
0.020355224609375,
0.00824737548828125,
0.0008182525634765625,
-0.0159759521484375,
0.005970001220703125,
0.01015472412109375,
-0.004695892333984375,
-0.01953125,
0.01369476318359375,
0.003978729248046875,
-0.0118408203125,
0.019378662109375,
0.02471923828125,
-0.005901336669921875,
-0.01007843017578125,
0.034271240234375,
0.0357666015625,
0.007236480712890625,
0.00421142578125,
-0.01242828369140625,
-0.033416748046875,
0.00519561767578125,
-0.020782470703125,
-0.01409149169921875,
0.0170135498046875,
-0.0240631103515625,
-0.002811431884765625,
-0.0146942138671875,
-0.00689697265625,
0.024200439453125,
0.00724029541015625,
0.0029506683349609375,
-0.00847625732421875,
-0.00015223026275634766,
0.0109100341796875,
0.0026874542236328125,
-0.00469207763671875,
0.015838623046875,
0.0092620849609375,
0.00791168212890625,
0.0092926025390625,
0.0292510986328125,
0.0078277587890625,
-0.0077362060546875,
0.00311279296875,
0.023040771484375,
0.0119476318359375,
-0.0325927734375,
0.01617431640625,
0.0038928985595703125,
-0.003803253173828125,
0.0158843994140625,
-0.01189422607421875,
-0.01434326171875,
-0.0097808837890625,
-0.004192352294921875,
0.01165771484375,
0.000034689903259277344,
0.01291656494140625,
-0.00926971435546875,
-0.01406097412109375,
0.0213470458984375,
-0.0147552490234375,
0.02667236328125,
0.03472900390625,
0.00519561767578125,
-0.033111572265625,
0.01284027099609375,
0.00914764404296875,
-0.01213836669921875,
-0.036407470703125,
0.036956787109375,
-0.00335693359375,
-0.03302001953125,
0.00004690885543823242,
0.0208892822265625,
-0.0015163421630859375,
-0.035430908203125,
-0.03326416015625,
0.021881103515625,
-0.025054931640625,
-0.04254150390625,
-0.0187225341796875,
-0.012420654296875,
0.001567840576171875,
-0.0168304443359375,
0.0153045654296875,
-0.01245880126953125,
0.0034618377685546875,
0.007419586181640625,
0.034912109375,
-0.01229095458984375,
0.0200958251953125,
0.019073486328125,
0.016143798828125,
0.02020263671875,
-0.0252685546875,
0.0019969940185546875,
0.0178680419921875,
0.004619598388671875,
0.028900146484375,
-0.00951385498046875,
0.002414703369140625,
-0.007381439208984375,
-0.007354736328125,
0.005321502685546875,
0.03765869140625,
0.019561767578125,
0.014404296875,
0.00417327880859375,
0.022186279296875,
-0.007556915283203125,
-0.000743865966796875,
-0.0290679931640625,
0.0183868408203125,
-0.01326751708984375,
0.01132965087890625,
-0.0345458984375,
-0.0045928955078125,
-0.0250091552734375,
-0.01605224609375,
-0.0168609619140625,
0.00982666015625,
0.0416259765625,
-0.0143585205078125,
-0.017730712890625,
-0.0084075927734375,
0.00370025634765625,
0.02978515625,
-0.005191802978515625,
0.0002865791320800781,
-0.00850677490234375,
0.016265869140625,
0.03265380859375,
-0.040283203125,
0.0001952648162841797,
-0.010711669921875,
0.023681640625,
0.00618743896484375,
0.0110015869140625,
0.0078887939453125,
-0.019561767578125,
-0.0004413127899169922,
-0.01465606689453125,
-0.01097869873046875,
-0.03448486328125,
0.0201416015625,
0.007740020751953125,
-0.006500244140625,
-0.006084442138671875,
-0.04156494140625,
0.020660400390625,
-0.005695343017578125,
0.01174163818359375,
-0.0016851425170898438,
0.00385284423828125,
-0.035552978515625,
0.0073394775390625,
0.015899658203125,
-0.01910400390625,
0.0002644062042236328,
-0.020416259765625,
0.0109405517578125,
0.0477294921875,
0.041595458984375,
-0.005741119384765625,
-0.016448974609375,
-0.0283966064453125,
-0.0203857421875,
-0.01456451416015625,
-0.0523681640625,
0.0108489990234375,
-0.011322021484375,
0.0076141357421875,
0.011932373046875,
0.01629638671875,
0.0101165771484375,
-0.0013675689697265625,
-0.035430908203125,
0.006885528564453125,
-0.001743316650390625,
-0.001270294189453125,
-0.035858154296875,
-0.0016717910766601562,
-0.0015707015991210938,
0.0003285408020019531,
-0.01392364501953125,
-0.037841796875,
0.01512908935546875,
0.00450897216796875,
0.010040283203125,
0.001102447509765625,
0.0021724700927734375,
-0.015869140625,
-0.020721435546875,
0.0301513671875,
-0.054931640625,
0.0288848876953125,
0.041168212890625,
-0.00815582275390625,
-0.0176239013671875,
-0.007843017578125,
0.0112762451171875,
0.0226287841796875,
-0.0017375946044921875,
0.01873779296875,
-0.01535797119140625,
-0.039337158203125,
-0.0002110004425048828,
-0.0265960693359375,
0.01470184326171875,
0.026336669921875,
0.0073394775390625,
-0.02734375,
-0.01447296142578125,
-0.007476806640625,
-0.012939453125,
-0.01422119140625,
-0.002338409423828125,
-0.0032253265380859375,
-0.0172576904296875,
0.003650665283203125,
0.00508880615234375,
0.009002685546875,
0.0235137939453125,
-0.007068634033203125,
-0.005077362060546875,
0.0293731689453125,
0.005428314208984375,
-0.004192352294921875,
-0.0198211669921875,
0.037567138671875,
-0.0307769775390625,
-0.00821685791015625,
-0.031097412109375,
-0.0084228515625,
0.027587890625,
0.0004787445068359375,
-0.0533447265625,
-0.00714874267578125,
0.01343536376953125,
0.00396728515625,
-0.034027099609375,
-0.005855560302734375,
0.01441192626953125,
-0.009918212890625,
-0.0307769775390625,
-0.007282257080078125,
0.02410888671875,
0.022552490234375,
0.00496673583984375,
-0.0191497802734375,
0.0015048980712890625,
0.007373809814453125,
0.0189361572265625,
0.0167388916015625,
-0.0018129348754882812,
0.0025787353515625,
0.0135955810546875,
0.0208740234375,
-0.0007715225219726562,
0.037017822265625,
0.01462554931640625,
-0.0214691162109375,
-0.0038604736328125,
-0.034515380859375,
0.00722503662109375,
0.0003056526184082031,
-0.012969970703125,
-0.026885986328125,
-0.0016841888427734375,
-0.0026683807373046875,
-0.00839996337890625,
-0.0241241455078125,
0.01922607421875,
-0.0018167495727539062,
-0.01067352294921875,
-0.005214691162109375,
0.000850677490234375,
0.036834716796875,
0.017181396484375,
0.00360107421875,
-0.016326904296875,
0.00853729248046875,
0.009490966796875,
0.0038604736328125,
-0.05438232421875,
0.0224761962890625,
-0.005748748779296875,
0.0203704833984375,
-0.03277587890625,
0.0391845703125,
0.0020351409912109375,
-0.021759033203125,
0.00461578369140625,
0.0007877349853515625,
0.0233306884765625,
-0.00521087646484375,
-0.0084075927734375,
-0.01197052001953125,
-0.02703857421875,
-0.01751708984375,
-0.036865234375,
-0.024261474609375,
0.004291534423828125,
0.0160980224609375,
0.00904083251953125,
0.00606536865234375,
-0.004581451416015625,
0.0114898681640625,
-0.01898193359375,
0.026275634765625,
-0.0233612060546875,
0.03350830078125,
0.0259552001953125,
-0.022979736328125,
0.0167694091796875,
-0.0107879638671875,
0.005115509033203125,
-0.003627777099609375,
0.00751495361328125,
0.0286865234375,
-0.0048675537109375,
-0.0088043212890625,
0.004970550537109375,
-0.0099334716796875,
-0.0154266357421875,
0.0192108154296875,
0.01024627685546875,
0.0014181137084960938,
-0.0126190185546875,
0.01190185546875,
0.020843505859375,
-0.0008177757263183594,
0.0260467529296875,
-0.0162200927734375,
-0.002117156982421875,
-0.061248779296875,
-0.005016326904296875,
-0.017852783203125,
-0.021331787109375,
0.0222015380859375,
0.0035552978515625,
0.034576416015625,
0.01552581787109375,
-0.0077667236328125,
0.0185394287109375,
-0.0174560546875,
-0.01983642578125,
0.01143646240234375,
-0.049591064453125,
-0.018524169921875,
0.046112060546875,
-0.0186767578125,
0.0173492431640625,
-0.0033473968505859375,
0.0114593505859375,
-0.00513458251953125,
0.028839111328125,
-0.0258331298828125,
0.006195068359375,
-0.003078460693359375,
-0.04229736328125,
0.0230560302734375,
-0.053619384765625,
0.006984710693359375,
-0.01251983642578125,
0.00374603271484375,
0.039764404296875,
-0.019439697265625,
-0.048431396484375,
0.04095458984375,
-0.017303466796875,
-0.0030384063720703125,
-0.0282440185546875,
-0.04168701171875,
-0.011871337890625,
-0.0088043212890625,
-0.0019521713256835938,
0.006732940673828125,
0.0156097412109375,
0.00351715087890625,
0.01183319091796875,
-0.0013484954833984375,
-0.0179595947265625,
0.0002052783966064453,
-0.02239990234375,
0.0235137939453125,
-0.034912109375,
-0.0028171539306640625,
-0.038787841796875,
-0.01739501953125,
0.025115966796875,
0.01464080810546875,
0.0233001708984375,
-0.0413818359375,
-0.0004825592041015625,
0.01520538330078125,
-0.019012451171875,
0.01116180419921875,
-0.006229400634765625,
0.01483917236328125,
0.0219573974609375,
0.0309295654296875,
0.01265716552734375,
0.033935546875,
0.01059722900390625,
0.00734710693359375,
0.006366729736328125,
-0.05047607421875,
0.0019359588623046875,
-0.003498077392578125,
0.0029048919677734375,
0.00632476806640625,
-0.0013074874877929688,
-0.03594970703125,
-0.009796142578125,
0.0222320556640625,
-0.0059814453125,
-0.0222320556640625,
0.0178680419921875,
0.0153350830078125,
-0.00316619873046875,
0.042022705078125,
-0.00629425048828125,
0.041412353515625,
-0.009246826171875,
0.0228424072265625,
-0.03790283203125,
-0.00617218017578125,
-0.0028839111328125,
0.006195068359375,
0.016265869140625,
-0.0133819580078125,
0.0096282958984375,
-0.0009484291076660156,
-0.00006449222564697266,
-0.012237548828125,
0.005950927734375,
-0.0234527587890625,
0.00916290283203125,
-0.003986358642578125,
-0.005458831787109375,
0.00861358642578125,
0.0071868896484375,
0.0038547515869140625,
0.002559661865234375,
0.00664520263671875,
-0.00937652587890625,
-0.004001617431640625,
0.049530029296875,
0.033203125,
-0.0145721435546875,
0.01561737060546875,
-0.0176849365234375,
0.00922393798828125,
0.0026760101318359375,
0.00811767578125,
-0.006832122802734375,
0.014678955078125,
-0.027435302734375,
0.023223876953125,
0.0269927978515625,
0.02288818359375,
-0.01476287841796875,
-0.001499176025390625,
0.00836181640625,
-0.005344390869140625,
0.007602691650390625,
0.0167999267578125,
-0.035186767578125,
0.01357269287109375,
0.0038356781005859375,
0.01183319091796875,
-0.003208160400390625,
-0.0181121826171875,
0.04364013671875,
0.0177764892578125,
-0.0220947265625,
0.028961181640625,
-0.0288848876953125,
0.02862548828125,
-0.01824951171875,
-0.00807952880859375,
-0.0005893707275390625,
-0.019500732421875,
0.0205230712890625,
0.0148162841796875,
0.007099151611328125,
0.0013227462768554688,
-0.018310546875,
-0.0007085800170898438,
0.001247406005859375,
0.00995635986328125,
0.0059661865234375,
0.001171112060546875,
0.01129913330078125,
-0.01031494140625,
-0.01416015625,
-0.02105712890625,
-0.055328369140625,
0.045196533203125,
0.01220703125,
-0.0333251953125,
-0.032958984375,
-0.018218994140625,
0.0010700225830078125,
0.0159912109375,
-0.004810333251953125,
-0.0188140869140625,
-0.0223846435546875,
0.00022220611572265625,
0.0230865478515625,
0.01171112060546875,
-0.0170440673828125,
0.0170745849609375,
0.015899658203125,
0.0126800537109375,
0.002773284912109375,
0.0404052734375,
-0.016754150390625,
-0.0024051666259765625,
-0.007434844970703125,
-0.0005707740783691406,
0.002170562744140625,
-0.005115509033203125,
0.047393798828125,
-0.0091094970703125,
-0.0157623291015625,
-0.0110015869140625,
0.00333404541015625,
-0.0023097991943359375,
0.03314208984375,
-0.016998291015625,
0.0287933349609375,
0.0030155181884765625,
-0.031494140625,
-0.00148773193359375,
-0.016571044921875,
0.0245819091796875,
-0.0102996826171875,
0.01056671142578125,
-0.0141143798828125,
0.01113128662109375,
0.017913818359375,
-0.0006594657897949219,
-0.0263214111328125,
0.01629638671875,
0.00629425048828125,
-0.01399993896484375,
-0.0238800048828125,
0.0240936279296875,
-0.035552978515625,
0.0137176513671875,
0.0011701583862304688,
0.01220703125,
-0.004093170166015625,
0.01276397705078125,
0.0333251953125,
0.00225067138671875,
-0.0122833251953125,
0.0033702850341796875,
-0.007244110107421875,
0.0211639404296875,
0.0120391845703125,
0.028900146484375,
-0.0189666748046875,
0.0116424560546875,
-0.02606201171875,
0.007740020751953125,
0.00838470458984375,
-0.0115966796875,
-0.0052947998046875,
0.023590087890625,
-0.0263824462890625,
0.0086517333984375,
0.005584716796875,
0.0205230712890625,
0.03424072265625,
-0.01190948486328125,
0.01409149169921875,
-0.0222015380859375,
0.006317138671875,
-0.0435791015625,
-0.0190277099609375,
0.00861358642578125,
0.00360870361328125,
-0.0295867919921875,
0.03271484375,
-0.0160675048828125,
-0.01122283935546875,
-0.0308837890625,
0.040679931640625,
-0.027679443359375,
0.025421142578125,
0.01053619384765625,
0.001850128173828125,
-0.005062103271484375,
0.0081329345703125,
0.00235748291015625,
0.006504058837890625,
-0.0031490325927734375,
0.04345703125,
0.0011796951293945312,
-0.0242767333984375,
0.01384735107421875,
0.002429962158203125,
0.004711151123046875,
-0.031982421875,
-0.00528717041015625,
-0.0000947713851928711,
-0.01263427734375,
-0.021240234375,
-0.0038700103759765625,
-0.0188446044921875,
-0.0352783203125,
-0.0134735107421875,
-0.017730712890625,
0.0020236968994140625,
0.0021686553955078125,
0.0284271240234375,
-0.027679443359375,
-0.008148193359375,
-0.002338409423828125,
0.04815673828125,
-0.03314208984375,
0.00905609130859375,
-0.0189666748046875,
0.0192413330078125,
-0.033203125,
0.00711822509765625,
0.00933074951171875,
0.037750244140625,
-0.025421142578125,
0.0149383544921875,
-0.0171966552734375,
0.0161590576171875,
-0.00705718994140625,
-0.01751708984375,
0.007236480712890625,
-0.014678955078125,
0.0092620849609375,
-0.005153656005859375,
0.01375579833984375,
-0.01076507568359375,
-0.00417327880859375,
-0.03485107421875,
-0.00403594970703125,
-0.04107666015625,
-0.01070404052734375,
0.006984710693359375,
-0.035675048828125,
-0.01018524169921875,
-0.01076507568359375,
0.0172882080078125,
0.007114410400390625,
0.02862548828125,
-0.0059814453125,
0.00908660888671875,
-0.00921630859375,
0.01593017578125,
0.01190948486328125,
0.036834716796875,
0.0032024383544921875,
-0.006923675537109375,
-0.0269622802734375,
0.01209259033203125,
0.011932373046875,
-0.0242919921875,
-0.028656005859375,
0.0198974609375,
-0.0075836181640625,
-0.00946807861328125,
-0.03912353515625,
-0.006160736083984375,
0.0035266876220703125,
-0.0186920166015625,
-0.027374267578125,
0.0004825592041015625,
-0.0391845703125,
-0.01166534423828125,
0.05584716796875,
-0.0204620361328125,
0.004505157470703125,
0.036712646484375,
-0.01291656494140625,
0.006572723388671875,
-0.0170745849609375,
0.0160980224609375,
-0.0033130645751953125,
0.0158843994140625,
-0.00962066650390625,
-0.027496337890625,
0.007549285888671875,
0.0101470947265625,
-0.023040771484375,
0.0204315185546875,
-0.007106781005859375,
-0.00812530517578125,
-0.01355743408203125,
0.00923919677734375,
0.00687408447265625,
0.0012693405151367188,
0.015716552734375,
-0.004550933837890625,
0.0110931396484375,
-0.0089569091796875,
-0.01081085205078125,
-0.0167083740234375,
0.01104736328125,
-0.01184844970703125,
-0.0036640167236328125,
0.0285797119140625,
0.0250091552734375,
0.03173828125,
0.032745361328125,
0.0301055908203125,
0.0284271240234375,
-0.0157623291015625,
0.0246734619140625,
-0.0270843505859375,
0.0308380126953125,
-0.021148681640625,
0.0201416015625,
-0.0218353271484375,
-0.037506103515625,
-0.0018587112426757812,
0.0172271728515625,
-0.0072021484375,
-0.002658843994140625,
0.01305389404296875,
-0.006732940673828125,
-0.020721435546875,
-0.005374908447265625,
-0.04620361328125,
0.0111083984375,
-0.015777587890625,
-0.0184783935546875,
-0.00283050537109375,
0.0084381103515625,
0.007656097412109375,
-0.006526947021484375,
-0.024749755859375,
-0.00922393798828125,
0.0159149169921875,
-0.0200347900390625,
0.0187225341796875,
0.0168609619140625,
0.030426025390625,
0.03765869140625,
-0.0189056396484375,
-0.041259765625,
-0.004634857177734375,
0.0084228515625,
0.05560302734375,
-0.017059326171875,
0.00995635986328125,
0.018218994140625,
0.044769287109375,
-0.00705718994140625,
-0.0185394287109375,
-0.00180816650390625,
0.00908660888671875,
-0.0066680908203125,
0.005847930908203125,
0.0021419525146484375,
0.033294677734375,
0.0238494873046875,
0.023284912109375,
-0.0178375244140625,
-0.00140380859375,
-0.01180267333984375,
-0.005168914794921875,
-0.0299072265625,
-0.048828125,
0.0287322998046875,
0.006931304931640625,
0.0086517333984375,
-0.01062774658203125,
-0.007282257080078125,
-0.0105438232421875,
-0.008514404296875,
-0.016326904296875,
0.0047149658203125,
0.02447509765625,
0.0009098052978515625,
-0.027618408203125,
0.01110076904296875,
0.01068115234375,
-0.01132965087890625,
0.0007739067077636719,
0.01000213623046875,
0.0013818740844726562,
-0.004184722900390625,
0.003231048583984375,
-0.01407623291015625,
-0.024017333984375,
-0.01209259033203125,
0.0288543701171875,
0.019805908203125,
0.017364501953125,
-0.0104522705078125,
0.01380157470703125,
0.005313873291015625,
0.0108489990234375,
-0.0024700164794921875,
0.01092529296875,
0.03912353515625,
0.004459381103515625,
-0.00975799560546875,
-0.0022220611572265625,
0.0295257568359375,
0.0252227783203125,
0.00888824462890625,
-0.0092926025390625,
-0.010406494140625,
0.07568359375,
-0.00783538818359375,
0.0288238525390625,
0.035003662109375,
0.0017633438110351562,
0.00390625,
-0.00897979736328125,
0.0161590576171875,
0.03369140625,
-0.002452850341796875,
0.0088043212890625,
-0.013885498046875,
0.004734039306640625,
0.03363037109375,
0.02105712890625,
-0.00655364990234375,
-0.0004367828369140625,
-0.03753662109375,
-0.013702392578125,
-0.013336181640625,
0.0217132568359375,
0.0394287109375,
0.0179901123046875,
0.0110626220703125,
0.05419921875,
0.0016994476318359375,
-0.00017058849334716797,
-0.0183868408203125,
0.004543304443359375,
0.0035762786865234375,
-0.01617431640625,
0.0310516357421875,
0.005870819091796875,
-0.015777587890625,
0.0007143020629882812,
-0.0121612548828125,
-0.0003578662872314453,
0.01526641845703125,
-0.00870513916015625,
-0.02752685546875,
-0.0287017822265625,
0.031768798828125,
-0.0192108154296875,
-0.0017480850219726562,
0.03143310546875,
-0.005126953125,
0.018951416015625,
-0.0115966796875,
-0.0202484130859375,
-0.01409912109375,
0.0231170654296875,
-0.00033473968505859375,
0.0169830322265625,
-0.04595947265625,
-0.0015325546264648438,
0.007534027099609375,
0.012664794921875,
-0.01444244384765625,
0.0015993118286132812,
-0.01367950439453125,
0.023406982421875,
0.0013837814331054688,
0.0127105712890625,
0.01409149169921875,
0.0015172958374023438,
0.0022869110107421875,
0.01560211181640625,
-0.0012273788452148438,
-0.01678466796875,
0.045867919921875,
-0.0229034423828125,
0.022308349609375,
0.020782470703125,
-0.0006375312805175781,
-0.012664794921875,
-0.01001739501953125,
-0.0025310516357421875,
0.045623779296875,
-0.001491546630859375,
0.006565093994140625,
0.02203369140625,
0.01129150390625,
0.0283660888671875,
-0.00818634033203125,
-0.004642486572265625,
-0.0014591217041015625,
0.0117340087890625,
-0.022064208984375,
0.00852203369140625,
-0.0012912750244140625,
0.0120391845703125,
-0.034912109375,
0.036102294921875,
-0.016357421875,
-0.0022430419921875,
-0.00901031494140625,
-0.01050567626953125,
0.0091705322265625,
-0.002410888671875,
-0.0208892822265625,
0.0308837890625,
0.0125579833984375,
-0.0209503173828125,
-0.01116180419921875,
-0.01346588134765625,
0.02862548828125,
0.0576171875,
-0.0020046234130859375,
0.01788330078125,
-0.0008440017700195312,
-0.027923583984375,
-0.006134033203125,
-0.037353515625,
-0.0183563232421875,
0.01203155517578125,
-0.049530029296875,
-0.02825927734375,
0.0026302337646484375,
0.034576416015625,
0.0090789794921875,
0.01482391357421875,
0.02099609375,
0.0004482269287109375,
-0.018524169921875,
0.0186004638671875,
0.000017344951629638672,
-0.030914306640625,
-0.0035457611083984375,
0.0011682510375976562,
0.0005459785461425781,
0.01183319091796875,
-0.0009670257568359375,
0.0306243896484375,
0.041748046875,
0.0107269287109375,
0.0254364013671875,
-0.0253753662109375,
-0.0203399658203125,
-0.028228759765625,
-0.0121612548828125,
-0.00798797607421875,
-0.01032257080078125,
0.002330780029296875,
0.00189971923828125,
-0.0033626556396484375,
0.033599853515625,
0.0010404586791992188,
0.01120758056640625,
0.03271484375,
-0.03289794921875,
-0.0033054351806640625,
0.038787841796875,
-0.016876220703125,
0.0225677490234375,
0.02203369140625,
-0.006679534912109375,
0.0225982666015625,
-0.0090179443359375,
-0.003448486328125,
-0.0240478515625,
0.01922607421875,
-0.0218048095703125,
-0.019622802734375,
-0.01336669921875,
0.0166168212890625,
-0.021484375,
-0.010498046875,
0.0273590087890625,
-0.0025539398193359375,
-0.0090179443359375,
0.0255889892578125,
-0.0084075927734375,
-0.0010776519775390625,
-0.007091522216796875,
0.028594970703125,
-0.003726959228515625,
0.019622802734375,
0.03057861328125,
0.038787841796875,
0.0012645721435546875,
0.0027408599853515625,
-0.033050537109375,
-0.013580322265625,
0.01276397705078125,
-0.0176544189453125,
-0.006069183349609375,
0.01114654541015625,
0.004451751708984375,
-0.0088958740234375,
0.0262908935546875,
0.01210784912109375,
-0.01328277587890625,
0.002468109130859375,
0.00972747802734375,
0.01195526123046875,
-0.020965576171875,
-0.031768798828125,
-0.0100555419921875,
-0.0048980712890625,
0.0007462501525878906,
0.01085662841796875,
-0.0008878707885742188,
-0.013092041015625,
0.013031005859375,
-0.0242767333984375,
0.024139404296875,
-0.008758544921875,
0.02191162109375,
0.0230255126953125,
-0.01287841796875,
0.0036830902099609375,
0.01369476318359375,
0.024017333984375,
0.01580810546875,
0.0198974609375,
-0.016876220703125,
-0.01279449462890625,
-0.03314208984375,
-0.018096923828125,
-0.006099700927734375,
0.0238800048828125,
0.00550079345703125,
-0.016326904296875,
-0.0292205810546875,
-0.032745361328125,
0.0313720703125,
-0.039886474609375,
-0.02496337890625,
0.0217742919921875,
-0.00420379638671875,
0.034576416015625,
-0.01552581787109375,
-0.00647735595703125,
0.036224365234375,
-0.03387451171875,
0.01129913330078125,
-0.0296630859375,
-0.0270233154296875,
0.02154541015625,
0.020111083984375,
-0.012664794921875,
-0.044342041015625,
0.01515960693359375,
-0.0037136077880859375,
0.040802001953125,
-0.004566192626953125,
-0.010345458984375,
0.0123291015625,
0.04583740234375,
0.01477813720703125,
-0.007579803466796875,
-0.007144927978515625,
-0.022064208984375,
0.0091400146484375,
-0.007183074951171875,
-0.00870513916015625,
-0.0163421630859375,
-0.01416778564453125,
-0.0255889892578125,
-0.0078125,
0.04095458984375,
0.01152801513671875,
-0.01317596435546875,
0.0216064453125,
0.022705078125,
-0.022064208984375,
0.028900146484375,
-0.015289306640625,
0.00616455078125,
0.00412750244140625,
-0.0145111083984375,
-0.01003265380859375,
-0.0185546875,
-0.01470184326171875,
0.01532745361328125,
-0.01248931884765625,
-0.01361083984375,
-0.01192474365234375,
0.042083740234375,
0.016387939453125,
0.006500244140625,
0.0240631103515625,
0.016204833984375,
0.0177764892578125,
0.005344390869140625,
0.041778564453125,
-0.0007390975952148438,
-0.0005412101745605469,
-0.0160064697265625,
0.034698486328125,
0.00826263427734375,
0.043792724609375,
-0.0090484619140625,
-0.00461578369140625,
-0.007640838623046875,
-0.0007886886596679688,
-0.0074462890625,
-0.0082855224609375,
0.0167999267578125,
-0.01229095458984375,
0.0021686553955078125,
-0.0017719268798828125,
-0.0299530029296875,
0.0037841796875,
0.0035495758056640625,
-0.028839111328125,
-0.004253387451171875,
0.036651611328125,
-0.04449462890625,
0.0302276611328125,
0.013519287109375,
-0.0024929046630859375,
-0.013519287109375,
-0.013824462890625,
-0.00791168212890625,
-0.01001739501953125,
-0.015594482421875,
-0.0102081298828125,
-0.01180267333984375,
-0.0106964111328125,
0.0105133056640625,
0.0523681640625,
0.0440673828125,
-0.0012149810791015625,
-0.0009374618530273438,
-0.0194244384765625,
0.00969696044921875,
0.0010042190551757812,
0.04144287109375,
-0.006450653076171875,
-0.006114959716796875,
-0.005542755126953125,
0.0013055801391601562,
-0.0167083740234375,
0.018768310546875,
0.015777587890625,
0.00555419921875,
-0.0014142990112304688,
0.0084686279296875,
0.0091094970703125,
0.01654052734375,
0.0207366943359375,
0.02581787109375,
-0.00018298625946044922,
-0.0253143310546875,
0.0229034423828125,
-0.02142333984375,
-0.0046539306640625,
0.0182342529296875,
-0.00913238525390625,
0.01172637939453125,
0.00650787353515625,
0.0272674560546875,
0.038909912109375,
0.01104736328125,
-0.0057830810546875,
0.0129852294921875,
-0.04827880859375,
0.008544921875,
0.0134735107421875,
0.00600433349609375,
-0.027984619140625,
-0.004669189453125,
0.03582763671875,
-0.013397216796875,
-0.01428985595703125,
-0.0014066696166992188,
-0.031707763671875,
-0.022491455078125,
-0.03167724609375,
0.031890869140625,
-0.0171966552734375,
-0.0083465576171875,
0.01079559326171875,
-0.01214599609375,
-0.0012969970703125,
0.01404571533203125,
0.035736083984375,
-0.01445770263671875,
-0.0279083251953125,
-0.0010519027709960938,
0.0187835693359375,
-0.00652313232421875,
-0.039276123046875,
-0.0003135204315185547,
-0.01092529296875,
-0.0207977294921875,
0.02197265625,
0.007259368896484375,
-0.00897979736328125,
0.0013055801391601562,
0.01227569580078125,
-0.0206146240234375,
0.0082855224609375,
0.01264190673828125,
0.0028400421142578125,
-0.0090789794921875,
0.0102386474609375,
-0.023895263671875,
0.0231475830078125,
-0.003879547119140625,
0.01241302490234375,
0.00457763671875,
-0.004161834716796875,
-0.01514434814453125,
-0.01605224609375,
0.0474853515625,
0.0196990966796875,
0.006855010986328125,
-0.0168304443359375,
-0.005596160888671875,
-0.0008945465087890625,
0.0294647216796875,
-0.0030765533447265625,
-0.022857666015625,
-0.04718017578125,
0.01561737060546875,
0.01220703125,
-0.037750244140625,
0.01708984375,
-0.01258087158203125,
-0.0042266845703125,
-0.004795074462890625,
0.00403594970703125,
0.0156402587890625,
0.007061004638671875,
0.00727081298828125,
-0.01806640625,
-0.013641357421875,
0.02764892578125,
0.005390167236328125,
-0.003215789794921875,
0.00382232666015625,
-0.021514892578125,
-0.0018215179443359375,
-0.0013723373413085938,
0.050567626953125,
0.020965576171875,
0.015472412109375,
-0.008209228515625,
0.0157470703125,
-0.004436492919921875,
0.018341064453125,
0.00716400146484375,
-0.0011119842529296875,
-0.01593017578125,
-0.002593994140625,
0.0328369140625,
-0.00475311279296875,
-0.01387786865234375,
-0.006702423095703125,
0.01195526123046875,
-0.024749755859375,
0.0303802490234375,
0.009002685546875,
0.0163726806640625,
0.00925445556640625,
-0.0004715919494628906,
0.0003314018249511719,
0.006778717041015625,
-0.004444122314453125,
0.0001361370086669922,
-0.0172882080078125,
0.0001646280288696289,
-0.005046844482421875,
0.0214385986328125,
-0.001323699951171875,
0.01873779296875,
0.03509521484375,
0.01087188720703125,
-0.0386962890625,
0.0074310302734375,
0.021148681640625,
-0.0003592967987060547,
-0.0148468017578125,
-0.017578125,
-0.01241302490234375,
-0.00018537044525146484,
0.0275726318359375,
-0.006450653076171875,
-0.041015625,
0.0068511962890625,
0.006259918212890625,
-0.00034356117248535156,
-0.0103759765625,
0.00617218017578125,
0.0114288330078125,
-0.0137939453125,
0.01229095458984375,
-0.01342010498046875,
-0.01568603515625,
0.01377105712890625,
0.01209259033203125,
-0.03680419921875,
0.00302886962890625,
0.02484130859375,
-0.015594482421875,
0.0183868408203125,
0.0201263427734375,
0.0411376953125,
-0.0142822265625,
0.01256561279296875,
0.046142578125,
-0.015899658203125,
-0.003917694091796875,
0.01508331298828125,
0.012237548828125,
-0.021636962890625,
-0.01605224609375,
-0.005214691162109375,
0.02105712890625,
0.005290985107421875,
-0.0208282470703125,
0.0248870849609375,
-0.01355743408203125,
0.00676727294921875,
0.04022216796875,
0.00403594970703125,
0.002521514892578125,
-0.0036830902099609375,
0.004276275634765625,
-0.006160736083984375,
0.03125,
0.01555633544921875,
-0.0103607177734375,
-0.0009918212890625,
-0.0103302001953125,
0.0162811279296875,
-0.04315185546875,
0.00666046142578125,
0.0052490234375,
-0.008148193359375,
-0.015899658203125,
0.017181396484375,
0.0155029296875,
-0.01166534423828125,
0.0205841064453125,
-0.0255279541015625,
0.0028400421142578125,
0.002475738525390625,
0.019287109375,
-0.0338134765625,
-0.01959228515625,
0.053436279296875,
0.00641632080078125,
-0.037445068359375,
0.016632080078125,
0.0008025169372558594,
0.005321502685546875,
0.0257568359375,
0.0182037353515625,
0.01178741455078125,
-0.01502227783203125,
-0.0364990234375,
-0.0031147003173828125,
-0.005828857421875,
-0.0201263427734375,
0.00844573974609375,
0.0295562744140625,
-0.01476287841796875,
0.0233917236328125,
-0.017852783203125,
-0.0058441162109375,
0.0151214599609375,
0.022216796875,
0.00473785400390625,
0.001094818115234375,
-0.0278167724609375,
0.0355224609375,
-0.022918701171875,
-0.03533935546875,
0.00881195068359375,
0.0106964111328125,
-0.0024509429931640625,
-0.0101470947265625,
-0.027191162109375,
-0.01824951171875,
-0.00388336181640625,
-0.010223388671875,
-0.0024204254150390625,
0.01178741455078125,
0.0273590087890625,
-0.0172271728515625,
0.008697509765625,
-0.0026226043701171875,
0.041748046875,
-0.006053924560546875,
0.030670166015625,
0.01398468017578125,
-0.0096282958984375,
-0.03887939453125,
0.0041046142578125,
0.020263671875,
-0.0289764404296875,
-0.0016984939575195312,
-0.004550933837890625,
0.02423095703125,
0.01189422607421875,
-0.009613037109375,
-0.0024700164794921875,
0.05133056640625,
0.004459381103515625,
0.0163421630859375,
0.00933837890625,
0.0200958251953125,
-0.0095367431640625,
-0.0247650146484375,
0.0302734375,
0.0121002197265625,
-0.00022459030151367188,
0.0005869865417480469,
-0.021209716796875,
0.01165771484375,
-0.008056640625,
0.03558349609375,
-0.005168914794921875,
-0.037506103515625,
-0.0045166015625,
0.004985809326171875,
-0.01323699951171875,
0.02642822265625,
-0.00760650634765625,
-0.003696441650390625,
0.01654052734375,
0.01776123046875,
0.00897979736328125,
0.03204345703125,
-0.0290679931640625,
0.0171051025390625,
-0.0276336669921875,
-0.01213836669921875,
0.017181396484375,
-0.007198333740234375,
0.004833221435546875,
0.00147247314453125,
-0.00083160400390625,
0.047149658203125,
-0.01255035400390625,
0.007572174072265625,
-0.0037403106689453125,
-0.029541015625,
0.0211639404296875,
0.0223236083984375,
0.00800323486328125,
-0.0270843505859375,
-0.0211334228515625,
-0.0210113525390625,
-0.0050811767578125,
-0.020965576171875,
-0.012542724609375,
0.0244598388671875,
-0.0017080307006835938,
0.039947509765625,
-0.0207366943359375,
-0.006214141845703125,
0.01520538330078125,
0.0281982421875,
0.0328369140625,
0.023040771484375,
0.01416778564453125,
0.0170745849609375,
-0.0160369873046875,
-0.00107574462890625,
-0.01209259033203125,
-0.007373809814453125,
0.0254974365234375,
-0.0178375244140625,
-0.006534576416015625,
-0.00865936279296875,
0.0208740234375,
-0.012451171875,
-0.037078857421875,
0.0079498291015625,
-0.0078125,
-0.00807952880859375,
0.011474609375,
0.002735137939453125,
0.005985260009765625,
0.00037789344787597656,
0.01702880859375,
-0.0005936622619628906,
-0.006618499755859375,
0.0111236572265625,
-0.0287322998046875,
0.00966644287109375,
-0.024627685546875,
0.0089263916015625,
-0.0186004638671875,
0.022613525390625,
-0.00015604496002197266,
-0.0296630859375,
-0.006732940673828125,
0.027740478515625,
-0.0238800048828125,
0.0225830078125,
0.00396728515625,
0.00803375244140625,
-0.0233154296875,
-0.0208587646484375,
0.00104522705078125,
-0.0005311965942382812,
0.0028896331787109375,
-0.0128173828125,
0.01030731201171875,
0.004909515380859375,
0.004207611083984375,
0.032684326171875,
-0.0203094482421875,
-0.003978729248046875,
-0.0280303955078125,
-0.0224609375,
-0.0063018798828125,
0.0191802978515625,
0.0291748046875,
-0.0318603515625,
-0.016204833984375,
0.0034580230712890625,
-0.00045609474182128906,
-0.0166168212890625,
0.01678466796875,
0.05303955078125,
0.0066375732421875,
-0.0238037109375,
0.00984954833984375,
-0.0289459228515625,
0.024322509765625,
0.0027313232421875,
0.040679931640625,
0.020660400390625,
0.0089111328125,
-0.01146697998046875,
0.006099700927734375,
0.01067352294921875,
-0.0007290840148925781,
-0.01012420654296875,
-0.0140533447265625,
0.0168304443359375,
-0.0040130615234375,
0.00173187255859375,
-0.0013561248779296875,
-0.00762939453125,
0.006183624267578125,
-0.032135009765625,
-0.026275634765625,
-0.023101806640625,
0.022674560546875,
-0.010833740234375,
-0.01568603515625,
0.01326751708984375,
-0.0074615478515625,
0.00189208984375,
-0.0025920867919921875,
-0.0012140274047851562,
0.0130462646484375,
-0.03167724609375,
0.0026721954345703125,
-0.031707763671875,
-0.01812744140625,
-0.007053375244140625,
-0.01406097412109375,
0.0166473388671875,
-0.0239410400390625,
0.0013532638549804688,
0.0197601318359375,
0.0003204345703125,
0.022369384765625,
-0.00981903076171875,
-0.0027904510498046875,
-0.0246429443359375,
-0.0235748291015625,
-0.007068634033203125,
-0.0099945068359375,
0.0166168212890625,
0.010223388671875,
0.006824493408203125,
-0.00168609619140625,
0.01055908203125,
-0.0186920166015625,
-0.0113983154296875,
0.04156494140625,
0.0264129638671875,
-0.0098876953125,
0.005157470703125,
0.0164337158203125,
0.01268768310546875,
0.039154052734375,
0.00034737586975097656,
0.0214385986328125,
0.0005025863647460938,
-0.00334930419921875,
0.0015707015991210938,
-0.008544921875,
-0.006633758544921875,
0.006519317626953125,
0.0406494140625,
0.01285552978515625,
-0.0003561973571777344,
0.038177490234375,
-0.006259918212890625,
0.0117645263671875,
-0.0213165283203125,
0.005069732666015625,
-0.044097900390625,
0.00580596923828125,
-0.0011739730834960938,
0.0152435302734375,
0.02496337890625,
0.003948211669921875,
-0.006938934326171875,
0.032928466796875,
-0.0008420944213867188,
0.0204620361328125,
0.003856658935546875,
-0.0040435791015625,
-0.021575927734375,
0.0206146240234375,
-0.016693115234375,
0.035552978515625,
-0.0169219970703125,
0.0007848739624023438,
-0.009613037109375,
-0.0218048095703125,
-0.0186767578125,
0.0144195556640625,
-0.01464080810546875,
-0.009735107421875,
-0.0218505859375,
-0.0069427490234375,
-0.0021610260009765625,
-0.0357666015625,
0.002300262451171875,
-0.01093292236328125,
-0.0243072509765625,
-0.0210723876953125,
-0.006183624267578125,
0.0041046142578125,
0.044830322265625,
-0.007785797119140625,
-0.0047454833984375,
-0.0235748291015625,
0.01410675048828125,
0.0000616908073425293,
-0.0266876220703125,
0.00789642333984375,
0.0135498046875,
-0.0265655517578125,
0.0183563232421875,
0.04486083984375,
0.0049285888671875,
0.0204925537109375,
-0.00722503662109375,
0.0284881591796875,
0.048126220703125,
0.0323486328125,
-0.0211639404296875,
-0.015350341796875,
-0.0225372314453125,
0.0643310546875,
0.0341796875,
0.0037078857421875,
0.025482177734375,
0.0276947021484375,
-0.008758544921875,
-0.016632080078125,
-0.0014753341674804688,
-0.021697998046875,
0.00600433349609375,
0.0277099609375,
-0.04632568359375,
-0.0004093647003173828,
-0.0474853515625,
0.003620147705078125,
-0.01666259765625,
-0.00812530517578125,
0.042236328125,
0.01849365234375,
0.029052734375,
0.01032257080078125,
0.004360198974609375,
-0.0247039794921875,
0.0103912353515625,
0.0101776123046875,
-0.00554656982421875,
-0.001850128173828125,
0.017791748046875,
0.006053924560546875,
-0.00386810302734375,
0.003993988037109375,
-0.01126861572265625,
-0.01995849609375,
-0.005352020263671875,
0.0166015625,
0.0032749176025390625,
0.01088714599609375,
-0.0047454833984375,
0.00887298583984375,
0.01141357421875,
0.0031986236572265625,
0.006008148193359375,
-0.0121612548828125,
-0.024688720703125,
-0.033905029296875,
0.023101806640625,
-0.00921630859375,
0.0287628173828125,
-0.020660400390625,
0.02880859375,
-0.0195770263671875,
0.0338134765625,
-0.029632568359375,
-0.005504608154296875,
-0.0182952880859375,
-0.004421234130859375,
-0.0028553009033203125,
-0.01953125,
-0.00991058349609375,
-0.04241943359375,
-0.0285797119140625,
-0.020843505859375,
0.0020275115966796875,
0.0105438232421875,
-0.0189361572265625,
0.0235595703125,
0.022735595703125,
-0.0004858970642089844,
-0.0006251335144042969,
-0.00868988037109375,
-0.014312744140625,
0.010498046875,
-0.0077362060546875,
-0.001110076904296875,
0.043212890625,
0.0077362060546875,
-0.00469970703125,
-0.0008540153503417969,
0.004741668701171875,
-0.0117034912109375,
0.04205322265625,
-0.0140380859375,
0.01128387451171875,
0.035736083984375,
0.023162841796875,
0.0279998779296875,
-0.0203399658203125,
0.01068115234375,
0.0012845993041992188,
0.0018367767333984375,
0.0181884765625,
0.0118408203125,
0.021270751953125,
-0.004360198974609375,
0.018890380859375,
0.0323486328125,
-0.00537872314453125,
0.002777099609375,
0.0030422210693359375,
-0.00278472900390625,
0.0011873245239257812,
0.04998779296875,
-0.0232696533203125,
0.028564453125,
0.0207061767578125,
0.018280029296875,
0.0183563232421875
] |
ours_525
|
The answer is \( 187120 \).
If \( K_{1} \) is used to unlock \( D_{1} \), then \( D_{i} \) must be unlocked by \( K_{i} \) for all \( i \); otherwise, if \( K_{1} \) is used to unlock \( D_{2} \), then \( D_{i+1} \) must be unlocked by \( K_{i} \) for all \( i \). Let \( A \) denote the set of proper configurations of the first kind (i.e., in which \( D_{i} \) always appears after \( K_{i} \)), and \( B \) of the second (i.e., in which \( D_{i+1} \) always appears after \( K_{i} \)); then our answer is \(|A \cup B|=|A|+|B|-|A \cap B|\).
First, it's clear that \(|A|=|B|=\binom{10}{2}\binom{8}{2}\binom{6}{2}\binom{4}{2}\binom{2}{2}=5!(2 \cdot 5-1)!! = 113400\), since proper configurations in \( A \) (and \( B \)) simply correspond to pairings \((K_{i}, D_{i})\) (resp. \((K_{i}, D_{i+1})\)) of \(\{1,2, \ldots, 10\}\).
It remains to compute \(|A \cap B|\), the number of proper configurations in which \( D_{i}, D_{i+1} \) appear after \( K_{i} \) for all \( i \). It suffices to count the number \( X \) of such configurations with \( D_{1} \) as the first door and \( D_{2} \) or \( D_{3} \) as the second, since \( 5 \cdot 2 \cdot X=|A \cap B| \) by symmetry. Indeed, we can first cyclically shift the indices so that \( D_{1} \) is the first door, and then observe that the properness-preserving involution taking \( K_{i} \rightarrow K_{6-i} \) and \( D_{i} \rightarrow D_{7-i} \) (all indices modulo 5) exchanges the second door between the sets \(\{D_{2}, D_{3}\}\) and \(\{D_{4}, D_{5}\}\).
We now do casework based on the 5-tuple \((i_{1}, \ldots, i_{5})\) such that \( D_{i_{1}}, \ldots, D_{i_{5}} \) are in order from left to right. For \((1,2,3,4,5)\) and \((1,2,3,5,4)\), we choose (the positions of) \( K_{1}, K_{5}, K_{2}, K_{3}, K_{4} \) (in that order) for a total of \( 1 \cdot 2 \cdot 4 \cdot 6 \cdot 8=384 \) configurations; for \((1,2,4,5,3)\) and \((1,2,4,3,5)\), we choose \( K_{1}, K_{5}, K_{2}, K_{3}, K_{4} \) for \( 1 \cdot 2 \cdot 4 \cdot 6 \cdot 7=336 \); for \((1,2,5,3,4)\) and \((1,2,5,4,3)\), we choose \( K_{1}, K_{5}, K_{2}, K_{4}, K_{3} \) for \( 1 \cdot 2 \cdot 4 \cdot 6 \cdot 8=384 \); for \((1,3,2,4,5)\) and \((1,3,2,5,4)\), we choose \( K_{1}, K_{5}, K_{2}, K_{3}, K_{4} \) for \( 1 \cdot 2 \cdot 4 \cdot 5 \cdot 8=320 \); for the remaining four cases (with \( i_{1}=1, i_{2}=3 \), and \( i_{3} \in\{4,5\} \)), we choose \( K_{1}, K_{5}, K_{2}, K_{3}, K_{4} \) for \( 1 \cdot 2 \cdot 4 \cdot 5 \cdot 7=280 \).
Thus \( X=384 \cdot 2+336 \cdot 2+384 \cdot 2+320 \cdot 2+280 \cdot 4=3968 \) ways to do this, so \(|A \cap B|=10 X=39680\) and \(|A \cup B|=2 \cdot 113400-39680=187120\).
\(\boxed{187120}\)
|
187120
|
{
"competition": "us_comps",
"dataset": "Ours",
"posts": null,
"source": "OMOSoln2-2.md"
}
|
Let \( K_{1}, K_{2}, K_{3}, K_{4}, K_{5} \) be 5 distinguishable keys, and let \( D_{1}, D_{2}, D_{3}, D_{4}, D_{5} \) be 5 distinguishable doors. For \( 1 \leq i \leq 5 \), key \( K_{i} \) opens doors \( D_{i} \) and \( D_{i+1} \) (where \( D_{6}=D_{1} \)) and can only be used once. The keys and doors are placed in some order along a hallway. Keysha walks into the hallway, picks a key and opens a door with it, such that she never obtains a key before all the doors in front of it are unlocked. In how many such ways can the keys and doors be ordered if Keysha can open all the doors?
Clarifications:
- The doors and keys are in series. In other words, the doors aren't lined up along the side of the hallway. They are blocking Keysha's path to the end, and the only way she can get past them is by getting the appropriate keys along the hallway.
- The doors and keys appear consecutively along the hallway. For example, she might find \( K_{1} D_{1} K_{2} D_{2} K_{3} D_{3} K_{4} D_{4} K_{5} D_{5} \) down the hallway in that order. Also, by "she never obtains a key before all the doors in front of it are unlocked," we mean that she cannot obtain a key before all the doors appearing before the key are unlocked. In essence, it merely states that locked doors cannot be passed.
- The doors and keys do not need to alternate down the hallway.
|
[
"/Mathematics/DiscreteMathematics/Combinatorics/Enumeration",
"/Mathematics/DiscreteMathematics/Combinatorics/GeneralCombinatorics",
"/Mathematics/DiscreteMathematics/GeneralDiscreteMathematics/ConcreteMath",
"/Mathematics/DiscreteMathematics/GeneralDiscreteMathematics/ConcreteMathematics",
"/Mathematics/DiscreteMathematics/GeneralDiscreteMathematics/DiscreteMath",
"/Mathematics/DiscreteMathematics/GeneralDiscreteMathematics/DiscreteMathematics",
"/Mathematics/RecreationalMathematics/Puzzles/Puzzle"
] |
Separate the arrangements into two exclusive families based on whether each key opens its own‑indexed door or the next one, then apply inclusion–exclusion.
|
[
0.00034332275390625,
-0.063232421875,
-0.004451751708984375,
-0.0250244140625,
0.00146484375,
-0.0068511962890625,
0.02838134765625,
-0.03363037109375,
0.0196380615234375,
0.01250457763671875,
-0.009490966796875,
-0.05426025390625,
0.0002397298812866211,
-0.0357666015625,
-0.04193115234375,
-0.04132080078125,
0.0253143310546875,
0.06341552734375,
0.007488250732421875,
-0.0024890899658203125,
-0.0156707763671875,
-0.006927490234375,
0.01146697998046875,
0.03375244140625,
0.025299072265625,
-0.0443115234375,
-0.0171356201171875,
0.0038909912109375,
-0.0218505859375,
-0.03558349609375,
-0.01380157470703125,
-0.0205841064453125,
0.0242156982421875,
-0.0128326416015625,
0.0023822784423828125,
0.0290679931640625,
0.0088043212890625,
-0.0016241073608398438,
-0.031982421875,
0.0007429122924804688,
-0.0112457275390625,
-0.00899505615234375,
0.008514404296875,
-0.01136016845703125,
-0.005413055419921875,
-0.007568359375,
0.0007319450378417969,
-0.0102996826171875,
-0.0340576171875,
0.004680633544921875,
-0.004604339599609375,
0.01611328125,
-0.016082763671875,
0.0110015869140625,
-0.0013208389282226562,
-0.054656982421875,
-0.021697998046875,
0.003635406494140625,
-0.00902557373046875,
-0.0025634765625,
0.00428009033203125,
0.01123809814453125,
-0.00004798173904418945,
-0.00475311279296875,
-0.00003838539123535156,
0.003467559814453125,
-0.0104827880859375,
0.01995849609375,
-0.002532958984375,
-0.0096435546875,
-0.0272979736328125,
-0.0301361083984375,
-0.033447265625,
0.037628173828125,
-0.00042438507080078125,
-0.024139404296875,
-0.004390716552734375,
0.00888824462890625,
0.01953125,
0.01074981689453125,
-0.01274871826171875,
0.0006089210510253906,
0.0158843994140625,
0.034088134765625,
-0.00821685791015625,
0.031524658203125,
0.0289306640625,
-0.003143310546875,
0.0028133392333984375,
0.0198974609375,
-0.0111541748046875,
-0.0284271240234375,
-0.00408935546875,
0.0216217041015625,
0.015838623046875,
0.005096435546875,
0.006801605224609375,
-0.006443023681640625,
-0.0121917724609375,
0.01190948486328125,
0.007419586181640625,
-0.01047515869140625,
0.0277099609375,
-0.007152557373046875,
-0.01873779296875,
0.0023822784423828125,
-0.0011005401611328125,
-0.00269317626953125,
-0.018951416015625,
0.000050902366638183594,
-0.006946563720703125,
0.00548553466796875,
0.04962158203125,
0.012725830078125,
-0.0030727386474609375,
-0.0011119842529296875,
0.03497314453125,
-0.02325439453125,
-0.01678466796875,
-0.00432586669921875,
0.0205535888671875,
0.004146575927734375,
0.001972198486328125,
0.020172119140625,
0.0172882080078125,
-0.0018787384033203125,
-0.010833740234375,
-0.0062103271484375,
0.00557708740234375,
0.00017583370208740234,
0.0177459716796875,
0.006305694580078125,
-0.0025615692138671875,
0.006168365478515625,
-0.01386260986328125,
-0.01013946533203125,
0.00952911376953125,
-0.00690460205078125,
-0.00217437744140625,
0.0011310577392578125,
-0.0080108642578125,
-0.0038909912109375,
-0.003650665283203125,
-0.0012407302856445312,
-0.00525665283203125,
0.04443359375,
0.0176544189453125,
-0.032440185546875,
0.00531005859375,
0.0022640228271484375,
-0.00490570068359375,
0.0073699951171875,
0.0180206298828125,
0.0035533905029296875,
0.0128936767578125,
0.0169677734375,
-0.0040435791015625,
-0.011077880859375,
0.0028743743896484375,
0.01290130615234375,
0.0020599365234375,
-0.0028629302978515625,
0.0164794921875,
0.0457763671875,
0.0037250518798828125,
-0.0050201416015625,
0.046905517578125,
-0.0148468017578125,
-0.0046234130859375,
0.0264129638671875,
-0.00923919677734375,
-0.0193328857421875,
-0.005218505859375,
-0.01430511474609375,
0.00652313232421875,
-0.0015325546264648438,
0.021575927734375,
0.0142822265625,
0.00469970703125,
0.02374267578125,
0.00940704345703125,
-0.057464599609375,
-0.0259552001953125,
0.022430419921875,
0.0121307373046875,
0.01424407958984375,
0.0030059814453125,
-0.0167388916015625,
0.019805908203125,
0.01507568359375,
0.02374267578125,
-0.0250396728515625,
0.00391387939453125,
0.0009775161743164062,
-0.007266998291015625,
0.00734710693359375,
-0.0014219284057617188,
0.032867431640625,
0.0265045166015625,
-0.0025634765625,
-0.006298065185546875,
-0.0089874267578125,
-0.01251220703125,
0.0119171142578125,
0.024871826171875,
-0.007183074951171875,
-0.006488800048828125,
-0.00467681884765625,
0.0016841888427734375,
0.003662109375,
-0.0153656005859375,
0.0196990966796875,
-0.03143310546875,
-0.01739501953125,
0.011505126953125,
0.0017137527465820312,
-0.005584716796875,
-0.0004558563232421875,
0.0039005279541015625,
-0.03057861328125,
-0.0019407272338867188,
0.007625579833984375,
-0.010650634765625,
-0.01007843017578125,
-0.033416748046875,
-0.007083892822265625,
0.01092529296875,
0.0003802776336669922,
0.0006213188171386719,
0.0027751922607421875,
-0.0118865966796875,
-0.0169219970703125,
-0.02264404296875,
-0.00691986083984375,
-0.015045166015625,
0.0091400146484375,
0.0162353515625,
-0.006046295166015625,
-0.002071380615234375,
-0.0016927719116210938,
0.08331298828125,
0.0165863037109375,
-0.0149688720703125,
0.00835418701171875,
-0.0169830322265625,
-0.0026111602783203125,
0.01311492919921875,
0.005260467529296875,
-0.0125579833984375,
-0.00499725341796875,
-0.0361328125,
0.00982666015625,
0.0199127197265625,
0.0202789306640625,
-0.0009746551513671875,
-0.01334381103515625,
0.0176849365234375,
-0.019927978515625,
0.0108642578125,
-0.007808685302734375,
-0.01085662841796875,
0.0028533935546875,
0.014678955078125,
0.002094268798828125,
-0.01306915283203125,
0.0191497802734375,
-0.0039215087890625,
0.00801849365234375,
-0.00955963134765625,
0.002635955810546875,
0.052154541015625,
-0.0206146240234375,
-0.0120391845703125,
0.00945281982421875,
-0.006664276123046875,
0.002208709716796875,
-0.0260162353515625,
-0.01435089111328125,
0.0014514923095703125,
0.0002589225769042969,
-0.00225830078125,
0.00036716461181640625,
-0.040130615234375,
0.00818634033203125,
0.00974273681640625,
-0.013916015625,
-0.030792236328125,
0.01094818115234375,
0.00628662109375,
0.005512237548828125,
0.006008148193359375,
-0.02093505859375,
-0.0270538330078125,
-0.0181427001953125,
0.0340576171875,
-0.075927734375,
0.00646209716796875,
-0.0157012939453125,
0.0199432373046875,
-0.008209228515625,
0.01015472412109375,
-0.01049041748046875,
0.00821685791015625,
0.062103271484375,
0.0118408203125,
-0.0018720626831054688,
0.01177978515625,
-0.0242919921875,
0.007549285888671875,
0.01541900634765625,
-0.002185821533203125,
-0.007373809814453125,
0.01139068603515625,
-0.0114898681640625,
0.011077880859375,
-0.0102691650390625,
0.0168609619140625,
0.00948333740234375,
0.0005159378051757812,
0.00785064697265625,
0.0043182373046875,
-0.0120391845703125,
0.015777587890625,
-0.01157379150390625,
0.03741455078125,
-0.0011730194091796875,
0.0130157470703125,
-0.0106964111328125,
-0.0117340087890625,
0.003936767578125,
-0.027587890625,
0.01331329345703125,
-0.022369384765625,
0.01189422607421875,
-0.0291595458984375,
0.0022983551025390625,
0.0018711090087890625,
0.008026123046875,
-0.02191162109375,
0.007720947265625,
-0.0262603759765625,
0.009033203125,
0.005695343017578125,
0.032440185546875,
0.033660888671875,
0.0240631103515625,
-0.034942626953125,
-0.005130767822265625,
-0.0279998779296875,
0.0208587646484375,
0.0033626556396484375,
0.01107025146484375,
-0.006710052490234375,
0.01514434814453125,
-0.01453399658203125,
-0.00693511962890625,
-0.0035114288330078125,
0.013031005859375,
-0.01898193359375,
-0.0172576904296875,
-0.0068511962890625,
-0.01467132568359375,
0.01116180419921875,
-0.0032806396484375,
0.04852294921875,
-0.0295257568359375,
0.00673675537109375,
0.0234527587890625,
0.0135040283203125,
0.0118408203125,
-0.005619049072265625,
0.026123046875,
-0.01532745361328125,
-0.0280609130859375,
-0.0207366943359375,
-0.0216217041015625,
0.0019207000732421875,
0.00567626953125,
-0.01885986328125,
-0.023529052734375,
-0.0091552734375,
0.054779052734375,
-0.005390167236328125,
0.01549530029296875,
-0.0183258056640625,
-0.01424407958984375,
-0.011993408203125,
-0.0256805419921875,
-0.01319122314453125,
0.00470733642578125,
0.0200042724609375,
0.026885986328125,
0.0037555694580078125,
0.0005145072937011719,
-0.005649566650390625,
-0.00629425048828125,
-0.004486083984375,
0.011016845703125,
0.06793212890625,
-0.01132965087890625,
0.006496429443359375,
0.01056671142578125,
-0.01352691650390625,
-0.010498046875,
0.01192474365234375,
-0.00969696044921875,
-0.0162506103515625,
-0.039703369140625,
0.005687713623046875,
-0.007488250732421875,
-0.002410888671875,
-0.00342559814453125,
0.007305145263671875,
0.0367431640625,
-0.00218963623046875,
0.01293182373046875,
-0.0118865966796875,
-0.0038909912109375,
0.0006585121154785156,
-0.007663726806640625,
-0.0120849609375,
-0.043243408203125,
0.0184173583984375,
-0.00258636474609375,
0.006900787353515625,
0.0027790069580078125,
-0.004047393798828125,
0.03240966796875,
0.0157318115234375,
-0.004810333251953125,
-0.01107025146484375,
-0.0032596588134765625,
-0.0102691650390625,
0.0150604248046875,
-0.016876220703125,
0.0176849365234375,
-0.0234527587890625,
-0.0016584396362304688,
-0.0135040283203125,
0.0019779205322265625,
-0.0022983551025390625,
-0.016754150390625,
0.006488800048828125,
-0.0200653076171875,
-0.007091522216796875,
-0.0016222000122070312,
-0.01377105712890625,
-0.0017852783203125,
-0.0037975311279296875,
0.01274871826171875,
-0.0015459060668945312,
0.000385284423828125,
-0.03631591796875,
-0.0143280029296875,
-0.01415252685546875,
0.0122222900390625,
0.00189971923828125,
0.01032257080078125,
-0.0042877197265625,
-0.0041351318359375,
0.00726318359375,
-0.027008056640625,
-0.0008687973022460938,
-0.01239013671875,
-0.01491546630859375,
-0.023651123046875,
0.0219879150390625,
0.0185089111328125,
0.01473236083984375,
0.0090484619140625,
0.001262664794921875,
-0.033782958984375,
0.01369476318359375,
-0.012237548828125,
-0.0185699462890625,
0.024932861328125,
0.0213470458984375,
0.034271240234375,
0.0008139610290527344,
-0.020172119140625,
0.01220703125,
0.00939178466796875,
0.006275177001953125,
0.032196044921875,
0.021575927734375,
-0.029022216796875,
0.020233154296875,
0.005672454833984375,
-0.0282135009765625,
0.0188446044921875,
-0.0019550323486328125,
0.0169219970703125,
-0.03564453125,
-0.0142974853515625,
0.04144287109375,
-0.030303955078125,
-0.01236724853515625,
-0.01947021484375,
0.0007171630859375,
0.0154876708984375,
0.01406097412109375,
-0.0012836456298828125,
0.010345458984375,
0.01125335693359375,
0.0117950439453125,
0.01061248779296875,
0.0467529296875,
-0.0022125244140625,
-0.0286865234375,
0.01555633544921875,
0.0111541748046875,
-0.005889892578125,
0.00690460205078125,
-0.0243682861328125,
-0.00530242919921875,
0.0222930908203125,
0.041046142578125,
-0.0242156982421875,
-0.0213470458984375,
0.0034313201904296875,
0.00431060791015625,
-0.018035888671875,
0.042938232421875,
0.028961181640625,
0.00424957275390625,
0.00676727294921875,
0.04620361328125,
-0.0123138427734375,
-0.0154266357421875,
-0.011505126953125,
0.01299285888671875,
-0.06134033203125,
-0.00042057037353515625,
-0.026275634765625,
0.0154876708984375,
0.0153961181640625,
0.00485992431640625,
-0.006702423095703125,
-0.01369476318359375,
-0.0049591064453125,
0.005443572998046875,
-0.0034770965576171875,
0.017242431640625,
0.030029296875,
-0.044158935546875,
-0.007415771484375,
0.0117034912109375,
-0.01438140869140625,
-0.02630615234375,
0.0034618377685546875,
-0.021209716796875,
-0.007434844970703125,
0.00270843505859375,
-0.042205810546875,
-0.0229034423828125,
-0.0228118896484375,
0.0189971923828125,
-0.0018720626831054688,
0.01242828369140625,
-0.0207672119140625,
-0.0223236083984375,
0.01326751708984375,
-0.0025157928466796875,
0.01611328125,
0.0172882080078125,
-0.0006570816040039062,
0.01849365234375,
-0.0016603469848632812,
-0.00849151611328125,
-0.0321044921875,
-0.0174407958984375,
0.009521484375,
0.0005407333374023438,
-0.00597381591796875,
-0.0195465087890625,
0.017669677734375,
0.006824493408203125,
-0.0103912353515625,
-0.0146636962890625,
0.003383636474609375,
-0.0019054412841796875,
0.022674560546875,
-0.01036834716796875,
0.00894927978515625,
0.002681732177734375,
-0.024200439453125,
0.020263671875,
-0.01233673095703125,
0.0027027130126953125,
-0.01538848876953125,
-0.0205230712890625,
-0.0289764404296875,
0.0129547119140625,
-0.015289306640625,
0.00832366943359375,
-0.0271453857421875,
0.0311737060546875,
-0.0030059814453125,
0.00978851318359375,
-0.0209197998046875,
-0.0086212158203125,
-0.00994873046875,
0.0166473388671875,
-0.0007719993591308594,
-0.004093170166015625,
-0.02850341796875,
-0.0257720947265625,
0.0292510986328125,
0.0026397705078125,
-0.006591796875,
0.016754150390625,
-0.0027008056640625,
0.039337158203125,
0.009552001953125,
0.0206756591796875,
-0.0214996337890625,
0.0009455680847167969,
-0.028656005859375,
-0.0008835792541503906,
0.006038665771484375,
-0.0024929046630859375,
0.0192718505859375,
0.00839996337890625,
0.017181396484375,
-0.02105712890625,
-0.006343841552734375,
-0.0228271484375,
-0.00926971435546875,
-0.000012516975402832031,
-0.034423828125,
-0.04730224609375,
-0.01324462890625,
0.01275634765625,
0.0032501220703125,
-0.0186004638671875,
-0.0006537437438964844,
0.00763702392578125,
0.04095458984375,
0.007457733154296875,
0.006500244140625,
0.0153656005859375,
0.024261474609375,
0.00823974609375,
-0.0482177734375,
0.01605224609375,
0.0216217041015625,
0.01561737060546875,
0.0055389404296875,
-0.02276611328125,
-0.01454925537109375,
0.0234527587890625,
-0.005218505859375,
-0.0279693603515625,
-0.00611114501953125,
0.014862060546875,
0.003459930419921875,
0.00917816162109375,
0.007686614990234375,
0.026947021484375,
-0.013763427734375,
0.00818634033203125,
0.01369476318359375,
0.0074920654296875,
-0.01111602783203125,
-0.0330810546875,
-0.00402069091796875,
0.047119140625,
0.01241302490234375,
0.01328277587890625,
0.0119476318359375,
-0.00281524658203125,
-0.028076171875,
-0.0224761962890625,
0.00057220458984375,
0.0601806640625,
0.00025391578674316406,
0.038482666015625,
-0.0284423828125,
-0.004192352294921875,
0.0220184326171875,
0.003692626953125,
0.01401519775390625,
0.036041259765625,
0.003208160400390625,
0.0248260498046875,
-0.03961181640625,
0.005779266357421875,
-0.04559326171875,
0.0211334228515625,
-0.01056671142578125,
0.0210418701171875,
0.002216339111328125,
-0.017852783203125,
0.00860595703125,
-0.0234222412109375,
-0.028350830078125,
-0.00606536865234375,
0.00852203369140625,
0.0006613731384277344,
-0.0090789794921875,
-0.03497314453125,
-0.0154266357421875,
0.028533935546875,
0.0137939453125,
0.041229248046875,
-0.0040740966796875,
0.01087188720703125,
0.0263214111328125,
-0.05010986328125,
-0.022186279296875,
-0.035003662109375,
0.01441192626953125,
0.0075531005859375,
-0.0120086669921875,
-0.0027179718017578125,
0.007389068603515625,
0.0197906494140625,
0.0148773193359375,
0.01447296142578125,
0.0150146484375,
0.0085906982421875,
0.00411224365234375,
-0.015716552734375,
-0.0173797607421875,
0.0012111663818359375,
-0.006092071533203125,
-0.044891357421875,
-0.03961181640625,
-0.0367431640625,
-0.0210113525390625,
0.0164031982421875,
0.0039215087890625,
0.0068511962890625,
0.0019931793212890625,
-0.0450439453125,
-0.0031642913818359375,
0.00543212890625,
-0.01959228515625,
-0.0357666015625,
-0.0183868408203125,
-0.007350921630859375,
-0.005298614501953125,
0.0068511962890625,
-0.0185546875,
-0.01165771484375,
-0.02081298828125,
0.0159759521484375,
-0.0008249282836914062,
0.04339599609375,
-0.00545501708984375,
0.0186767578125,
-0.01062774658203125,
-0.0131378173828125,
0.00611114501953125,
0.01453399658203125,
0.03607177734375,
0.0283355712890625,
-0.01029205322265625,
-0.038360595703125,
0.0107421875,
-0.0293731689453125,
-0.0070648193359375,
-0.0205535888671875,
-0.01500701904296875,
0.0280914306640625,
0.040191650390625,
-0.001811981201171875,
-0.01363372802734375,
-0.018035888671875,
-0.007038116455078125,
-0.026763916015625,
0.005275726318359375,
0.020050048828125,
0.0101776123046875,
-0.0152740478515625,
0.03179931640625,
-0.0304718017578125,
0.0036144256591796875,
-0.024200439453125,
-0.023681640625,
-0.048828125,
-0.008636474609375,
-0.0285186767578125,
-0.00708770751953125,
-0.01025390625,
-0.01544189453125,
0.02178955078125,
-0.022247314453125,
0.01117706298828125,
-0.010711669921875,
0.01314544677734375,
0.016265869140625,
0.00537872314453125,
-0.02691650390625,
0.01055145263671875,
-0.0239105224609375,
0.0301513671875,
-0.0379638671875,
-0.01318359375,
0.0219573974609375,
0.024261474609375,
-0.00882720947265625,
-0.001689910888671875,
0.03607177734375,
0.003734588623046875,
0.030792236328125,
0.013031005859375,
-0.0165863037109375,
0.004016876220703125,
-0.01165008544921875,
0.01441192626953125,
-0.00677490234375,
0.02130126953125,
-0.027557373046875,
0.0094757080078125,
0.0007781982421875,
-0.0406494140625,
-0.010498046875,
0.0012502670288085938,
0.0163421630859375,
0.004467010498046875,
0.0106048583984375,
-0.02264404296875,
-0.0025424957275390625,
-0.042816162109375,
0.0311431884765625,
0.0061798095703125,
-0.01464080810546875,
-0.044342041015625,
-0.0011749267578125,
0.004894256591796875,
0.0236358642578125,
-0.03509521484375,
0.00750732421875,
0.004741668701171875,
-0.0408935546875,
0.0010175704956054688,
-0.01235198974609375,
-0.016326904296875,
0.0018157958984375,
0.01486968994140625,
-0.01174163818359375,
-0.01006317138671875,
-0.0251617431640625,
0.013641357421875,
0.0027942657470703125,
0.00897216796875,
-0.007965087890625,
0.0282135009765625,
-0.0035610198974609375,
0.0178985595703125,
0.0096893310546875,
-0.0096435546875,
0.004909515380859375,
0.0080718994140625,
-0.0018072128295898438,
0.0384521484375,
-0.01064300537109375,
0.00145721435546875,
0.0081787109375,
0.015533447265625,
-0.03204345703125,
0.0382080078125,
-0.004329681396484375,
-0.0022296905517578125,
-0.0221405029296875,
-0.0173492431640625,
-0.01026153564453125,
0.02783203125,
-0.036102294921875,
-0.02447509765625,
-0.0219573974609375,
0.037750244140625,
0.024444580078125,
0.018829345703125,
-0.008758544921875,
0.0091552734375,
-0.011199951171875,
0.006626129150390625,
-0.0185394287109375,
-0.0194091796875,
-0.01517486572265625,
-0.01971435546875,
-0.01195526123046875,
0.0071258544921875,
-0.0139007568359375,
0.0202178955078125,
-0.0016222000122070312,
0.0308380126953125,
-0.016845703125,
0.0253753662109375,
0.003818511962890625,
0.0340576171875,
-0.00574493408203125,
0.0027942657470703125,
0.0019025802612304688,
-0.0167999267578125,
-0.019317626953125,
0.0170440673828125,
-0.01389312744140625,
0.01104736328125,
-0.0059967041015625,
-0.0024051666259765625,
0.011871337890625,
0.005130767822265625,
-0.003910064697265625,
-0.0231475830078125,
0.00049591064453125,
0.01531219482421875,
0.0200347900390625,
-0.03179931640625,
0.00681304931640625,
0.007572174072265625,
-0.027618408203125,
-0.0268402099609375,
-0.003681182861328125,
0.01232147216796875,
-0.0107879638671875,
-0.00106048583984375,
0.0250091552734375,
0.01220703125,
-0.022705078125,
-0.004459381103515625,
-0.0209808349609375,
-0.0108489990234375,
0.0307159423828125,
0.0172271728515625,
-0.023590087890625,
-0.0016012191772460938,
0.0280914306640625,
0.005901336669921875,
0.013519287109375,
0.00853729248046875,
0.009613037109375,
0.004547119140625,
0.04034423828125,
-0.0111846923828125,
-0.031829833984375,
0.026519775390625,
0.0054473876953125,
-0.0179290771484375,
0.031280517578125,
-0.02655029296875,
-0.0064697265625,
0.0036144256591796875,
-0.0225830078125,
0.003971099853515625,
-0.0160064697265625,
0.0036163330078125,
-0.019287109375,
-0.02215576171875,
0.0150909423828125,
-0.00765228271484375,
0.00421142578125,
-0.026885986328125,
-0.059906005859375,
-0.0118865966796875,
-0.01629638671875,
0.033538818359375,
-0.027587890625,
-0.0242156982421875,
-0.05377197265625,
-0.006290435791015625,
-0.002536773681640625,
0.007213592529296875,
0.0307464599609375,
0.00913238525390625,
0.0181732177734375,
0.01116943359375,
0.0380859375,
0.0064849853515625,
-0.021942138671875,
-0.0068206787109375,
-0.0178985595703125,
-0.003208160400390625,
0.0246734619140625,
0.0017423629760742188,
-0.01413726806640625,
-0.0018396377563476562,
0.00667572021484375,
-0.035308837890625,
0.03619384765625,
-0.01080322265625,
-0.02557373046875,
0.0009317398071289062,
-0.0021228790283203125,
0.00609588623046875,
0.01313018798828125,
-0.0164794921875,
-0.043182373046875,
-0.0184173583984375,
0.005374908447265625,
0.0305633544921875,
0.00872039794921875,
0.0058441162109375,
0.007350921630859375,
0.0231781005859375,
-0.00008338689804077148,
0.0233917236328125,
-0.01212310791015625,
0.0084381103515625,
0.0296173095703125,
0.00968170166015625,
-0.01134490966796875,
0.06201171875,
-0.0294952392578125,
0.00260162353515625,
0.005527496337890625,
0.0333251953125,
-0.01340484619140625,
-0.0004699230194091797,
0.01369476318359375,
-0.0300445556640625,
-0.01861572265625,
0.0005965232849121094,
0.00530242919921875,
-0.019989013671875,
0.00878143310546875,
-0.021514892578125,
0.003040313720703125,
0.000050008296966552734,
0.002666473388671875,
-0.0284881591796875,
-0.000858306884765625,
-0.03094482421875,
0.0174713134765625,
-0.046661376953125,
0.038726806640625,
-0.01126861572265625,
0.00608062744140625,
0.01020050048828125,
-0.036224365234375,
-0.004642486572265625,
-0.0027618408203125,
0.002384185791015625,
0.0023670196533203125,
0.015594482421875,
-0.031646728515625,
0.0006017684936523438,
-0.028045654296875,
-0.013336181640625,
0.01367950439453125,
0.003963470458984375,
-0.01372528076171875,
-0.0005145072937011719,
-0.0238189697265625,
0.006084442138671875,
0.01517486572265625,
-0.03607177734375,
0.00814056396484375,
-0.005992889404296875,
0.0204620361328125,
-0.035369873046875,
0.0124969482421875,
-0.0015459060668945312,
0.0118560791015625,
0.0017080307006835938,
0.01099395751953125,
-0.0005679130554199219,
0.005191802978515625,
0.01361846923828125,
-0.021514892578125,
-0.0200347900390625,
-0.0086517333984375,
0.007389068603515625,
-0.004367828369140625,
0.0016193389892578125,
0.00673675537109375,
0.0024433135986328125,
-0.004329681396484375,
0.01239013671875,
0.0113525390625,
0.044830322265625,
-0.008941650390625,
0.0031185150146484375,
0.016571044921875,
0.0175628662109375,
0.0203399658203125,
-0.0277099609375,
-0.005977630615234375,
-0.0185089111328125,
0.023223876953125,
-0.01666259765625,
-0.01392364501953125,
0.00009417533874511719,
0.01082611083984375,
-0.006130218505859375,
0.005504608154296875,
0.020233154296875,
0.03289794921875,
-0.0207672119140625,
-0.0182037353515625,
0.01226806640625,
0.01617431640625,
0.00643157958984375,
0.0304718017578125,
0.0018491744995117188,
0.030517578125,
0.0008687973022460938,
0.017364501953125,
0.004520416259765625,
0.038482666015625,
-0.00972747802734375,
0.00841522216796875,
-0.004482269287109375,
0.03997802734375,
-0.0235443115234375,
0.01226043701171875,
-0.005970001220703125,
0.004180908203125,
-0.04071044921875,
0.014373779296875,
-0.004474639892578125,
0.012664794921875,
0.00014710426330566406,
0.027069091796875,
0.0006375312805175781,
-0.0316162109375,
-0.025604248046875,
0.0288238525390625,
0.050994873046875,
0.036712646484375,
0.01544952392578125,
0.06927490234375,
-0.0181884765625,
-0.015899658203125,
-0.01861572265625,
-0.02996826171875,
-0.00310516357421875,
-0.011322021484375,
-0.036407470703125,
0.042633056640625,
0.008026123046875,
-0.01529693603515625,
-0.0025196075439453125,
0.0362548828125,
-0.0124053955078125,
0.0002084970474243164,
0.02105712890625,
-0.017242431640625,
-0.033905029296875,
0.027008056640625,
-0.0235595703125,
-0.01497650146484375,
-0.0260772705078125,
-0.02215576171875,
0.0259857177734375,
-0.0265960693359375,
0.040313720703125,
0.0035457611083984375,
-0.0322265625,
0.009918212890625,
-0.0010099411010742188,
-0.005252838134765625,
-0.030548095703125,
-0.03857421875,
-0.0028896331787109375,
-0.0167388916015625,
0.0234222412109375,
0.0018596649169921875,
-0.004726409912109375,
-0.0011806488037109375,
-0.0006427764892578125,
-0.028594970703125,
-0.0190277099609375,
-0.01065826416015625,
-0.0168304443359375,
0.015289306640625,
0.00640106201171875,
0.00574493408203125,
-0.0207061767578125,
0.00510406494140625,
-0.00957489013671875,
0.01552581787109375,
-0.0169219970703125,
0.00572967529296875,
0.033203125,
-0.02301025390625,
-0.043365478515625,
0.02252197265625,
-0.033416748046875,
0.0218658447265625,
-0.0018796920776367188,
0.0167083740234375,
-0.020721435546875,
-0.02105712890625,
0.006175994873046875,
-0.01702880859375,
0.003932952880859375,
0.0116119384765625,
-0.0290985107421875,
-0.03155517578125,
0.0230712890625,
-0.026947021484375,
-0.0209503173828125,
-0.039276123046875,
-0.04742431640625,
0.01430511474609375,
0.005329132080078125,
0.023468017578125,
0.0157928466796875,
0.018280029296875,
-0.0182952880859375,
-0.0153961181640625,
-0.00421905517578125,
-0.004337310791015625,
0.01751708984375,
0.01488494873046875,
-0.00046443939208984375,
0.0223541259765625,
-0.004405975341796875,
-0.00699615478515625,
-0.0175323486328125,
0.02130126953125,
-0.00881195068359375,
0.0180816650390625,
-0.0269775390625,
-0.0098114013671875,
-0.022613525390625,
-0.044525146484375,
-0.0013494491577148438,
0.038665771484375,
0.01245880126953125,
-0.00469207763671875,
0.01251220703125,
0.011962890625,
-0.057891845703125,
0.017059326171875,
-0.00026226043701171875,
-0.01416778564453125,
0.052215576171875,
-0.0284576416015625,
-0.026153564453125,
-0.01445770263671875,
-0.03570556640625,
-0.0013494491577148438,
-0.003101348876953125,
0.05224609375,
-0.007701873779296875,
0.0106048583984375,
0.01219940185546875,
-0.0011358261108398438,
0.00659942626953125,
-0.018951416015625,
-0.000782012939453125,
-0.01267242431640625,
-0.0189666748046875,
0.0215911865234375,
-0.00930023193359375,
-0.004962921142578125,
-0.0258026123046875,
0.04766845703125,
-0.017852783203125,
-0.00605010986328125,
0.02154541015625,
-0.055694580078125,
-0.017791748046875,
-0.0232086181640625,
0.006702423095703125,
-0.01763916015625,
-0.0027923583984375,
0.0018987655639648438,
-0.01093292236328125,
-0.023162841796875,
-0.003795623779296875,
0.01934814453125,
-0.0140380859375,
-0.0037479400634765625,
-0.01457977294921875,
-0.0177459716796875,
0.0239105224609375,
-0.01019287109375,
-0.006916046142578125,
-0.0008187294006347656,
0.005176544189453125,
-0.019378662109375,
-0.026580810546875,
-0.021697998046875,
0.0193328857421875,
-0.005329132080078125,
-0.01012420654296875,
0.02587890625,
-0.00292205810546875,
-0.00324249267578125,
-0.0137786865234375,
-0.0008606910705566406,
-0.0104827880859375,
-0.0087738037109375,
0.01277923583984375,
-0.0097503662109375,
-0.005344390869140625,
-0.027313232421875,
-0.03900146484375,
-0.0205230712890625,
-0.0318603515625,
0.0011720657348632812,
0.01093292236328125,
0.0025482177734375,
0.0118408203125,
-0.0165557861328125,
-0.0005865097045898438,
0.0016202926635742188,
-0.0032863616943359375,
-0.001705169677734375,
-0.000152587890625,
-0.036041259765625,
0.0221710205078125,
0.021087646484375,
0.006374359130859375,
-0.032012939453125,
-0.0083160400390625,
0.019775390625,
0.001720428466796875,
-0.0139923095703125,
0.0014524459838867188,
-0.0226898193359375,
0.0014362335205078125,
-0.000408172607421875,
-0.005947113037109375,
-0.0175628662109375,
-0.01213836669921875,
0.01319122314453125,
-0.020233154296875,
0.013519287109375,
0.007701873779296875,
0.0076141357421875,
0.00618743896484375,
0.004638671875,
0.01445770263671875,
-0.029205322265625,
0.0230865478515625,
0.006717681884765625,
0.004199981689453125,
0.025299072265625,
0.001979827880859375,
0.0087890625,
0.043853759765625,
-0.041839599609375,
0.00955963134765625,
-0.006130218505859375,
-0.008941650390625,
0.0247650146484375,
-0.01287078857421875,
-0.0080108642578125,
-0.01016998291015625,
0.0095367431640625,
-0.040679931640625,
0.004421234130859375,
0.005229949951171875,
-0.00682830810546875,
0.02703857421875,
-0.0004165172576904297,
-0.01383209228515625,
-0.0040740966796875,
-0.0197296142578125,
0.0293426513671875,
-0.0137939453125,
-0.03125,
0.03057861328125,
-0.02154541015625,
0.0267181396484375,
-0.005207061767578125,
0.014495849609375,
0.0026111602783203125,
0.000579833984375,
-0.01409149169921875,
-0.0428466796875,
0.00850677490234375,
0.0011014938354492188,
0.0103607177734375,
-0.0137786865234375,
0.00933074951171875,
-0.0099334716796875,
-0.006961822509765625,
0.01317596435546875,
-0.0257568359375,
0.0081939697265625,
-0.0038585662841796875,
-0.020660400390625,
0.018585205078125,
-0.045135498046875,
-0.040802001953125,
-0.0005855560302734375,
0.023101806640625,
0.02850341796875,
0.0211334228515625,
-0.0206756591796875,
0.01251983642578125,
0.0034389495849609375,
0.00888824462890625,
0.019775390625,
-0.025726318359375,
0.0113525390625,
0.0168914794921875,
0.01212310791015625,
-0.0163726806640625,
-0.004055023193359375,
0.02618408203125,
0.0071563720703125,
-0.01212310791015625,
0.02825927734375,
0.009033203125,
-0.0005178451538085938,
0.006748199462890625,
-0.0036869049072265625,
0.03204345703125,
-0.003108978271484375,
0.033111572265625,
0.00067901611328125,
0.0165863037109375,
-0.012542724609375,
0.0302276611328125,
-0.0194854736328125,
-0.0259857177734375,
-0.0140533447265625,
-0.0255889892578125,
0.0034084320068359375,
-0.006664276123046875,
0.00156402587890625,
0.024261474609375,
0.00873565673828125,
0.0157012939453125,
0.0022296905517578125,
0.00001615285873413086,
0.0049591064453125,
0.01187896728515625,
-0.0008091926574707031,
-0.0009379386901855469,
0.00930023193359375,
0.02655029296875,
-0.01137542724609375,
-0.0306396484375,
-0.0018243789672851562,
0.0113677978515625,
-0.0262451171875,
-0.009429931640625,
0.015960693359375,
-0.021087646484375,
0.0239410400390625,
0.0089569091796875,
-0.023529052734375,
-0.007724761962890625,
-0.03131103515625,
0.00402069091796875,
-0.00441741943359375,
0.006366729736328125,
0.035797119140625,
0.00807952880859375,
0.00951385498046875,
0.021636962890625,
-0.020904541015625,
-0.024993896484375,
0.0093841552734375,
0.01430511474609375,
0.0002455711364746094,
-0.0330810546875,
-0.00991058349609375,
-0.01013946533203125,
-0.0002884864807128906,
-0.04071044921875,
0.0025997161865234375,
0.00041222572326660156,
-0.035308837890625,
-0.002979278564453125,
0.007396697998046875,
-0.00415802001953125,
0.0010786056518554688,
0.02056884765625,
-0.00396728515625,
0.001712799072265625,
-0.024444580078125,
-0.0056610107421875,
0.0019283294677734375,
0.0277862548828125,
0.010009765625,
-0.0006589889526367188,
0.0034275054931640625,
0.0016031265258789062,
0.00537109375,
-0.03253173828125,
0.0338134765625,
0.00421142578125,
-0.00659942626953125,
-0.0153045654296875,
-0.021026611328125,
-0.01044464111328125,
0.0100250244140625,
0.0243682861328125,
0.017730712890625,
0.010589599609375,
-0.0006012916564941406,
-0.008544921875,
-0.00437164306640625,
0.0058135986328125,
0.013763427734375,
0.02288818359375,
-0.0189666748046875,
0.018707275390625,
-0.0039215087890625,
-0.011260986328125,
0.004573822021484375,
0.031494140625,
0.000029265880584716797,
0.0018024444580078125,
0.00299072265625,
0.01000213623046875,
-0.0160980224609375,
-0.0011072158813476562,
-0.002780914306640625,
-0.01517486572265625,
0.0021762847900390625,
-0.02655029296875,
-0.0012054443359375,
0.00981903076171875,
0.0024127960205078125,
-0.013397216796875,
0.001720428466796875,
-0.02734375,
-0.0082550048828125,
-0.013763427734375,
0.012054443359375,
0.01508331298828125,
-0.0195770263671875,
0.004337310791015625,
-0.017547607421875,
0.01256561279296875,
0.0208892822265625,
0.0118255615234375,
0.01047515869140625,
-0.004680633544921875,
0.04052734375,
-0.019866943359375,
0.027435302734375,
-0.002490997314453125,
-0.0178985595703125,
-0.0246429443359375,
0.0011091232299804688,
0.00254058837890625,
0.03814697265625,
0.00644683837890625,
-0.02655029296875,
-0.0020122528076171875,
0.00513458251953125,
0.0176239013671875,
0.015411376953125,
0.01245880126953125,
0.0007028579711914062,
-0.030364990234375,
0.004680633544921875,
-0.006649017333984375,
0.00014698505401611328,
-0.0110321044921875,
0.013702392578125,
-0.016357421875,
-0.01080322265625,
0.003131866455078125,
-0.03106689453125,
0.03076171875,
0.0023250579833984375,
-0.0201873779296875,
0.007572174072265625,
0.0299835205078125,
-0.031951904296875,
0.00756072998046875,
-0.004840850830078125,
0.007720947265625,
-0.004779815673828125,
-0.0027942657470703125,
0.00920867919921875,
0.0022296905517578125,
0.004878997802734375,
0.0016756057739257812,
-0.0001512765884399414,
0.003887176513671875,
-0.002864837646484375,
0.0018482208251953125,
0.0012884140014648438,
0.015472412109375,
-0.01233673095703125,
0.006427764892578125,
0.032012939453125,
-0.0298004150390625,
0.0259552001953125,
0.015411376953125,
-0.0035495758056640625,
0.0011386871337890625,
0.0006113052368164062,
-0.00667572021484375,
-0.046142578125,
0.0167083740234375,
0.03839111328125,
-0.0213165283203125,
-0.01087188720703125,
0.019378662109375,
0.01047515869140625,
-0.031829833984375,
0.005512237548828125,
0.04443359375,
0.0206756591796875,
0.015167236328125,
-0.01508331298828125,
0.024993896484375,
0.007068634033203125,
0.0078887939453125,
0.03350830078125,
-0.014862060546875,
0.03082275390625,
-0.03289794921875,
-0.0095367431640625,
-0.0194854736328125,
-0.0037975311279296875,
-0.0208282470703125,
0.033782958984375,
-0.031768798828125,
0.01023101806640625,
-0.044769287109375,
0.002544403076171875,
0.0235137939453125,
-0.007762908935546875,
0.0024585723876953125,
0.033294677734375,
0.006381988525390625,
0.0204620361328125,
-0.005664825439453125,
0.0177459716796875,
0.048370361328125,
-0.0026607513427734375,
0.0045166015625,
0.0173187255859375,
0.01480865478515625,
0.03045654296875,
0.002582550048828125,
-0.035400390625,
0.03961181640625,
-0.023895263671875,
0.00978851318359375,
-0.03143310546875,
0.017425537109375,
0.01293182373046875,
0.022216796875,
0.022552490234375,
-0.028350830078125,
-0.0261383056640625,
-0.04217529296875,
0.00356292724609375,
0.004940032958984375,
-0.006305694580078125,
0.028533935546875,
0.01422882080078125,
-0.03118896484375,
-0.0364990234375,
-0.0220184326171875,
0.036895751953125,
-0.041717529296875,
0.038543701171875,
-0.021697998046875,
0.0008077621459960938,
-0.046722412109375,
0.0223388671875,
0.0097198486328125,
0.0293731689453125,
0.00618743896484375,
-0.00208282470703125,
-0.007366180419921875,
0.00588226318359375,
0.0033550262451171875,
-0.01363372802734375,
0.0189208984375,
-0.0268402099609375,
0.0219879150390625,
-0.0347900390625,
-0.025360107421875,
0.011962890625,
0.01158905029296875,
-0.0023059844970703125,
-0.00302886962890625,
0.00527191162109375,
0.00899505615234375,
-0.048370361328125,
0.006351470947265625,
0.0191192626953125,
0.0020809173583984375,
-0.005092620849609375,
0.04205322265625,
-0.0010595321655273438,
-0.0523681640625,
0.0040740966796875,
0.004657745361328125,
-0.0289154052734375,
-0.042724609375,
0.0374755859375,
-0.038604736328125,
0.0223541259765625,
-0.01313018798828125,
0.032135009765625,
0.0204010009765625,
0.031463623046875,
0.004642486572265625,
-0.00855255126953125,
0.005367279052734375,
-0.00018274784088134766,
0.024322509765625,
-0.039459228515625,
0.007755279541015625,
-0.005794525146484375,
0.01494598388671875,
0.004650115966796875,
0.0275726318359375,
-0.0205841064453125,
0.016021728515625,
0.015533447265625,
-0.0213470458984375,
-0.00977325439453125,
0.007236480712890625,
0.01690673828125,
0.0072021484375,
0.00469970703125,
0.0174407958984375,
0.01029205322265625,
-0.02813720703125,
0.00042891502380371094,
-0.014373779296875,
0.0093994140625,
-0.000888824462890625,
-0.0149383544921875,
0.0218658447265625,
0.021209716796875,
0.026580810546875,
0.034027099609375,
0.00995635986328125,
0.009918212890625,
0.013916015625,
-0.01268768310546875,
-0.04254150390625,
0.01715087890625,
0.016265869140625,
0.048736572265625,
-0.00714111328125,
-0.0293731689453125,
0.0006809234619140625,
0.007801055908203125,
-0.00910186767578125,
0.0006580352783203125,
0.00016570091247558594,
-0.00202178955078125,
0.0045318603515625,
-0.016326904296875,
0.00836181640625,
0.02618408203125,
0.0222320556640625,
-0.01055908203125,
-0.0135498046875,
0.048248291015625,
-0.01245880126953125,
0.0169219970703125,
-0.036468505859375,
0.0187225341796875,
-0.029937744140625,
-0.036285400390625,
0.0120391845703125,
-0.0004627704620361328,
-0.006107330322265625,
-0.00815582275390625,
-0.000568389892578125,
0.006343841552734375,
0.01412200927734375,
-0.0433349609375,
-0.025421142578125,
0.0006060600280761719,
-0.0224609375,
-0.03887939453125,
0.0090789794921875,
-0.0001779794692993164,
0.00981903076171875,
-0.00426483154296875,
0.019500732421875,
0.0438232421875,
0.00969696044921875,
0.01313018798828125,
0.00897216796875,
-0.00540924072265625,
0.00885009765625,
-0.017822265625,
-0.00363922119140625,
0.011627197265625,
-0.0007495880126953125,
-0.0013151168823242188,
-0.0124664306640625,
-0.006805419921875,
-0.039306640625,
-0.0186920166015625,
-0.00025272369384765625,
0.0172882080078125,
0.01605224609375,
-0.00021409988403320312,
-0.015899658203125,
-0.003528594970703125,
-0.01451873779296875,
-0.01122283935546875,
-0.007293701171875,
-0.00655364990234375,
0.007038116455078125,
-0.0217132568359375,
0.00893402099609375,
0.003787994384765625,
-0.002613067626953125,
0.004974365234375,
-0.0364990234375,
0.0024852752685546875,
-0.004901885986328125,
0.0019044876098632812,
0.01535797119140625,
-0.0018787384033203125,
-0.0350341796875,
-0.003963470458984375,
-0.02020263671875,
0.005313873291015625,
0.005863189697265625,
0.0167083740234375,
-0.01922607421875,
-0.011749267578125,
-0.006870269775390625,
-0.0279388427734375,
0.01312255859375,
0.0164337158203125,
0.025177001953125,
-0.00860595703125,
-0.00664520263671875,
-0.01294708251953125,
0.01482391357421875,
-0.01317596435546875,
0.01161956787109375,
-0.033905029296875,
0.00504302978515625,
0.00213623046875,
-0.0255584716796875,
-0.06011962890625,
-0.00815582275390625,
-0.00743865966796875,
-0.005916595458984375,
-0.004238128662109375,
0.01141357421875,
-0.0114593505859375,
0.0090484619140625,
-0.007434844970703125,
-0.024932861328125,
0.00829315185546875,
0.00904083251953125,
0.0264892578125,
0.00946044921875,
-0.0034847259521484375,
-0.03759765625,
0.037200927734375,
-0.01222991943359375,
0.0031337738037109375,
-0.00298309326171875,
-0.007472991943359375,
0.02740478515625,
-0.016998291015625,
-0.027923583984375,
-0.00984954833984375,
-0.00946807861328125,
0.006870269775390625,
-0.008575439453125,
0.022308349609375,
-0.01436614990234375,
0.04364013671875,
0.0237884521484375,
-0.00811004638671875,
0.00390625,
0.0186309814453125,
-0.0014171600341796875,
0.0021343231201171875,
-0.008575439453125,
-0.0122528076171875,
-0.01033782958984375,
-0.00983428955078125,
0.0090179443359375,
0.03717041015625,
0.025482177734375,
-0.004791259765625,
0.00756072998046875,
0.03753662109375,
0.0027484893798828125,
0.002483367919921875,
0.01061248779296875,
-0.006336212158203125,
0.0032711029052734375,
0.01165008544921875,
0.018402099609375,
0.02978515625,
0.0009436607360839844,
0.004016876220703125,
0.011993408203125,
0.030517578125,
-0.0094451904296875,
-0.0127716064453125,
0.02679443359375,
-0.010986328125,
0.0233917236328125,
0.0295867919921875,
-0.02252197265625,
-0.0064239501953125,
0.021942138671875,
0.00884246826171875,
0.00952911376953125,
0.00978851318359375,
-0.004123687744140625,
0.0270843505859375,
0.004711151123046875,
0.006855010986328125,
0.0174713134765625,
-0.0230255126953125,
-0.025146484375,
-0.01233673095703125,
0.016815185546875,
-0.031005859375,
0.03216552734375,
-0.03692626953125,
0.01439666748046875,
-0.0289764404296875,
-0.00576019287109375,
0.018096923828125,
0.0083160400390625,
-0.015380859375,
-0.01371002197265625,
0.016937255859375,
0.0205841064453125,
-0.0261688232421875,
-0.035430908203125,
0.005565643310546875,
0.01152801513671875,
0.0104217529296875,
-0.0028362274169921875,
0.022979736328125,
0.003055572509765625,
-0.0208282470703125,
0.021087646484375,
-0.0250396728515625,
-0.0017309188842773438,
-0.01904296875,
-0.002277374267578125,
0.00627899169921875,
0.011199951171875,
-0.0238800048828125,
0.042205810546875,
0.034271240234375,
0.0023632049560546875,
-0.04278564453125,
-0.0014019012451171875,
-0.02978515625,
-0.041961669921875,
-0.03228759765625,
0.01947021484375,
-0.00421905517578125,
-0.01495361328125,
-0.0133819580078125,
0.00345611572265625,
0.0272369384765625,
0.042266845703125,
0.00981903076171875,
-0.03759765625,
0.006687164306640625,
-0.011322021484375,
0.00385284423828125,
-0.0516357421875,
0.0209197998046875,
0.0038776397705078125,
-0.0261688232421875,
0.006649017333984375,
0.009307861328125,
-0.004253387451171875,
0.00771331787109375,
0.027496337890625,
0.01348876953125,
0.002239227294921875,
-0.013458251953125,
0.0118865966796875,
0.0057830810546875,
0.005931854248046875,
-0.003631591796875,
-0.0589599609375,
0.0171966552734375,
-0.0121612548828125,
0.02508544921875,
-0.033599853515625,
0.02337646484375,
0.0170135498046875,
-0.00341033935546875,
0.005519866943359375,
-0.0036563873291015625,
-0.01052093505859375,
0.007781982421875,
0.004970550537109375,
-0.009979248046875,
0.038543701171875,
-0.0037212371826171875,
-0.0458984375,
0.0059661865234375,
-0.01065826416015625,
-0.021087646484375,
-0.00951385498046875,
0.0302276611328125,
0.001125335693359375,
-0.0241546630859375,
0.01215362548828125,
0.036529541015625,
-0.004913330078125,
0.00695037841796875,
-0.005245208740234375,
-0.015716552734375,
-0.0280914306640625,
0.04034423828125,
-0.004405975341796875,
0.007541656494140625,
0.0213623046875,
-0.01251983642578125,
-0.0146026611328125,
0.0006670951843261719,
0.005096435546875,
-0.0038604736328125,
-0.0055694580078125,
0.041015625,
0.004283905029296875,
0.0006937980651855469,
0.006427764892578125,
0.00702667236328125,
0.032440185546875,
-0.00955963134765625,
0.0243072509765625,
0.01361846923828125,
-0.003040313720703125,
-0.0013103485107421875,
0.0228118896484375,
-0.003322601318359375,
-0.016143798828125,
-0.0167999267578125,
-0.00982666015625,
-0.0251922607421875,
0.00467681884765625,
-0.00374603271484375,
-0.0089569091796875,
0.006954193115234375,
0.00469207763671875,
-0.00988006591796875,
0.00972747802734375,
0.016754150390625,
-0.0229339599609375,
0.01071929931640625,
0.01198577880859375,
-0.006923675537109375,
0.0217437744140625,
-0.0265655517578125,
-0.0077972412109375,
0.00916290283203125,
-0.004062652587890625,
0.0269317626953125,
0.0244598388671875,
-0.00952911376953125,
0.0198516845703125,
-0.0112457275390625,
0.04052734375,
0.032501220703125,
-0.015594482421875,
0.00760650634765625,
0.02508544921875,
-0.01142120361328125,
0.0177001953125,
-0.0311279296875,
0.0269317626953125,
-0.0200042724609375,
0.03741455078125,
-0.01580810546875,
0.0261993408203125,
0.0302734375,
-0.01453399658203125,
0.00543975830078125,
0.0224151611328125,
0.0016317367553710938,
-0.0231781005859375,
-0.0011653900146484375,
-0.01544952392578125,
-0.0025348663330078125,
0.0386962890625,
0.0159454345703125,
-0.003101348876953125,
0.0283660888671875,
0.0008935928344726562,
-0.04534912109375,
0.042694091796875,
-0.0374755859375,
0.0033626556396484375,
0.00394439697265625,
-0.0093231201171875,
0.0094146728515625,
-0.006206512451171875,
0.0034770965576171875,
0.007297515869140625,
0.0300750732421875,
0.007396697998046875,
-0.0272979736328125,
-0.05145263671875,
0.016326904296875,
0.0127105712890625,
0.0285797119140625,
0.0194091796875,
-0.00864410400390625,
-0.0250091552734375,
-0.00826263427734375,
0.0005612373352050781,
0.01959228515625,
-0.0261383056640625,
-0.0203704833984375,
-0.0021209716796875,
0.0239105224609375,
0.021636962890625,
0.0155029296875,
0.0012025833129882812,
0.01904296875,
0.0006289482116699219,
0.0362548828125,
-0.000012159347534179688,
0.0118408203125,
-0.033935546875,
0.01073455810546875,
-0.031646728515625,
0.0070648193359375,
0.0031719207763671875,
-0.0177459716796875,
-0.01186370849609375,
-0.0182647705078125,
-0.00865936279296875,
-0.02801513671875,
-0.019775390625,
0.0042572021484375,
0.006198883056640625,
0.03631591796875,
-0.013824462890625,
-0.049774169921875,
0.0103759765625,
0.00506591796875,
0.044189453125,
0.00763702392578125,
0.015960693359375,
0.027099609375,
0.0291748046875,
0.02178955078125,
0.01183319091796875,
-0.01806640625,
0.03662109375,
-0.00782012939453125,
-0.0101165771484375,
-0.0239410400390625,
0.0137939453125,
-0.012359619140625,
0.01554107666015625,
0.0031223297119140625,
-0.0193634033203125,
0.024688720703125,
-0.0200042724609375,
0.0120697021484375,
-0.0289764404296875,
-0.0014982223510742188,
0.01036834716796875,
0.0124969482421875,
-0.016815185546875,
-0.02056884765625,
-0.0269317626953125,
0.0243377685546875,
-0.00820159912109375,
-0.024658203125,
0.009552001953125,
-0.0237579345703125,
0.0124969482421875,
-0.00730133056640625,
0.0029048919677734375,
-0.01690673828125,
0.039886474609375,
0.016571044921875,
-0.0400390625,
0.004665374755859375,
0.0072174072265625,
-0.034912109375,
0.0238189697265625,
-0.00800323486328125,
0.0210418701171875,
0.0294647216796875,
0.00907135009765625,
0.0086822509765625,
0.00868988037109375,
-0.017669677734375,
-0.0294342041015625,
0.0008893013000488281,
0.01117706298828125,
-0.003765106201171875,
-0.0018405914306640625,
0.01190185546875,
-0.019134521484375,
0.004474639892578125,
0.00598907470703125,
0.0253753662109375,
-0.0229949951171875,
-0.024993896484375,
0.00878143310546875,
-0.015106201171875,
0.00982666015625,
0.04150390625,
0.019500732421875,
-0.0160064697265625,
-0.010711669921875,
0.0004487037658691406,
-0.0038967132568359375,
0.01323699951171875,
0.05047607421875,
-0.02032470703125,
0.005069732666015625,
0.0218353271484375,
-0.022125244140625,
0.03887939453125,
0.01190948486328125,
0.0088958740234375,
-0.0203857421875,
0.0075225830078125,
0.0007929801940917969,
0.0131683349609375,
0.007549285888671875,
-0.0017719268798828125,
0.005992889404296875,
-0.03497314453125,
-0.0015735626220703125,
0.01727294921875,
0.0161895751953125,
0.0136566162109375,
-0.014556884765625,
0.01910400390625,
0.01212310791015625,
-0.00925445556640625,
0.036651611328125,
0.00016450881958007812,
0.0009493827819824219,
-0.0097808837890625,
0.0173492431640625,
-0.01007843017578125,
-0.00720977783203125,
0.01146697998046875,
-0.020843505859375,
0.0229644775390625,
0.0103912353515625,
0.0098114013671875,
0.05755615234375,
0.0067291259765625,
-0.003643035888671875,
-0.0260772705078125,
0.036285400390625,
-0.00714874267578125,
0.039031982421875,
-0.0110015869140625,
0.00417327880859375,
-0.002777099609375,
-0.0226593017578125,
0.002185821533203125,
0.01403045654296875,
0.01508331298828125,
-0.006343841552734375,
-0.030792236328125,
0.010528564453125,
-0.016845703125,
-0.00878143310546875,
-0.037567138671875,
-0.0225067138671875,
-0.0080413818359375,
-0.0103607177734375,
-0.004352569580078125,
-0.01288604736328125,
-0.018646240234375,
-0.0108184814453125,
0.0216064453125,
0.0024967193603515625,
-0.0007605552673339844,
0.00786590576171875,
0.00042247772216796875,
-0.0038661956787109375,
-0.005279541015625,
-0.0194549560546875,
0.026153564453125,
-0.01110076904296875,
-0.0185089111328125,
0.0270843505859375,
0.037261962890625,
0.007137298583984375,
-0.002231597900390625,
0.004154205322265625,
0.003513336181640625,
0.003231048583984375,
-0.0285186767578125,
-0.0132904052734375,
0.0218048095703125,
-0.01233673095703125,
0.032470703125,
0.00335693359375,
-0.006954193115234375,
0.0088348388671875,
0.023834228515625,
-0.005664825439453125,
0.0087890625,
0.007770538330078125,
-0.050506591796875,
-0.0174102783203125,
-0.01509857177734375,
0.034423828125,
-0.0005931854248046875,
0.00848388671875,
0.030303955078125,
-0.0088653564453125,
-0.0249481201171875,
0.005207061767578125,
0.00299835205078125,
0.03875732421875,
0.03399658203125,
-0.0262451171875,
-0.02001953125,
0.0105133056640625,
0.01010894775390625,
0.01332855224609375,
-0.03143310546875,
0.0264739990234375,
0.004161834716796875,
-0.035797119140625,
-0.0019283294677734375,
0.0259552001953125,
0.037017822265625,
-0.0214385986328125,
0.00693511962890625,
-0.00269317626953125,
0.0036449432373046875,
-0.007564544677734375,
0.0192413330078125,
-0.0191497802734375,
-0.0281524658203125,
-0.0136260986328125,
-0.00867462158203125,
-0.006229400634765625,
-0.0031795501708984375,
0.023468017578125,
0.0207061767578125,
-0.00041365623474121094,
-0.06109619140625,
-0.0078582763671875,
-0.001789093017578125,
0.0303497314453125,
0.004878997802734375,
-0.00904083251953125,
-0.0191192626953125,
0.0203094482421875,
-0.00582122802734375,
0.0201873779296875,
0.0012655258178710938,
0.0022640228271484375,
0.0107879638671875,
-0.0303192138671875,
-0.01068878173828125,
-0.01531219482421875,
0.02471923828125,
-0.0159454345703125,
-0.00199127197265625,
-0.012359619140625,
0.004787445068359375,
-0.005878448486328125,
0.0098114013671875,
0.0014486312866210938,
0.0281524658203125,
-0.0243072509765625,
-0.01532745361328125,
-0.039276123046875,
-0.026885986328125,
0.022735595703125,
0.037689208984375,
0.0036773681640625,
0.003795623779296875,
0.0282440185546875,
0.02960205078125,
0.0189666748046875,
-0.004535675048828125,
0.0190582275390625,
-0.01158905029296875,
-0.00824737548828125,
0.0308380126953125,
0.006923675537109375,
0.0308685302734375,
-0.003002166748046875,
-0.008758544921875,
-0.0032978057861328125,
0.0275726318359375,
0.019561767578125,
0.0242462158203125,
-0.0031642913818359375,
-0.0281829833984375,
-0.0032634735107421875,
-0.00019729137420654297,
0.00882720947265625,
-0.0006480216979980469,
-0.006557464599609375,
-0.00794219970703125,
0.0095062255859375,
-0.0352783203125,
0.00833892822265625,
0.0122528076171875,
-0.0012426376342773438,
0.01016998291015625,
-0.006076812744140625,
-0.0038661956787109375,
0.0251312255859375,
-0.01340484619140625,
0.006526947021484375,
-0.0012788772583007812,
0.0198822021484375,
-0.01078033447265625,
0.0163421630859375,
0.0246734619140625,
0.0183868408203125,
0.030029296875,
-0.007511138916015625,
0.013153076171875,
-0.0005064010620117188,
0.0148773193359375,
-0.0238189697265625,
0.026397705078125,
0.0162353515625,
-0.0189666748046875,
-0.0263519287109375,
0.0264892578125,
0.01128387451171875,
0.01342010498046875,
-0.0125579833984375,
0.027374267578125,
-0.0019521713256835938,
0.0108489990234375,
0.00827789306640625,
-0.05712890625,
0.01097869873046875,
0.00453948974609375,
-0.01123046875,
0.0135498046875,
-0.0062713623046875,
-0.001964569091796875,
-0.01336669921875,
-0.01372528076171875,
-0.0121002197265625,
-0.009429931640625,
0.0250701904296875,
-0.0257720947265625,
-0.01517486572265625,
-0.032073974609375,
-0.00998687744140625,
-0.0180511474609375,
-0.033599853515625,
0.00841522216796875,
0.0015659332275390625,
-0.00983428955078125,
0.004779815673828125,
0.006305694580078125,
-0.00690460205078125,
0.0260162353515625,
0.009796142578125,
-0.040924072265625,
-0.042510986328125,
-0.0263214111328125,
0.025787353515625,
0.007724761962890625,
0.0200347900390625,
0.01496124267578125,
0.003204345703125,
-0.0086517333984375,
-0.006008148193359375,
-0.01873779296875,
0.026611328125,
0.003520965576171875,
0.044219970703125,
-0.0302734375,
0.026702880859375,
-0.006694793701171875,
0.01367950439453125,
0.00868988037109375,
0.0129241943359375,
0.01073455810546875,
-0.0169219970703125,
-0.0118255615234375,
-0.0155181884765625,
0.0159454345703125,
-0.027984619140625,
-0.0274505615234375,
0.01065826416015625,
-0.01922607421875,
-0.02996826171875,
0.0099945068359375,
0.004215240478515625,
-0.02410888671875,
-0.01055145263671875,
-0.0021915435791015625,
0.0107269287109375,
0.006832122802734375,
-0.031219482421875,
0.0024204254150390625,
0.004734039306640625,
0.0034847259521484375,
0.0133514404296875,
-0.0184478759765625,
-0.0228729248046875,
-0.0012531280517578125,
0.004261016845703125,
0.0109405517578125,
-0.01485443115234375,
-0.0113983154296875,
-0.030181884765625,
-0.002422332763671875,
-0.012237548828125,
0.00724029541015625,
0.0347900390625,
0.0124053955078125,
0.024871826171875,
-0.026153564453125,
-0.009735107421875,
0.01506805419921875,
-0.01082611083984375,
-0.01094818115234375,
-0.006832122802734375,
0.03900146484375,
0.0298614501953125,
0.0352783203125,
0.01016998291015625,
0.02105712890625,
0.03887939453125,
-0.035247802734375,
-0.014404296875,
0.0169830322265625,
-0.02069091796875,
0.003917694091796875,
-0.0181884765625,
-0.023712158203125,
-0.01540374755859375,
0.0029239654541015625,
-0.004573822021484375,
0.0200042724609375,
0.0191650390625,
-0.018798828125,
0.006130218505859375,
0.001995086669921875,
0.02374267578125,
0.036163330078125,
-0.0294189453125,
-0.01276397705078125,
0.0091094970703125,
-0.0163421630859375,
-0.0186767578125,
0.0209503173828125,
0.01467132568359375,
-0.00901031494140625,
-0.0072174072265625,
-0.00798797607421875,
-0.015106201171875
] |
ours_526
|
The function \( f: \mathbb{Z}^{+} \rightarrow \mathbb{Z}^{+} \) has the following properties for all \( x, y \):
- \( f(x) \leq x^{2} \)
- \( f(f^{2}(x) f^{2}(y))=x y \) where \( f^{n}(x) \) denotes the \( n \)-th iterate of \( f \).
From the first property, we deduce that \( f(1)=1 \). Substituting \( y=1 \) into the second property gives us \( x = f(f^{2}(x) f^{2}(1)) = f^{3}(x) \) for all \( x \).
**Lemma 1.** \( f \) is a bijection.
*Proof.* If \( x \neq y \) and \( f(x) = f(y) \), then \( x = f^{3}(x) = f^{3}(y) = y \), a contradiction, so \( f \) is injective. Since \( f^{3}(x) = x \) for all \( x \), for every \( x \) there exists \( y = f^{2}(x) \) such that \( f(y) = x \), so \( f \) is surjective.
This means we can discuss the inverse function, \( f^{-1} \), and note that \( f^{-1} = f^{2} \).
**Lemma 2.** \( f(x) f(y) = f(x y) \) and \( f^{-1}(x) f^{-1}(y) = f^{-1}(x y) \) for all \( x, y \).
*Proof.* By the second property, \( f(f^{-1}(x) f^{-1}(y)) = f(f^{2}(x) f^{2}(y)) = x y \). Applying \( f^{-1} \) to both sides gives \( f^{-1}(x) f^{-1}(y) = f^{-1}(x y) \). This also holds for \( f \) itself: \( f(x) f(y) = f(f^{-1}(f(x) f(y))) = f(f^{-1}(f(x)) f^{-1}(f(y))) = f(x y) \).
In particular, if we know \( f(p) \) for all primes \( p \), then we know \( f(x) \) for all \( x \).
**Lemma 3.** If \( p \) is prime, then \( f(p) \) is prime.
*Proof.* Suppose \( f(p) = q r \) for some prime \( p \) and some product \( q r \) with \( q, r \geq 2 \). Then \( p = f^{-1}(q r) = f^{-1}(q) f^{-1}(r) \), so \( p \) is the product of two numbers greater than 1, a contradiction.
We can describe all possible \( f \) as a set of ordered triples of primes \( (p, q, r) \), defining \( f(p) = q, f(q) = r \), and \( f(r) = p \) (assuming \( p < q, r \)) such that every prime appears in at most one triple and for all triples, \( p^{4} \geq q^{2} \geq r \). If a prime \( s \) appears in no triple, then \( f(s) = s \).
**Lemma 4.** All such sets of triples describe a valid \( f \).
*Proof.* Consider any \( x = \prod p_{i} \) where each \( p_{i} \) is prime. \( f(x) = f\left(\prod p_{i}\right) = \prod f(p_{i}) \leq \prod p_{i}^{2} = x^{2} \), so \( f \) satisfies the first property. Let \( y = \prod q_{i} \) where each \( q_{i} \) is prime. \( f(x) f(y) = \left(\prod f(p_{i})\right)\left(\prod f(q_{i})\right) = f(x y) \), so \( f \) satisfies the second property.
We can now consider \( f(30) = f(2) f(3) f(5) \). We know \( f(2) \in \{2,3\} \). If \( f(2) = 3 \), then \( f(3) \in \{5,7\} \). If \( f(3) = 5 \) then \( f(5) = 2 \) and \( f(30) = 30 \); if \( f(3) = 7 \) then \( f(5) \in \{5,11,13,17,19,23\} \), each of which gives a new value for \( f(30) \). That's 7 values so far, all of them odd except for 30.
If \( f(2) = 2 \), then \( f(3) \in \{3,5,7\} \). Either way, \( f(5) \in \{5,7,11,13,17,19,23\} \), except:
- \( f(5) \neq 5 \) if \( f(3) = 5 \).
- \( f(5) \neq 7 \) if \( f(3) = 7 \).
- If \( f(3) = 3 \) and \( f(5) = 5 \) then \( f(30) = 30 \), which we've already counted.
- We count \( f(30) = 2 \cdot 5 \cdot 7 \) twice.
That's a total of \( 7 \cdot 3 - 4 = 17 \) more values, all of them even and none of them 30.
This makes \( 7 + 17 = 24 \) possible values.
\(\boxed{24}\)
|
24
|
{
"competition": "us_comps",
"dataset": "Ours",
"posts": null,
"source": "OMOSoln2-2.md"
}
|
\( f \) is a function from the set of positive integers to itself such that \( f(x) \leq x^{2} \) for all natural numbers \( x \), and \( f(f(f(x)) f(f(y)))=x y \) for all natural numbers \( x \) and \( y \). Find the number of possible values of \( f(30) \).
|
[
"/Mathematics/DiscreteMathematics/GeneralDiscreteMathematics/DiscreteMath",
"/Mathematics/DiscreteMathematics/GeneralDiscreteMathematics/DiscreteMathematics",
"/Mathematics/NumberTheory/GeneralNumberTheory/ElementaryMethods",
"/Mathematics/NumberTheory/GeneralNumberTheory/ElementaryNumberTheory",
"/Mathematics/NumberTheory/GeneralNumberTheory/HigherArithmetic",
"/Mathematics/NumberTheory/GeneralNumberTheory/NumberTheory",
"/Mathematics/NumberTheory/NumberTheoreticFunctions/IntegerFunctions",
"/Mathematics/NumberTheory/PrimeNumbers/PrimeFactorization"
] |
Use the condition f³ = identity to prove f is a bijection and multiplicative, forcing a permutation of primes in 3‑cycles, so f(30) depends only on choices for 2,3,5.
|
[
-0.000316619873046875,
0.007598876953125,
0.025146484375,
0.0083465576171875,
-0.001708984375,
-0.0046844482421875,
0.054290771484375,
0.006961822509765625,
0.01058197021484375,
-0.0182647705078125,
0.0264892578125,
-0.038909912109375,
0.0009784698486328125,
0.0128326416015625,
-0.007442474365234375,
-0.0170135498046875,
0.00475311279296875,
0.010955810546875,
0.0269317626953125,
-0.00917816162109375,
-0.01373291015625,
0.00628662109375,
-0.037200927734375,
0.0258331298828125,
-0.0321044921875,
-0.00690460205078125,
-0.0273895263671875,
-0.00980377197265625,
-0.029144287109375,
0.030731201171875,
0.0245513916015625,
-0.01110076904296875,
0.0096588134765625,
-0.0302886962890625,
0.004486083984375,
-0.0211639404296875,
-0.043212890625,
-0.0004115104675292969,
-0.04913330078125,
-0.034576416015625,
0.007678985595703125,
-0.00395965576171875,
0.0206451416015625,
0.03570556640625,
-0.01554107666015625,
-0.0037059783935546875,
0.0082550048828125,
-0.0008568763732910156,
-0.021514892578125,
0.00460052490234375,
-0.003406524658203125,
-0.001605987548828125,
-0.04010009765625,
-0.0202178955078125,
-0.0229339599609375,
-0.05975341796875,
-0.006267547607421875,
0.00624847412109375,
-0.00957489013671875,
0.00411224365234375,
-0.0010938644409179688,
-0.01267242431640625,
-0.032012939453125,
-0.01190185546875,
-0.006488800048828125,
-0.00583648681640625,
0.00000476837158203125,
0.0066375732421875,
0.015625,
-0.0019216537475585938,
0.0262298583984375,
-0.0169677734375,
-0.00502777099609375,
0.038360595703125,
0.028045654296875,
-0.016937255859375,
-0.01042938232421875,
0.01519012451171875,
0.036041259765625,
0.00801849365234375,
0.0168304443359375,
0.016998291015625,
0.0218505859375,
-0.021026611328125,
0.0173187255859375,
0.0037250518798828125,
0.02984619140625,
-0.01103973388671875,
-0.00485992431640625,
0.005260467529296875,
0.016082763671875,
0.02197265625,
-0.0090789794921875,
0.0178375244140625,
-0.0000737309455871582,
0.01458740234375,
-0.00951385498046875,
-0.00737762451171875,
-0.0244903564453125,
0.01273345947265625,
-0.0169830322265625,
0.00963592529296875,
0.03289794921875,
0.0021762847900390625,
-0.06011962890625,
-0.0213165283203125,
0.00048351287841796875,
-0.0017566680908203125,
-0.0197296142578125,
0.0019369125366210938,
0.0092010498046875,
-0.019134521484375,
0.05462646484375,
0.031707763671875,
0.00010246038436889648,
0.0082244873046875,
0.01351165771484375,
0.0275421142578125,
-0.0004987716674804688,
-0.00334930419921875,
-0.008514404296875,
0.01136016845703125,
0.00952911376953125,
0.0293121337890625,
0.00435638427734375,
0.008697509765625,
0.000705718994140625,
-0.021820068359375,
-0.040069580078125,
-0.0095062255859375,
0.006320953369140625,
0.00295257568359375,
-0.009368896484375,
-0.00949859619140625,
-0.04498291015625,
0.0117645263671875,
-0.0024700164794921875,
-0.005153656005859375,
-0.00498199462890625,
-0.004459381103515625,
-0.005359649658203125,
-0.0125274658203125,
0.00652313232421875,
-0.001811981201171875,
-0.0044403076171875,
-0.01068115234375,
-0.00701904296875,
-0.035247802734375,
0.0041656494140625,
-0.01258087158203125,
-0.0024394989013671875,
0.006954193115234375,
-0.0010690689086914062,
-0.0007638931274414062,
-0.00888824462890625,
0.0089111328125,
-0.0031528472900390625,
0.0049896240234375,
-0.004791259765625,
0.006153106689453125,
-0.0032329559326171875,
-0.001983642578125,
0.01336669921875,
0.009765625,
0.00714111328125,
-0.012725830078125,
0.0105743408203125,
-0.00989532470703125,
-0.0219573974609375,
-0.0189971923828125,
0.018707275390625,
-0.01276397705078125,
0.0038604736328125,
-0.03265380859375,
-0.002315521240234375,
-0.01192474365234375,
-0.0272064208984375,
0.0262908935546875,
-0.0100860595703125,
0.028594970703125,
0.00408935546875,
-0.01690673828125,
-0.0122222900390625,
0.0215301513671875,
-0.00571441650390625,
-0.02313232421875,
-0.01458740234375,
0.010284423828125,
0.00732421875,
-0.01119232177734375,
0.009368896484375,
0.0010738372802734375,
-0.0080413818359375,
0.01316070556640625,
-0.005542755126953125,
0.00434112548828125,
0.0036983489990234375,
-0.00682830810546875,
0.037139892578125,
0.02313232421875,
-0.004547119140625,
0.02630615234375,
-0.00833892822265625,
0.005096435546875,
-0.00402069091796875,
-0.0177001953125,
0.01922607421875,
-0.00884246826171875,
-0.00342559814453125,
0.006893157958984375,
0.004711151123046875,
-0.01134490966796875,
-0.0138092041015625,
-0.04083251953125,
-0.006420135498046875,
-0.00799560546875,
-0.027862548828125,
-0.0172882080078125,
0.0153350830078125,
-0.040557861328125,
-0.007518768310546875,
-0.006031036376953125,
-0.0024566650390625,
0.0009279251098632812,
-0.005130767822265625,
-0.00160980224609375,
0.0028896331787109375,
-0.0009860992431640625,
0.004177093505859375,
-0.0085601806640625,
0.0238800048828125,
0.01506805419921875,
-0.024383544921875,
0.0157012939453125,
0.0004477500915527344,
0.00318145751953125,
-0.00823974609375,
-0.01248931884765625,
0.0290679931640625,
-0.0198822021484375,
0.00975799560546875,
-0.0177001953125,
0.0001308917999267578,
0.006839752197265625,
0.0013055801391601562,
-0.0024509429931640625,
0.01166534423828125,
-0.01198577880859375,
-0.01323699951171875,
-0.03387451171875,
0.0283355712890625,
0.005107879638671875,
-0.0017347335815429688,
-0.00439453125,
-0.0022430419921875,
-0.004848480224609375,
0.0123291015625,
-0.0143890380859375,
-0.02740478515625,
0.01256561279296875,
0.00006705522537231445,
-0.02374267578125,
0.009307861328125,
0.0082244873046875,
-0.01953125,
0.00696563720703125,
0.01555633544921875,
0.0148773193359375,
-0.00255584716796875,
-0.0122528076171875,
0.033843994140625,
-0.0160369873046875,
0.005039215087890625,
0.006999969482421875,
0.0162506103515625,
-0.0098114013671875,
-0.0069580078125,
-0.003704071044921875,
0.005649566650390625,
-0.0135040283203125,
0.0210418701171875,
0.007274627685546875,
-0.01568603515625,
0.0141143798828125,
0.00595855712890625,
-0.0305328369140625,
0.0025920867919921875,
-0.00777435302734375,
-0.027496337890625,
0.0089874267578125,
0.00977325439453125,
-0.0030422210693359375,
-0.00628662109375,
-0.0277557373046875,
0.05902099609375,
0.0016374588012695312,
-0.0109710693359375,
0.00908660888671875,
-0.0204315185546875,
0.0033779144287109375,
0.02142333984375,
-0.0013875961303710938,
-0.025787353515625,
0.01401519775390625,
0.01678466796875,
0.0036411285400390625,
-0.0013141632080078125,
-0.00237274169921875,
-0.03717041015625,
-0.01088714599609375,
0.003559112548828125,
-0.023406982421875,
-0.00008147954940795898,
0.0032024383544921875,
-0.001171112060546875,
-0.037139892578125,
-0.0038776397705078125,
0.01473236083984375,
-0.01192474365234375,
-0.035858154296875,
0.004344940185546875,
-0.02581787109375,
-0.005859375,
0.013397216796875,
-0.01366424560546875,
0.01244354248046875,
0.00540924072265625,
-0.0000794529914855957,
-0.0513916015625,
0.016510009765625,
-0.017822265625,
0.03076171875,
-0.016387939453125,
-0.01751708984375,
-0.012603759765625,
-0.003971099853515625,
-0.0023670196533203125,
0.0113677978515625,
-0.00299072265625,
-0.019439697265625,
0.0033817291259765625,
-0.00946044921875,
0.035003662109375,
-0.04205322265625,
-0.0241241455078125,
0.0020465850830078125,
0.007587432861328125,
-0.00513458251953125,
-0.014801025390625,
-0.03155517578125,
0.0306549072265625,
0.020660400390625,
-0.0035152435302734375,
-0.00803375244140625,
-0.0291900634765625,
0.0152740478515625,
-0.0196990966796875,
-0.00421905517578125,
0.0295867919921875,
0.0071563720703125,
-0.01177978515625,
-0.0108642578125,
0.00066375732421875,
0.005664825439453125,
-0.0283203125,
-0.01009368896484375,
0.007106781005859375,
0.006771087646484375,
-0.0289459228515625,
0.0113525390625,
-0.01050567626953125,
-0.032379150390625,
0.018798828125,
-0.0172882080078125,
-0.0304718017578125,
0.0007190704345703125,
0.0015697479248046875,
-0.01532745361328125,
-0.005191802978515625,
0.01849365234375,
0.0166168212890625,
0.0163421630859375,
-0.0181884765625,
0.032440185546875,
-0.01410675048828125,
-0.032135009765625,
-0.006618499755859375,
-0.035400390625,
-0.0049285888671875,
0.0125732421875,
-0.019012451171875,
0.0015516281127929688,
-0.01306915283203125,
0.0008449554443359375,
-0.0457763671875,
-0.00574493408203125,
0.0034046173095703125,
0.028533935546875,
0.05712890625,
-0.024810791015625,
0.0010137557983398438,
0.005123138427734375,
-0.0284271240234375,
0.0248565673828125,
0.005702972412109375,
-0.004306793212890625,
-0.00907135009765625,
0.00603485107421875,
-0.0101165771484375,
0.00536346435546875,
-0.00312042236328125,
-0.0257568359375,
0.00604248046875,
0.003536224365234375,
0.05975341796875,
-0.00879669189453125,
0.022613525390625,
-0.0175018310546875,
-0.04779052734375,
-0.0178985595703125,
-0.027252197265625,
-0.004238128662109375,
0.0070953369140625,
-0.01617431640625,
0.01244354248046875,
0.0145416259765625,
-0.0168609619140625,
0.01812744140625,
0.01424407958984375,
0.006481170654296875,
-0.0031948089599609375,
-0.032196044921875,
-0.0171966552734375,
0.02313232421875,
0.006732940673828125,
0.00962066650390625,
0.01499176025390625,
0.0026340484619140625,
-0.015655517578125,
-0.0016927719116210938,
-0.0259552001953125,
-0.006378173828125,
0.0095367431640625,
-0.0288238525390625,
0.00612640380859375,
0.0015497207641601562,
0.01041412353515625,
0.00725555419921875,
0.010284423828125,
0.01861572265625,
-0.006214141845703125,
0.005992889404296875,
-0.00963592529296875,
-0.007549285888671875,
-0.0016412734985351562,
0.015625,
0.0104522705078125,
0.0032482147216796875,
-0.0075225830078125,
-0.05194091796875,
-0.01282501220703125,
-0.006866455078125,
-0.0249481201171875,
-0.0213470458984375,
0.0011873245239257812,
-0.0036411285400390625,
-0.0194091796875,
0.00732421875,
0.00112152099609375,
0.03668212890625,
0.011260986328125,
-0.0172882080078125,
-0.0233612060546875,
0.00525665283203125,
-0.041046142578125,
0.00531005859375,
-0.01340484619140625,
0.0328369140625,
-0.0197601318359375,
0.00907135009765625,
0.03680419921875,
-0.013153076171875,
0.0202178955078125,
0.0478515625,
0.00925445556640625,
0.0079193115234375,
0.01206207275390625,
0.0212249755859375,
-0.0200653076171875,
0.002902984619140625,
0.0261688232421875,
0.072509765625,
-0.028167724609375,
-0.037628173828125,
-0.0159912109375,
-0.02581787109375,
-0.0028972625732421875,
0.004085540771484375,
-0.01242828369140625,
0.0086212158203125,
0.0233154296875,
-0.03839111328125,
-0.0084991455078125,
0.0247650146484375,
-0.0155029296875,
-0.0092926025390625,
-0.00423431396484375,
0.00800323486328125,
-0.032073974609375,
0.000033915042877197266,
0.0234832763671875,
0.0117034912109375,
-0.016998291015625,
-0.01110076904296875,
0.03521728515625,
-0.011383056640625,
-0.0089874267578125,
0.0078125,
0.0299072265625,
-0.0264892578125,
-0.04852294921875,
-0.006336212158203125,
0.0184173583984375,
-0.01019287109375,
0.02606201171875,
0.03826904296875,
-0.01204681396484375,
-0.01155853271484375,
-0.0012655258178710938,
0.005420684814453125,
-0.04486083984375,
-0.0268096923828125,
-0.002338409423828125,
0.00567626953125,
-0.0390625,
0.002620697021484375,
0.01151275634765625,
0.00801849365234375,
0.032196044921875,
0.062469482421875,
0.025238037109375,
-0.0008177757263183594,
0.007793426513671875,
-0.0288238525390625,
0.001544952392578125,
0.005950927734375,
-0.0025787353515625,
0.0157470703125,
0.022064208984375,
0.03192138671875,
0.0169830322265625,
0.0142974853515625,
-0.005359649658203125,
0.016510009765625,
0.01117706298828125,
0.00690460205078125,
0.0246124267578125,
0.01959228515625,
-0.0114288330078125,
0.007083892822265625,
0.01404571533203125,
-0.0021572113037109375,
0.0276336669921875,
-0.0049591064453125,
0.016204833984375,
-0.0224456787109375,
-0.0002582073211669922,
0.01335906982421875,
0.0295562744140625,
-0.0283050537109375,
-0.0150146484375,
-0.00008589029312133789,
-0.00667572021484375,
-0.010894775390625,
0.004787445068359375,
-0.011199951171875,
-0.006214141845703125,
0.0003628730773925781,
-0.01540374755859375,
-0.005584716796875,
0.019622802734375,
0.0289306640625,
0.004520416259765625,
-0.04571533203125,
0.01001739501953125,
-0.019744873046875,
0.0013208389282226562,
0.0191802978515625,
0.0175933837890625,
-0.0211944580078125,
0.01271820068359375,
0.0004496574401855469,
-0.0022907257080078125,
-0.005992889404296875,
0.0347900390625,
-0.022705078125,
0.0023860931396484375,
-0.0175933837890625,
-0.004940032958984375,
-0.031524658203125,
0.06689453125,
-0.0010318756103515625,
-0.040863037109375,
-0.01219940185546875,
0.0034809112548828125,
-0.04046630859375,
0.01184844970703125,
-0.0104827880859375,
0.007694244384765625,
0.0224609375,
0.0031681060791015625,
-0.01506805419921875,
0.005199432373046875,
0.0127410888671875,
-0.0014066696166992188,
0.0148468017578125,
0.01203155517578125,
-0.047393798828125,
0.00768280029296875,
0.0030689239501953125,
-0.016082763671875,
0.01197052001953125,
0.01236724853515625,
0.043731689453125,
-0.016357421875,
-0.00148773193359375,
0.02490234375,
-0.0183258056640625,
0.00865936279296875,
0.0369873046875,
-0.01849365234375,
-0.00160980224609375,
0.043609619140625,
0.01023101806640625,
-0.001239776611328125,
0.01409149169921875,
-0.009429931640625,
0.01372528076171875,
-0.0207977294921875,
-0.01270294189453125,
0.03521728515625,
0.0269317626953125,
0.021148681640625,
-0.054168701171875,
0.020233154296875,
0.030609130859375,
0.036468505859375,
-0.004245758056640625,
-0.0254974365234375,
0.00748443603515625,
-0.032318115234375,
0.008056640625,
-0.0130615234375,
0.0093841552734375,
0.0161895751953125,
0.003780364990234375,
0.0183563232421875,
-0.0294189453125,
0.00629425048828125,
0.00018858909606933594,
0.01317596435546875,
-0.0228118896484375,
-0.0010194778442382812,
-0.0233001708984375,
-0.018951416015625,
-0.003978729248046875,
0.0190887451171875,
-0.014251708984375,
0.02587890625,
-0.0119476318359375,
-0.0102996826171875,
-0.0267486572265625,
-0.0036182403564453125,
-0.004253387451171875,
-0.007778167724609375,
-0.0213623046875,
-0.007598876953125,
0.0031585693359375,
0.0164031982421875,
0.018951416015625,
0.010406494140625,
-0.0032024383544921875,
0.03662109375,
-0.002079010009765625,
0.0311431884765625,
0.0016193389892578125,
-0.01468658447265625,
-0.0170135498046875,
-0.00595855712890625,
0.005710601806640625,
-0.002254486083984375,
0.023284912109375,
0.0033893585205078125,
0.005451202392578125,
0.007198333740234375,
-0.0207366943359375,
0.01480865478515625,
0.00536346435546875,
0.01018524169921875,
-0.0016450881958007812,
-0.01419830322265625,
-0.00787353515625,
0.005340576171875,
0.01543426513671875,
-0.0033473968505859375,
-0.060577392578125,
-0.03607177734375,
0.01268768310546875,
-0.03533935546875,
0.04046630859375,
-0.00848388671875,
-0.00859832763671875,
-0.0015134811401367188,
0.0010309219360351562,
0.0005335807800292969,
0.01103973388671875,
0.023468017578125,
0.005603790283203125,
0.010101318359375,
-0.0081787109375,
-0.0268707275390625,
0.02325439453125,
-0.021209716796875,
0.0056610107421875,
-0.00617218017578125,
0.0015516281127929688,
0.0203399658203125,
-0.01456451416015625,
-0.013214111328125,
0.0184326171875,
-0.0003991127014160156,
-0.029632568359375,
-0.0289764404296875,
0.0021514892578125,
-0.03765869140625,
-0.022613525390625,
0.0011053085327148438,
-0.033660888671875,
-0.0220489501953125,
0.0106048583984375,
0.047637939453125,
-0.0005693435668945312,
0.00289154052734375,
-0.01233673095703125,
0.00258636474609375,
0.010345458984375,
0.00041413307189941406,
0.0007686614990234375,
0.0153656005859375,
0.005352020263671875,
0.0017423629760742188,
-0.0136260986328125,
0.020660400390625,
-0.055419921875,
-0.0200653076171875,
-0.03729248046875,
0.004364013671875,
-0.003570556640625,
0.00878143310546875,
-0.00014269351959228516,
-0.03546142578125,
0.0200042724609375,
-0.045806884765625,
-0.01015472412109375,
0.0008563995361328125,
-0.0034618377685546875,
-0.0155792236328125,
-0.048187255859375,
-0.0369873046875,
0.00836944580078125,
-0.025115966796875,
0.00579071044921875,
0.01104736328125,
0.00276947021484375,
0.0178985595703125,
0.01212310791015625,
-0.01611328125,
-0.0152435302734375,
0.02813720703125,
-0.0401611328125,
0.0196533203125,
-0.0170440673828125,
0.0267333984375,
-0.007694244384765625,
-0.03662109375,
0.0228729248046875,
-0.032623291015625,
-0.0099945068359375,
0.055023193359375,
0.010955810546875,
0.00885009765625,
-0.005252838134765625,
0.02008056640625,
0.0272216796875,
-0.0238494873046875,
-0.004886627197265625,
-0.0025386810302734375,
-0.007579803466796875,
-0.0296173095703125,
0.02093505859375,
0.00400543212890625,
-0.014068603515625,
-0.0014486312866210938,
0.026397705078125,
0.0133056640625,
-0.004756927490234375,
0.0277252197265625,
0.00888824462890625,
-0.0011816024780273438,
0.01116943359375,
0.018798828125,
-0.0251617431640625,
0.025909423828125,
0.01535797119140625,
0.035980224609375,
-0.041259765625,
0.00792694091796875,
0.0215301513671875,
0.002521514892578125,
0.00609588623046875,
0.0020427703857421875,
-0.0024166107177734375,
-0.0022735595703125,
-0.0005197525024414062,
-0.0107269287109375,
0.0192413330078125,
-0.02783203125,
0.0161285400390625,
0.024383544921875,
0.0161285400390625,
-0.00890350341796875,
0.00957489013671875,
-0.0286865234375,
0.022216796875,
0.024261474609375,
0.010467529296875,
-0.0277862548828125,
-0.0174713134765625,
-0.00968170166015625,
0.0006284713745117188,
0.01329803466796875,
0.00736236572265625,
0.036224365234375,
-0.021453857421875,
-0.006744384765625,
-0.015716552734375,
-0.010772705078125,
0.003894805908203125,
0.00829315185546875,
-0.000006973743438720703,
0.046966552734375,
0.002017974853515625,
-0.034271240234375,
-0.01340484619140625,
0.02325439453125,
0.00867462158203125,
-0.00447845458984375,
0.041900634765625,
0.0006642341613769531,
-0.0063018798828125,
-0.0041656494140625,
-0.0022983551025390625,
-0.006992340087890625,
0.009521484375,
-0.00536346435546875,
-0.0263214111328125,
-0.00482940673828125,
-0.0245513916015625,
0.0206146240234375,
-0.01154327392578125,
0.0262603759765625,
0.0300445556640625,
0.0156402587890625,
0.01131439208984375,
0.03857421875,
0.00299835205078125,
0.01666259765625,
0.006534576416015625,
0.03826904296875,
0.003143310546875,
0.01251983642578125,
-0.044189453125,
-0.01812744140625,
-0.0024871826171875,
-0.021759033203125,
-0.00690460205078125,
0.032867431640625,
0.00788116455078125,
-0.03570556640625,
-0.0229644775390625,
-0.0118255615234375,
-0.0031337738037109375,
-0.010772705078125,
-0.012115478515625,
0.0153350830078125,
-0.01541900634765625,
-0.0151519775390625,
-0.0101165771484375,
0.01439666748046875,
-0.01947021484375,
-0.0169219970703125,
0.00014126300811767578,
0.01312255859375,
0.0234222412109375,
-0.004375457763671875,
0.00014293193817138672,
-0.004734039306640625,
-0.01263427734375,
0.0189971923828125,
-0.01279449462890625,
-0.003475189208984375,
-0.0257110595703125,
0.005016326904296875,
0.00511932373046875,
-0.0256805419921875,
-0.03240966796875,
0.0050506591796875,
-0.000013232231140136719,
0.01230621337890625,
0.006580352783203125,
0.0204315185546875,
-0.0003426074981689453,
0.0066680908203125,
0.0017194747924804688,
-0.005008697509765625,
0.0202789306640625,
-0.00414276123046875,
-0.0114898681640625,
-0.067138671875,
0.0135955810546875,
-0.007587432861328125,
0.021392822265625,
0.0104522705078125,
0.0257110595703125,
0.01152801513671875,
0.003734588623046875,
0.0012359619140625,
0.01204681396484375,
0.0258636474609375,
0.0029354095458984375,
-0.0265045166015625,
0.028839111328125,
0.02667236328125,
0.032379150390625,
-0.00995635986328125,
-0.00507354736328125,
0.0298919677734375,
0.017822265625,
-0.028167724609375,
-0.0247650146484375,
-0.0154266357421875,
-0.0057220458984375,
0.0185089111328125,
0.01122283935546875,
-0.002124786376953125,
-0.028717041015625,
-0.0145263671875,
-0.0258636474609375,
0.002239227294921875,
-0.03179931640625,
-0.01287841796875,
0.005218505859375,
-0.0640869140625,
0.028228759765625,
0.032989501953125,
0.00543212890625,
0.01012420654296875,
-0.013336181640625,
-0.02191162109375,
-0.0017681121826171875,
-0.025299072265625,
-0.0151214599609375,
-0.01190185546875,
-0.0151824951171875,
-0.0084686279296875,
0.0188140869140625,
-0.021942138671875,
0.0032558441162109375,
0.030792236328125,
0.0225830078125,
-0.02960205078125,
-0.0079803466796875,
0.0173187255859375,
-0.01068878173828125,
-0.00128936767578125,
0.00574493408203125,
0.035186767578125,
0.002460479736328125,
0.0182342529296875,
0.00528717041015625,
-0.038116455078125,
0.0175628662109375,
-0.0010662078857421875,
0.0389404296875,
-0.00823211669921875,
0.01715087890625,
-0.02447509765625,
-0.01251983642578125,
0.00498199462890625,
0.0083160400390625,
-0.049957275390625,
0.00574493408203125,
-0.00479888916015625,
-0.019195556640625,
0.02685546875,
-0.0162506103515625,
0.0134735107421875,
0.00672149658203125,
0.0024394989013671875,
0.016937255859375,
0.004573822021484375,
-0.01806640625,
-0.032745361328125,
0.001018524169921875,
0.0002372264862060547,
-0.0013885498046875,
0.017547607421875,
0.0176239013671875,
-0.04644775390625,
0.01513671875,
0.01424407958984375,
0.04095458984375,
-0.01268768310546875,
0.003055572509765625,
-0.0103759765625,
0.02032470703125,
-0.014007568359375,
0.009735107421875,
0.024444580078125,
-0.0131072998046875,
-0.0128631591796875,
-0.017974853515625,
0.00588226318359375,
-0.0028133392333984375,
-0.005939483642578125,
-0.0192718505859375,
0.0017147064208984375,
-0.037689208984375,
0.00959014892578125,
-0.003429412841796875,
0.0159149169921875,
0.01554107666015625,
0.00710296630859375,
0.0142059326171875,
0.002704620361328125,
-0.00872039794921875,
0.032867431640625,
-0.00585174560546875,
-0.007289886474609375,
0.00923919677734375,
0.034820556640625,
0.002593994140625,
-0.0030670166015625,
0.0011577606201171875,
0.0208282470703125,
-0.0033111572265625,
0.0220184326171875,
-0.0169525146484375,
0.019683837890625,
0.034698486328125,
-0.00323486328125,
-0.003276824951171875,
0.0026760101318359375,
-0.0205841064453125,
-0.020416259765625,
-0.0018434524536132812,
-0.0228271484375,
-0.030731201171875,
-0.028656005859375,
0.03497314453125,
-0.0256500244140625,
-0.0036945343017578125,
0.0198516845703125,
0.00524139404296875,
0.0186309814453125,
-0.0137786865234375,
0.045135498046875,
0.0158233642578125,
0.0057830810546875,
0.0047149658203125,
-0.01096343994140625,
0.0035228729248046875,
-0.03826904296875,
-0.002208709716796875,
0.0207672119140625,
0.0078887939453125,
-0.0281829833984375,
-0.022857666015625,
-0.00693511962890625,
0.0173187255859375,
0.0229949951171875,
-0.00373077392578125,
0.00787353515625,
0.0010433197021484375,
-0.0015974044799804688,
0.0070037841796875,
0.007083892822265625,
0.0136566162109375,
0.005580902099609375,
0.01351165771484375,
-0.0106353759765625,
0.0224151611328125,
0.01042938232421875,
-0.0197906494140625,
-0.0004017353057861328,
-0.0021915435791015625,
-0.00033092498779296875,
0.019927978515625,
-0.017242431640625,
0.00959014892578125,
-0.043182373046875,
0.0088348388671875,
0.0004215240478515625,
0.0091400146484375,
-0.0116119384765625,
-0.0013217926025390625,
-0.03094482421875,
-0.0221405029296875,
-0.0155029296875,
0.014434814453125,
0.0148773193359375,
0.029449462890625,
0.0010166168212890625,
0.0203857421875,
0.0016632080078125,
0.0291900634765625,
0.0026226043701171875,
-0.00614166259765625,
-0.00637054443359375,
0.02166748046875,
0.0278167724609375,
0.01238250732421875,
-0.00870513916015625,
-0.01349639892578125,
0.0303955078125,
0.0308837890625,
-0.0018434524536132812,
0.0166168212890625,
0.03253173828125,
0.01103973388671875,
-0.0018014907836914062,
0.0335693359375,
-0.0137481689453125,
-0.0189208984375,
0.006793975830078125,
0.006877899169921875,
-0.0157318115234375,
0.0169525146484375,
0.0174560546875,
-0.00615692138671875,
-0.0256195068359375,
0.0303192138671875,
-0.031494140625,
-0.019561767578125,
-0.020538330078125,
0.01337432861328125,
-0.0102386474609375,
-0.007579803466796875,
0.006290435791015625,
-0.003070831298828125,
0.00732421875,
-0.028076171875,
0.002899169921875,
-0.019073486328125,
-0.060089111328125,
0.01152801513671875,
0.0118408203125,
-0.006290435791015625,
-0.0279083251953125,
-0.0274200439453125,
-0.0106048583984375,
-0.031219482421875,
0.003543853759765625,
-0.023345947265625,
-0.00701141357421875,
0.0384521484375,
0.0159149169921875,
-0.0167694091796875,
-0.0128021240234375,
0.00449371337890625,
-0.05145263671875,
0.032135009765625,
0.0029582977294921875,
-0.01293182373046875,
-0.01116943359375,
0.0025501251220703125,
-0.0037364959716796875,
-0.0015001296997070312,
-0.0280303955078125,
0.0172119140625,
-0.043426513671875,
0.001377105712890625,
-0.03411865234375,
-0.01027679443359375,
0.0200042724609375,
-0.00183868408203125,
-0.011444091796875,
-0.0168609619140625,
-0.02716064453125,
-0.007266998291015625,
-0.0003974437713623047,
-0.01447296142578125,
-0.035186767578125,
-0.03521728515625,
0.0060577392578125,
0.0144805908203125,
0.03179931640625,
0.021392822265625,
-0.0005064010620117188,
0.007022857666015625,
0.0218048095703125,
-0.0112762451171875,
-0.006076812744140625,
-0.01441192626953125,
-0.03509521484375,
-0.0027332305908203125,
0.04132080078125,
-0.004482269287109375,
-0.011810302734375,
-0.03411865234375,
0.013885498046875,
-0.01122283935546875,
-0.0196075439453125,
-0.004669189453125,
-0.0140380859375,
0.006793975830078125,
-0.0185546875,
0.039398193359375,
0.01067352294921875,
0.0216522216796875,
0.016082763671875,
-0.010345458984375,
-0.00704193115234375,
0.006504058837890625,
-0.0309295654296875,
-0.041961669921875,
0.0100250244140625,
0.01425933837890625,
0.01168060302734375,
0.036865234375,
-0.01546478271484375,
0.052459716796875,
-0.00817108154296875,
-0.01555633544921875,
0.039337158203125,
-0.01812744140625,
-0.033050537109375,
0.0101318359375,
-0.028045654296875,
0.006031036376953125,
0.033294677734375,
0.02374267578125,
-0.025970458984375,
0.004787445068359375,
0.0175933837890625,
-0.01629638671875,
-0.016021728515625,
0.00928497314453125,
0.0298004150390625,
0.0303802490234375,
-0.0294952392578125,
0.01654052734375,
-0.0149383544921875,
-0.00890350341796875,
0.003910064697265625,
-0.00232696533203125,
0.0115814208984375,
0.0185699462890625,
-0.01446533203125,
0.027984619140625,
0.0202484130859375,
-0.0020160675048828125,
-0.0013723373413085938,
0.01551055908203125,
0.0029811859130859375,
0.0173187255859375,
-0.0025482177734375,
-0.04296875,
0.0044403076171875,
0.0008158683776855469,
-0.01560211181640625,
0.01139068603515625,
0.0198822021484375,
-0.015899658203125,
-0.037933349609375,
-0.007381439208984375,
-0.00916290283203125,
0.030242919921875,
-0.00849151611328125,
0.009307861328125,
0.006072998046875,
-0.01544189453125,
-0.01904296875,
-0.0010290145874023438,
0.0139923095703125,
-0.026397705078125,
-0.007175445556640625,
-0.01438140869140625,
-0.0160675048828125,
-0.004947662353515625,
0.0199737548828125,
-0.027435302734375,
0.0182037353515625,
-0.0175323486328125,
-0.0040740966796875,
-0.0166778564453125,
0.017913818359375,
0.0185546875,
-0.005924224853515625,
0.0172119140625,
0.001209259033203125,
0.002735137939453125,
0.016082763671875,
0.016143798828125,
0.0188751220703125,
0.00444793701171875,
0.00942230224609375,
-0.0020809173583984375,
-0.017242431640625,
-0.00962066650390625,
0.003528594970703125,
0.0248870849609375,
0.005008697509765625,
-0.016510009765625,
0.030426025390625,
0.0106658935546875,
-0.034881591796875,
0.01390838623046875,
-0.0310821533203125,
-0.0147552490234375,
-0.010345458984375,
0.0199737548828125,
-0.047637939453125,
0.017303466796875,
-0.0166015625,
0.02056884765625,
0.0035552978515625,
0.040435791015625,
0.01107025146484375,
-0.000614166259765625,
-0.0443115234375,
0.02325439453125,
-0.028717041015625,
-0.00324249267578125,
0.011077880859375,
0.0184478759765625,
-0.0310211181640625,
0.01470184326171875,
0.038970947265625,
-0.037353515625,
0.033416748046875,
0.009674072265625,
-0.01134490966796875,
0.0010242462158203125,
-0.0169219970703125,
-0.01520538330078125,
0.014251708984375,
-0.0305328369140625,
0.01763916015625,
-0.01166534423828125,
0.006282806396484375,
-0.01050567626953125,
-0.00376129150390625,
-0.021942138671875,
0.020355224609375,
0.0238037109375,
-0.0124664306640625,
0.0086212158203125,
0.007350921630859375,
-0.006809234619140625,
-0.033203125,
0.03204345703125,
-0.013336181640625,
0.004627227783203125,
0.01348114013671875,
-0.0036163330078125,
-0.00914764404296875,
0.003170013427734375,
-0.0243988037109375,
0.0251922607421875,
0.004657745361328125,
-0.0269317626953125,
0.00394439697265625,
-0.015625,
0.0205230712890625,
0.009307861328125,
-0.01201629638671875,
0.03204345703125,
0.0256805419921875,
-0.00792694091796875,
0.003368377685546875,
-0.01090240478515625,
-0.00958251953125,
0.011444091796875,
-0.0016002655029296875,
-0.01284027099609375,
0.0167083740234375,
-0.00592803955078125,
-0.028289794921875,
0.027252197265625,
0.0094451904296875,
0.01220703125,
0.0111083984375,
-0.00971221923828125,
-0.006824493408203125,
-0.0232086181640625,
0.03778076171875,
-0.0260772705078125,
0.03570556640625,
-0.0023593902587890625,
-0.008209228515625,
0.017913818359375,
0.00446319580078125,
-0.037322998046875,
0.01342010498046875,
-0.00830841064453125,
0.0107879638671875,
-0.01302337646484375,
0.02252197265625,
0.02508544921875,
0.01593017578125,
0.01052093505859375,
-0.01447296142578125,
-0.0010404586791992188,
-0.01544189453125,
0.0005135536193847656,
0.00574493408203125,
-0.0036220550537109375,
-0.01062774658203125,
-0.006206512451171875,
0.031524658203125,
-0.035888671875,
-0.0249786376953125,
-0.006870269775390625,
0.00424957275390625,
0.01142120361328125,
0.028564453125,
-0.005084991455078125,
0.0635986328125,
0.023345947265625,
-0.0338134765625,
-0.01068878173828125,
0.0285186767578125,
-0.003734588623046875,
-0.007785797119140625,
-0.005504608154296875,
0.0153961181640625,
0.043701171875,
-0.03369140625,
-0.00778961181640625,
-0.0219573974609375,
-0.011322021484375,
-0.020782470703125,
0.03369140625,
0.02423095703125,
-0.00514984130859375,
0.0050506591796875,
0.004238128662109375,
-0.0237274169921875,
0.00972747802734375,
-0.0189971923828125,
0.0194854736328125,
0.0014362335205078125,
0.03887939453125,
0.038909912109375,
0.0130615234375,
-0.0142669677734375,
0.01812744140625,
0.0283355712890625,
0.0014791488647460938,
0.00818634033203125,
0.00490570068359375,
0.01080322265625,
-0.01031494140625,
0.0082855224609375,
-0.0190582275390625,
0.0015659332275390625,
-0.00508880615234375,
0.0016298294067382812,
0.00707244873046875,
0.01412200927734375,
-0.013946533203125,
0.0406494140625,
0.02099609375,
-0.0293426513671875,
0.00002282857894897461,
0.0108795166015625,
-0.029449462890625,
-0.00408935546875,
-0.0294036865234375,
-0.04071044921875,
-0.0316162109375,
0.0190277099609375,
-0.00024890899658203125,
0.036865234375,
0.01629638671875,
-0.0251312255859375,
-0.0271453857421875,
0.005168914794921875,
0.00508880615234375,
0.040069580078125,
0.00036334991455078125,
0.023040771484375,
-0.0192413330078125,
0.01464080810546875,
-0.035980224609375,
0.00908660888671875,
0.007167816162109375,
0.048675537109375,
-0.0026187896728515625,
-0.003559112548828125,
-0.006328582763671875,
0.01500701904296875,
0.0152130126953125,
-0.01904296875,
0.003643035888671875,
0.0023632049560546875,
0.01328277587890625,
-0.00365447998046875,
0.01123046875,
0.0322265625,
-0.0117340087890625,
-0.01433563232421875,
0.0108184814453125,
0.004730224609375,
-0.01496124267578125,
0.00354766845703125,
-0.01103973388671875,
-0.00853729248046875,
0.0198211669921875,
0.00010675191879272461,
0.006374359130859375,
-0.022491455078125,
0.032470703125,
0.024444580078125,
-0.04351806640625,
0.006866455078125,
-0.0249786376953125,
0.01114654541015625,
-0.0127105712890625,
0.020721435546875,
-0.0009512901306152344,
0.01311492919921875,
0.0189361572265625,
-0.010009765625,
0.00756072998046875,
-0.00444793701171875,
-0.0022449493408203125,
0.01374053955078125,
0.0102691650390625,
0.057830810546875,
0.01019287109375,
0.001041412353515625,
-0.01221466064453125,
-0.0213165283203125,
0.005657196044921875,
0.00830841064453125,
0.0244598388671875,
-0.02679443359375,
-0.0200347900390625,
0.0017881393432617188,
-0.000545501708984375,
0.0015239715576171875,
-0.01073455810546875,
-0.01555633544921875,
0.0313720703125,
0.0189056396484375,
-0.0037288665771484375,
-0.004055023193359375,
0.01128387451171875,
-0.015289306640625,
0.005275726318359375,
-0.0065460205078125,
0.01511383056640625,
0.0027332305908203125,
-0.0195465087890625,
0.017791748046875,
-0.0134124755859375,
-0.0021266937255859375,
-0.003818511962890625,
0.00853729248046875,
-0.0214691162109375,
0.0125274658203125,
-0.0189666748046875,
0.004673004150390625,
-0.01494598388671875,
-0.00611114501953125,
0.0310516357421875,
-0.03021240234375,
-0.00445556640625,
0.002353668212890625,
-0.0135498046875,
-0.024688720703125,
0.0241851806640625,
0.0018033981323242188,
0.0029850006103515625,
0.04901123046875,
-0.00914764404296875,
0.010955810546875,
0.03607177734375,
-0.0098419189453125,
-0.0151824951171875,
0.006320953369140625,
0.003963470458984375,
0.01026153564453125,
-0.005718231201171875,
0.0198211669921875,
-0.005489349365234375,
0.0122222900390625,
0.0142364501953125,
-0.0170440673828125,
-0.0008792877197265625,
0.0288848876953125,
0.0174713134765625,
0.014129638671875,
0.00174713134765625,
0.021087646484375,
0.02899169921875,
-0.01268768310546875,
-0.0068511962890625,
0.034515380859375,
0.00897979736328125,
-0.004161834716796875,
-0.0191802978515625,
0.047393798828125,
0.01441192626953125,
-0.021484375,
-0.004791259765625,
-0.0246734619140625,
-0.002056121826171875,
0.0131683349609375,
-0.002780914306640625,
-0.023101806640625,
0.022979736328125,
0.0011014938354492188,
-0.037078857421875,
0.004451751708984375,
-0.00955963134765625,
-0.014404296875,
0.0063934326171875,
-0.0048828125,
-0.012664794921875,
0.007289886474609375,
-0.029022216796875,
-0.0296630859375,
-0.01061248779296875,
-0.02130126953125,
0.01421356201171875,
-0.019378662109375,
-0.0194549560546875,
-0.0106353759765625,
0.03167724609375,
0.0177459716796875,
0.00202178955078125,
0.0144805908203125,
-0.0178985595703125,
0.008575439453125,
0.022003173828125,
0.044586181640625,
0.0163421630859375,
-0.00783538818359375,
0.007114410400390625,
0.015777587890625,
0.030853271484375,
-0.019287109375,
0.043609619140625,
-0.0165557861328125,
-0.0093994140625,
-0.0310821533203125,
0.03363037109375,
-0.0249176025390625,
-0.005496978759765625,
0.0131072998046875,
0.0273284912109375,
-0.024078369140625,
-0.01004791259765625,
-0.0147247314453125,
0.004268646240234375,
-0.03863525390625,
0.00954437255859375,
0.00197601318359375,
-0.052276611328125,
0.00397491455078125,
-0.029052734375,
-0.048797607421875,
-0.01349639892578125,
0.0328369140625,
0.0107574462890625,
0.0309295654296875,
-0.01506805419921875,
0.047760009765625,
0.00958251953125,
-0.00147247314453125,
0.02301025390625,
0.01397705078125,
0.01181793212890625,
0.035125732421875,
-0.024017333984375,
-0.027984619140625,
0.0222625732421875,
-0.0110015869140625,
-0.0031642913818359375,
-0.03057861328125,
-0.01020050048828125,
0.0224761962890625,
0.0068359375,
-0.005229949951171875,
-0.007312774658203125,
-0.0211029052734375,
0.0025386810302734375,
0.0096588134765625,
-0.01306915283203125,
-0.0304412841796875,
-0.0211334228515625,
-0.000118255615234375,
-0.006549835205078125,
0.0286407470703125,
0.005008697509765625,
0.01486968994140625,
-0.02764892578125,
0.0105133056640625,
0.00252532958984375,
0.0228424072265625,
-0.0287933349609375,
-0.0079193115234375,
0.005184173583984375,
0.01467132568359375,
0.0107421875,
0.00612640380859375,
0.01372528076171875,
0.016387939453125,
0.035675048828125,
-0.0153961181640625,
-0.008331298828125,
0.006267547607421875,
-0.00318145751953125,
0.00948333740234375,
-0.0076141357421875,
-0.0528564453125,
0.003955841064453125,
-0.00946044921875,
0.00870513916015625,
0.0018053054809570312,
-0.00197601318359375,
0.004596710205078125,
-0.00814056396484375,
-0.022308349609375,
0.0078582763671875,
0.0092926025390625,
0.00736236572265625,
0.036651611328125,
-0.040191650390625,
-0.0012788772583007812,
0.0192413330078125,
-0.026153564453125,
0.0153350830078125,
0.0009527206420898438,
0.01090240478515625,
-0.006214141845703125,
0.0203704833984375,
-0.0277557373046875,
0.01056671142578125,
-0.01078033447265625,
-0.00890350341796875,
-0.00638580322265625,
0.005901336669921875,
0.01666259765625,
-0.043182373046875,
-0.048370361328125,
-0.0304412841796875,
-0.009063720703125,
0.02490234375,
0.0294189453125,
-0.004146575927734375,
-0.0085296630859375,
-0.0237274169921875,
0.0003943443298339844,
-0.0011234283447265625,
-0.038330078125,
-0.0145263671875,
0.021636962890625,
0.0124053955078125,
0.0014553070068359375,
0.0050506591796875,
0.0199737548828125,
0.00707244873046875,
0.0004305839538574219,
-0.007221221923828125,
-0.0010805130004882812,
-0.003154754638671875,
-0.0248565673828125,
-0.00974273681640625,
-0.00875091552734375,
-0.0166778564453125,
0.004550933837890625,
-0.01242828369140625,
-0.0162353515625,
0.0113067626953125,
-0.00817108154296875,
0.062744140625,
-0.030975341796875,
0.00817108154296875,
0.007598876953125,
-0.0190582275390625,
0.059967041015625,
0.006298065185546875,
-0.004810333251953125,
-0.021636962890625,
0.0379638671875,
-0.0093231201171875,
-0.0221099853515625,
0.005199432373046875,
-0.010040283203125,
0.0111236572265625,
-0.02752685546875,
-0.0215301513671875,
0.004863739013671875,
0.04058837890625,
-0.0250701904296875,
0.01201629638671875,
-0.0265655517578125,
0.02435302734375,
-0.016571044921875,
-0.0206756591796875,
-0.01056671142578125,
0.0132293701171875,
0.03118896484375,
0.00238800048828125,
-0.008514404296875,
0.04681396484375,
-0.0187225341796875,
0.024017333984375,
-0.0005488395690917969,
-0.016021728515625,
-0.01543426513671875,
0.0182952880859375,
-0.017669677734375,
-0.01343536376953125,
0.005573272705078125,
0.0026569366455078125,
-0.00913238525390625,
-0.00479888916015625,
-0.0165557861328125,
0.00833892822265625,
0.020416259765625,
-0.012115478515625,
-0.02105712890625,
0.0122222900390625,
0.003681182861328125,
0.018463134765625,
0.0276031494140625,
-0.00484466552734375,
-0.0123443603515625,
-0.00811004638671875,
-0.0166778564453125,
-0.00859832763671875,
-0.00815582275390625,
-0.02667236328125,
-0.031646728515625,
-0.0423583984375,
0.01385498046875,
-0.01192474365234375,
-0.0084075927734375,
-0.0196075439453125,
-0.000629425048828125,
0.034088134765625,
0.01264190673828125,
-0.00252532958984375,
0.01071929931640625,
0.01453399658203125,
0.0177459716796875,
-0.035064697265625,
-0.0208740234375,
0.0142059326171875,
0.01031494140625,
0.0033855438232421875,
0.00202178955078125,
0.02294921875,
0.023040771484375,
-0.0018377304077148438,
-0.006683349609375,
0.037353515625,
0.032440185546875,
-0.03314208984375,
-0.00418853759765625,
-0.0013065338134765625,
0.0290679931640625,
0.05633544921875,
0.0100860595703125,
-0.0005846023559570312,
-0.01334381103515625,
-0.00832366943359375,
0.01142120361328125,
-0.0228271484375,
0.004405975341796875,
0.002193450927734375,
-0.0067596435546875,
0.0182342529296875,
-0.01422119140625,
0.0027523040771484375,
-0.021575927734375,
-0.0099334716796875,
-0.038360595703125,
0.0059967041015625,
0.0016794204711914062,
0.0302886962890625,
-0.018157958984375,
-0.046875,
-0.011566162109375,
0.0202789306640625,
-0.01666259765625,
-0.033416748046875,
-0.047882080078125,
-0.0177154541015625,
-0.0282135009765625,
0.03076171875,
0.0136566162109375,
0.028961181640625,
-0.04608154296875,
-0.00742340087890625,
0.016632080078125,
-0.02410888671875,
0.0254058837890625,
-0.01194000244140625,
0.0193634033203125,
-0.01165771484375,
-0.01378631591796875,
-0.0255584716796875,
0.005847930908203125,
-0.02288818359375,
0.046478271484375,
-0.00983428955078125,
-0.0278167724609375,
-0.0115814208984375,
-0.01483917236328125,
0.016815185546875,
-0.0246124267578125,
0.006748199462890625,
-0.01302337646484375,
0.00534820556640625,
0.0188751220703125,
-0.0025043487548828125,
0.0201568603515625,
0.00037407875061035156,
-0.00433349609375,
-0.00998687744140625,
0.01111602783203125,
-0.0020809173583984375,
0.012603759765625,
-0.022491455078125,
-0.01103973388671875,
-0.01047515869140625,
-0.030670166015625,
-0.02178955078125,
-0.034912109375,
-0.006534576416015625,
0.01180267333984375,
-0.0305633544921875,
-0.007373809814453125,
0.029937744140625,
-0.017120361328125,
-0.01275634765625,
-0.011199951171875,
-0.04034423828125,
-0.049560546875,
-0.00203704833984375,
0.01222991943359375,
-0.053131103515625,
-0.026031494140625,
-0.01401519775390625,
0.02392578125,
0.01177215576171875,
-0.01049041748046875,
-0.01015472412109375,
0.045318603515625,
-0.0234832763671875,
0.02587890625,
0.01058197021484375,
0.005702972412109375,
-0.0217132568359375,
0.003704071044921875,
0.0105133056640625,
-0.0030670166015625,
-0.025054931640625,
0.006511688232421875,
-0.0188751220703125,
0.03729248046875,
-0.006671905517578125,
-0.006725311279296875,
0.0236663818359375,
0.0195465087890625,
-0.0248565673828125,
0.021484375,
0.0187530517578125,
0.0102081298828125,
0.00667572021484375,
0.035491943359375,
0.01279449462890625,
0.02191162109375,
-0.01354217529296875,
0.0007205009460449219,
0.0206146240234375,
0.035858154296875,
-0.003875732421875,
0.00916290283203125,
-0.002635955810546875,
-0.00047278404235839844,
0.009796142578125,
0.012176513671875,
-0.018463134765625,
0.01021575927734375,
-0.0291748046875,
0.020538330078125,
0.0127105712890625,
-0.003936767578125,
0.0199432373046875,
-0.045013427734375,
-0.01177978515625,
-0.033477783203125,
0.0019044876098632812,
-0.01450347900390625,
-0.0108795166015625,
0.01132965087890625,
-0.00482940673828125,
-0.032989501953125,
0.0039215087890625,
-0.0146942138671875,
0.0007958412170410156,
0.03369140625,
0.0159912109375,
0.0179595947265625,
-0.026824951171875,
0.00913238525390625,
0.031036376953125,
0.027740478515625,
-0.013702392578125,
-0.025909423828125,
-0.00301361083984375,
0.0024089813232421875,
-0.01129150390625,
-0.0011987686157226562,
-0.01332855224609375,
0.0032138824462890625,
0.0086517333984375,
-0.0065460205078125,
-0.028472900390625,
0.0186767578125,
0.0269622802734375,
-0.0164642333984375,
0.01526641845703125,
0.023345947265625,
0.01367950439453125,
0.01212310791015625,
0.0196685791015625,
-0.00762176513671875,
0.003932952880859375,
0.0239715576171875,
-0.009002685546875,
-0.0086669921875,
-0.016937255859375,
-0.0186004638671875,
0.02349853515625,
-0.0169830322265625,
-0.028167724609375,
-0.014862060546875,
0.004638671875,
-0.03265380859375,
-0.012939453125,
0.024444580078125,
-0.0296630859375,
-0.00008314847946166992,
0.00022470951080322266,
-0.01727294921875,
-0.00873565673828125,
0.0124969482421875,
-0.004337310791015625,
-0.0288848876953125,
0.0157012939453125,
-0.008209228515625,
0.01451873779296875,
-0.0321044921875,
0.01345062255859375,
0.0015058517456054688,
0.0187225341796875,
-0.0009608268737792969,
-0.00611114501953125,
-0.04150390625,
-0.0037841796875,
0.0191192626953125,
-0.0179901123046875,
-0.0209808349609375,
-0.0360107421875,
0.01294708251953125,
-0.0002346038818359375,
0.0077972412109375,
-0.00035953521728515625,
-0.01360321044921875,
-0.01360321044921875,
0.0287017822265625,
-0.02801513671875,
-0.027496337890625,
0.0031147003173828125,
0.0103607177734375,
0.0162200927734375,
0.01169586181640625,
0.03338623046875,
-0.0005040168762207031,
-0.0013942718505859375,
0.0019855499267578125,
0.00342559814453125,
-0.00864410400390625,
0.005565643310546875,
0.0189361572265625,
-0.020050048828125,
0.0369873046875,
0.0308074951171875,
0.01235198974609375,
-0.02569580078125,
-0.00905609130859375,
-0.020172119140625,
-0.007610321044921875,
0.0116119384765625,
-0.016845703125,
-0.0172576904296875,
-0.005035400390625,
0.00926971435546875,
-0.0408935546875,
0.0107879638671875,
0.003795623779296875,
-0.0276947021484375,
-0.00966644287109375,
-0.00024330615997314453,
-0.007671356201171875,
-0.0156707763671875,
-0.0008492469787597656,
0.0005483627319335938,
-0.00679779052734375,
-0.0167999267578125,
0.00995635986328125,
0.017333984375,
0.017913818359375,
-0.0180511474609375,
0.01971435546875,
0.00896453857421875,
0.031341552734375,
-0.0101318359375,
0.00145721435546875,
0.01016998291015625,
0.0350341796875,
-0.025787353515625,
0.001613616943359375,
0.014007568359375,
-0.026458740234375,
0.01739501953125,
0.01690673828125,
0.0136260986328125,
0.0136566162109375,
0.02716064453125,
-0.014617919921875,
0.0159454345703125,
-0.013214111328125,
-0.0196990966796875,
-0.0173492431640625,
-0.00008827447891235352,
-0.0098876953125,
-0.0005908012390136719,
-0.0209197998046875,
-0.00896453857421875,
0.01045989990234375,
-0.004642486572265625,
0.005695343017578125,
-0.0494384765625,
0.01070404052734375,
-0.0203704833984375,
0.03271484375,
-0.004756927490234375,
0.032318115234375,
0.06103515625,
0.017791748046875,
0.01922607421875,
-0.023406982421875,
0.01050567626953125,
-0.0501708984375,
0.0301971435546875,
0.0281982421875,
0.01763916015625,
-0.026519775390625,
0.0225830078125,
0.010986328125,
-0.0323486328125,
0.0257415771484375,
-0.0011320114135742188,
0.023590087890625,
-0.0133819580078125,
0.007587432861328125,
-0.0172271728515625,
0.0002168416976928711,
-0.024139404296875,
-0.0187530517578125,
0.0154266357421875,
0.015045166015625,
-0.0093994140625,
-0.0357666015625,
-0.00858306884765625,
0.028045654296875,
-0.022796630859375,
-0.03369140625,
-0.005767822265625,
0.0127410888671875,
-0.00966644287109375,
-0.00295257568359375,
0.0218505859375,
-0.007785797119140625,
0.006317138671875,
-0.0211181640625,
0.020355224609375,
0.005550384521484375,
-0.024139404296875,
0.01509857177734375,
0.0005979537963867188,
-0.016937255859375,
-0.00859832763671875,
0.019927978515625,
-0.0025959014892578125,
0.0261383056640625,
-0.0267333984375,
0.0205230712890625,
-0.016204833984375,
0.034027099609375,
0.01049041748046875,
0.0070953369140625,
0.01308441162109375,
0.0261077880859375,
0.004009246826171875,
-0.01397705078125,
-0.0224456787109375,
-0.004566192626953125,
-0.01016998291015625,
-0.01074981689453125,
0.0218658447265625,
-0.01727294921875,
0.01187896728515625,
-0.018768310546875,
-0.003582000732421875,
-0.0241546630859375,
-0.0120697021484375,
0.0038623809814453125,
-0.01551055908203125,
0.0303497314453125,
0.0018329620361328125,
-0.00801849365234375,
-0.0191497802734375,
-0.033660888671875,
0.03131103515625,
0.0192413330078125,
-0.0038433074951171875,
0.0172271728515625,
0.0227813720703125,
-0.039337158203125,
0.006801605224609375,
0.018829345703125,
0.009735107421875,
-0.00464630126953125,
0.0292205810546875,
0.00147247314453125,
0.01275634765625,
-0.00777435302734375,
0.00817108154296875,
0.0148162841796875,
-0.004535675048828125,
-0.022705078125,
-0.03070068359375,
-0.0068817138671875,
0.018280029296875,
0.00992584228515625,
-0.004848480224609375,
-0.0036411285400390625,
0.005779266357421875,
-0.001495361328125,
-0.00014591217041015625,
0.0037136077880859375,
0.0053253173828125,
-0.01090240478515625,
-0.04754638671875,
-0.0149078369140625,
0.025115966796875,
-0.006008148193359375,
-0.01293182373046875,
0.0192413330078125,
-0.002300262451171875,
-0.016998291015625,
-0.002094268798828125,
-0.009490966796875,
-0.0068206787109375,
-0.0008597373962402344,
0.01044464111328125,
0.044158935546875,
0.002288818359375,
-0.017181396484375,
-0.00835418701171875,
0.01525115966796875,
-0.037933349609375,
-0.00962066650390625,
-0.00917816162109375,
0.00103759765625,
-0.01168060302734375,
-0.01088714599609375,
0.0164947509765625,
-0.01035308837890625,
0.004001617431640625,
0.0170135498046875,
-0.00461578369140625,
-0.029693603515625,
0.0022335052490234375,
-0.0499267578125,
0.011138916015625,
-0.0004057884216308594,
0.024383544921875,
0.0018978118896484375,
-0.0215911865234375,
-0.0177154541015625,
-0.0181732177734375,
0.01409912109375,
0.036590576171875,
0.004047393798828125,
-0.01617431640625,
0.014678955078125,
0.023895263671875,
-0.0089569091796875,
-0.020843505859375,
-0.007656097412109375,
-0.0306243896484375,
0.005916595458984375,
0.00933837890625,
0.01171875,
0.006290435791015625,
0.0193939208984375,
-0.0302276611328125,
0.0017490386962890625,
0.019439697265625,
-0.00962066650390625,
0.0008563995361328125,
-0.006591796875,
-0.009674072265625,
-0.0176544189453125,
-0.0005865097045898438,
0.03131103515625,
-0.0228424072265625,
-0.03216552734375,
-0.01074981689453125,
-0.0164031982421875,
-0.009063720703125,
-0.01025390625,
-0.00823211669921875,
-0.031768798828125,
-0.0004146099090576172,
-0.004390716552734375,
0.013275146484375,
0.03204345703125,
-0.0178070068359375,
0.01824951171875,
0.0187530517578125,
0.01035308837890625,
0.03167724609375,
-0.0318603515625,
0.00437164306640625,
0.01528167724609375,
-0.01328277587890625,
-0.026153564453125,
0.01036834716796875,
0.019622802734375,
-0.01253509521484375,
-0.004543304443359375,
-0.01151275634765625,
-0.007450103759765625,
0.034271240234375,
0.023406982421875,
-0.03875732421875,
0.004848480224609375,
0.027099609375,
0.029296875,
0.0428466796875,
-0.04168701171875,
0.0217132568359375,
-0.00464630126953125,
-0.004245758056640625,
0.0112152099609375,
-0.015869140625,
0.03131103515625,
-0.0036525726318359375,
0.00690460205078125,
0.0121612548828125,
-0.006500244140625,
-0.0276641845703125,
0.005558013916015625,
0.0081329345703125,
-0.0245361328125,
0.0274658203125,
0.0137939453125,
0.0247344970703125,
0.0173187255859375,
-0.006916046142578125,
0.005008697509765625,
-0.0238800048828125,
0.0036144256591796875,
-0.0032482147216796875,
-0.00047516822814941406,
0.0203094482421875,
-0.00678253173828125,
0.0045928955078125,
0.00965118408203125,
-0.0079345703125,
-0.0178375244140625,
0.051971435546875,
0.005710601806640625,
-0.0017023086547851562,
0.00675201416015625,
-0.00386810302734375,
-0.01102447509765625,
-0.0135650634765625,
0.0408935546875,
-0.04681396484375,
-0.021942138671875,
0.00299835205078125,
0.0018367767333984375,
-0.00823974609375,
0.020660400390625,
0.034271240234375,
-0.005466461181640625,
0.0128631591796875,
-0.0174102783203125,
-0.0303192138671875,
0.055633544921875,
-0.04193115234375,
0.00406646728515625,
-0.0014934539794921875,
0.053497314453125,
0.0035400390625,
-0.012481689453125,
0.0152587890625,
-0.0161895751953125,
-0.00858306884765625,
0.043182373046875,
-0.0105743408203125,
-0.004909515380859375,
0.018524169921875,
-0.006313323974609375,
0.0166473388671875,
-0.036651611328125,
0.00958251953125,
-0.028564453125,
-0.00823974609375,
-0.0003116130828857422,
-0.01178741455078125,
0.0005903244018554688,
-0.01381683349609375,
-0.0226898193359375,
-0.0158233642578125,
0.00476837158203125,
0.00274658203125,
-0.019805908203125,
0.03460693359375,
0.053680419921875,
-0.0026454925537109375,
-0.0274810791015625,
-0.0189666748046875,
-0.027923583984375,
-0.005157470703125,
-0.0572509765625,
0.0094757080078125,
0.039825439453125,
-0.0027141571044921875,
-0.0101165771484375,
-0.005847930908203125,
-0.007537841796875,
0.0007915496826171875,
-0.01525115966796875,
-0.0127716064453125,
-0.028045654296875,
0.014678955078125,
0.037078857421875,
0.004638671875,
0.01067352294921875,
0.0167388916015625,
-0.005939483642578125,
0.00301361083984375,
-0.0067291259765625,
0.0014019012451171875,
0.01222991943359375,
-0.0223846435546875,
0.004375457763671875,
-0.0288848876953125,
-0.0012845993041992188,
-0.006275177001953125,
-0.0113983154296875,
-0.005596160888671875,
-0.0163726806640625,
0.0012521743774414062,
0.033660888671875,
0.0292510986328125,
-0.0138702392578125,
-0.0252532958984375,
0.0048065185546875,
-0.00872039794921875,
-0.0090484619140625,
-0.0063629150390625,
0.0026149749755859375,
-0.001644134521484375,
-0.026336669921875,
0.01074981689453125,
-0.0013399124145507812,
-0.00760650634765625,
-0.051513671875,
-0.0005846023559570312,
-0.0027828216552734375,
0.0030059814453125,
0.0229034423828125,
0.01544952392578125,
0.0013856887817382812,
0.01338958740234375,
-0.01490020751953125,
0.0115509033203125,
0.0004646778106689453,
-0.0235748291015625,
0.0218658447265625,
-0.0105438232421875,
0.006465911865234375,
-0.0173187255859375,
0.005977630615234375,
-0.014434814453125,
-0.00897979736328125,
0.006153106689453125,
-0.03173828125,
0.0018568038940429688,
-0.0228729248046875,
0.01096343994140625,
0.00734710693359375,
0.0169219970703125,
-0.00885772705078125,
-0.00034499168395996094,
0.006015777587890625,
-0.00580596923828125,
0.0124359130859375,
0.0110015869140625,
0.01111602783203125,
0.0203399658203125,
-0.00567626953125,
-0.007457733154296875,
0.004032135009765625,
-0.023529052734375,
-0.014984130859375,
-0.0111083984375,
-0.0118255615234375,
-0.0070953369140625,
-0.0006656646728515625,
-0.0017385482788085938,
-0.01120758056640625,
-0.048675537109375,
-0.0004973411560058594,
0.0196075439453125
] |
ours_527
|
The answer is \(122\).
Since \(\triangle BDC\) is oppositely oriented to \(\triangle ADC\), we have that \(BE\) is a symmedian of \(\triangle BDC\). Therefore, \(BDEC\) is a harmonic quadrilateral, and so the tangent at \(B\) and \(E\) to \(\omega\), and \(ON\) meet at \(Q\). This implies \(BE\) is the polar of \(Q\) with respect to \(\omega\).
Therefore, \((DPCQ)\) is harmonic, and since \(CR\) is an angle bisector of \(\angle PRQ\), we have \(\angle DRC = 90^\circ\). This means that \(RP\) is an angle bisector of \(\angle DRC\).
We therefore have \(\frac{DR}{RC} = \frac{DP}{PC} = \frac{DB^2}{BC^2}\) (by Steiner's Theorem). By Ptolemy's, \(DB^2 = (AB)(CD) + (BC)(AD) = 75\). Therefore, \(\frac{DR}{RC} = \frac{15}{8}\). Using this along with \(DR^2 + RC^2 = 21^2\) (since \(\angle DRC = 90^\circ\)), we have \(DR = \frac{105}{17}\), and the answer is \(122\).
\(\boxed{122}\)
|
122
|
{
"competition": "us_comps",
"dataset": "Ours",
"posts": null,
"source": "OMOSoln2-2.md"
}
|
Let \(ABCD\) be an isosceles trapezoid with bases \(AB = 5\) and \(CD = 7\) and legs \(BC = AD = 2\sqrt{10}\). A circle \(\omega\) with center \(O\) passes through \(A, B, C,\) and \(D\). Let \(M\) be the midpoint of segment \(CD\), and ray \(AM\) meet \(\omega\) again at \(E\). Let \(N\) be the midpoint of \(BE\) and \(P\) be the intersection of \(BE\) with \(CD\). Let \(Q\) be the intersection of ray \(ON\) with ray \(DC\). There is a point \(R\) on the circumcircle of \(PNQ\) such that \(\angle PRC = 45^\circ\). The length of \(DR\) can be expressed in the form \(\frac{m}{n}\) where \(m\) and \(n\) are relatively prime positive integers. What is \(m+n\)?
|
[
"/Mathematics/Geometry/InversiveGeometry/Polar",
"/Mathematics/Geometry/PlaneGeometry/Circles/Circle",
"/Mathematics/Geometry/PlaneGeometry/Circles/Concyclic",
"/Mathematics/Geometry/PlaneGeometry/Polygons/ConvexPolygon",
"/Mathematics/Geometry/PlaneGeometry/Polygons/CyclicPolygon",
"/Mathematics/Geometry/PlaneGeometry/Quadrangles",
"/Mathematics/Geometry/PlaneGeometry/Quadrilaterals/IsoscelesTrapezium",
"/Mathematics/Geometry/PlaneGeometry/Quadrilaterals/IsoscelesTrapezoid",
"/Mathematics/Geometry/PlaneGeometry/Quadrilaterals/Trapezoid",
"/Mathematics/Geometry/ProjectiveGeometry/GeneralProjectiveGeometry/ProjectiveGeometry"
] |
Recognize BE as a symmedian of triangle BDC, making BDEC harmonic and thus DPCQ harmonic, which lets you apply the angle‑bisector ratio DR/RC = DB²/BC².
|
[
-0.0002830028533935547,
-0.033355712890625,
-0.005252838134765625,
-0.01342010498046875,
-0.0009474754333496094,
0.06640625,
0.01395416259765625,
0.024871826171875,
-0.00815582275390625,
0.0196380615234375,
-0.00861358642578125,
0.0316162109375,
-0.003143310546875,
0.0308837890625,
0.0188751220703125,
0.0178985595703125,
0.00920867919921875,
0.00559234619140625,
0.020233154296875,
0.00434112548828125,
-0.008880615234375,
0.00788116455078125,
-0.037017822265625,
0.006191253662109375,
-0.00585174560546875,
-0.004184722900390625,
-0.0139923095703125,
-0.008697509765625,
-0.026702880859375,
-0.0241546630859375,
-0.007648468017578125,
0.0252532958984375,
0.031524658203125,
-0.004276275634765625,
-0.005191802978515625,
0.009002685546875,
-0.025146484375,
0.0015439987182617188,
-0.04254150390625,
-0.055145263671875,
0.01322174072265625,
0.01085662841796875,
-0.0166473388671875,
0.01078033447265625,
0.01297760009765625,
0.03094482421875,
-0.01355743408203125,
-0.0023651123046875,
-0.00823211669921875,
0.00013589859008789062,
0.0038089752197265625,
0.01125335693359375,
-0.045013427734375,
-0.00299072265625,
-0.0186920166015625,
-0.051513671875,
-0.0445556640625,
-0.000698089599609375,
0.00969696044921875,
-0.00791168212890625,
0.00382232666015625,
0.00482177734375,
-0.00301361083984375,
-0.01300811767578125,
-0.0043792724609375,
0.0005822181701660156,
0.00701141357421875,
-0.0034236907958984375,
0.005855560302734375,
-0.0362548828125,
0.0047149658203125,
-0.029327392578125,
0.0038089752197265625,
-0.00362396240234375,
0.031036376953125,
-0.016693115234375,
-0.00955963134765625,
0.024993896484375,
-0.0220184326171875,
0.03131103515625,
0.00646209716796875,
0.005786895751953125,
0.004573822021484375,
-0.032928466796875,
0.01042938232421875,
0.004100799560546875,
-0.0209808349609375,
0.006946563720703125,
0.01409912109375,
0.0032863616943359375,
-0.01216888427734375,
-0.0160675048828125,
-0.0261993408203125,
-0.0078582763671875,
0.01020050048828125,
-0.01297760009765625,
0.008697509765625,
0.005428314208984375,
-0.0197601318359375,
0.0051116943359375,
-0.01438140869140625,
-0.007293701171875,
-0.0361328125,
0.0044403076171875,
-0.010223388671875,
-0.01555633544921875,
-0.0190582275390625,
0.0011835098266601562,
-0.0100250244140625,
-0.00887298583984375,
0.01030731201171875,
0.00140380859375,
0.027496337890625,
0.0350341796875,
-0.0004372596740722656,
-0.0140380859375,
0.0250396728515625,
0.011016845703125,
0.005992889404296875,
-0.01593017578125,
0.0054473876953125,
0.01507568359375,
-0.04803466796875,
-0.0006933212280273438,
0.0237274169921875,
-0.01412200927734375,
0.00531005859375,
-0.006923675537109375,
-0.0221710205078125,
0.030120849609375,
0.0038509368896484375,
-0.0029354095458984375,
-0.030303955078125,
-0.0150909423828125,
-0.007167816162109375,
-0.0038433074951171875,
0.0011072158813476562,
-0.0010156631469726562,
-0.0108489990234375,
0.0064849853515625,
-0.00920867919921875,
-0.0223236083984375,
-0.0018568038940429688,
-0.08807373046875,
-0.004337310791015625,
-0.007305145263671875,
0.01102447509765625,
0.01629638671875,
-0.0023746490478515625,
0.002117156982421875,
-0.0009975433349609375,
-0.0188140869140625,
0.036407470703125,
-0.0013647079467773438,
-0.0002052783966064453,
0.01087188720703125,
0.0101470947265625,
0.020751953125,
0.0026683807373046875,
-0.0006051063537597656,
0.00702667236328125,
-0.01494598388671875,
0.0040740966796875,
0.015411376953125,
0.01123809814453125,
-0.0026702880859375,
0.00936126708984375,
-0.00008851289749145508,
-0.023681640625,
-0.01507568359375,
-0.023101806640625,
-0.0105438232421875,
0.0032863616943359375,
-0.00494384765625,
-0.00022089481353759766,
0.004146575927734375,
-0.0116729736328125,
0.0061492919921875,
-0.0069580078125,
0.029083251953125,
0.01065826416015625,
-0.02178955078125,
-0.00707244873046875,
0.00923919677734375,
0.0155029296875,
0.006153106689453125,
-0.005420684814453125,
0.029571533203125,
0.0104827880859375,
0.00485992431640625,
-0.0118865966796875,
-0.04345703125,
0.007373809814453125,
0.0016632080078125,
0.004505157470703125,
-0.0178070068359375,
-0.01444244384765625,
0.01142120361328125,
0.0120391845703125,
0.006893157958984375,
0.0011167526245117188,
0.00392913818359375,
0.025482177734375,
0.015625,
0.00623321533203125,
-0.0017681121826171875,
-0.0199127197265625,
-0.00004571676254272461,
-0.006103515625,
0.013336181640625,
0.0231781005859375,
0.01409912109375,
-0.03253173828125,
-0.0201568603515625,
-0.01192474365234375,
-0.0279083251953125,
-0.00234222412109375,
-0.003875732421875,
-0.003826141357421875,
0.01050567626953125,
0.01219940185546875,
-0.015472412109375,
0.00853729248046875,
-0.0161590576171875,
-0.026153564453125,
-0.01499176025390625,
-0.004482269287109375,
-0.01457977294921875,
0.0031261444091796875,
-0.00832366943359375,
-0.00409698486328125,
0.009002685546875,
-0.0191802978515625,
0.0001900196075439453,
-0.0175323486328125,
-0.01207733154296875,
-0.003963470458984375,
0.00391387939453125,
0.01256561279296875,
0.0221405029296875,
0.01654052734375,
-0.01300048828125,
-0.00982666015625,
0.0007801055908203125,
-0.0009531974792480469,
-0.00428009033203125,
-0.005985260009765625,
-0.0167694091796875,
0.006732940673828125,
0.01102447509765625,
-0.032379150390625,
0.0184326171875,
0.0167083740234375,
-0.007717132568359375,
-0.0218048095703125,
0.0251312255859375,
0.000896453857421875,
-0.009490966796875,
-0.01415252685546875,
0.003326416015625,
-0.0197906494140625,
-0.005054473876953125,
0.0130767822265625,
-0.0108184814453125,
-0.029510498046875,
0.0286102294921875,
0.0187225341796875,
0.0013284683227539062,
0.02978515625,
-0.014312744140625,
0.04241943359375,
-0.04168701171875,
-0.005157470703125,
0.026885986328125,
0.00852203369140625,
-0.0080718994140625,
-0.0066986083984375,
0.00232696533203125,
-0.018157958984375,
0.0211944580078125,
-0.003917694091796875,
-0.023712158203125,
-0.032470703125,
-0.004669189453125,
-0.005863189697265625,
-0.006927490234375,
-0.01123809814453125,
-0.0033473968505859375,
0.0022869110107421875,
0.01104736328125,
-0.0008530616760253906,
0.00589752197265625,
-0.0203857421875,
-0.01392364501953125,
0.01751708984375,
-0.0206298828125,
-0.01206207275390625,
-0.0028553009033203125,
0.01305389404296875,
-0.01062774658203125,
0.0250701904296875,
-0.01001739501953125,
0.0034046173095703125,
0.0110015869140625,
0.01197052001953125,
0.0241546630859375,
0.0161285400390625,
0.01336669921875,
-0.03857421875,
0.017547607421875,
0.04754638671875,
0.006938934326171875,
-0.011505126953125,
-0.01103973388671875,
-0.004085540771484375,
-0.0157012939453125,
0.00870513916015625,
0.008209228515625,
-0.010711669921875,
0.0157470703125,
-0.0017414093017578125,
0.03729248046875,
0.01885986328125,
0.002094268798828125,
0.01372528076171875,
-0.0247039794921875,
0.0284881591796875,
-0.00215911865234375,
0.0247802734375,
0.0019044876098632812,
-0.00780487060546875,
0.0191192626953125,
0.0010576248168945312,
0.0022296905517578125,
0.01479339599609375,
0.00832366943359375,
-0.02093505859375,
0.004894256591796875,
-0.0024013519287109375,
0.006183624267578125,
-0.0086517333984375,
0.012298583984375,
0.03521728515625,
-0.0670166015625,
-0.044647216796875,
0.0144195556640625,
-0.04827880859375,
0.00911712646484375,
-0.038970947265625,
-0.03863525390625,
0.015777587890625,
0.00733184814453125,
0.0009350776672363281,
-0.0176239013671875,
-0.0276947021484375,
-0.0046844482421875,
0.006252288818359375,
0.03167724609375,
-0.0189666748046875,
0.00548553466796875,
0.0164642333984375,
-0.007320404052734375,
-0.0203094482421875,
0.0036754608154296875,
-0.01953125,
-0.0148773193359375,
-0.00197601318359375,
0.01003265380859375,
-0.0273895263671875,
0.00946044921875,
-0.0008015632629394531,
-0.037384033203125,
-0.0015954971313476562,
-0.0181884765625,
0.0029087066650390625,
0.0086212158203125,
-0.00954437255859375,
0.0280303955078125,
-0.021820068359375,
-0.0159759521484375,
0.01446533203125,
-0.0150909423828125,
-0.006572723388671875,
-0.005382537841796875,
-0.0018129348754882812,
0.00553131103515625,
0.036956787109375,
-0.0151519775390625,
0.0002548694610595703,
0.0277862548828125,
0.0006299018859863281,
-0.0024280548095703125,
0.002841949462890625,
-0.00337982177734375,
-0.01385498046875,
0.0236663818359375,
0.001659393310546875,
0.0009775161743164062,
0.01953125,
-0.0018262863159179688,
-0.0290069580078125,
0.0012235641479492188,
-0.01380157470703125,
-0.03131103515625,
-0.0014696121215820312,
-0.0283355712890625,
-0.00730133056640625,
-0.00982666015625,
-0.0151519775390625,
0.022796630859375,
-0.045166015625,
-0.009521484375,
-0.0092315673828125,
-0.0083770751953125,
-0.003810882568359375,
-0.00787353515625,
-0.006710052490234375,
0.0218353271484375,
-0.016937255859375,
0.0265960693359375,
0.017333984375,
-0.006679534912109375,
0.0236358642578125,
0.0196685791015625,
-0.003147125244140625,
0.0185699462890625,
0.002048492431640625,
0.03759765625,
-0.0194549560546875,
-0.0199127197265625,
0.0222320556640625,
-0.0025177001953125,
-0.01503753662109375,
0.00836944580078125,
0.007266998291015625,
0.016021728515625,
0.047943115234375,
-0.01126861572265625,
0.0032520294189453125,
0.0081329345703125,
0.001399993896484375,
-0.02447509765625,
-0.00504302978515625,
0.0031032562255859375,
-0.0014896392822265625,
-0.016571044921875,
0.004840850830078125,
-0.00878143310546875,
0.0189056396484375,
-0.004520416259765625,
-0.01092529296875,
-0.008819580078125,
0.0010557174682617188,
-0.055877685546875,
0.0126495361328125,
0.021240234375,
0.01113128662109375,
0.002971649169921875,
-0.01206207275390625,
0.0299835205078125,
-0.015838623046875,
-0.0002799034118652344,
-0.0163116455078125,
0.008087158203125,
-0.033905029296875,
-0.0216217041015625,
0.017303466796875,
0.0269622802734375,
-0.01561737060546875,
-0.01523590087890625,
-0.0002301931381225586,
-0.036773681640625,
-0.0015163421630859375,
-0.00946807861328125,
-0.0013742446899414062,
0.00960540771484375,
0.031402587890625,
0.008209228515625,
-0.002964019775390625,
0.032470703125,
-0.0246429443359375,
0.01435089111328125,
-0.0099639892578125,
-0.0249176025390625,
-0.0271148681640625,
0.0179290771484375,
0.01337432861328125,
-0.0126953125,
-0.0258026123046875,
-0.0218658447265625,
-0.00423431396484375,
0.050689697265625,
-0.0175323486328125,
-0.0246734619140625,
-0.0157928466796875,
-0.00615692138671875,
0.0146636962890625,
-0.01751708984375,
-0.00335693359375,
-0.007770538330078125,
0.0174560546875,
-0.025299072265625,
0.01399993896484375,
0.0005702972412109375,
0.016326904296875,
-0.035186767578125,
0.019622802734375,
-0.037567138671875,
0.029815673828125,
-0.01219940185546875,
0.00492095947265625,
0.0117340087890625,
0.016357421875,
-0.026336669921875,
0.0238189697265625,
-0.0222320556640625,
-0.002567291259765625,
-0.0291290283203125,
0.0052947998046875,
0.0251312255859375,
0.01021575927734375,
0.0293121337890625,
-0.0127716064453125,
0.026397705078125,
0.03466796875,
0.020599365234375,
-0.002323150634765625,
-0.0017242431640625,
0.0057525634765625,
-0.00015270709991455078,
-0.0098724365234375,
-0.02935791015625,
-0.032073974609375,
0.0223236083984375,
-0.030975341796875,
0.0250701904296875,
0.006656646728515625,
0.0165863037109375,
0.007534027099609375,
-0.0243072509765625,
-0.00844573974609375,
-0.004680633544921875,
0.007686614990234375,
0.01910400390625,
-0.013824462890625,
-0.00274658203125,
-0.0181884765625,
0.007755279541015625,
-0.031890869140625,
0.0160064697265625,
-0.006450653076171875,
-0.00048279762268066406,
-0.037872314453125,
-0.000919342041015625,
-0.0151519775390625,
-0.0101776123046875,
-0.027130126953125,
-0.00786590576171875,
0.0165557861328125,
0.03643798828125,
0.0206451416015625,
-0.02252197265625,
0.005519866943359375,
0.01824951171875,
0.0010576248168945312,
-0.01303863525390625,
0.02703857421875,
-0.0021266937255859375,
0.00927734375,
-0.0308074951171875,
0.0024871826171875,
-0.00959014892578125,
-0.0228118896484375,
-0.0190277099609375,
0.0090484619140625,
-0.026580810546875,
0.01264190673828125,
0.020904541015625,
0.0033473968505859375,
-0.0193023681640625,
0.01824951171875,
0.036041259765625,
-0.0302276611328125,
-0.004306793212890625,
0.01331329345703125,
0.000667572021484375,
-0.0234375,
0.0010833740234375,
-0.00027632713317871094,
-0.005710601806640625,
-0.0248260498046875,
0.0192413330078125,
0.026641845703125,
-0.0282745361328125,
0.005596160888671875,
-0.027740478515625,
0.0037746429443359375,
-0.005626678466796875,
0.04278564453125,
0.0095672607421875,
0.00482177734375,
-0.026458740234375,
0.0194549560546875,
0.00949859619140625,
-0.00960540771484375,
-0.0269012451171875,
-0.01123046875,
-0.00652313232421875,
0.051025390625,
0.01268768310546875,
-0.02587890625,
-0.004268646240234375,
-0.0002789497375488281,
0.0176544189453125,
0.01959228515625,
-0.005901336669921875,
0.0018405914306640625,
-0.0286407470703125,
0.0100555419921875,
0.02178955078125,
0.0218658447265625,
0.01062774658203125,
-0.00786590576171875,
0.04119873046875,
-0.021392822265625,
-0.0050811767578125,
-0.0147247314453125,
0.013214111328125,
0.0128631591796875,
0.0022830963134765625,
-0.01155853271484375,
0.018035888671875,
-0.0199432373046875,
-0.004638671875,
-0.0211944580078125,
0.0166473388671875,
0.00644683837890625,
0.01934814453125,
0.034271240234375,
-0.00548553466796875,
0.0105743408203125,
0.0240631103515625,
0.02044677734375,
-0.0282745361328125,
-0.00933837890625,
-0.0063018798828125,
-0.005279541015625,
-0.00728607177734375,
-0.009674072265625,
-0.0222930908203125,
0.01149749755859375,
-0.0115509033203125,
0.0023899078369140625,
0.006191253662109375,
0.0035400390625,
-0.02178955078125,
0.00007528066635131836,
0.0017690658569335938,
0.01319122314453125,
-0.0103302001953125,
-0.0163421630859375,
0.01166534423828125,
-0.01284027099609375,
-0.001911163330078125,
-0.01605224609375,
-0.0020694732666015625,
-0.03228759765625,
-0.0125732421875,
0.0060882568359375,
0.028533935546875,
0.0004074573516845703,
-0.022125244140625,
0.026519775390625,
-0.03228759765625,
-0.01549530029296875,
0.00414276123046875,
-0.06170654296875,
0.0301666259765625,
-0.0259857177734375,
-0.0085296630859375,
-0.00034236907958984375,
0.0104827880859375,
0.0218963623046875,
0.043914794921875,
-0.036102294921875,
0.02838134765625,
-0.002471923828125,
0.00218963623046875,
-0.0286712646484375,
0.0256195068359375,
-0.00769805908203125,
0.01910400390625,
0.00567626953125,
-0.007061004638671875,
-0.0048370361328125,
0.01192474365234375,
0.0176239013671875,
0.00466156005859375,
-0.0018510818481445312,
-0.0220184326171875,
-0.0164794921875,
-0.012969970703125,
0.003284454345703125,
-0.0222320556640625,
-0.0016355514526367188,
-0.048492431640625,
0.0092010498046875,
0.040863037109375,
-0.0345458984375,
0.00742340087890625,
-0.0347900390625,
-0.0247955322265625,
0.0190887451171875,
-0.007175445556640625,
0.0084686279296875,
-0.034637451171875,
-0.01094818115234375,
-0.0008425712585449219,
-0.007633209228515625,
0.0282440185546875,
0.0197296142578125,
-0.031829833984375,
-0.00502777099609375,
-0.025909423828125,
0.0298309326171875,
0.005523681640625,
-0.03265380859375,
-0.0021419525146484375,
-0.042388916015625,
0.0179595947265625,
0.019744873046875,
0.030731201171875,
0.0290985107421875,
0.00563812255859375,
-0.0306549072265625,
0.0053863525390625,
0.0061492919921875,
-0.030548095703125,
-0.026214599609375,
-0.0191802978515625,
0.0291900634765625,
-0.0118865966796875,
0.0079193115234375,
-0.01055908203125,
0.0112457275390625,
0.018829345703125,
-0.01474761962890625,
-0.03851318359375,
0.0083770751953125,
-0.00698089599609375,
0.012542724609375,
0.0170440673828125,
0.005161285400390625,
-0.0221710205078125,
-0.004093170166015625,
0.0165252685546875,
0.0022907257080078125,
-0.0033893585205078125,
-0.0140228271484375,
-0.0166473388671875,
-0.041839599609375,
-0.0022487640380859375,
-0.0151214599609375,
0.005542755126953125,
0.0185089111328125,
-0.0009860992431640625,
0.005313873291015625,
-0.0148773193359375,
-0.023681640625,
-0.00951385498046875,
0.0157318115234375,
0.0255126953125,
-0.004589080810546875,
-0.002010345458984375,
0.0146636962890625,
0.0191497802734375,
-0.044952392578125,
-0.01480865478515625,
0.0212554931640625,
-0.01039886474609375,
-0.0007405281066894531,
0.025482177734375,
-0.0338134765625,
0.03228759765625,
-0.027435302734375,
-0.01097869873046875,
-0.0384521484375,
-0.0127410888671875,
0.004116058349609375,
-0.005680084228515625,
0.028350830078125,
0.0172882080078125,
-0.0040435791015625,
-0.0295867919921875,
0.00563812255859375,
-0.005542755126953125,
-0.004550933837890625,
-0.017242431640625,
-0.0009675025939941406,
-0.00650787353515625,
0.01070404052734375,
-0.0188751220703125,
-0.005767822265625,
0.0256500244140625,
0.019927978515625,
-0.006412506103515625,
0.00579833984375,
-0.0068511962890625,
-0.0284271240234375,
0.034393310546875,
-0.0008525848388671875,
0.006557464599609375,
-0.01514434814453125,
-0.0020732879638671875,
0.001476287841796875,
-0.0301666259765625,
0.021270751953125,
-0.0247955322265625,
0.004161834716796875,
0.01552581787109375,
0.00711822509765625,
0.01611328125,
-0.028472900390625,
0.004852294921875,
-0.03192138671875,
-0.02825927734375,
-0.00983428955078125,
-0.0180206298828125,
-0.0244140625,
-0.0220794677734375,
0.036651611328125,
-0.0004944801330566406,
-0.0201568603515625,
-0.01071929931640625,
-0.002010345458984375,
-0.0007848739624023438,
-0.002773284912109375,
-0.013397216796875,
-0.019195556640625,
0.018890380859375,
-0.0032024383544921875,
-0.0013446807861328125,
0.037200927734375,
0.017181396484375,
0.036468505859375,
0.00004649162292480469,
-0.0123138427734375,
0.00958251953125,
0.00701141357421875,
0.016815185546875,
0.017333984375,
0.00426483154296875,
-0.0240325927734375,
0.0120086669921875,
-0.037109375,
0.0219268798828125,
0.01300048828125,
0.008575439453125,
0.0066680908203125,
0.016815185546875,
0.035797119140625,
-0.0161590576171875,
0.0217437744140625,
0.0146484375,
0.01303863525390625,
-0.03375244140625,
-0.00295257568359375,
-0.033172607421875,
0.047454833984375,
0.003360748291015625,
0.03277587890625,
-0.0210723876953125,
0.021148681640625,
0.017486572265625,
0.0194244384765625,
0.0295562744140625,
-0.00214385986328125,
-0.0085906982421875,
0.0318603515625,
0.0297393798828125,
0.0019044876098632812,
-0.0129241943359375,
-0.0125885009765625,
0.0013837814331054688,
-0.0010347366333007812,
0.007965087890625,
-0.0190887451171875,
0.02838134765625,
0.0287628173828125,
-0.005756378173828125,
0.0234527587890625,
-0.0260009765625,
0.004207611083984375,
-0.0084075927734375,
0.0089263916015625,
0.0018749237060546875,
0.00862884521484375,
-0.033477783203125,
0.00847625732421875,
-0.01953125,
-0.0161895751953125,
0.0232391357421875,
0.00669097900390625,
0.0119171142578125,
0.033782958984375,
-0.036651611328125,
0.003452301025390625,
0.0250244140625,
0.035369873046875,
-0.00814056396484375,
-0.0340576171875,
0.01085662841796875,
0.01375579833984375,
0.007801055908203125,
-0.007366180419921875,
-0.0004019737243652344,
-0.02301025390625,
-0.031097412109375,
0.00675201416015625,
0.00884246826171875,
0.009002685546875,
-0.0203399658203125,
-0.007297515869140625,
-0.014495849609375,
0.00774383544921875,
-0.0260009765625,
-0.005893707275390625,
-0.0072784423828125,
-0.01335906982421875,
0.0180816650390625,
-0.03778076171875,
0.005680084228515625,
-0.0157928466796875,
-0.01033782958984375,
0.00765228271484375,
0.0179901123046875,
0.0008382797241210938,
-0.0241851806640625,
0.0002048015594482422,
0.003955841064453125,
0.0097808837890625,
-0.0123291015625,
0.0186920166015625,
-0.005733489990234375,
-0.00222015380859375,
0.01540374755859375,
0.02056884765625,
-0.0016412734985351562,
0.021026611328125,
-0.00482177734375,
0.0249176025390625,
-0.00000762939453125,
-0.00872039794921875,
0.0142669677734375,
-0.0246124267578125,
-0.006221771240234375,
-0.0080718994140625,
-0.01354217529296875,
-0.00968170166015625,
-0.0129547119140625,
-0.01219940185546875,
0.01129150390625,
0.0173187255859375,
-0.01276397705078125,
-0.017578125,
0.01275634765625,
0.06793212890625,
0.0145721435546875,
-0.0013523101806640625,
-0.00826263427734375,
0.0260162353515625,
-0.01169586181640625,
-0.0155487060546875,
-0.03839111328125,
0.018707275390625,
0.00879669189453125,
0.0255584716796875,
0.00434112548828125,
0.027618408203125,
0.0186004638671875,
-0.053436279296875,
0.020355224609375,
0.0217437744140625,
0.0231475830078125,
-0.0191192626953125,
0.0219879150390625,
0.01873779296875,
0.002155303955078125,
0.012939453125,
-0.033355712890625,
-0.040618896484375,
0.0203704833984375,
-0.0243072509765625,
0.055419921875,
-0.01145172119140625,
0.0268707275390625,
-0.00894927978515625,
-0.0169525146484375,
0.0300140380859375,
-0.00042629241943359375,
-0.001708984375,
0.009857177734375,
0.0175933837890625,
0.019561767578125,
-0.005146026611328125,
-0.0108184814453125,
-0.0010442733764648438,
-0.00955963134765625,
0.037506103515625,
0.0086822509765625,
-0.001850128173828125,
0.00968170166015625,
-0.003475189208984375,
-0.013671875,
0.01409912109375,
0.00004011392593383789,
0.0160064697265625,
0.0159454345703125,
-0.043975830078125,
-0.01515960693359375,
0.040924072265625,
0.0014543533325195312,
-0.038665771484375,
-0.03326416015625,
0.0080413818359375,
-0.01236724853515625,
-0.03411865234375,
0.01290130615234375,
0.00904083251953125,
0.02581787109375,
-0.017578125,
-0.003772735595703125,
-0.043792724609375,
-0.007259368896484375,
0.00676727294921875,
-0.007198333740234375,
0.014312744140625,
-0.03350830078125,
0.0100250244140625,
0.018890380859375,
-0.0190582275390625,
0.01141357421875,
0.0209503173828125,
-0.005260467529296875,
-0.020538330078125,
0.0231781005859375,
0.0033664703369140625,
-0.00679779052734375,
-0.007694244384765625,
0.002437591552734375,
0.01277923583984375,
-0.0169219970703125,
-0.01074981689453125,
-0.00252532958984375,
0.013427734375,
0.0259857177734375,
0.0175018310546875,
0.018707275390625,
-0.0094757080078125,
0.0020427703857421875,
0.0038623809814453125,
-0.0380859375,
-0.0169677734375,
-0.0229644775390625,
-0.01030731201171875,
0.0147705078125,
-0.005878448486328125,
0.03045654296875,
0.0115509033203125,
0.0305023193359375,
-0.037109375,
0.0167694091796875,
0.0032196044921875,
-0.0180206298828125,
0.0012998580932617188,
0.0008029937744140625,
0.0088653564453125,
-0.0099334716796875,
-0.0023136138916015625,
0.01052093505859375,
-0.0005803108215332031,
0.005218505859375,
-0.00388336181640625,
-0.0352783203125,
0.0123291015625,
-0.00017452239990234375,
0.0218963623046875,
-0.01052093505859375,
0.0169219970703125,
-0.007099151611328125,
-0.0030574798583984375,
0.01279449462890625,
-0.00872802734375,
0.01509857177734375,
-0.00481414794921875,
-0.01593017578125,
0.0108489990234375,
0.03350830078125,
0.040252685546875,
0.003040313720703125,
0.00421905517578125,
0.0219573974609375,
0.0101165771484375,
0.0006461143493652344,
0.00244903564453125,
-0.03057861328125,
-0.029693603515625,
0.007511138916015625,
0.0012111663818359375,
-0.039459228515625,
-0.01427459716796875,
0.0159912109375,
-0.0052947998046875,
0.00450897216796875,
-0.01042938232421875,
0.0152435302734375,
-0.0139923095703125,
-0.037322998046875,
-0.00806427001953125,
0.0089111328125,
0.06787109375,
0.01363372802734375,
0.0156402587890625,
0.021881103515625,
-0.0071563720703125,
-0.006572723388671875,
-0.00536346435546875,
-0.006011962890625,
-0.017181396484375,
0.0225982666015625,
-0.0231170654296875,
-0.0015544891357421875,
-0.01568603515625,
-0.0292816162109375,
0.0290985107421875,
0.0263519287109375,
0.006763458251953125,
0.0002034902572631836,
0.005847930908203125,
-0.0100555419921875,
-0.02166748046875,
-0.0230865478515625,
-0.030120849609375,
0.0029850006103515625,
-0.022308349609375,
-0.006977081298828125,
0.0205078125,
-0.013702392578125,
0.04144287109375,
0.0047607421875,
-0.030609130859375,
-0.020355224609375,
0.007266998291015625,
-0.00045180320739746094,
0.00970458984375,
-0.019287109375,
-0.017578125,
-0.0233306884765625,
0.018585205078125,
-0.02386474609375,
0.0192718505859375,
0.02947998046875,
0.00975799560546875,
-0.006561279296875,
-0.00818634033203125,
0.005817413330078125,
0.00949859619140625,
-0.00939178466796875,
-0.03240966796875,
0.0011148452758789062,
0.006198883056640625,
-0.011688232421875,
-0.01035308837890625,
-0.00460052490234375,
-0.01143646240234375,
0.0230255126953125,
0.0024280548095703125,
-0.016357421875,
-0.0206298828125,
0.01073455810546875,
-0.0303955078125,
0.02484130859375,
0.02703857421875,
-0.01971435546875,
-0.0227203369140625,
0.01177978515625,
-0.041412353515625,
0.0017061233520507812,
-0.0303955078125,
0.0093841552734375,
-0.0137939453125,
0.0008916854858398438,
-0.026336669921875,
-0.00433349609375,
0.0205535888671875,
-0.008056640625,
-0.01007843017578125,
-0.0151519775390625,
-0.0211181640625,
-0.023895263671875,
-0.00997161865234375,
-0.006107330322265625,
-0.01351165771484375,
0.004520416259765625,
0.01053619384765625,
-0.0012416839599609375,
0.0100860595703125,
0.0236053466796875,
0.0065460205078125,
0.02545166015625,
-0.02178955078125,
0.0031681060791015625,
0.01055145263671875,
-0.0099334716796875,
0.016998291015625,
0.007175445556640625,
-0.0237579345703125,
-0.011566162109375,
-0.01910400390625,
-0.0177001953125,
0.0011749267578125,
0.0130157470703125,
0.0073699951171875,
-0.011688232421875,
0.007534027099609375,
0.01010894775390625,
-0.0164031982421875,
0.0113067626953125,
0.00530242919921875,
0.00691986083984375,
0.0271453857421875,
0.0021724700927734375,
-0.0119476318359375,
0.0014200210571289062,
-0.04083251953125,
-0.0114288330078125,
-0.0297088623046875,
0.017578125,
-0.0182647705078125,
0.0231781005859375,
-0.018280029296875,
-0.0036258697509765625,
-0.00466156005859375,
-0.041961669921875,
0.0171051025390625,
0.006137847900390625,
-0.0242919921875,
0.01409149169921875,
-0.04742431640625,
0.017913818359375,
-0.0206451416015625,
0.027557373046875,
0.025604248046875,
0.00475311279296875,
-0.023895263671875,
-0.029266357421875,
0.00201416015625,
0.01403045654296875,
-0.00901031494140625,
-0.0101470947265625,
-0.0080718994140625,
-0.0102691650390625,
0.00804901123046875,
-0.01125335693359375,
-0.00970458984375,
-0.003513336181640625,
-0.0025959014892578125,
0.04095458984375,
0.00682830810546875,
-0.02069091796875,
0.0010528564453125,
0.00873565673828125,
0.006763458251953125,
0.03497314453125,
0.0088348388671875,
-0.01261138916015625,
-0.03472900390625,
-0.0261993408203125,
0.0150299072265625,
0.01348114013671875,
0.009796142578125,
0.0022335052490234375,
0.0193939208984375,
0.003997802734375,
-0.024627685546875,
-0.01641845703125,
-0.0204315185546875,
0.01044464111328125,
-0.0029697418212890625,
-0.00469207763671875,
0.0005698204040527344,
0.03631591796875,
-0.0155029296875,
0.033294677734375,
0.0013103485107421875,
0.0183563232421875,
0.00003069639205932617,
0.0255889892578125,
0.0002853870391845703,
-0.01096343994140625,
0.03338623046875,
0.0279541015625,
0.0075225830078125,
-0.019805908203125,
-0.007053375244140625,
-0.0168304443359375,
0.01236724853515625,
0.0242156982421875,
-0.006931304931640625,
0.0103759765625,
0.0218353271484375,
0.029693603515625,
-0.004364013671875,
0.014617919921875,
0.03668212890625,
-0.005458831787109375,
0.01326751708984375,
-0.0313720703125,
-0.007411956787109375,
-0.010345458984375,
0.011566162109375,
0.02752685546875,
-0.00832366943359375,
-0.0211181640625,
-0.00804901123046875,
-0.03814697265625,
0.004604339599609375,
-0.0087890625,
-0.01107025146484375,
-0.0147705078125,
-0.01183319091796875,
-0.00576019287109375,
-0.022979736328125,
0.03253173828125,
-0.01885986328125,
0.0252685546875,
0.0140228271484375,
-0.0032329559326171875,
0.01491546630859375,
-0.00255584716796875,
-0.009552001953125,
0.0018091201782226562,
-0.01025390625,
0.034210205078125,
0.01549530029296875,
0.02783203125,
-0.01273345947265625,
0.00766754150390625,
-0.016815185546875,
-0.0074310302734375,
0.0279693603515625,
-0.00548553466796875,
-0.016845703125,
0.07379150390625,
-0.02935791015625,
0.005573272705078125,
0.00882720947265625,
0.0516357421875,
-0.00262451171875,
0.00800323486328125,
0.0094146728515625,
-0.029083251953125,
0.0216827392578125,
-0.0302734375,
0.0133514404296875,
-0.0122833251953125,
0.0128326416015625,
-0.0401611328125,
-0.020416259765625,
0.010986328125,
-0.0272979736328125,
-0.00019931793212890625,
0.002803802490234375,
-0.0263671875,
-0.0106658935546875,
-0.0086517333984375,
0.0215301513671875,
-0.0015745162963867188,
-0.0118560791015625,
0.0063018798828125,
0.0020961761474609375,
0.0101776123046875,
-0.0179443359375,
-0.0300750732421875,
0.04541015625,
0.00530242919921875,
-0.00922393798828125,
-0.00902557373046875,
0.015838623046875,
-0.020660400390625,
0.0295257568359375,
0.019134521484375,
-0.005523681640625,
0.01343536376953125,
0.0206756591796875,
-0.04986572265625,
0.0198516845703125,
-0.002216339111328125,
0.0053558349609375,
0.00618743896484375,
-0.00948333740234375,
-0.021392822265625,
-0.00821685791015625,
0.0081329345703125,
0.01385498046875,
0.014617919921875,
0.001071929931640625,
-0.0005631446838378906,
-0.0187835693359375,
0.01233673095703125,
-0.050018310546875,
-0.00308990478515625,
-0.0157318115234375,
-0.0175933837890625,
-0.00568389892578125,
-0.0430908203125,
-0.005359649658203125,
0.000926971435546875,
0.01134490966796875,
0.0148162841796875,
0.00799560546875,
0.0107421875,
-0.00939178466796875,
-0.006195068359375,
-0.005413055419921875,
-0.0179901123046875,
0.010650634765625,
-0.026947021484375,
0.00244903564453125,
0.01154327392578125,
-0.00882720947265625,
-0.01033782958984375,
-0.0202789306640625,
-0.0031223297119140625,
0.00836181640625,
-0.0113525390625,
0.01496124267578125,
0.024444580078125,
0.00975799560546875,
-0.0052490234375,
-0.007617950439453125,
0.0253143310546875,
0.005176544189453125,
0.005565643310546875,
-0.01397705078125,
-0.00893402099609375,
0.0121612548828125,
0.026397705078125,
0.021209716796875,
0.0011386871337890625,
0.0081634521484375,
-0.033172607421875,
-0.042877197265625,
0.0017805099487304688,
0.0360107421875,
-0.048553466796875,
-0.028961181640625,
0.0009946823120117188,
0.0179443359375,
-0.01097869873046875,
-0.022430419921875,
0.0214691162109375,
-0.0278167724609375,
0.02069091796875,
0.02313232421875,
0.006900787353515625,
-0.0020389556884765625,
0.035308837890625,
0.0157318115234375,
-0.0088958740234375,
-0.0024318695068359375,
-0.0240478515625,
-0.0071563720703125,
0.00405120849609375,
0.0201416015625,
-0.011444091796875,
0.0184478759765625,
0.005344390869140625,
0.00396728515625,
-0.015777587890625,
-0.03143310546875,
-0.03167724609375,
0.003932952880859375,
0.001712799072265625,
-0.0213165283203125,
-0.0017452239990234375,
0.017333984375,
0.0180816650390625,
0.006927490234375,
-0.025726318359375,
0.0019083023071289062,
-0.001312255859375,
0.014312744140625,
0.0188751220703125,
0.02508544921875,
0.018951416015625,
-0.01107025146484375,
-0.01055145263671875,
-0.01221466064453125,
-0.045684814453125,
0.0281219482421875,
0.01183319091796875,
0.036285400390625,
0.051055908203125,
0.0231170654296875,
-0.0163726806640625,
-0.00649261474609375,
-0.0283050537109375,
0.0167083740234375,
0.0007138252258300781,
-0.00916290283203125,
-0.0091552734375,
-0.02239990234375,
0.0008807182312011719,
-0.050689697265625,
-0.00005549192428588867,
-0.017852783203125,
0.01036834716796875,
0.0172119140625,
-0.0199737548828125,
0.03936767578125,
-0.0008311271667480469,
0.01155853271484375,
0.0183563232421875,
0.0217132568359375,
-0.006000518798828125,
0.019683837890625,
-0.0113677978515625,
-0.006610870361328125,
0.0260009765625,
0.00504302978515625,
-0.021392822265625,
0.03961181640625,
-0.0201568603515625,
0.021331787109375,
-0.0113677978515625,
-0.0247802734375,
0.016143798828125,
0.0131378173828125,
-0.0079498291015625,
0.010833740234375,
-0.01006317138671875,
-0.027923583984375,
0.018707275390625,
0.00905609130859375,
0.0096435546875,
0.0232391357421875,
0.00914764404296875,
0.041107177734375,
-0.00850677490234375,
0.047576904296875,
0.001827239990234375,
-0.0015974044799804688,
-0.045013427734375,
0.035980224609375,
0.01629638671875,
0.0095977783203125,
0.036834716796875,
0.0092010498046875,
-0.039337158203125,
0.0183563232421875,
0.034912109375,
-0.04058837890625,
-0.0127410888671875,
0.005603790283203125,
-0.031463623046875,
-0.019683837890625,
-0.011871337890625,
0.01059722900390625,
-0.003253936767578125,
0.0267333984375,
0.007717132568359375,
0.032501220703125,
0.0013399124145507812,
0.0294342041015625,
0.003025054931640625,
-0.00872039794921875,
0.0017070770263671875,
-0.005054473876953125,
0.01824951171875,
-0.00948333740234375,
-0.0229339599609375,
0.01297760009765625,
0.02923583984375,
0.01520538330078125,
0.0068206787109375,
0.00019109249114990234,
0.0276641845703125,
-0.0328369140625,
-0.0211181640625,
0.01261138916015625,
0.0162811279296875,
0.0073394775390625,
-0.018310546875,
-0.005397796630859375,
0.0089263916015625,
0.025634765625,
0.0205230712890625,
0.057647705078125,
0.04693603515625,
0.01348876953125,
0.01061248779296875,
-0.0197601318359375,
0.0257110595703125,
-0.01265716552734375,
-0.044219970703125,
0.0017948150634765625,
-0.018096923828125,
0.012725830078125,
0.0028076171875,
-0.0285491943359375,
-0.007709503173828125,
0.050140380859375,
0.0252838134765625,
-0.003032684326171875,
-0.0160369873046875,
0.0017004013061523438,
0.0214691162109375,
-0.0154876708984375,
-0.0191497802734375,
0.00499725341796875,
-0.0171356201171875,
-0.0187225341796875,
0.0126800537109375,
-0.010467529296875,
-0.0079193115234375,
-0.01409912109375,
0.0252685546875,
-0.0208282470703125,
-0.018707275390625,
0.007595062255859375,
0.00009697675704956055,
-0.041229248046875,
0.012237548828125,
0.0035610198974609375,
-0.0031833648681640625,
-0.021942138671875,
0.007373809814453125,
-0.0009756088256835938,
0.0103302001953125,
-0.0113067626953125,
-0.0267486572265625,
0.01108551025390625,
-0.018890380859375,
0.00038242340087890625,
0.0145721435546875,
-0.005451202392578125,
-0.0049896240234375,
-0.0145263671875,
-0.019561767578125,
-0.008331298828125,
0.037017822265625,
0.034393310546875,
-0.00913238525390625,
0.028656005859375,
0.0006866455078125,
0.0060577392578125,
-0.01812744140625,
-0.03485107421875,
0.0037174224853515625,
-0.01242828369140625,
0.01096343994140625,
0.007663726806640625,
0.00909423828125,
-0.018951416015625,
-0.017486572265625,
0.00528717041015625,
0.040374755859375,
-0.0186920166015625,
-0.029754638671875,
-0.0012769699096679688,
-0.0301666259765625,
0.0245513916015625,
0.00424957275390625,
-0.00949859619140625,
-0.014434814453125,
-0.004482269287109375,
-0.0211029052734375,
-0.01309967041015625,
0.0268402099609375,
-0.005218505859375,
0.0031414031982421875,
-0.009613037109375,
0.0288543701171875,
-0.00879669189453125,
-0.00894927978515625,
-0.0283966064453125,
-0.011383056640625,
0.002193450927734375,
-0.0005383491516113281,
-0.002902984619140625,
0.01447296142578125,
-0.02337646484375,
0.02166748046875,
-0.0161895751953125,
0.04254150390625,
0.00782012939453125,
9.5367431640625e-7,
-0.023162841796875,
0.0177764892578125,
-0.0005025863647460938,
-0.047454833984375,
0.0038242340087890625,
-0.013702392578125,
0.02886962890625,
0.040618896484375,
-0.042327880859375,
0.0146331787109375,
-0.019317626953125,
0.01044464111328125,
0.0233154296875,
-0.01549530029296875,
-0.0028591156005859375,
-0.0024204254150390625,
-0.005046844482421875,
0.02947998046875,
0.0283355712890625,
0.0062103271484375,
-0.006740570068359375,
-0.0411376953125,
-0.002567291259765625,
-0.00567626953125,
-0.006999969482421875,
0.0135955810546875,
-0.006977081298828125,
-0.0179290771484375,
0.0077667236328125,
0.01404571533203125,
0.0225067138671875,
0.0028629302978515625,
-0.01076507568359375,
0.0033969879150390625,
-0.0054779052734375,
-0.0183258056640625,
-0.0013685226440429688,
-0.0017833709716796875,
0.0240020751953125,
-0.014068603515625,
0.0160675048828125,
0.03619384765625,
-0.0286865234375,
0.031402587890625,
0.01033782958984375,
0.026611328125,
0.0151214599609375,
0.00234222412109375,
-0.019378662109375,
0.0102386474609375,
0.0137786865234375,
0.0323486328125,
-0.0014247894287109375,
0.0053863525390625,
0.00624847412109375,
0.00640106201171875,
-0.0201416015625,
0.007297515869140625,
0.015716552734375,
-0.047393798828125,
-0.02984619140625,
-0.035430908203125,
0.042388916015625,
-0.0260009765625,
-0.00571441650390625,
-0.032928466796875,
0.021484375,
-0.0249481201171875,
-0.00011974573135375977,
0.0025196075439453125,
0.0220947265625,
0.0113525390625,
-0.0196990966796875,
0.048583984375,
0.020904541015625,
-0.003780364990234375,
0.035491943359375,
0.019256591796875,
0.038299560546875,
0.02423095703125,
-0.02081298828125,
0.00365447998046875,
0.0113983154296875,
0.01195526123046875,
-0.004177093505859375,
-0.01432037353515625,
-0.00592803955078125,
-0.0036182403564453125,
-0.0008134841918945312,
0.0032024383544921875,
-0.0279541015625,
0.01334381103515625,
-0.0021305084228515625,
-0.0019083023071289062,
-0.00995635986328125,
0.00019562244415283203,
-0.01316070556640625,
0.0328369140625,
0.00989532470703125,
-0.04638671875,
-0.00855255126953125,
0.0039825439453125,
0.002216339111328125,
-0.0167999267578125,
-0.025909423828125,
0.01143646240234375,
0.01800537109375,
-0.00888824462890625,
0.01751708984375,
0.012298583984375,
-0.006862640380859375,
-0.01410675048828125,
0.0224609375,
0.00952911376953125,
0.00888824462890625,
0.0152130126953125,
-0.0021457672119140625,
0.00234222412109375,
0.01337432861328125,
0.0002665519714355469,
-0.012908935546875,
0.00754547119140625,
0.0021762847900390625,
-0.0023250579833984375,
-0.04241943359375,
-0.01401519775390625,
-0.0272369384765625,
-0.0272979736328125,
0.01268768310546875,
-0.00685882568359375,
-0.00525665283203125,
-0.00951385498046875,
0.01824951171875,
-0.0037021636962890625,
-0.00933837890625,
0.001598358154296875,
0.01226043701171875,
-0.0293731689453125,
-0.045379638671875,
-0.0096893310546875,
0.01202392578125,
-0.0098419189453125,
0.036163330078125,
0.0120849609375,
-0.0047149658203125,
0.05377197265625,
0.01531219482421875,
-0.008087158203125,
-0.00414276123046875,
0.0241851806640625,
-0.01473236083984375,
0.0287933349609375,
-0.008636474609375,
0.038177490234375,
0.004917144775390625,
0.002346038818359375,
-0.035980224609375,
0.01617431640625,
0.023468017578125,
0.007686614990234375,
0.005847930908203125,
-0.014923095703125,
0.0025310516357421875,
-0.06402587890625,
-0.022125244140625,
-0.002765655517578125,
-0.01611328125,
-0.00313568115234375,
-0.020477294921875,
-0.0229644775390625,
-0.00913238525390625,
-0.0027256011962890625,
-0.004009246826171875,
-0.0181884765625,
0.0306396484375,
-0.0200042724609375,
-0.006290435791015625,
0.0034332275390625,
0.0165863037109375,
0.0294342041015625,
0.006191253662109375,
0.04791259765625,
0.00655364990234375,
0.03472900390625,
0.01422119140625,
0.01800537109375,
0.00968170166015625,
-0.01128387451171875,
-0.006256103515625,
-0.006198883056640625,
0.039093017578125,
0.03521728515625,
0.033843994140625,
-0.0181884765625,
-0.0080108642578125,
0.00531768798828125,
0.040283203125,
-0.02484130859375,
-0.01561737060546875,
0.0408935546875,
0.001987457275390625,
0.00904083251953125,
0.00295257568359375,
0.01251983642578125,
-0.0167694091796875,
0.0232696533203125,
-0.01111602783203125,
0.018157958984375,
-0.00469970703125,
0.0120697021484375,
0.017120361328125,
-0.02142333984375,
-0.00201416015625,
0.00237274169921875,
-0.034332275390625,
-0.0260467529296875,
-0.0233917236328125,
0.029693603515625,
-0.020416259765625,
0.035400390625,
-0.0033111572265625,
-0.004177093505859375,
-0.01122283935546875,
-0.01068115234375,
0.034454345703125,
0.0166015625,
0.0078582763671875,
-0.007110595703125,
0.01708984375,
0.0086212158203125,
0.00836181640625,
-0.026611328125,
0.05474853515625,
-0.0220489501953125,
0.045440673828125,
-0.019195556640625,
0.0252227783203125,
0.0160980224609375,
-0.0003628730773925781,
0.0012388229370117188,
0.003185272216796875,
-0.00030231475830078125,
-0.0015459060668945312,
0.01102447509765625,
-0.014434814453125,
-0.00757598876953125,
-0.0040130615234375,
-0.003631591796875,
0.0174713134765625,
-0.0092010498046875,
-0.006389617919921875,
0.0128631591796875,
-0.0179290771484375,
-0.0263824462890625,
-0.007328033447265625,
-0.001972198486328125,
-0.0005340576171875,
0.0233001708984375,
-0.0042266845703125,
0.0236968994140625,
-0.00960540771484375,
-0.021575927734375,
0.0089569091796875,
-0.017425537109375,
-0.052581787109375,
-0.033660888671875,
0.0002734661102294922,
0.007297515869140625,
-0.0223388671875,
-0.0154876708984375,
0.002399444580078125,
-0.0379638671875,
0.009552001953125,
0.01386260986328125,
-0.017730712890625,
0.00826263427734375,
-0.0014600753784179688,
0.0050811767578125,
0.006984710693359375,
0.0233154296875,
0.005573272705078125,
-0.01483917236328125,
0.0192413330078125,
-0.00626373291015625,
-0.037353515625,
0.0019350051879882812,
0.051605224609375,
-0.0222015380859375,
0.01300811767578125,
0.00934600830078125,
-0.00495147705078125,
0.0171051025390625,
0.021331787109375,
0.002849578857421875,
-0.00719451904296875,
0.04364013671875,
-0.003963470458984375,
0.00040411949157714844,
-0.012664794921875,
0.0079498291015625,
-0.013397216796875,
-0.0045166015625,
-0.03662109375,
-0.003292083740234375,
0.032745361328125,
-0.0231781005859375,
0.0123748779296875,
-0.007659912109375,
0.026824951171875,
-0.0023365020751953125,
-0.0182647705078125,
-0.02923583984375,
0.0009064674377441406,
-0.0252838134765625,
0.00748443603515625,
-0.0037746429443359375,
-0.032684326171875,
0.01629638671875,
-0.0229949951171875,
0.0012102127075195312,
0.017791748046875,
-0.01476287841796875,
-0.0450439453125,
0.02838134765625,
-0.01120758056640625,
-0.0255889892578125,
0.0015735626220703125,
-0.011444091796875,
-0.00514984130859375,
0.02252197265625,
-0.00484466552734375,
-0.0258026123046875,
0.01654052734375,
-0.01265716552734375,
0.032135009765625,
0.043212890625,
0.02374267578125,
0.007404327392578125,
-0.037445068359375,
-0.0085296630859375,
-0.0085296630859375,
-0.041473388671875,
-0.00598907470703125,
-0.006175994873046875,
0.00921630859375,
0.0260467529296875,
0.00855255126953125,
-0.0262451171875,
0.04364013671875,
-0.0003993511199951172,
0.0138092041015625,
-0.01027679443359375,
0.00264739990234375,
0.01439666748046875,
-0.036529541015625,
-0.0154266357421875,
-0.018310546875,
-0.01141357421875,
0.0289764404296875,
-0.01348114013671875,
0.0037860870361328125,
0.00817108154296875,
0.01151275634765625,
0.0195159912109375,
0.0228271484375,
-0.0005993843078613281,
0.0019464492797851562,
-0.0252685546875,
0.0022602081298828125,
0.0021915435791015625,
0.0005121231079101562,
0.0115966796875,
-0.01490020751953125,
0.0147552490234375,
-0.058319091796875,
-0.0174713134765625,
0.0009927749633789062,
0.032867431640625,
-0.0113525390625,
0.0230255126953125,
-0.0111846923828125,
0.0196380615234375,
-0.035369873046875,
-0.00350189208984375,
0.0011444091796875,
0.043792724609375,
0.0283660888671875,
-0.0217742919921875,
-0.01739501953125,
-0.00637054443359375,
-0.0223388671875,
-0.0004725456237792969,
-0.0266571044921875,
-0.006519317626953125,
0.0208892822265625,
0.004425048828125,
0.0281982421875,
0.0184326171875,
-0.00318145751953125,
-0.011138916015625,
0.0148162841796875,
-0.0189971923828125,
0.01427459716796875,
-0.008941650390625,
0.006622314453125,
-0.000720977783203125,
-0.031280517578125,
-0.001842498779296875,
-0.02593994140625,
-0.005512237548828125,
-0.04888916015625,
0.02838134765625,
-0.013763427734375,
-0.00560760498046875,
0.023651123046875,
0.00830841064453125,
0.037872314453125,
0.03759765625,
0.022491455078125,
-0.032379150390625,
0.0171966552734375,
0.0172576904296875,
0.0004887580871582031,
0.0084228515625,
0.0140533447265625,
0.0124664306640625,
-0.0006422996520996094,
0.0164794921875,
0.017059326171875,
0.01435089111328125,
-0.005245208740234375,
-0.001102447509765625,
0.008758544921875,
0.034332275390625,
-0.0233001708984375,
-0.02130126953125,
-0.00902557373046875,
-0.01206207275390625,
0.03265380859375,
-0.00281524658203125,
-0.00621795654296875,
0.0034656524658203125,
0.0079498291015625,
0.025146484375,
0.036865234375,
0.0162200927734375,
0.0304412841796875,
-0.01233673095703125,
0.0328369140625,
0.00554656982421875,
0.01438140869140625,
0.00041413307189941406,
-0.016998291015625,
0.025787353515625,
-0.00650787353515625,
0.01059722900390625,
0.039764404296875,
-0.02996826171875,
0.01226043701171875,
-0.0174407958984375,
0.0021686553955078125,
0.00872802734375,
0.0217742919921875,
-0.005168914794921875,
-0.0191497802734375,
0.01450347900390625,
0.005992889404296875,
-0.01529693603515625,
-0.048675537109375,
0.00423431396484375,
0.021392822265625,
0.0286407470703125,
-0.0022487640380859375,
-0.0162506103515625,
0.0175628662109375,
-0.01529693603515625,
-0.01378631591796875,
-0.006008148193359375,
0.01235198974609375,
-0.0221710205078125,
0.007541656494140625,
-0.019500732421875,
0.0096435546875,
0.01092529296875,
-0.0219268798828125,
0.040985107421875,
-0.02056884765625,
0.0185089111328125,
0.0193328857421875,
0.030731201171875,
0.01255035400390625,
-0.00643157958984375,
0.022186279296875,
-0.006824493408203125,
0.00426483154296875,
0.0308074951171875,
-0.0007886886596679688,
0.0301361083984375,
0.00687408447265625,
0.0017757415771484375,
-0.00322723388671875,
0.00769805908203125,
-0.003345489501953125,
-0.021881103515625,
0.00205230712890625,
-0.0231475830078125,
-0.005420684814453125,
-0.00814056396484375,
0.019683837890625,
0.01342010498046875,
-0.0027294158935546875,
-0.013519287109375,
0.0011243820190429688,
0.004673004150390625,
-0.025909423828125,
0.0210418701171875,
0.018218994140625,
-0.04656982421875,
0.0233612060546875,
-0.0109710693359375,
-0.0108489990234375,
-0.01163482666015625,
-0.01226806640625,
-0.038421630859375,
0.0282440185546875,
0.0212860107421875,
0.031341552734375,
-0.0006341934204101562,
-0.0034732818603515625,
0.006359100341796875,
0.005237579345703125,
-0.00829315185546875,
0.0328369140625,
0.02520751953125,
0.01425933837890625,
-0.0148773193359375,
0.023193359375,
0.017242431640625,
-0.004985809326171875,
0.009674072265625,
-0.004215240478515625,
-0.0013189315795898438,
-0.0015316009521484375,
0.0022449493408203125,
-0.01212310791015625,
0.0242767333984375,
-0.0170440673828125,
-0.0282745361328125,
0.012054443359375,
-0.01465606689453125,
0.00978851318359375,
0.0199737548828125,
-0.0272216796875,
-0.00307464599609375,
0.01248931884765625,
0.0112762451171875,
0.024688720703125,
0.00569915771484375,
-0.01016998291015625,
-0.029266357421875,
-0.00191497802734375,
0.01959228515625,
0.019927978515625,
0.0254364013671875,
0.031524658203125,
0.004779815673828125,
-0.03533935546875,
0.0186920166015625,
0.007778167724609375,
-0.02191162109375,
-0.041961669921875,
-0.0374755859375,
-0.004852294921875,
0.022918701171875,
-0.0074920654296875,
0.00760650634765625,
-0.0151214599609375,
0.0114288330078125,
0.0080718994140625,
0.0283050537109375,
-0.012969970703125,
0.0276947021484375,
-0.0042266845703125,
0.01280975341796875,
-0.025909423828125,
-0.01242828369140625,
0.0057220458984375,
0.027984619140625,
-0.041656494140625,
-0.01361083984375,
0.021087646484375,
-0.00850677490234375,
0.00791168212890625,
-0.03118896484375,
0.018280029296875,
0.01535797119140625,
-0.0007314682006835938,
-0.0026912689208984375,
0.0264129638671875,
0.02801513671875,
0.005329132080078125,
0.043182373046875,
0.007659912109375,
0.01161956787109375,
0.036773681640625,
0.0006823539733886719,
0.005748748779296875,
0.0123138427734375,
0.007354736328125,
-0.0186767578125,
-0.025115966796875,
0.0264434814453125,
0.0185394287109375,
-0.041046142578125,
0.0266876220703125,
-0.01548004150390625,
-0.0078887939453125,
0.00994873046875,
-0.006053924560546875,
-0.003162384033203125,
0.006397247314453125,
0.0037403106689453125,
-0.01146697998046875,
-0.037139892578125,
-0.0121612548828125,
-0.00035381317138671875,
-0.0158233642578125,
0.00969696044921875,
0.0028591156005859375,
0.011260986328125,
0.0242156982421875,
0.0028324127197265625,
-0.00728607177734375,
-0.00553131103515625,
-0.01517486572265625,
0.03033447265625,
-0.00396728515625,
0.037261962890625,
-0.0030269622802734375,
0.00649261474609375,
-0.01053619384765625,
0.01465606689453125,
0.007080078125,
-0.03680419921875,
0.007434844970703125,
-0.005275726318359375,
0.00020074844360351562,
0.0182647705078125,
-0.03521728515625,
-0.0032138824462890625,
0.00927734375,
0.005512237548828125,
0.0110626220703125,
0.002285003662109375,
-0.0328369140625,
0.01197052001953125,
-0.00640106201171875,
0.001018524169921875,
-0.03271484375,
0.0005426406860351562,
0.013946533203125,
0.0101165771484375,
-0.037353515625,
0.01104736328125,
-0.0235595703125,
-0.00531768798828125,
-0.0247344970703125,
-0.002086639404296875,
0.004947662353515625,
0.005283355712890625,
0.053497314453125,
0.0188751220703125,
0.02679443359375,
0.005062103271484375,
-0.053436279296875,
0.0013418197631835938,
0.0014123916625976562,
0.016326904296875,
0.01471710205078125,
-0.006229400634765625,
0.017913818359375,
0.020538330078125,
0.0178375244140625,
-0.007190704345703125,
-0.0100860595703125,
0.002048492431640625,
0.0322265625,
0.024810791015625,
-0.00792694091796875,
-0.0452880859375,
0.0112152099609375,
-0.0019474029541015625,
0.01084136962890625,
0.05535888671875,
-0.0004787445068359375,
0.00421142578125,
0.0138702392578125,
-0.009918212890625,
0.005344390869140625,
0.00771331787109375,
0.005741119384765625,
0.01476287841796875,
0.0535888671875,
0.0011529922485351562,
0.002338409423828125,
0.0020465850830078125,
-0.01490020751953125,
0.046478271484375,
0.01558685302734375,
0.005985260009765625,
0.01483154296875,
-0.0088653564453125,
0.0178070068359375,
-0.0014705657958984375,
-0.03228759765625,
0.0004794597625732422,
-0.0215606689453125,
-0.004947662353515625,
0.01549530029296875,
-0.0244598388671875,
0.01506805419921875,
-0.016571044921875,
0.0142059326171875,
-0.00612640380859375,
0.01105499267578125,
0.003757476806640625,
0.007259368896484375,
-0.0260467529296875,
0.00505828857421875,
0.0275726318359375,
-0.0263519287109375,
0.006000518798828125,
0.01690673828125,
-0.000522613525390625,
0.00847625732421875,
-0.024505615234375,
0.02264404296875,
-0.0014171600341796875,
0.040252685546875,
-0.0014562606811523438,
-0.031768798828125,
0.0238189697265625,
-0.024169921875,
0.02117919921875,
0.0138702392578125,
-0.0014886856079101562,
0.0281982421875,
0.004367828369140625,
-0.0205535888671875,
0.0243682861328125,
-0.00279998779296875,
0.01340484619140625,
-0.04913330078125,
-0.0105743408203125,
-0.0162506103515625,
0.041900634765625,
-0.01256561279296875,
-0.01486968994140625,
-0.01416015625,
0.0145263671875,
0.00567626953125,
0.0008387565612792969,
-0.0206756591796875,
-0.0273284912109375,
0.0031185150146484375,
-0.01251220703125,
-0.016143798828125,
0.0097808837890625,
-0.01546478271484375,
0.041900634765625,
-0.0139007568359375,
-0.0262603759765625,
0.01525115966796875,
-0.0008487701416015625,
0.027008056640625,
0.0017976760864257812,
-0.0135955810546875,
-0.0283050537109375,
0.0269927978515625,
-0.00722503662109375,
-0.005466461181640625,
0.003253936767578125,
-0.00849151611328125,
-0.0203704833984375,
0.004352569580078125,
0.01898193359375,
0.0101470947265625,
-0.006595611572265625,
-0.0037479400634765625,
-0.0008058547973632812,
0.0224456787109375,
-0.033935546875,
-0.064208984375,
-0.0152130126953125,
0.0165863037109375,
0.0089263916015625,
0.007495880126953125,
-0.011688232421875,
-0.0576171875,
-0.00473785400390625,
-0.007793426513671875,
0.0343017578125,
0.00738525390625,
-0.02337646484375,
-0.006160736083984375,
-0.0260467529296875,
0.012451171875,
-0.046142578125,
-0.0027179718017578125,
-0.039764404296875,
0.01480865478515625,
-0.0093231201171875,
-0.0119171142578125,
0.007205963134765625,
-0.05023193359375,
-0.0379638671875,
-0.0027065277099609375,
-0.016510009765625,
0.0191497802734375,
-0.00910186767578125,
-0.03271484375,
0.0258636474609375,
-0.05072021484375,
0.02587890625,
-0.027252197265625,
0.001842498779296875,
0.0135040283203125,
-0.040679931640625,
0.01016998291015625,
-0.007144927978515625,
0.0225067138671875,
-0.054595947265625,
-0.01434326171875,
0.001155853271484375,
-0.007785797119140625,
-0.011627197265625,
0.03192138671875,
0.00310516357421875,
0.025238037109375,
-0.0231475830078125,
0.005001068115234375,
0.0271453857421875,
-0.00208282470703125,
-0.030548095703125,
-0.01837158203125,
-0.034149169921875,
0.006816864013671875,
-0.0156707763671875,
-0.0159759521484375,
-0.0165863037109375,
-0.003307342529296875,
0.0037689208984375,
0.00392913818359375,
-0.0038166046142578125,
0.01012420654296875,
0.0008230209350585938,
-0.031402587890625,
-0.0248565673828125,
-0.0111083984375,
-0.007053375244140625,
0.018402099609375,
0.0109100341796875
] |
ours_528
|
We start by noting that \(7^{491} \equiv 1 \pmod{983}\), since 983 is prime and 491 is a factor of 982. Therefore, the sum can be simplified as:
$$
S = \sum_{i=1}^{982} 7^{i^{2}} = 2 \sum_{i=1}^{491} 7^{i^{2}} = 2\left(1 + 2 \sum_{i=1}^{245} 7^{i^{2}}\right)
$$
Consider the set \(S\) of all nonzero residues \(x\) such that there exists an integer \(a\) with \(x \equiv a^{2} \pmod{491}\). We call \(S\) the set of quadratic residues. Let
$$
T = \sum_{i=1}^{245} 7^{i^{2}} = \sum_{k \in S} 7^{k}
$$
A known result shows that any quadratic residue can be expressed as the sum of two other quadratic residues in exactly 122 ways, and any nonzero \(x \notin S\) can be expressed as the sum of two other elements of \(S\) in exactly 123 ways. Since \(491 \equiv 3 \pmod{4}\), no two quadratic residues sum to zero. Therefore, when we square \(T\), we get
$$
T^{2} = \sum_{i, j \in S} 7^{i+j} = 122 \sum_{k \in S} 7^{k} + 123 \sum_{k \notin S} 7^{k} = 123 \sum_{k=1}^{490} 7^{k} - \sum_{k \in S} 7^{k}
$$
Evaluating the geometric series on the right-hand side, we get \(T^{2} + T + 123 \equiv 0 \pmod{983}\). Multiplying by 4, we have \(4T^{2} + 4T + 492 \equiv (2T+1)^{2} + 491 \equiv 0\), so \((2T+1)^{2} \equiv 492\). We find that \(T = 450\) works.
Thus, the remainder \(r\) is \(\boxed{450}\).
|
450
|
{
"competition": "us_comps",
"dataset": "Ours",
"posts": null,
"source": "OMOSoln2-2.md"
}
|
Suppose that
$$
\sum_{i=1}^{982} 7^{i^{2}}
$$
can be expressed in the form \(983 q + r\), where \(q\) and \(r\) are integers and \(0 \leq r \leq 492\). Find \(r\).
|
[
"/Mathematics/DiscreteMathematics/DivisionProblems",
"/Mathematics/DiscreteMathematics/GeneralDiscreteMathematics/DiscreteMath",
"/Mathematics/DiscreteMathematics/GeneralDiscreteMathematics/DiscreteMathematics",
"/Mathematics/NumberTheory/Congruences/Congruence",
"/Mathematics/NumberTheory/Congruences/Mod",
"/Mathematics/NumberTheory/Congruences/ModularArithmetic",
"/Mathematics/NumberTheory/Congruences/Modulus",
"/Mathematics/NumberTheory/Congruences/Residue",
"/Mathematics/NumberTheory/GeneralNumberTheory/ElementaryMethods",
"/Mathematics/NumberTheory/GeneralNumberTheory/ElementaryNumberTheory",
"/Mathematics/NumberTheory/GeneralNumberTheory/NumberTheory",
"/Mathematics/NumberTheory/PrimeNumbers/PrimeNumberProperties"
] |
Use the order of 7 modulo 983 and the structure of quadratic residues modulo 491 to convert the sum into a quadratic congruence for a smaller sub‑sum.
|
[
0.00006312131881713867,
-0.0186767578125,
0.03692626953125,
0.0020046234130859375,
0.0005855560302734375,
0.0011548995971679688,
0.00351715087890625,
0.000007092952728271484,
0.020050048828125,
-0.0002541542053222656,
0.029876708984375,
-0.048065185546875,
0.0017633438110351562,
0.0184326171875,
0.0011453628540039062,
-0.051361083984375,
0.0160980224609375,
0.01230621337890625,
0.02325439453125,
0.0015869140625,
-0.0144805908203125,
-0.0158538818359375,
-0.04541015625,
0.023101806640625,
-0.0335693359375,
0.006397247314453125,
-0.02685546875,
0.00007587671279907227,
0.0221710205078125,
0.018280029296875,
-0.00983428955078125,
-0.01502227783203125,
-0.004253387451171875,
-0.00493621826171875,
-0.0022487640380859375,
-0.0123748779296875,
0.0048980712890625,
-0.002689361572265625,
-0.0079498291015625,
0.0206146240234375,
-0.0205535888671875,
0.00971221923828125,
-0.01201629638671875,
0.00531005859375,
-0.005817413330078125,
0.0001779794692993164,
0.0009484291076660156,
-0.01293182373046875,
-0.00238800048828125,
0.004974365234375,
-0.0100250244140625,
-0.00774383544921875,
-0.0010395050048828125,
-0.00859832763671875,
-0.00411224365234375,
-0.06671142578125,
-0.00211334228515625,
0.005237579345703125,
-0.006420135498046875,
-0.01383209228515625,
0.00794219970703125,
0.0333251953125,
-0.0594482421875,
-0.0270538330078125,
0.004791259765625,
-0.0030364990234375,
-0.0002779960632324219,
-0.04022216796875,
-0.0086669921875,
0.00936126708984375,
-0.00614166259765625,
0.0159149169921875,
-0.0180816650390625,
0.0092315673828125,
0.045196533203125,
-0.00799560546875,
-0.0122833251953125,
0.0132598876953125,
-0.0074005126953125,
0.005077362060546875,
-0.0060882568359375,
0.01497650146484375,
0.011016845703125,
-0.00189208984375,
0.00885009765625,
-0.01251220703125,
0.0104827880859375,
0.01195526123046875,
0.042022705078125,
-0.01091766357421875,
0.0019197463989257812,
0.01403045654296875,
0.04510498046875,
-0.03515625,
0.001331329345703125,
0.0018663406372070312,
-0.00994873046875,
-0.004024505615234375,
-0.003032684326171875,
0.01462554931640625,
-0.006351470947265625,
-0.0043792724609375,
-0.003978729248046875,
0.007686614990234375,
-0.0584716796875,
-0.0088043212890625,
-0.0014219284057617188,
0.0070343017578125,
0.0008091926574707031,
0.03179931640625,
0.0009784698486328125,
0.01055145263671875,
0.0333251953125,
0.0259552001953125,
-0.0018224716186523438,
-0.007602691650390625,
0.0009717941284179688,
0.00021409988403320312,
-0.006618499755859375,
-0.01117706298828125,
-0.0089111328125,
-0.0007143020629882812,
-0.000980377197265625,
0.0011196136474609375,
0.0072784423828125,
-0.017669677734375,
-0.002197265625,
-0.01004791259765625,
-0.0034427642822265625,
0.0220947265625,
0.01641845703125,
0.003719329833984375,
-0.03143310546875,
-0.0243682861328125,
-0.045318603515625,
0.0019073486328125,
-0.006885528564453125,
-0.01446533203125,
-0.00714111328125,
0.0147705078125,
0.00550079345703125,
-0.00719451904296875,
0.01331329345703125,
0.03289794921875,
-0.01015472412109375,
0.010101318359375,
0.006988525390625,
-0.0048065185546875,
0.0207366943359375,
-0.00858306884765625,
0.0092315673828125,
0.0069580078125,
-0.0004830360412597656,
0.004047393798828125,
0.005924224853515625,
0.0118865966796875,
0.0199127197265625,
0.00890350341796875,
-0.0281219482421875,
0.017730712890625,
0.0004982948303222656,
-0.00441741943359375,
-0.0102386474609375,
0.005306243896484375,
-0.005878448486328125,
-0.0079498291015625,
-0.021026611328125,
0.02655029296875,
-0.01513671875,
0.0030384063720703125,
0.02166748046875,
-0.01055908203125,
-0.0284271240234375,
-0.0141143798828125,
-0.0013189315795898438,
-0.0020122528076171875,
-0.00927734375,
0.0401611328125,
-0.0154571533203125,
0.0205535888671875,
0.0079193115234375,
-0.05145263671875,
-0.017852783203125,
0.005641937255859375,
0.00431060791015625,
0.00574493408203125,
0.006801605224609375,
0.0033130645751953125,
0.0237884521484375,
0.0146484375,
0.0288238525390625,
-0.01739501953125,
-0.00157928466796875,
0.0163726806640625,
-0.03619384765625,
-0.01500701904296875,
0.0091552734375,
-0.0145111083984375,
0.0213623046875,
0.01392364501953125,
-0.01800537109375,
0.0194244384765625,
0.006053924560546875,
0.006702423095703125,
0.0257415771484375,
-0.0024242401123046875,
-0.0035247802734375,
0.01959228515625,
0.001953125,
0.0096435546875,
0.0135650634765625,
-0.00980377197265625,
-0.001369476318359375,
-0.087890625,
-0.007110595703125,
-0.0133056640625,
-0.0202484130859375,
0.014495849609375,
0.0026378631591796875,
-0.0007333755493164062,
-0.01186370849609375,
0.00946807861328125,
-0.0122222900390625,
-0.00975799560546875,
-0.0268707275390625,
-0.011993408203125,
0.01462554931640625,
-0.0008001327514648438,
-0.01371002197265625,
0.01366424560546875,
0.033294677734375,
0.0144195556640625,
-0.0195770263671875,
-0.007488250732421875,
-0.02044677734375,
0.004611968994140625,
-0.0170440673828125,
-0.02191162109375,
0.01175689697265625,
-0.0169219970703125,
0.01230621337890625,
0.00035643577575683594,
0.01629638671875,
0.00737762451171875,
-0.000537872314453125,
0.006717681884765625,
-0.00800323486328125,
0.0028057098388671875,
-0.0009579658508300781,
-0.011322021484375,
-0.0044097900390625,
0.01031494140625,
-0.026702880859375,
-0.005924224853515625,
0.024810791015625,
-0.00531768798828125,
0.0188751220703125,
-0.01204681396484375,
-0.026031494140625,
0.01152801513671875,
0.0145721435546875,
-0.01495361328125,
-0.0099639892578125,
-0.0084228515625,
0.00177764892578125,
-0.0037689208984375,
0.0043792724609375,
-0.0113677978515625,
0.0171356201171875,
0.00231170654296875,
0.047119140625,
0.00399017333984375,
0.008331298828125,
-0.002582550048828125,
0.024017333984375,
-0.0118865966796875,
0.002010345458984375,
-0.00766754150390625,
0.01544952392578125,
-0.0043792724609375,
0.00878143310546875,
-0.013641357421875,
0.002452850341796875,
0.0017862319946289062,
0.0011310577392578125,
-0.016021728515625,
0.01288604736328125,
-0.01016998291015625,
-0.006481170654296875,
0.0012035369873046875,
-0.0020542144775390625,
-0.0135345458984375,
-0.0137939453125,
0.005237579345703125,
0.0743408203125,
-0.0218353271484375,
-0.004238128662109375,
0.0114898681640625,
-0.00439453125,
-0.0272674560546875,
0.0204315185546875,
0.005016326904296875,
-0.004528045654296875,
-0.0088348388671875,
-0.011077880859375,
-0.0010595321655273438,
0.0005779266357421875,
0.0202178955078125,
0.0037593841552734375,
-0.04071044921875,
0.01284027099609375,
0.024261474609375,
-0.004070281982421875,
0.0161590576171875,
-0.030120849609375,
-0.0186309814453125,
0.0053253173828125,
0.016845703125,
-0.005847930908203125,
0.004852294921875,
0.0008153915405273438,
0.041839599609375,
-0.006984710693359375,
-0.00437164306640625,
-0.029388427734375,
0.00562286376953125,
0.0182647705078125,
-0.01325225830078125,
-0.0207672119140625,
0.021728515625,
-0.07623291015625,
-0.01141357421875,
0.0166168212890625,
-0.022796630859375,
0.004329681396484375,
0.022125244140625,
-0.0032329559326171875,
0.0318603515625,
0.00304412841796875,
-0.020904541015625,
0.005702972412109375,
-0.0097808837890625,
0.01548004150390625,
-0.010986328125,
-0.0215606689453125,
0.0111083984375,
0.014495849609375,
0.0011186599731445312,
0.03729248046875,
-0.007129669189453125,
0.005680084228515625,
0.0006175041198730469,
0.0021190643310546875,
0.0159454345703125,
-0.0374755859375,
-0.0162353515625,
-0.00473785400390625,
-0.00203704833984375,
-0.0113067626953125,
0.01340484619140625,
0.003993988037109375,
0.002422332763671875,
-0.00763702392578125,
0.0169677734375,
-0.0216217041015625,
-0.00963592529296875,
-0.0300140380859375,
0.011810302734375,
-0.048065185546875,
-0.00557708740234375,
-0.017181396484375,
-0.08563232421875,
0.01435089111328125,
-0.001209259033203125,
-0.038177490234375,
-0.01079559326171875,
-0.0007677078247070312,
0.002140045166015625,
0.002166748046875,
-0.00182342529296875,
0.00904083251953125,
0.0231170654296875,
-0.028900146484375,
0.01447296142578125,
-0.008697509765625,
-0.0013713836669921875,
-0.01259613037109375,
-0.0347900390625,
-0.03369140625,
0.00628662109375,
-0.03271484375,
0.0038242340087890625,
-0.01195526123046875,
-0.0172119140625,
0.0139312744140625,
-0.00664520263671875,
-0.00467681884765625,
-0.0008492469787597656,
0.024200439453125,
-0.0153045654296875,
0.0020771026611328125,
-0.02197265625,
-0.016632080078125,
-0.0009593963623046875,
-0.01215362548828125,
-0.0031909942626953125,
0.006031036376953125,
0.0010242462158203125,
-0.01568603515625,
0.01959228515625,
0.0197296142578125,
0.03350830078125,
-0.0132293701171875,
0.004047393798828125,
-0.0284271240234375,
-0.005222320556640625,
-0.0017766952514648438,
-0.0005679130554199219,
-0.04193115234375,
-0.0033855438232421875,
0.010284423828125,
0.0019426345825195312,
0.0307464599609375,
0.0089569091796875,
-0.0017595291137695312,
0.01152801513671875,
-0.053497314453125,
0.005306243896484375,
0.043609619140625,
-0.0277252197265625,
0.0066070556640625,
-0.01068115234375,
0.011016845703125,
-0.0011625289916992188,
-0.0015087127685546875,
0.0257568359375,
-0.0089874267578125,
0.0262603759765625,
-0.0330810546875,
0.002437591552734375,
0.020721435546875,
-0.01934814453125,
-0.00524139404296875,
-0.018707275390625,
-0.0423583984375,
-0.00024437904357910156,
0.0445556640625,
0.01153564453125,
-0.00799560546875,
0.009765625,
-0.01558685302734375,
0.0210113525390625,
-0.0150909423828125,
0.01326751708984375,
0.004505157470703125,
-0.00003039836883544922,
0.0210723876953125,
0.007114410400390625,
-0.00571441650390625,
-0.001903533935546875,
-0.022613525390625,
0.015411376953125,
0.003925323486328125,
0.016204833984375,
-0.038787841796875,
-0.01047515869140625,
0.0005464553833007812,
0.0133819580078125,
0.0134124755859375,
0.0209197998046875,
-0.0194854736328125,
0.00817108154296875,
-0.00505828857421875,
-0.01513671875,
-0.0278472900390625,
0.02410888671875,
0.0179443359375,
-0.002910614013671875,
-0.004520416259765625,
0.0028667449951171875,
0.0281829833984375,
0.008819580078125,
0.0025501251220703125,
0.035888671875,
0.0012111663818359375,
0.04052734375,
0.032440185546875,
0.018463134765625,
0.037261962890625,
-0.002986907958984375,
0.0016565322875976562,
0.06658935546875,
-0.010345458984375,
-0.0174102783203125,
-0.0171051025390625,
0.0003643035888671875,
0.0009579658508300781,
0.0129547119140625,
0.0029430389404296875,
0.006923675537109375,
-0.03485107421875,
-0.040069580078125,
-0.0176849365234375,
0.004116058349609375,
0.024322509765625,
-0.0255889892578125,
0.03515625,
-0.015716552734375,
0.0166168212890625,
-0.037994384765625,
0.0195770263671875,
0.0169219970703125,
0.02001953125,
-0.038116455078125,
0.00749969482421875,
0.014251708984375,
-0.006702423095703125,
-0.01314544677734375,
-0.0008273124694824219,
-0.01397705078125,
-0.01038360595703125,
0.0257568359375,
0.026641845703125,
-0.00820159912109375,
0.0094451904296875,
0.0152740478515625,
0.017913818359375,
0.01374053955078125,
0.0010890960693359375,
0.005031585693359375,
0.0019311904907226562,
-0.01430511474609375,
0.03277587890625,
0.0139312744140625,
-0.02508544921875,
-0.01107025146484375,
-0.0005373954772949219,
-0.0244293212890625,
0.00830841064453125,
0.020416259765625,
-0.0187530517578125,
-0.011474609375,
0.001331329345703125,
-0.032470703125,
-0.002872467041015625,
-0.0010623931884765625,
-0.026397705078125,
0.023101806640625,
-0.04266357421875,
0.0268707275390625,
0.0022525787353515625,
0.0009255409240722656,
0.0206756591796875,
-0.01410675048828125,
-0.050872802734375,
0.0226593017578125,
0.022552490234375,
-0.00927734375,
-0.00688934326171875,
0.0218048095703125,
-0.018157958984375,
-0.0231475830078125,
0.03057861328125,
0.0078277587890625,
0.02618408203125,
-0.007602691650390625,
0.0004019737243652344,
0.019012451171875,
-0.0099334716796875,
-0.021728515625,
0.0022296905517578125,
0.01263427734375,
-0.0184326171875,
-0.00022041797637939453,
-0.03314208984375,
-0.00750732421875,
-0.00531768798828125,
0.00785064697265625,
0.01910400390625,
-0.02716064453125,
0.044036865234375,
0.001209259033203125,
-0.01398468017578125,
-0.0196380615234375,
-0.0233917236328125,
-0.01245880126953125,
0.0302886962890625,
-0.0013446807861328125,
0.026336669921875,
0.019256591796875,
-0.0321044921875,
-0.018157958984375,
-0.01477813720703125,
-0.01059722900390625,
0.01055145263671875,
0.011962890625,
-0.0005350112915039062,
-0.0249176025390625,
-0.007678985595703125,
-0.002773284912109375,
0.047698974609375,
-0.00311279296875,
0.003971099853515625,
-0.01418304443359375,
-0.009002685546875,
-0.029449462890625,
0.0005054473876953125,
0.00988006591796875,
0.0007891654968261719,
-0.013397216796875,
-0.004779815673828125,
-0.00872802734375,
0.009246826171875,
0.0253753662109375,
0.0227508544921875,
0.001140594482421875,
-0.0017995834350585938,
0.007171630859375,
0.0190277099609375,
-0.0087890625,
-0.01303863525390625,
0.0195770263671875,
-0.015167236328125,
0.004665374755859375,
-0.02740478515625,
-0.00817108154296875,
0.01227569580078125,
-0.0196075439453125,
0.022125244140625,
0.0015077590942382812,
-0.020294189453125,
0.01325225830078125,
0.0176239013671875,
-0.021392822265625,
0.0194549560546875,
0.005573272705078125,
0.012908935546875,
0.036712646484375,
0.0135040283203125,
-0.011566162109375,
0.0023822784423828125,
0.011138916015625,
0.0033664703369140625,
-0.05059814453125,
0.0018339157104492188,
-0.001953125,
0.0142974853515625,
0.0201416015625,
-0.0166473388671875,
0.00859832763671875,
-0.0140228271484375,
-0.002044677734375,
0.00021028518676757812,
-0.00644683837890625,
0.0031890869140625,
0.004703521728515625,
-0.00603485107421875,
-0.00823974609375,
0.01537322998046875,
-0.00018918514251708984,
-0.00852203369140625,
-0.00803375244140625,
-0.0184326171875,
-0.027587890625,
-0.0484619140625,
-0.01904296875,
-0.013427734375,
-0.019683837890625,
0.0504150390625,
-0.0293426513671875,
0.016571044921875,
-0.037506103515625,
0.03338623046875,
0.0062255859375,
-0.0384521484375,
0.01000213623046875,
-0.0038394927978515625,
-0.032135009765625,
-0.0313720703125,
0.0096588134765625,
0.0031642913818359375,
0.017730712890625,
0.0295562744140625,
0.037689208984375,
0.0238800048828125,
0.041046142578125,
-0.00910186767578125,
-0.00421905517578125,
0.011077880859375,
-0.00843048095703125,
-0.00681304931640625,
-0.00347900390625,
0.032470703125,
-0.0020465850830078125,
-0.01146697998046875,
0.0091552734375,
0.0088653564453125,
-0.004192352294921875,
-0.040435791015625,
-0.001590728759765625,
0.00457000732421875,
-0.011016845703125,
0.0008001327514648438,
0.019805908203125,
-0.016815185546875,
-0.01502227783203125,
-0.007625579833984375,
0.0012874603271484375,
-0.0374755859375,
0.01093292236328125,
-0.01497650146484375,
0.0153656005859375,
0.00475311279296875,
-0.0186767578125,
-0.006259918212890625,
0.004673004150390625,
0.018035888671875,
0.00211334228515625,
0.01788330078125,
0.0006999969482421875,
-0.0230560302734375,
0.00421142578125,
-0.044342041015625,
0.0171356201171875,
0.014404296875,
0.0161285400390625,
-0.00830841064453125,
-0.04583740234375,
-0.0091400146484375,
0.01180267333984375,
-0.022216796875,
0.02874755859375,
-0.00030422210693359375,
0.03509521484375,
-0.01136016845703125,
-0.0005502700805664062,
-0.007007598876953125,
-0.031097412109375,
0.01064300537109375,
-0.01031494140625,
0.0148162841796875,
-0.0004227161407470703,
0.0316162109375,
0.005199432373046875,
0.04827880859375,
0.0031986236572265625,
-0.006198883056640625,
-0.020782470703125,
0.01132965087890625,
-0.03350830078125,
0.0101165771484375,
-0.012237548828125,
0.01476287841796875,
-0.041839599609375,
0.00933074951171875,
0.01519775390625,
0.028656005859375,
-0.00891876220703125,
-0.0169219970703125,
0.035491943359375,
-0.03955078125,
-0.0161285400390625,
-0.032318115234375,
0.006954193115234375,
0.0213470458984375,
-0.024993896484375,
-0.0160675048828125,
0.0017528533935546875,
0.00037598609924316406,
0.057525634765625,
0.0257415771484375,
0.015777587890625,
-0.007030487060546875,
-0.00475311279296875,
0.01552581787109375,
0.00409698486328125,
-0.044586181640625,
0.01041412353515625,
0.056732177734375,
-0.006488800048828125,
0.0273590087890625,
-0.01247406005859375,
-0.0169219970703125,
0.0037860870361328125,
-0.0245361328125,
0.01168060302734375,
0.00861358642578125,
-0.040618896484375,
-0.00482940673828125,
-0.026214599609375,
0.046722412109375,
0.00785064697265625,
0.0281829833984375,
-0.010772705078125,
0.0042572021484375,
0.0196685791015625,
0.0069580078125,
-0.041900634765625,
-0.028839111328125,
0.017974853515625,
0.04071044921875,
-0.0225830078125,
0.01373291015625,
0.0248565673828125,
-0.0152587890625,
-0.03741455078125,
-0.00225067138671875,
0.006679534912109375,
-0.0221099853515625,
0.042266845703125,
0.0009741783142089844,
-0.0225982666015625,
0.0020236968994140625,
-0.01312255859375,
0.0200347900390625,
-0.002716064453125,
-0.0172119140625,
-0.004425048828125,
0.01239013671875,
0.041839599609375,
0.00806427001953125,
0.0219268798828125,
-0.0202484130859375,
-0.013336181640625,
-0.007152557373046875,
0.0165252685546875,
0.037078857421875,
0.006114959716796875,
0.02642822265625,
-0.004299163818359375,
0.00606536865234375,
-0.0004074573516845703,
-0.0010213851928710938,
-0.001346588134765625,
0.0030422210693359375,
-0.00788116455078125,
0.00792694091796875,
-0.0196990966796875,
-0.001483917236328125,
0.00952911376953125,
0.00667572021484375,
0.030853271484375,
-0.00035858154296875,
-0.05242919921875,
0.00867462158203125,
-0.00003409385681152344,
-0.0035991668701171875,
-0.0302581787109375,
0.01181793212890625,
-0.0158843994140625,
0.010833740234375,
-0.031646728515625,
-0.00476837158203125,
0.019561767578125,
0.003444671630859375,
0.01500701904296875,
0.007770538330078125,
0.0223388671875,
-0.00537109375,
-0.0004076957702636719,
-0.00026679039001464844,
-0.0386962890625,
-0.033935546875,
-0.0087890625,
-0.00799560546875,
0.0009632110595703125,
0.026123046875,
-0.008087158203125,
0.0283660888671875,
0.027618408203125,
0.0150146484375,
0.0169830322265625,
0.00736236572265625,
0.0009694099426269531,
-0.020538330078125,
0.010284423828125,
0.019561767578125,
-0.016021728515625,
-0.0113983154296875,
0.01522064208984375,
0.0036296844482421875,
-0.07293701171875,
0.01248931884765625,
0.00475311279296875,
-0.00684356689453125,
0.045135498046875,
0.0156402587890625,
0.031036376953125,
-0.02496337890625,
-0.0189208984375,
0.00948333740234375,
0.002655029296875,
-0.0005764961242675781,
-0.01007080078125,
-0.02508544921875,
0.00905609130859375,
0.01142120361328125,
0.0022182464599609375,
-0.01358795166015625,
-0.06011962890625,
0.01837158203125,
0.0277862548828125,
0.01436614990234375,
0.033782958984375,
-0.003269195556640625,
-0.0200042724609375,
-0.0220947265625,
-0.0289459228515625,
-0.026031494140625,
0.01151275634765625,
0.02984619140625,
-0.0189056396484375,
0.0003764629364013672,
-0.0302581787109375,
-0.00333404541015625,
0.0036487579345703125,
-0.004642486572265625,
-0.0039825439453125,
-0.01116943359375,
-0.01551055908203125,
0.023834228515625,
-0.004467010498046875,
0.00785064697265625,
-0.004730224609375,
0.033355712890625,
-0.0206451416015625,
-0.0078277587890625,
-0.0218353271484375,
-0.01513671875,
0.02783203125,
-0.0186920166015625,
-0.00176239013671875,
0.0153350830078125,
-0.003917694091796875,
-0.00043201446533203125,
0.015655517578125,
0.0201416015625,
0.0076141357421875,
0.006160736083984375,
0.03515625,
-0.0305328369140625,
-0.005435943603515625,
0.01158905029296875,
0.0169677734375,
0.0021953582763671875,
0.0037975311279296875,
-0.016387939453125,
0.027587890625,
-0.033538818359375,
0.0207977294921875,
-0.001667022705078125,
0.01104736328125,
-0.024444580078125,
-0.00479888916015625,
-0.005664825439453125,
-0.01189422607421875,
0.0011873245239257812,
-0.0199737548828125,
0.0274505615234375,
-0.028472900390625,
-0.0006079673767089844,
0.036224365234375,
-0.016510009765625,
0.0294952392578125,
-0.032928466796875,
-0.01265716552734375,
0.006893157958984375,
-0.005840301513671875,
-0.0023345947265625,
0.0287322998046875,
-0.047027587890625,
-0.005641937255859375,
-0.0181427001953125,
-0.00791168212890625,
0.01129150390625,
0.0236358642578125,
0.02484130859375,
-0.00550079345703125,
0.0155029296875,
0.04107666015625,
-0.02545166015625,
0.0252227783203125,
-0.01415252685546875,
-0.0016832351684570312,
-0.05364990234375,
0.0038051605224609375,
0.0001480579376220703,
-0.032470703125,
0.050933837890625,
-0.01300811767578125,
-0.02752685546875,
0.03790283203125,
-0.0018205642700195312,
0.023345947265625,
0.020721435546875,
0.0377197265625,
-0.023193359375,
-0.00913238525390625,
0.0262451171875,
-0.00579071044921875,
-0.0200042724609375,
-0.0044403076171875,
-0.0130615234375,
0.0246734619140625,
0.005908966064453125,
-0.00592041015625,
-0.00852203369140625,
0.0022125244140625,
0.0218658447265625,
-0.004154205322265625,
-0.01519012451171875,
-0.0229339599609375,
0.011688232421875,
0.01088714599609375,
0.032379150390625,
0.01042938232421875,
0.01898193359375,
-0.016845703125,
-0.058563232421875,
-0.01316070556640625,
0.006038665771484375,
0.006549835205078125,
-0.015289306640625,
-0.031341552734375,
0.002391815185546875,
-0.007965087890625,
-0.00884246826171875,
0.039337158203125,
0.041534423828125,
-0.0005016326904296875,
0.004947662353515625,
-0.03912353515625,
0.0094757080078125,
-0.0202789306640625,
-0.0208892822265625,
-0.023529052734375,
0.02178955078125,
0.0045318603515625,
0.035614013671875,
-0.00937652587890625,
-0.0167999267578125,
-0.022430419921875,
0.0005121231079101562,
0.00946807861328125,
-0.006351470947265625,
0.0003039836883544922,
-0.041748046875,
0.0127410888671875,
-0.01531982421875,
-0.024078369140625,
0.004833221435546875,
0.033843994140625,
-0.01519775390625,
-0.0126800537109375,
0.0234527587890625,
0.0014505386352539062,
0.007762908935546875,
-0.0024738311767578125,
0.00940704345703125,
0.00896453857421875,
0.0272674560546875,
-0.0343017578125,
0.0111541748046875,
-0.06280517578125,
0.01486968994140625,
-0.0122833251953125,
-0.025299072265625,
-0.01450347900390625,
-0.01049041748046875,
0.039764404296875,
-0.00921630859375,
0.004825592041015625,
-0.0290679931640625,
-0.018890380859375,
0.0010967254638671875,
0.0093536376953125,
0.0294189453125,
0.00127410888671875,
-0.026092529296875,
0.013214111328125,
-0.0290069580078125,
0.0018482208251953125,
-0.0184326171875,
-0.0016756057739257812,
0.03204345703125,
-0.0006842613220214844,
-0.04437255859375,
-0.00893402099609375,
0.02215576171875,
-0.00963592529296875,
0.0016870498657226562,
0.01541900634765625,
-0.0007429122924804688,
-0.00888824462890625,
0.021697998046875,
-0.025115966796875,
-0.026763916015625,
0.007965087890625,
0.0005769729614257812,
0.0227203369140625,
0.017852783203125,
0.022308349609375,
-0.014373779296875,
0.005931854248046875,
0.007633209228515625,
-0.007518768310546875,
-0.025360107421875,
0.002727508544921875,
-0.01329803466796875,
-0.01271820068359375,
-0.004055023193359375,
0.01309967041015625,
0.022216796875,
0.020965576171875,
-0.008636474609375,
-0.004627227783203125,
-0.0245361328125,
0.00586700439453125,
-0.006977081298828125,
-0.03936767578125,
-0.0011749267578125,
0.025299072265625,
0.0018329620361328125,
-0.0007677078247070312,
-0.00986480712890625,
-0.0130462646484375,
0.00621795654296875,
-0.0090179443359375,
-0.0139923095703125,
0.037567138671875,
0.01393890380859375,
0.0165557861328125,
0.0188446044921875,
-0.002105712890625,
-0.003971099853515625,
-0.032012939453125,
-0.01922607421875,
-0.006378173828125,
0.0030460357666015625,
-0.0133209228515625,
-0.00008696317672729492,
-0.01351165771484375,
-0.020355224609375,
0.0002906322479248047,
0.002582550048828125,
0.00440216064453125,
-0.002529144287109375,
0.0007276535034179688,
0.0350341796875,
0.00218963623046875,
-0.01593017578125,
0.006427764892578125,
-0.022796630859375,
0.0129241943359375,
-0.0120391845703125,
0.0254364013671875,
-0.01384735107421875,
-0.0025005340576171875,
-0.0005826950073242188,
-0.0377197265625,
-0.00543212890625,
-0.03253173828125,
-0.003936767578125,
0.006378173828125,
-0.033416748046875,
0.01456451416015625,
0.0204315185546875,
0.032196044921875,
-0.03448486328125,
-0.00730133056640625,
-0.0052490234375,
-0.0200653076171875,
0.00475311279296875,
0.007427215576171875,
-0.00409698486328125,
0.005062103271484375,
0.01219940185546875,
-0.0272216796875,
-0.01287841796875,
0.01378631591796875,
-0.00971221923828125,
-0.0032367706298828125,
0.0149688720703125,
-0.00908660888671875,
-0.02294921875,
-0.0201568603515625,
0.0247344970703125,
-0.00743865966796875,
0.004001617431640625,
0.022705078125,
0.0229034423828125,
0.00783538818359375,
0.005039215087890625,
-0.0321044921875,
-0.00606536865234375,
-0.015655517578125,
-0.0321044921875,
0.01377105712890625,
0.0311431884765625,
-0.01666259765625,
-0.044830322265625,
0.006237030029296875,
-0.038726806640625,
-0.01499176025390625,
0.0090789794921875,
0.0227203369140625,
0.0160064697265625,
0.027984619140625,
-0.0100860595703125,
-0.0017461776733398438,
-0.01535797119140625,
0.00762176513671875,
-0.0013856887817382812,
-0.01027679443359375,
0.046295166015625,
-0.005649566650390625,
0.049896240234375,
-0.039154052734375,
-0.009613037109375,
-0.03790283203125,
-0.0003802776336669922,
-0.0008187294006347656,
0.0016813278198242188,
0.003856658935546875,
-0.015228271484375,
0.00262451171875,
0.0017442703247070312,
0.03924560546875,
0.0211181640625,
-0.004291534423828125,
-0.0023822784423828125,
-0.00499725341796875,
-0.017974853515625,
0.0306854248046875,
-0.05023193359375,
-0.034637451171875,
-0.018798828125,
0.0079803466796875,
0.031768798828125,
0.0186614990234375,
-0.0101165771484375,
0.05596923828125,
-0.0021457672119140625,
0.00225067138671875,
0.0122833251953125,
-0.039459228515625,
-0.031402587890625,
-0.010589599609375,
-0.03448486328125,
0.01055908203125,
-0.0007352828979492188,
-0.0169677734375,
-0.0254974365234375,
0.004550933837890625,
0.0052947998046875,
-0.004222869873046875,
0.024078369140625,
0.0196685791015625,
-0.006298065185546875,
-0.0169830322265625,
-0.01904296875,
-0.012451171875,
-0.04559326171875,
-0.01136016845703125,
-0.0123291015625,
-0.032012939453125,
0.0132293701171875,
0.0240631103515625,
-0.005695343017578125,
0.0238037109375,
-0.01336669921875,
-0.008544921875,
0.00899505615234375,
0.037200927734375,
-0.01296234130859375,
-0.01171875,
-0.028167724609375,
-0.0281982421875,
-0.01155853271484375,
0.007904052734375,
0.01186370849609375,
0.0158538818359375,
0.056427001953125,
-0.0085601806640625,
-0.008087158203125,
-0.0278778076171875,
-0.0216064453125,
-0.00959014892578125,
-0.01345062255859375,
0.03515625,
-0.019683837890625,
0.0205230712890625,
-0.036712646484375,
0.006107330322265625,
-0.0024871826171875,
-0.004611968994140625,
0.016204833984375,
0.0079193115234375,
-0.02099609375,
0.00757598876953125,
-0.0272064208984375,
-0.032928466796875,
0.016937255859375,
-0.0177001953125,
-0.007495880126953125,
0.01403045654296875,
0.021514892578125,
0.00504302978515625,
0.006130218505859375,
-0.005214691162109375,
-0.018829345703125,
0.041290283203125,
0.0031032562255859375,
0.029815673828125,
0.04052734375,
0.033660888671875,
-0.00609588623046875,
0.0173797607421875,
-0.004886627197265625,
-0.0301971435546875,
0.004840850830078125,
0.0251312255859375,
-0.0084075927734375,
0.023773193359375,
-0.01016998291015625,
0.008514404296875,
-0.018280029296875,
0.0207672119140625,
-0.0180511474609375,
-0.011932373046875,
-0.0089111328125,
-0.00930023193359375,
-0.00528717041015625,
0.00734710693359375,
-0.0343017578125,
0.03155517578125,
-0.0246734619140625,
0.011322021484375,
-0.003719329833984375,
-0.028594970703125,
-0.010406494140625,
0.0142059326171875,
-0.0086212158203125,
0.0196075439453125,
-0.0003991127014160156,
-0.01053619384765625,
-0.04156494140625,
0.031494140625,
0.0188446044921875,
0.002899169921875,
-0.01371002197265625,
0.003910064697265625,
0.011749267578125,
0.031097412109375,
-0.02294921875,
-0.02362060546875,
-0.00206756591796875,
0.023223876953125,
0.00916290283203125,
0.0023193359375,
0.0010967254638671875,
-0.01229095458984375,
0.0162200927734375,
0.0189971923828125,
0.00008112192153930664,
-0.0018682479858398438,
-0.009124755859375,
0.0118408203125,
0.005802154541015625,
-0.0109710693359375,
-0.0313720703125,
0.008209228515625,
0.00572967529296875,
0.01279449462890625,
0.0011692047119140625,
-0.0036640167236328125,
-0.029632568359375,
-0.0050506591796875,
-0.0191192626953125,
0.02728271484375,
0.008331298828125,
-0.0087127685546875,
-0.0147247314453125,
-0.02099609375,
0.0345458984375,
-0.0002658367156982422,
0.004245758056640625,
0.03173828125,
0.022674560546875,
-0.0438232421875,
0.0066375732421875,
-0.016876220703125,
-0.001224517822265625,
0.00492095947265625,
-0.023223876953125,
0.0038051605224609375,
0.006519317626953125,
0.0023899078369140625,
-0.012603759765625,
0.01439666748046875,
0.032562255859375,
0.031280517578125,
-0.01486968994140625,
0.04534912109375,
0.01366424560546875,
-0.046478271484375,
-0.01055145263671875,
-0.0219268798828125,
-0.01666259765625,
0.0024166107177734375,
-0.045013427734375,
0.04815673828125,
0.00045299530029296875,
-0.0161285400390625,
0.0034008026123046875,
-0.002170562744140625,
0.017822265625,
-0.0007143020629882812,
0.005756378173828125,
0.04449462890625,
-0.00347137451171875,
-0.006267547607421875,
-0.036163330078125,
-0.004093170166015625,
-0.0123291015625,
-0.025177001953125,
-0.0023021697998046875,
-0.01291656494140625,
-0.0084686279296875,
-0.0129852294921875,
0.022735595703125,
-0.037811279296875,
0.0035839080810546875,
0.0014009475708007812,
-0.007389068603515625,
-0.0016756057739257812,
0.0374755859375,
0.00403594970703125,
0.033294677734375,
0.0240631103515625,
0.0196685791015625,
0.03131103515625,
-0.017913818359375,
-0.0172119140625,
-0.0343017578125,
0.0019626617431640625,
0.01263427734375,
0.0094757080078125,
0.007778167724609375,
-0.030914306640625,
-0.0047607421875,
-0.0194549560546875,
0.007904052734375,
0.0181884765625,
0.0169677734375,
-0.0036163330078125,
-0.01247406005859375,
0.01074981689453125,
0.017578125,
0.0298309326171875,
-0.0321044921875,
0.0261383056640625,
0.0186309814453125,
0.039703369140625,
0.0136871337890625,
-0.00975799560546875,
-0.0283966064453125,
0.00443267822265625,
-0.007904052734375,
0.0084228515625,
0.0207672119140625,
-0.0220947265625,
0.0018939971923828125,
-0.027252197265625,
-0.035797119140625,
0.00939178466796875,
0.02313232421875,
0.007732391357421875,
0.0164947509765625,
-0.0220489501953125,
-0.00942230224609375,
-0.0006761550903320312,
0.0258331298828125,
0.00632476806640625,
-0.0033092498779296875,
-0.0138397216796875,
0.0247955322265625,
0.0136260986328125,
0.0011730194091796875,
-0.007007598876953125,
-0.0019855499267578125,
-0.006519317626953125,
-0.004711151123046875,
-0.00989532470703125,
0.0231475830078125,
0.02801513671875,
-0.00904083251953125,
-0.04608154296875,
-0.00037288665771484375,
-0.002651214599609375,
0.0203704833984375,
0.00189971923828125,
0.03265380859375,
-0.0095062255859375,
-0.00812530517578125,
0.01287841796875,
-0.033416748046875,
0.00860595703125,
-0.0006499290466308594,
-0.0050506591796875,
-0.005558013916015625,
-0.01544952392578125,
-0.01174163818359375,
-0.00864410400390625,
-0.017974853515625,
-0.0106353759765625,
-0.01451873779296875,
-0.020965576171875,
0.007656097412109375,
-0.01038360595703125,
0.0280914306640625,
0.012725830078125,
-0.0286865234375,
0.0011768341064453125,
0.0019521713256835938,
-0.0261383056640625,
0.0049285888671875,
0.002025604248046875,
-0.026458740234375,
0.004604339599609375,
-0.0022296905517578125,
0.000054717063903808594,
-0.01323699951171875,
0.035430908203125,
0.022674560546875,
0.0250244140625,
-0.001239776611328125,
-0.0005750656127929688,
-0.015472412109375,
0.0257110595703125,
0.03192138671875,
-0.0189971923828125,
-0.01019287109375,
-0.0009632110595703125,
0.0120391845703125,
-0.0011310577392578125,
0.024169921875,
0.0034847259521484375,
-0.0008301734924316406,
0.004703521728515625,
0.0278778076171875,
-0.01248931884765625,
-0.0173492431640625,
-0.00457000732421875,
-0.00836944580078125,
0.006229400634765625,
-0.00576019287109375,
0.0411376953125,
-0.0011968612670898438,
-0.0361328125,
-0.0117645263671875,
0.01111602783203125,
0.0281829833984375,
0.01480865478515625,
0.01320648193359375,
0.00466156005859375,
-0.0023136138916015625,
0.03173828125,
0.0013666152954101562,
-0.024383544921875,
0.024627685546875,
0.004985809326171875,
0.01505279541015625,
-0.00878143310546875,
0.0084075927734375,
-0.0110321044921875,
-0.0032672882080078125,
0.007434844970703125,
0.001995086669921875,
-0.00933074951171875,
0.003376007080078125,
-0.035858154296875,
0.0006985664367675781,
0.0017786026000976562,
0.0303192138671875,
-0.0157470703125,
-0.01666259765625,
0.004150390625,
0.005401611328125,
-0.013519287109375,
0.022735595703125,
0.01125335693359375,
0.0081787109375,
0.0005345344543457031,
-0.0222625732421875,
-0.0225067138671875,
0.0033168792724609375,
-0.016326904296875,
0.01178741455078125,
0.0384521484375,
-0.016448974609375,
-0.0187225341796875,
0.0113525390625,
0.01372528076171875,
0.0069732666015625,
-0.0196990966796875,
0.003665924072265625,
-0.0013828277587890625,
0.0171051025390625,
0.01020050048828125,
0.0019445419311523438,
0.0007605552673339844,
0.03326416015625,
0.00627899169921875,
0.004795074462890625,
0.025970458984375,
-0.0015497207641601562,
0.0007367134094238281,
-0.040557861328125,
-0.01499176025390625,
0.01342010498046875,
0.017364501953125,
0.01230621337890625,
0.00943756103515625,
0.04351806640625,
0.020050048828125,
-0.01800537109375,
-0.00274658203125,
-0.0294342041015625,
0.00653076171875,
0.0098876953125,
-0.004520416259765625,
-0.0137481689453125,
0.0120086669921875,
0.0006494522094726562,
0.0325927734375,
0.01308441162109375,
0.019134521484375,
-0.01525115966796875,
-0.0017852783203125,
-0.030731201171875,
-0.031951904296875,
-0.0143280029296875,
-0.027435302734375,
-0.0005311965942382812,
-0.000667572021484375,
0.0269927978515625,
0.007320404052734375,
-0.01678466796875,
-0.0004315376281738281,
0.002803802490234375,
-0.01183319091796875,
0.017974853515625,
0.0290374755859375,
0.0174713134765625,
-0.01153564453125,
-0.0013799667358398438,
-0.00399017333984375,
0.0252532958984375,
-0.005886077880859375,
-0.0002257823944091797,
0.023681640625,
0.0266571044921875,
-0.0011510848999023438,
-0.0011930465698242188,
-0.01279449462890625,
0.0028858184814453125,
-0.0030670166015625,
-0.02117919921875,
0.01605224609375,
-0.01300811767578125,
-0.0230865478515625,
0.0006699562072753906,
0.03887939453125,
-0.0310516357421875,
-0.0007753372192382812,
-0.0186767578125,
-0.018524169921875,
-0.006458282470703125,
-0.0247650146484375,
-0.023345947265625,
-0.0157470703125,
-0.004241943359375,
0.016845703125,
-0.0184478759765625,
0.024322509765625,
0.0032596588134765625,
-0.0016546249389648438,
0.01148223876953125,
0.023834228515625,
0.039764404296875,
0.0263519287109375,
0.006305694580078125,
0.0196075439453125,
0.027374267578125,
0.016937255859375,
0.0298919677734375,
-0.0103759765625,
-0.0006089210510253906,
0.0290679931640625,
0.004978179931640625,
0.0219879150390625,
0.00992584228515625,
-0.03973388671875,
0.00885009765625,
0.02880859375,
-0.020233154296875,
0.01113128662109375,
-0.01025390625,
0.014739990234375,
-0.00679779052734375,
-0.004848480224609375,
-0.044158935546875,
-0.01270294189453125,
-0.0137176513671875,
0.039031982421875,
0.01453399658203125,
0.0011444091796875,
-0.0311279296875,
-0.017608642578125,
0.004047393798828125,
-0.0147857666015625,
0.0194854736328125,
0.005645751953125,
0.033660888671875,
-0.01119232177734375,
0.006328582763671875,
0.005435943603515625,
0.015869140625,
0.0034084320068359375,
0.00894927978515625,
0.0193328857421875,
-0.00653839111328125,
-0.01226806640625,
0.046722412109375,
-0.01910400390625,
-0.0100555419921875,
-0.0029621124267578125,
-0.0236663818359375,
0.00365447998046875,
-0.0027904510498046875,
-0.00228118896484375,
0.006343841552734375,
0.00099945068359375,
-0.0430908203125,
0.01641845703125,
-0.012420654296875,
0.014434814453125,
-0.003307342529296875,
0.005329132080078125,
-0.01560211181640625,
-0.00341796875,
0.0272979736328125,
-0.059814453125,
-0.054962158203125,
0.010162353515625,
-0.00357818603515625,
-0.05035400390625,
0.0005512237548828125,
0.0007576942443847656,
-0.01323699951171875,
-0.0285797119140625,
-0.04241943359375,
-0.00025343894958496094,
-0.0142669677734375,
-0.007633209228515625,
-0.0176849365234375,
-0.0119781494140625,
0.006267547607421875,
0.012725830078125,
0.00604248046875,
-0.0011749267578125,
0.0186004638671875,
0.0058441162109375,
0.00897216796875,
-0.0300750732421875,
0.044586181640625,
-0.005096435546875,
-0.0234222412109375,
-0.00551605224609375,
0.01593017578125,
0.0156707763671875,
0.01458740234375,
-0.003936767578125,
0.019195556640625,
-0.0078125,
-0.00508880615234375,
-0.0058135986328125,
-0.0135345458984375,
-0.0138092041015625,
-0.02734375,
-0.015869140625,
0.0027751922607421875,
-0.0197601318359375,
0.0007181167602539062,
-0.0011072158813476562,
0.0005373954772949219,
0.009674072265625,
-0.00609588623046875,
0.005157470703125,
0.01491546630859375,
0.0007457733154296875,
0.0253753662109375,
0.0090484619140625,
-0.0162353515625,
-0.0127716064453125,
-0.01032257080078125,
0.0190887451171875,
-0.014129638671875,
0.009246826171875,
0.01885986328125,
-0.0031452178955078125,
-0.0006384849548339844,
0.035247802734375,
-0.0007686614990234375,
-0.026641845703125,
0.01435089111328125,
0.0202178955078125,
-0.01158905029296875,
0.0156707763671875,
-0.0094757080078125,
0.02716064453125,
-0.0094451904296875,
-0.006259918212890625,
-0.0059051513671875,
-0.005519866943359375,
0.030364990234375,
0.0092620849609375,
0.004123687744140625,
0.0107421875,
0.003551483154296875,
0.0168914794921875,
-0.004764556884765625,
-0.01190185546875,
0.0154571533203125,
-0.036163330078125,
0.01073455810546875,
-0.01560211181640625,
-0.01593017578125,
0.01186370849609375,
0.01136016845703125,
0.0428466796875,
-0.01139068603515625,
0.0104522705078125,
0.00133514404296875,
-0.0250701904296875,
-0.0199127197265625,
-0.000022411346435546875,
-0.004619598388671875,
0.01064300537109375,
0.0143585205078125,
-0.01385498046875,
-0.0035076141357421875,
0.013580322265625,
-0.008514404296875,
-0.005237579345703125,
-0.0182647705078125,
0.00159454345703125,
0.00794219970703125,
0.01494598388671875,
0.024993896484375,
-0.045166015625,
-0.0012664794921875,
-0.010009765625,
0.0242462158203125,
0.01100921630859375,
0.0162811279296875,
-0.0226593017578125,
0.021240234375,
0.01467132568359375,
0.0221710205078125,
-0.0087127685546875,
-0.0306243896484375,
-0.01551055908203125,
0.016815185546875,
-0.01702880859375,
-0.0284881591796875,
0.0063018798828125,
-0.0120849609375,
0.0247344970703125,
-0.01551055908203125,
0.0183563232421875,
-0.017913818359375,
0.0157012939453125,
0.0255889892578125,
0.0238037109375,
0.015960693359375,
0.034271240234375,
0.0121917724609375,
0.006275177001953125,
0.0022373199462890625,
-0.016845703125,
0.043853759765625,
-0.020416259765625,
-0.01038360595703125,
-0.01458740234375,
-0.01168060302734375,
0.032958984375,
0.0010309219360351562,
0.01983642578125,
-0.00542449951171875,
0.00559234619140625,
0.0213165283203125,
-0.0201263427734375,
-0.014190673828125,
0.004718780517578125,
-0.0213775634765625,
-0.035186767578125,
0.0048980712890625,
-0.00672149658203125,
0.007373809814453125,
0.01103973388671875,
-0.072265625,
-0.04388427734375,
0.01271820068359375,
0.042144775390625,
0.01323699951171875,
0.007663726806640625,
-0.017303466796875,
0.00957489013671875,
0.00806427001953125,
-0.00514984130859375,
-0.0030460357666015625,
0.005096435546875,
-0.02154541015625,
-0.0021038055419921875,
-0.043548583984375,
0.04058837890625,
-0.009307861328125,
0.00272369384765625,
0.006862640380859375,
0.005214691162109375,
0.0161895751953125,
-0.0078277587890625,
-0.0283660888671875,
0.006229400634765625,
-0.00800323486328125,
-0.0185394287109375,
0.0213165283203125,
-0.02313232421875,
0.0012969970703125,
0.0163421630859375,
-0.019683837890625,
0.0266876220703125,
0.01212310791015625,
0.00969696044921875,
0.01082611083984375,
-0.01035308837890625,
0.006656646728515625,
-0.01214599609375,
0.0021343231201171875,
-0.01381683349609375,
-0.0123748779296875,
0.00140380859375,
-0.0243072509765625,
0.018218994140625,
0.02105712890625,
0.004291534423828125,
-0.01483154296875,
0.0159759521484375,
-0.022003173828125,
-0.006298065185546875,
-0.006969451904296875,
-0.044158935546875,
0.0051116943359375,
-0.0140838623046875,
0.0188751220703125,
-0.046417236328125,
-0.00848388671875,
-0.005901336669921875,
0.004840850830078125,
0.006633758544921875,
0.006744384765625,
-0.0155181884765625,
0.031005859375,
0.01427459716796875,
0.01015472412109375,
0.013153076171875,
0.009857177734375,
0.00469970703125,
-0.00302886962890625,
-0.0166168212890625,
0.0019435882568359375,
-0.004497528076171875,
0.02374267578125,
-0.021484375,
0.01544952392578125,
-0.002681732177734375,
-0.0216522216796875,
0.0028285980224609375,
-0.01296234130859375,
-0.01113128662109375,
0.00897216796875,
-0.00954437255859375,
0.0284423828125,
-0.004337310791015625,
0.0044403076171875,
0.0167999267578125,
0.0175323486328125,
-0.028411865234375,
0.0104217529296875,
0.041229248046875,
0.034332275390625,
0.0097503662109375,
0.0181427001953125,
-0.0017995834350585938,
0.01374053955078125,
0.01120758056640625,
-0.004180908203125,
0.0048370361328125,
-0.00742340087890625,
0.007549285888671875,
0.01523590087890625,
-0.0433349609375,
-0.005458831787109375,
-0.007190704345703125,
-0.01305389404296875,
0.01525115966796875,
0.010009765625,
0.013092041015625,
-0.021026611328125,
0.00746917724609375,
-0.0068511962890625,
-0.041961669921875,
-0.0167388916015625,
0.02252197265625,
-0.0126800537109375,
-0.0089263916015625,
0.0026264190673828125,
-0.01033782958984375,
0.008636474609375,
-0.01299285888671875,
0.0222625732421875,
0.0302581787109375,
0.037506103515625,
0.0014019012451171875,
0.01422882080078125,
0.00337982177734375,
-0.00693511962890625,
-0.00797271728515625,
-0.0014801025390625,
0.00943756103515625,
-0.01934814453125,
0.025543212890625,
-0.0297698974609375,
0.004352569580078125,
0.022186279296875,
-0.007625579833984375,
0.0181121826171875,
0.047454833984375,
0.00933837890625,
0.023101806640625,
0.038116455078125,
0.00647735595703125,
-0.029876708984375,
-0.0037078857421875,
0.044891357421875,
-0.0230255126953125,
0.0021820068359375,
0.0057525634765625,
0.025054931640625,
0.01367950439453125,
0.005462646484375,
-0.00894927978515625,
0.033233642578125,
0.018768310546875,
-0.03778076171875,
0.006500244140625,
-0.000988006591796875,
-0.0086212158203125,
-0.0035457611083984375,
0.036834716796875,
-0.0266571044921875,
-0.0157012939453125,
-0.014923095703125,
0.00965118408203125,
0.024200439453125,
0.0125274658203125,
0.01361846923828125,
0.006786346435546875,
-0.042755126953125,
0.0343017578125,
0.036376953125,
0.013671875,
0.00336456298828125,
-0.031463623046875,
-0.036712646484375,
-0.0173492431640625,
0.0022640228271484375,
-0.019989013671875,
-0.05108642578125,
0.00905609130859375,
0.0157470703125,
0.0209503173828125,
0.0154876708984375,
-0.026031494140625,
-0.02301025390625,
-0.01155853271484375,
0.03277587890625,
-0.0406494140625,
-0.0126190185546875,
0.00453948974609375,
-0.0013446807861328125,
-0.00572967529296875,
-0.0117645263671875,
0.0143585205078125,
0.0205535888671875,
-0.02435302734375,
-0.0247650146484375,
0.026885986328125,
-0.0379638671875,
-0.0247802734375,
0.0200347900390625,
0.008819580078125,
0.044189453125,
0.00078582763671875,
0.000522613525390625,
-0.0394287109375,
0.016448974609375,
0.0218658447265625,
0.032562255859375,
0.0026340484619140625,
-0.02581787109375,
-0.01090240478515625,
0.0080413818359375,
-0.004543304443359375,
-0.0173492431640625,
0.00299072265625,
-0.042999267578125,
0.02557373046875,
-0.006778717041015625,
0.029510498046875,
0.00982666015625,
-0.004795074462890625,
-0.00928497314453125,
-0.0213623046875,
0.00896453857421875,
-0.004856109619140625,
-0.007568359375,
0.00009822845458984375,
0.04498291015625,
0.01715087890625,
0.004108428955078125,
0.015960693359375,
-0.01277923583984375,
0.0143890380859375,
-0.01171875,
-0.00455474853515625,
0.0321044921875,
0.006011962890625,
-0.02734375,
-0.003662109375,
-0.040985107421875,
0.01739501953125,
0.0116729736328125,
0.026580810546875,
0.01287078857421875,
0.005084991455078125,
-0.0137939453125,
-0.02325439453125,
0.01442718505859375,
-0.03955078125,
-0.0258026123046875,
-0.01430511474609375,
0.0025730133056640625,
-0.0235443115234375,
-0.0022220611572265625,
-0.0107879638671875,
0.00789642333984375,
0.01143646240234375,
0.00948333740234375,
-0.00902557373046875,
0.02197265625,
0.01476287841796875,
-0.005970001220703125,
-0.020050048828125,
-0.0012865066528320312,
0.0206298828125,
0.01267242431640625,
-0.022186279296875,
0.00432586669921875,
0.0155792236328125,
-0.013275146484375,
-0.00450897216796875,
0.0296173095703125,
-0.0260162353515625,
0.0107574462890625,
-0.006633758544921875,
-0.01385498046875,
-0.0078887939453125,
0.00009900331497192383,
-0.000019550323486328125,
0.0175018310546875,
0.018402099609375,
-0.01110076904296875,
-0.017486572265625,
-0.0206146240234375,
0.0347900390625,
-0.01226806640625,
0.0026569366455078125,
-0.01200103759765625,
0.0028858184814453125,
0.007808685302734375,
-0.00555419921875,
-0.00014734268188476562,
-0.0171661376953125,
-0.0154266357421875,
-0.0533447265625,
-0.0010843276977539062,
-0.0035991668701171875,
-0.00533294677734375,
0.0006089210510253906,
-0.0173492431640625,
0.00463104248046875,
0.004913330078125,
0.0039215087890625,
-0.016876220703125,
-0.0196990966796875,
0.019775390625,
-0.02691650390625,
0.01641845703125,
-0.01479339599609375,
0.0182647705078125,
-0.01503753662109375,
0.0205535888671875,
-0.01317596435546875,
-0.0028553009033203125,
-0.001651763916015625,
0.0159759521484375,
0.006572723388671875,
0.0136260986328125,
-0.01093292236328125,
0.0124053955078125,
-0.0010805130004882812,
0.032562255859375,
-0.006313323974609375,
0.0002875328063964844,
-0.0089569091796875,
0.01947021484375,
0.011932373046875,
-0.04144287109375,
-0.005664825439453125,
-0.035888671875,
-0.005306243896484375,
-0.022491455078125,
-0.0259552001953125,
0.029937744140625,
-0.038787841796875,
0.0280303955078125,
-0.006275177001953125,
-0.047393798828125,
0.0197906494140625,
-0.002307891845703125,
-0.033447265625,
0.020416259765625,
-0.007411956787109375,
-0.021026611328125,
-0.0182342529296875,
-0.0160369873046875,
-0.007843017578125,
-0.0223388671875,
0.037109375,
-0.0117950439453125,
0.01314544677734375,
-0.0266265869140625,
0.005504608154296875,
-0.0254364013671875,
-0.0265960693359375,
-0.01221466064453125,
0.005828857421875,
-0.02435302734375,
0.0164642333984375,
-0.022430419921875,
0.0126190185546875,
0.017242431640625,
-0.002490997314453125,
0.026519775390625,
-0.04718017578125,
-0.026947021484375,
0.006130218505859375,
0.00879669189453125,
0.0277557373046875,
-0.041259765625,
-0.0037384033203125,
0.0091705322265625,
-0.029052734375,
-0.003353118896484375,
0.01470947265625,
0.0302276611328125,
0.0171661376953125,
-0.0008578300476074219,
-0.04815673828125,
0.017669677734375,
0.0108184814453125,
0.005603790283203125,
0.0130615234375,
0.0159454345703125,
0.005950927734375,
0.0009226799011230469,
0.04351806640625,
0.016387939453125,
-0.015167236328125,
0.04022216796875,
-0.01171875,
0.04803466796875,
-0.036651611328125,
-0.0277862548828125,
0.01064300537109375,
0.01519775390625,
0.0017566680908203125,
0.0201416015625,
-0.0038051605224609375,
0.00743865966796875,
-0.0347900390625,
-0.031585693359375,
-0.00701141357421875,
-0.0025463104248046875,
-0.0112152099609375,
-0.00469970703125,
-0.01357269287109375,
-0.027740478515625,
0.004756927490234375,
0.01085662841796875,
0.02020263671875,
-0.0178375244140625,
-0.00322723388671875,
0.007030487060546875,
-0.006488800048828125,
0.00829315185546875,
0.006084442138671875,
0.0335693359375,
-0.0234222412109375,
-0.015655517578125,
0.01654052734375,
-0.040191650390625,
0.0013942718505859375,
0.0104217529296875,
0.00949859619140625,
0.039764404296875,
-0.004192352294921875,
-0.017303466796875,
-0.0013036727905273438,
0.0088653564453125,
0.0020046234130859375,
-0.023651123046875,
0.01412200927734375,
-0.00893402099609375,
-0.034881591796875,
0.0015277862548828125,
-0.03912353515625,
-0.00733184814453125,
-0.020599365234375,
0.0089111328125,
0.01419830322265625,
-0.0170440673828125,
-0.0176849365234375,
-0.04510498046875,
-0.0019779205322265625,
0.0360107421875,
-0.043365478515625,
0.0020313262939453125,
-0.01523590087890625,
0.031829833984375,
0.007732391357421875,
0.0001531839370727539,
0.015960693359375,
-0.022674560546875,
-0.024627685546875,
-0.007289886474609375,
0.0095977783203125,
0.0034809112548828125,
-0.00392913818359375,
-0.0003859996795654297,
-0.025634765625,
-0.00864410400390625,
0.01493072509765625,
0.0151214599609375,
-0.03240966796875,
0.046142578125,
0.020538330078125,
0.03851318359375,
0.046844482421875,
-0.0028228759765625,
-0.00824737548828125,
-0.0170745849609375,
0.01348876953125,
-0.020477294921875,
-0.006755828857421875,
-0.0113525390625,
-0.00244903564453125,
-0.0028743743896484375,
0.0043792724609375,
-0.0261077880859375,
-0.0269622802734375,
-0.01806640625,
0.0151214599609375,
-0.00817108154296875,
0.01953125,
-0.025726318359375,
-0.011962890625,
0.0211334228515625,
-0.032257080078125,
0.0230560302734375,
-0.02984619140625,
-0.0137786865234375,
0.00836181640625,
0.0011034011840820312,
0.0196380615234375,
-0.006740570068359375,
-0.034759521484375,
-0.0005474090576171875,
0.0050811767578125,
-0.01495361328125,
-0.0189208984375,
-0.00495147705078125,
-0.0176544189453125,
-0.0095977783203125,
-0.01204681396484375,
-0.01343536376953125,
0.00026416778564453125,
0.01189422607421875,
-0.023406982421875,
0.029296875,
-0.00807952880859375,
0.0015811920166015625,
-0.05035400390625,
0.0008263587951660156,
0.00409698486328125,
-0.019805908203125,
0.0207672119140625,
-0.0147705078125,
-0.007049560546875,
0.01142120361328125,
-0.0477294921875,
0.0059356689453125,
0.0034160614013671875,
0.0224609375,
-0.03558349609375,
-0.01485443115234375,
0.014312744140625,
0.01959228515625,
-0.022125244140625,
0.0212860107421875,
0.00748443603515625,
0.01206207275390625,
-0.0069122314453125,
0.0021648406982421875,
0.0009946823120117188,
-0.017120361328125,
0.058868408203125,
0.0068511962890625,
-0.020660400390625,
-0.0347900390625,
0.022186279296875,
0.0230560302734375,
-0.0159912109375,
0.0014715194702148438,
-0.0156707763671875,
0.0033111572265625,
-0.00902557373046875,
-0.032562255859375,
-0.00759124755859375,
0.0226593017578125,
-0.023590087890625,
-0.01557159423828125,
-0.01036834716796875,
-0.007511138916015625,
0.0172271728515625,
0.0217742919921875,
0.0035953521728515625,
0.038787841796875,
-0.008331298828125,
-0.01324462890625,
-0.00980377197265625,
-0.03546142578125,
0.003246307373046875,
0.03564453125,
-0.0054168701171875,
-0.00908660888671875,
0.006244659423828125,
-0.0127105712890625,
0.0035877227783203125,
0.017608642578125,
0.01488494873046875,
0.00574493408203125,
-0.03094482421875,
-0.01076507568359375,
0.01045989990234375,
-0.01433563232421875,
0.0015268325805664062,
-0.0147552490234375,
0.003650665283203125,
0.0214080810546875,
0.0032978057861328125,
-0.0143280029296875,
-0.0012044906616210938,
-0.020294189453125,
0.0077362060546875,
-0.005130767822265625,
0.0067596435546875,
-0.0059967041015625,
-0.02264404296875,
0.007434844970703125,
0.00921630859375,
0.006793975830078125,
-0.021270751953125,
0.0092010498046875,
-0.019622802734375,
-0.036102294921875,
-0.010406494140625,
-0.0016374588012695312,
-0.01299285888671875,
0.0041656494140625,
-0.0028018951416015625,
-0.0128021240234375,
0.0222930908203125,
0.016845703125,
-0.01416015625,
0.002590179443359375,
0.033111572265625,
-0.017608642578125,
0.0219879150390625,
-0.032257080078125,
-0.0030040740966796875,
0.006885528564453125,
-0.036346435546875,
0.00489044189453125,
-0.00405120849609375,
0.002338409423828125,
-0.005466461181640625,
-0.01306915283203125,
-0.01161956787109375,
-0.0264892578125,
-0.00502777099609375,
-0.00031065940856933594,
-0.032623291015625,
-0.00038123130798339844,
-0.01519775390625,
0.01027679443359375,
0.0011816024780273438,
-0.01190185546875,
0.025177001953125,
0.0014925003051757812,
-0.01244354248046875,
0.0020542144775390625,
-0.0268402099609375,
0.0134735107421875,
0.0019931793212890625,
0.0164642333984375,
-0.0194549560546875,
-0.003864288330078125,
-0.020904541015625,
-0.0208740234375,
-0.0249481201171875,
0.015472412109375,
-0.0271148681640625,
-0.0223388671875,
-0.0013828277587890625,
0.018829345703125,
0.01152801513671875
] |
ours_529
|
First, observe that for every \( n \geq 1 \), there exists a monic polynomial \( P_{n} \in \mathbb{Z}[x] \) such that \( x_{n}=P_{n}(c) \) for all complex numbers \( c \). By induction, \( P_{n}(0)=6n-5 \) for \( n \geq 1 \), so \( P_{1006}(0)=6031 \). Similarly, we can show that \( (x-2)^{2} \mid P_{n}(x)-2n+1 \) for \( n \geq 1 \).
Write \( P_{1006}(x)-2011 \) (which is monic with integer coefficients) in the form \(\prod_{i=1}^{m} f_{i}(x)^{k_{i}}\) for distinct nonconstant monic irreducible polynomials \( f_{i} \in \mathbb{Z}[x] \) and positive integers \( k_{i} \). The desired product of \( c \) such that \( P_{1006}(c)=2011 \) is simply \( P=\prod_{i=1}^{m}\left|f_{i}(0)\right| \), since no monic irreducible polynomial has a double root, and no two distinct monic irreducible polynomials with integer coefficients can share a root.
Note that for any \( i, f_{i}(0)^{k_{i}} \mid P_{1006}(0)-2011=4020=2^{2} \cdot 3 \cdot 5 \cdot 67 \). If \( k_{i}>1 \) for some \( i \), then we must have \( f_{i}(0) \mid 2 \) (and if \( f_{i}(0)= \pm 2 \), then \( k_{i}=2 \)). Thus for every \( i,\left|f_{i}(0)^{k_{i}}\right|=\left|f_{i}(0)\right| \) unless \( f_{i}(0)= \pm 2 \) and \( k_{i}=2 \) (in which case \(\left.\left|f_{i}(0)^{k_{i}}\right|=2\left|f_{i}(0)\right|\right)\), so \( P=\prod_{i=1}^{m}\left|f_{i}(0)\right|=\frac{1}{2^{r}} \prod_{i=1}^{m}\left|f_{i}(x)^{k_{i}}\right|=\frac{4020}{2^{r}} \), where \( r \) is the number of \( i \) such that \( f_{i}(0)= \pm 2 \) and \( k_{i}=2 \). Since \(\left(2^{2}\right)^{2} \nmid 4020\), we have \( r \leq 1 \). But we know \( (x-2)^{2} \mid P_{1006}(x)-2011 \) from above, so \( r \geq 1 \Longrightarrow r=1 \), and \( P=2010 \).
\(\boxed{2010}\)
|
2010
|
{
"competition": "us_comps",
"dataset": "Ours",
"posts": null,
"source": "OMOSoln2-2.md"
}
|
Find the magnitude of the product of all complex numbers \( c \) such that the recurrence defined by \( x_{1}=1 \), \( x_{2}=c^{2}-4c+7 \), and \( x_{n+1}=(c^{2}-2c)^{2}x_{n}x_{n-1}+2x_{n}-x_{n-1} \) also satisfies \( x_{1006}=2011 \).
|
[
"/Mathematics/Algebra/AlgebraicEquations/AlgebraicEquation",
"/Mathematics/Algebra/GeneralAlgebra/AbstractAlgebra",
"/Mathematics/Algebra/GeneralAlgebra/Algebra",
"/Mathematics/Algebra/NumberTheory/AlgebraicNumberTheory/AlgebraicInteger",
"/Mathematics/Algebra/NumberTheory/AlgebraicNumberTheory/AlgebraicNumber",
"/Mathematics/Algebra/NumberTheory/GeneralNumberTheory/ElementaryNumberTheory",
"/Mathematics/Algebra/NumberTheory/GeneralNumberTheory/NumberTheory",
"/Mathematics/Algebra/Polynomials/Factorization",
"/Mathematics/Algebra/Polynomials/IntegerPolynomial",
"/Mathematics/Algebra/Polynomials/IrreduciblePolynomial",
"/Mathematics/Algebra/Polynomials/MonicPolynomial",
"/Mathematics/Algebra/Polynomials/Polynomial",
"/Mathematics/Algebra/Polynomials/PolynomialFactorization",
"/Mathematics/Algebra/Products/Product",
"/Mathematics/Algebra/RingTheory/PolynomialRing",
"/Mathematics/Algebra/RingTheory/UniqueFactorization",
"/Mathematics/Algebra/RingTheory/UniqueFactorizationDomain",
"/Mathematics/NumberTheory/AlgebraicNumberTheory/AlgebraicInteger",
"/Mathematics/NumberTheory/AlgebraicNumberTheory/AlgebraicNumber",
"/Mathematics/NumberTheory/Arithmetic/GeneralArithmetic",
"/Mathematics/NumberTheory/Arithmetic/MultiplicationandDivision",
"/Mathematics/NumberTheory/Divisors/Divides",
"/Mathematics/NumberTheory/Divisors/Divisible",
"/Mathematics/NumberTheory/Divisors/Divisor",
"/Mathematics/NumberTheory/GeneralNumberTheory/ElementaryNumberTheory",
"/Mathematics/NumberTheory/GeneralNumberTheory/NumberTheory",
"/Mathematics/NumberTheory/Integers/Integer",
"/Mathematics/NumberTheory/Integers/RationalInteger",
"/Mathematics/NumberTheory/Integers/Z"
] |
Express the equation as a monic integer polynomial and use its factorisation to link the product of all roots to the constant term at 0, then restrict possibilities with divisor information and the known double root at 2.
|
[
-0.00010961294174194336,
0.00600433349609375,
0.050933837890625,
0.029998779296875,
-0.0003695487976074219,
0.046142578125,
-0.002994537353515625,
-0.01433563232421875,
0.0006680488586425781,
0.0133056640625,
0.031494140625,
-0.049591064453125,
-0.007526397705078125,
-0.01104736328125,
-0.048065185546875,
-0.0284423828125,
0.015899658203125,
-0.0165252685546875,
0.001972198486328125,
-0.0020580291748046875,
-0.006122589111328125,
0.0084228515625,
-0.026702880859375,
0.01342010498046875,
-0.0439453125,
0.00015211105346679688,
-0.01142120361328125,
-0.0283050537109375,
0.035400390625,
-0.0161285400390625,
-0.02197265625,
-0.050079345703125,
0.000021576881408691406,
-0.018402099609375,
0.0016345977783203125,
-0.017730712890625,
0.0217132568359375,
-0.005626678466796875,
-0.026031494140625,
-0.00693511962890625,
-0.004383087158203125,
-0.00421142578125,
-0.0130157470703125,
0.01031494140625,
-0.031341552734375,
-0.0081329345703125,
-0.006008148193359375,
0.0301666259765625,
0.0134429931640625,
0.01110076904296875,
0.001678466796875,
0.01398468017578125,
-0.0149993896484375,
-0.0120697021484375,
-0.0193023681640625,
-0.0374755859375,
-0.0134124755859375,
-0.004497528076171875,
-0.0135650634765625,
-0.0182037353515625,
0.0037479400634765625,
-0.00007849931716918945,
-0.00646209716796875,
-0.013336181640625,
-0.00653839111328125,
-0.01329803466796875,
0.0518798828125,
-0.025970458984375,
0.005161285400390625,
-0.007781982421875,
0.018646240234375,
0.0033168792724609375,
0.005512237548828125,
0.03466796875,
0.044158935546875,
-0.005123138427734375,
-0.011260986328125,
0.04400634765625,
0.019775390625,
-0.0085296630859375,
-0.0010576248168945312,
0.00925445556640625,
-0.0038509368896484375,
-0.0223388671875,
0.00013518333435058594,
0.0229644775390625,
-0.0338134765625,
0.0060272216796875,
0.0253448486328125,
-0.020050048828125,
-0.003482818603515625,
0.008544921875,
-0.005184173583984375,
-0.005435943603515625,
0.00006914138793945312,
0.003246307373046875,
0.0166778564453125,
-0.00910186767578125,
-0.0380859375,
0.0140380859375,
-0.0165557861328125,
0.007038116455078125,
-0.0088653564453125,
-0.004436492919921875,
-0.041534423828125,
-0.02325439453125,
-0.0164794921875,
0.04058837890625,
0.01470184326171875,
0.00629425048828125,
0.01343536376953125,
0.0007624626159667969,
0.01448822021484375,
0.01088714599609375,
-0.0298309326171875,
-0.0054931640625,
-0.00152587890625,
-0.00988006591796875,
-0.01062774658203125,
-0.0009698867797851562,
-0.004589080810546875,
0.008056640625,
-0.002620697021484375,
-0.0106353759765625,
0.01204681396484375,
0.00547027587890625,
0.00374603271484375,
-0.004711151123046875,
-0.0008802413940429688,
0.0186767578125,
0.0084075927734375,
-0.02587890625,
-0.058685302734375,
-0.02764892578125,
-0.07366943359375,
-0.01354217529296875,
-0.01214599609375,
-0.0192108154296875,
-0.022796630859375,
-0.0114593505859375,
0.0018720626831054688,
0.007083892822265625,
0.01476287841796875,
-0.0303802490234375,
0.00737762451171875,
-0.01305389404296875,
0.0018854141235351562,
0.004009246826171875,
0.0083160400390625,
-0.008270263671875,
0.0029296875,
0.005207061767578125,
0.01476287841796875,
0.002471923828125,
0.0006537437438964844,
0.003391265869140625,
0.0028362274169921875,
0.0176849365234375,
0.0019817352294921875,
0.0167388916015625,
0.00494384765625,
0.0017547607421875,
-0.00897216796875,
0.0224761962890625,
0.0022430419921875,
0.0036907196044921875,
-0.00318145751953125,
-0.0059356689453125,
-0.0164794921875,
0.0198211669921875,
-0.0011358261108398438,
-0.005931854248046875,
-0.00814056396484375,
-0.0104522705078125,
-0.01568603515625,
0.01232147216796875,
-0.04376220703125,
0.01065826416015625,
0.0014600753784179688,
-0.0009312629699707031,
0.004734039306640625,
-0.035858154296875,
-0.017364501953125,
-0.01451873779296875,
-0.0036029815673828125,
-0.0159149169921875,
0.00785064697265625,
0.0039215087890625,
0.01554107666015625,
-0.00959014892578125,
-0.0118408203125,
-0.01052093505859375,
0.007678985595703125,
0.00188446044921875,
-0.03546142578125,
0.0008440017700195312,
-0.00893402099609375,
0.0138092041015625,
0.01525115966796875,
0.0259246826171875,
-0.007740020751953125,
-0.00130462646484375,
0.033416748046875,
0.018890380859375,
0.0028514862060546875,
0.002063751220703125,
0.00830841064453125,
-0.03131103515625,
0.00524139404296875,
-0.00811767578125,
0.0156402587890625,
-0.01026153564453125,
0.0005908012390136719,
-0.05450439453125,
-0.01015472412109375,
0.0019931793212890625,
-0.0033283233642578125,
0.005016326904296875,
0.016387939453125,
-0.005519866943359375,
0.023193359375,
0.006160736083984375,
0.004669189453125,
-0.00994110107421875,
-0.0188446044921875,
-0.0076751708984375,
0.01430511474609375,
0.004772186279296875,
-0.0078582763671875,
-0.000028192996978759766,
0.0014181137084960938,
0.00469970703125,
-0.0215606689453125,
-0.0024662017822265625,
0.003265380859375,
0.006626129150390625,
-0.011444091796875,
-0.00812530517578125,
-0.027008056640625,
-0.015777587890625,
-0.0020122528076171875,
-0.005390167236328125,
0.0189056396484375,
0.0015726089477539062,
0.01332855224609375,
-0.012451171875,
0.00016689300537109375,
-0.00966644287109375,
-0.007167816162109375,
-0.00617218017578125,
-0.0253753662109375,
-0.0028743743896484375,
-0.007282257080078125,
-0.0011234283447265625,
0.005588531494140625,
-0.0184173583984375,
0.0011434555053710938,
-0.0303955078125,
-0.0084381103515625,
0.021759033203125,
-0.0092010498046875,
0.00974273681640625,
-0.01080322265625,
-0.003520965576171875,
-0.0233306884765625,
0.01186370849609375,
-0.025787353515625,
-0.000377655029296875,
0.004711151123046875,
-0.033355712890625,
0.0333251953125,
-0.0184173583984375,
-0.008026123046875,
0.01473236083984375,
0.0300750732421875,
0.0048065185546875,
-0.0014781951904296875,
0.02398681640625,
0.0139007568359375,
0.01300811767578125,
-0.0151519775390625,
-0.007289886474609375,
-0.01377105712890625,
-0.0008268356323242188,
0.00666046142578125,
0.01068878173828125,
0.01433563232421875,
-0.04168701171875,
-0.01399993896484375,
0.007137298583984375,
0.0079498291015625,
0.01442718505859375,
-0.009765625,
-0.0091094970703125,
0.0390625,
-0.02532958984375,
-0.01099395751953125,
0.0187835693359375,
-0.01284027099609375,
-0.026275634765625,
0.026519775390625,
-0.0007548332214355469,
0.00864410400390625,
-0.01175689697265625,
0.021240234375,
0.007167816162109375,
-0.0014543533325195312,
0.004962921142578125,
-0.03509521484375,
-0.0214996337890625,
0.024749755859375,
0.005420684814453125,
-0.0171051025390625,
-0.0179901123046875,
-0.03515625,
-0.04998779296875,
0.01325225830078125,
0.01010894775390625,
-0.0186614990234375,
0.0172576904296875,
0.007251739501953125,
0.0120391845703125,
0.0062408447265625,
0.01273345947265625,
-0.04791259765625,
-0.0063323974609375,
0.02655029296875,
0.0124664306640625,
0.01224517822265625,
0.01355743408203125,
-0.072509765625,
0.0102691650390625,
0.0269317626953125,
-0.027923583984375,
-0.01314544677734375,
-0.00476837158203125,
-0.007965087890625,
0.022430419921875,
-0.004116058349609375,
0.0204010009765625,
0.0199432373046875,
0.00597381591796875,
0.0202789306640625,
-0.01336669921875,
-0.0443115234375,
0.00301361083984375,
-0.024200439453125,
-0.0149688720703125,
-0.0263519287109375,
-0.007720947265625,
0.00391387939453125,
0.00836181640625,
-0.005008697509765625,
-0.01039886474609375,
-0.017425537109375,
0.0145721435546875,
-0.0007109642028808594,
0.0252685546875,
0.0017337799072265625,
0.01557159423828125,
0.0025882720947265625,
0.0021076202392578125,
-0.00179290771484375,
0.006084442138671875,
-0.0306396484375,
-0.01544189453125,
-0.0103759765625,
0.0266265869140625,
-0.044342041015625,
0.00737762451171875,
-0.0220184326171875,
-0.003398895263671875,
-0.0036678314208984375,
0.01319122314453125,
0.00534820556640625,
-0.01009368896484375,
0.0080718994140625,
0.004009246826171875,
-0.0038127899169921875,
-0.0020599365234375,
-0.00508880615234375,
0.01666259765625,
-0.0184326171875,
0.0200042724609375,
0.00313568115234375,
-0.00910186767578125,
0.00372314453125,
-0.01427459716796875,
-0.025482177734375,
0.0211639404296875,
0.00864410400390625,
0.023895263671875,
-0.0031070709228515625,
-0.01342010498046875,
-0.04510498046875,
-0.0177001953125,
0.00008380413055419922,
0.0196075439453125,
-0.0005435943603515625,
-0.0236968994140625,
-0.00022161006927490234,
-0.0256805419921875,
-0.00872039794921875,
0.017852783203125,
-0.01131439208984375,
-0.0303497314453125,
-0.004474639892578125,
0.01424407958984375,
-0.023834228515625,
0.005767822265625,
0.00803375244140625,
0.0198974609375,
0.037353515625,
-0.007526397705078125,
-0.01078033447265625,
0.005828857421875,
-0.00005537271499633789,
-0.01465606689453125,
0.0036296844482421875,
0.00098419189453125,
-0.01470184326171875,
0.0073089599609375,
-0.007366180419921875,
0.00007349252700805664,
0.01611328125,
0.01314544677734375,
-0.005767822265625,
0.0247650146484375,
0.0008625984191894531,
-0.00814056396484375,
-0.0128631591796875,
-0.00864410400390625,
0.0267333984375,
-0.0025234222412109375,
0.0025272369384765625,
0.03741455078125,
0.00911712646484375,
0.00685882568359375,
-0.005245208740234375,
0.00955963134765625,
-0.005889892578125,
0.0276336669921875,
-0.004009246826171875,
0.0161895751953125,
-0.010406494140625,
-0.01337432861328125,
-0.0085601806640625,
0.01788330078125,
0.00673675537109375,
0.023406982421875,
0.006744384765625,
0.0018749237060546875,
0.00208282470703125,
-0.015106201171875,
0.00984954833984375,
0.037994384765625,
0.03955078125,
-0.006683349609375,
0.002117156982421875,
-0.00736236572265625,
-0.015472412109375,
-0.0127105712890625,
0.017852783203125,
-0.0016489028930664062,
-0.00894927978515625,
-0.0195465087890625,
-0.00887298583984375,
0.004642486572265625,
0.004001617431640625,
-0.0018825531005859375,
-0.01239776611328125,
-0.0215911865234375,
-0.0101776123046875,
-0.0277862548828125,
-0.034271240234375,
0.031524658203125,
0.01055908203125,
0.03277587890625,
-0.0064239501953125,
0.016021728515625,
0.005550384521484375,
0.00045418739318847656,
0.0214385986328125,
-0.006496429443359375,
-0.00841522216796875,
0.01140594482421875,
0.0167083740234375,
0.018096923828125,
-0.0167999267578125,
0.0036773681640625,
0.0035419464111328125,
0.05474853515625,
0.01207733154296875,
-0.021514892578125,
0.00421905517578125,
-0.0182952880859375,
0.0097808837890625,
0.0200042724609375,
-0.01548004150390625,
0.011260986328125,
0.0006518363952636719,
-0.021148681640625,
-0.01319122314453125,
-0.0059661865234375,
-0.002506256103515625,
-0.03546142578125,
0.0121307373046875,
-0.0012598037719726562,
0.0260467529296875,
0.0013437271118164062,
0.0186309814453125,
-0.00029754638671875,
0.0178985595703125,
-0.037261962890625,
0.02130126953125,
0.02301025390625,
0.00936126708984375,
0.0081024169921875,
0.00484466552734375,
-0.0041351318359375,
0.0032520294189453125,
0.03155517578125,
0.005084991455078125,
-0.03662109375,
0.00478363037109375,
0.01561737060546875,
-0.0030574798583984375,
0.0029582977294921875,
0.0211181640625,
0.00624847412109375,
-0.026611328125,
-0.01380157470703125,
0.0115966796875,
0.0224456787109375,
-0.0268707275390625,
0.0110626220703125,
0.01248931884765625,
-0.01132965087890625,
0.006000518798828125,
-0.020050048828125,
-0.033966064453125,
-0.009521484375,
-0.00923919677734375,
-0.01544189453125,
-0.01129150390625,
-0.0043792724609375,
-0.031341552734375,
0.0095977783203125,
-0.0193634033203125,
0.01837158203125,
0.0210418701171875,
-0.002071380615234375,
0.00884246826171875,
-0.0200042724609375,
-0.01593017578125,
-0.0027027130126953125,
0.0300140380859375,
-0.016571044921875,
-0.039886474609375,
0.0301513671875,
0.01470947265625,
0.00496673583984375,
0.01198577880859375,
0.00865936279296875,
-0.0033817291259765625,
-0.028076171875,
-0.006595611572265625,
-0.00555419921875,
-0.01087188720703125,
-0.05523681640625,
0.0229949951171875,
0.0318603515625,
-0.0168609619140625,
0.0292205810546875,
-0.01041412353515625,
-0.021697998046875,
-0.03375244140625,
0.03118896484375,
0.009857177734375,
-0.0175018310546875,
0.020965576171875,
0.025604248046875,
-0.031646728515625,
-0.01424407958984375,
0.01458740234375,
-0.01294708251953125,
-0.0031719207763671875,
-0.003314971923828125,
-0.00007444620132446289,
-0.00487518310546875,
-0.0279693603515625,
-0.0023899078369140625,
-0.055908203125,
0.0021419525146484375,
0.0035037994384765625,
-0.005924224853515625,
0.0225830078125,
0.0154876708984375,
0.007534027099609375,
-0.03900146484375,
0.033447265625,
-0.01105499267578125,
-0.0126953125,
0.020416259765625,
0.00292205810546875,
-0.026611328125,
-0.022674560546875,
0.044952392578125,
-0.0173797607421875,
-0.009490966796875,
0.0162353515625,
-0.003139495849609375,
-0.0019931793212890625,
0.0064239501953125,
0.0174407958984375,
-0.0204315185546875,
-0.01349639892578125,
-0.0159149169921875,
0.011993408203125,
-0.0033817291259765625,
-0.02593994140625,
-0.00170135498046875,
-0.02349853515625,
-0.004360198974609375,
0.00243377685546875,
0.0095062255859375,
0.033111572265625,
0.0127105712890625,
0.0020236968994140625,
-0.005290985107421875,
-0.001476287841796875,
0.002780914306640625,
0.0389404296875,
-0.00021636486053466797,
-0.00922393798828125,
0.0066070556640625,
-0.015350341796875,
-0.009368896484375,
-0.02337646484375,
0.0024967193603515625,
0.01259613037109375,
-0.0113067626953125,
0.0192413330078125,
-0.06768798828125,
-0.005352020263671875,
0.01348114013671875,
-0.034698486328125,
-0.004802703857421875,
0.0019102096557617188,
0.0293121337890625,
-0.020050048828125,
0.004787445068359375,
-0.0213623046875,
0.01445770263671875,
-0.006816864013671875,
-0.002887725830078125,
0.0264739990234375,
0.00882720947265625,
0.0216827392578125,
-0.006504058837890625,
0.01088714599609375,
-0.024993896484375,
-0.0140838623046875,
-0.006389617919921875,
-0.0001609325408935547,
0.00437164306640625,
-0.014373779296875,
-0.05499267578125,
0.03582763671875,
-0.0284881591796875,
0.00270843505859375,
0.00257110595703125,
0.01678466796875,
-0.0136260986328125,
0.01885986328125,
0.000583648681640625,
0.00850677490234375,
-0.007709503173828125,
0.0144805908203125,
0.00856781005859375,
0.0171661376953125,
-0.0022907257080078125,
0.00713348388671875,
-0.013885498046875,
0.024322509765625,
0.006679534912109375,
-0.01221466064453125,
-0.00502777099609375,
0.01031494140625,
-0.00791168212890625,
-0.02044677734375,
-0.006927490234375,
0.015655517578125,
0.013275146484375,
-0.006999969482421875,
0.009063720703125,
-0.005649566650390625,
-0.01325225830078125,
-0.0008420944213867188,
-0.02496337890625,
0.017333984375,
-0.0020618438720703125,
0.0246734619140625,
-0.003406524658203125,
-0.0184326171875,
-0.0166015625,
0.0173492431640625,
0.0034351348876953125,
-0.04449462890625,
0.025115966796875,
-0.0159912109375,
-0.0079498291015625,
-0.0248260498046875,
-0.0169677734375,
-0.01439666748046875,
0.010833740234375,
-0.0110931396484375,
-0.0026454925537109375,
0.01251220703125,
-0.003055572509765625,
-0.0157623291015625,
0.006435394287109375,
-0.05767822265625,
-0.009857177734375,
0.0167083740234375,
0.013824462890625,
-0.029266357421875,
-0.03509521484375,
-0.006595611572265625,
0.01100921630859375,
0.0323486328125,
-0.007144927978515625,
-0.0050811767578125,
0.007579803466796875,
0.0133819580078125,
0.005207061767578125,
0.0207366943359375,
-0.004451751708984375,
0.0079193115234375,
-0.0202484130859375,
0.024627685546875,
0.00962066650390625,
0.0302886962890625,
0.0123138427734375,
-0.002323150634765625,
-0.041717529296875,
-0.0005025863647460938,
0.023101806640625,
0.01381683349609375,
0.00029850006103515625,
0.036651611328125,
0.0108489990234375,
0.02288818359375,
-0.035675048828125,
-0.039276123046875,
0.018218994140625,
0.02972412109375,
-0.01409149169921875,
0.043426513671875,
0.0215301513671875,
-0.02703857421875,
0.023712158203125,
0.029205322265625,
-0.0183868408203125,
0.002391815185546875,
0.002147674560546875,
0.01433563232421875,
0.0008864402770996094,
-0.02606201171875,
0.02801513671875,
-0.027557373046875,
-0.00611114501953125,
-0.0031909942626953125,
-0.0042572021484375,
0.0249481201171875,
-0.0126953125,
-0.0447998046875,
-0.002788543701171875,
0.03533935546875,
-0.023651123046875,
0.0341796875,
0.0118255615234375,
-0.0196533203125,
0.0163726806640625,
-0.03851318359375,
0.02777099609375,
0.006439208984375,
-0.01053619384765625,
0.03228759765625,
0.0271759033203125,
0.0322265625,
0.0209503173828125,
0.017669677734375,
-0.00836181640625,
0.004390716552734375,
0.00792694091796875,
-0.004673004150390625,
-0.0169525146484375,
-0.030303955078125,
-0.033050537109375,
-0.0010595321655273438,
-0.0028324127197265625,
0.01137542724609375,
-0.006839752197265625,
-0.006687164306640625,
0.029144287109375,
0.0021343231201171875,
0.00799560546875,
-0.01181793212890625,
0.0119476318359375,
-0.004016876220703125,
-0.0274810791015625,
0.0005922317504882812,
-0.01236724853515625,
0.02880859375,
-0.0125732421875,
-0.005260467529296875,
0.016510009765625,
-0.007694244384765625,
0.017974853515625,
-0.00003248453140258789,
0.0087432861328125,
0.0125274658203125,
-0.004825592041015625,
0.0025386810302734375,
0.006435394287109375,
0.0167694091796875,
0.0220947265625,
0.043365478515625,
0.00653076171875,
-0.0023365020751953125,
-0.006404876708984375,
-0.005523681640625,
0.01319122314453125,
-0.016510009765625,
-0.01146697998046875,
-0.0237274169921875,
0.00846099853515625,
0.0193634033203125,
-0.0182952880859375,
-0.0018968582153320312,
0.041778564453125,
0.02947998046875,
-0.036590576171875,
0.0016498565673828125,
-0.0284271240234375,
-0.04248046875,
0.0287322998046875,
-0.00807952880859375,
0.00036978721618652344,
0.02008056640625,
0.00882720947265625,
-0.03094482421875,
0.00263214111328125,
-0.0060272216796875,
0.02899169921875,
-0.024658203125,
0.01366424560546875,
-0.013824462890625,
-0.0169830322265625,
-0.006328582763671875,
-0.0066680908203125,
-0.023406982421875,
0.00627899169921875,
-0.016510009765625,
0.0069732666015625,
0.01446533203125,
0.009796142578125,
0.0165252685546875,
0.00843048095703125,
0.034027099609375,
-0.0031223297119140625,
0.024932861328125,
-0.048736572265625,
-0.004375457763671875,
-0.016082763671875,
0.01044464111328125,
0.0001932382583618164,
-0.0018062591552734375,
-0.0013484954833984375,
-0.016082763671875,
-0.030426025390625,
0.0044708251953125,
-0.04376220703125,
-0.01580810546875,
0.032867431640625,
0.01018524169921875,
0.01049041748046875,
-0.01983642578125,
-0.0242919921875,
0.0070648193359375,
-0.027618408203125,
-0.01187896728515625,
-0.0205078125,
0.01430511474609375,
0.005741119384765625,
0.0087432861328125,
-0.019683837890625,
-0.0036830902099609375,
-0.038330078125,
0.04302978515625,
-0.01232147216796875,
0.0223541259765625,
0.0004475116729736328,
-0.039825439453125,
0.004848480224609375,
-0.0220489501953125,
-0.0141143798828125,
0.0163116455078125,
0.01312255859375,
-0.0153350830078125,
-0.0095672607421875,
0.025543212890625,
0.0052032470703125,
-0.045562744140625,
-0.012115478515625,
-0.03131103515625,
0.0285797119140625,
-0.0209503173828125,
0.0160369873046875,
0.0035991668701171875,
-0.0264129638671875,
-0.01299285888671875,
0.0029392242431640625,
0.0036640167236328125,
0.007190704345703125,
0.017669677734375,
0.01287078857421875,
-0.03912353515625,
0.018096923828125,
-0.00036907196044921875,
0.046844482421875,
-0.0133056640625,
-0.0272674560546875,
0.00684356689453125,
0.034271240234375,
0.01763916015625,
-0.017608642578125,
0.009674072265625,
-0.01428985595703125,
-0.006740570068359375,
0.01242828369140625,
0.004924774169921875,
0.03955078125,
0.032073974609375,
-0.01605224609375,
-0.001522064208984375,
0.007415771484375,
-0.018157958984375,
-0.0128936767578125,
-0.007091522216796875,
-0.0050048828125,
-0.001094818115234375,
0.0205230712890625,
-0.0207366943359375,
-0.0202484130859375,
-0.005382537841796875,
-0.0092315673828125,
0.01052093505859375,
0.0025196075439453125,
-0.0190277099609375,
0.0018558502197265625,
-0.0222015380859375,
0.0070037841796875,
0.00815582275390625,
-0.00872039794921875,
0.0217437744140625,
0.00780487060546875,
-0.005970001220703125,
-0.0088653564453125,
-0.004756927490234375,
0.005336761474609375,
-0.022918701171875,
-0.0098114013671875,
0.023681640625,
0.0039520263671875,
0.01666259765625,
0.004085540771484375,
0.00571441650390625,
0.0188751220703125,
-0.0179595947265625,
-0.00858306884765625,
0.006378173828125,
-0.0007033348083496094,
-0.007904052734375,
0.0229034423828125,
0.0075225830078125,
0.01389312744140625,
0.046600341796875,
-0.038421630859375,
-0.0292816162109375,
0.034149169921875,
0.002773284912109375,
0.04412841796875,
-0.0085296630859375,
0.015838623046875,
-0.01529693603515625,
-0.002269744873046875,
-0.0017023086547851562,
0.0012292861938476562,
-0.0222320556640625,
-0.00902557373046875,
0.015625,
-0.006908416748046875,
0.03240966796875,
-0.0076141357421875,
0.0159759521484375,
0.0187835693359375,
0.043182373046875,
-0.02349853515625,
-0.00408935546875,
-0.005588531494140625,
-0.031280517578125,
-0.009979248046875,
-0.050048828125,
0.00934600830078125,
-0.00984954833984375,
-0.0231170654296875,
-0.028411865234375,
-0.01161956787109375,
0.0406494140625,
0.0121002197265625,
-0.02630615234375,
-0.018768310546875,
0.0193939208984375,
0.0084991455078125,
-0.040740966796875,
0.0294342041015625,
0.0218963623046875,
0.01194000244140625,
0.006961822509765625,
-0.0131683349609375,
0.0279388427734375,
-0.0031223297119140625,
0.00753021240234375,
-0.039276123046875,
-0.0258331298828125,
-0.00522613525390625,
0.03057861328125,
0.018890380859375,
-0.03314208984375,
0.0211944580078125,
0.008148193359375,
-0.00164031982421875,
0.012359619140625,
-0.018768310546875,
0.000640869140625,
0.01806640625,
-0.0184478759765625,
-0.013885498046875,
0.00418853759765625,
0.01432037353515625,
-0.02154541015625,
0.0003228187561035156,
0.0247650146484375,
0.0232391357421875,
0.01959228515625,
-0.0186309814453125,
0.0184326171875,
0.01274871826171875,
0.015899658203125,
0.0018663406372070312,
-0.027313232421875,
-0.0258331298828125,
-0.006206512451171875,
0.01422119140625,
-0.034637451171875,
0.00689697265625,
-0.0018358230590820312,
0.0516357421875,
-0.0206756591796875,
-0.0169219970703125,
-0.0069427490234375,
-0.0293731689453125,
0.007232666015625,
-0.019134521484375,
0.01313018798828125,
-0.00848388671875,
0.0181121826171875,
-0.01715087890625,
-0.0237579345703125,
-0.04034423828125,
-0.0288238525390625,
-0.0254058837890625,
0.032989501953125,
-0.017913818359375,
-0.0052642822265625,
-0.00858306884765625,
0.01012420654296875,
0.0015630722045898438,
0.0073089599609375,
-0.0037994384765625,
-0.05767822265625,
0.00811767578125,
0.0181427001953125,
-0.0181732177734375,
0.006259918212890625,
-0.021636962890625,
0.034515380859375,
-0.0238494873046875,
0.03094482421875,
-0.005611419677734375,
0.0072479248046875,
-0.01296234130859375,
-0.008270263671875,
-0.0112457275390625,
-0.033843994140625,
0.03289794921875,
-0.01230621337890625,
-0.01328277587890625,
0.0015869140625,
0.040557861328125,
-0.00643157958984375,
0.01393890380859375,
0.007083892822265625,
0.0202789306640625,
-0.01235198974609375,
-0.01068878173828125,
0.01055145263671875,
-0.01490020751953125,
0.00867462158203125,
0.0135955810546875,
0.0015869140625,
-0.0232391357421875,
-0.01129150390625,
-0.0133209228515625,
0.006168365478515625,
-0.007663726806640625,
-0.01508331298828125,
0.01522064208984375,
-0.00994873046875,
0.032562255859375,
-0.0168914794921875,
-0.0237274169921875,
0.0028705596923828125,
-0.004322052001953125,
-0.0051422119140625,
0.01092529296875,
-0.0078125,
0.0208740234375,
-0.0014781951904296875,
0.0037078857421875,
-0.00510406494140625,
0.0025501251220703125,
-0.00885009765625,
0.022613525390625,
-0.01389312744140625,
-0.01088714599609375,
-0.001323699951171875,
0.01514434814453125,
-0.005970001220703125,
0.0167999267578125,
-0.0178985595703125,
-0.031280517578125,
0.006317138671875,
-0.0033054351806640625,
-0.031158447265625,
0.027557373046875,
0.024505615234375,
-0.0301361083984375,
0.007350921630859375,
-0.0011129379272460938,
0.003856658935546875,
0.006786346435546875,
-0.01316070556640625,
-0.007595062255859375,
-0.0008816719055175781,
0.01324462890625,
-0.04888916015625,
-0.00103759765625,
-0.0142974853515625,
-0.0218048095703125,
-0.0181884765625,
-0.00817108154296875,
-0.01207733154296875,
0.018463134765625,
0.018524169921875,
-0.052642822265625,
-0.0192413330078125,
0.007625579833984375,
-0.036651611328125,
-0.00921630859375,
0.006481170654296875,
0.0023975372314453125,
-0.013702392578125,
-0.0227203369140625,
0.0010786056518554688,
-0.0018672943115234375,
0.011077880859375,
-0.0129852294921875,
0.0184478759765625,
-0.00951385498046875,
0.009185791015625,
0.01064300537109375,
0.0166778564453125,
0.01334381103515625,
-0.007720947265625,
-0.00662994384765625,
0.001041412353515625,
-0.005626678466796875,
0.01214599609375,
-0.0175933837890625,
-0.01192474365234375,
-0.01526641845703125,
0.005580902099609375,
0.0139007568359375,
0.005558013916015625,
0.0122222900390625,
-0.027435302734375,
0.0084686279296875,
-0.01074981689453125,
0.0129241943359375,
-0.0015020370483398438,
-0.01470184326171875,
0.0204010009765625,
-0.02593994140625,
0.0227813720703125,
0.0278472900390625,
-0.04296875,
-0.0321044921875,
-0.0072479248046875,
0.017730712890625,
-0.0029430389404296875,
-0.004596710205078125,
-0.012481689453125,
0.004283905029296875,
-0.020751953125,
0.0311431884765625,
-0.018707275390625,
0.006134033203125,
0.03070068359375,
0.01202392578125,
-0.02459716796875,
0.002582550048828125,
-0.033538818359375,
-0.015472412109375,
-0.0097503662109375,
0.0517578125,
-0.01525115966796875,
0.019927978515625,
-0.02783203125,
-0.0069122314453125,
0.002582550048828125,
0.006866455078125,
0.0176544189453125,
0.005443572998046875,
-0.028778076171875,
0.00960540771484375,
-0.015411376953125,
0.01995849609375,
0.0009160041809082031,
0.036773681640625,
-0.0143585205078125,
-0.004047393798828125,
-0.0215606689453125,
-0.040557861328125,
0.045318603515625,
-0.01369476318359375,
-0.00865936279296875,
0.005352020263671875,
-0.046630859375,
-0.03131103515625,
-0.01195526123046875,
-0.0204315185546875,
0.007137298583984375,
-0.042510986328125,
-0.0037288665771484375,
0.0216064453125,
-0.0012874603271484375,
-0.007770538330078125,
0.01137542724609375,
0.0092926025390625,
-0.0017242431640625,
-0.016265869140625,
0.01364898681640625,
0.02520751953125,
-0.022430419921875,
-0.0312042236328125,
0.034637451171875,
-0.00998687744140625,
-0.0226898193359375,
0.0323486328125,
0.002513885498046875,
-0.0269622802734375,
0.0093231201171875,
-0.0291900634765625,
-0.04443359375,
0.021881103515625,
0.0018301010131835938,
0.0079498291015625,
0.0134735107421875,
0.001964569091796875,
-0.003955841064453125,
0.007221221923828125,
0.034149169921875,
0.006496429443359375,
0.011932373046875,
0.00830841064453125,
-0.00418853759765625,
-0.00848388671875,
0.006092071533203125,
-0.025726318359375,
0.00815582275390625,
0.00444793701171875,
-0.00457000732421875,
-0.0038623809814453125,
0.002044677734375,
-0.00980377197265625,
-0.01338958740234375,
-0.005962371826171875,
-0.00586700439453125,
0.030853271484375,
-0.005077362060546875,
0.0081634521484375,
0.04302978515625,
0.036773681640625,
-0.045135498046875,
-0.01277923583984375,
-0.0268707275390625,
-0.004150390625,
0.0411376953125,
-0.0004906654357910156,
-0.0008835792541503906,
-0.01525115966796875,
0.025726318359375,
-0.012969970703125,
-0.00408935546875,
0.00777435302734375,
-0.0162200927734375,
-0.03173828125,
0.0130157470703125,
0.004482269287109375,
-0.0003495216369628906,
0.00827789306640625,
-0.01358795166015625,
-0.00650787353515625,
0.0111083984375,
-0.003299713134765625,
0.00402069091796875,
0.0020809173583984375,
-0.01549530029296875,
0.015655517578125,
-0.0280609130859375,
0.003551483154296875,
0.01465606689453125,
-0.001979827880859375,
-0.049591064453125,
0.042510986328125,
0.030731201171875,
-0.012054443359375,
0.0057373046875,
0.0213470458984375,
0.0181427001953125,
0.005702972412109375,
-0.02911376953125,
0.007198333740234375,
-0.0250244140625,
0.0251617431640625,
0.027130126953125,
0.045562744140625,
0.0164947509765625,
-0.0177764892578125,
0.00855255126953125,
-0.0221710205078125,
0.02178955078125,
0.039215087890625,
-0.0305633544921875,
0.0080718994140625,
0.005672454833984375,
0.0004458427429199219,
-0.0294342041015625,
0.02874755859375,
-0.011932373046875,
-0.027618408203125,
0.0161285400390625,
-0.0035686492919921875,
-0.0242156982421875,
0.006351470947265625,
0.012969970703125,
-0.017669677734375,
0.039642333984375,
-0.01445770263671875,
-0.0089569091796875,
-0.03680419921875,
0.0184783935546875,
0.02740478515625,
-0.01116943359375,
0.0289306640625,
0.029937744140625,
-0.03631591796875,
0.033294677734375,
-0.0165557861328125,
0.00653076171875,
-0.01291656494140625,
0.016571044921875,
-0.02728271484375,
0.005382537841796875,
0.01473236083984375,
0.0095367431640625,
-0.0005288124084472656,
0.0296173095703125,
-0.01293182373046875,
-0.019500732421875,
0.0129241943359375,
0.01812744140625,
-0.032073974609375,
-0.0188751220703125,
-0.007205963134765625,
0.0260772705078125,
-0.007709503173828125,
-0.0140380859375,
-0.00989532470703125,
0.0013856887817382812,
-0.02783203125,
0.0181427001953125,
-0.0189361572265625,
-0.0110321044921875,
0.022552490234375,
0.0012569427490234375,
0.0189971923828125,
0.0252227783203125,
0.0261383056640625,
-0.00948333740234375,
-0.0055999755859375,
-0.0037555694580078125,
-0.0231781005859375,
0.035430908203125,
0.00664520263671875,
-0.0169830322265625,
0.01360321044921875,
0.026397705078125,
0.005664825439453125,
-0.026123046875,
-0.0190887451171875,
0.0260009765625,
-0.0045318603515625,
0.03375244140625,
0.0045623779296875,
0.026519775390625,
0.007740020751953125,
0.01074981689453125,
-0.0257415771484375,
0.02789306640625,
-0.0174560546875,
-0.0198211669921875,
0.0202484130859375,
0.00725555419921875,
0.04595947265625,
-0.00400543212890625,
-0.013397216796875,
-0.013824462890625,
-0.01279449462890625,
0.00942230224609375,
0.0276947021484375,
0.0133819580078125,
0.0037136077880859375,
0.004146575927734375,
0.0051727294921875,
0.01413726806640625,
-0.002468109130859375,
0.0010547637939453125,
0.0274200439453125,
-0.0147857666015625,
0.0159759521484375,
0.0125274658203125,
-0.0377197265625,
-0.01554107666015625,
0.0117340087890625,
0.037384033203125,
-0.0140533447265625,
-0.01450347900390625,
-0.00536346435546875,
-0.02227783203125,
-0.006092071533203125,
0.012908935546875,
-0.032562255859375,
0.0115966796875,
-0.0191192626953125,
0.046630859375,
-0.0428466796875,
-0.00738525390625,
-0.00833892822265625,
0.01406097412109375,
0.044281005859375,
0.001575469970703125,
0.005222320556640625,
-0.005092620849609375,
0.002155303955078125,
-0.01039886474609375,
0.01153564453125,
-0.018463134765625,
-0.00766754150390625,
0.0061798095703125,
-0.017822265625,
0.03594970703125,
-0.00046324729919433594,
-0.011810302734375,
-0.0026950836181640625,
0.005702972412109375,
-0.0005316734313964844,
0.0316162109375,
-0.0058746337890625,
0.00803375244140625,
-0.01953125,
0.03179931640625,
-0.036895751953125,
0.016937255859375,
0.03314208984375,
0.0010881423950195312,
0.00335693359375,
0.00881195068359375,
-0.04010009765625,
-0.01953125,
0.02142333984375,
-0.05615234375,
-0.003658294677734375,
0.007625579833984375,
0.0100860595703125,
-0.0290069580078125,
-0.0202789306640625,
0.016571044921875,
-0.01580810546875,
-0.0132598876953125,
0.003383636474609375,
0.030975341796875,
-0.0168609619140625,
-0.00482177734375,
-0.0192718505859375,
-0.0007266998291015625,
0.0037746429443359375,
0.00888824462890625,
-0.004924774169921875,
-0.0005922317504882812,
0.00787353515625,
0.01922607421875,
-0.003204345703125,
-0.0085906982421875,
0.00975799560546875,
0.022491455078125,
0.01120758056640625,
-0.0023250579833984375,
-0.00690460205078125,
-0.020355224609375,
0.0030193328857421875,
-0.00020623207092285156,
-0.00949859619140625,
0.0137786865234375,
0.0106964111328125,
0.0416259765625,
0.01506805419921875,
0.0511474609375,
-0.02752685546875,
-0.01024627685546875,
0.00351715087890625,
-0.014312744140625,
0.0190277099609375,
0.0222625732421875,
0.00846099853515625,
-0.01166534423828125,
-0.060760498046875,
-0.01393890380859375,
0.0002503395080566406,
0.0104827880859375,
-0.0044708251953125,
-0.029510498046875,
-0.0217437744140625,
-0.0028533935546875,
0.024017333984375,
-0.00609588623046875,
-0.01885986328125,
-0.00004565715789794922,
0.00949859619140625,
-0.01056671142578125,
0.0144500732421875,
0.0032825469970703125,
0.01288604736328125,
0.0104217529296875,
-0.032379150390625,
0.00835418701171875,
0.006275177001953125,
-0.0005006790161132812,
-0.0009708404541015625,
-0.023712158203125,
0.01529693603515625,
0.00215911865234375,
-0.02313232421875,
-0.037353515625,
0.06793212890625,
-0.0014772415161132812,
-0.018402099609375,
-0.0006403923034667969,
-0.003711700439453125,
-0.027191162109375,
-0.01238250732421875,
-0.0157928466796875,
-0.0082855224609375,
0.0157470703125,
-0.0178985595703125,
0.037567138671875,
0.02154541015625,
-0.0015544891357421875,
-0.0272674560546875,
0.01213836669921875,
-0.0056915283203125,
-0.03594970703125,
0.035491943359375,
0.0106048583984375,
0.0032634735107421875,
-0.0018491744995117188,
0.0112457275390625,
-0.004058837890625,
-0.01806640625,
0.0103759765625,
-0.0106048583984375,
-0.01348114013671875,
0.0262451171875,
0.0210113525390625,
0.0027008056640625,
-0.0017299652099609375,
0.0223541259765625,
0.0060882568359375,
-0.0167999267578125,
-0.0239410400390625,
-0.0198516845703125,
0.035736083984375,
0.030303955078125,
0.0169830322265625,
0.0172576904296875,
-0.01806640625,
-0.047607421875,
0.041351318359375,
-0.0163726806640625,
-0.019622802734375,
-0.0008368492126464844,
-0.0235748291015625,
0.0293426513671875,
0.006786346435546875,
0.0248870849609375,
-0.0238189697265625,
0.0011301040649414062,
-0.0009441375732421875,
-0.033416748046875,
0.00501251220703125,
-0.038238525390625,
-0.022491455078125,
-0.00978851318359375,
-0.012481689453125,
0.046630859375,
-0.04730224609375,
-0.0269775390625,
0.0299072265625,
0.01271820068359375,
0.032379150390625,
0.00018405914306640625,
-0.00562286376953125,
-0.005039215087890625,
0.0108489990234375,
0.007568359375,
0.01206207275390625,
0.0103607177734375,
-0.0145721435546875,
-0.00417327880859375,
0.0092926025390625,
0.005504608154296875,
0.01123046875,
0.024871826171875,
-0.007030487060546875,
0.0009937286376953125,
-0.0144805908203125,
0.01092529296875,
0.0304412841796875,
-0.0125732421875,
0.015838623046875,
0.002716064453125,
-0.029632568359375,
0.004116058349609375,
-0.0325927734375,
0.004161834716796875,
-0.00798797607421875,
-0.0181732177734375,
0.0040740966796875,
-0.0252838134765625,
-0.01209259033203125,
0.0204010009765625,
-0.01061248779296875,
-0.0196533203125,
0.01268768310546875,
0.03179931640625,
0.00753021240234375,
0.0290985107421875,
0.035797119140625,
0.020965576171875,
-0.006557464599609375,
0.022857666015625,
0.03192138671875,
0.05926513671875,
0.0011005401611328125,
-0.01447296142578125,
-0.00399017333984375,
0.0179595947265625,
0.031524658203125,
-0.01006317138671875,
-0.01201629638671875,
-0.0262298583984375,
-0.00453948974609375,
0.01116943359375,
-0.024017333984375,
0.0229339599609375,
-0.0150604248046875,
0.014190673828125,
0.00394439697265625,
0.006526947021484375,
-0.0002130270004272461,
-0.0019273757934570312,
0.0092010498046875,
0.009857177734375,
0.031585693359375,
-0.024932861328125,
0.0240478515625,
-0.005886077880859375,
0.00968170166015625,
-0.01308441162109375,
0.00823974609375,
-0.0272216796875,
-0.00696563720703125,
0.00287628173828125,
0.030548095703125,
0.00746917724609375,
-0.023345947265625,
0.0021991729736328125,
-0.007419586181640625,
0.0275115966796875,
0.0178070068359375,
-0.0439453125,
0.0256500244140625,
-0.033477783203125,
0.00583648681640625,
-0.01445770263671875,
-0.0143280029296875,
-0.01290130615234375,
-0.005161285400390625,
0.005069732666015625,
0.0023651123046875,
-0.01259613037109375,
-0.00644683837890625,
-0.0198974609375,
-0.0165863037109375,
0.01274871826171875,
0.00710296630859375,
-0.035125732421875,
-0.0088348388671875,
-0.035797119140625,
0.007171630859375,
0.011932373046875,
-0.025299072265625,
-0.016571044921875,
-0.025299072265625,
0.01181793212890625,
0.0020904541015625,
0.0120697021484375,
-0.00841522216796875,
-0.0187835693359375,
-0.0004277229309082031,
-0.00913238525390625,
-0.010711669921875,
-0.01340484619140625,
0.046417236328125,
-0.03363037109375,
0.00601959228515625,
-0.04583740234375,
0.0083770751953125,
0.0220489501953125,
0.038299560546875,
0.004364013671875,
0.0019359588623046875,
-0.01097869873046875,
0.06512451171875,
0.013702392578125,
-0.02294921875,
0.00047969818115234375,
0.007717132568359375,
0.00893402099609375,
0.033660888671875,
-0.0171051025390625,
0.0244598388671875,
0.00959014892578125,
0.00191497802734375,
0.012786865234375,
0.015533447265625,
0.00981903076171875,
-0.0220184326171875,
0.01383209228515625,
0.0212249755859375,
-0.00365447998046875,
-0.01129150390625,
-0.001239776611328125,
-0.001678466796875,
0.026458740234375,
-0.004337310791015625,
0.0142822265625,
0.007633209228515625,
0.006641387939453125,
0.02581787109375,
0.031494140625,
-0.0077667236328125,
0.0197601318359375,
-0.0309295654296875,
-0.006008148193359375,
0.029266357421875,
-0.00014710426330566406,
0.01250457763671875,
-0.008544921875,
-0.01293182373046875,
0.007843017578125,
-0.042724609375,
-0.050872802734375,
0.0068511962890625,
0.009063720703125,
0.0019121170043945312,
0.0017995834350585938,
-0.01551055908203125,
0.018280029296875,
-0.0167999267578125,
-0.034393310546875,
0.0155792236328125,
-0.0220947265625,
0.0201568603515625,
-0.003902435302734375,
-0.0014142990112304688,
0.03521728515625,
-0.0343017578125,
0.005718231201171875,
-0.0294036865234375,
-0.0450439453125,
0.0229644775390625,
0.0150146484375,
-0.0046539306640625,
0.0011081695556640625,
-0.01511383056640625,
0.0041351318359375,
-0.0027637481689453125,
0.016937255859375,
-0.0237884521484375,
-0.01385498046875,
0.040863037109375,
-0.0234527587890625,
-0.003025054931640625,
0.021148681640625,
0.005413055419921875,
0.0219573974609375,
0.0175933837890625,
0.001186370849609375,
-0.0260009765625,
0.0182952880859375,
-0.0047607421875,
-0.01131439208984375,
-0.0109100341796875,
0.00838470458984375,
0.0223846435546875,
0.02398681640625,
0.017364501953125,
0.000362396240234375,
-0.036346435546875,
-0.004009246826171875,
0.0032939910888671875,
-0.0333251953125,
-0.0137481689453125,
-0.01323699951171875,
-0.01934814453125,
0.0307464599609375,
-0.00487518310546875,
-0.013397216796875,
-0.0178680419921875,
0.00719451904296875,
0.0038700103759765625,
0.0101318359375,
-0.0172119140625,
0.00972747802734375,
-0.0104217529296875,
0.0218963623046875,
-0.0236053466796875,
0.028076171875,
-0.0036602020263671875,
0.037506103515625,
0.0062103271484375,
0.0172576904296875,
0.0223846435546875,
0.025543212890625,
0.0076446533203125,
-0.005374908447265625,
-0.00914764404296875,
0.007526397705078125,
0.0223541259765625,
-0.01708984375,
0.01332855224609375,
-0.0019083023071289062,
-0.049224853515625,
-0.00652313232421875,
-0.0013780593872070312,
0.024993896484375,
-0.021392822265625,
0.01038360595703125,
-0.026458740234375,
-0.0077667236328125,
-0.0207672119140625,
0.0259552001953125,
0.006103515625,
-0.0168914794921875,
0.042694091796875,
0.005710601806640625,
-0.0166473388671875,
-0.016082763671875,
-0.044464111328125,
0.0004112720489501953,
0.0009713172912597656,
0.050323486328125,
0.016510009765625,
-0.01158905029296875,
0.01322174072265625,
0.00809478759765625,
-0.01666259765625,
-0.0195770263671875,
0.0147857666015625,
-0.0088043212890625,
0.027191162109375,
0.0167999267578125,
0.0069580078125,
-0.0267791748046875,
0.0005502700805664062,
0.01033782958984375,
-0.011749267578125,
0.0252838134765625,
0.023681640625,
-0.0303955078125,
0.0078582763671875,
0.01242828369140625,
-0.00806427001953125,
0.0195465087890625,
0.00954437255859375,
0.021087646484375,
-0.024658203125,
-0.018951416015625,
0.0227203369140625,
-0.022308349609375,
0.01462554931640625,
0.0084686279296875,
0.002651214599609375,
-0.0023479461669921875,
0.0201568603515625,
-0.0335693359375,
-0.03070068359375,
-0.0007114410400390625,
-0.006683349609375,
-0.004100799560546875,
0.0128631591796875,
0.0113525390625,
0.0165557861328125,
0.007770538330078125,
0.046966552734375,
0.01403045654296875,
-0.0347900390625,
-0.0128936767578125,
-0.0204315185546875,
-0.028656005859375,
-0.03741455078125,
0.0118408203125,
0.0328369140625,
-0.0066986083984375,
-0.0082855224609375,
-0.04107666015625,
-0.0007867813110351562,
-0.00852203369140625,
-0.00090789794921875,
-0.00974273681640625,
0.029296875,
-0.040008544921875,
-0.00036406517028808594,
0.03216552734375,
0.019866943359375,
-0.023651123046875,
-0.0256195068359375,
-0.0303192138671875,
-0.004108428955078125,
-0.011810302734375,
0.003467559814453125,
-0.0020465850830078125,
0.0205535888671875,
-0.0265655517578125,
0.0102996826171875,
0.036376953125,
0.00981903076171875,
-0.0166168212890625,
-0.0228118896484375,
0.00785064697265625,
0.006587982177734375,
0.01837158203125,
0.01100921630859375,
0.038848876953125,
0.0165252685546875,
-0.007335662841796875,
0.042449951171875,
0.0037822723388671875,
0.00362396240234375,
-0.00820159912109375,
-0.0029811859130859375,
-0.00925445556640625,
0.01233673095703125,
0.0078582763671875,
-0.0079803466796875,
-0.0357666015625,
0.00849151611328125,
-0.055755615234375,
0.0115966796875,
-0.011627197265625,
-0.01509857177734375,
0.02716064453125,
-0.00907135009765625,
-0.0028858184814453125,
-0.0008525848388671875,
0.0186767578125,
-0.04071044921875,
0.0071258544921875,
-0.0023250579833984375,
-0.0011167526245117188,
0.0290374755859375,
0.0014934539794921875,
-0.0150299072265625,
-0.016998291015625,
-0.0197906494140625,
-0.01081085205078125,
-0.0156402587890625,
-0.0018758773803710938,
0.00989532470703125,
0.06072998046875,
0.0206146240234375,
0.00445556640625,
-0.039520263671875,
-0.00203704833984375,
-0.0084991455078125,
0.0084075927734375,
-0.037322998046875,
0.00873565673828125,
-0.02142333984375,
0.0184783935546875,
-0.013153076171875,
-0.044097900390625,
0.03314208984375,
0.003292083740234375,
0.01416778564453125,
0.026397705078125,
0.004711151123046875,
0.01059722900390625,
-0.022247314453125,
0.01074981689453125,
-0.0009164810180664062,
-0.00403594970703125,
0.02117919921875,
0.0008039474487304688,
-0.0020580291748046875,
0.0307769775390625,
-0.00864410400390625,
0.035736083984375,
-0.004962921142578125,
-0.0284576416015625,
-0.0060577392578125,
0.01511383056640625,
-0.03314208984375,
-0.007099151611328125,
0.01444244384765625,
0.0186004638671875,
-0.01001739501953125,
0.006999969482421875,
-0.0051727294921875,
-0.0029621124267578125,
0.0120391845703125,
-0.0037403106689453125,
-0.0147552490234375,
-0.0028324127197265625,
-0.041748046875,
0.01641845703125,
-0.0118560791015625,
0.005523681640625,
0.03497314453125,
0.03497314453125,
0.012786865234375,
0.0009579658508300781,
0.007312774658203125,
-0.0216217041015625,
-0.034515380859375,
-0.03955078125,
-0.00029778480529785156,
0.003398895263671875,
0.022430419921875,
-0.00321197509765625,
0.00567626953125,
0.00269317626953125,
-0.0258941650390625,
-0.0117950439453125,
0.044708251953125,
-0.057037353515625,
-0.03369140625,
0.0048370361328125,
0.00743865966796875,
-0.00914764404296875,
0.0205535888671875,
0.01036834716796875,
0.02978515625,
-0.0299530029296875,
0.002414703369140625,
0.0162353515625,
-0.0273284912109375,
0.0101470947265625,
0.0029296875,
0.012725830078125,
0.0229644775390625,
-0.0198822021484375,
-0.0179901123046875,
-0.0478515625,
0.0211029052734375,
-0.008544921875,
-0.00888824462890625,
0.005340576171875,
-0.01290130615234375,
0.019439697265625,
-0.044708251953125,
-0.002246856689453125,
-0.01305389404296875,
0.005565643310546875,
-0.0196533203125,
0.0016641616821289062,
-0.0178375244140625,
0.01306915283203125,
-0.0121612548828125,
-0.0216522216796875,
-0.00621795654296875,
-0.01132965087890625,
0.0109405517578125,
-0.016815185546875,
0.00640106201171875,
0.012603759765625,
0.003582000732421875,
-0.006740570068359375,
0.019775390625,
0.00007528066635131836,
0.0277099609375,
-0.0204315185546875,
-0.0061798095703125,
0.020111083984375,
0.042327880859375,
0.01114654541015625,
0.006130218505859375,
0.041412353515625,
-0.03131103515625,
0.00940704345703125,
0.019561767578125,
0.013763427734375,
-0.0011835098266601562,
-0.022705078125,
-0.005645751953125,
0.0164642333984375,
0.0210418701171875,
-0.011749267578125,
-0.03424072265625,
0.0006108283996582031,
-0.01873779296875,
-0.031829833984375,
0.008087158203125,
-0.035247802734375,
0.006328582763671875,
0.0083770751953125,
0.0081329345703125,
0.01454925537109375,
0.01139068603515625,
0.003787994384765625,
-0.026885986328125,
-0.004337310791015625,
-0.0169677734375,
0.0216522216796875,
0.0287017822265625,
0.0018520355224609375,
0.006732940673828125,
0.01300048828125,
-0.02880859375,
0.0181884765625,
0.01483917236328125,
-0.01477813720703125,
-0.0080108642578125,
0.0001405477523803711,
0.0034027099609375,
0.01154327392578125,
-0.013427734375,
-0.00786590576171875,
0.0238800048828125,
0.0018377304077148438,
-0.0079345703125,
-0.02581787109375,
0.024627685546875,
0.014892578125,
-0.01296234130859375,
-0.002628326416015625,
0.03076171875,
0.032135009765625,
0.0123748779296875,
0.0100555419921875,
0.0219573974609375,
-0.01450347900390625,
-0.0030841827392578125,
-0.01367950439453125,
0.01904296875,
0.019805908203125,
-0.008209228515625,
0.02276611328125,
-0.0180511474609375,
0.0018367767333984375,
0.0102081298828125,
0.0105743408203125,
-0.005001068115234375,
0.01186370849609375,
-0.01053619384765625,
0.0180816650390625,
0.0152740478515625,
-0.0312042236328125,
0.0016460418701171875,
0.0092620849609375,
0.0026454925537109375,
-0.00024890899658203125,
0.01094818115234375,
0.010040283203125,
-0.0251007080078125,
0.0027751922607421875,
0.0203704833984375,
0.007236480712890625,
0.0021724700927734375,
-0.0214385986328125,
-0.0201263427734375,
-0.00982666015625,
0.018310546875,
0.03594970703125,
0.0043487548828125,
0.029754638671875,
0.0186004638671875,
-0.01238250732421875,
-0.019805908203125,
0.0011138916015625,
-0.00787353515625,
-0.0037441253662109375,
0.01143646240234375,
0.017181396484375,
0.01058197021484375,
-0.0281829833984375,
-0.050994873046875,
-0.0244903564453125,
-0.00565338134765625,
-0.024078369140625,
0.02239990234375,
-0.00574493408203125,
-0.0198211669921875,
-0.00940704345703125,
-0.01329803466796875,
-0.0205230712890625,
0.00965118408203125,
-0.0206756591796875,
-0.019287109375,
-0.0007171630859375,
-0.016937255859375,
0.01374053955078125,
-0.004047393798828125,
-0.00498199462890625,
-0.01218414306640625,
-0.037750244140625,
0.0193939208984375,
-0.01123046875,
0.0005602836608886719,
-0.0004134178161621094,
-0.002838134765625,
0.0345458984375,
0.00475311279296875,
0.017120361328125,
-0.004222869873046875,
-0.007801055908203125,
0.0478515625,
-0.02545166015625,
-0.055908203125,
-0.0158843994140625,
-0.0235595703125,
-0.021453857421875,
-0.0236663818359375,
-0.0221099853515625,
0.03143310546875,
0.00324249267578125,
-0.003360748291015625,
-0.006885528564453125,
-0.006717681884765625,
0.038543701171875,
0.040130615234375,
0.0142059326171875,
0.049774169921875,
0.0106658935546875,
0.000637054443359375,
0.0169677734375,
0.0191497802734375,
-0.00177764892578125,
-0.01517486572265625,
-0.035614013671875,
0.0011148452758789062,
-0.0305938720703125,
-0.04541015625,
-0.0058135986328125,
-0.0050506591796875,
0.0005354881286621094,
0.01497650146484375,
-0.03179931640625,
-0.01381683349609375,
0.01154327392578125,
-0.027130126953125,
0.0090789794921875,
-0.024749755859375,
-0.0027675628662109375,
-0.0197906494140625,
-0.034881591796875,
-0.044525146484375,
-0.0161590576171875,
0.0174407958984375,
0.01427459716796875,
0.015777587890625,
-0.0119171142578125,
0.024658203125,
0.006595611572265625,
0.00812530517578125,
-0.0037059783935546875,
-0.0249481201171875,
-0.006282806396484375,
-0.00995635986328125,
-0.0173797607421875,
-0.0305633544921875,
-0.0274505615234375,
-0.00777435302734375,
-0.00888824462890625,
0.00867462158203125,
0.0206451416015625,
-0.03076171875,
0.0107421875,
0.005535125732421875,
-0.00702667236328125,
0.0125579833984375,
0.0185699462890625,
0.0265960693359375,
-0.003078460693359375,
-0.01332855224609375,
-0.031524658203125,
-0.020660400390625,
-0.0187530517578125,
-0.0183563232421875,
-0.00836181640625,
-0.0211181640625,
0.007297515869140625,
-0.007503509521484375,
-0.02838134765625,
-0.002140045166015625,
-0.041595458984375,
-0.026519775390625,
-0.003818511962890625,
-0.0058746337890625,
-0.0277099609375,
-0.0031642913818359375,
0.034515380859375,
0.0178680419921875,
0.01476287841796875,
0.0193634033203125,
0.0167083740234375,
0.01165008544921875,
-0.01500701904296875,
-0.0004038810729980469,
0.01421356201171875,
-0.00733184814453125,
0.0024700164794921875,
0.02978515625,
-0.04144287109375,
0.01393890380859375,
-0.0048370361328125,
0.0170440673828125,
0.055999755859375,
-0.031829833984375,
0.0191192626953125,
0.00959014892578125,
0.0081024169921875,
0.007236480712890625,
-0.0002837181091308594,
-0.0020313262939453125,
0.029571533203125,
0.0173492431640625,
0.01123809814453125,
-0.023468017578125,
0.0076904296875,
0.0125579833984375,
0.03802490234375,
-0.00180816650390625,
-0.01458740234375,
-0.009735107421875,
0.017333984375,
0.03924560546875,
0.0001533031463623047,
-0.0016326904296875,
-0.01459503173828125,
-0.00617218017578125,
0.0166168212890625,
-0.008514404296875,
0.038909912109375,
-0.003093719482421875,
0.01337432861328125,
0.0280609130859375,
-0.010345458984375,
-0.007297515869140625,
0.00933074951171875,
0.0207061767578125,
-0.00193023681640625,
0.0032062530517578125,
0.0037670135498046875,
0.0031375885009765625,
0.001728057861328125,
0.01476287841796875,
-0.0033893585205078125,
0.03436279296875,
0.006137847900390625,
0.002399444580078125,
-0.02056884765625,
-0.00966644287109375,
0.01284027099609375,
-0.009124755859375,
-0.0259857177734375,
0.0084381103515625,
-0.01666259765625,
0.044403076171875,
-0.0212554931640625,
-0.02386474609375,
0.022674560546875,
0.0046844482421875,
-0.0276031494140625,
-0.009857177734375,
0.0034656524658203125,
0.0184478759765625,
-0.0039825439453125,
0.0148468017578125,
-0.00982666015625,
0.015228271484375,
0.032440185546875,
0.0057220458984375,
-0.01212310791015625,
0.0058441162109375,
0.0263671875,
0.00893402099609375,
0.002948760986328125,
-0.0298614501953125,
0.0308837890625,
0.0255889892578125,
-0.017852783203125,
-0.00142669677734375,
0.004180908203125,
-0.0070648193359375,
0.001033782958984375,
-0.016815185546875,
-0.003849029541015625,
0.02490234375,
0.0029354095458984375,
-0.0261688232421875,
-0.034271240234375,
0.026275634765625,
0.02667236328125,
-0.021331787109375,
-0.00496673583984375,
0.005664825439453125,
0.00875091552734375,
-0.0172882080078125,
-0.0123138427734375,
-0.041351318359375,
-0.0020656585693359375,
-0.0034389495849609375,
0.006866455078125,
0.0045318603515625,
0.0228729248046875,
-0.006114959716796875,
0.02117919921875,
-0.03228759765625,
-0.01316070556640625,
-0.01552581787109375,
0.0009393692016601562,
0.024322509765625,
0.00923919677734375,
-0.020782470703125,
-0.047454833984375,
-0.01380157470703125,
0.003589630126953125,
-0.0160980224609375,
0.02410888671875,
0.01470184326171875,
-0.0136871337890625,
-0.057525634765625,
-0.0128936767578125,
0.03900146484375,
0.0133209228515625,
0.00728607177734375,
0.0016489028930664062,
-0.01493072509765625,
-0.005992889404296875,
-0.005306243896484375,
0.003559112548828125,
-0.0052490234375,
-0.031158447265625,
-0.039154052734375,
-0.00495147705078125,
-0.0181732177734375,
-0.014251708984375,
0.02264404296875,
-0.042999267578125,
-0.02227783203125,
0.0007004737854003906,
0.0006794929504394531,
-0.04119873046875,
0.0171966552734375,
0.01934814453125,
-0.01873779296875,
-0.0264739990234375,
-0.025299072265625,
0.0094757080078125,
0.00345611572265625,
0.01334381103515625,
-0.01190948486328125,
-0.005580902099609375,
0.015869140625,
0.02313232421875,
0.02752685546875,
-0.0106201171875,
-0.0160369873046875,
-0.04852294921875,
0.01509857177734375,
0.018585205078125,
0.0254669189453125,
-0.019927978515625,
-0.01519012451171875,
0.012542724609375,
-0.0199737548828125,
0.040130615234375,
0.02459716796875,
0.00514984130859375,
-0.005558013916015625,
-0.006427764892578125,
0.01509857177734375,
0.01436614990234375,
0.027435302734375,
0.0018596649169921875,
0.019439697265625,
-0.014251708984375,
0.0043182373046875,
-0.01727294921875,
0.0177764892578125,
-0.0208892822265625,
-0.0380859375,
-0.01336669921875,
-0.0002646446228027344,
0.01342010498046875
] |
ours_530
|
Let \(r=35\), \(s=125\), \(a=108\), and \(v=\sqrt{s^{2}-r^{2}}=120\). Let \(\omega\) be the insphere of \(S A B C\), and \(u\) be the circumradius of \(S A B C\). Let \(O\) be the circumcenter of \(S A B C\), and let \(O_{A}, O_{B}\), and \(O_{C}\) be the circumcenters of faces \(S B C, S C A\), and \(S A B\), respectively. Since \(O O_{A}\) is perpendicular to face \(S B C\), by the Pythagorean theorem \(O O_{A}^{2}=u^{2}-a^{2}\). Similarly, we must have \(O O_{B}^{2}=O O_{C}^{2}=u^{2}-a^{2}\), so \(O\) is equidistant from the three faces of \(S A B C\). Thus, \(S, I\), and \(O\) are collinear. If we let the tangency point of the insphere with \(S A B C\) be \(I_{A}\), then \(\triangle S I_{A} I \sim \triangle S O_{A} O\), so \(\frac{s}{u}=\frac{S I}{S O}=\frac{r}{\sqrt{u^{2}-a^{2}}}\), whence \(\frac{u^{2}}{u^{2}-a^{2}}=\frac{s^{2}}{r^{2}}\). Solving, we get \(u=\frac{a s}{v}=\frac{225}{2}\).
Let \(h\) be the altitude from \(S\) to face \(A B C\). We claim that the altitude of \(h\) is uniquely determined from the information given. To see this, we perform an inversion centered about \(S\) with radius 1. For any point or solid \(X\) in the original diagram, let \(X^{\prime}\) denote its inverse under this inversion. Let \(\Gamma\) be the circumsphere of \(S A^{\prime} B^{\prime} C^{\prime}\), and let \(K\) be its center and \(R^{\prime}\) be its circumradius. \(\Gamma\) is the image of plane \(A B C\) under the inversion. \(\omega^{\prime}\) is externally tangent to \(\Gamma\) at a point \(T\), and tangent to faces \(S A^{\prime} B^{\prime}, S B^{\prime} C^{\prime}\), and \(S C^{\prime} B^{\prime}\). We first compute the radius of \(\omega^{\prime}\) and the distance \(S I^{\prime}\).
Let line \(S I\) meet \(\omega\) at \(A\) and \(B\), with \(A\) closer to \(S\) than \(B\). We have \(S A=s-r\) and \(S B=s+r\). Thus, \(S A^{\prime}=\frac{1}{s-r}\) and \(S B^{\prime}=\frac{1}{s+r}\). Consequently, the radius \(r^{\prime}\) of \(\omega^{\prime}\) is \(\frac{\frac{1}{s-r}-\frac{1}{s+r}}{2}=\frac{r}{v^{2}}\), and the distance \(s^{\prime}\) from \(S\) to \(I^{\prime}\) is \(\frac{\frac{1}{s-r}+\frac{1}{s+r}}{2}=\frac{s}{v^{2}}\).
Let \(F\) be the foot of the perpendicular from \(S\) to face \(A^{\prime} B^{\prime} C^{\prime}\). \(F\) is the image of the antipode of \(S\) in the circumsphere of \(S A B C\), so \(S F=\frac{1}{2 u}\). Since \(S, O\), and \(I\) are collinear, \(S, F\), and \(I^{\prime}\) are collinear. Thus, \(S I^{\prime}\) is perpendicular to face \(A^{\prime} B^{\prime} C^{\prime}\).
Draw all the lines through \(S\) tangent to \(\omega\). Because \(S I^{\prime}\) is perpendicular to plane \(A^{\prime} B^{\prime} C^{\prime}\), the intersections of these lines with plane \(A^{\prime} B^{\prime} C^{\prime}\) will be a circle \(\omega_{0}\). Let any of these tangent lines meet \(\omega^{\prime}\) at \(P\) and \(A^{\prime} B^{\prime} C^{\prime}\) at \(Q\). \(\omega^{\prime}\) is the incircle of \(\triangle A^{\prime} B^{\prime} C^{\prime}\). Also, \(F Q\) is a radius (since \(F\) is the center of \(\omega_{0}\), as \(S, F\), and \(I^{\prime}\) are collinear.) We have \(\triangle S Q F \sim \triangle S I^{\prime} P\), so \(\frac{F Q}{F S}=\frac{I^{\prime} P}{S P}\). Thus,
\[
F Q=F S \cdot \frac{r^{\prime}}{\sqrt{s^{\prime 2}-r^{\prime 2}}}=\frac{1}{2 u} \cdot \frac{r / v^{2}}{\sqrt{\left(s^{2}-r^{2}\right) / v^{4}}}=\frac{r}{2 u v}
\]
Let \(O_{0}\) be the center of the circumcircle of \(A^{\prime} B^{\prime} C^{\prime}\), and let \(x\) be its radius. By Euler's distance formula applied to \(A^{\prime} B^{\prime} C^{\prime}\), we have that \(O_{0} F^{2}=x\left(x-\frac{r}{u v}\right)\). Now, consider the cross-section of \(\Gamma\) on the plane through \(S\) and \(K\) perpendicular to plane \(A^{\prime} B^{\prime} C^{\prime}\), which must thus pass through \(O_{0}, F\), and \(I^{\prime}\). In this cross-section there is a circle with radius \(R^{\prime}\) centered at \(K^{\prime}\). \(A B\) is a chord inside the circle, \(O_{0}\) is its midpoint, \(A O_{0}=x, O_{0} F=\sqrt{x\left(x-\frac{r}{u v}\right)}\), and \(S\) is a point on the circle on the same side of \(A B\) as \(K\) with distance \(\frac{1}{2 u}\) from \(A B\). There is a circle centered at \(I^{\prime}\) with radius \(r^{\prime}\) tangent to the circle, and \(S I^{\prime}=s^{\prime}\). Let \(J\) be the foot of the perpendicular from \(K\) to \(S J\).
By the Pythagorean theorem,
\[
R^{\prime 2}=K S^{2}=S J^{2}+K J^{2}=\left(S F-J F\right)^{2}+O_{0} F^{2}=\left(\frac{1}{2 u}-\sqrt{R^{\prime 2}-x^{2}}\right)^{2}+x\left(x-\frac{r}{u v}\right)
\]
and
\[
\left(R^{\prime}+r^{\prime}\right)^{2}=K I^{\prime 2}=J I^{\prime 2}+K J^{2}=\left(S I^{\prime}-S J\right)^{2}+x\left(x-\frac{r}{u v}\right)
\]
We leave the relatively straightforward but tedious computations to the interested reader.
The answer is \(\sqrt{\frac{35925411600}{3433609}}\), so \(m+n = 35928845209\).
\(\boxed{35928845209}\)
|
35928845209
|
{
"competition": "us_comps",
"dataset": "Ours",
"posts": null,
"source": "OMOSoln2-2.md"
}
|
In tetrahedron \(S A B C\), the circumcircles of faces \(S A B, S B C\), and \(S C A\) each have radius 108. The inscribed sphere of \(S A B C\), centered at \(I\), has radius 35. Additionally, \(S I=125\). Let \(R\) be the largest possible value of the circumradius of face \(A B C\). Given that \(R\) can be expressed in the form \(\sqrt{\frac{m}{n}}\), where \(m\) and \(n\) are relatively prime positive integers, find \(m+n\).
|
[
"/Mathematics/Geometry/Distance/Point-PlaneDistance",
"/Mathematics/Geometry/Distance/Point-PointDistance3-Dimensional",
"/Mathematics/Geometry/InversiveGeometry/Inversion",
"/Mathematics/Geometry/InversiveGeometry/InversionSphere",
"/Mathematics/Geometry/SolidGeometry/Polyhedra/Tetrahedra",
"/Mathematics/Geometry/SolidGeometry/Spheres/Circumsphere",
"/Mathematics/Geometry/SolidGeometry/Spheres/Insphere",
"/Mathematics/Geometry/SolidGeometry/Spheres/InversionSphere",
"/Mathematics/Geometry/Transformations/GeometricTransformations"
] |
Invert the tetrahedron about vertex S to convert the three equal face circumcircles into tangent circles, reducing the problem to planar triangle geometry where Euler’s formula yields the maximal base circumradius.
|
[
0.00011026859283447266,
0.01520538330078125,
0.0105438232421875,
0.044158935546875,
0.0007123947143554688,
0.013275146484375,
0.0105743408203125,
0.006134033203125,
0.007080078125,
-0.019500732421875,
-0.0107269287109375,
0.0158843994140625,
-0.0101318359375,
0.05267333984375,
-0.01629638671875,
0.006664276123046875,
-0.0198516845703125,
-0.0197906494140625,
0.038299560546875,
0.0002961158752441406,
-0.01006317138671875,
0.0027923583984375,
-0.07275390625,
0.003070831298828125,
-0.0169525146484375,
0.0181121826171875,
-0.0227203369140625,
-0.01049041748046875,
-0.0028076171875,
0.00311279296875,
-0.01174163818359375,
0.0005412101745605469,
0.00424957275390625,
0.0026454925537109375,
-0.0018024444580078125,
-0.01317596435546875,
0.016632080078125,
-0.00691986083984375,
-0.045928955078125,
-0.052520751953125,
0.00974273681640625,
0.020263671875,
-0.03558349609375,
0.007312774658203125,
-0.0262451171875,
0.0006170272827148438,
-0.00818634033203125,
-0.0241546630859375,
0.01360321044921875,
0.006847381591796875,
0.00394439697265625,
0.01149749755859375,
-0.0204010009765625,
-0.01020050048828125,
-0.014434814453125,
-0.045654296875,
0.01000213623046875,
0.0002200603485107422,
-0.0198211669921875,
-0.01739501953125,
0.007266998291015625,
0.00917816162109375,
0.0018758773803710938,
-0.0236053466796875,
0.0007662773132324219,
-0.0078582763671875,
-0.01171112060546875,
-0.04986572265625,
-0.00431060791015625,
0.0201568603515625,
0.0207977294921875,
-0.021484375,
0.01374053955078125,
0.0113067626953125,
0.040771484375,
-0.007251739501953125,
-0.0091552734375,
0.002620697021484375,
-0.033203125,
0.0033550262451171875,
-0.0005383491516113281,
0.0017833709716796875,
0.0176849365234375,
-0.02728271484375,
0.006256103515625,
0.018218994140625,
-0.003337860107421875,
-0.00016295909881591797,
0.0162353515625,
-0.0135040283203125,
-0.005283355712890625,
0.0016622543334960938,
-0.01044464111328125,
0.0347900390625,
0.01528167724609375,
0.0188446044921875,
0.00934600830078125,
-0.0080718994140625,
0.006160736083984375,
0.007228851318359375,
-0.0125885009765625,
-0.00493621826171875,
-0.0109710693359375,
-0.0013103485107421875,
0.002620697021484375,
-0.014862060546875,
0.0029354095458984375,
0.0295257568359375,
0.0130462646484375,
0.0005331039428710938,
0.0221405029296875,
-0.006229400634765625,
-0.00020956993103027344,
0.03155517578125,
-0.020965576171875,
-0.01165771484375,
0.0140228271484375,
-0.006244659423828125,
-0.004154205322265625,
0.00916290283203125,
-0.01522064208984375,
0.00852203369140625,
0.00439453125,
0.002471923828125,
0.00760650634765625,
-0.0225677490234375,
0.01149749755859375,
-0.02557373046875,
-0.004413604736328125,
0.0003581047058105469,
0.01123046875,
-0.01187896728515625,
-0.036041259765625,
-0.004177093505859375,
-0.053741455078125,
-0.02447509765625,
-0.00289154052734375,
0.004459381103515625,
-0.001964569091796875,
-0.029998779296875,
0.0072174072265625,
-0.017578125,
-0.0021228790283203125,
-0.027618408203125,
-0.005695343017578125,
-0.035125732421875,
0.01178741455078125,
-0.01561737060546875,
0.01392364501953125,
0.004123687744140625,
0.004116058349609375,
-0.025238037109375,
0.01226043701171875,
0.0011119842529296875,
0.004116058349609375,
0.00014472007751464844,
0.00562286376953125,
0.022491455078125,
-0.0013637542724609375,
0.0034027099609375,
0.0013208389282226562,
-0.012420654296875,
-0.00711822509765625,
0.0308990478515625,
0.01345062255859375,
-0.0228118896484375,
0.00264739990234375,
0.00296783447265625,
-0.0144805908203125,
0.00975799560546875,
0.01331329345703125,
0.011322021484375,
-0.006999969482421875,
0.01107025146484375,
-0.033843994140625,
-0.0094451904296875,
-0.0015583038330078125,
0.0078582763671875,
-0.0013380050659179688,
0.0252838134765625,
-0.00067901611328125,
-0.014251708984375,
0.004199981689453125,
-0.0096282958984375,
0.01476287841796875,
0.0018987655639648438,
0.0092010498046875,
0.02618408203125,
0.0275726318359375,
0.0197601318359375,
-0.03558349609375,
-0.0012664794921875,
0.0046844482421875,
-0.0015764236450195312,
0.024749755859375,
-0.016448974609375,
-0.0028667449951171875,
0.0012807846069335938,
0.018798828125,
-0.0023059844970703125,
-0.0150146484375,
-0.00962066650390625,
0.0438232421875,
0.00865936279296875,
0.003734588623046875,
0.01346588134765625,
-0.005970001220703125,
0.0076751708984375,
0.0028076171875,
0.0004093647003173828,
-0.00811004638671875,
0.0264129638671875,
-0.001026153564453125,
-0.006221771240234375,
-0.0112762451171875,
-0.0012683868408203125,
-0.0159454345703125,
0.0036182403564453125,
-0.00786590576171875,
0.01515960693359375,
0.03802490234375,
0.0002715587615966797,
0.017425537109375,
-0.0123138427734375,
-0.0116729736328125,
0.0181121826171875,
-0.0123443603515625,
-0.006694793701171875,
-0.0017499923706054688,
-0.0008435249328613281,
-0.019805908203125,
-0.00036406517028808594,
-0.001689910888671875,
-0.0150299072265625,
-0.01091766357421875,
0.0007109642028808594,
-0.051910400390625,
-0.004032135009765625,
0.00791168212890625,
0.00738525390625,
0.0821533203125,
-0.01519012451171875,
-0.00033164024353027344,
0.00435638427734375,
0.00826263427734375,
0.00838470458984375,
0.01092529296875,
-0.01001739501953125,
-0.0128631591796875,
-0.0267486572265625,
-0.031585693359375,
0.0251617431640625,
0.005706787109375,
-0.0118865966796875,
-0.0340576171875,
0.006328582763671875,
0.01218414306640625,
0.01470184326171875,
-0.0182342529296875,
0.0235137939453125,
0.004810333251953125,
-0.0120391845703125,
-0.005580902099609375,
-0.0099029541015625,
-0.014434814453125,
0.032135009765625,
0.01141357421875,
-0.00865936279296875,
0.0229644775390625,
-0.01509857177734375,
0.01226043701171875,
-0.02099609375,
-0.0290985107421875,
0.0085601806640625,
-0.03240966796875,
-0.01433563232421875,
-0.007335662841796875,
0.031890869140625,
0.0141754150390625,
0.01373291015625,
0.0035686492919921875,
0.008941650390625,
0.004974365234375,
-0.0202178955078125,
0.00551605224609375,
0.0163116455078125,
-0.0005941390991210938,
-0.03338623046875,
0.0014591217041015625,
0.01425933837890625,
0.001056671142578125,
0.0279541015625,
-0.033599853515625,
-0.00251007080078125,
0.035980224609375,
0.0015697479248046875,
-0.0005311965942382812,
0.020751953125,
0.0146636962890625,
0.01104736328125,
0.02020263671875,
0.0042266845703125,
0.001522064208984375,
0.01519012451171875,
0.00853729248046875,
-0.0021152496337890625,
-0.0031795501708984375,
0.00467681884765625,
-0.01384735107421875,
-0.006526947021484375,
-0.0004811286926269531,
-0.003940582275390625,
-0.0057373046875,
-0.0008912086486816406,
-0.035736083984375,
-0.043243408203125,
0.00429534912109375,
-0.0014505386352539062,
-0.0249176025390625,
0.0100555419921875,
0.0077056884765625,
-0.0147247314453125,
0.042388916015625,
0.01421356201171875,
0.020111083984375,
-0.01654052734375,
0.0018014907836914062,
0.0010967254638671875,
0.02020263671875,
0.0135040283203125,
-0.005565643310546875,
0.0037078857421875,
0.018707275390625,
0.0091094970703125,
-0.0070343017578125,
-0.035614013671875,
0.00605010986328125,
0.015228271484375,
0.00974273681640625,
0.0205230712890625,
0.0072784423828125,
0.002918243408203125,
0.00498199462890625,
-0.08184814453125,
0.00730133056640625,
0.032623291015625,
-0.0011529922485351562,
0.011627197265625,
-0.0056610107421875,
-0.0115966796875,
-0.0215606689453125,
-0.0179443359375,
0.0191650390625,
-0.0032501220703125,
-0.0296783447265625,
-0.0263824462890625,
0.007488250732421875,
0.02899169921875,
-0.0135498046875,
-0.00009125471115112305,
0.0204925537109375,
-0.028961181640625,
-0.01202392578125,
-0.0008363723754882812,
-0.03863525390625,
0.0183563232421875,
-0.034820556640625,
0.004894256591796875,
-0.046783447265625,
0.00011241436004638672,
-0.00412750244140625,
0.005100250244140625,
-0.005207061767578125,
-0.00466156005859375,
0.01087188720703125,
0.006893157958984375,
-0.0017910003662109375,
0.00909423828125,
-0.004657745361328125,
0.00229644775390625,
-0.0170440673828125,
-0.0067901611328125,
-0.0283966064453125,
0.0330810546875,
-0.006107330322265625,
0.00809478759765625,
0.040313720703125,
-0.0421142578125,
-0.014739990234375,
0.00431060791015625,
-0.016448974609375,
-0.00013780593872070312,
-0.006656646728515625,
-0.020599365234375,
-0.01000213623046875,
-0.03753662109375,
-0.01019287109375,
0.0013666152954101562,
0.023040771484375,
-0.0149383544921875,
-0.05047607421875,
-0.009613037109375,
-0.01116180419921875,
-0.0294036865234375,
-0.001003265380859375,
-0.0153656005859375,
-0.0132598876953125,
0.053131103515625,
0.002338409423828125,
0.019439697265625,
0.01507568359375,
-0.0085601806640625,
0.0186767578125,
-0.002910614013671875,
-0.04962158203125,
0.0109100341796875,
0.0018491744995117188,
0.0211944580078125,
-0.0216827392578125,
-0.0057525634765625,
0.008209228515625,
-0.007171630859375,
0.03155517578125,
0.007274627685546875,
0.02276611328125,
0.006011962890625,
-0.0215301513671875,
0.014404296875,
0.0031719207763671875,
-0.03802490234375,
0.04742431640625,
0.01047515869140625,
-0.0250396728515625,
0.0079193115234375,
0.00449371337890625,
-0.0145416259765625,
0.0140380859375,
-0.01203155517578125,
0.00530242919921875,
0.023651123046875,
0.01108551025390625,
-0.01267242431640625,
-0.005458831787109375,
0.00604248046875,
0.001506805419921875,
0.0120086669921875,
0.03277587890625,
-0.00445556640625,
0.02789306640625,
-0.01108551025390625,
-0.005035400390625,
-0.039947509765625,
0.0135040283203125,
-0.041351318359375,
-0.03216552734375,
0.005435943603515625,
0.0477294921875,
-0.047607421875,
-0.02850341796875,
0.0005774497985839844,
0.0005793571472167969,
0.006931304931640625,
-0.003826141357421875,
0.03826904296875,
0.0029125213623046875,
-0.004547119140625,
-0.0134124755859375,
0.04449462890625,
-0.0207977294921875,
0.019989013671875,
-0.0016651153564453125,
0.0019121170043945312,
0.0264434814453125,
-0.02056884765625,
-0.035430908203125,
0.0491943359375,
0.006618499755859375,
0.0026721954345703125,
0.033905029296875,
0.01078033447265625,
0.0018100738525390625,
0.01806640625,
-0.01404571533203125,
0.0220489501953125,
-0.0166168212890625,
-0.0045928955078125,
0.0189971923828125,
-0.0144195556640625,
0.016448974609375,
-0.056640625,
0.01549530029296875,
0.022705078125,
-0.006580352783203125,
-0.003643035888671875,
-0.06072998046875,
-0.02520751953125,
0.018798828125,
-0.0047454833984375,
0.01311492919921875,
-0.004245758056640625,
0.0303192138671875,
-0.042327880859375,
-0.02166748046875,
0.0231170654296875,
0.020233154296875,
-0.0267486572265625,
0.038421630859375,
-0.0025997161865234375,
0.0311279296875,
0.004329681396484375,
0.007160186767578125,
0.00848388671875,
0.032562255859375,
-0.037261962890625,
0.017242431640625,
0.01497650146484375,
-0.006160736083984375,
0.00891876220703125,
0.0185546875,
0.029205322265625,
-0.02313232421875,
0.03570556640625,
0.0183563232421875,
-0.013641357421875,
-0.0088653564453125,
0.0245208740234375,
0.000919342041015625,
0.02435302734375,
0.01898193359375,
-0.0208740234375,
-0.0063018798828125,
-0.021240234375,
-0.00820159912109375,
0.0197296142578125,
-0.02166748046875,
0.0095977783203125,
-0.0047454833984375,
-0.035003662109375,
0.0180816650390625,
0.03076171875,
-0.01140594482421875,
0.0100250244140625,
-0.01082611083984375,
-0.023223876953125,
-0.005146026611328125,
-0.004772186279296875,
0.0029010772705078125,
0.01043701171875,
0.005359649658203125,
0.0257110595703125,
-0.0252685546875,
0.0036067962646484375,
-0.01751708984375,
-0.00298309326171875,
-0.007564544677734375,
0.011077880859375,
-0.005550384521484375,
0.020751953125,
-0.027008056640625,
0.0171661376953125,
0.036834716796875,
-0.0404052734375,
0.032440185546875,
0.0328369140625,
-0.0029087066650390625,
-0.022796630859375,
0.00787353515625,
-0.041412353515625,
-0.00507354736328125,
-0.03717041015625,
0.005764007568359375,
0.0006604194641113281,
0.0012578964233398438,
0.034454345703125,
0.0283203125,
-0.01471710205078125,
0.0029850006103515625,
0.0026950836181640625,
0.0206451416015625,
-0.003692626953125,
0.02880859375,
0.027130126953125,
-0.023773193359375,
-0.01458740234375,
-0.0202789306640625,
-0.027069091796875,
-0.01140594482421875,
-0.0004572868347167969,
0.01132965087890625,
-0.01026153564453125,
-0.04278564453125,
0.02166748046875,
0.011077880859375,
-0.00592803955078125,
0.0099945068359375,
-0.0089263916015625,
0.01219940185546875,
0.00196075439453125,
0.0623779296875,
-0.01221466064453125,
0.007965087890625,
0.0209503173828125,
-0.01023101806640625,
0.0085296630859375,
-0.0035114288330078125,
0.0002384185791015625,
-0.022857666015625,
-0.0357666015625,
0.0241241455078125,
-0.0024623870849609375,
0.00786590576171875,
0.0145111083984375,
-0.03204345703125,
0.0271759033203125,
0.00994873046875,
-0.02960205078125,
0.0155029296875,
-0.007328033447265625,
-0.00873565673828125,
-0.0210113525390625,
0.004207611083984375,
0.01171875,
0.01013946533203125,
0.02117919921875,
-0.029510498046875,
-0.034912109375,
-0.01329803466796875,
-0.03814697265625,
0.0010156631469726562,
-0.039703369140625,
-0.0187530517578125,
0.048492431640625,
-0.003170013427734375,
-0.012969970703125,
-0.03533935546875,
-0.007617950439453125,
-0.0055694580078125,
0.01904296875,
-0.00740814208984375,
-0.0030517578125,
0.01432037353515625,
-0.005615234375,
0.03656005859375,
-0.033203125,
-0.01499176025390625,
-0.0013790130615234375,
-0.0265350341796875,
-0.00003451108932495117,
0.00514984130859375,
0.0162353515625,
-0.01168060302734375,
-0.0017232894897460938,
0.00922393798828125,
0.01080322265625,
0.0032978057861328125,
-0.0232391357421875,
-0.0287017822265625,
-0.038909912109375,
0.0282135009765625,
0.00243377685546875,
-0.00518798828125,
0.03253173828125,
-0.014312744140625,
-0.005176544189453125,
0.0061492919921875,
-0.0270538330078125,
-0.056884765625,
-0.054534912109375,
0.01338958740234375,
0.025848388671875,
-0.01468658447265625,
-0.0036830902099609375,
0.018829345703125,
-0.0499267578125,
-0.0300750732421875,
-0.004795074462890625,
-0.0257110595703125,
0.00624847412109375,
0.0020618438720703125,
0.01548004150390625,
0.0167694091796875,
0.0279998779296875,
0.03973388671875,
0.0052642822265625,
-0.00443267822265625,
0.0394287109375,
0.036376953125,
0.02154541015625,
0.0016889572143554688,
0.00875091552734375,
-0.01378631591796875,
-0.0220489501953125,
0.0007700920104980469,
0.0224609375,
-0.0110321044921875,
-0.0049591064453125,
-0.01032257080078125,
-0.005619049072265625,
-0.01092529296875,
-0.0147857666015625,
0.0162811279296875,
-0.01422119140625,
0.031494140625,
-0.0223236083984375,
-0.0015382766723632812,
-0.02850341796875,
-0.00997161865234375,
0.01947021484375,
-0.0384521484375,
0.01366424560546875,
-0.041595458984375,
-0.0304412841796875,
-0.00485992431640625,
-0.014923095703125,
-0.0238189697265625,
-0.025390625,
-0.0269012451171875,
0.035797119140625,
0.0217132568359375,
0.019195556640625,
0.03961181640625,
0.0201416015625,
-0.0263824462890625,
-0.0006613731384277344,
0.0015382766723632812,
0.0120391845703125,
-0.006435394287109375,
-0.0072784423828125,
-0.04205322265625,
0.023193359375,
0.0058441162109375,
0.0005717277526855469,
0.0307159423828125,
0.0032558441162109375,
-0.01555633544921875,
-0.011383056640625,
-0.03985595703125,
-0.051849365234375,
-0.02606201171875,
0.00988006591796875,
0.0408935546875,
-0.0261383056640625,
0.024444580078125,
0.0196533203125,
-0.0035247802734375,
-0.00748443603515625,
-0.01025390625,
0.0021839141845703125,
0.005260467529296875,
-0.00405120849609375,
0.030731201171875,
0.037994384765625,
0.0026226043701171875,
-0.01438140869140625,
-0.0173492431640625,
-0.0184173583984375,
0.006256103515625,
0.01751708984375,
-0.0010976791381835938,
0.014190673828125,
-0.03125,
-0.048858642578125,
0.038848876953125,
0.006641387939453125,
-0.032958984375,
-0.0060882568359375,
-0.0054473876953125,
-0.0081634521484375,
-0.00977325439453125,
0.0013055801391601562,
-0.02099609375,
-0.01042938232421875,
0.0222625732421875,
-0.0121612548828125,
0.0302276611328125,
-0.019134521484375,
-0.031585693359375,
-0.01245880126953125,
0.0130615234375,
-0.013458251953125,
0.01300048828125,
0.03277587890625,
-0.03338623046875,
0.00970458984375,
-0.025299072265625,
0.0026073455810546875,
-0.005924224853515625,
0.0014553070068359375,
0.0178985595703125,
-0.0023708343505859375,
0.0266571044921875,
-0.0057830810546875,
0.026214599609375,
0.0073699951171875,
-0.0168914794921875,
-0.0170745849609375,
-0.0066375732421875,
-0.017242431640625,
0.012969970703125,
-0.0221099853515625,
-0.0186767578125,
-0.0297088623046875,
-0.005523681640625,
0.0257110595703125,
0.01096343994140625,
0.019561767578125,
0.0056610107421875,
0.0024089813232421875,
-0.0193023681640625,
0.0179290771484375,
0.039825439453125,
-0.00196075439453125,
0.01107025146484375,
-0.0091094970703125,
-0.0157318115234375,
-0.01300048828125,
0.01386260986328125,
0.0296630859375,
0.00959014892578125,
0.004924774169921875,
-0.0055999755859375,
0.00630950927734375,
-0.0401611328125,
-0.005847930908203125,
-0.0172271728515625,
-0.01296234130859375,
-0.027099609375,
0.00505828857421875,
-0.01020050048828125,
-0.002971649169921875,
0.0084686279296875,
0.0169525146484375,
-0.0172271728515625,
0.01058197021484375,
-0.03973388671875,
0.060150146484375,
0.01514434814453125,
-0.01898193359375,
0.006175994873046875,
-0.006717681884765625,
0.0273284912109375,
-0.0189666748046875,
0.0171356201171875,
0.0211334228515625,
0.039093017578125,
0.00461578369140625,
0.003570556640625,
0.01152801513671875,
0.0206298828125,
-0.0253143310546875,
0.0007562637329101562,
0.01052093505859375,
-0.04779052734375,
0.0264434814453125,
0.007457733154296875,
-0.005672454833984375,
0.0105133056640625,
-0.0107879638671875,
0.0026798248291015625,
-0.01311492919921875,
0.00994873046875,
-0.02569580078125,
0.034881591796875,
0.0305328369140625,
-0.007350921630859375,
-0.00847625732421875,
0.004985809326171875,
-0.0343017578125,
0.01374053955078125,
-0.0025653839111328125,
0.051055908203125,
-0.037139892578125,
-0.01097869873046875,
0.00989532470703125,
0.0184326171875,
0.03570556640625,
0.0149993896484375,
-0.007724761962890625,
0.01259613037109375,
0.0009026527404785156,
0.01666259765625,
-0.00981903076171875,
-0.036041259765625,
0.00870513916015625,
-0.0033397674560546875,
0.0026340484619140625,
0.01146697998046875,
-0.035736083984375,
0.0175628662109375,
-0.00894927978515625,
-0.0017385482788085938,
0.00846099853515625,
-0.00960540771484375,
-0.010833740234375,
0.0291595458984375,
-0.016571044921875,
-0.01229095458984375,
-0.01268768310546875,
0.004650115966796875,
-0.0291900634765625,
-0.017364501953125,
0.034515380859375,
0.02142333984375,
-0.028228759765625,
-0.0011339187622070312,
-0.023345947265625,
-0.0026226043701171875,
0.0195770263671875,
0.036590576171875,
0.038116455078125,
0.020599365234375,
0.04827880859375,
0.006145477294921875,
0.01348114013671875,
-0.00007551908493041992,
0.00911712646484375,
0.0073394775390625,
-0.01192474365234375,
-0.01617431640625,
0.026611328125,
0.0016078948974609375,
-0.005878448486328125,
-0.007312774658203125,
-0.002620697021484375,
0.0263671875,
-0.0269317626953125,
-0.0029773712158203125,
-0.0009746551513671875,
-0.0033893585205078125,
0.029815673828125,
-0.0013971328735351562,
0.0024166107177734375,
-0.006771087646484375,
-0.0016241073608398438,
0.0034637451171875,
0.004669189453125,
-0.0197296142578125,
-0.01003265380859375,
0.0017404556274414062,
-0.00920867919921875,
-0.0024662017822265625,
-0.022491455078125,
-0.0020351409912109375,
0.004150390625,
-0.0274810791015625,
0.01267242431640625,
0.005786895751953125,
0.005825042724609375,
0.028564453125,
-0.035980224609375,
0.006000518798828125,
0.00832366943359375,
-0.004390716552734375,
-0.0235595703125,
-0.021209716796875,
-0.0220947265625,
0.01739501953125,
-0.005771636962890625,
0.00839996337890625,
0.0160980224609375,
0.00189208984375,
-0.00336456298828125,
0.004802703857421875,
-0.0012416839599609375,
-0.031890869140625,
-0.0189208984375,
0.04437255859375,
0.0543212890625,
0.0170135498046875,
0.0105743408203125,
0.01198577880859375,
0.003276824951171875,
-0.012908935546875,
-0.049713134765625,
-0.00278472900390625,
-0.0075836181640625,
0.0180206298828125,
0.0096435546875,
0.059112548828125,
-0.0119781494140625,
-0.023406982421875,
0.023162841796875,
-0.005092620849609375,
0.01360321044921875,
0.025299072265625,
-0.0004115104675292969,
0.006931304931640625,
-0.0236053466796875,
0.0271759033203125,
0.0027599334716796875,
-0.006427764892578125,
0.024688720703125,
-0.030548095703125,
0.03582763671875,
-0.0167999267578125,
-0.00792694091796875,
0.006771087646484375,
-0.0032501220703125,
-0.0009074211120605469,
-0.0203399658203125,
-0.01617431640625,
0.005100250244140625,
-0.01247406005859375,
0.0027179718017578125,
0.00826263427734375,
0.015533447265625,
-0.0194244384765625,
0.0130462646484375,
0.01514434814453125,
0.00783538818359375,
-0.0022144317626953125,
-0.0234222412109375,
-0.004058837890625,
0.00933837890625,
-0.02630615234375,
0.0274810791015625,
0.0087432861328125,
0.0005512237548828125,
-0.0251312255859375,
-0.0001608133316040039,
0.028717041015625,
-0.001983642578125,
-0.039886474609375,
-0.011627197265625,
0.01076507568359375,
0.01383209228515625,
-0.00812530517578125,
-0.0180206298828125,
0.0208587646484375,
0.0020198822021484375,
-0.00240325927734375,
0.00318145751953125,
-0.0205841064453125,
-0.00870513916015625,
0.01194000244140625,
-0.0240631103515625,
-0.0310516357421875,
-0.02679443359375,
-0.002399444580078125,
-0.0009174346923828125,
-0.00400543212890625,
0.015472412109375,
0.0095672607421875,
-0.0187225341796875,
-0.0305023193359375,
-0.0163421630859375,
0.0139312744140625,
-0.0038318634033203125,
0.006988525390625,
-0.0062103271484375,
0.0123291015625,
0.025604248046875,
-0.001705169677734375,
-0.0109405517578125,
0.0164794921875,
0.037628173828125,
-0.00543975830078125,
-0.01361846923828125,
-0.01160430908203125,
0.005641937255859375,
0.006595611572265625,
-0.020263671875,
0.01153564453125,
-0.0137939453125,
0.0255889892578125,
0.0204010009765625,
-0.00954437255859375,
-0.012481689453125,
0.01016998291015625,
0.0275726318359375,
-0.01270294189453125,
0.013458251953125,
-0.00858306884765625,
0.0024127960205078125,
0.018768310546875,
0.005596160888671875,
0.01544952392578125,
-0.04669189453125,
0.01554107666015625,
0.015380859375,
0.0190277099609375,
0.0282135009765625,
-0.0279693603515625,
-0.0270538330078125,
0.0430908203125,
-0.003475189208984375,
0.051513671875,
-0.035858154296875,
-0.0012645721435546875,
-0.0352783203125,
0.01690673828125,
0.01476287841796875,
-0.01557159423828125,
0.0123138427734375,
-0.001850128173828125,
-0.024383544921875,
-0.020721435546875,
0.0254364013671875,
0.015960693359375,
0.007465362548828125,
-0.0012483596801757812,
0.006649017333984375,
0.00832366943359375,
-0.00827789306640625,
-0.010528564453125,
-0.03509521484375,
-0.00572967529296875,
0.01058197021484375,
-0.0029010772705078125,
0.0002605915069580078,
0.0008931159973144531,
0.01079559326171875,
0.0229949951171875,
0.01480865478515625,
0.01861572265625,
-0.017364501953125,
-0.029998779296875,
-0.02197265625,
-0.0038738250732421875,
-0.0219879150390625,
0.0081024169921875,
0.006256103515625,
-0.001102447509765625,
0.01203155517578125,
-0.00939178466796875,
0.00177764892578125,
-0.015777587890625,
0.01000213623046875,
-0.01055145263671875,
0.01004791259765625,
0.0135955810546875,
-0.01541900634765625,
0.0079193115234375,
-0.029937744140625,
0.0165252685546875,
0.01171112060546875,
-0.00323486328125,
0.0007572174072265625,
0.023406982421875,
-0.012451171875,
-0.0187225341796875,
0.010833740234375,
0.01177978515625,
-0.016326904296875,
-0.00559234619140625,
-0.00389862060546875,
-0.004482269287109375,
0.01934814453125,
0.0264739990234375,
0.01056671142578125,
-0.008392333984375,
0.0114288330078125,
0.01253509521484375,
-0.0017156600952148438,
0.028106689453125,
-0.0282745361328125,
-0.032806396484375,
0.005191802978515625,
0.00762176513671875,
0.032806396484375,
0.01491546630859375,
-0.0028896331787109375,
-0.004673004150390625,
-0.0033435821533203125,
-0.01422882080078125,
0.0265655517578125,
-0.0047760009765625,
0.0268402099609375,
-0.01432037353515625,
0.029449462890625,
-0.0076751708984375,
-0.0152740478515625,
-0.0045623779296875,
0.010345458984375,
0.001216888427734375,
-0.01306915283203125,
-0.032257080078125,
-0.023406982421875,
0.006923675537109375,
0.007701873779296875,
-0.0012617111206054688,
-0.0178985595703125,
0.0255126953125,
0.0119476318359375,
0.017852783203125,
-0.024017333984375,
0.00594329833984375,
-0.0212554931640625,
0.0162353515625,
0.007808685302734375,
-0.036376953125,
-0.0155029296875,
-0.005931854248046875,
-0.030914306640625,
-0.023223876953125,
-0.01058197021484375,
0.0089569091796875,
0.0008339881896972656,
-0.03570556640625,
-0.01006317138671875,
-0.01132965087890625,
-0.0176849365234375,
-0.0312042236328125,
0.0022945404052734375,
0.031951904296875,
0.03729248046875,
-0.0157470703125,
0.0225677490234375,
-0.032745361328125,
0.02288818359375,
-0.006023406982421875,
-0.00665283203125,
0.0210113525390625,
-0.01500701904296875,
0.016754150390625,
-0.031280517578125,
-0.024383544921875,
-0.00679779052734375,
-0.007778167724609375,
-0.0161590576171875,
0.020263671875,
-0.00569915771484375,
0.01910400390625,
-0.000023126602172851562,
-0.0214996337890625,
0.0026950836181640625,
0.0015954971313476562,
0.00684356689453125,
-0.01178741455078125,
0.030853271484375,
0.019866943359375,
0.0455322265625,
0.002262115478515625,
0.03363037109375,
-0.021484375,
-0.032073974609375,
0.01226043701171875,
0.033966064453125,
-0.01374053955078125,
0.00099945068359375,
0.0027027130126953125,
-0.01174163818359375,
-0.0413818359375,
-0.01776123046875,
0.0293731689453125,
-0.003742218017578125,
-0.0183258056640625,
0.0063323974609375,
-0.0224761962890625,
0.036773681640625,
-0.035888671875,
0.0280303955078125,
-0.01070404052734375,
-0.01178741455078125,
0.002620697021484375,
-0.0272979736328125,
0.005512237548828125,
0.0226593017578125,
0.0164642333984375,
-0.022613525390625,
0.002315521240234375,
0.0013942718505859375,
-0.0164031982421875,
-0.0292816162109375,
0.0175018310546875,
-0.0240478515625,
0.01174163818359375,
0.044830322265625,
0.013458251953125,
0.031585693359375,
0.0146484375,
0.01788330078125,
-0.02197265625,
0.01413726806640625,
0.01105499267578125,
0.0032787322998046875,
-0.006862640380859375,
-0.00634765625,
0.006618499755859375,
0.0218505859375,
0.0017976760864257812,
0.005710601806640625,
0.01763916015625,
-0.00469970703125,
-0.00994110107421875,
-0.00737762451171875,
0.01180267333984375,
0.0106658935546875,
0.0168609619140625,
0.005462646484375,
0.020263671875,
0.021453857421875,
-0.004543304443359375,
0.0272064208984375,
-0.0088348388671875,
0.0030803680419921875,
-0.0298004150390625,
0.032501220703125,
0.0241241455078125,
0.01532745361328125,
-0.01085662841796875,
0.005702972412109375,
0.0009355545043945312,
-0.01267242431640625,
-0.0173187255859375,
-0.01453399658203125,
0.015625,
0.00623321533203125,
0.01275634765625,
0.0165863037109375,
-0.00012022256851196289,
0.0126953125,
-0.0099945068359375,
0.0216522216796875,
0.0179595947265625,
-0.032928466796875,
-0.006687164306640625,
-0.01058197021484375,
-0.009002685546875,
-0.0031528472900390625,
0.01262664794921875,
0.0164794921875,
-0.020172119140625,
-0.01462554931640625,
-0.0194244384765625,
-0.0092620849609375,
-0.01922607421875,
-0.006526947021484375,
-0.01080322265625,
-0.0092926025390625,
-0.026702880859375,
0.0037670135498046875,
-0.0285186767578125,
0.00391387939453125,
0.0011348724365234375,
0.0021076202392578125,
0.00046372413635253906,
0.028106689453125,
-0.02685546875,
-0.015838623046875,
-0.01032257080078125,
-0.00399017333984375,
-0.032684326171875,
0.0092315673828125,
0.0202789306640625,
0.005710601806640625,
-0.0263671875,
0.0032978057861328125,
0.00787353515625,
0.006053924560546875,
-0.0059051513671875,
-0.00954437255859375,
0.019317626953125,
0.048553466796875,
-0.037872314453125,
0.00835418701171875,
0.0257110595703125,
0.032135009765625,
-0.031219482421875,
0.021392822265625,
0.01332855224609375,
-0.00966644287109375,
0.007625579833984375,
0.021331787109375,
0.01702880859375,
-0.0020771026611328125,
-0.0056915283203125,
-0.02349853515625,
-0.0057220458984375,
-0.00262451171875,
-0.00672149658203125,
0.04681396484375,
0.0120697021484375,
-0.024139404296875,
0.0096588134765625,
0.0097503662109375,
-0.0067138671875,
0.0232696533203125,
-0.0034236907958984375,
-0.01186370849609375,
-0.006725311279296875,
-0.01560211181640625,
0.0301055908203125,
-0.05242919921875,
0.0312347412109375,
-0.005496978759765625,
-0.0323486328125,
-0.045501708984375,
-0.0171661376953125,
-0.016204833984375,
0.0006766319274902344,
0.0066070556640625,
-0.050323486328125,
0.015655517578125,
0.004230499267578125,
-0.0161895751953125,
0.0121002197265625,
0.007114410400390625,
-0.01273345947265625,
0.01812744140625,
0.01727294921875,
0.0008325576782226562,
-0.007904052734375,
0.0012521743774414062,
-0.01282501220703125,
-0.047393798828125,
0.00931549072265625,
0.01268768310546875,
0.0027523040771484375,
-0.0139007568359375,
-0.01425933837890625,
-0.01525115966796875,
-0.002948760986328125,
-0.045074462890625,
0.023590087890625,
-0.0296783447265625,
0.00884246826171875,
0.0161895751953125,
-0.0203704833984375,
0.01035308837890625,
-0.0217437744140625,
0.00315093994140625,
-0.01361083984375,
-0.0186767578125,
-0.0023059844970703125,
-0.015106201171875,
0.0185699462890625,
-0.033416748046875,
0.01143646240234375,
-0.040191650390625,
0.013702392578125,
0.02325439453125,
0.00025725364685058594,
-0.01313018798828125,
0.0129241943359375,
0.0294189453125,
0.029296875,
0.011993408203125,
0.039398193359375,
-0.01287078857421875,
0.0268096923828125,
0.008758544921875,
-0.004764556884765625,
0.02960205078125,
-0.0002579689025878906,
0.0166015625,
0.0167999267578125,
-0.005786895751953125,
-0.0113677978515625,
-0.01444244384765625,
-0.004070281982421875,
-0.0252685546875,
-0.03759765625,
-0.0106201171875,
0.0108795166015625,
-0.004108428955078125,
-0.02178955078125,
0.01861572265625,
0.0222625732421875,
-0.01096343994140625,
-0.0233917236328125,
-0.0221099853515625,
-0.0016469955444335938,
0.042449951171875,
-0.0183258056640625,
0.021728515625,
-0.00820159912109375,
0.011566162109375,
-0.00882720947265625,
0.0023403167724609375,
0.03240966796875,
-0.01528167724609375,
0.0113677978515625,
0.0272674560546875,
0.01088714599609375,
-0.008941650390625,
0.03350830078125,
-0.01261138916015625,
0.0193023681640625,
-0.0012426376342773438,
-0.0014314651489257812,
-0.003429412841796875,
0.034088134765625,
0.0114593505859375,
0.016143798828125,
-0.03912353515625,
0.0057525634765625,
0.0082855224609375,
0.0123138427734375,
-0.035675048828125,
-0.0178375244140625,
-0.006877899169921875,
0.0030651092529296875,
0.01812744140625,
0.0382080078125,
0.02227783203125,
-0.0145416259765625,
-0.034149169921875,
-0.01419830322265625,
-0.037689208984375,
0.0271453857421875,
0.00362396240234375,
0.031707763671875,
0.004058837890625,
0.0321044921875,
-0.03277587890625,
-0.006134033203125,
-0.0310211181640625,
0.0167236328125,
0.00492095947265625,
-0.0246124267578125,
0.0021610260009765625,
0.0080108642578125,
0.0251617431640625,
-0.0103912353515625,
0.01247406005859375,
0.01483917236328125,
-0.0025501251220703125,
0.002086639404296875,
-0.01666259765625,
0.01329803466796875,
-0.01148223876953125,
0.035400390625,
0.005611419677734375,
0.0169677734375,
0.000020265579223632812,
0.02294921875,
-0.0018787384033203125,
-0.017822265625,
0.01050567626953125,
-0.0257568359375,
0.0100860595703125,
0.02447509765625,
0.013427734375,
0.0228271484375,
-0.0249481201171875,
0.0086822509765625,
-0.02276611328125,
0.0191650390625,
0.0043792724609375,
0.013092041015625,
-0.00547027587890625,
0.02349853515625,
-0.0035858154296875,
0.01715087890625,
-0.008026123046875,
0.0258941650390625,
0.0164947509765625,
-0.009613037109375,
-0.01265716552734375,
0.043121337890625,
-0.0110626220703125,
0.0228729248046875,
-0.0325927734375,
-0.008575439453125,
0.01061248779296875,
0.01151275634765625,
0.007476806640625,
-0.01142120361328125,
-0.0158233642578125,
-0.002002716064453125,
0.0513916015625,
0.00913238525390625,
0.0020999908447265625,
-0.007488250732421875,
-0.0295562744140625,
0.0296173095703125,
0.0135040283203125,
-0.012298583984375,
-0.0280914306640625,
0.006195068359375,
0.0240478515625,
-0.00797271728515625,
-0.024383544921875,
-0.01171112060546875,
0.0204620361328125,
0.01161956787109375,
0.006534576416015625,
-0.0022487640380859375,
-0.00635528564453125,
-0.0023326873779296875,
-0.0260009765625,
0.01739501953125,
0.0298309326171875,
0.053497314453125,
0.0052642822265625,
0.009521484375,
0.02191162109375,
0.0004253387451171875,
-0.0210723876953125,
0.00931549072265625,
0.019622802734375,
0.01338958740234375,
-0.0187530517578125,
0.003662109375,
-0.02154541015625,
-0.0198516845703125,
-0.005222320556640625,
0.051513671875,
0.023834228515625,
-0.005588531494140625,
0.019927978515625,
0.016387939453125,
-0.0115814208984375,
-0.034088134765625,
-0.0196075439453125,
0.004180908203125,
-0.006870269775390625,
-0.0035724639892578125,
0.001819610595703125,
-0.007110595703125,
0.0176544189453125,
-0.00055694580078125,
-0.0168914794921875,
0.00017690658569335938,
0.01160430908203125,
0.01385498046875,
0.032257080078125,
-0.019500732421875,
0.0207366943359375,
0.00923919677734375,
-0.01038360595703125,
0.0155487060546875,
-0.007568359375,
-0.030731201171875,
0.018768310546875,
0.0012035369873046875,
-0.00431060791015625,
0.0220794677734375,
0.005657196044921875,
0.004070281982421875,
-0.006008148193359375,
0.0379638671875,
0.012542724609375,
-0.0089111328125,
-0.00420379638671875,
-0.0056610107421875,
0.03314208984375,
-0.0030040740966796875,
0.0230255126953125,
0.022552490234375,
-0.011077880859375,
0.0408935546875,
-0.007213592529296875,
-0.017364501953125,
-0.01393890380859375,
-0.018524169921875,
-0.0018558502197265625,
0.00579833984375,
-0.0283050537109375,
0.01419830322265625,
0.0007061958312988281,
0.00867462158203125,
0.01995849609375,
0.0201873779296875,
-0.00445556640625,
0.005199432373046875,
-0.0308685302734375,
-0.015899658203125,
-0.01544952392578125,
0.0075225830078125,
0.038909912109375,
-0.015472412109375,
0.0099029541015625,
-0.0218963623046875,
-0.0179595947265625,
-0.0042572021484375,
0.0019330978393554688,
-0.02276611328125,
-0.0042724609375,
0.03204345703125,
-0.00870513916015625,
0.00566864013671875,
0.023468017578125,
-0.00287628173828125,
-0.0244598388671875,
-0.0001571178436279297,
-0.000293731689453125,
0.01013946533203125,
0.021820068359375,
-0.004657745361328125,
-0.0201873779296875,
0.0014400482177734375,
-0.005466461181640625,
0.014007568359375,
-0.017486572265625,
-0.0010824203491210938,
-0.00042748451232910156,
0.01126861572265625,
0.01544189453125,
0.0102081298828125,
-0.005084991455078125,
-0.04461669921875,
0.0099334716796875,
-0.011688232421875,
0.0154876708984375,
-0.00836944580078125,
-0.0146942138671875,
0.0118408203125,
0.01751708984375,
-0.007686614990234375,
-0.02197265625,
-0.0016536712646484375,
-0.00838470458984375,
-0.01776123046875,
0.0012569427490234375,
-0.0232696533203125,
0.006481170654296875,
-0.0132598876953125,
0.0249481201171875,
-0.003448486328125,
-0.03399658203125,
-0.0224151611328125,
-0.0008296966552734375,
-0.01027679443359375,
-0.0268402099609375,
0.00960540771484375,
0.041259765625,
0.006145477294921875,
-0.050323486328125,
0.0167083740234375,
-0.0092926025390625,
0.0245819091796875,
-0.0111236572265625,
0.0085601806640625,
-0.00823211669921875,
0.0164947509765625,
-0.00875091552734375,
-0.0079803466796875,
0.0169219970703125,
0.0189056396484375,
0.003536224365234375,
-0.006946563720703125,
-0.00926971435546875,
-0.01910400390625,
-0.053375244140625,
0.0037631988525390625,
-0.005649566650390625,
0.00986480712890625,
0.0184783935546875,
-0.0181884765625,
0.0163421630859375,
0.0294036865234375,
0.01296234130859375,
0.01067352294921875,
0.0030384063720703125,
0.021820068359375,
0.0011844635009765625,
0.0093841552734375,
0.015228271484375,
-0.01374053955078125,
-0.006137847900390625,
0.01238250732421875,
0.01313018798828125,
-0.0005326271057128906,
-0.0129241943359375,
0.000324249267578125,
-0.0212554931640625,
-0.01012420654296875,
-0.003047943115234375,
0.021392822265625,
-0.0284576416015625,
0.0112457275390625,
-0.03936767578125,
-0.039215087890625,
0.02178955078125,
-0.0105743408203125,
-0.0169525146484375,
0.00189208984375,
0.0162506103515625,
0.00827789306640625,
0.025787353515625,
0.0240478515625,
-0.00908660888671875,
0.0225982666015625,
-0.028045654296875,
0.0321044921875,
0.0273284912109375,
-0.023895263671875,
-0.0230712890625,
-0.005542755126953125,
0.001617431640625,
0.01012420654296875,
-0.00302886962890625,
-0.0019350051879882812,
0.00550079345703125,
-0.01316070556640625,
-0.01702880859375,
-0.06329345703125,
-0.00910186767578125,
-0.019317626953125,
0.01241302490234375,
-0.0272369384765625,
-0.0379638671875,
-0.004138946533203125,
-0.007389068603515625,
-0.015960693359375,
-0.0182647705078125,
-0.00783538818359375,
0.020416259765625,
-0.009033203125,
0.00913238525390625,
-0.0258941650390625,
-0.00255584716796875,
0.004177093505859375,
-0.00023853778839111328,
-0.0024471282958984375,
0.006439208984375,
0.0038585662841796875,
-0.0185394287109375,
0.01027679443359375,
0.029022216796875,
-0.0264892578125,
0.0008087158203125,
-0.0362548828125,
-0.01019287109375,
-0.00738525390625,
-0.02667236328125,
-0.018341064453125,
0.0188751220703125,
0.019378662109375,
0.0271148681640625,
-0.0131988525390625,
-0.01439666748046875,
-0.02752685546875,
-0.0259552001953125,
0.0103302001953125,
-0.0075531005859375,
-0.0194244384765625,
0.024566650390625,
0.027191162109375,
0.0236053466796875,
-0.006839752197265625,
-0.00968170166015625,
0.04327392578125,
-0.0218505859375,
-0.0269622802734375,
-0.020843505859375,
0.0006818771362304688,
-0.0267181396484375,
0.0289306640625,
0.03424072265625,
0.0011072158813476562,
0.0166168212890625,
0.020599365234375,
-0.00873565673828125,
0.01351165771484375,
0.00897216796875,
-0.0028743743896484375,
0.0011339187622070312,
-0.042449951171875,
-0.017242431640625,
-0.031524658203125,
0.020965576171875,
-0.00188446044921875,
0.004489898681640625,
0.0006103515625,
0.0186309814453125,
-0.016265869140625,
0.0217132568359375,
0.0289764404296875,
-0.034759521484375,
-0.0138397216796875,
0.0200042724609375,
-0.01100921630859375,
-0.0192413330078125,
-0.009124755859375,
-0.0144805908203125,
-0.0036182403564453125,
-0.00653839111328125,
-0.00525665283203125,
-0.0245819091796875,
0.004116058349609375,
0.007427215576171875,
0.00261688232421875,
0.0163116455078125,
-0.0133056640625,
0.004451751708984375,
0.0255126953125,
0.007587432861328125,
0.0222930908203125,
-0.006999969482421875,
-0.0160980224609375,
0.007694244384765625,
-0.01558685302734375,
-0.015655517578125,
-0.02044677734375,
0.0312042236328125,
0.01549530029296875,
-0.017547607421875,
0.006801605224609375,
0.01302337646484375,
0.013336181640625,
0.0239715576171875,
0.022186279296875,
-0.0048675537109375,
-0.031158447265625,
0.00954437255859375,
-0.007633209228515625,
0.0216827392578125,
-0.01995849609375,
0.00038504600524902344,
0.004180908203125,
0.03448486328125,
-0.037567138671875,
0.0131072998046875,
0.00960540771484375,
-0.0256805419921875,
-0.01849365234375,
0.0188446044921875,
-0.0036830902099609375,
-0.007015228271484375,
0.0019779205322265625,
-0.0022525787353515625,
-0.03021240234375,
0.0292816162109375,
-0.00412750244140625,
0.0330810546875,
-0.01434326171875,
-0.0008678436279296875,
-0.0276336669921875,
-0.00041174888610839844,
0.0269775390625,
-0.01473236083984375,
0.0213470458984375,
-0.009552001953125,
0.011444091796875,
0.006305694580078125,
0.0199127197265625,
-0.0059661865234375,
0.0167388916015625,
0.0138702392578125,
-0.01428985595703125,
0.006938934326171875,
-0.0003726482391357422,
-0.00888824462890625,
-0.0283355712890625,
0.021942138671875,
0.00335693359375,
0.0008144378662109375,
0.00948333740234375,
-0.02398681640625,
-0.0360107421875,
-0.0008382797241210938,
0.0229034423828125,
-0.011199951171875,
0.016082763671875,
0.0123443603515625,
0.0032958984375,
0.0196685791015625,
-0.004451751708984375,
-0.032257080078125,
0.00039887428283691406,
-0.0184783935546875,
0.033172607421875,
0.0255279541015625,
-0.01070404052734375,
0.00901031494140625,
0.017578125,
0.01080322265625,
0.004245758056640625,
-0.0233306884765625,
-0.038970947265625,
0.0217437744140625,
0.027557373046875,
0.031219482421875,
0.0142974853515625,
-0.0428466796875,
0.041473388671875,
-0.0259246826171875,
-0.007160186767578125,
0.0021343231201171875,
0.003223419189453125,
0.02752685546875,
0.032440185546875,
-0.0295562744140625,
0.00675201416015625,
0.04620361328125,
-0.0206146240234375,
0.002788543701171875,
0.00417327880859375,
-0.00022685527801513672,
-0.00685882568359375,
-0.0163726806640625,
-0.005573272705078125,
-0.0287322998046875,
0.002201080322265625,
-0.0209503173828125,
0.01076507568359375,
0.01161956787109375,
0.041778564453125,
-0.00605010986328125,
-0.0301666259765625,
0.0071868896484375,
0.016632080078125,
-0.0029239654541015625,
0.011810302734375,
0.01502227783203125,
0.0229034423828125,
-0.0157012939453125,
-0.0169677734375,
0.0223541259765625,
0.044097900390625,
0.005123138427734375,
-0.01285552978515625,
-0.0201873779296875,
-0.01348876953125,
-0.0156097412109375,
0.0205230712890625,
-0.01473236083984375,
0.018829345703125,
-0.00858306884765625,
0.031494140625,
-0.00955963134765625,
0.002166748046875,
0.02630615234375,
-0.00782012939453125,
-0.0063323974609375,
-0.00439453125,
0.01509857177734375,
0.007305145263671875,
0.0164642333984375,
-0.005809783935546875,
-0.0137939453125,
0.0256805419921875,
-0.02001953125,
0.0006151199340820312,
0.0275115966796875,
0.014617919921875,
0.01666259765625,
-0.005176544189453125,
0.0085296630859375,
0.031463623046875,
0.004657745361328125,
-0.00432586669921875,
-0.0160064697265625,
-0.004550933837890625,
0.00885772705078125,
0.021026611328125,
-0.0279541015625,
-0.005771636962890625,
-0.005771636962890625,
-0.00304412841796875,
0.0158538818359375,
-0.00823211669921875,
-0.0007476806640625,
0.0140228271484375,
0.0254669189453125,
-0.061737060546875,
-0.0037822723388671875,
0.00331878662109375,
0.03839111328125,
-0.020904541015625,
-0.00815582275390625,
-0.01062774658203125,
0.01227569580078125,
0.005069732666015625,
-0.028564453125,
0.01081085205078125,
0.01090240478515625,
-0.0056915283203125,
0.01079559326171875,
0.0050811767578125,
0.0215911865234375,
-0.0040740966796875,
0.01519775390625,
-0.00960540771484375,
0.0024394989013671875,
-0.00238800048828125,
0.00664520263671875,
-0.00624847412109375,
0.0509033203125,
-0.0177459716796875,
-0.0013628005981445312,
0.01470947265625,
-0.00621795654296875,
-0.050750732421875,
0.004108428955078125,
-0.00811767578125,
0.00839996337890625,
-0.0400390625,
-0.01580810546875,
0.007495880126953125,
0.00266265869140625,
0.0357666015625,
-0.0494384765625,
-0.005519866943359375,
0.0186614990234375,
0.0027866363525390625,
-0.017608642578125,
0.0010900497436523438,
0.0056304931640625,
0.00922393798828125,
-0.01100921630859375,
0.0008249282836914062,
-0.007205963134765625,
0.01971435546875,
-0.01171875,
0.00901031494140625,
-0.0258941650390625,
0.01373291015625,
-0.00974273681640625,
0.00926971435546875,
-0.01552581787109375,
-0.0136566162109375,
-0.036224365234375,
0.021209716796875,
-0.0259552001953125,
-0.0265350341796875,
-0.0016374588012695312,
-0.0228271484375,
0.0034885406494140625,
-0.00112152099609375,
0.007129669189453125,
0.01509857177734375,
0.017791748046875,
0.00576019287109375,
-0.0161895751953125,
0.01357269287109375,
0.0007677078247070312,
0.0148468017578125,
0.006214141845703125,
0.0130767822265625,
0.0167999267578125,
-0.0007295608520507812,
0.03411865234375,
-0.0006976127624511719,
-0.0191650390625,
0.005229949951171875,
0.00820159912109375,
0.0015535354614257812,
-0.008636474609375,
0.0017709732055664062,
-0.0237579345703125,
-0.01010894775390625,
0.0112762451171875,
0.0180816650390625,
-0.009429931640625,
-0.005645751953125,
-0.0090484619140625,
0.0146331787109375,
-0.004970550537109375,
0.012115478515625,
0.0240325927734375,
-0.01296234130859375,
0.006305694580078125,
0.0079498291015625,
0.01232147216796875,
0.01824951171875,
-0.05157470703125,
0.01325225830078125,
0.0265350341796875,
-0.0265960693359375,
-0.0173797607421875,
0.0300140380859375,
-0.0325927734375,
0.0099029541015625,
-0.02691650390625,
0.0180206298828125,
0.0250701904296875,
0.022369384765625,
-0.004680633544921875,
-0.0024089813232421875,
0.0112762451171875,
0.027587890625,
-0.020782470703125,
-0.023468017578125,
-0.02423095703125,
0.0086517333984375,
0.03460693359375,
0.029815673828125,
0.005290985107421875,
0.00991058349609375,
-0.0156402587890625,
-0.022552490234375,
0.01448822021484375,
-0.006908416748046875,
0.03558349609375,
-0.0162811279296875,
-0.0291748046875,
0.0025997161865234375,
0.0110931396484375,
-0.032012939453125,
0.0012407302856445312,
0.0061187744140625,
0.004276275634765625,
0.01068878173828125,
0.038238525390625,
0.033050537109375,
-0.0261993408203125,
-0.00786590576171875,
-0.0124969482421875,
0.0066070556640625,
0.0231781005859375,
-0.023284912109375,
0.019500732421875,
0.04620361328125,
-0.00524139404296875,
0.003040313720703125,
-0.006561279296875,
-0.003948211669921875,
-0.0024471282958984375,
-0.01424407958984375,
-0.002590179443359375,
0.009735107421875,
-0.03155517578125,
0.006305694580078125,
0.010772705078125,
-0.00431060791015625,
-0.0236358642578125,
-0.0268707275390625,
0.01861572265625,
-0.038238525390625,
0.01255035400390625,
0.004352569580078125,
-0.028594970703125,
-0.00496673583984375,
0.0009489059448242188,
-0.0033283233642578125,
0.01233673095703125,
0.004436492919921875,
-0.005367279052734375,
0.0391845703125,
0.0078887939453125,
0.0225830078125,
0.003021240234375,
0.0088348388671875,
0.0275421142578125,
0.0224456787109375,
0.01399993896484375,
-0.0030536651611328125,
-0.00018668174743652344,
-0.0091552734375,
0.00138092041015625,
0.0251922607421875,
-0.005584716796875,
-0.0291290283203125,
0.005977630615234375,
-0.01519775390625,
-0.0025653839111328125,
-0.045166015625,
-0.005153656005859375,
-0.0167694091796875,
0.0167388916015625,
-0.0013837814331054688,
-0.027587890625,
-0.00811004638671875,
-0.046966552734375,
0.01123809814453125,
0.0032672882080078125,
0.0003070831298828125,
0.034698486328125,
0.0121917724609375,
-0.00920867919921875,
-0.0186309814453125,
0.0104522705078125,
-0.0278472900390625,
-0.031646728515625,
-0.01666259765625,
0.00925445556640625,
-0.0140838623046875,
-0.00670623779296875,
0.0203857421875,
0.00551605224609375,
-0.004863739013671875,
-0.01003265380859375,
0.0252532958984375,
-0.00978851318359375,
-0.0248870849609375,
-0.0197906494140625,
0.00669097900390625,
0.041656494140625,
-0.019622802734375,
0.00003123283386230469,
-0.01812744140625,
0.03179931640625,
-0.0030269622802734375,
-0.00484466552734375,
-0.0095062255859375,
-0.0018129348754882812,
0.0026912689208984375,
0.01140594482421875,
-0.0256500244140625,
-0.0234375,
0.02197265625,
0.0032558441162109375,
-0.0372314453125,
-0.0206756591796875,
0.002269744873046875,
-0.00945281982421875,
-0.00677490234375,
-0.02056884765625,
-0.01207733154296875,
0.013397216796875,
0.0113067626953125,
0.03387451171875,
0.0222015380859375,
-0.01885986328125,
0.004940032958984375,
0.00691986083984375,
0.03289794921875,
-0.033355712890625,
0.035675048828125,
0.001117706298828125,
-0.0152740478515625,
-0.0253143310546875,
0.0009765625,
-0.030242919921875,
-0.0098724365234375,
0.021026611328125,
0.0287933349609375,
-0.0214996337890625,
0.0001302957534790039,
0.013824462890625,
-0.04071044921875,
-0.019500732421875,
0.01318359375,
0.0350341796875,
-0.029205322265625,
0.0029277801513671875,
-0.0166015625,
-0.0283660888671875,
-0.0024166107177734375,
-0.0158538818359375,
0.01143646240234375,
0.003856658935546875,
0.01141357421875,
0.006099700927734375,
0.05194091796875,
-0.00455474853515625,
0.0035419464111328125,
-0.007541656494140625,
-0.0679931640625,
0.0380859375,
-0.00604248046875,
0.003017425537109375,
0.01439666748046875,
0.0018558502197265625,
0.0113525390625,
0.036895751953125,
-0.0037059783935546875,
-0.004718780517578125,
0.00023472309112548828,
0.0065460205078125,
0.0033054351806640625,
-0.0028839111328125,
0.0230255126953125,
0.0019197463989257812,
0.0005822181701660156,
-0.0282135009765625,
0.0049591064453125,
0.00982666015625,
-0.006237030029296875,
0.01461029052734375,
-0.030609130859375,
-0.01137542724609375,
-0.0219573974609375,
-0.0021228790283203125,
-0.0218963623046875,
0.0146636962890625,
0.004566192626953125,
0.031585693359375,
-0.0021877288818359375,
0.03717041015625,
0.025848388671875,
-0.0003948211669921875,
-0.0047454833984375,
-0.019622802734375,
0.023406982421875,
0.002239227294921875,
0.0684814453125,
0.02618408203125,
-0.01180267333984375,
-0.0197601318359375,
-0.006072998046875,
0.0268402099609375,
-0.02203369140625,
-0.0037555694580078125,
0.033233642578125,
0.0249786376953125,
0.0032176971435546875,
-0.01531982421875,
-0.017242431640625,
-0.00872039794921875,
0.0159759521484375,
-0.01904296875,
0.0137939453125,
-0.035003662109375,
0.01549530029296875,
0.0099639892578125,
-0.0010824203491210938,
0.0188140869140625,
0.00005060434341430664,
0.0308837890625,
0.020416259765625,
-0.034515380859375,
-0.03875732421875,
0.02215576171875,
-0.0088043212890625,
0.012969970703125,
0.02777099609375,
-0.01062774658203125,
-0.0009636878967285156,
-0.01103973388671875,
-0.054473876953125,
0.036773681640625,
-0.0016765594482421875,
0.00565338134765625,
0.0025615692138671875,
-0.033203125,
0.01080322265625,
0.0175628662109375,
-0.03076171875,
0.04241943359375,
-0.047210693359375,
-0.0003638267517089844,
0.0289459228515625,
0.0059051513671875,
-0.0347900390625,
-0.0193328857421875,
-0.003124237060546875,
-0.0142822265625,
-0.01367950439453125,
-0.0286712646484375,
0.017486572265625,
-0.023040771484375,
0.00804901123046875,
0.0026397705078125,
0.0168609619140625,
-0.00910186767578125,
-0.005764007568359375,
0.0076751708984375,
0.018341064453125,
0.0164337158203125,
-0.0213165283203125,
-0.023162841796875,
0.03424072265625,
-0.0226287841796875,
0.00010454654693603516,
0.000652313232421875,
-0.0177001953125,
0.0014295578002929688,
0.0012273788452148438,
0.01027679443359375,
0.021881103515625,
0.055694580078125,
-0.028167724609375,
0.0020599365234375,
0.00730133056640625,
-0.0196990966796875,
-0.0029354095458984375,
0.0025920867919921875,
-0.0248260498046875,
0.0226898193359375,
-0.003261566162109375,
0.00273895263671875,
0.02618408203125,
0.0162200927734375,
-0.0152587890625,
-0.01499176025390625,
-0.002086639404296875,
0.01666259765625,
0.01496124267578125,
0.050048828125,
0.0305938720703125,
-0.0031108856201171875,
-0.0007672309875488281,
0.0310821533203125,
0.00807952880859375,
-0.0035190582275390625,
0.0218963623046875,
-0.0167083740234375,
-0.0264129638671875,
-0.0031528472900390625,
-0.0298614501953125,
-0.01139068603515625,
0.0175018310546875,
0.01277923583984375,
0.003665924072265625,
0.01335906982421875,
-0.0191650390625,
-0.0073699951171875,
-0.0092926025390625,
0.0158233642578125,
-0.0129241943359375,
-0.020751953125,
-0.005146026611328125,
0.02288818359375,
0.0124969482421875,
-0.03802490234375,
-0.0292205810546875,
-0.024200439453125,
0.0013828277587890625,
-0.002071380615234375,
-0.00933837890625,
0.036407470703125,
-0.023681640625,
-0.01351165771484375,
-0.0114898681640625,
0.03851318359375,
-0.01372528076171875,
0.0004875659942626953,
-0.019012451171875,
-0.044525146484375,
0.00745391845703125,
-0.0107574462890625,
0.006465911865234375,
-0.0193023681640625,
0.00904083251953125,
0.006015777587890625,
-0.0088653564453125,
-0.00455474853515625,
-0.0106048583984375,
-0.02777099609375,
-0.035491943359375,
0.0228729248046875,
0.005878448486328125,
-0.008880615234375,
0.007503509521484375,
0.01044464111328125,
-0.035491943359375,
-0.0229339599609375,
0.0018968582153320312,
0.0122222900390625,
-0.02459716796875,
0.00731658935546875,
0.00029587745666503906,
0.0028018951416015625,
-0.022186279296875,
-0.02301025390625,
0.026824951171875,
0.00676727294921875,
-0.01904296875,
0.0002644062042236328,
0.0181732177734375,
0.01277923583984375,
0.00853729248046875,
0.00730133056640625,
0.006595611572265625,
0.0176849365234375,
-0.0035858154296875,
-0.0008749961853027344,
0.01306915283203125,
-0.032562255859375,
-0.005237579345703125,
-0.0203857421875,
-0.03729248046875,
0.0009474754333496094,
0.025146484375,
0.005222320556640625,
-0.0014371871948242188,
0.0018758773803710938,
-0.007518768310546875,
0.01529693603515625,
0.02215576171875,
-0.0018720626831054688,
-0.0131988525390625,
0.0007824897766113281,
0.02679443359375,
0.01511383056640625
] |
ours_531
|
Let the numbers be \(x\) and \(y\) and assume without loss of generality \(x > y\). Then we have \(\frac{x+y}{2} = x-y\). It follows that \(x+y = 2x - 2y\), so \(x = 3y\). Therefore, the ratio of the larger number to the smaller one is \(\boxed{3}\).
|
3
|
{
"competition": "us_comps",
"dataset": "Ours",
"posts": null,
"source": "OMOSoln2.md"
}
|
The average of two positive real numbers is equal to their difference. What is the ratio of the larger number to the smaller one?
|
[
"/Mathematics/Algebra/AlgebraicEquations/AlgebraicEquation",
"/Mathematics/Algebra/AlgebraicEquations/LinearEquation",
"/Mathematics/Algebra/AlgebraicIdentities/AlgebraicIdentity",
"/Mathematics/Algebra/AlgebraicOperations/GeneralAlgebraicOperations",
"/Mathematics/Algebra/GeneralAlgebra/AffineEquation",
"/Mathematics/Algebra/GeneralAlgebra/Algebra",
"/Mathematics/Algebra/RateProblems"
] |
Set the equality (x+y)/2 = x‑y and solve the resulting linear equation for the ratio.
|
[
-0.000354766845703125,
0.005039215087890625,
0.036285400390625,
0.005016326904296875,
-0.0017452239990234375,
0.031982421875,
0.020721435546875,
0.037078857421875,
0.0093231201171875,
-0.00995635986328125,
-0.0196380615234375,
-0.0233306884765625,
0.0029468536376953125,
-0.01947021484375,
-0.0039520263671875,
0.03570556640625,
-0.0020465850830078125,
0.0274200439453125,
0.044586181640625,
-0.0060577392578125,
-0.007511138916015625,
0.008087158203125,
-0.05230712890625,
-0.001026153564453125,
-0.035308837890625,
-0.022247314453125,
-0.0195465087890625,
-0.0256195068359375,
0.00461578369140625,
0.036590576171875,
-0.00799560546875,
-0.006717681884765625,
0.034637451171875,
-0.013641357421875,
0.0031585693359375,
0.0129852294921875,
0.0018777847290039062,
-0.002536773681640625,
0.004749298095703125,
-0.0233612060546875,
0.006259918212890625,
-0.017578125,
0.0121307373046875,
0.01332855224609375,
-0.002239227294921875,
0.0087432861328125,
0.0092620849609375,
-0.0018167495727539062,
-0.00772857666015625,
-0.01479339599609375,
0.00725555419921875,
0.00484466552734375,
0.00005251169204711914,
-0.010528564453125,
-0.00916290283203125,
-0.02850341796875,
0.030517578125,
0.0033111572265625,
-0.0246734619140625,
-0.0153045654296875,
-0.00464630126953125,
0.007476806640625,
0.0007047653198242188,
-0.0223236083984375,
-0.004947662353515625,
-0.01119232177734375,
0.0092620849609375,
-0.03851318359375,
0.0018663406372070312,
0.0212554931640625,
0.01233673095703125,
0.0107269287109375,
-0.01010894775390625,
0.0032482147216796875,
-0.0178375244140625,
-0.006500244140625,
-0.009857177734375,
0.0171051025390625,
0.0214080810546875,
0.0063323974609375,
0.005214691162109375,
0.018707275390625,
0.01103973388671875,
0.0178070068359375,
0.021484375,
-0.005817413330078125,
0.0006060600280761719,
0.005458831787109375,
0.027099609375,
-0.0187225341796875,
0.01015472412109375,
0.051116943359375,
-0.02728271484375,
0.025238037109375,
-0.00537872314453125,
-0.002475738525390625,
-0.0128936767578125,
-0.004787445068359375,
-0.0196075439453125,
0.0188140869140625,
-0.01491546630859375,
-0.0272979736328125,
-0.0080108642578125,
-0.0124359130859375,
0.0034427642822265625,
-0.011810302734375,
-0.00928497314453125,
-0.00672149658203125,
-0.0020771026611328125,
-0.00997161865234375,
0.0149078369140625,
0.01055908203125,
0.0634765625,
0.03302001953125,
-0.000385284423828125,
0.0081634521484375,
0.018890380859375,
0.020172119140625,
0.00830078125,
0.00653076171875,
0.00493621826171875,
0.0117340087890625,
-0.02801513671875,
-0.01168060302734375,
0.01068115234375,
0.011566162109375,
-0.011138916015625,
-0.01910400390625,
-0.0069427490234375,
0.00884246826171875,
-0.00339508056640625,
-0.0113983154296875,
-0.022125244140625,
-0.0142059326171875,
-0.032073974609375,
0.01065826416015625,
0.005153656005859375,
-0.000392913818359375,
-0.00864410400390625,
0.0018568038940429688,
0.000736236572265625,
0.0005464553833007812,
0.006534576416015625,
-0.044464111328125,
-0.00418853759765625,
0.0018978118896484375,
0.01076507568359375,
0.01268768310546875,
0.016876220703125,
0.00019860267639160156,
0.00016963481903076172,
-0.008575439453125,
-0.002490997314453125,
0.024627685546875,
0.00007009506225585938,
0.0164031982421875,
0.0023937225341796875,
0.0170440673828125,
-0.00444793701171875,
0.00951385498046875,
0.01416015625,
0.004291534423828125,
-0.007659912109375,
0.0275115966796875,
-0.00653076171875,
-0.01059722900390625,
0.003070831298828125,
0.020294189453125,
-0.024505615234375,
0.009979248046875,
-0.00305938720703125,
0.004329681396484375,
-0.012847900390625,
-0.01245880126953125,
-0.01019287109375,
0.005832672119140625,
-0.0308685302734375,
-0.01953125,
-0.01788330078125,
-0.019775390625,
-0.0014705657958984375,
-0.013580322265625,
0.037445068359375,
0.00360107421875,
0.018798828125,
-0.0121307373046875,
0.005435943603515625,
-0.006748199462890625,
0.01377105712890625,
0.017730712890625,
0.0132904052734375,
-0.0228118896484375,
-0.0205841064453125,
-0.006931304931640625,
-0.01242828369140625,
-0.0165252685546875,
-0.012969970703125,
-0.01593017578125,
0.0238494873046875,
0.021026611328125,
-0.0020656585693359375,
-0.016876220703125,
-0.0323486328125,
-0.0210418701171875,
0.005405426025390625,
0.0023021697998046875,
-0.0080718994140625,
-0.0093994140625,
-0.005878448486328125,
0.00328826904296875,
0.02056884765625,
0.01433563232421875,
0.00022864341735839844,
-0.035247802734375,
-0.0211334228515625,
0.0020294189453125,
-0.0169677734375,
-0.020751953125,
0.0157318115234375,
0.043609619140625,
0.002002716064453125,
0.00803375244140625,
0.0014791488647460938,
0.01442718505859375,
-0.024383544921875,
-0.00281524658203125,
0.00262451171875,
-0.0012540817260742188,
-0.00044465065002441406,
0.002838134765625,
0.025665283203125,
0.0090484619140625,
0.00960540771484375,
-0.017181396484375,
-0.0144195556640625,
0.022613525390625,
-0.049835205078125,
-0.0052032470703125,
0.0111083984375,
-0.0207061767578125,
-0.00516510009765625,
-0.0182342529296875,
0.0005159378051757812,
0.0215911865234375,
0.006488800048828125,
-0.011993408203125,
-0.003185272216796875,
-0.0226593017578125,
0.0002932548522949219,
-0.02764892578125,
-0.00420379638671875,
0.0059814453125,
0.006229400634765625,
-0.017608642578125,
0.004291534423828125,
0.00041031837463378906,
-0.005859375,
-0.020965576171875,
-0.0189971923828125,
0.0297088623046875,
0.0019855499267578125,
-0.029327392578125,
-0.0183258056640625,
-0.00838470458984375,
-0.0045013427734375,
0.03436279296875,
0.02288818359375,
-0.0164337158203125,
0.00943756103515625,
-0.00424957275390625,
0.0252227783203125,
-0.0089111328125,
-0.005443572998046875,
0.00843048095703125,
-0.00000947713851928711,
-0.00682830810546875,
0.004276275634765625,
0.003643035888671875,
0.00811004638671875,
0.0195465087890625,
0.01235198974609375,
-0.0134124755859375,
-0.0306854248046875,
0.0106964111328125,
-0.00725555419921875,
0.0260162353515625,
0.033416748046875,
0.0119781494140625,
-0.0119476318359375,
0.01702880859375,
-0.005435943603515625,
-0.03863525390625,
0.004367828369140625,
0.000016868114471435547,
0.0400390625,
0.0216064453125,
0.004123687744140625,
0.0099945068359375,
0.01611328125,
-0.01715087890625,
0.01030731201171875,
-0.0198516845703125,
-0.007843017578125,
-0.0234832763671875,
0.01206207275390625,
0.04693603515625,
0.0029144287109375,
0.01203155517578125,
-0.003055572509765625,
-0.0258636474609375,
-0.031982421875,
-0.0183868408203125,
-0.029052734375,
0.00055694580078125,
0.0038738250732421875,
-0.052825927734375,
-0.0014219284057617188,
-0.01091766357421875,
-0.0208740234375,
0.020965576171875,
0.00011873245239257812,
-0.033447265625,
0.01491546630859375,
0.00527191162109375,
0.04583740234375,
-0.0014858245849609375,
0.011627197265625,
0.0127410888671875,
-0.005779266357421875,
0.055389404296875,
-0.01690673828125,
0.0268707275390625,
-0.026031494140625,
-0.017486572265625,
0.01126861572265625,
0.0168304443359375,
-0.01369476318359375,
0.0189208984375,
0.007678985595703125,
0.0031566619873046875,
0.025970458984375,
-0.022735595703125,
0.01364898681640625,
-0.036773681640625,
-0.051727294921875,
-0.00418853759765625,
-0.026580810546875,
-0.0092926025390625,
0.004791259765625,
-0.006694793701171875,
0.03863525390625,
0.00861358642578125,
0.0103759765625,
-0.0129241943359375,
-0.025634765625,
0.0200958251953125,
0.003246307373046875,
-0.006427764892578125,
0.04339599609375,
0.004245758056640625,
-0.00421142578125,
-0.0208740234375,
-0.00870513916015625,
0.0038013458251953125,
-0.01096343994140625,
-0.040191650390625,
-0.00917816162109375,
0.01727294921875,
-0.028778076171875,
0.0163116455078125,
0.00033664703369140625,
-0.010009765625,
0.024383544921875,
0.004131317138671875,
0.0020046234130859375,
0.028411865234375,
0.0168304443359375,
0.0026073455810546875,
0.01206207275390625,
0.007465362548828125,
0.00746917724609375,
0.00501251220703125,
-0.0458984375,
-0.002918243408203125,
-0.0012950897216796875,
0.0125579833984375,
-0.0377197265625,
-0.00565338134765625,
-0.0179595947265625,
0.00789642333984375,
0.01142120361328125,
-0.0235595703125,
-0.0056304931640625,
0.0048980712890625,
-0.034576416015625,
-0.001171112060546875,
0.00925445556640625,
0.0025386810302734375,
0.053863525390625,
-0.0119781494140625,
-0.01070404052734375,
-0.0176239013671875,
-0.0379638671875,
0.0335693359375,
-0.0019168853759765625,
-0.0197906494140625,
-0.0152587890625,
0.01434326171875,
0.00022399425506591797,
0.00010269880294799805,
0.034149169921875,
0.02313232421875,
-0.01093292236328125,
-0.0136871337890625,
-0.0230560302734375,
0.00685882568359375,
0.0147552490234375,
-0.006565093994140625,
-0.03643798828125,
0.005901336669921875,
-0.00798797607421875,
0.005260467529296875,
-0.037109375,
0.0279998779296875,
0.0211639404296875,
0.0129547119140625,
-0.043304443359375,
0.036590576171875,
-0.020050048828125,
-0.01453399658203125,
0.0239410400390625,
0.0182037353515625,
-0.0012273788452148438,
0.032470703125,
0.0007424354553222656,
0.02203369140625,
-0.00408172607421875,
-0.0233917236328125,
-0.0026988983154296875,
-0.004199981689453125,
-0.04827880859375,
0.013519287109375,
0.0287933349609375,
0.007396697998046875,
0.0086212158203125,
0.0005474090576171875,
-0.003444671630859375,
0.0169677734375,
-0.024810791015625,
0.01617431640625,
-0.03631591796875,
0.02264404296875,
0.0202484130859375,
-0.02545166015625,
-0.0157012939453125,
0.0225982666015625,
0.025390625,
-0.03143310546875,
-0.0296783447265625,
-0.01055145263671875,
-0.01947021484375,
0.0210723876953125,
-0.0168304443359375,
0.024993896484375,
-0.01534271240234375,
0.00586700439453125,
-0.018798828125,
0.01177978515625,
0.004413604736328125,
-0.01776123046875,
0.0015964508056640625,
-0.01158905029296875,
0.0093231201171875,
-0.0140533447265625,
-0.01259613037109375,
0.03936767578125,
-0.004329681396484375,
0.0034198760986328125,
-0.014007568359375,
0.0087890625,
0.022491455078125,
-0.0016927719116210938,
0.01971435546875,
-0.023101806640625,
-0.00606536865234375,
0.0251312255859375,
0.01151275634765625,
0.01560211181640625,
-0.036834716796875,
0.01009368896484375,
0.0168914794921875,
-0.009429931640625,
-0.018951416015625,
-0.055145263671875,
-0.01482391357421875,
-0.01294708251953125,
0.00839996337890625,
-0.0303955078125,
0.0195465087890625,
-0.01457977294921875,
0.01428985595703125,
0.006130218505859375,
0.01392364501953125,
-0.02191162109375,
-0.01267242431640625,
-0.056396484375,
0.047393798828125,
-0.0206298828125,
0.01727294921875,
0.0007085800170898438,
0.024078369140625,
0.034088134765625,
0.025665283203125,
-0.0271759033203125,
0.0190277099609375,
0.00439453125,
-0.018951416015625,
-0.03448486328125,
-0.0045166015625,
0.0093841552734375,
-0.0280914306640625,
-0.0228271484375,
0.031951904296875,
-0.003665924072265625,
-0.004840850830078125,
-0.0078582763671875,
0.01580810546875,
0.00484466552734375,
-0.022705078125,
-0.0010251998901367188,
-0.0229339599609375,
-0.002315521240234375,
-0.01137542724609375,
0.03533935546875,
-0.01154327392578125,
0.01031494140625,
0.00479888916015625,
0.040252685546875,
0.0074920654296875,
0.0157470703125,
-0.017120361328125,
-0.025360107421875,
-0.01348876953125,
0.020233154296875,
0.01934814453125,
-0.0022792816162109375,
0.007762908935546875,
0.00969696044921875,
-0.01177215576171875,
0.025299072265625,
0.0191497802734375,
0.003765106201171875,
0.01160430908203125,
0.0102386474609375,
0.00469207763671875,
0.0283050537109375,
-0.0499267578125,
-0.0014200210571289062,
-0.0033626556396484375,
0.0167388916015625,
0.01538848876953125,
-0.0066375732421875,
0.01180267333984375,
-0.0245361328125,
0.0034503936767578125,
-0.0241851806640625,
0.006603240966796875,
0.0115814208984375,
-0.0021533966064453125,
-0.0200042724609375,
0.0168609619140625,
-0.0262451171875,
-0.01073455810546875,
0.021209716796875,
-0.023406982421875,
0.0050506591796875,
0.0005083084106445312,
0.00658416748046875,
0.01399993896484375,
-0.036895751953125,
0.02392578125,
0.031402587890625,
0.0125274658203125,
-0.03326416015625,
-0.02520751953125,
-0.0005002021789550781,
-0.024627685546875,
0.007537841796875,
0.0182037353515625,
-0.0034198760986328125,
-0.014923095703125,
0.0029087066650390625,
-0.00484466552734375,
-0.01528167724609375,
-0.0102081298828125,
-0.0343017578125,
-0.00872039794921875,
-0.0164947509765625,
-0.01226043701171875,
0.0004870891571044922,
0.023468017578125,
-0.0157623291015625,
-0.01654052734375,
0.0171051025390625,
-0.0175933837890625,
0.005184173583984375,
-0.02423095703125,
0.038665771484375,
-0.006786346435546875,
0.01390838623046875,
0.006107330322265625,
-0.01776123046875,
-0.0297698974609375,
0.0280914306640625,
0.003810882568359375,
0.0135345458984375,
-0.03326416015625,
0.0023517608642578125,
0.00666046142578125,
0.00179290771484375,
-0.03057861328125,
-0.021331787109375,
-0.00144195556640625,
-0.024169921875,
-0.016357421875,
-0.03118896484375,
0.00566864013671875,
-0.0145721435546875,
0.0009207725524902344,
-0.01251983642578125,
-0.01085662841796875,
-0.01904296875,
0.034332275390625,
-0.01165771484375,
0.0023632049560546875,
-0.0159912109375,
-0.035614013671875,
0.04736328125,
-0.006130218505859375,
-0.0198974609375,
0.01763916015625,
-0.00173187255859375,
0.02142333984375,
-0.054779052734375,
-0.01024627685546875,
0.0022029876708984375,
-0.039306640625,
-0.003231048583984375,
-0.058380126953125,
0.023834228515625,
0.0024013519287109375,
0.02471923828125,
0.01308441162109375,
0.0094146728515625,
0.01397705078125,
0.01373291015625,
0.005268096923828125,
0.0011358261108398438,
0.034942626953125,
0.01027679443359375,
-0.007122039794921875,
-0.0026702880859375,
0.023223876953125,
-0.0013332366943359375,
-0.03521728515625,
0.02264404296875,
-0.0115814208984375,
0.0104217529296875,
0.04510498046875,
0.00684356689453125,
-0.0382080078125,
0.019622802734375,
0.0030155181884765625,
-0.0014657974243164062,
-0.0241546630859375,
0.0117034912109375,
0.0146636962890625,
-0.01081085205078125,
0.0240936279296875,
-0.007549285888671875,
0.01380157470703125,
0.0093994140625,
0.005039215087890625,
0.0089111328125,
0.037200927734375,
0.018341064453125,
-0.017333984375,
0.01837158203125,
0.01202392578125,
0.0128631591796875,
-0.0058135986328125,
0.0062255859375,
0.006031036376953125,
0.0148162841796875,
-0.0013904571533203125,
-0.025238037109375,
0.03118896484375,
-0.00569915771484375,
-0.0274658203125,
-0.018585205078125,
0.0211944580078125,
0.020050048828125,
0.0292510986328125,
-0.0204010009765625,
0.00231170654296875,
0.0037174224853515625,
0.012939453125,
0.010162353515625,
-0.0400390625,
0.02972412109375,
-0.010162353515625,
-0.0411376953125,
-0.024627685546875,
-0.00958251953125,
-0.0110931396484375,
0.031219482421875,
-0.04052734375,
-0.02508544921875,
-0.0284576416015625,
-0.0018463134765625,
-0.0284881591796875,
-0.0191802978515625,
-0.01392364501953125,
-0.0263671875,
0.0099945068359375,
0.0181884765625,
0.01387786865234375,
-0.0284881591796875,
0.01873779296875,
0.02288818359375,
-0.002429962158203125,
0.01129913330078125,
-0.0174713134765625,
0.048919677734375,
-0.003925323486328125,
0.003795623779296875,
-0.0017719268798828125,
-0.0171661376953125,
0.0186004638671875,
0.030975341796875,
0.0222930908203125,
0.0085906982421875,
0.0144805908203125,
0.01233673095703125,
0.01213836669921875,
0.01605224609375,
-0.011260986328125,
-0.024322509765625,
0.0236663818359375,
0.0002689361572265625,
0.0173492431640625,
-0.0330810546875,
-0.016326904296875,
-0.0283050537109375,
0.003910064697265625,
0.0074310302734375,
0.0128173828125,
-0.0225982666015625,
-0.0007143020629882812,
0.039764404296875,
-0.00962066650390625,
0.020111083984375,
-0.0190582275390625,
-0.0255889892578125,
-0.007274627685546875,
-0.052093505859375,
-0.0173797607421875,
-0.04937744140625,
-0.004058837890625,
0.041259765625,
-0.0184173583984375,
0.0294189453125,
-0.02862548828125,
0.0032806396484375,
0.01519775390625,
0.012237548828125,
-0.0440673828125,
-0.0030307769775390625,
0.00907135009765625,
0.0096893310546875,
0.031982421875,
-0.0145263671875,
0.00531005859375,
-0.0012722015380859375,
-0.0185394287109375,
-0.006683349609375,
-0.0076751708984375,
-0.005840301513671875,
0.004291534423828125,
-0.0001323223114013672,
0.03839111328125,
0.007965087890625,
-0.0091705322265625,
-0.0389404296875,
-0.0192718505859375,
-0.002590179443359375,
-0.0275726318359375,
0.023468017578125,
0.007518768310546875,
-0.01419830322265625,
0.01490020751953125,
0.0018968582153320312,
-0.03375244140625,
0.005645751953125,
0.0018968582153320312,
-0.01898193359375,
0.0103912353515625,
-0.0287017822265625,
0.007205963134765625,
0.01471710205078125,
0.01434326171875,
-0.00563812255859375,
-0.0211944580078125,
-0.0252532958984375,
0.0100860595703125,
-0.0204925537109375,
0.0012350082397460938,
-0.0027923583984375,
0.0142669677734375,
0.029754638671875,
-0.005828857421875,
0.0462646484375,
-0.0208740234375,
-0.005161285400390625,
0.019989013671875,
-0.0181732177734375,
-0.018707275390625,
-0.007686614990234375,
0.01226806640625,
0.03228759765625,
0.0224761962890625,
-0.00537872314453125,
-0.03515625,
0.0286407470703125,
0.0028133392333984375,
0.0140228271484375,
0.0003991127014160156,
-0.01251220703125,
-0.08013916015625,
-0.031341552734375,
-0.0069732666015625,
-0.0156402587890625,
0.0225982666015625,
-0.01024627685546875,
-0.0165863037109375,
0.002201080322265625,
0.00429534912109375,
-0.009979248046875,
0.01409149169921875,
0.01409912109375,
0.011322021484375,
0.06243896484375,
-0.0150146484375,
0.04132080078125,
0.0061798095703125,
0.0010824203491210938,
0.04730224609375,
0.006465911865234375,
0.00785064697265625,
0.02447509765625,
0.01080322265625,
-0.04193115234375,
-0.0070037841796875,
-0.0035305023193359375,
-0.01104736328125,
-0.032501220703125,
0.0156707763671875,
-0.00946044921875,
0.0169525146484375,
-0.02130126953125,
0.01497650146484375,
0.0266265869140625,
0.0179595947265625,
-0.0058135986328125,
0.0156707763671875,
0.0240478515625,
0.0136566162109375,
0.031219482421875,
0.015777587890625,
-0.00901031494140625,
0.04376220703125,
-0.03619384765625,
0.01004791259765625,
-0.00007486343383789062,
-0.01296234130859375,
-0.00872039794921875,
0.004360198974609375,
0.0133514404296875,
0.003253936767578125,
-0.01300811767578125,
-0.0256805419921875,
0.022918701171875,
-0.0089263916015625,
-0.004489898681640625,
0.0204315185546875,
-0.0123748779296875,
0.0154571533203125,
-0.005039215087890625,
0.00366973876953125,
-0.0167083740234375,
-0.0213623046875,
0.00936126708984375,
0.0418701171875,
0.0120697021484375,
-0.027923583984375,
-0.01222991943359375,
-0.0167083740234375,
0.0204620361328125,
0.0013885498046875,
0.022064208984375,
-0.05670166015625,
-0.0004849433898925781,
0.01427459716796875,
0.0235748291015625,
-0.051361083984375,
-0.01055908203125,
-0.0435791015625,
-0.038330078125,
-0.0156707763671875,
-0.0003554821014404297,
0.0484619140625,
-0.0182952880859375,
-0.0217742919921875,
-0.00125885009765625,
0.042205810546875,
-0.017669677734375,
-0.01239776611328125,
-0.0095062255859375,
-0.048370361328125,
-0.009246826171875,
-0.0025310516357421875,
0.0248870849609375,
-0.0196380615234375,
-0.017730712890625,
0.0196075439453125,
-0.034423828125,
-0.0115203857421875,
0.0183868408203125,
0.024658203125,
0.000023603439331054688,
0.005626678466796875,
-0.037139892578125,
0.01788330078125,
0.0361328125,
-0.00997161865234375,
0.019927978515625,
-0.003749847412109375,
0.0039043426513671875,
-0.03704833984375,
0.029815673828125,
0.00048613548278808594,
0.0273590087890625,
-0.00649261474609375,
0.004955291748046875,
-0.01436614990234375,
-0.011077880859375,
0.01654052734375,
0.01202392578125,
0.006038665771484375,
-0.007083892822265625,
-0.0180816650390625,
0.01412200927734375,
-0.058837890625,
0.0031185150146484375,
-0.002010345458984375,
-0.01348876953125,
0.00846099853515625,
-0.035888671875,
-0.0053863525390625,
-0.008331298828125,
0.008514404296875,
0.0086212158203125,
0.0032329559326171875,
-0.0191192626953125,
0.0308380126953125,
0.03863525390625,
-0.00827789306640625,
0.0268402099609375,
0.03668212890625,
0.017852783203125,
-0.0457763671875,
-0.00817108154296875,
-0.0318603515625,
-0.002239227294921875,
-0.0087432861328125,
0.00232696533203125,
0.02032470703125,
-0.0211029052734375,
0.01306915283203125,
-0.0043792724609375,
-0.007671356201171875,
0.010467529296875,
0.01526641845703125,
-0.0031948089599609375,
-0.0170745849609375,
0.034698486328125,
-0.045806884765625,
-0.0007348060607910156,
0.04351806640625,
0.01319122314453125,
-0.024505615234375,
0.01357269287109375,
0.01544189453125,
0.001155853271484375,
0.045928955078125,
0.00689697265625,
0.019744873046875,
-0.00365447998046875,
0.024444580078125,
-0.00475311279296875,
0.01502227783203125,
-0.005496978759765625,
-0.003414154052734375,
0.0080108642578125,
-0.01568603515625,
0.0012378692626953125,
-0.007205963134765625,
-0.001255035400390625,
-0.01407623291015625,
-0.0082855224609375,
-0.024688720703125,
-0.037811279296875,
-0.01287841796875,
-0.0159454345703125,
0.0189666748046875,
-0.0165557861328125,
-0.01444244384765625,
0.03704833984375,
0.0210723876953125,
0.025421142578125,
0.0283050537109375,
-0.01146697998046875,
-0.01983642578125,
0.007053375244140625,
0.0109100341796875,
-0.0323486328125,
0.0096588134765625,
-0.002826690673828125,
0.043212890625,
0.03997802734375,
-0.03692626953125,
0.0018033981323242188,
0.033538818359375,
-0.0171051025390625,
-0.0147552490234375,
-0.03033447265625,
0.00403594970703125,
0.050933837890625,
-0.0239410400390625,
0.004039764404296875,
0.0011148452758789062,
-0.00921630859375,
-0.0294036865234375,
0.0186614990234375,
0.0087738037109375,
0.03179931640625,
-0.01029205322265625,
0.031768798828125,
0.0069732666015625,
0.04046630859375,
-0.014434814453125,
-0.0102081298828125,
0.00601959228515625,
0.0013484954833984375,
-0.021636962890625,
0.01751708984375,
-0.044219970703125,
0.0029296875,
-0.0093536376953125,
0.02032470703125,
-0.04071044921875,
-0.01751708984375,
0.007450103759765625,
-0.041534423828125,
0.01128387451171875,
-0.0521240234375,
0.007476806640625,
-0.02667236328125,
0.0208587646484375,
-0.01013946533203125,
0.00434112548828125,
-0.0010557174682617188,
-0.048126220703125,
0.047698974609375,
0.00930023193359375,
0.020263671875,
0.0192413330078125,
0.0206451416015625,
0.0008349418640136719,
0.00311279296875,
0.00928497314453125,
-0.0202484130859375,
-0.00980377197265625,
-0.0226287841796875,
0.005947113037109375,
-0.016387939453125,
0.01042938232421875,
0.008209228515625,
0.037139892578125,
-0.01446533203125,
0.017852783203125,
0.01070404052734375,
0.017547607421875,
-0.03619384765625,
0.0018510818481445312,
-0.0054931640625,
-0.0001970529556274414,
0.005733489990234375,
0.009521484375,
0.02337646484375,
-0.010345458984375,
0.0283660888671875,
0.0174102783203125,
0.004638671875,
0.00638580322265625,
0.005123138427734375,
-0.019256591796875,
-0.00542449951171875,
-0.029876708984375,
-0.030364990234375,
-0.00965118408203125,
0.0290069580078125,
-0.006450653076171875,
0.00905609130859375,
0.0218505859375,
-0.03839111328125,
0.00484466552734375,
-0.03173828125,
0.014404296875,
0.017120361328125,
-0.013641357421875,
0.045013427734375,
0.00350189208984375,
0.0004892349243164062,
0.04388427734375,
0.005863189697265625,
0.02105712890625,
-0.0004477500915527344,
0.004917144775390625,
-0.013427734375,
0.0026302337646484375,
0.01546478271484375,
-0.0102996826171875,
-0.0026874542236328125,
0.00047135353088378906,
0.021484375,
-0.031463623046875,
-0.028076171875,
0.0240020751953125,
0.019500732421875,
-0.0079498291015625,
0.01424407958984375,
0.00899505615234375,
0.006771087646484375,
0.00846099853515625,
0.005069732666015625,
-0.01389312744140625,
0.01300048828125,
0.00510406494140625,
0.00811004638671875,
-0.01305389404296875,
-0.004322052001953125,
0.0001615285873413086,
0.0177459716796875,
-0.028411865234375,
-0.00699615478515625,
-0.00911712646484375,
0.01261138916015625,
-0.0192413330078125,
-0.019287109375,
-0.0005249977111816406,
-0.06536865234375,
0.03985595703125,
-0.00966644287109375,
-0.0015306472778320312,
0.04345703125,
0.04205322265625,
0.014862060546875,
-0.021759033203125,
-0.01528167724609375,
-0.0024280548095703125,
-0.00421905517578125,
0.026092529296875,
-0.0244903564453125,
0.0017299652099609375,
0.01849365234375,
-0.02362060546875,
-0.0121612548828125,
-0.045379638671875,
-0.008087158203125,
0.035369873046875,
0.002452850341796875,
-0.04608154296875,
-0.003833770751953125,
0.0080108642578125,
-0.0242919921875,
-0.014251708984375,
-0.0288543701171875,
-0.020660400390625,
-0.021881103515625,
-0.0256500244140625,
0.00131988525390625,
-0.01593017578125,
-0.00017571449279785156,
0.01027679443359375,
0.01303863525390625,
-0.015411376953125,
0.03253173828125,
0.0203094482421875,
0.0306396484375,
0.016448974609375,
0.014312744140625,
0.028839111328125,
0.008087158203125,
0.00925445556640625,
0.0034999847412109375,
-0.0065765380859375,
-0.003879547119140625,
0.006481170654296875,
-0.019195556640625,
0.00411224365234375,
0.0021839141845703125,
0.0270843505859375,
0.0014886856079101562,
-0.0139312744140625,
-0.00431060791015625,
-0.00875091552734375,
0.0518798828125,
0.0089569091796875,
0.0340576171875,
0.005039215087890625,
0.01421356201171875,
0.00821685791015625,
0.0097808837890625,
0.0018739700317382812,
0.0031948089599609375,
-0.01430511474609375,
-0.01446533203125,
-0.024688720703125,
0.022857666015625,
-0.0169677734375,
0.003387451171875,
-0.00391387939453125,
0.02227783203125,
0.0284576416015625,
0.027618408203125,
-0.0258026123046875,
0.0018672943115234375,
-0.01120758056640625,
-0.0089569091796875,
0.0144805908203125,
0.014984130859375,
0.00016367435455322266,
-0.01031494140625,
0.01434326171875,
-0.0166168212890625,
-0.005329132080078125,
-0.0184783935546875,
-0.0079193115234375,
0.01177215576171875,
0.004611968994140625,
-0.0194854736328125,
0.0144195556640625,
-0.0318603515625,
0.019683837890625,
-0.0086212158203125,
0.0029296875,
0.04296875,
-0.0008130073547363281,
-0.015838623046875,
0.015960693359375,
0.0202178955078125,
-0.021636962890625,
0.058837890625,
0.020751953125,
-0.0009441375732421875,
0.005252838134765625,
-0.056884765625,
-0.032257080078125,
-0.01523590087890625,
-0.0200653076171875,
0.0265350341796875,
0.023193359375,
-0.00496673583984375,
-0.00400543212890625,
-0.0428466796875,
-0.0198974609375,
0.0203399658203125,
0.01702880859375,
-0.01129913330078125,
0.00885009765625,
-0.0158233642578125,
-0.01947021484375,
0.034912109375,
0.0101318359375,
-0.00908660888671875,
0.031707763671875,
-0.0181884765625,
0.00878143310546875,
-0.037200927734375,
0.005008697509765625,
-0.0215301513671875,
-0.00583648681640625,
0.00588226318359375,
0.00644683837890625,
-0.0298919677734375,
-0.0016355514526367188,
0.010284423828125,
-0.011688232421875,
0.00524139404296875,
0.0251007080078125,
0.004291534423828125,
0.02862548828125,
0.0311279296875,
0.061920166015625,
0.00655364990234375,
-0.0033550262451171875,
-0.0156402587890625,
0.01158905029296875,
0.004528045654296875,
0.0010433197021484375,
0.00782012939453125,
-0.021697998046875,
0.01861572265625,
0.03814697265625,
-0.0300140380859375,
-0.00890350341796875,
-0.0176849365234375,
-0.007720947265625,
0.01438140869140625,
-0.00623321533203125,
-0.0006494522094726562,
-0.0015802383422851562,
0.01395416259765625,
-0.005870819091796875,
0.0184326171875,
0.0191497802734375,
0.0123748779296875,
0.022918701171875,
-0.0300750732421875,
-0.01154327392578125,
0.0075225830078125,
-0.01226043701171875,
0.0062713623046875,
-0.003772735595703125,
0.006252288818359375,
-0.033447265625,
0.00482940673828125,
0.007465362548828125,
-0.043182373046875,
-0.0009431838989257812,
-0.01180267333984375,
0.0238494873046875,
-0.01094818115234375,
-0.0153045654296875,
0.0007300376892089844,
-0.01374053955078125,
0.0070037841796875,
0.00035691261291503906,
0.006267547607421875,
0.01446533203125,
-0.03521728515625,
-0.007038116455078125,
-0.00262451171875,
0.0207672119140625,
0.043975830078125,
-0.015869140625,
0.0066375732421875,
-0.0173492431640625,
0.00537109375,
0.00969696044921875,
-0.004688262939453125,
0.0172119140625,
0.002689361572265625,
0.0224761962890625,
0.00848388671875,
-0.0232086181640625,
-0.0030193328857421875,
0.02325439453125,
0.0157928466796875,
-0.0065765380859375,
-0.005474090576171875,
0.0035533905029296875,
-0.00553131103515625,
0.026611328125,
0.010284423828125,
-0.0197296142578125,
0.034515380859375,
0.0171966552734375,
0.0189971923828125,
0.03875732421875,
0.00319671630859375,
-0.003917694091796875,
0.015472412109375,
0.005828857421875,
-0.033203125,
0.01233673095703125,
-0.0279388427734375,
-0.00742340087890625,
0.026336669921875,
0.01149749755859375,
0.006824493408203125,
0.003963470458984375,
0.045166015625,
0.033416748046875,
-0.0023345947265625,
0.004894256591796875,
-0.007465362548828125,
-0.015625,
-0.007049560546875,
0.0027618408203125,
0.01280975341796875,
-0.0270843505859375,
-0.056060791015625,
0.01374053955078125,
-0.0285797119140625,
0.016265869140625,
0.00208282470703125,
-0.01329803466796875,
-0.00655364990234375,
0.002353668212890625,
0.006099700927734375,
-0.022125244140625,
0.01384735107421875,
-0.0011758804321289062,
0.00672149658203125,
0.006916046142578125,
-0.0189361572265625,
-0.00008594989776611328,
-0.0103912353515625,
0.00417327880859375,
-0.005268096923828125,
-0.01407623291015625,
-0.01383209228515625,
0.00885772705078125,
0.02484130859375,
0.0008969306945800781,
0.0200347900390625,
0.0186004638671875,
0.0121002197265625,
-0.03656005859375,
-0.0020046234130859375,
0.020355224609375,
0.0159149169921875,
-0.0010480880737304688,
0.007061004638671875,
0.0261993408203125,
0.0030975341796875,
0.01800537109375,
0.0081329345703125,
-0.02423095703125,
-0.031005859375,
0.031494140625,
-0.0113372802734375,
0.0333251953125,
-0.00850677490234375,
-0.01390838623046875,
0.0207672119140625,
0.01416778564453125,
-0.021209716796875,
-0.0004169940948486328,
0.0221710205078125,
-0.0196533203125,
0.01505279541015625,
0.033111572265625,
-0.01763916015625,
0.002567291259765625,
-0.0018339157104492188,
0.007354736328125,
0.0087890625,
-0.0185546875,
-0.0229034423828125,
0.027069091796875,
-0.014862060546875,
-0.017303466796875,
-0.0076751708984375,
0.044464111328125,
-0.00919342041015625,
0.0021114349365234375,
-0.0172271728515625,
-0.012725830078125,
0.024993896484375,
-0.005481719970703125,
-0.012908935546875,
0.00814056396484375,
-0.01493072509765625,
0.0014944076538085938,
0.000035822391510009766,
0.0040130615234375,
0.0236663818359375,
0.002605438232421875,
-0.024017333984375,
0.004222869873046875,
0.040924072265625,
0.0302276611328125,
-0.0139617919921875,
-0.0010881423950195312,
-0.0162200927734375,
-0.017547607421875,
-0.03570556640625,
0.0271759033203125,
0.007381439208984375,
0.039031982421875,
0.0008378028869628906,
0.013458251953125,
-0.037017822265625,
-0.0211334228515625,
0.003932952880859375,
0.0146484375,
0.00556182861328125,
0.01247406005859375,
-0.038604736328125,
0.01081085205078125,
0.0078277587890625,
-0.06427001953125,
-0.0200653076171875,
0.01568603515625,
0.01428985595703125,
-0.01200103759765625,
-0.0039825439453125,
0.01354217529296875,
-0.0299835205078125,
-0.02447509765625,
0.0229339599609375,
-0.0052642822265625,
-0.01383209228515625,
-0.023193359375,
0.0012750625610351562,
-0.0013065338134765625,
-0.00024116039276123047,
-0.0026531219482421875,
-0.02728271484375,
0.00220489501953125,
-0.005889892578125,
-0.0228118896484375,
-0.01247406005859375,
-0.038665771484375,
0.005767822265625,
-0.00672149658203125,
0.01273345947265625,
0.0322265625,
-0.017547607421875,
0.00263214111328125,
0.00042510032653808594,
0.0096893310546875,
0.0010528564453125,
-0.01270294189453125,
0.0187835693359375,
0.052978515625,
-0.0223236083984375,
0.02392578125,
-0.049713134765625,
-0.01232147216796875,
0.01428985595703125,
-0.0161895751953125,
0.003692626953125,
-0.0016326904296875,
0.0302886962890625,
0.01113128662109375,
-0.0030670166015625,
0.009002685546875,
0.0013895034790039062,
0.006134033203125,
0.01507568359375,
-0.00879669189453125,
-0.006221771240234375,
-0.02001953125,
0.045196533203125,
-0.0010156631469726562,
-0.0030155181884765625,
-0.015625,
0.011932373046875,
-0.00319671630859375,
0.005481719970703125,
0.0144805908203125,
-0.003124237060546875,
0.016265869140625,
0.0036144256591796875,
0.0167694091796875,
0.006076812744140625,
-0.0092926025390625,
-0.00771331787109375,
0.0291595458984375,
-0.006435394287109375,
0.010986328125,
0.00937652587890625,
-0.00736236572265625,
0.036041259765625,
-0.004039764404296875,
-0.017486572265625,
0.0053863525390625,
-0.019927978515625,
-0.0206451416015625,
0.00958251953125,
0.0222015380859375,
-0.037872314453125,
0.007602691650390625,
-0.0233306884765625,
0.025543212890625,
0.0167694091796875,
0.0030651092529296875,
-0.012664794921875,
-0.0249481201171875,
0.032196044921875,
-0.0272674560546875,
-0.02484130859375,
0.0142974853515625,
0.004241943359375,
0.007381439208984375,
-0.0018787384033203125,
-0.0079498291015625,
0.00543212890625,
-0.01971435546875,
-0.0186309814453125,
0.0003941059112548828,
0.0277557373046875,
0.020965576171875,
0.0156402587890625,
0.0280609130859375,
0.0018663406372070312,
0.024139404296875,
-0.00894927978515625,
-0.006748199462890625,
-0.0298004150390625,
0.0167083740234375,
0.027862548828125,
-0.00316619873046875,
0.0106201171875,
-0.025360107421875,
-0.04278564453125,
0.0068359375,
-0.0034542083740234375,
-0.01215362548828125,
0.0015621185302734375,
-0.0226593017578125,
-0.00830841064453125,
-0.01806640625,
0.0232696533203125,
-0.0009465217590332031,
0.01107025146484375,
-0.0221099853515625,
0.01239776611328125,
0.0206756591796875,
-0.041168212890625,
-0.026763916015625,
-0.00476837158203125,
-0.0282745361328125,
0.0266265869140625,
0.01025390625,
-0.0130767822265625,
0.025909423828125,
0.01152801513671875,
0.002056121826171875,
0.01381683349609375,
0.001674652099609375,
-0.00989532470703125,
0.00037407875061035156,
-0.0132293701171875,
0.00824737548828125,
-0.0271759033203125,
0.00894927978515625,
-0.01183319091796875,
0.035980224609375,
0.00928497314453125,
-0.0205078125,
0.001468658447265625,
-0.0106048583984375,
0.007160186767578125,
-0.017791748046875,
0.0063018798828125,
0.01181793212890625,
-0.00891876220703125,
0.033111572265625,
0.01113128662109375,
-0.01334381103515625,
-0.03131103515625,
-0.03143310546875,
0.02642822265625,
-0.02203369140625,
-0.034759521484375,
-0.01201629638671875,
-0.0291900634765625,
0.006099700927734375,
0.0200958251953125,
-0.023956298828125,
-0.0238189697265625,
-0.004756927490234375,
0.0074920654296875,
0.0235595703125,
-0.010833740234375,
0.00850677490234375,
-0.010162353515625,
-0.004917144775390625,
0.0222625732421875,
0.0162811279296875,
0.035125732421875,
0.0114898681640625,
-0.0191802978515625,
-0.0198211669921875,
-0.005298614501953125,
0.0009937286376953125,
0.01306915283203125,
-0.003910064697265625,
-0.0538330078125,
0.0117034912109375,
0.0233001708984375,
-0.01407623291015625,
-0.017547607421875,
-0.026214599609375,
0.0005350112915039062,
0.00838470458984375,
0.00957489013671875,
-0.021392822265625,
0.00040793418884277344,
-0.0170745849609375,
0.03594970703125,
-0.00214385986328125,
0.00724029541015625,
0.01885986328125,
0.0005774497985839844,
-0.0143280029296875,
0.00534820556640625,
-0.022796630859375,
-0.047393798828125,
0.0294647216796875,
0.01108551025390625,
-0.00415802001953125,
-0.019622802734375,
0.01273345947265625,
0.0283355712890625,
0.00928497314453125,
0.01491546630859375,
-0.028533935546875,
-0.017913818359375,
0.019561767578125,
-0.0085601806640625,
0.006580352783203125,
-0.01071929931640625,
-0.0111846923828125,
0.0028362274169921875,
-0.0261383056640625,
0.036224365234375,
-0.0168609619140625,
-0.008453369140625,
-0.007251739501953125,
-0.0014209747314453125,
-0.00885772705078125,
0.0311431884765625,
0.022064208984375,
-0.001708984375,
0.00005137920379638672,
-0.007293701171875,
0.0182952880859375,
-0.00004786252975463867,
-0.033477783203125,
0.0134735107421875,
-0.0210418701171875,
0.00730133056640625,
0.0087738037109375,
0.037078857421875,
0.026947021484375,
-0.0076446533203125,
0.006542205810546875,
-0.0224761962890625,
-0.031982421875,
-0.032684326171875,
0.00376129150390625,
-0.025543212890625,
-0.0023097991943359375,
-0.004001617431640625,
0.0014743804931640625,
0.0323486328125,
0.01806640625,
-0.017425537109375,
0.034912109375,
0.0102081298828125,
0.026580810546875,
0.0227203369140625,
-0.045013427734375,
0.0128936767578125,
0.0117034912109375,
0.00891876220703125,
-0.005443572998046875,
-0.0146026611328125,
0.0023250579833984375,
-0.026763916015625,
0.00946807861328125,
-0.01381683349609375,
0.01702880859375,
-0.0019292831420898438,
-0.0099639892578125,
0.0008039474487304688,
0.0115509033203125,
-0.00027060508728027344,
-0.01462554931640625,
-0.0125274658203125,
-0.037811279296875,
0.00542449951171875,
-0.00027370452880859375,
0.04168701171875,
-0.01398468017578125,
0.0243682861328125,
0.0187530517578125,
-0.0194244384765625,
0.037933349609375,
0.0012445449829101562,
-0.0027942657470703125,
-0.017822265625,
0.0003979206085205078,
-0.0196075439453125,
0.034698486328125,
0.028228759765625,
-0.0157928466796875,
-0.03411865234375,
-0.0116424560546875,
0.0188140869140625,
-0.0095977783203125,
-0.0082244873046875,
-0.0196685791015625,
-0.0223236083984375,
-0.036895751953125,
0.0054473876953125,
-0.0198211669921875,
-0.0303192138671875,
-0.0130462646484375,
-0.0343017578125,
0.03778076171875,
-0.021820068359375,
-0.0078277587890625,
0.027191162109375,
-0.0133209228515625,
-0.00341796875,
-0.034820556640625,
-0.00286102294921875,
-0.0098419189453125,
0.01052093505859375,
0.0018815994262695312,
-0.01593017578125,
0.0008611679077148438,
0.004779815673828125,
0.0236358642578125,
0.031280517578125,
0.0005202293395996094,
0.0249786376953125,
0.00598907470703125,
-0.0180206298828125,
-0.00208282470703125,
0.0193328857421875,
-0.00954437255859375,
0.00754547119140625,
-0.011016845703125,
-0.02093505859375,
-0.0208892822265625,
0.0007572174072265625,
-0.00415802001953125,
0.0065460205078125,
-0.0256805419921875,
0.0108184814453125,
-0.002834320068359375,
0.002849578857421875,
-0.006443023681640625,
-0.0204925537109375,
-0.00679779052734375,
0.031951904296875,
-0.00966644287109375,
0.0228729248046875,
-0.00522613525390625,
-0.0264739990234375,
-0.01198577880859375,
0.01226806640625,
-0.0101318359375,
-0.017669677734375,
0.005352020263671875,
0.002086639404296875,
0.0187835693359375,
0.0036220550537109375,
-0.03692626953125,
0.007843017578125,
0.0400390625,
-0.0176239013671875,
0.0173492431640625,
0.01154327392578125,
-0.002613067626953125,
0.0264892578125,
0.027862548828125,
-0.0048980712890625,
0.0285797119140625,
0.0264892578125,
-0.03375244140625,
0.003467559814453125,
-0.01540374755859375,
0.0248260498046875,
0.0028591156005859375,
-0.0104217529296875,
0.018310546875,
-0.0139923095703125,
0.01898193359375,
-0.00672149658203125,
-0.018096923828125,
0.004817962646484375,
-0.0178680419921875,
-0.003017425537109375,
-0.02099609375,
0.01336669921875,
-0.011810302734375,
0.0084228515625,
-0.036773681640625,
-0.0084075927734375,
-0.00787353515625,
-0.0257415771484375,
-0.041778564453125,
-0.042388916015625,
0.0015993118286132812,
-0.0114288330078125,
-0.02813720703125,
0.038604736328125,
0.0260467529296875,
0.0152740478515625,
-0.00270843505859375,
-0.0211639404296875,
0.01422882080078125,
-0.0004916191101074219,
-0.004695892333984375,
-0.0168609619140625,
-0.0027217864990234375,
0.016693115234375,
0.00836944580078125,
-0.0254058837890625,
0.009765625,
-0.0313720703125,
-0.004520416259765625,
-0.022918701171875,
-0.0279693603515625,
-0.036956787109375,
0.010772705078125,
0.0193328857421875,
0.0018606185913085938,
0.00958251953125,
0.05133056640625,
-0.0247650146484375,
-0.01080322265625,
-0.0223388671875,
-0.00415802001953125,
-0.009185791015625,
0.0010061264038085938,
0.0040130615234375,
-0.01554107666015625,
0.0010652542114257812,
0.01514434814453125,
-0.009796142578125,
-0.0187835693359375,
-0.01477813720703125,
0.00424957275390625,
-0.0240936279296875,
-0.00481414794921875,
0.0173187255859375,
0.023773193359375,
-0.01204681396484375,
0.0010213851928710938,
-0.00396728515625,
-0.001377105712890625,
0.0106658935546875,
-0.01708984375,
-0.043853759765625,
-0.002124786376953125,
-0.0158233642578125,
0.017181396484375,
-0.0080718994140625,
0.001468658447265625,
-0.0187225341796875,
-0.0114593505859375,
0.0185089111328125,
0.00901031494140625,
-0.0038051605224609375,
0.016265869140625,
-0.002960205078125,
-0.016571044921875,
0.0274810791015625,
-0.01410675048828125,
-0.02069091796875,
0.0104522705078125,
-0.00447845458984375,
-0.033599853515625,
-0.017669677734375,
0.025146484375,
-0.0112762451171875,
0.030181884765625,
-0.00843048095703125,
0.005367279052734375,
0.0257110595703125,
0.00566864013671875,
-0.0296478271484375,
-0.0380859375,
-0.001194000244140625,
0.05657958984375,
-0.0019741058349609375,
0.0135345458984375,
0.042388916015625,
0.00975799560546875,
-0.01507568359375,
-0.021148681640625,
0.0274658203125,
0.0272674560546875,
-0.00826263427734375,
0.01300811767578125,
-0.015716552734375,
-0.01171875,
0.0092315673828125,
0.012237548828125,
-0.0216217041015625,
-0.00017321109771728516,
-0.047882080078125,
0.01010894775390625,
-0.005664825439453125,
-0.0180511474609375,
0.002223968505859375,
-0.026702880859375,
-0.035125732421875,
-0.03485107421875,
-0.0019330978393554688,
-0.005214691162109375,
-0.01367950439453125,
0.001956939697265625,
-0.056732177734375,
-0.0233306884765625,
0.016357421875,
-0.0245361328125,
0.020660400390625,
0.0260467529296875,
0.0235595703125,
-0.011444091796875,
0.00963592529296875,
0.0278472900390625,
0.0180206298828125,
0.01366424560546875,
-0.01004791259765625,
-0.0236968994140625,
0.005397796630859375,
-0.01154327392578125,
-0.03216552734375,
0.0015745162963867188,
0.0098876953125,
-0.0034427642822265625,
0.017425537109375,
0.000009179115295410156,
-0.029815673828125,
0.019134521484375,
0.006481170654296875,
-0.006092071533203125,
0.012664794921875,
-0.016632080078125,
0.0220947265625,
-0.04400634765625,
0.015380859375,
0.004825592041015625,
-0.031585693359375,
0.01084136962890625,
0.0049896240234375,
-0.0230712890625,
-0.01410675048828125,
-0.0120849609375,
0.0282135009765625,
-0.0073699951171875,
-0.0283966064453125,
-0.006763458251953125,
0.0054168701171875,
-0.02301025390625,
-0.0103912353515625,
0.001068115234375,
-0.01020050048828125,
-0.02496337890625,
0.0025634765625,
-0.04083251953125,
-0.007251739501953125,
0.0188140869140625,
-0.006866455078125,
0.0021877288818359375,
-0.00557708740234375,
-0.004596710205078125,
0.017364501953125,
-0.0188446044921875,
-0.00887298583984375,
0.0164794921875,
-0.00119781494140625,
-0.01800537109375,
-0.015594482421875,
-0.01494598388671875,
-0.01371002197265625,
-0.002231597900390625,
-0.01358795166015625,
-0.0209503173828125,
-0.003002166748046875,
0.01690673828125,
-0.01548004150390625,
0.07257080078125,
0.00390625,
0.0076446533203125,
0.0233154296875,
0.00626373291015625,
-0.0028076171875,
0.014312744140625,
0.042572021484375,
-0.003932952880859375,
0.005825042724609375,
0.01739501953125,
0.027435302734375,
0.0257415771484375,
-0.028900146484375,
0.0018978118896484375,
0.02374267578125,
-0.004261016845703125,
-0.0094146728515625,
-0.01027679443359375,
-0.00377655029296875,
0.009765625,
-0.01229095458984375,
0.0218505859375,
-0.0236663818359375,
0.007137298583984375,
0.005580902099609375,
0.0179443359375,
0.01108551025390625,
-0.0155181884765625,
-0.02642822265625,
-0.007488250732421875,
-0.0027866363525390625,
-0.0283355712890625,
-0.00926971435546875,
-0.016510009765625,
0.00508880615234375,
-0.00812530517578125,
0.015899658203125,
0.01525115966796875,
-0.027801513671875,
-0.01143646240234375,
-0.0160064697265625,
0.03741455078125,
-0.0209197998046875,
-0.036376953125,
0.030029296875,
0.0067901611328125,
0.00814056396484375,
0.00501251220703125,
0.0124359130859375,
0.0004229545593261719,
0.007198333740234375,
0.01313018798828125,
-0.0005459785461425781,
0.0005817413330078125,
-0.00232696533203125,
-0.0047760009765625,
-0.00875091552734375,
-0.0499267578125,
-0.0000890493392944336,
0.0199127197265625,
-0.00843048095703125,
0.0164947509765625,
0.006420135498046875,
-0.027313232421875,
0.0038604736328125,
-0.03826904296875,
-0.013092041015625,
0.013946533203125,
-0.04376220703125,
0.0037994384765625,
-0.04156494140625,
-0.006328582763671875,
-0.03668212890625,
0.00933837890625,
-0.026336669921875,
0.0081024169921875,
-0.01947021484375,
-0.00450897216796875,
0.023223876953125,
-0.0018701553344726562,
0.00457000732421875,
-0.006267547607421875,
0.0088348388671875,
-0.0250091552734375,
0.001667022705078125,
0.0204315185546875,
0.018402099609375,
-0.022186279296875,
0.021820068359375,
-0.005268096923828125,
0.0048370361328125,
-0.0259552001953125,
-0.01381683349609375,
0.0426025390625,
0.00555419921875,
0.01171875,
-0.00982666015625,
0.05126953125,
0.00870513916015625,
0.006282806396484375,
-0.00023365020751953125,
0.00507354736328125,
-0.00386810302734375,
-0.019256591796875,
-0.00457000732421875,
-0.0185089111328125,
0.0157928466796875,
-0.018280029296875,
0.0003275871276855469,
-0.018096923828125,
-0.0016260147094726562,
-0.0179595947265625,
-0.057342529296875,
-0.0143890380859375,
-0.0106964111328125,
-0.00888824462890625,
-0.003284454345703125,
-0.014312744140625,
0.006008148193359375,
0.00005060434341430664,
0.01544189453125,
0.032379150390625,
0.0023212432861328125,
-0.00873565673828125,
-0.0008687973022460938,
-0.002956390380859375,
-0.0249786376953125,
0.0235443115234375,
0.0184478759765625,
0.01140594482421875,
0.016326904296875,
0.02294921875,
0.0238037109375,
0.01004791259765625,
0.0088653564453125,
-0.0168609619140625,
-0.0108642578125,
0.0239410400390625,
-0.0325927734375,
0.0182647705078125,
0.01531219482421875,
-0.004764556884765625,
0.00884246826171875,
0.002819061279296875,
0.0114593505859375,
-0.0083465576171875,
-0.01259613037109375,
-0.0234222412109375,
-0.0018796920776367188,
-0.00128936767578125,
-0.0227508544921875,
0.0151519775390625,
-0.00037789344787597656,
-0.00958251953125,
-0.018951416015625,
-0.037200927734375,
-0.0153045654296875,
-0.00919342041015625,
0.0060882568359375,
0.035064697265625,
-0.0016317367553710938,
0.002902984619140625,
-0.0171051025390625,
-0.02984619140625,
-0.0221710205078125,
0.01837158203125,
0.017822265625,
-0.0110321044921875,
0.0094146728515625,
0.01049041748046875,
-0.007686614990234375,
-0.00777435302734375,
-0.006732940673828125,
-0.0298614501953125,
-0.00799560546875,
0.0123291015625,
-0.0157470703125,
-0.03338623046875,
-0.002445220947265625,
-0.0002911090850830078,
0.004199981689453125,
-0.0201263427734375,
0.02117919921875,
-0.023406982421875,
0.00882720947265625,
-0.016082763671875,
-0.007442474365234375,
-0.0151519775390625,
-0.0140380859375,
0.02191162109375,
0.01230621337890625,
-0.0276641845703125,
-0.0152740478515625,
0.00763702392578125,
0.0079803466796875,
-0.003353118896484375,
0.0132293701171875,
0.022552490234375,
0.0222320556640625,
-0.0079345703125,
0.008392333984375,
0.0278167724609375,
0.0155487060546875,
0.02105712890625,
0.030731201171875,
0.0231781005859375,
0.006591796875,
0.0227813720703125,
-0.00872039794921875,
-0.017303466796875,
0.005527496337890625,
-0.0009765625,
-0.00029015541076660156,
0.0221405029296875,
0.035064697265625,
-0.01715087890625,
-0.01030731201171875,
0.01142120361328125,
-0.00771331787109375,
-0.036956787109375,
-0.0242156982421875,
0.0131988525390625,
-0.0006384849548339844,
0.006793975830078125,
0.00749969482421875,
0.002025604248046875,
-0.036346435546875,
0.0119476318359375,
0.01425933837890625,
0.0022830963134765625,
-0.0335693359375,
-0.02520751953125,
-0.006053924560546875,
-0.00046753883361816406,
-0.018768310546875,
-0.019683837890625,
-0.0119171142578125,
-0.0079803466796875,
0.01273345947265625,
-0.046173095703125,
0.005420684814453125,
0.01139068603515625,
-0.00618743896484375,
-0.0121307373046875,
0.01480865478515625,
-0.00484466552734375,
0.0106048583984375,
-0.0235443115234375,
-0.020355224609375,
0.0010852813720703125,
-0.0009551048278808594,
0.01197052001953125,
-0.01898193359375,
-0.003192901611328125,
0.00858306884765625,
-0.010894775390625,
-0.005306243896484375,
-0.0217437744140625,
-0.0222625732421875,
-0.0238494873046875,
-0.0450439453125,
0.0089874267578125,
-0.017547607421875,
-0.0050201416015625,
-0.01678466796875,
-0.0251617431640625,
0.01715087890625,
-0.0047760009765625,
0.0306854248046875,
-0.00635528564453125,
-0.03155517578125,
0.0178985595703125,
0.0272979736328125,
0.0186920166015625,
-0.00021326541900634766,
0.005146026611328125,
0.009674072265625,
-0.013885498046875,
0.033111572265625,
-0.01267242431640625,
0.0198822021484375,
0.0208740234375,
-0.01174163818359375,
0.037628173828125,
-0.000022232532501220703,
0.01189422607421875,
0.054229736328125,
-0.0130615234375,
0.0146636962890625,
-0.004405975341796875,
0.00823974609375,
0.0108184814453125,
0.00457000732421875,
-0.018157958984375,
0.01328277587890625,
0.01241302490234375,
0.043365478515625,
-0.01678466796875,
0.016204833984375,
-0.007568359375,
0.0047149658203125,
0.0008950233459472656,
0.036590576171875,
-0.01099395751953125,
0.0268096923828125,
0.0232086181640625,
-0.02276611328125,
0.0151214599609375,
-0.015869140625,
-0.01580810546875,
0.01247406005859375,
-0.0303802490234375,
0.028076171875,
-0.003662109375,
0.03692626953125,
-0.00714874267578125,
0.01125335693359375,
-0.00560760498046875,
0.0081329345703125,
0.0014543533325195312,
-0.00385284423828125,
0.0248260498046875,
-0.037017822265625,
-0.0187225341796875,
0.002887725830078125,
0.01508331298828125,
0.01511383056640625,
-0.00791168212890625,
0.00963592529296875,
0.005580902099609375,
-0.0236053466796875,
-0.01525115966796875,
-0.007686614990234375,
-0.01361846923828125,
-0.02069091796875,
-0.0124053955078125,
-0.016845703125,
0.03717041015625,
-0.00533294677734375,
-0.01044464111328125,
0.0016717910766601562,
0.022613525390625,
-0.00612640380859375,
-0.01372528076171875,
0.002838134765625,
0.037261962890625,
0.004535675048828125,
-0.0250244140625,
0.020294189453125,
-0.005870819091796875,
0.00414276123046875,
0.022247314453125,
0.02667236328125,
-0.0026683807373046875,
-0.0023345947265625,
-0.006443023681640625,
-0.0015077590942382812,
-0.005725860595703125,
0.00016319751739501953,
-0.0213470458984375,
-0.0011835098266601562,
0.004940032958984375,
0.0142822265625,
-0.0249481201171875,
-0.013275146484375,
-0.0257568359375,
0.01126861572265625,
0.036712646484375,
0.038726806640625,
-0.002902984619140625,
0.01318359375,
0.00592041015625,
-0.0027008056640625,
-0.01009368896484375,
-0.018280029296875,
-0.0180206298828125,
0.0026607513427734375,
0.00542449951171875,
0.003917694091796875,
-0.0225677490234375,
-0.02606201171875,
0.03863525390625,
-0.02490234375,
-0.0145111083984375,
-0.0146331787109375,
0.0020999908447265625,
0.012969970703125,
0.006931304931640625,
-0.0002205371856689453,
-0.018341064453125,
-0.008270263671875,
-0.043792724609375,
0.0240936279296875,
0.01206207275390625,
-0.039764404296875,
0.0025081634521484375,
-0.0164642333984375,
0.02044677734375,
-0.0086517333984375,
0.0085296630859375,
-0.0233917236328125,
-0.00830841064453125,
0.020050048828125,
0.0119476318359375,
0.01447296142578125,
-0.0225982666015625,
-0.00455474853515625,
-0.0165557861328125,
-0.0262451171875,
-0.007724761962890625,
-0.002887725830078125,
0.0007371902465820312,
-0.0167999267578125,
-0.01009368896484375,
0.031951904296875,
0.007099151611328125,
0.010345458984375,
0.011993408203125,
-0.01561737060546875,
-0.01468658447265625,
-0.01451873779296875,
0.0138092041015625,
0.0029926300048828125,
-0.0020694732666015625,
0.007083892822265625,
-0.00983428955078125,
-0.0073394775390625,
-0.007282257080078125,
0.015228271484375,
-0.0014858245849609375,
-0.014068603515625,
0.0201416015625,
0.032501220703125,
-0.0153350830078125,
-0.0008082389831542969,
-0.007144927978515625,
0.0099945068359375,
-0.016204833984375,
-0.0126190185546875,
0.00971221923828125,
0.01338958740234375,
0.00209808349609375,
0.00638580322265625,
0.01195526123046875,
0.00186920166015625,
0.0189056396484375,
0.0200958251953125,
0.02685546875,
-0.006298065185546875,
-0.0013132095336914062,
0.006549835205078125,
0.031341552734375,
-0.0223846435546875,
0.019805908203125,
0.0030612945556640625,
-0.001708984375,
0.0002956390380859375,
0.007843017578125,
-0.023284912109375,
0.01410675048828125,
0.0193634033203125,
0.01099395751953125,
-0.003749847412109375,
-0.001895904541015625,
-0.0067596435546875
] |
ours_532
|
To find the number of ways to arrange the letters \(A, A, A, H, H\) such that the sequence \(H A\) appears at least once, we first calculate the total number of arrangements of the letters without any restrictions. The total number of arrangements is given by:
\[
\frac{5!}{3! \times 2!} = \frac{120}{6 \times 2} = 10
\]
Next, we subtract the number of arrangements where the sequence \(H A\) does not appear at all. The only arrangement where \(H A\) does not appear is \(A A A H H\).
Thus, the number of arrangements where \(H A\) appears at least once is:
\[
10 - 1 = 9
\]
Therefore, the number of ways to arrange the letters such that the sequence \(H A\) appears at least once is \(\boxed{9}\).
|
9
|
{
"competition": "us_comps",
"dataset": "Ours",
"posts": null,
"source": "OMOSoln2.md"
}
|
How many ways are there to arrange the letters \(A, A, A, H, H\) in a row so that the sequence \(H A\) appears at least once?
|
[
"/Mathematics/DiscreteMathematics/Combinatorics/Enumeration",
"/Mathematics/DiscreteMathematics/Combinatorics/GeneralCombinatorics",
"/Mathematics/DiscreteMathematics/Combinatorics/Permutations",
"/Mathematics/DiscreteMathematics/GeneralDiscreteMathematics/DiscreteMath",
"/Mathematics/DiscreteMathematics/GeneralDiscreteMathematics/DiscreteMathematics"
] |
Count all arrangements then subtract the ones that avoid the pattern HA (use the complement principle).
|
[
-0.00024390220642089844,
-0.068115234375,
0.043731689453125,
0.0034770965576171875,
-0.0013294219970703125,
-0.01348876953125,
0.035064697265625,
-0.0136566162109375,
-0.0015687942504882812,
-0.03900146484375,
0.023162841796875,
-0.0159454345703125,
-0.005458831787109375,
-0.0228271484375,
-0.03509521484375,
-0.00783538818359375,
0.05474853515625,
0.0091705322265625,
0.0065460205078125,
-0.00399017333984375,
-0.012298583984375,
-0.0197601318359375,
0.0005574226379394531,
-0.008056640625,
0.0188446044921875,
0.0016450881958007812,
-0.0200653076171875,
0.0164947509765625,
0.04205322265625,
0.0292205810546875,
0.00926971435546875,
0.01052093505859375,
0.020599365234375,
0.00839996337890625,
0.002498626708984375,
0.0156402587890625,
0.0404052734375,
-0.007160186767578125,
0.00045752525329589844,
-0.039215087890625,
0.005451202392578125,
-0.031463623046875,
0.008270263671875,
0.0203704833984375,
0.0052032470703125,
0.0263214111328125,
-0.0034847259521484375,
0.037872314453125,
-0.0220794677734375,
-0.032806396484375,
-0.0107574462890625,
0.00676727294921875,
-0.025848388671875,
-0.032989501953125,
-0.022705078125,
-0.04998779296875,
-0.04559326171875,
0.0017614364624023438,
-0.033935546875,
-0.01132965087890625,
-0.0098724365234375,
-0.006793975830078125,
-0.01274871826171875,
0.002330780029296875,
0.0006394386291503906,
-0.01464080810546875,
-0.0226287841796875,
-0.0308837890625,
0.002552032470703125,
-0.01456451416015625,
0.00005811452865600586,
0.00565338134765625,
-0.034942626953125,
0.00540924072265625,
0.0200347900390625,
-0.0103759765625,
-0.0089569091796875,
0.00211334228515625,
0.033233642578125,
0.00811004638671875,
-0.017578125,
-0.0150146484375,
0.002109527587890625,
-0.0047607421875,
0.0158233642578125,
-0.0134429931640625,
0.02520751953125,
0.00005125999450683594,
-0.01081085205078125,
-0.00623321533203125,
0.0021953582763671875,
-0.00836181640625,
-0.004726409912109375,
0.0101470947265625,
-0.003139495849609375,
0.051055908203125,
-0.00704193115234375,
-0.00997161865234375,
0.0027179718017578125,
0.01192474365234375,
-0.018829345703125,
-0.02410888671875,
0.071044921875,
0.00044417381286621094,
0.0204315185546875,
-0.0207366943359375,
-0.0171661376953125,
0.0024852752685546875,
-0.0107269287109375,
0.0039215087890625,
0.01544952392578125,
0.0154266357421875,
0.05914306640625,
0.017608642578125,
0.003040313720703125,
-0.01438140869140625,
0.0286407470703125,
-0.0265655517578125,
-0.0102081298828125,
0.01104736328125,
0.017333984375,
0.0255584716796875,
0.00722503662109375,
0.018798828125,
0.017730712890625,
0.042083740234375,
-0.015655517578125,
0.00771331787109375,
0.019256591796875,
-0.034423828125,
0.039215087890625,
-0.013580322265625,
-0.0025634765625,
-0.0094451904296875,
-0.0015735626220703125,
-0.01256561279296875,
-0.0217132568359375,
-0.0039825439453125,
0.00873565673828125,
-0.0027828216552734375,
0.0012798309326171875,
-0.00461578369140625,
0.007091522216796875,
0.007305145263671875,
0.006488800048828125,
-0.0347900390625,
0.0037593841552734375,
-0.031494140625,
0.002593994140625,
0.0159454345703125,
0.0007996559143066406,
0.0061492919921875,
0.0010366439819335938,
0.016815185546875,
-0.01186370849609375,
0.00878143310546875,
0.0019016265869140625,
0.0059661865234375,
-0.002124786376953125,
0.019317626953125,
0.00803375244140625,
0.0137939453125,
-0.0036678314208984375,
0.025848388671875,
-0.00897216796875,
0.0050048828125,
0.01320648193359375,
0.0002715587615966797,
-0.0164031982421875,
0.03289794921875,
0.0038909912109375,
0.019744873046875,
-0.0034694671630859375,
-0.0169525146484375,
0.0104522705078125,
0.01522064208984375,
0.002910614013671875,
0.0242767333984375,
0.0056304931640625,
0.04266357421875,
-0.00887298583984375,
-0.046661376953125,
0.004878997802734375,
0.00405120849609375,
0.0146026611328125,
0.020294189453125,
0.0099945068359375,
0.0101470947265625,
0.036407470703125,
0.011199951171875,
-0.0005784034729003906,
-0.044830322265625,
-0.018035888671875,
0.01641845703125,
0.010284423828125,
-0.00629425048828125,
-0.0172271728515625,
0.003391265869140625,
0.0271148681640625,
0.0005235671997070312,
-0.0296783447265625,
0.006500244140625,
-0.01052093505859375,
0.0028743743896484375,
-0.01137542724609375,
0.00431060791015625,
0.01788330078125,
-0.002227783203125,
0.00591278076171875,
0.0019397735595703125,
-0.0197601318359375,
-0.0034885406494140625,
-0.01036834716796875,
0.00782012939453125,
-0.0235748291015625,
0.01244354248046875,
-0.01050567626953125,
0.00777435302734375,
0.005889892578125,
0.004451751708984375,
0.0007677078247070312,
0.00208282470703125,
-0.03125,
0.00672149658203125,
-0.03179931640625,
0.0126495361328125,
0.0113067626953125,
-0.00437164306640625,
-0.005126953125,
0.00807952880859375,
-0.0010652542114257812,
0.0184478759765625,
0.0013885498046875,
0.0027065277099609375,
-0.01047515869140625,
-0.0075225830078125,
-0.0036792755126953125,
-0.0132904052734375,
0.0311126708984375,
0.017364501953125,
0.054931640625,
0.0030536651611328125,
0.00333404541015625,
-0.00731658935546875,
-0.0166015625,
-0.01690673828125,
0.017669677734375,
0.0068511962890625,
-0.00841522216796875,
-0.00882720947265625,
-0.0009860992431640625,
0.0121002197265625,
0.004230499267578125,
-0.00815582275390625,
0.002323150634765625,
-0.01271820068359375,
-0.0020198822021484375,
0.0311126708984375,
0.01267242431640625,
-0.002826690673828125,
-0.00608062744140625,
-0.02740478515625,
-0.00030159950256347656,
-0.0220794677734375,
0.008514404296875,
-0.0271759033203125,
0.039154052734375,
-0.000713348388671875,
-0.00992584228515625,
-0.00942230224609375,
0.033599853515625,
-0.0084381103515625,
0.00908660888671875,
-0.0161895751953125,
0.003162384033203125,
-0.01108551025390625,
-0.0225982666015625,
-0.00983428955078125,
0.0020923614501953125,
-0.0020771026611328125,
-0.0181121826171875,
-0.01177978515625,
-0.039459228515625,
-0.003772735595703125,
0.0060577392578125,
0.01355743408203125,
0.0223846435546875,
-0.0010271072387695312,
0.00579833984375,
-0.006053924560546875,
0.02783203125,
0.0290069580078125,
0.0007872581481933594,
-0.01317596435546875,
0.0219879150390625,
-0.04327392578125,
0.01393890380859375,
-0.0236968994140625,
0.0161895751953125,
-0.0142364501953125,
0.0290679931640625,
-0.033294677734375,
0.01282501220703125,
0.039825439453125,
0.0015192031860351562,
0.048431396484375,
-0.0113983154296875,
-0.013702392578125,
-0.005184173583984375,
-0.005817413330078125,
-0.0217437744140625,
0.004230499267578125,
0.019195556640625,
0.00690460205078125,
0.021087646484375,
-0.01251983642578125,
-0.00750732421875,
0.0151824951171875,
-0.0050506591796875,
0.0301055908203125,
-0.0011386871337890625,
-0.0286865234375,
-0.00592041015625,
0.0061798095703125,
0.0196990966796875,
0.03057861328125,
0.0283660888671875,
0.0230560302734375,
-0.00006020069122314453,
0.055999755859375,
-0.053466796875,
0.0011777877807617188,
-0.040985107421875,
-0.0124053955078125,
-0.014495849609375,
0.005451202392578125,
-0.01427459716796875,
0.038482666015625,
-0.02325439453125,
0.00153350830078125,
-0.0196075439453125,
0.0105743408203125,
0.0279693603515625,
0.00592041015625,
0.005962371826171875,
0.01546478271484375,
0.01202392578125,
-0.00946044921875,
-0.000484466552734375,
0.03765869140625,
-0.0404052734375,
0.032867431640625,
0.0269775390625,
0.0160064697265625,
-0.0301513671875,
0.0018320083618164062,
-0.0131988525390625,
0.006549835205078125,
-0.005695343017578125,
-0.015625,
-0.007495880126953125,
0.01221466064453125,
-0.003658294677734375,
0.005443572998046875,
0.00357818603515625,
-0.0008597373962402344,
0.0233917236328125,
0.0137786865234375,
0.0009484291076660156,
-0.0248260498046875,
0.003997802734375,
0.004238128662109375,
-0.0076904296875,
-0.002269744873046875,
-0.0082244873046875,
-0.01113128662109375,
-0.00975799560546875,
-0.0012331008911132812,
-0.03314208984375,
-0.0051727294921875,
-0.00762176513671875,
0.028717041015625,
-0.0246734619140625,
0.029052734375,
-0.0260162353515625,
0.0257110595703125,
-0.0127410888671875,
-0.0281829833984375,
-0.007808685302734375,
-0.006290435791015625,
0.0169219970703125,
0.0104217529296875,
-0.0032253265380859375,
-0.01146697998046875,
0.03814697265625,
-0.014984130859375,
0.0005736351013183594,
-0.0126190185546875,
0.064453125,
-0.009185791015625,
-0.00811004638671875,
-0.0007996559143066406,
-0.0128936767578125,
-0.047515869140625,
0.0217742919921875,
-0.0274658203125,
-0.023651123046875,
-0.01302337646484375,
-0.01496124267578125,
-0.0098419189453125,
0.005340576171875,
0.02630615234375,
0.00673675537109375,
0.01033782958984375,
0.00421142578125,
0.00881195068359375,
-0.00507354736328125,
-0.0228271484375,
-0.015228271484375,
-0.01445770263671875,
-0.00975799560546875,
-0.0197296142578125,
-0.0014524459838867188,
-0.0282440185546875,
0.0197601318359375,
0.01453399658203125,
-0.0038318634033203125,
0.01297760009765625,
0.0159759521484375,
0.002857208251953125,
-0.00423431396484375,
-0.005985260009765625,
-0.02313232421875,
0.032684326171875,
-0.0245513916015625,
0.0175628662109375,
0.01157379150390625,
-0.0242462158203125,
-0.006847381591796875,
0.0274810791015625,
-0.004398345947265625,
-0.0260162353515625,
0.0053253173828125,
-0.008758544921875,
-0.01418304443359375,
0.021697998046875,
0.006343841552734375,
0.0252685546875,
-0.03668212890625,
-0.006198883056640625,
-0.01255035400390625,
0.0013599395751953125,
-0.008758544921875,
-0.02813720703125,
-0.0232391357421875,
0.0218963623046875,
0.01509857177734375,
-0.045074462890625,
-0.006557464599609375,
-0.035675048828125,
-0.02685546875,
0.01141357421875,
0.042694091796875,
-0.00628662109375,
-0.00933074951171875,
0.0118408203125,
-0.0011224746704101562,
0.002777099609375,
0.0234832763671875,
-0.0183258056640625,
-0.0071868896484375,
-0.0182647705078125,
-0.0010862350463867188,
0.01026153564453125,
-0.013397216796875,
0.01187896728515625,
0.027496337890625,
0.0310516357421875,
0.0032634735107421875,
-0.00414276123046875,
-0.0195770263671875,
0.0244293212890625,
-0.031097412109375,
0.0230865478515625,
0.01409912109375,
0.003692626953125,
0.00882720947265625,
-0.0014467239379882812,
-0.0194091796875,
-0.004299163818359375,
0.00836944580078125,
0.044281005859375,
-0.0245361328125,
-0.01263427734375,
-0.007335662841796875,
-0.006229400634765625,
0.020233154296875,
-0.0223236083984375,
-0.03277587890625,
0.0107879638671875,
-0.02813720703125,
-0.03521728515625,
-0.017578125,
0.0229644775390625,
-0.0108184814453125,
0.0118408203125,
0.00791168212890625,
-0.0038356781005859375,
0.00409698486328125,
-0.004306793212890625,
0.0074005126953125,
0.00189208984375,
0.00612640380859375,
-0.020263671875,
0.004688262939453125,
-0.01375579833984375,
0.0202178955078125,
-0.0159912109375,
-0.01261138916015625,
0.0233001708984375,
-0.0146636962890625,
0.0232391357421875,
-0.015045166015625,
-0.02001953125,
0.0089569091796875,
0.0132598876953125,
0.0294036865234375,
-0.02978515625,
-0.0288543701171875,
0.02691650390625,
0.0180206298828125,
-0.00838470458984375,
0.00559234619140625,
-0.0333251953125,
0.021575927734375,
0.02410888671875,
-0.0511474609375,
0.002574920654296875,
-0.007457733154296875,
0.02484130859375,
-0.035491943359375,
0.0023040771484375,
-0.00567626953125,
0.004291534423828125,
0.0083770751953125,
0.0108642578125,
0.006565093994140625,
-0.0204925537109375,
-0.04449462890625,
0.0287322998046875,
-0.00231170654296875,
0.0020771026611328125,
0.0073089599609375,
-0.018707275390625,
-0.034149169921875,
-0.0229034423828125,
0.0146636962890625,
0.01137542724609375,
-0.01462554931640625,
-0.036468505859375,
-0.002635955810546875,
0.022552490234375,
-0.035125732421875,
0.00844573974609375,
0.01082611083984375,
-0.00428009033203125,
-0.017974853515625,
0.0165557861328125,
-0.0222015380859375,
0.0010395050048828125,
-0.0037441253662109375,
-0.0020351409912109375,
-0.02984619140625,
0.00986480712890625,
0.0087432861328125,
0.0148162841796875,
-0.019073486328125,
0.01285552978515625,
-0.0183868408203125,
-0.00910186767578125,
0.01363372802734375,
0.032073974609375,
-0.0110931396484375,
0.018646240234375,
-0.02099609375,
-0.0015773773193359375,
-0.00894927978515625,
0.023162841796875,
0.012969970703125,
-0.0110321044921875,
-0.01189422607421875,
-0.0015058517456054688,
0.01497650146484375,
0.020965576171875,
0.01430511474609375,
-0.00847625732421875,
0.0102996826171875,
-0.007175445556640625,
0.004364013671875,
0.021331787109375,
-0.01132965087890625,
-0.020782470703125,
-0.018707275390625,
-0.03021240234375,
0.0172119140625,
0.0069580078125,
-0.00754547119140625,
0.028900146484375,
0.007381439208984375,
-0.008209228515625,
0.03448486328125,
-0.043853759765625,
0.00913238525390625,
-0.0008287429809570312,
0.067626953125,
-0.00884246826171875,
-0.00943756103515625,
-0.0186614990234375,
-0.0679931640625,
-0.045806884765625,
0.016937255859375,
0.027862548828125,
0.01158905029296875,
0.013458251953125,
0.0008707046508789062,
0.011016845703125,
-0.0030689239501953125,
-0.01302337646484375,
0.025482177734375,
0.002593994140625,
-0.0002758502960205078,
-0.00440216064453125,
0.0238800048828125,
0.0263519287109375,
-0.04132080078125,
0.013214111328125,
0.005023956298828125,
0.05487060546875,
0.01114654541015625,
-0.04010009765625,
-0.00568389892578125,
0.01464080810546875,
0.018035888671875,
-0.024566650390625,
-0.00988006591796875,
0.0204010009765625,
0.0004911422729492188,
-0.02313232421875,
-0.03973388671875,
0.003387451171875,
0.027313232421875,
-0.0008368492126464844,
-0.0137481689453125,
0.0219268798828125,
-0.005847930908203125,
-0.01053619384765625,
0.00948333740234375,
0.010406494140625,
0.0048370361328125,
-0.0249481201171875,
0.01519775390625,
-0.004993438720703125,
0.005126953125,
0.028839111328125,
-0.0242767333984375,
0.0007543563842773438,
-0.005901336669921875,
-0.033233642578125,
0.0181427001953125,
0.022796630859375,
0.0062408447265625,
-0.01078033447265625,
-0.02252197265625,
-0.00551605224609375,
0.0227813720703125,
-0.004467010498046875,
0.001125335693359375,
0.01094818115234375,
0.046966552734375,
0.006206512451171875,
0.005458831787109375,
-0.01177215576171875,
0.0270843505859375,
0.0010595321655273438,
0.01540374755859375,
-0.005390167236328125,
-0.011474609375,
-0.012298583984375,
-0.0013456344604492188,
0.0185089111328125,
-0.004711151123046875,
-0.02734375,
0.005764007568359375,
0.048126220703125,
-0.011077880859375,
0.000640869140625,
-0.0214996337890625,
-0.0123291015625,
-0.030029296875,
-0.026519775390625,
0.0005717277526855469,
0.0009131431579589844,
0.0265045166015625,
-0.0006227493286132812,
-0.0175018310546875,
-0.0010433197021484375,
-0.0018949508666992188,
-0.005054473876953125,
-0.028167724609375,
-0.0078125,
-0.01479339599609375,
-0.0404052734375,
-0.006763458251953125,
-0.0245208740234375,
-0.0164642333984375,
-0.005550384521484375,
0.03125,
-0.00902557373046875,
-0.0174407958984375,
0.03497314453125,
-0.007747650146484375,
-0.0217437744140625,
0.04498291015625,
-0.0260467529296875,
0.03289794921875,
-0.0162506103515625,
-0.04107666015625,
-0.012054443359375,
-0.004108428955078125,
0.01776123046875,
0.0074310302734375,
-0.01019287109375,
0.0084075927734375,
0.0284881591796875,
0.00710296630859375,
0.00820159912109375,
0.01313018798828125,
-0.054534912109375,
-0.01459503173828125,
0.00588226318359375,
0.011962890625,
0.022430419921875,
0.005645751953125,
-0.037322998046875,
-0.007495880126953125,
0.01265716552734375,
-0.0029888153076171875,
-0.0201416015625,
0.00982666015625,
0.0007715225219726562,
0.0265655517578125,
0.006866455078125,
-0.019256591796875,
-0.026885986328125,
-0.032623291015625,
0.0299072265625,
0.036834716796875,
0.0015344619750976562,
-0.01434326171875,
0.02215576171875,
-0.04425048828125,
-0.01302337646484375,
-0.0168304443359375,
-0.0218505859375,
0.029296875,
0.01422882080078125,
-0.00936126708984375,
0.01258087158203125,
0.01506805419921875,
0.0195159912109375,
-0.031158447265625,
-0.0137176513671875,
0.00876617431640625,
0.01861572265625,
0.000039577484130859375,
-0.0033359527587890625,
-0.038818359375,
-0.010040283203125,
0.0272369384765625,
-0.0283203125,
-0.03802490234375,
-0.0278472900390625,
-0.016204833984375,
0.01163482666015625,
-0.0163421630859375,
-0.0029354095458984375,
0.01448822021484375,
-0.032501220703125,
0.005886077880859375,
-0.002590179443359375,
0.029632568359375,
0.027008056640625,
-0.0010776519775390625,
-0.005245208740234375,
0.01227569580078125,
-0.0293731689453125,
0.0013399124145507812,
-0.0164947509765625,
-0.0254364013671875,
0.0246124267578125,
0.0132904052734375,
-0.01522064208984375,
-0.0119781494140625,
0.034515380859375,
-0.005970001220703125,
0.017669677734375,
-0.020904541015625,
-0.00428009033203125,
-0.01027679443359375,
0.00814056396484375,
0.03582763671875,
0.0178070068359375,
-0.0126800537109375,
-0.038177490234375,
0.005420684814453125,
0.00490570068359375,
-0.01800537109375,
-0.01540374755859375,
0.0284271240234375,
-0.01174163818359375,
-0.003582000732421875,
0.03582763671875,
0.005767822265625,
0.0147247314453125,
0.015106201171875,
0.01544189453125,
0.00788116455078125,
-0.00244140625,
-0.0193939208984375,
0.0174102783203125,
-0.0036106109619140625,
0.00469970703125,
-0.01232147216796875,
-0.01324462890625,
0.0084686279296875,
0.0070343017578125,
-0.003498077392578125,
0.004100799560546875,
-0.03521728515625,
-0.006717681884765625,
0.0190277099609375,
-0.009063720703125,
0.01531219482421875,
-0.0293426513671875,
-0.0021381378173828125,
-0.0274505615234375,
0.0205230712890625,
-0.0139312744140625,
-0.01102447509765625,
-0.007640838623046875,
-0.0224456787109375,
0.02764892578125,
0.0245208740234375,
0.0201263427734375,
0.00389862060546875,
0.0178680419921875,
0.018768310546875,
0.0020885467529296875,
0.0139617919921875,
0.004695892333984375,
0.002166748046875,
-0.01148223876953125,
-0.0019779205322265625,
0.004253387451171875,
0.047271728515625,
-0.0009984970092773438,
-0.0013675689697265625,
-0.002490997314453125,
-0.00034236907958984375,
-0.012969970703125,
-0.0284881591796875,
-0.01389312744140625,
0.054168701171875,
0.00791168212890625,
0.05926513671875,
0.0109405517578125,
0.025604248046875,
0.058441162109375,
0.0008220672607421875,
-0.0021915435791015625,
0.0224761962890625,
-0.0330810546875,
-0.0014963150024414062,
0.020355224609375,
-0.0207061767578125,
0.0130615234375,
0.015045166015625,
0.0147247314453125,
0.0087432861328125,
-0.0275115966796875,
0.02685546875,
0.024871826171875,
-0.003208160400390625,
-0.003482818603515625,
0.01251220703125,
-0.025299072265625,
-0.0008392333984375,
-0.0161590576171875,
-0.004512786865234375,
-0.0031948089599609375,
-0.01129913330078125,
0.0200958251953125,
-0.025115966796875,
0.005535125732421875,
-0.005786895751953125,
0.0003094673156738281,
-0.032073974609375,
-0.034423828125,
-0.0078887939453125,
0.0183258056640625,
-0.0208740234375,
0.02557373046875,
-0.01525115966796875,
-0.0061187744140625,
-0.01099395751953125,
-0.01424407958984375,
-0.0225982666015625,
0.032501220703125,
-0.0270538330078125,
0.02655029296875,
0.0193634033203125,
-0.01068115234375,
-0.02197265625,
-0.01102447509765625,
-0.00905609130859375,
0.0183868408203125,
0.02069091796875,
0.0188446044921875,
-0.0204315185546875,
-0.00040602684020996094,
-0.00004857778549194336,
0.017120361328125,
-0.004665374755859375,
-0.01641845703125,
-0.0034770965576171875,
-0.0226287841796875,
-0.0172576904296875,
-0.0215606689453125,
0.029144287109375,
0.0007719993591308594,
0.01456451416015625,
0.01446533203125,
-0.06646728515625,
0.00027871131896972656,
0.020477294921875,
-0.0138702392578125,
0.010711669921875,
0.02081298828125,
-0.035186767578125,
-0.00579071044921875,
0.00820159912109375,
0.020294189453125,
0.007740020751953125,
-0.008056640625,
-0.00983428955078125,
-0.0192413330078125,
0.0161590576171875,
-0.00937652587890625,
0.0162353515625,
-0.0237579345703125,
0.0033931732177734375,
-0.0157470703125,
-0.0031681060791015625,
-0.00969696044921875,
0.02886962890625,
0.0246429443359375,
0.0228424072265625,
0.0181121826171875,
-0.0200042724609375,
0.00785064697265625,
0.03155517578125,
0.03082275390625,
0.0166015625,
-0.0027751922607421875,
0.004390716552734375,
0.040985107421875,
-0.012451171875,
0.0092926025390625,
0.016082763671875,
-0.012664794921875,
-0.054229736328125,
-0.004222869873046875,
-0.002223968505859375,
-0.003894805908203125,
-0.0214080810546875,
0.0214385986328125,
0.0234527587890625,
-0.00975799560546875,
-0.04815673828125,
-0.0592041015625,
0.004535675048828125,
0.0230255126953125,
0.0019502639770507812,
0.0092315673828125,
0.018646240234375,
0.007671356201171875,
0.0113983154296875,
-0.0032138824462890625,
0.006160736083984375,
-0.016357421875,
0.0106353759765625,
-0.0064239501953125,
0.01523590087890625,
-0.0198211669921875,
0.039947509765625,
-0.037109375,
0.004058837890625,
0.005626678466796875,
0.0546875,
-0.024688720703125,
0.00775909423828125,
0.039947509765625,
-0.037506103515625,
-0.0166473388671875,
0.00033092498779296875,
0.0200347900390625,
-0.019256591796875,
0.00206756591796875,
-0.042694091796875,
0.0027713775634765625,
-0.035797119140625,
0.020538330078125,
0.01427459716796875,
-0.0027141571044921875,
0.020355224609375,
-0.0033416748046875,
-0.00850677490234375,
-0.0023059844970703125,
-0.02093505859375,
0.041900634765625,
0.0098724365234375,
-0.03314208984375,
0.0209808349609375,
-0.0213623046875,
0.01593017578125,
-0.022308349609375,
0.004291534423828125,
-0.0018835067749023438,
0.01399993896484375,
0.0025539398193359375,
-0.0435791015625,
0.006084442138671875,
0.00363922119140625,
-0.0206756591796875,
-0.0053558349609375,
0.01338958740234375,
0.0021381378173828125,
0.0182037353515625,
-0.01255035400390625,
0.0185394287109375,
0.007904052734375,
-0.0208282470703125,
-0.010406494140625,
0.01192474365234375,
-0.0390625,
0.00905609130859375,
-0.00844573974609375,
-0.0128021240234375,
-0.011627197265625,
0.024505615234375,
0.01006317138671875,
-0.0004055500030517578,
-0.03131103515625,
0.021240234375,
0.02685546875,
-0.00710296630859375,
0.0026531219482421875,
-0.01056671142578125,
0.005580902099609375,
0.0247955322265625,
0.00965118408203125,
-0.0228271484375,
0.007843017578125,
0.0131072998046875,
-0.008331298828125,
0.00787353515625,
-0.0386962890625,
0.0312347412109375,
-0.032440185546875,
-0.02044677734375,
-0.0065460205078125,
0.0295867919921875,
-0.045135498046875,
-0.0226593017578125,
0.0062103271484375,
0.0097808837890625,
0.0157470703125,
0.0188751220703125,
0.01502227783203125,
-0.035400390625,
-0.00820159912109375,
-0.0406494140625,
-0.0022640228271484375,
-0.0020961761474609375,
0.0123748779296875,
0.0086212158203125,
0.0244903564453125,
-0.0191192626953125,
0.00772857666015625,
-0.017578125,
-0.010345458984375,
0.001476287841796875,
-0.0179290771484375,
0.0026302337646484375,
0.0088958740234375,
0.008819580078125,
-0.021942138671875,
0.021759033203125,
0.0164337158203125,
-0.006343841552734375,
-0.02471923828125,
-0.001331329345703125,
0.004650115966796875,
0.01555633544921875,
0.0261383056640625,
-0.00579833984375,
-0.015716552734375,
-0.0047760009765625,
-0.002216339111328125,
-0.0079803466796875,
0.006565093994140625,
0.021697998046875,
0.00675201416015625,
0.032745361328125,
-0.0104217529296875,
-0.005710601806640625,
0.0099029541015625,
0.006298065185546875,
-0.01013946533203125,
0.021026611328125,
-0.005184173583984375,
0.00823974609375,
0.0079803466796875,
-0.005420684814453125,
0.02154541015625,
-0.00861358642578125,
-0.0014524459838867188,
0.0179443359375,
-0.003509521484375,
-0.042266845703125,
0.0028285980224609375,
0.0168304443359375,
-0.042449951171875,
-0.00887298583984375,
-0.01305389404296875,
0.0020313262939453125,
-0.00348663330078125,
-0.005802154541015625,
0.01491546630859375,
0.0187835693359375,
-0.038543701171875,
0.00960540771484375,
-0.02178955078125,
0.0180206298828125,
-0.025146484375,
-0.0219268798828125,
-0.00152587890625,
0.010498046875,
0.02545166015625,
0.01007843017578125,
0.0087738037109375,
-0.0272369384765625,
0.02392578125,
-0.007640838623046875,
0.019500732421875,
0.006229400634765625,
-0.0190582275390625,
0.041717529296875,
0.0017566680908203125,
-0.0067901611328125,
0.007762908935546875,
-0.0303497314453125,
0.012603759765625,
-0.0006628036499023438,
-0.020111083984375,
-0.01128387451171875,
0.0196380615234375,
-0.027496337890625,
-0.0064849853515625,
-0.027679443359375,
0.01116180419921875,
0.0455322265625,
0.01552581787109375,
-0.007354736328125,
-0.010711669921875,
-0.01318359375,
0.00019693374633789062,
-0.0218353271484375,
-0.0025424957275390625,
-0.031097412109375,
0.014892578125,
-0.04547119140625,
0.0281524658203125,
-0.002269744873046875,
0.0142669677734375,
-0.004123687744140625,
-0.0246124267578125,
0.006572723388671875,
-0.0428466796875,
-0.012054443359375,
-0.039154052734375,
0.00907135009765625,
-0.0318603515625,
-0.0240478515625,
-0.043792724609375,
-0.004180908203125,
0.044097900390625,
0.02679443359375,
-0.0276947021484375,
0.013916015625,
-0.0110015869140625,
-0.0419921875,
0.006679534912109375,
0.0224151611328125,
0.01081085205078125,
-0.003147125244140625,
0.0245361328125,
-0.01306915283203125,
0.0070953369140625,
-0.03192138671875,
-0.002277374267578125,
0.01152801513671875,
0.0289154052734375,
-0.0213470458984375,
0.0199127197265625,
0.0006809234619140625,
-0.00732421875,
0.005947113037109375,
-0.010711669921875,
0.011627197265625,
0.0005106925964355469,
-0.038604736328125,
-0.0169677734375,
-0.020172119140625,
-0.035003662109375,
0.01125335693359375,
0.022247314453125,
0.0159454345703125,
-0.01349639892578125,
-0.02947998046875,
-0.00829315185546875,
-0.00823211669921875,
0.01104736328125,
0.017608642578125,
0.0001214742660522461,
-0.0012464523315429688,
-0.02423095703125,
-0.0313720703125,
-0.0196685791015625,
0.041351318359375,
0.004627227783203125,
0.01190948486328125,
0.000009894371032714844,
-0.004367828369140625,
0.0209503173828125,
0.007709503173828125,
0.0018796920776367188,
-0.0193634033203125,
-0.0058441162109375,
-0.01067352294921875,
-0.00200653076171875,
0.00907135009765625,
-0.00952911376953125,
-0.01522064208984375,
0.006305694580078125,
0.00452423095703125,
-0.0020313262939453125,
-0.00904083251953125,
0.006378173828125,
-0.0135345458984375,
0.006572723388671875,
0.006542205810546875,
-0.0013942718505859375,
0.0306396484375,
-0.008880615234375,
-0.00643157958984375,
-0.027099609375,
-0.031341552734375,
-0.03948974609375,
-0.0261383056640625,
-0.01071929931640625,
-0.01253509521484375,
0.023040771484375,
0.01155853271484375,
0.0016460418701171875,
-0.02880859375,
0.009185791015625,
0.00359344482421875,
0.01241302490234375,
-0.0124359130859375,
0.00746917724609375,
-0.0185546875,
-0.024993896484375,
0.009765625,
0.01849365234375,
0.0038471221923828125,
0.00856781005859375,
-0.0223236083984375,
-0.0016946792602539062,
-0.00974273681640625,
-0.016632080078125,
0.005756378173828125,
0.0328369140625,
0.0056915283203125,
-0.020538330078125,
-0.044219970703125,
0.025726318359375,
-0.018096923828125,
-0.0192413330078125,
0.01548004150390625,
0.020233154296875,
-0.005451202392578125,
0.005413055419921875,
-0.010284423828125,
0.0286865234375,
-0.01139068603515625,
-0.0132598876953125,
-0.01059722900390625,
-0.018951416015625,
0.0029754638671875,
-0.01006317138671875,
-0.001392364501953125,
-0.033538818359375,
0.0408935546875,
0.0045318603515625,
0.029144287109375,
0.0128173828125,
-0.0048370361328125,
0.0114898681640625,
-0.01043701171875,
-0.00901031494140625,
0.01104736328125,
-0.0248260498046875,
-0.012237548828125,
0.01291656494140625,
0.0005097389221191406,
0.032806396484375,
-0.01708984375,
-0.01140594482421875,
-0.02093505859375,
-0.0133056640625,
0.0206146240234375,
-0.01508331298828125,
-0.01091766357421875,
0.021514892578125,
0.041473388671875,
-0.023162841796875,
-0.01146697998046875,
0.0216217041015625,
-0.02490234375,
0.0079803466796875,
0.028289794921875,
-0.0260009765625,
-0.00850677490234375,
0.0028057098388671875,
0.0260162353515625,
-0.040008544921875,
0.0009813308715820312,
0.0098114013671875,
0.0188446044921875,
0.01171112060546875,
-0.01145172119140625,
-0.01483154296875,
0.001834869384765625,
0.02593994140625,
0.0125274658203125,
-0.0179901123046875,
-0.01416778564453125,
0.01197052001953125,
-0.0026073455810546875,
-0.032501220703125,
0.0272369384765625,
-0.010955810546875,
0.00875091552734375,
0.04071044921875,
-0.004741668701171875,
-0.0084228515625,
-0.006336212158203125,
-0.0019407272338867188,
-0.01294708251953125,
0.0041351318359375,
-0.014068603515625,
0.007740020751953125,
0.01180267333984375,
0.036590576171875,
0.0269012451171875,
-0.01244354248046875,
0.0197296142578125,
0.006320953369140625,
-0.011932373046875,
-0.0012578964233398438,
-0.0274200439453125,
-0.0038585662841796875,
0.025177001953125,
-0.006000518798828125,
0.0024662017822265625,
0.0010023117065429688,
0.0015087127685546875,
-0.032073974609375,
-0.00168609619140625,
-0.01239013671875,
0.0129241943359375,
-0.03460693359375,
0.00777435302734375,
0.0218658447265625,
0.0005259513854980469,
0.0028133392333984375,
0.0222015380859375,
-0.0228424072265625,
-0.003631591796875,
0.00011080503463745117,
0.01134490966796875,
-0.01538848876953125,
-0.0210113525390625,
-0.00527191162109375,
-0.0178375244140625,
0.0021228790283203125,
-0.013916015625,
0.0004413127899169922,
0.025360107421875,
0.01395416259765625,
-0.0088348388671875,
-0.007236480712890625,
0.0014591217041015625,
0.00846099853515625,
-0.0184173583984375,
0.01259613037109375,
-0.0192108154296875,
-0.005893707275390625,
0.0179290771484375,
-0.00592803955078125,
-0.01739501953125,
-0.038482666015625,
-0.0201873779296875,
0.03973388671875,
0.010650634765625,
0.010955810546875,
-0.005069732666015625,
0.00725555419921875,
-0.0218658447265625,
-0.00844573974609375,
-0.03619384765625,
-0.016021728515625,
-0.01934814453125,
0.033477783203125,
0.0173797607421875,
0.05767822265625,
-0.0195159912109375,
-0.0142669677734375,
-0.00856781005859375,
-0.040679931640625,
-0.00901031494140625,
-0.03363037109375,
-0.035552978515625,
0.0097808837890625,
-0.01016998291015625,
0.011138916015625,
0.0114288330078125,
-0.0025501251220703125,
-0.01139068603515625,
0.01200103759765625,
0.017578125,
-0.0034313201904296875,
0.03424072265625,
0.0080718994140625,
-0.0230712890625,
-0.0124664306640625,
0.045745849609375,
-0.0006475448608398438,
-0.0203857421875,
-0.041015625,
0.0164642333984375,
0.0032215118408203125,
0.0694580078125,
-0.00008416175842285156,
-0.0098724365234375,
-0.001819610595703125,
0.01186370849609375,
0.01404571533203125,
-0.0380859375,
0.02105712890625,
0.0108642578125,
-0.0086822509765625,
-0.00006878376007080078,
-0.0038204193115234375,
0.0048370361328125,
-0.0222320556640625,
0.0082855224609375,
0.036834716796875,
-0.007678985595703125,
0.0067901611328125,
-0.0237579345703125,
-0.0186309814453125,
-0.0044403076171875,
0.004306793212890625,
-0.034912109375,
-0.01033782958984375,
-0.02850341796875,
-0.00469207763671875,
0.010986328125,
0.02764892578125,
0.0179901123046875,
-0.00609588623046875,
0.020477294921875,
0.013763427734375,
-0.0096282958984375,
0.0070953369140625,
0.006195068359375,
-0.023468017578125,
-0.01111602783203125,
-0.01039886474609375,
-0.012908935546875,
-0.003997802734375,
0.0186920166015625,
-0.01296234130859375,
0.02880859375,
0.017242431640625,
0.0231170654296875,
-0.00556182861328125,
-0.00588226318359375,
0.01515960693359375,
-0.0025196075439453125,
-0.0102691650390625,
0.0217437744140625,
-0.01424407958984375,
-0.0216522216796875,
-0.00222015380859375,
0.051544189453125,
0.016876220703125,
-0.0144195556640625,
-0.00431060791015625,
0.039642333984375,
-0.016937255859375,
-0.006160736083984375,
-0.0024318695068359375,
0.0151824951171875,
-0.0150604248046875,
-0.0020694732666015625,
0.007785797119140625,
-0.0007562637329101562,
-0.00926971435546875,
0.021392822265625,
0.0178375244140625,
0.0158538818359375,
-0.0189666748046875,
0.00933074951171875,
-0.00524139404296875,
-0.0179443359375,
0.0171356201171875,
-0.0016536712646484375,
0.0194091796875,
-0.00600433349609375,
0.01187896728515625,
-0.004756927490234375,
-0.0228271484375,
0.01181793212890625,
0.0025310516357421875,
0.030029296875,
0.026763916015625,
-0.01477813720703125,
0.003978729248046875,
0.02923583984375,
-0.00766754150390625,
-0.0013341903686523438,
-0.004673004150390625,
-0.0006394386291503906,
-0.000007331371307373047,
-0.0156402587890625,
0.00457000732421875,
-0.00008684396743774414,
-0.0014972686767578125,
0.01078033447265625,
0.0158233642578125,
0.0229644775390625,
-0.017974853515625,
0.0081329345703125,
-0.01107025146484375,
-0.00913238525390625,
0.0295562744140625,
-0.003147125244140625,
-0.037872314453125,
-0.0124969482421875,
0.0167083740234375,
0.0192718505859375,
-0.00037407875061035156,
-0.0031375885009765625,
-0.026763916015625,
0.007778167724609375,
-0.01050567626953125,
-0.0002849102020263672,
0.0008249282836914062,
0.034515380859375,
-0.02886962890625,
-0.0043182373046875,
-0.0054931640625,
-0.0122528076171875,
0.003787994384765625,
0.00402069091796875,
0.0014705657958984375,
0.008636474609375,
-0.003650665283203125,
-0.0160675048828125,
0.004974365234375,
-0.0028057098388671875,
0.005046844482421875,
-0.0210113525390625,
-0.005489349365234375,
-0.03179931640625,
-0.0132293701171875,
-0.0216217041015625,
0.015106201171875,
-0.01071929931640625,
0.03045654296875,
-0.01509857177734375,
-0.0004494190216064453,
0.01617431640625,
0.0250396728515625,
0.010772705078125,
-0.00946807861328125,
-0.0057830810546875,
0.0615234375,
-0.003742218017578125,
0.0022068023681640625,
-0.032745361328125,
0.0014314651489257812,
0.02008056640625,
0.002826690673828125,
-0.034759521484375,
0.00864410400390625,
0.005084991455078125,
0.015045166015625,
-0.00807952880859375,
0.00927734375,
0.0238800048828125,
-0.0435791015625,
-0.02001953125,
0.00968170166015625,
0.03338623046875,
-0.026947021484375,
-0.0024871826171875,
-0.0010204315185546875,
-0.0223846435546875,
-0.0010938644409179688,
-0.042999267578125,
0.01079559326171875,
0.006076812744140625,
-0.001964569091796875,
0.00909423828125,
0.013824462890625,
-0.033203125,
0.014373779296875,
-0.00875091552734375,
-0.0011854171752929688,
0.005413055419921875,
-0.0032558441162109375,
-0.031494140625,
0.0164642333984375,
0.0009489059448242188,
0.00934600830078125,
0.0119476318359375,
0.0010309219360351562,
-0.00698089599609375,
0.0294952392578125,
0.002208709716796875,
0.0039520263671875,
-0.006969451904296875,
0.034759521484375,
-0.0015506744384765625,
-0.01690673828125,
0.0093231201171875,
-0.038421630859375,
-0.02178955078125,
0.00890350341796875,
0.009979248046875,
-0.0313720703125,
-0.019989013671875,
-0.011505126953125,
0.027069091796875,
-0.01088714599609375,
-0.01004791259765625,
0.029052734375,
-0.037261962890625,
-0.0026493072509765625,
0.034698486328125,
-0.0457763671875,
-0.000040531158447265625,
0.0164947509765625,
-0.0161285400390625,
0.023681640625,
-0.00992584228515625,
0.0203857421875,
0.0008678436279296875,
0.00513458251953125,
0.00913238525390625,
-0.0103759765625,
0.0357666015625,
0.0305938720703125,
0.005214691162109375,
0.01265716552734375,
-0.005340576171875,
0.000148773193359375,
-0.03167724609375,
-0.0205078125,
-0.0235748291015625,
0.00792694091796875,
0.0129241943359375,
0.005527496337890625,
-0.003467559814453125,
-0.0208282470703125,
0.0159759521484375,
0.02581787109375,
-0.0030879974365234375,
-0.032135009765625,
0.002796173095703125,
-0.017486572265625,
0.016448974609375,
-0.0028362274169921875,
0.00032830238342285156,
-0.0249176025390625,
-0.024017333984375,
-0.01137542724609375,
0.003002166748046875,
-0.0325927734375,
0.01445770263671875,
0.0192718505859375,
-0.00860595703125,
-0.0198516845703125,
-0.0191192626953125,
0.015625,
0.00995635986328125,
-0.01264190673828125,
0.036468505859375,
0.0214691162109375,
-0.0262298583984375,
0.03033447265625,
-0.0283660888671875,
0.006259918212890625,
0.0044403076171875,
-0.036407470703125,
0.0037250518798828125,
0.007476806640625,
-0.0028285980224609375,
-0.00998687744140625,
-0.020721435546875,
-0.0169219970703125,
-0.0079803466796875,
-0.0078887939453125,
-0.01343536376953125,
-0.00428009033203125,
0.007480621337890625,
0.005504608154296875,
-0.052337646484375,
0.031158447265625,
-0.01140594482421875,
-0.04376220703125,
-0.01354217529296875,
-0.0263671875,
-0.0007266998291015625,
-0.0181884765625,
0.00531005859375,
0.00574493408203125,
-0.0100555419921875,
-0.0128631591796875,
-0.018951416015625,
0.014129638671875,
-0.02435302734375,
-0.039276123046875,
-0.01337432861328125,
-0.003719329833984375,
0.0145721435546875,
0.0262603759765625,
-0.004314422607421875,
0.01947021484375,
0.028228759765625,
-0.029449462890625,
0.0164031982421875,
0.017547607421875,
0.013275146484375,
0.005733489990234375,
0.0170440673828125,
0.01474761962890625,
-0.03369140625,
0.0164337158203125,
0.00038051605224609375,
0.01021575927734375,
-0.0022430419921875,
-0.02227783203125,
0.0115814208984375,
0.004123687744140625,
-0.049774169921875,
-0.002384185791015625,
0.00013434886932373047,
-0.01081085205078125,
-0.004116058349609375,
-0.00852203369140625,
-0.00698089599609375,
-0.01174163818359375,
0.002166748046875,
-0.022735595703125,
0.003917694091796875,
-0.02276611328125,
0.01525115966796875,
-0.0019702911376953125,
-0.0025234222412109375,
0.01271820068359375,
0.0009379386901855469,
-0.03289794921875,
-0.046295166015625,
0.0028972625732421875,
-0.01290130615234375,
0.01427459716796875,
-0.012237548828125,
-0.0179290771484375,
0.00620269775390625,
-0.01345062255859375,
-0.029449462890625,
0.0350341796875,
-0.0131072998046875,
0.0033359527587890625,
0.030609130859375,
-0.004932403564453125,
0.0017156600952148438,
-0.01727294921875,
-0.034149169921875,
0.0268402099609375,
0.045013427734375,
0.00316619873046875,
0.0167236328125,
-0.0266876220703125,
0.036956787109375,
0.00896453857421875,
0.0139312744140625,
-0.0308074951171875,
-0.02203369140625,
0.0036869049072265625,
0.0029449462890625,
0.0163421630859375,
0.01084136962890625,
0.0160369873046875,
0.0007505416870117188,
0.0013103485107421875,
0.0169525146484375,
-0.00006413459777832031,
-0.01091766357421875,
-0.0157623291015625,
-0.02392578125,
0.0171966552734375,
-0.0033931732177734375,
0.03253173828125,
0.043212890625,
-0.006572723388671875,
-0.021148681640625,
0.042755126953125,
-0.00012886524200439453,
-0.020477294921875,
0.031585693359375,
-0.003856658935546875,
0.03265380859375,
0.005870819091796875,
-0.01093292236328125,
-0.0030765533447265625,
-0.018310546875,
0.01593017578125,
-0.003917694091796875,
0.0026073455810546875,
-0.0105438232421875,
0.007160186767578125,
-0.00850677490234375,
0.01727294921875,
-0.0238189697265625,
0.0275115966796875,
-0.0306396484375,
-0.0136871337890625,
0.003925323486328125,
-0.003353118896484375,
0.0140228271484375,
0.0087432861328125,
0.031463623046875,
0.01519775390625,
0.01375579833984375,
-0.010894775390625,
0.038787841796875,
0.0034809112548828125,
0.01039886474609375,
0.01410675048828125,
0.014373779296875,
0.00824737548828125,
0.010284423828125,
0.0127716064453125,
-0.00556182861328125,
0.00630950927734375,
0.0235595703125,
-0.0011758804321289062,
0.008148193359375,
0.031097412109375,
0.004901885986328125,
-0.01617431640625,
-0.0015869140625,
-0.01458740234375,
0.01702880859375,
-0.00701904296875,
0.003475189208984375,
-0.0018529891967773438,
0.01273345947265625,
-0.00519561767578125,
0.03277587890625,
-0.01010894775390625,
-0.0002448558807373047,
0.0178375244140625,
0.0048675537109375,
-0.0308837890625,
0.0295867919921875,
-0.002216339111328125,
-0.028228759765625,
-0.03387451171875,
0.0173797607421875,
0.01363372802734375,
0.003490447998046875,
0.007099151611328125,
-0.0265655517578125,
0.0005807876586914062,
-0.0200042724609375,
-0.0060882568359375,
0.01555633544921875,
-0.0127716064453125,
-0.0122528076171875,
-0.0191192626953125,
0.006778717041015625,
-0.0023670196533203125,
-0.0108795166015625,
0.002838134765625,
0.029754638671875,
0.0018787384033203125,
-0.0082550048828125,
-0.00229644775390625,
0.01296234130859375,
0.0031070709228515625,
-0.027130126953125,
-0.007312774658203125,
0.044036865234375,
-0.00923919677734375,
-0.0179290771484375,
-0.005870819091796875,
-0.0012054443359375,
-0.01058197021484375,
-0.00733184814453125,
-0.00537109375,
0.00469970703125,
-0.0190277099609375,
0.01065826416015625,
-0.01141357421875,
-0.0270233154296875,
-0.06243896484375,
-0.027740478515625,
-0.0101318359375,
-0.022613525390625,
0.0073394775390625,
-0.0193634033203125,
0.032806396484375,
0.01091766357421875,
0.0303955078125,
-0.0115966796875,
0.001705169677734375,
-0.01491546630859375,
-0.030517578125,
-0.033050537109375,
0.034820556640625,
-0.0340576171875,
-0.01206207275390625,
0.001506805419921875,
-0.0169830322265625,
0.0194549560546875,
0.0240325927734375,
0.015899658203125,
0.03558349609375,
-0.0175628662109375,
-0.00662994384765625,
0.027923583984375,
-0.00396728515625,
-0.0210418701171875,
-0.02471923828125,
-0.0372314453125,
-0.0003070831298828125,
0.01357269287109375,
0.014434814453125,
-0.0108184814453125,
0.00353240966796875,
-0.00106048583984375,
0.0190887451171875,
0.04559326171875,
-0.012054443359375,
-0.0222015380859375,
-0.029632568359375,
0.01078033447265625,
0.005962371826171875,
-0.000025153160095214844,
0.015167236328125,
-0.0055999755859375,
0.0225067138671875,
-0.0208892822265625,
-0.0291595458984375,
0.00998687744140625,
0.025726318359375,
0.01317596435546875,
-0.0156707763671875,
-0.00040411949157714844,
-0.00037384033203125,
-0.0103607177734375,
-0.004558563232421875,
-0.0288543701171875,
-0.00878143310546875,
-0.043548583984375,
0.004669189453125,
0.0034656524658203125,
0.0205841064453125,
-0.0118408203125,
0.0165557861328125,
-0.0101318359375,
0.038726806640625,
0.0249481201171875,
-0.01080322265625,
-0.01617431640625,
0.01055908203125,
-0.003261566162109375,
-0.01255035400390625,
0.0118408203125,
-0.0101318359375,
0.03131103515625,
0.00635528564453125,
0.0080718994140625,
0.0056304931640625,
0.00838470458984375,
0.0072784423828125,
0.0086669921875,
0.006015777587890625,
-0.019287109375,
-0.0003037452697753906,
0.015106201171875,
-0.027374267578125,
0.0263214111328125,
-0.03802490234375,
-0.020843505859375,
-0.0044708251953125,
-0.01201629638671875,
0.0189361572265625,
-0.0003066062927246094,
0.062347412109375,
-0.0083465576171875,
0.00009238719940185547,
-0.02679443359375,
0.009918212890625,
0.01806640625,
-0.0029544830322265625,
0.0088958740234375,
-0.00914764404296875,
0.022125244140625,
0.007488250732421875,
0.002048492431640625,
0.007251739501953125,
-0.0010919570922851562,
-0.004009246826171875,
0.00406646728515625,
0.0240478515625,
-0.02166748046875,
-0.0185089111328125,
0.0201873779296875,
-0.0236358642578125,
-0.029144287109375,
-0.0276031494140625,
0.00994110107421875,
-0.0345458984375,
-0.015869140625,
-0.01861572265625,
0.020050048828125,
0.0188751220703125,
0.010589599609375,
-0.004085540771484375,
-0.047454833984375,
0.002292633056640625,
0.017425537109375,
-0.01375579833984375,
0.0194091796875,
0.0172271728515625,
0.0124969482421875,
-0.0038318634033203125,
-0.00724029541015625,
0.005489349365234375,
0.0242462158203125,
-0.00885772705078125,
0.0247344970703125,
-0.01336669921875,
-0.0184326171875,
-0.006610870361328125,
-0.00931549072265625,
-0.01483154296875,
-0.000274658203125,
0.001499176025390625,
0.02996826171875,
0.025146484375,
0.01708984375,
-0.01448822021484375,
-0.0165557861328125,
0.0015325546264648438,
0.026947021484375,
0.0131683349609375,
0.01189422607421875,
0.031280517578125,
-0.0251922607421875,
0.0034961700439453125,
0.00351715087890625,
-0.0214080810546875,
-0.01177215576171875,
0.0192413330078125,
-0.00640106201171875,
-0.00643157958984375,
-0.02020263671875,
-0.016754150390625,
-0.0206146240234375,
-0.02044677734375,
-0.0049285888671875,
0.0231170654296875,
0.010528564453125,
0.0170135498046875,
-0.00847625732421875,
-0.008453369140625,
0.00036144256591796875,
0.0215911865234375,
0.01534271240234375,
0.01031494140625,
0.00716400146484375,
-0.00457763671875,
0.01092529296875,
-0.01263427734375,
-0.02496337890625,
-0.008270263671875,
0.0012903213500976562,
0.0455322265625,
-0.00627899169921875,
-0.023406982421875,
0.0217742919921875,
-0.017852783203125,
0.033721923828125,
0.01215362548828125,
-0.021331787109375,
0.0030975341796875,
0.0318603515625,
0.052947998046875,
0.031280517578125,
0.026824951171875,
0.0096435546875,
-0.0211029052734375,
0.01026153564453125,
-0.02947998046875,
-0.0116119384765625,
-0.01702880859375,
-0.0002739429473876953,
-0.00341033935546875,
0.026519775390625,
-0.00891876220703125,
0.01055145263671875,
0.024871826171875,
-0.035125732421875,
0.0278167724609375,
-0.044158935546875,
0.02532958984375,
-0.012725830078125,
-0.030609130859375,
0.0304107666015625,
-0.01194000244140625,
0.005779266357421875,
-0.0010309219360351562,
0.0126190185546875,
-0.03021240234375,
0.00008022785186767578,
-0.0034084320068359375,
-0.0152740478515625,
-0.01763916015625,
0.00782012939453125,
0.018035888671875,
-0.006622314453125,
-0.0196990966796875,
0.01416015625,
-0.048675537109375,
0.01947021484375,
-0.00943756103515625,
-0.00408935546875,
-0.01430511474609375,
0.003292083740234375,
0.01727294921875,
-0.020660400390625,
-0.0293121337890625,
0.01291656494140625,
0.01430511474609375,
-0.0179901123046875,
-0.0166473388671875,
0.0233001708984375,
-0.00499725341796875,
-0.0275421142578125,
-0.0087738037109375,
-0.0057373046875,
-0.005748748779296875,
0.019439697265625,
-0.0017347335815429688,
-0.0245361328125,
0.0009489059448242188,
-0.00820159912109375,
0.028656005859375,
0.012847900390625,
0.00433349609375,
0.008514404296875,
-0.03363037109375,
-0.01097869873046875,
-0.0170135498046875,
0.01506805419921875,
0.0046234130859375,
-0.02496337890625,
0.0310821533203125,
-0.005611419677734375,
0.052886962890625,
0.0004534721374511719,
0.0014429092407226562,
-0.035186767578125,
0.015869140625,
-0.043304443359375,
-0.01336669921875,
0.0162811279296875,
-0.00399017333984375,
0.02734375,
-0.0010423660278320312,
-0.01271820068359375,
-0.00482177734375,
-0.01471710205078125,
0.031890869140625,
0.00853729248046875,
0.0301513671875,
0.006298065185546875,
-0.01076507568359375,
0.0208740234375,
0.005870819091796875,
-0.0114288330078125,
-0.028411865234375,
0.0011806488037109375,
-0.03076171875,
-0.00789642333984375,
-0.0031032562255859375,
0.0128021240234375,
0.002986907958984375,
0.05224609375,
-0.01219940185546875,
0.0267486572265625,
0.0176239013671875,
-0.0073089599609375,
-0.042449951171875,
-0.00429534912109375,
0.0198516845703125,
0.00225830078125,
0.01010894775390625,
-0.0038604736328125,
-0.00728607177734375,
0.0155487060546875,
0.01348876953125,
0.005260467529296875,
-0.0029201507568359375,
0.01284027099609375,
0.005889892578125,
0.0019512176513671875,
0.0006690025329589844,
-0.0094757080078125,
-0.037933349609375,
-0.01174163818359375,
0.0079803466796875,
-0.00736236572265625,
0.0130767822265625,
-0.01296234130859375,
-0.01195526123046875,
0.005481719970703125,
0.0036373138427734375,
-0.0032291412353515625,
0.0021514892578125,
-0.01099395751953125,
-0.01410675048828125,
0.02716064453125,
-0.0089111328125,
-0.00812530517578125,
0.034515380859375,
0.0205535888671875,
0.0111541748046875,
0.003955841064453125,
0.0219268798828125,
0.00946044921875,
0.003719329833984375,
0.026519775390625,
0.01416778564453125,
-0.01146697998046875,
-0.01800537109375,
0.016021728515625,
0.02880859375,
0.006710052490234375,
0.035430908203125,
-0.00525665283203125,
0.0428466796875,
0.035186767578125,
0.01113128662109375,
0.0298919677734375,
0.0126953125,
-0.0021209716796875,
-0.043121337890625,
-0.02227783203125,
-0.000843048095703125,
0.01523590087890625,
-0.0203094482421875,
0.0056610107421875,
0.00714874267578125,
-0.0006847381591796875,
-0.0304412841796875,
-0.0227203369140625,
-0.00545501708984375,
-0.001979827880859375,
0.0506591796875,
-0.0390625,
-0.027862548828125,
0.0020809173583984375,
-0.015960693359375,
-0.004547119140625,
-0.0213165283203125,
0.007274627685546875,
-0.0036296844482421875,
0.004451751708984375,
0.0350341796875,
0.00030612945556640625,
0.03802490234375,
-0.04736328125,
0.0256500244140625,
-0.006755828857421875,
-0.0108184814453125,
-0.018646240234375,
0.013275146484375,
-0.001926422119140625,
-0.0161590576171875,
0.0174713134765625,
-0.0447998046875,
0.0216064453125,
-0.00907135009765625,
-0.018157958984375,
-0.00397491455078125,
-0.01129913330078125,
0.0036525726318359375,
-0.0037212371826171875,
-0.00494384765625,
-0.00933837890625,
-0.00276947021484375,
-0.0133209228515625,
0.009429931640625,
0.02288818359375,
-0.0033550262451171875,
-0.0220947265625,
-0.03326416015625,
-0.015655517578125,
0.01372528076171875,
0.020263671875,
0.0234527587890625,
0.006561279296875,
-0.0007281303405761719,
0.01345062255859375,
-0.0213775634765625,
0.00937652587890625,
0.057403564453125,
0.028289794921875,
-0.0108489990234375,
0.002643585205078125,
0.0035915374755859375,
0.007793426513671875,
-0.0164031982421875,
-0.03009033203125,
-0.0102996826171875,
0.01129150390625,
0.0187530517578125,
0.00042128562927246094,
-0.0194549560546875,
0.033721923828125,
0.021148681640625,
0.031707763671875,
-0.01617431640625,
0.007720947265625,
-0.011993408203125,
-0.006626129150390625,
0.03924560546875,
0.0130462646484375,
0.006927490234375,
0.01025390625,
0.01038360595703125,
-0.00437164306640625,
-0.01666259765625,
-0.00820159912109375,
0.0275421142578125,
-0.013671875,
-0.007266998291015625,
-0.006870269775390625,
0.003704071044921875,
-0.00433349609375,
0.013916015625,
0.0297698974609375,
-0.0029087066650390625,
-0.005512237548828125,
-0.022796630859375,
0.0018072128295898438,
0.01324462890625,
0.0016231536865234375,
0.0098724365234375,
-0.0158233642578125,
-0.031768798828125,
0.00337982177734375,
-0.0274505615234375,
0.011566162109375,
0.0204925537109375,
0.0034618377685546875,
-0.015625,
0.0191192626953125,
0.0111236572265625,
-0.01161956787109375,
0.0245361328125,
0.00725555419921875,
0.005191802978515625,
0.01448822021484375,
0.03240966796875,
0.0053558349609375,
0.0032863616943359375,
0.01451873779296875,
-0.0220947265625,
-0.0007610321044921875,
0.05767822265625,
0.023590087890625,
0.048004150390625,
0.0013570785522460938,
-0.0294036865234375,
0.0031490325927734375,
-0.003475189208984375,
0.0173797607421875,
-0.04583740234375,
-0.00983428955078125,
0.0252685546875,
-0.00182342529296875,
0.018218994140625,
0.003047943115234375,
-0.021087646484375,
0.031341552734375,
-0.00658416748046875,
-0.00014472007751464844,
0.00699615478515625,
0.021728515625,
0.005878448486328125,
-0.0160369873046875,
-0.018218994140625,
-0.00940704345703125,
0.0135650634765625,
0.0239715576171875,
-0.0143585205078125,
0.0077667236328125,
-0.045166015625,
-0.0021381378173828125,
-0.01258087158203125,
0.018310546875,
0.01519775390625,
0.003131866455078125,
-0.0031871795654296875,
-0.02642822265625,
-0.002193450927734375,
0.006786346435546875,
-0.004665374755859375,
-0.00695037841796875,
0.0094451904296875,
0.0180816650390625,
-0.01346588134765625,
0.00838470458984375,
-0.048370361328125,
-0.01125335693359375,
0.029083251953125,
0.048583984375,
0.01348876953125,
0.027801513671875,
0.02362060546875,
0.0122833251953125,
0.013336181640625,
-0.005832672119140625,
-0.0068511962890625,
-0.026123046875,
0.0172576904296875,
0.00022792816162109375,
0.0109100341796875,
-0.01036834716796875,
0.0090179443359375,
-0.004337310791015625,
0.0021495819091796875,
-0.01474761962890625,
0.01435089111328125,
-0.0097198486328125,
-0.018310546875,
0.01337432861328125,
0.01483917236328125,
0.047515869140625,
0.0187530517578125,
-0.0095672607421875,
-0.00933837890625,
0.00027370452880859375,
0.0179443359375,
0.031341552734375,
0.0279388427734375,
-0.004913330078125,
0.0018177032470703125,
0.01503753662109375,
0.00783538818359375,
0.004131317138671875,
0.0024852752685546875,
0.016815185546875,
-0.0268096923828125,
0.028564453125,
-0.00908660888671875,
-0.033447265625,
-0.0012454986572265625,
0.023681640625,
-0.026641845703125,
-0.00836181640625,
-0.00017130374908447266,
-0.040496826171875,
-0.0242767333984375,
0.0123748779296875,
0.006069183349609375,
0.036834716796875,
0.00946044921875,
-0.0078125,
0.0253143310546875,
0.01215362548828125,
-0.062255859375,
-0.01232147216796875,
-0.0024166107177734375,
0.00089263916015625,
0.025390625,
-0.029937744140625,
0.020416259765625,
0.006786346435546875,
0.026397705078125,
0.0478515625,
0.008392333984375,
0.004825592041015625,
0.01258087158203125,
-0.01428985595703125,
-0.036224365234375,
-0.0225982666015625,
0.031524658203125,
0.005138397216796875,
-0.023834228515625,
0.01091766357421875,
-0.027496337890625,
-0.007701873779296875,
0.04034423828125,
0.0170135498046875,
-0.007293701171875,
0.0103302001953125,
-0.016571044921875,
-0.0159454345703125
] |
ours_533
|
The answer is \(4474\).
There are \(2\) one-digit lucky numbers: \(4\) and \(7\). There are \(4\) two-digit lucky numbers: \(44, 47, 74, 77\). There are \(8\) three-digit lucky numbers: \(444, 447, 474, 477, 744, 747, 774, 777\). Thus, we need the 3rd smallest four-digit lucky number. Listing them, we have: \(4444, 4447, 4474, 4477, \ldots\). Therefore, the 17th smallest lucky number is \(4474\).
\(\boxed{4474}\)
|
4474
|
{
"competition": "us_comps",
"dataset": "Ours",
"posts": null,
"source": "OMOSoln2.md"
}
|
A lucky number is a positive number whose digits are only \(4\) or \(7\). What is the 17th smallest lucky number?
|
[
"/Mathematics/DiscreteMathematics/Combinatorics/Enumeration",
"/Mathematics/DiscreteMathematics/Combinatorics/GeneralCombinatorics",
"/Mathematics/DiscreteMathematics/GeneralDiscreteMathematics/DiscreteMath",
"/Mathematics/DiscreteMathematics/GeneralDiscreteMathematics/DiscreteMathematics",
"/Mathematics/DiscreteMathematics/GeneralDiscreteMathematics/FiniteMathematics",
"/Mathematics/NumberTheory/Sequences/IntegerSequence",
"/Mathematics/NumberTheory/Sequences/Sequence",
"/Mathematics/RecreationalMathematics/Puzzles/Puzzle"
] |
Count lucky numbers by digit length using powers of 2 to locate the rank’s length, then pick the appropriate number in that block.
|
[
0.0003123283386230469,
-0.026123046875,
0.04547119140625,
-0.005115509033203125,
0.0014219284057617188,
0.027740478515625,
0.044464111328125,
-0.01519012451171875,
0.02032470703125,
-0.0262298583984375,
0.00868988037109375,
-0.0419921875,
-0.00002110004425048828,
-0.020172119140625,
-0.029937744140625,
-0.0023365020751953125,
0.0190277099609375,
0.017822265625,
-0.021820068359375,
-0.00223541259765625,
-0.01531982421875,
-0.050506591796875,
0.00415802001953125,
0.023223876953125,
-0.048370361328125,
-0.01251983642578125,
-0.019134521484375,
-0.00727081298828125,
0.03436279296875,
0.00502777099609375,
-0.01739501953125,
0.005878448486328125,
0.0478515625,
-0.03192138671875,
-0.00458526611328125,
0.0128631591796875,
0.0033931732177734375,
0.002765655517578125,
-0.0460205078125,
-0.024658203125,
0.00991058349609375,
0.0253448486328125,
0.0008487701416015625,
-0.004093170166015625,
-0.0455322265625,
0.0030670166015625,
-0.0091552734375,
0.00820159912109375,
-0.015167236328125,
-0.0266876220703125,
0.0018863677978515625,
0.004505157470703125,
-0.020782470703125,
-0.0074920654296875,
-0.034912109375,
-0.043548583984375,
0.02313232421875,
0.00641632080078125,
-0.030120849609375,
0.00909423828125,
-0.005237579345703125,
-0.0250244140625,
-0.042022705078125,
0.0001710653305053711,
0.00012230873107910156,
-0.01166534423828125,
0.020721435546875,
-0.0184783935546875,
0.021453857421875,
-0.01227569580078125,
-0.0304412841796875,
0.00528717041015625,
-0.0318603515625,
0.018035888671875,
0.0201873779296875,
-0.00580596923828125,
-0.0080718994140625,
0.00861358642578125,
-0.01399993896484375,
0.01482391357421875,
0.0184173583984375,
0.01015472412109375,
0.00445556640625,
0.0208282470703125,
-0.004711151123046875,
-0.00830841064453125,
0.041259765625,
0.01033782958984375,
0.048095703125,
-0.00539398193359375,
-0.00646209716796875,
0.016998291015625,
0.0199432373046875,
-0.00882720947265625,
-0.006061553955078125,
-0.00449371337890625,
0.0029010772705078125,
-0.01122283935546875,
-0.01055145263671875,
0.00492095947265625,
-0.0080718994140625,
-0.00969696044921875,
0.0244903564453125,
0.0037689208984375,
-0.0272369384765625,
-0.00406646728515625,
-0.0279388427734375,
-0.00884246826171875,
-0.01537322998046875,
0.030975341796875,
0.00682830810546875,
0.0091705322265625,
0.0447998046875,
0.00960540771484375,
0.006572723388671875,
-0.0017156600952148438,
0.0196990966796875,
0.0177001953125,
-0.027252197265625,
-0.03369140625,
-0.0013113021850585938,
-0.0083770751953125,
-0.016998291015625,
-0.00431060791015625,
-0.00015115737915039062,
-0.03118896484375,
-0.01221466064453125,
-0.005340576171875,
-0.0207977294921875,
0.0145416259765625,
0.0126190185546875,
-0.01561737060546875,
-0.044281005859375,
0.005496978759765625,
-0.0352783203125,
0.003704071044921875,
-0.022430419921875,
-0.017608642578125,
0.004291534423828125,
0.00872802734375,
-0.007480621337890625,
0.01003265380859375,
-0.00772857666015625,
0.02728271484375,
-0.0377197265625,
0.03033447265625,
0.0266571044921875,
-0.050628662109375,
0.01666259765625,
-0.0227813720703125,
0.00937652587890625,
-0.0094146728515625,
0.00363922119140625,
0.01381683349609375,
-0.01265716552734375,
0.0239105224609375,
0.02239990234375,
-0.00045990943908691406,
-0.0137786865234375,
0.02728271484375,
0.01372528076171875,
0.004421234130859375,
0.003787994384765625,
0.0364990234375,
0.0018949508666992188,
0.0028133392333984375,
0.0088653564453125,
0.0009102821350097656,
-0.01959228515625,
-0.0014753341674804688,
-0.00589752197265625,
-0.011932373046875,
-0.0143280029296875,
-0.01519012451171875,
-0.0036945343017578125,
-0.0145721435546875,
-0.00481414794921875,
0.00600433349609375,
-0.004535675048828125,
0.017181396484375,
-0.00974273681640625,
-0.042144775390625,
0.0450439453125,
-0.0032444000244140625,
-0.00047850608825683594,
-0.02081298828125,
0.0045928955078125,
0.0009326934814453125,
0.003936767578125,
-0.00756072998046875,
0.031524658203125,
-0.0457763671875,
-0.01629638671875,
-0.0015611648559570312,
-0.0155487060546875,
-0.03375244140625,
-0.004940032958984375,
0.00868988037109375,
0.017547607421875,
-0.0028228759765625,
-0.004108428955078125,
0.0186920166015625,
-0.0211944580078125,
0.00426483154296875,
0.0100860595703125,
0.002643585205078125,
-0.0289306640625,
0.00008797645568847656,
0.01776123046875,
0.00988006591796875,
-0.0103302001953125,
-0.01493072509765625,
-0.0234222412109375,
0.004974365234375,
-0.021331787109375,
0.0091705322265625,
-0.0099029541015625,
-0.0142364501953125,
0.026275634765625,
-0.02227783203125,
-0.0042877197265625,
-0.007080078125,
-0.00661468505859375,
0.0172882080078125,
-0.029296875,
-0.0014257431030273438,
0.012054443359375,
0.0003802776336669922,
0.0087432861328125,
0.0209197998046875,
0.0047760009765625,
0.00469207763671875,
-0.00850677490234375,
0.001621246337890625,
0.0008387565612792969,
-0.0018358230590820312,
0.00727081298828125,
-0.0114898681640625,
0.0226593017578125,
-0.0204925537109375,
0.060821533203125,
-0.017181396484375,
0.013397216796875,
-0.004302978515625,
0.0018472671508789062,
-0.0113677978515625,
-0.0152587890625,
-0.0161895751953125,
0.025299072265625,
-0.00333404541015625,
-0.0028228759765625,
0.0195465087890625,
-0.0004477500915527344,
-0.0166168212890625,
0.0118560791015625,
-0.0072174072265625,
-0.004314422607421875,
0.004909515380859375,
-0.01459503173828125,
0.004077911376953125,
-0.01491546630859375,
-0.040802001953125,
-0.025421142578125,
-0.0089874267578125,
-0.0087127685546875,
-0.0031280517578125,
-0.0114898681640625,
0.003711700439453125,
0.0008902549743652344,
0.007415771484375,
-0.0021266937255859375,
0.006542205810546875,
-0.029205322265625,
0.01544952392578125,
0.035614013671875,
-0.0189361572265625,
-0.0002524852752685547,
0.0007786750793457031,
0.004108428955078125,
0.012176513671875,
-0.00286865234375,
-0.007049560546875,
-0.0016298294067382812,
-0.0017871856689453125,
-0.0183868408203125,
-0.006389617919921875,
0.0006427764892578125,
-0.0247039794921875,
-0.0172119140625,
0.009063720703125,
0.00470733642578125,
0.012237548828125,
-0.0057525634765625,
-0.0088958740234375,
0.0279998779296875,
-0.053192138671875,
0.0219879150390625,
0.00200653076171875,
0.0189361572265625,
-0.007476806640625,
0.01275634765625,
0.0212249755859375,
-0.00945281982421875,
-0.0027980804443359375,
0.005962371826171875,
0.0250396728515625,
0.0006999969482421875,
0.00682830810546875,
-0.032867431640625,
-0.01258087158203125,
0.0014667510986328125,
-0.01383209228515625,
0.006175994873046875,
-0.0150604248046875,
0.01129150390625,
-0.061004638671875,
0.005558013916015625,
0.012481689453125,
-0.0213165283203125,
-0.002349853515625,
0.01232147216796875,
-0.01291656494140625,
-0.0243377685546875,
-0.004638671875,
-0.022369384765625,
0.018585205078125,
0.0310211181640625,
0.019256591796875,
-0.004436492919921875,
0.0234832763671875,
0.000008165836334228516,
0.00769805908203125,
0.0054168701171875,
-0.0267181396484375,
0.0045166015625,
0.00308990478515625,
-0.00414276123046875,
0.0115966796875,
-0.0239105224609375,
0.02764892578125,
0.0251312255859375,
0.0256500244140625,
-0.016998291015625,
0.024078369140625,
-0.01806640625,
0.0290374755859375,
-0.038970947265625,
-0.00962066650390625,
-0.039794921875,
-0.03204345703125,
-0.0217742919921875,
0.0197296142578125,
0.0257720947265625,
-0.01287841796875,
-0.03790283203125,
0.02105712890625,
-0.004547119140625,
-0.007297515869140625,
0.021148681640625,
0.018524169921875,
-0.00838470458984375,
-0.0234222412109375,
-0.0216827392578125,
-0.01068115234375,
0.01287841796875,
-0.0109405517578125,
0.002361297607421875,
0.0280609130859375,
-0.0091552734375,
0.0010290145874023438,
-0.01812744140625,
-0.055694580078125,
0.0190582275390625,
-0.0078887939453125,
-0.035400390625,
0.0038051605224609375,
-0.004215240478515625,
-0.007671356201171875,
-0.00797271728515625,
-0.005218505859375,
0.01081085205078125,
0.0204010009765625,
-0.007068634033203125,
0.0181427001953125,
0.0015230178833007812,
0.0009765625,
0.0188751220703125,
-0.0372314453125,
-0.015625,
0.0264892578125,
-0.004764556884765625,
-0.0094146728515625,
0.00958251953125,
0.00786590576171875,
0.017059326171875,
-0.0284576416015625,
0.0132293701171875,
0.029144287109375,
0.03790283203125,
0.004886627197265625,
0.003292083740234375,
-0.017059326171875,
-0.008514404296875,
0.0195159912109375,
-0.01300048828125,
-0.016998291015625,
-0.00119781494140625,
0.010467529296875,
-0.009002685546875,
-0.004619598388671875,
-0.0196990966796875,
0.0014753341674804688,
0.002178192138671875,
0.020782470703125,
-0.0224609375,
0.0008411407470703125,
-0.005565643310546875,
-0.016387939453125,
-0.053375244140625,
-0.0053558349609375,
0.02740478515625,
-0.0135040283203125,
-0.024871826171875,
-0.00659942626953125,
0.01329803466796875,
0.03656005859375,
-0.0217132568359375,
0.030364990234375,
0.0187225341796875,
-0.01136016845703125,
-0.001232147216796875,
0.0282135009765625,
0.0007548332214355469,
0.036041259765625,
0.004642486572265625,
0.0038318634033203125,
0.00331878662109375,
-0.0002875328063964844,
-0.01181793212890625,
0.00823211669921875,
-0.0111236572265625,
-0.0175628662109375,
0.01468658447265625,
-0.0189666748046875,
-0.01103973388671875,
0.00524139404296875,
-0.005100250244140625,
0.007633209228515625,
0.01153564453125,
0.0191650390625,
-0.0180206298828125,
-0.00977325439453125,
-0.03826904296875,
-0.0302276611328125,
-0.034942626953125,
-0.00749969482421875,
0.0161285400390625,
0.0019311904907226562,
-0.02301025390625,
-0.01776123046875,
-0.025238037109375,
-0.006488800048828125,
0.006092071533203125,
-0.01398468017578125,
-0.0004818439483642578,
0.008880615234375,
0.00005340576171875,
-0.01264190673828125,
-0.039459228515625,
0.005695343017578125,
-0.0063323974609375,
-0.0186920166015625,
-0.0214080810546875,
-0.01416778564453125,
-0.007171630859375,
0.050537109375,
-0.00170135498046875,
0.0143280029296875,
0.002471923828125,
0.0022106170654296875,
0.0074920654296875,
0.0279693603515625,
0.0052947998046875,
0.03900146484375,
-0.01515960693359375,
0.034576416015625,
0.0215301513671875,
-0.018829345703125,
-0.0069580078125,
-0.003204345703125,
0.051727294921875,
-0.001819610595703125,
-0.0251617431640625,
-0.03826904296875,
-0.00046706199645996094,
-0.036407470703125,
-0.0203857421875,
-0.0030002593994140625,
-0.0065155029296875,
0.00832366943359375,
-0.0175628662109375,
-0.0208892822265625,
-0.011749267578125,
0.01171875,
-0.0226593017578125,
0.0025119781494140625,
0.0196380615234375,
-0.0478515625,
-0.003879547119140625,
0.0079193115234375,
0.05865478515625,
0.0124053955078125,
0.03662109375,
-0.044189453125,
0.004550933837890625,
-0.0166015625,
0.01393890380859375,
-0.029815673828125,
-0.00299835205078125,
0.00084686279296875,
-0.0173492431640625,
-0.00420379638671875,
0.049835205078125,
-0.0047760009765625,
-0.0104827880859375,
0.03546142578125,
0.0335693359375,
-0.0267486572265625,
-0.01392364501953125,
0.022979736328125,
-0.0294342041015625,
-0.0175933837890625,
-0.0030059814453125,
-0.00382232666015625,
-0.005878448486328125,
0.00887298583984375,
-0.0003705024719238281,
-0.0008435249328613281,
-0.0213470458984375,
-0.027130126953125,
-0.00624847412109375,
-0.0069732666015625,
0.01763916015625,
0.00030231475830078125,
-0.0227813720703125,
-0.005878448486328125,
0.031280517578125,
0.0192718505859375,
-0.0274200439453125,
0.02496337890625,
-0.0011425018310546875,
0.020111083984375,
0.0170745849609375,
0.0103302001953125,
-0.0302734375,
0.03509521484375,
0.03936767578125,
-0.005596160888671875,
0.0175933837890625,
-0.004322052001953125,
0.0009093284606933594,
-0.0199432373046875,
-0.004749298095703125,
0.01561737060546875,
0.00673675537109375,
0.003429412841796875,
0.005268096923828125,
0.003337860107421875,
0.00963592529296875,
-0.034515380859375,
-0.011138916015625,
0.0256805419921875,
0.00888824462890625,
-0.03131103515625,
-0.035552978515625,
-0.0279541015625,
-0.052001953125,
0.007251739501953125,
0.0005898475646972656,
-0.0217437744140625,
0.0204315185546875,
0.01904296875,
-0.0179595947265625,
0.00262451171875,
-0.00868988037109375,
0.00955963134765625,
0.02935791015625,
0.0174102783203125,
0.0138092041015625,
-0.01580810546875,
-0.0277252197265625,
0.0164794921875,
0.0082855224609375,
0.020538330078125,
-0.00881195068359375,
-0.0208282470703125,
0.0213470458984375,
-0.017730712890625,
0.027862548828125,
0.0081634521484375,
0.03472900390625,
-0.0222625732421875,
0.03497314453125,
0.0287933349609375,
0.0019254684448242188,
0.00627899169921875,
-0.00307464599609375,
0.047515869140625,
-0.01113128662109375,
-0.01457977294921875,
0.03582763671875,
0.002918243408203125,
-0.00128173828125,
0.025146484375,
0.0202484130859375,
0.00736236572265625,
-0.024444580078125,
-0.0261688232421875,
-0.00495147705078125,
0.01419830322265625,
-0.0307159423828125,
-0.046539306640625,
0.013824462890625,
0.051239013671875,
-0.007434844970703125,
-0.0237274169921875,
0.0255889892578125,
-0.0048675537109375,
0.0045623779296875,
-0.0235748291015625,
-0.0146942138671875,
0.01416778564453125,
0.0161285400390625,
-0.0215606689453125,
-0.006855010986328125,
-0.0169219970703125,
-0.02044677734375,
0.01027679443359375,
0.0037670135498046875,
-0.01279449462890625,
-0.006500244140625,
0.0285797119140625,
0.00907135009765625,
-0.0089874267578125,
-0.00402069091796875,
0.0252838134765625,
-0.041748046875,
0.028076171875,
0.0017538070678710938,
-0.00998687744140625,
-0.0061187744140625,
0.0234375,
-0.0162506103515625,
0.00858306884765625,
-0.00551605224609375,
-0.0289764404296875,
-0.0023956298828125,
0.0213470458984375,
0.0084686279296875,
-0.02362060546875,
0.00003045797348022461,
0.036102294921875,
-0.00875091552734375,
0.0276641845703125,
-0.03369140625,
-0.0265960693359375,
0.002559661865234375,
0.007770538330078125,
0.040924072265625,
-0.0172882080078125,
-0.012664794921875,
-0.01715087890625,
0.00484466552734375,
-0.00897216796875,
0.047210693359375,
-0.0302276611328125,
-0.01126861572265625,
-0.01537322998046875,
-0.0014657974243164062,
-0.01546478271484375,
-0.0035533905029296875,
0.0272674560546875,
0.01006317138671875,
-0.00417327880859375,
0.0299835205078125,
0.0216522216796875,
0.0107879638671875,
-0.039642333984375,
-0.0008487701416015625,
0.041839599609375,
-0.01488494873046875,
-0.01068115234375,
0.021575927734375,
0.0322265625,
0.0186004638671875,
0.00292205810546875,
0.00457763671875,
-0.013641357421875,
-0.04339599609375,
0.01184844970703125,
0.009918212890625,
0.0017671585083007812,
-0.0259246826171875,
-0.0182952880859375,
-0.00531005859375,
-0.028472900390625,
-0.002902984619140625,
-0.01010894775390625,
-0.03692626953125,
0.014495849609375,
0.02239990234375,
0.016021728515625,
-0.0055694580078125,
0.00119781494140625,
0.0157012939453125,
-0.01239013671875,
-0.03076171875,
-0.029754638671875,
-0.006927490234375,
-0.0169525146484375,
-0.023193359375,
0.02294921875,
-0.037353515625,
-0.002269744873046875,
0.027435302734375,
0.0069732666015625,
-0.02911376953125,
-0.0316162109375,
-0.052093505859375,
0.00681304931640625,
-0.01251983642578125,
0.009521484375,
-0.012481689453125,
0.002819061279296875,
-0.01192474365234375,
-0.0005383491516113281,
0.0204010009765625,
-0.01044464111328125,
0.016265869140625,
0.001590728759765625,
0.0018835067749023438,
-0.003345489501953125,
0.01143646240234375,
-0.0047607421875,
0.0165252685546875,
0.0110931396484375,
0.005603790283203125,
0.006084442138671875,
0.004322052001953125,
0.0014333724975585938,
-0.016510009765625,
-0.01113128662109375,
0.0157623291015625,
-0.043853759765625,
-0.01560211181640625,
0.008148193359375,
0.0024280548095703125,
0.01062774658203125,
0.005828857421875,
0.005893707275390625,
-0.0235137939453125,
0.00421905517578125,
-0.0226593017578125,
-0.020965576171875,
0.0203857421875,
0.00655364990234375,
-0.053192138671875,
0.0146636962890625,
-0.0192413330078125,
0.029388427734375,
-0.032501220703125,
0.0225372314453125,
0.016204833984375,
0.01934814453125,
0.0266876220703125,
-0.00518798828125,
-0.0379638671875,
-0.0122833251953125,
0.029205322265625,
-0.0245513916015625,
0.01326751708984375,
0.00899505615234375,
0.0029850006103515625,
0.01416015625,
-0.0241241455078125,
0.018707275390625,
-0.01134490966796875,
-0.020660400390625,
0.019805908203125,
-0.0098724365234375,
0.0276031494140625,
0.037811279296875,
-0.0158233642578125,
-0.0142364501953125,
0.00714111328125,
0.0145416259765625,
-0.0063629150390625,
-0.005992889404296875,
-0.017913818359375,
-0.0134735107421875,
-0.02178955078125,
0.0264129638671875,
0.03240966796875,
0.039031982421875,
-0.00977325439453125,
-0.0205230712890625,
0.025787353515625,
0.0142822265625,
-0.01555633544921875,
0.02960205078125,
0.040863037109375,
-0.0153350830078125,
0.0256195068359375,
-0.004505157470703125,
0.0205535888671875,
-0.0279693603515625,
0.01593017578125,
-0.033538818359375,
0.023101806640625,
-0.01739501953125,
0.03472900390625,
0.02392578125,
-0.031402587890625,
0.0089874267578125,
0.0003833770751953125,
-0.00493621826171875,
-0.0019588470458984375,
-0.047943115234375,
-0.0013589859008789062,
-0.0133209228515625,
0.01031494140625,
0.0261688232421875,
-0.0291748046875,
0.01059722900390625,
-0.0164337158203125,
-0.0102691650390625,
0.01293182373046875,
0.01068115234375,
-0.0286407470703125,
-0.00737762451171875,
-0.0035457611083984375,
0.014068603515625,
0.01114654541015625,
-0.03582763671875,
0.0005211830139160156,
0.005382537841796875,
-0.025543212890625,
-0.0116119384765625,
-0.039886474609375,
0.005779266357421875,
0.039398193359375,
-0.006015777587890625,
0.01320648193359375,
-0.01297760009765625,
0.0206756591796875,
0.0088348388671875,
0.0182342529296875,
-0.00644683837890625,
0.029296875,
-0.0364990234375,
-0.01479339599609375,
-0.023468017578125,
-0.02862548828125,
-0.015960693359375,
0.01294708251953125,
-0.0123138427734375,
0.0023479461669921875,
-0.01355743408203125,
0.005229949951171875,
-0.001613616943359375,
-0.00283050537109375,
-0.0218505859375,
-0.00311279296875,
0.003498077392578125,
0.0269775390625,
-0.0011205673217773438,
0.0067596435546875,
-0.0084991455078125,
0.019073486328125,
-0.0264434814453125,
0.044830322265625,
-0.0301513671875,
0.0011224746704101562,
0.0253753662109375,
-0.0235137939453125,
0.01270294189453125,
-0.0117034912109375,
0.020660400390625,
0.0265045166015625,
-0.028472900390625,
0.00942230224609375,
-0.026885986328125,
-0.01436614990234375,
-0.0088958740234375,
0.0102081298828125,
-0.01302337646484375,
-0.020233154296875,
0.00003415346145629883,
-0.003253936767578125,
-0.014312744140625,
-0.02117919921875,
-0.0137939453125,
-0.02008056640625,
0.00865936279296875,
0.032928466796875,
-0.02294921875,
0.0015172958374023438,
-0.02874755859375,
-0.0213470458984375,
0.0157928466796875,
-0.05023193359375,
0.004764556884765625,
0.023101806640625,
0.0203094482421875,
-0.034942626953125,
-0.01279449462890625,
0.009124755859375,
-0.0189666748046875,
0.005886077880859375,
-0.03778076171875,
0.003765106201171875,
-0.01355743408203125,
-0.01229095458984375,
-0.00948333740234375,
0.0258026123046875,
-0.0379638671875,
0.0152740478515625,
-0.00278472900390625,
-0.0033931732177734375,
0.00891876220703125,
-0.038116455078125,
-0.0030155181884765625,
-0.0009412765502929688,
0.04150390625,
0.020111083984375,
0.022125244140625,
0.032012939453125,
0.0160369873046875,
0.0382080078125,
0.0205230712890625,
-0.0242156982421875,
-0.00222015380859375,
-0.007099151611328125,
0.0311431884765625,
-0.022705078125,
0.01560211181640625,
-0.008026123046875,
-0.0261993408203125,
-0.027557373046875,
-0.00530242919921875,
-0.025787353515625,
0.022705078125,
-0.031280517578125,
-0.0214080810546875,
-0.01317596435546875,
-0.0080413818359375,
0.013671875,
-0.059814453125,
-0.0037288665771484375,
-0.0194854736328125,
0.01294708251953125,
-0.007488250732421875,
-0.045806884765625,
-0.0277252197265625,
0.007465362548828125,
0.0125579833984375,
0.01340484619140625,
-0.0212554931640625,
0.00875091552734375,
-0.0015163421630859375,
0.0022907257080078125,
-0.032073974609375,
0.0182952880859375,
-0.0205841064453125,
-0.00569915771484375,
0.039306640625,
-0.037353515625,
0.03033447265625,
0.01070404052734375,
0.01776123046875,
-0.0220184326171875,
0.0010814666748046875,
-0.0187835693359375,
0.0177459716796875,
-0.01494598388671875,
0.004703521728515625,
-0.0098876953125,
-0.017913818359375,
0.00164031982421875,
-0.024871826171875,
-0.0400390625,
0.032440185546875,
-0.004467010498046875,
0.0233001708984375,
0.00305938720703125,
0.0245361328125,
-0.014923095703125,
0.00499725341796875,
0.006137847900390625,
0.0260009765625,
0.017852783203125,
-0.0171661376953125,
-0.0040130615234375,
0.02978515625,
0.01383209228515625,
-0.02239990234375,
0.0335693359375,
-0.01300048828125,
0.048370361328125,
-0.015594482421875,
0.029449462890625,
-0.008331298828125,
0.0204925537109375,
-0.0245513916015625,
-0.006923675537109375,
0.032379150390625,
0.01165008544921875,
-0.0231781005859375,
-0.037628173828125,
0.0504150390625,
-0.002979278564453125,
0.004062652587890625,
-0.0272064208984375,
-0.00911712646484375,
0.017608642578125,
-0.0246734619140625,
-0.0262298583984375,
-0.009796142578125,
-0.0169525146484375,
0.014862060546875,
-0.00678253173828125,
-0.0018720626831054688,
0.036163330078125,
0.003780364990234375,
0.00862884521484375,
0.00640106201171875,
-0.01018524169921875,
0.0146331787109375,
0.002635955810546875,
0.0243377685546875,
-0.006565093994140625,
0.007762908935546875,
0.01236724853515625,
-0.038665771484375,
0.0062713623046875,
-0.014190673828125,
-0.016204833984375,
-0.00357818603515625,
-0.0009565353393554688,
-0.001644134521484375,
-0.00551605224609375,
-0.01084136962890625,
-0.02655029296875,
-0.021331787109375,
-0.03631591796875,
0.0036754608154296875,
-0.0116424560546875,
-0.007633209228515625,
0.016021728515625,
0.046234130859375,
0.0277557373046875,
0.005855560302734375,
0.002285003662109375,
-0.016571044921875,
-0.00229644775390625,
-0.00988006591796875,
-0.02392578125,
0.003940582275390625,
0.0007176399230957031,
0.03466796875,
-0.01389312744140625,
0.004009246826171875,
-0.0024242401123046875,
-0.0101776123046875,
-0.0024356842041015625,
0.0165863037109375,
0.005764007568359375,
-0.016021728515625,
0.002223968505859375,
0.00756072998046875,
-0.0022983551025390625,
-0.00464630126953125,
-0.02252197265625,
-0.01396942138671875,
0.01354217529296875,
0.031890869140625,
-0.018524169921875,
0.021087646484375,
-0.0189208984375,
0.036041259765625,
0.00794219970703125,
0.0208587646484375,
-0.019775390625,
0.016632080078125,
0.00490570068359375,
-0.0288238525390625,
-0.020111083984375,
0.04638671875,
-0.00971221923828125,
-0.0241241455078125,
-0.00457000732421875,
0.0185394287109375,
0.006214141845703125,
-0.018890380859375,
-0.01465606689453125,
0.0008640289306640625,
-0.008819580078125,
0.0146484375,
0.01259613037109375,
-0.0168914794921875,
-0.016571044921875,
0.01922607421875,
0.01136016845703125,
0.0181732177734375,
-0.0017261505126953125,
-0.00743865966796875,
-0.03497314453125,
-0.00957489013671875,
0.0198974609375,
-0.00873565673828125,
0.0057830810546875,
0.0221405029296875,
-0.017669677734375,
0.0309600830078125,
0.000057220458984375,
0.01141357421875,
0.0390625,
0.00878143310546875,
0.031341552734375,
0.0202789306640625,
-0.0181732177734375,
0.011688232421875,
0.0159912109375,
-0.016937255859375,
-0.0027618408203125,
0.00946044921875,
-0.006061553955078125,
0.005153656005859375,
0.01351165771484375,
-0.009613037109375,
-0.0199432373046875,
-0.0164642333984375,
-0.0259857177734375,
0.012115478515625,
-0.00926971435546875,
-0.008056640625,
-0.005401611328125,
-0.016845703125,
0.0311126708984375,
0.01155853271484375,
-0.0009317398071289062,
0.02490234375,
-0.0257110595703125,
-0.006275177001953125,
0.00968170166015625,
-0.01233673095703125,
0.0094451904296875,
-0.00041866302490234375,
0.04669189453125,
-0.011016845703125,
-0.032928466796875,
-0.0276336669921875,
-0.021759033203125,
-0.0081329345703125,
-0.0292205810546875,
0.0012807846069335938,
-0.018890380859375,
-0.017303466796875,
-0.0259857177734375,
0.0169677734375,
-0.020233154296875,
-0.039459228515625,
0.023040771484375,
-0.0019245147705078125,
0.004764556884765625,
0.01251983642578125,
0.01861572265625,
-0.01519775390625,
-0.01168060302734375,
-0.0019969940185546875,
0.0010938644409179688,
0.0128326416015625,
0.01312255859375,
-0.0032958984375,
-0.0179901123046875,
0.010711669921875,
0.03887939453125,
-0.0162811279296875,
-0.0006303787231445312,
0.004871368408203125,
0.021240234375,
-0.0184326171875,
-0.01181793212890625,
-0.001861572265625,
0.0017261505126953125,
0.006328582763671875,
-0.03155517578125,
0.0145721435546875,
-0.0121002197265625,
-0.01226806640625,
-0.0180206298828125,
0.036285400390625,
-0.05804443359375,
-0.00200653076171875,
0.005573272705078125,
0.009857177734375,
0.031829833984375,
0.022613525390625,
-0.0033664703369140625,
-0.002841949462890625,
0.006763458251953125,
0.00787353515625,
-0.00997161865234375,
-0.018280029296875,
0.038330078125,
-0.020660400390625,
-0.006183624267578125,
-0.017913818359375,
-0.0225677490234375,
-0.021728515625,
-0.014434814453125,
0.005184173583984375,
0.052947998046875,
-0.00839996337890625,
-0.0020904541015625,
-0.01934814453125,
-0.01422119140625,
0.0270538330078125,
0.004978179931640625,
0.01806640625,
0.0263824462890625,
-0.0051116943359375,
-0.0457763671875,
0.03900146484375,
-0.0120086669921875,
-0.00873565673828125,
-0.002117156982421875,
0.0032501220703125,
0.0182037353515625,
0.005382537841796875,
-0.00193023681640625,
0.0340576171875,
0.014801025390625,
0.004993438720703125,
0.00514984130859375,
-0.022735595703125,
-0.03472900390625,
0.005397796630859375,
-0.0009217262268066406,
-0.004840850830078125,
-0.00707244873046875,
-0.00830078125,
-0.016876220703125,
-0.0178375244140625,
-0.00005650520324707031,
-0.01052093505859375,
0.0189208984375,
-0.0004982948303222656,
-0.030487060546875,
0.01727294921875,
-0.007110595703125,
-0.00820159912109375,
-0.031402587890625,
-0.0009179115295410156,
0.007305145263671875,
-0.01021575927734375,
-0.0034160614013671875,
-0.0006380081176757812,
-0.0242919921875,
0.006229400634765625,
-0.0008373260498046875,
0.0202178955078125,
0.0032672882080078125,
0.0250091552734375,
-0.016571044921875,
-0.0018758773803710938,
0.00775909423828125,
-0.04498291015625,
-0.0121002197265625,
-0.03448486328125,
-0.0263519287109375,
-0.0007052421569824219,
-0.002712249755859375,
0.01776123046875,
-0.03131103515625,
-0.015838623046875,
-0.0277252197265625,
0.01446533203125,
-0.0204620361328125,
0.00591278076171875,
0.0076751708984375,
-0.0176544189453125,
-0.0201263427734375,
0.01373291015625,
0.0019140243530273438,
0.01546478271484375,
-0.0020542144775390625,
0.001728057861328125,
-0.0129852294921875,
0.00885772705078125,
-0.01444244384765625,
-0.010345458984375,
-0.008575439453125,
-0.0091552734375,
0.004543304443359375,
-0.00418853759765625,
0.029449462890625,
0.008575439453125,
-0.0211944580078125,
-0.0118408203125,
-0.0018529891967773438,
0.0237579345703125,
0.01161956787109375,
-0.0002319812774658203,
0.0267333984375,
0.006351470947265625,
-0.0289459228515625,
0.010406494140625,
-0.00841522216796875,
0.0059051513671875,
0.0222625732421875,
0.030059814453125,
0.006687164306640625,
0.0259246826171875,
0.009765625,
-0.01436614990234375,
-0.0026092529296875,
0.0054931640625,
0.0005793571472167969,
-0.0187835693359375,
-0.028961181640625,
0.0005602836608886719,
-0.004932403564453125,
0.01332855224609375,
-0.01751708984375,
-0.01105499267578125,
0.019134521484375,
-0.0102996826171875,
-0.00133514404296875,
-0.0006771087646484375,
0.007671356201171875,
-0.006778717041015625,
0.006252288818359375,
0.031494140625,
-0.015716552734375,
0.0108642578125,
-0.06256103515625,
0.0006613731384277344,
0.004550933837890625,
-0.0099334716796875,
0.028656005859375,
-0.01305389404296875,
0.003437042236328125,
0.00017833709716796875,
-0.0072021484375,
-0.029052734375,
-0.005016326904296875,
0.005229949951171875,
0.034210205078125,
-0.0087432861328125,
0.058197021484375,
-0.041717529296875,
0.005977630615234375,
-0.00717926025390625,
0.01496124267578125,
0.02215576171875,
-0.02703857421875,
0.0013742446899414062,
0.0017023086547851562,
0.00916290283203125,
-0.00484466552734375,
0.003021240234375,
-0.0269012451171875,
0.008575439453125,
0.0010232925415039062,
0.006671905517578125,
0.0014600753784179688,
-0.007080078125,
0.0097503662109375,
0.00824737548828125,
0.0176544189453125,
0.00321197509765625,
-0.0112762451171875,
-0.0269622802734375,
0.040283203125,
0.026641845703125,
-0.020263671875,
0.0262451171875,
-0.004486083984375,
-0.0035247802734375,
0.0178375244140625,
0.00803375244140625,
-0.00701141357421875,
0.02813720703125,
-0.016143798828125,
-0.037322998046875,
-0.01788330078125,
-0.0014705657958984375,
0.0038700103759765625,
0.0306243896484375,
0.0537109375,
0.016021728515625,
-0.056640625,
0.032379150390625,
0.03668212890625,
-0.03460693359375,
0.0055084228515625,
0.01453399658203125,
-0.0042266845703125,
-0.0112457275390625,
-0.0116729736328125,
0.0139312744140625,
-0.022674560546875,
-0.037109375,
-0.0217742919921875,
-0.02825927734375,
0.01189422607421875,
0.002422332763671875,
-0.0026340484619140625,
0.0205535888671875,
-0.004817962646484375,
0.01029205322265625,
0.0037670135498046875,
0.0018510818481445312,
0.018463134765625,
0.0191802978515625,
0.0005340576171875,
-0.0081787109375,
-0.0220184326171875,
0.020843505859375,
0.00370025634765625,
-0.039398193359375,
0.0007157325744628906,
-0.0239410400390625,
-0.021148681640625,
0.0028514862060546875,
0.01403045654296875,
0.00809478759765625,
0.018341064453125,
-0.00809478759765625,
-0.02178955078125,
-0.0211029052734375,
0.010467529296875,
0.006145477294921875,
0.01020050048828125,
-0.0168609619140625,
-0.0169830322265625,
-0.0094757080078125,
0.022247314453125,
-0.00909423828125,
-0.022125244140625,
-0.03155517578125,
0.01479339599609375,
0.00992584228515625,
-0.006275177001953125,
-0.003021240234375,
-0.00925445556640625,
0.005084991455078125,
0.0193634033203125,
0.0140228271484375,
-0.0297393798828125,
0.04022216796875,
-0.0113525390625,
0.03985595703125,
0.0280303955078125,
-0.025421142578125,
-0.024566650390625,
-0.013336181640625,
0.0177001953125,
-0.01251220703125,
-0.0202178955078125,
0.00641632080078125,
-0.007755279541015625,
-0.0113983154296875,
-0.0443115234375,
-0.007965087890625,
-0.0214385986328125,
-0.05010986328125,
0.01203155517578125,
-0.0185546875,
0.01202392578125,
-0.0172576904296875,
0.0380859375,
0.0162506103515625,
-0.0240325927734375,
-0.0012083053588867188,
-0.028839111328125,
-0.0092926025390625,
0.006694793701171875,
0.0011348724365234375,
-0.01812744140625,
-0.0134124755859375,
0.01549530029296875,
0.0069580078125,
0.0254058837890625,
-0.00014543533325195312,
-0.02593994140625,
-0.0186920166015625,
0.0030460357666015625,
0.00312042236328125,
-0.00732421875,
0.012420654296875,
-0.0305938720703125,
0.0223541259765625,
-0.00585174560546875,
-0.01154327392578125,
-0.0308837890625,
-0.01678466796875,
0.0042724609375,
0.00679779052734375,
-0.02618408203125,
-0.006317138671875,
0.0029544830322265625,
0.0065765380859375,
0.0209808349609375,
-0.0036773681640625,
-0.00632476806640625,
0.0084381103515625,
0.00542449951171875,
0.00604248046875,
0.018585205078125,
0.0005478858947753906,
-0.0088043212890625,
-0.0149688720703125,
-0.0114898681640625,
-0.005458831787109375,
-0.0010251998901367188,
0.035614013671875,
0.01523590087890625,
0.00991058349609375,
0.0134735107421875,
-0.0181732177734375,
0.007266998291015625,
-0.00669097900390625,
0.0201568603515625,
0.02288818359375,
0.0099639892578125,
-0.01299285888671875,
0.0240325927734375,
0.0243682861328125,
0.042022705078125,
-0.0007524490356445312,
0.004734039306640625,
-0.0191802978515625,
-0.00270843505859375,
0.003139495849609375,
0.01275634765625,
-0.0179595947265625,
0.0033893585205078125,
0.00699615478515625,
0.0121917724609375,
-0.015777587890625,
0.0021533966064453125,
-0.0012197494506835938,
-0.0167083740234375,
0.021636962890625,
0.0018377304077148438,
0.05157470703125,
0.0200958251953125,
-0.023956298828125,
-0.01873779296875,
-0.0014667510986328125,
-0.01523590087890625,
0.00746917724609375,
0.0085296630859375,
-0.005786895751953125,
-0.007740020751953125,
0.03009033203125,
-0.0016908645629882812,
-0.01342010498046875,
-0.006229400634765625,
0.03143310546875,
0.00865936279296875,
-0.03350830078125,
-0.004955291748046875,
0.002399444580078125,
-0.01041412353515625,
0.0117645263671875,
-0.0092315673828125,
0.00687408447265625,
-0.002960205078125,
-0.01053619384765625,
0.01023101806640625,
-0.00027561187744140625,
0.008544921875,
0.0032444000244140625,
-0.002948760986328125,
0.02301025390625,
0.00868988037109375,
0.009490966796875,
-0.0090179443359375,
0.0005035400390625,
-0.01206207275390625,
-0.0029468536376953125,
0.01140594482421875,
-0.006519317626953125,
-0.0149993896484375,
-0.018524169921875,
0.016326904296875,
-0.00830841064453125,
0.00862884521484375,
0.023468017578125,
0.01067352294921875,
0.005107879638671875,
-0.01268768310546875,
-0.047515869140625,
0.006366729736328125,
-0.01425933837890625,
-0.010589599609375,
0.01342010498046875,
0.0136260986328125,
0.0234527587890625,
0.027679443359375,
-0.006809234619140625,
-0.001384735107421875,
-0.0235595703125,
0.0237274169921875,
0.031463623046875,
-0.009246826171875,
0.018768310546875,
0.029296875,
-0.01123809814453125,
0.013214111328125,
-0.0186767578125,
0.0285797119140625,
0.044464111328125,
0.005214691162109375,
-0.003231048583984375,
-0.00978851318359375,
-0.0273284912109375,
0.047119140625,
-0.01136016845703125,
-0.0225982666015625,
0.0023174285888671875,
-0.0209197998046875,
0.0237579345703125,
-0.0272674560546875,
0.059112548828125,
-0.0321044921875,
0.016876220703125,
-0.0181121826171875,
-0.0164031982421875,
-0.01204681396484375,
-0.03009033203125,
-0.00601959228515625,
-0.0020542144775390625,
0.0029964447021484375,
-0.004207611083984375,
0.01629638671875,
0.0153656005859375,
-0.004764556884765625,
-0.0173492431640625,
0.0235137939453125,
0.002468109130859375,
-0.005496978759765625,
0.0003886222839355469,
0.0042266845703125,
-0.0002810955047607422,
-0.0011653900146484375,
-0.003780364990234375,
-0.01216888427734375,
-0.0111083984375,
0.02215576171875,
-0.0043182373046875,
0.0033740997314453125,
0.01378631591796875,
0.000518798828125,
0.0237579345703125,
-0.016876220703125,
-0.005046844482421875,
-0.0096435546875,
-0.0299530029296875,
-0.00974273681640625,
0.0496826171875,
-0.0093231201171875,
-0.01531982421875,
-0.02008056640625,
-0.006015777587890625,
0.00833892822265625,
-0.009063720703125,
0.018890380859375,
-0.031768798828125,
-0.009063720703125,
0.010833740234375,
-0.01348876953125,
0.009490966796875,
0.00945281982421875,
0.004497528076171875,
0.006011962890625,
0.0178375244140625,
0.010528564453125,
0.015899658203125,
-0.0095977783203125,
0.05169677734375,
-0.003147125244140625,
0.01026153564453125,
-0.00445556640625,
-0.021820068359375,
0.012420654296875,
-0.004180908203125,
0.006580352783203125,
0.01384735107421875,
-0.0124969482421875,
0.002910614013671875,
0.004520416259765625,
0.0244293212890625,
-0.004344940185546875,
0.004184722900390625,
0.03240966796875,
-0.0287322998046875,
0.027374267578125,
-0.0013895034790039062,
-0.0027904510498046875,
-0.0007615089416503906,
-0.02117919921875,
-0.0016651153564453125,
0.0059051513671875,
0.033660888671875,
0.0005946159362792969,
-0.00948333740234375,
-0.0026760101318359375,
-0.015838623046875,
0.0102081298828125,
-0.031524658203125,
-0.02069091796875,
0.0001760721206665039,
0.026947021484375,
-0.0135955810546875,
0.032958984375,
0.0134429931640625,
0.00006633996963500977,
0.006755828857421875,
0.0056610107421875,
-0.01525115966796875,
0.01302337646484375,
-0.0264129638671875,
0.0034236907958984375,
-0.008026123046875,
-0.001007080078125,
0.0159149169921875,
-0.003337860107421875,
-0.00461578369140625,
-0.0248260498046875,
-0.00356292724609375,
0.00030803680419921875,
-0.005062103271484375,
-0.00814056396484375,
0.0419921875,
0.027374267578125,
0.01171875,
0.0177764892578125,
0.00411224365234375,
0.035491943359375,
-0.0158843994140625,
-0.021514892578125,
-0.0019969940185546875,
-0.010040283203125,
-0.0038051605224609375,
-0.021759033203125,
0.018035888671875,
0.0245819091796875,
0.007472991943359375,
-0.020111083984375,
-0.01690673828125,
-0.00965118408203125,
-0.0139617919921875,
-0.033782958984375,
-0.0175933837890625,
0.015167236328125,
-0.00031304359436035156,
0.024322509765625,
0.01361083984375,
0.032958984375,
0.0479736328125,
0.007755279541015625,
0.0026645660400390625,
-0.0159759521484375,
-0.0131378173828125,
-0.0310516357421875,
0.035980224609375,
0.01580810546875,
-0.0112457275390625,
0.007598876953125,
-0.006175994873046875,
0.029693603515625,
-0.007465362548828125,
-0.0185089111328125,
0.01479339599609375,
0.01093292236328125,
0.01461029052734375,
-0.0250091552734375,
-0.033935546875,
0.03253173828125,
0.0009255409240722656,
-0.0166015625,
0.00013935565948486328,
-0.043212890625,
0.003780364990234375,
-0.0121002197265625,
0.036834716796875,
0.005611419677734375,
0.0028705596923828125,
0.0210723876953125,
-0.00913238525390625,
-0.005985260009765625,
-0.0021533966064453125,
-0.02801513671875,
-0.016937255859375,
-0.0173797607421875,
-0.01947021484375,
-0.011688232421875,
0.046417236328125,
-0.00986480712890625,
-0.0123443603515625,
-0.032012939453125,
0.00004935264587402344,
0.007480621337890625,
0.03961181640625,
-0.0109710693359375,
-0.042755126953125,
-0.0104827880859375,
-0.0178985595703125,
-0.027923583984375,
-0.03790283203125,
-0.013153076171875,
-0.029571533203125,
0.00669097900390625,
0.0070037841796875,
-0.0124053955078125,
0.0169219970703125,
-0.0219268798828125,
0.01367950439453125,
0.016571044921875,
-0.04742431640625,
0.006000518798828125,
-0.0269317626953125,
-0.0204620361328125,
-0.0479736328125,
-0.0013227462768554688,
0.0103607177734375,
0.026611328125,
-0.007160186767578125,
-0.016632080078125,
0.006252288818359375,
0.0254058837890625,
0.0244903564453125,
-0.00193023681640625,
0.00461578369140625,
-0.01806640625,
0.008026123046875,
0.011749267578125,
-0.005786895751953125,
-0.01526641845703125,
0.00347137451171875,
0.011993408203125,
-0.00937652587890625,
-0.0108489990234375,
0.01560211181640625,
0.0384521484375,
0.007610321044921875,
-0.0263214111328125,
-0.032135009765625,
-0.0116729736328125,
-0.0025634765625,
0.006137847900390625,
-0.002155303955078125,
-0.0019550323486328125,
-0.0283966064453125,
0.01812744140625,
-0.01209259033203125,
-0.006313323974609375,
0.0008463859558105469,
-0.0034351348876953125,
-0.0074615478515625,
-0.0027446746826171875,
0.000008881092071533203,
-0.003200531005859375,
-0.005809783935546875,
0.0201263427734375,
-0.0124969482421875,
-0.006877899169921875,
0.00189208984375,
0.033905029296875,
0.007366180419921875,
0.005474090576171875,
0.03985595703125,
-0.00553131103515625,
0.01004791259765625,
0.0036907196044921875,
-0.0031566619873046875,
-0.008209228515625,
-0.00876617431640625,
-0.007537841796875,
-0.025726318359375,
0.0146331787109375,
-0.007648468017578125,
-0.02655029296875,
-0.03155517578125,
-0.0011949539184570312,
-0.00907135009765625,
0.0190887451171875,
0.0240020751953125,
-0.01049041748046875,
-0.029266357421875,
-0.01241302490234375,
-0.0181427001953125,
0.005084991455078125,
-0.01439666748046875,
-0.012603759765625,
-0.0084991455078125,
0.00238800048828125,
-0.004932403564453125,
-0.026580810546875,
-0.0052337646484375,
-0.0095062255859375,
0.05072021484375,
0.047454833984375,
0.021942138671875,
-0.023101806640625,
-0.0158233642578125,
-0.0190277099609375,
0.01261138916015625,
0.0012693405151367188,
-0.01110076904296875,
0.013671875,
-0.0094757080078125,
-0.02264404296875,
0.01165008544921875,
0.006927490234375,
-0.001407623291015625,
0.03143310546875,
0.0169677734375,
0.0183868408203125,
-0.0279083251953125,
-0.0010671615600585938,
0.02752685546875,
0.03125,
0.021514892578125,
0.0179443359375,
0.01983642578125,
-0.0170135498046875,
-0.0215301513671875,
-0.0141754150390625,
-0.014251708984375,
0.01419830322265625,
0.006061553955078125,
0.01168060302734375,
0.0135498046875,
0.01123046875,
0.0117645263671875,
0.0218048095703125,
-0.00966644287109375,
-0.0170135498046875,
0.01265716552734375,
-0.01212310791015625,
-0.0002701282501220703,
-0.0191192626953125,
-0.0246734619140625,
0.01020050048828125,
0.03271484375,
-0.0032558441162109375,
0.0058135986328125,
-0.03887939453125,
-0.036865234375,
-0.00276947021484375,
-0.01727294921875,
0.035980224609375,
-0.0239715576171875,
0.00008934736251831055,
-0.013885498046875,
0.0242462158203125,
0.004253387451171875,
0.034149169921875,
-0.0150299072265625,
0.0183563232421875,
-0.007843017578125,
0.00830078125,
0.01404571533203125,
-0.00862884521484375,
-0.0118865966796875,
0.016937255859375,
-0.0203094482421875,
-0.03485107421875,
-0.0116424560546875,
0.02801513671875,
-0.00978851318359375,
0.0026988983154296875,
-0.0106964111328125,
0.01629638671875,
0.021331787109375,
-0.0016927719116210938,
0.0009570121765136719,
-0.00445556640625,
-0.01422119140625,
0.016326904296875,
0.0025634765625,
0.018280029296875,
-0.00981903076171875,
-0.0053558349609375,
-0.005657196044921875,
-0.01410675048828125,
0.01708984375,
0.0443115234375,
-0.024169921875,
0.0112152099609375,
-0.029052734375,
-0.01401519775390625,
0.01502227783203125,
-0.021514892578125,
-0.011260986328125,
-0.021514892578125,
-0.039337158203125,
-0.007411956787109375,
-0.0189666748046875,
0.012725830078125,
0.029754638671875,
-0.012603759765625,
0.01995849609375,
-0.023223876953125,
-0.01204681396484375,
0.005855560302734375,
0.00621795654296875,
0.0175323486328125,
-0.026702880859375,
-0.027313232421875,
0.042572021484375,
-0.0059814453125,
0.0167999267578125,
0.0227508544921875,
-0.01788330078125,
0.01525115966796875,
0.0141448974609375,
-0.00279998779296875,
0.054473876953125,
0.0169677734375,
-0.0189361572265625,
-0.026611328125,
0.010528564453125,
0.031768798828125,
0.0087890625,
-0.005802154541015625,
-0.034210205078125,
-0.0014362335205078125,
0.0089874267578125,
0.0144195556640625,
-0.0093231201171875,
0.02093505859375,
-0.0298309326171875,
0.0142822265625,
0.0435791015625,
-0.002971649169921875,
0.0105133056640625,
0.0182647705078125,
0.01395416259765625,
-0.004833221435546875,
0.0003228187561035156,
0.00809478759765625,
0.0015726089477539062,
-0.0150299072265625,
-0.057098388671875,
-0.0136566162109375,
-0.01207733154296875,
-0.0025806427001953125,
-0.022705078125,
0.00708770751953125,
-0.01149749755859375,
-0.0565185546875,
0.02301025390625,
-0.0008912086486816406,
0.00652313232421875,
-0.038238525390625,
0.02081298828125,
-0.02294921875,
0.00024199485778808594,
-0.023651123046875,
-0.01454925537109375,
0.00911712646484375,
0.0161285400390625,
-0.01593017578125,
-0.020782470703125,
-0.0284881591796875,
-0.0175933837890625,
0.0284576416015625,
-0.01169586181640625,
-0.0260009765625,
-0.021087646484375,
-0.01480865478515625,
0.01483917236328125,
0.01837158203125,
0.00490570068359375,
0.004528045654296875,
-0.01190185546875,
-0.00754547119140625,
-0.0030670166015625,
0.040496826171875,
-0.005462646484375,
-0.021728515625,
-0.0054168701171875,
0.0277252197265625,
-0.037506103515625,
-0.0032939910888671875,
0.004123687744140625,
-0.0038604736328125,
-0.006717681884765625,
0.007114410400390625,
0.01331329345703125,
-0.0242919921875,
-0.030487060546875,
-0.0146331787109375,
-0.026519775390625,
0.022430419921875,
-0.005428314208984375,
-0.0044708251953125,
-0.0028858184814453125,
-0.0029621124267578125,
0.0037097930908203125,
0.0113677978515625,
-0.037109375,
0.0032978057861328125,
0.018890380859375,
-0.005222320556640625,
0.00543975830078125,
0.0068359375,
-0.0322265625,
0.0330810546875,
-0.003696441650390625,
-0.005275726318359375,
-0.0008487701416015625,
0.00818634033203125,
0.003589630126953125,
-0.0197296142578125,
-0.0268402099609375,
-0.0689697265625,
-0.050201416015625,
-0.01555633544921875,
0.0032863616943359375,
0.0252685546875,
-0.035247802734375,
-0.004566192626953125,
-0.003475189208984375,
0.01202392578125,
-0.00020384788513183594,
0.02252197265625,
-0.021820068359375,
-0.0128021240234375,
-0.00687408447265625,
0.00481414794921875,
-0.02252197265625,
0.033416748046875,
-0.0239715576171875,
-0.01479339599609375,
0.00313568115234375,
-0.03118896484375,
0.007350921630859375,
0.01290130615234375,
0.0279693603515625,
0.0175628662109375,
0.02362060546875,
-0.0017223358154296875,
-0.004474639892578125,
0.01390838623046875,
-0.012969970703125,
-0.00897979736328125,
0.00609588623046875,
-0.01313018798828125,
-0.0101776123046875,
-0.007297515869140625,
-0.0133514404296875,
0.0207672119140625,
-0.020599365234375,
0.0097503662109375,
-0.017059326171875,
0.015899658203125,
-0.01493072509765625,
-0.03271484375,
0.01849365234375,
-0.025604248046875,
0.03460693359375,
-0.010284423828125,
-0.00958251953125,
-0.004924774169921875,
0.052947998046875,
-0.036224365234375,
0.0614013671875,
0.0101470947265625,
-0.0135498046875,
-0.0011072158813476562,
-0.013336181640625,
-0.0120391845703125,
0.009735107421875,
0.019256591796875,
-0.024932861328125,
0.0193634033203125,
0.0082855224609375,
-0.044647216796875,
0.016265869140625,
-0.010650634765625,
-0.00321197509765625,
-0.034423828125,
-0.02093505859375,
0.0032253265380859375,
-0.012451171875,
0.0052337646484375,
0.0225677490234375,
-0.00936126708984375,
-0.031036376953125,
0.002716064453125,
-0.00772857666015625,
0.031219482421875,
-0.0010271072387695312,
-0.0279083251953125,
0.01275634765625,
-0.051727294921875,
0.0215606689453125,
-0.0010662078857421875,
0.01395416259765625,
0.042938232421875,
-0.03167724609375,
0.025054931640625,
0.0025806427001953125,
-0.017913818359375,
0.003173828125,
0.005611419677734375,
-0.016326904296875,
-0.0058135986328125,
-0.01519775390625,
-0.00342559814453125,
-0.01377105712890625,
0.00571441650390625,
0.0185089111328125,
0.021759033203125,
0.017181396484375,
0.022979736328125,
-0.0283203125,
-0.0010385513305664062,
-0.0172882080078125,
-0.002300262451171875,
-0.0011348724365234375,
0.005596160888671875,
0.00653076171875,
-0.01904296875,
-0.015777587890625,
-0.04296875,
0.003528594970703125,
0.00815582275390625,
-0.02545166015625,
0.003849029541015625,
-0.006671905517578125,
0.01371002197265625,
-0.0026988983154296875,
-0.0260467529296875,
0.022613525390625,
-0.0256500244140625,
0.0035533905029296875,
0.0257110595703125,
0.005096435546875,
0.005340576171875,
-0.01514434814453125,
0.0092010498046875,
0.004192352294921875,
0.0208587646484375,
0.022430419921875,
0.0020160675048828125,
-0.005466461181640625,
0.0240936279296875,
0.0020084381103515625,
0.0190277099609375,
-0.047454833984375,
-0.014739990234375,
-0.035003662109375,
0.007747650146484375,
-0.0236968994140625,
-0.01131439208984375,
-0.0027141571044921875,
0.01160430908203125,
0.00624847412109375,
-0.03173828125,
0.017120361328125,
-0.01273345947265625,
0.012847900390625,
-0.0018444061279296875,
-0.03399658203125,
-0.0391845703125,
0.00508880615234375,
0.01198577880859375,
-0.0157318115234375,
-0.01451873779296875,
-0.01617431640625,
0.0280609130859375,
0.0252532958984375,
0.006732940673828125,
-0.0015201568603515625,
0.0050506591796875,
0.01361083984375,
0.037811279296875,
0.00795745849609375,
-0.01261138916015625,
0.006683349609375,
0.01470947265625,
0.0019350051879882812,
0.029083251953125,
-0.004261016845703125,
0.016998291015625,
-0.0008301734924316406,
-0.0183258056640625,
0.0124969482421875,
-0.0281524658203125,
0.01154327392578125,
-0.01204681396484375,
-0.00421142578125,
-0.01392364501953125,
0.0372314453125,
-0.029144287109375,
-0.049224853515625,
-0.033538818359375,
-0.003673553466796875,
-0.0230560302734375,
-0.007137298583984375,
-0.00907135009765625,
-0.0142822265625,
-0.0313720703125,
-0.0160675048828125,
0.01108551025390625,
0.0215301513671875,
0.0009241104125976562,
-0.0010700225830078125,
0.004047393798828125,
0.002529144287109375,
0.0009398460388183594,
0.0199737548828125,
0.00922393798828125,
-0.036773681640625,
-0.0111846923828125,
0.0125579833984375,
-0.015716552734375,
-0.0011081695556640625,
0.0248565673828125,
-0.01158905029296875,
0.0254974365234375,
0.01312255859375,
-0.0244903564453125,
0.0032196044921875,
-0.0107574462890625,
0.0211029052734375,
0.007419586181640625,
0.042388916015625,
-0.0012426376342773438,
-0.0290374755859375,
-0.006725311279296875,
-0.04534912109375,
0.006435394287109375,
0.0037937164306640625,
-0.0211029052734375,
-0.01383209228515625,
-0.03662109375,
-0.0144500732421875,
-0.0248870849609375,
-0.01898193359375,
0.0037841796875,
-0.017486572265625,
0.0280609130859375,
0.0023708343505859375,
0.04046630859375,
0.052001953125,
0.0007414817810058594,
0.01139068603515625,
-0.003902435302734375,
0.0101318359375,
-0.00186920166015625,
0.034637451171875,
-0.0266876220703125,
0.0238494873046875,
-0.01800537109375,
0.0193023681640625,
0.01406097412109375,
0.0290679931640625,
0.00995635986328125,
-0.0131072998046875,
-0.0032367706298828125,
0.01537322998046875,
0.0132598876953125,
0.042572021484375,
0.01032257080078125,
0.01568603515625,
-0.0266265869140625,
-0.009765625,
-0.012359619140625,
0.0191192626953125,
-0.0229949951171875,
-0.005382537841796875,
0.006351470947265625,
0.0231475830078125,
-0.00934600830078125,
0.009857177734375,
-0.010498046875,
0.019989013671875,
0.016357421875,
0.011566162109375,
-0.0413818359375,
-0.00629425048828125,
0.0323486328125,
-0.041595458984375,
0.041656494140625,
-0.037841796875,
-0.0255889892578125,
0.0129241943359375,
-0.02459716796875,
0.01611328125,
0.01499176025390625,
0.01302337646484375,
-0.0167388916015625,
-0.0214080810546875,
-0.01503753662109375,
0.00994873046875,
0.018341064453125,
-0.004718780517578125,
0.011871337890625,
0.01904296875,
0.0041961669921875,
0.01110076904296875,
0.0099639892578125,
0.006805419921875,
-0.0163726806640625,
0.02215576171875,
0.005252838134765625,
-0.02984619140625,
0.0191497802734375,
-0.0189971923828125,
-0.02410888671875,
-0.00289154052734375,
-0.0262908935546875,
-0.013885498046875,
0.031524658203125,
-0.01450347900390625,
0.00988006591796875,
-0.0300445556640625,
0.0281829833984375,
0.0055694580078125,
-0.03912353515625,
0.007678985595703125,
-0.00019240379333496094,
-0.01190185546875,
0.025848388671875,
0.0180816650390625,
0.0294189453125,
0.02423095703125,
-0.01207733154296875,
-0.001129150390625,
-0.001819610595703125,
0.0037250518798828125,
0.005298614501953125,
0.00901031494140625,
-0.035186767578125,
0.0114898681640625,
0.0080718994140625,
0.0137786865234375,
0.01210784912109375,
0.0016088485717773438,
-0.027862548828125,
-0.008758544921875,
0.0005235671997070312,
-0.0181732177734375,
0.01468658447265625,
0.032012939453125,
-0.05615234375,
-0.023529052734375,
-0.03887939453125,
0.0150299072265625,
-0.003993988037109375,
-0.0029811859130859375,
0.00821685791015625,
0.009918212890625,
0.0156707763671875,
0.0196685791015625,
-0.01192474365234375,
-0.01476287841796875,
-0.007526397705078125,
-0.01922607421875,
-0.0205535888671875,
-0.01523590087890625,
-0.0164337158203125,
0.011993408203125,
-0.00775909423828125,
-0.0177001953125,
0.017852783203125,
-0.01239776611328125,
-0.029693603515625,
0.0173797607421875,
0.004756927490234375,
-0.0178985595703125,
-0.01580810546875,
-0.004047393798828125,
0.00408172607421875,
-0.00872039794921875,
0.01375579833984375,
0.00875091552734375,
-0.0224609375,
-0.02423095703125,
0.014984130859375,
0.040191650390625,
-0.03387451171875,
-0.01070404052734375,
-0.0099334716796875,
-0.0301055908203125,
-0.0089874267578125,
-0.03460693359375,
0.0074310302734375,
0.01387786865234375,
-0.0335693359375,
-0.0009326934814453125,
-0.019805908203125,
-0.0038890838623046875,
0.00603485107421875,
0.0023899078369140625,
0.0157012939453125,
-0.00716400146484375,
-0.0028400421142578125,
-0.0242156982421875,
0.016082763671875,
0.019866943359375,
-0.0216522216796875,
0.00754547119140625,
-0.01007843017578125,
0.01224517822265625,
0.017578125,
-0.0126190185546875,
0.0256195068359375,
-0.00606536865234375,
0.00970458984375,
-0.0086669921875,
-0.006519317626953125,
-0.029022216796875,
-0.01788330078125,
-0.01055908203125,
-0.0027256011962890625,
0.004169464111328125,
-0.00786590576171875,
0.0182647705078125,
-0.007122039794921875,
-0.0164947509765625,
0.00124359130859375,
0.0162353515625,
0.0177001953125,
0.00803375244140625,
-0.0129547119140625,
-0.00580596923828125,
0.026763916015625,
-0.013763427734375,
-0.01457977294921875,
-0.008148193359375,
-0.0167388916015625,
0.0015039443969726562,
0.0270538330078125,
-0.0215911865234375,
0.0174713134765625,
-0.0010623931884765625,
0.0137481689453125,
0.013702392578125,
0.003997802734375,
0.018310546875
] |
ours_534
|
Exactly half of the \(90\) 2-digit numbers and exactly half of the \(9000\) 4-digit numbers are even, giving a total of \(\frac{90 + 9000}{2} = 4545\) numbers.
\(\boxed{4545}\)
|
4545
|
{
"competition": "us_comps",
"dataset": "Ours",
"posts": null,
"source": "OMOSoln2.md"
}
|
How many positive even numbers have an even number of digits and are less than \(10000\)?
|
[
"/Mathematics/DiscreteMathematics/Combinatorics/Enumeration",
"/Mathematics/DiscreteMathematics/GeneralDiscreteMathematics/DiscreteMath",
"/Mathematics/DiscreteMathematics/GeneralDiscreteMathematics/DiscreteMathematics",
"/Mathematics/DiscreteMathematics/GeneralDiscreteMathematics/FiniteMathematics",
"/Mathematics/NumberTheory/Integers/EvenNumber",
"/Mathematics/NumberTheory/Integers/PositiveInteger",
"/Mathematics/NumberTheory/Numbers/SmallNumbers",
"/Mathematics/NumberTheory/Parity/EvenNumber"
] |
Count all numbers with the given digit lengths and take half, because exactly half of them are even.
|
[
0.000037670135498046875,
0.016326904296875,
0.0138092041015625,
0.00688934326171875,
0.00044226646423339844,
-0.00492095947265625,
0.0341796875,
-0.0015201568603515625,
0.00315093994140625,
-0.01776123046875,
-0.0018739700317382812,
-0.00585174560546875,
-0.0005927085876464844,
-0.0200347900390625,
-0.057647705078125,
0.02166748046875,
0.0293731689453125,
0.012176513671875,
-0.019989013671875,
-0.005126953125,
0.0014543533325195312,
0.005619049072265625,
-0.031768798828125,
-0.0015659332275390625,
-0.0157012939453125,
-0.02447509765625,
-0.01023101806640625,
0.0421142578125,
0.044891357421875,
0.0268402099609375,
0.0127410888671875,
0.00875091552734375,
0.01995849609375,
-0.014892578125,
0.00557708740234375,
0.003238677978515625,
-0.00554656982421875,
-0.00295257568359375,
0.026397705078125,
-0.0094757080078125,
-0.005558013916015625,
-0.011810302734375,
-0.0167694091796875,
-0.0007071495056152344,
-0.0156402587890625,
0.03369140625,
0.00315093994140625,
0.0006351470947265625,
-0.01171875,
-0.00623321533203125,
0.0052490234375,
0.0029048919677734375,
-0.0006051063537597656,
-0.0193023681640625,
-0.0236053466796875,
-0.02581787109375,
0.01160430908203125,
0.004291534423828125,
-0.0080108642578125,
-0.0105133056640625,
0.005283355712890625,
-0.022125244140625,
0.0033550262451171875,
-0.0208892822265625,
0.0006709098815917969,
-0.0024051666259765625,
0.07647705078125,
-0.0131072998046875,
0.00664520263671875,
-0.007122039794921875,
-0.0283355712890625,
-0.01430511474609375,
0.00852203369140625,
0.01367950439453125,
0.034637451171875,
-0.00992584228515625,
-0.0015096664428710938,
0.0195770263671875,
-0.008209228515625,
0.00543975830078125,
0.026763916015625,
0.004909515380859375,
0.0011653900146484375,
0.0210723876953125,
-0.0099029541015625,
0.0166168212890625,
-0.006317138671875,
-0.00939178466796875,
-0.006725311279296875,
-0.0174560546875,
-0.0059356689453125,
0.039154052734375,
0.01013946533203125,
0.0159149169921875,
0.0028896331787109375,
0.010345458984375,
-0.0024566650390625,
-0.0107879638671875,
0.00868988037109375,
0.01094818115234375,
-0.0157470703125,
-0.007404327392578125,
0.020721435546875,
-0.021087646484375,
-0.0087738037109375,
-0.003597259521484375,
-0.0134735107421875,
0.0032482147216796875,
-0.00870513916015625,
0.00018286705017089844,
-0.00006604194641113281,
-0.00414276123046875,
0.0104827880859375,
-0.00557708740234375,
-0.0101776123046875,
-0.01056671142578125,
0.0106353759765625,
-0.00908660888671875,
-0.00669097900390625,
0.0148468017578125,
0.005748748779296875,
0.016937255859375,
-0.006671905517578125,
-0.0036334991455078125,
0.007747650146484375,
-0.0033817291259765625,
-0.00930023193359375,
0.007740020751953125,
-0.0010967254638671875,
0.02020263671875,
-0.00555419921875,
0.00154876708984375,
-0.0251007080078125,
-0.016845703125,
-0.00978851318359375,
-0.012359619140625,
-0.00136566162109375,
-0.004550933837890625,
-0.006214141845703125,
0.002166748046875,
0.0044403076171875,
-0.004749298095703125,
0.0008749961853027344,
-0.01641845703125,
0.0010499954223632812,
0.0093994140625,
-0.003025054931640625,
-0.05133056640625,
0.005970001220703125,
-0.0193023681640625,
0.0026607513427734375,
0.007297515869140625,
0.00064849853515625,
0.01434326171875,
-0.002681732177734375,
0.00438690185546875,
0.0001729726791381836,
0.004657745361328125,
0.01203155517578125,
0.016815185546875,
0.0065460205078125,
-0.001728057861328125,
-0.0172119140625,
0.0355224609375,
-0.0307769775390625,
0.007080078125,
0.04864501953125,
-0.005588531494140625,
0.00018167495727539062,
-0.0340576171875,
-0.01629638671875,
-0.0085296630859375,
0.018402099609375,
-0.01436614990234375,
-0.01153564453125,
0.006114959716796875,
0.0014238357543945312,
-0.009796142578125,
0.00333404541015625,
-0.01444244384765625,
0.007404327392578125,
-0.046478271484375,
0.05096435546875,
0.020172119140625,
-0.0014371871948242188,
0.0225982666015625,
-0.0012645721435546875,
0.0247955322265625,
0.01009368896484375,
0.0022487640380859375,
-0.00887298583984375,
-0.007030487060546875,
0.0006246566772460938,
0.01233673095703125,
-0.0177154541015625,
-0.0141143798828125,
0.0185699462890625,
-0.02203369140625,
0.025848388671875,
0.0062103271484375,
0.0009441375732421875,
-0.004535675048828125,
-0.01424407958984375,
0.007228851318359375,
0.018280029296875,
-0.0093231201171875,
0.004802703857421875,
-0.0168914794921875,
0.005535125732421875,
0.005157470703125,
0.00827789306640625,
-0.00579071044921875,
-0.00989532470703125,
0.033203125,
-0.00847625732421875,
0.0036449432373046875,
-0.006229400634765625,
-0.00661468505859375,
0.0240478515625,
-0.04583740234375,
0.0207061767578125,
-0.0009016990661621094,
-0.0081024169921875,
0.01262664794921875,
-0.0311126708984375,
-0.0083160400390625,
-0.030487060546875,
0.0025043487548828125,
0.0298004150390625,
0.018402099609375,
0.031982421875,
0.01444244384765625,
-0.0021610260009765625,
0.00458526611328125,
0.004154205322265625,
0.0023021697998046875,
0.016143798828125,
-0.020751953125,
0.0076141357421875,
-0.0162811279296875,
0.03118896484375,
0.01091766357421875,
-0.014404296875,
-0.005687713623046875,
0.016021728515625,
-0.0118408203125,
0.0006146430969238281,
0.0126800537109375,
0.00385284423828125,
-0.0006866455078125,
-0.0028018951416015625,
0.00537109375,
-0.00876617431640625,
-0.0175018310546875,
0.002105712890625,
0.003082275390625,
0.002300262451171875,
0.03765869140625,
0.0014982223510742188,
-0.006435394287109375,
-0.022247314453125,
0.006359100341796875,
-0.00862884521484375,
-0.00469970703125,
-0.007305145263671875,
0.00494384765625,
0.006679534912109375,
0.01198577880859375,
0.00467681884765625,
0.0115203857421875,
0.0269775390625,
0.00269317626953125,
0.0007119178771972656,
0.0244598388671875,
0.0175018310546875,
-0.0155792236328125,
0.005641937255859375,
-0.01476287841796875,
0.029510498046875,
-0.0005292892456054688,
-0.004016876220703125,
-0.040313720703125,
-0.0268402099609375,
0.0170745849609375,
0.01433563232421875,
-0.021453857421875,
-0.0241851806640625,
-0.0020542144775390625,
-0.02423095703125,
0.01372528076171875,
0.003421783447265625,
-0.0079498291015625,
-0.01143646240234375,
0.01329803466796875,
0.01165771484375,
-0.011749267578125,
0.033355712890625,
-0.02044677734375,
0.01071929931640625,
-0.01486968994140625,
0.02703857421875,
-0.000705718994140625,
0.00443267822265625,
-0.00015211105346679688,
0.007404327392578125,
0.031280517578125,
0.00579833984375,
0.0003898143768310547,
-0.007755279541015625,
-0.027587890625,
0.01279449462890625,
0.00341796875,
0.002552032470703125,
0.0045928955078125,
-0.00786590576171875,
-0.019775390625,
-0.0019855499267578125,
0.00986480712890625,
-0.0057830810546875,
-0.0482177734375,
0.00850677490234375,
0.0021724700927734375,
-0.035400390625,
-0.018524169921875,
0.0288238525390625,
0.01363372802734375,
-0.0089569091796875,
0.0203094482421875,
-0.017059326171875,
0.01099395751953125,
0.01558685302734375,
0.005886077880859375,
0.015899658203125,
-0.0157012939453125,
-0.001190185546875,
0.005039215087890625,
0.034515380859375,
0.02099609375,
-0.0175323486328125,
0.006069183349609375,
0.0250396728515625,
-0.0157623291015625,
-0.0250244140625,
0.01470947265625,
-0.02142333984375,
0.00748443603515625,
-0.045684814453125,
-0.024383544921875,
0.000553131103515625,
-0.0250396728515625,
-0.007724761962890625,
0.033416748046875,
-0.02392578125,
-0.01071929931640625,
-0.047760009765625,
0.020050048828125,
-0.013275146484375,
0.0009613037109375,
0.01171112060546875,
0.0204010009765625,
-0.01291656494140625,
-0.017974853515625,
0.00919342041015625,
0.016571044921875,
0.0254058837890625,
-0.02288818359375,
-0.0177459716796875,
0.0022563934326171875,
-0.0224456787109375,
-0.018798828125,
0.007488250732421875,
-0.034271240234375,
-0.013153076171875,
0.0077667236328125,
-0.02911376953125,
0.0008831024169921875,
0.02032470703125,
-0.0005359649658203125,
0.002086639404296875,
-0.014434814453125,
0.026947021484375,
0.023101806640625,
-0.014923095703125,
0.0066680908203125,
0.0008730888366699219,
0.01102447509765625,
-0.00469207763671875,
-0.05078125,
0.000972747802734375,
-0.015960693359375,
0.0209808349609375,
-0.00704193115234375,
-0.018218994140625,
0.010467529296875,
-0.0159149169921875,
0.0155792236328125,
-0.0010538101196289062,
-0.01026153564453125,
0.01165008544921875,
0.011810302734375,
0.00215911865234375,
0.0211334228515625,
-0.022552490234375,
0.020538330078125,
-0.0110626220703125,
-0.01425933837890625,
0.00022912025451660156,
-0.03961181640625,
-0.006572723388671875,
0.0089263916015625,
0.022186279296875,
-0.0161285400390625,
-0.0024356842041015625,
-0.018890380859375,
0.033050537109375,
0.0219573974609375,
0.021484375,
0.02130126953125,
-0.0556640625,
-0.0221099853515625,
0.00582122802734375,
0.01337432861328125,
-0.0252532958984375,
0.0038547515869140625,
0.01074981689453125,
0.00965118408203125,
0.010101318359375,
0.04388427734375,
0.011505126953125,
0.00922393798828125,
-0.0025234222412109375,
-0.00592041015625,
0.018280029296875,
-0.0027713775634765625,
0.0104522705078125,
0.03271484375,
0.021728515625,
0.021148681640625,
-0.028594970703125,
0.0013751983642578125,
-0.00841522216796875,
-0.005832672119140625,
0.0015497207641601562,
0.00977325439453125,
0.0389404296875,
0.0027332305908203125,
-0.000006854534149169922,
0.0161590576171875,
-0.01407623291015625,
0.01041412353515625,
-0.010772705078125,
-0.022308349609375,
-0.0276031494140625,
-0.02996826171875,
-0.0284881591796875,
0.023956298828125,
-0.002735137939453125,
-0.003536224365234375,
-0.03851318359375,
-0.0137939453125,
-0.017608642578125,
-0.0006589889526367188,
-0.00643157958984375,
-0.004909515380859375,
-0.03302001953125,
0.0006213188171386719,
-0.0099029541015625,
-0.02642822265625,
-0.0129852294921875,
-0.0116729736328125,
-0.0118560791015625,
-0.0330810546875,
-0.0195159912109375,
0.0033206939697265625,
-0.005611419677734375,
0.019927978515625,
0.0010814666748046875,
0.00907135009765625,
0.012969970703125,
-0.0121307373046875,
0.0131378173828125,
0.010955810546875,
-0.022308349609375,
0.027587890625,
-0.00432586669921875,
0.0195159912109375,
0.023895263671875,
-0.0007104873657226562,
-0.0411376953125,
-0.00251007080078125,
0.027618408203125,
0.0014257431030273438,
-0.046630859375,
-0.007457733154296875,
-0.0064544677734375,
-0.032562255859375,
0.005680084228515625,
-0.0279083251953125,
-0.002887725830078125,
-0.0161590576171875,
0.01459503173828125,
-0.002407073974609375,
-0.013427734375,
0.0029811859130859375,
-0.0024871826171875,
-0.0058135986328125,
0.0330810546875,
-0.023590087890625,
-0.0027523040771484375,
-0.012786865234375,
-0.0113983154296875,
-0.005092620849609375,
0.0253448486328125,
-0.02996826171875,
-0.0249481201171875,
-0.039459228515625,
0.01715087890625,
-0.0008211135864257812,
0.005893707275390625,
-0.0137481689453125,
-0.0029926300048828125,
-0.0014696121215820312,
-0.022369384765625,
0.0094451904296875,
0.00731658935546875,
-0.006587982177734375,
0.00873565673828125,
-0.05389404296875,
-0.0008330345153808594,
0.01474761962890625,
-0.01271820068359375,
-0.00582122802734375,
0.037750244140625,
0.0058746337890625,
-0.006259918212890625,
0.01134490966796875,
0.00618743896484375,
0.021636962890625,
0.01312255859375,
0.01551055908203125,
-0.0012369155883789062,
0.00887298583984375,
0.042938232421875,
-0.031951904296875,
-0.003559112548828125,
-0.0099639892578125,
0.04302978515625,
0.008087158203125,
-0.02008056640625,
0.0246124267578125,
0.0113983154296875,
0.009735107421875,
-0.037689208984375,
0.0341796875,
-0.0027637481689453125,
0.04339599609375,
0.005504608154296875,
-0.0281829833984375,
-0.01340484619140625,
0.009674072265625,
0.007251739501953125,
0.001056671142578125,
0.0178070068359375,
0.017333984375,
0.00879669189453125,
-0.0233306884765625,
0.00986480712890625,
0.0006728172302246094,
-0.014068603515625,
-0.05865478515625,
-0.01496124267578125,
-0.0284881591796875,
-0.0168914794921875,
0.001781463623046875,
-0.01898193359375,
0.004425048828125,
-0.01331329345703125,
-0.0200042724609375,
-0.01265716552734375,
-0.037841796875,
-0.00015413761138916016,
-0.00543975830078125,
-0.0221405029296875,
0.01493072509765625,
0.0191650390625,
0.002246856689453125,
-0.0023651123046875,
0.0125885009765625,
0.00830078125,
-0.00021779537200927734,
0.0088653564453125,
0.01369476318359375,
0.016357421875,
-0.013580322265625,
0.004055023193359375,
-0.0233001708984375,
0.025726318359375,
-0.0269317626953125,
-0.0158233642578125,
0.0262298583984375,
0.0145111083984375,
-0.0088043212890625,
0.018951416015625,
-0.0004038810729980469,
0.002655029296875,
-0.00724029541015625,
0.039154052734375,
0.0160675048828125,
0.013641357421875,
-0.0022602081298828125,
0.0294952392578125,
0.00783538818359375,
-0.02093505859375,
-0.00902557373046875,
0.0180816650390625,
-0.0057830810546875,
-0.0246734619140625,
-0.030303955078125,
0.01611328125,
-0.034423828125,
-0.0164031982421875,
-0.040069580078125,
-0.00218963623046875,
0.0183868408203125,
0.0152587890625,
-0.026092529296875,
-0.0027179718017578125,
0.0161590576171875,
0.0199737548828125,
0.00928497314453125,
-0.0176239013671875,
-0.00865936279296875,
-0.0172271728515625,
-0.00007724761962890625,
-0.01739501953125,
0.00411224365234375,
-0.01715087890625,
-0.001743316650390625,
-0.01010894775390625,
-0.054046630859375,
-0.0194854736328125,
0.04754638671875,
-0.0010585784912109375,
0.0017242431640625,
0.00495147705078125,
0.0279083251953125,
-0.06524658203125,
0.0161285400390625,
-0.0248870849609375,
0.01031494140625,
-0.0341796875,
-0.01556396484375,
-0.0181884765625,
-0.0156097412109375,
0.01401519775390625,
0.00743865966796875,
0.0187530517578125,
0.002063751220703125,
-0.01273345947265625,
-0.026458740234375,
0.0181427001953125,
0.00951385498046875,
-0.0021457672119140625,
-0.0063629150390625,
-0.046600341796875,
-0.03533935546875,
0.050445556640625,
0.02947998046875,
0.045562744140625,
-0.00939178466796875,
-0.005634307861328125,
-0.00934600830078125,
0.034942626953125,
0.01087188720703125,
0.0218658447265625,
-0.026092529296875,
-0.0033702850341796875,
-0.031219482421875,
0.0218353271484375,
0.0006146430969238281,
-0.011932373046875,
0.016876220703125,
0.007587432861328125,
-0.0233001708984375,
0.020172119140625,
0.01319122314453125,
0.0285797119140625,
-0.01216888427734375,
-0.00841522216796875,
0.0213165283203125,
0.01995849609375,
0.0105438232421875,
0.0100860595703125,
-0.005512237548828125,
0.01488494873046875,
0.004566192626953125,
0.03662109375,
-0.011016845703125,
-0.03985595703125,
0.018890380859375,
-0.0263519287109375,
0.03125,
-0.00824737548828125,
0.00975799560546875,
-0.0147552490234375,
-0.021026611328125,
-0.0300140380859375,
-0.016448974609375,
-0.01276397705078125,
0.015594482421875,
-0.006145477294921875,
-0.002414703369140625,
-0.0245208740234375,
-0.007442474365234375,
-0.005710601806640625,
0.030029296875,
-0.0011425018310546875,
-0.015411376953125,
0.0139312744140625,
-0.0047607421875,
-0.0217437744140625,
0.047576904296875,
-0.00122833251953125,
0.031524658203125,
0.01318359375,
0.005359649658203125,
-0.0184783935546875,
-0.0201263427734375,
-0.0478515625,
-0.01519775390625,
-0.0013246536254882812,
0.00015151500701904297,
-0.01093292236328125,
0.0038814544677734375,
-0.0298309326171875,
0.0006346702575683594,
0.029571533203125,
-0.006725311279296875,
-0.02423095703125,
0.0210418701171875,
0.025238037109375,
-0.005619049072265625,
0.0148468017578125,
-0.01428985595703125,
0.007617950439453125,
0.01788330078125,
0.01145172119140625,
0.00655364990234375,
-0.0031032562255859375,
-0.0223541259765625,
0.0228271484375,
0.0182647705078125,
0.034881591796875,
-0.04119873046875,
-0.006114959716796875,
-0.00988006591796875,
0.0020847320556640625,
-0.01690673828125,
0.0162811279296875,
0.00024580955505371094,
0.016265869140625,
0.0242156982421875,
-0.0276336669921875,
-0.0005888938903808594,
0.0175628662109375,
-0.018707275390625,
-0.0281829833984375,
0.0010747909545898438,
-0.07513427734375,
0.0005812644958496094,
-0.0640869140625,
-0.004619598388671875,
0.0150604248046875,
0.0282440185546875,
0.00640869140625,
-0.01076507568359375,
-0.0272369384765625,
-0.005462646484375,
0.03009033203125,
-0.050537109375,
-0.025115966796875,
0.01154327392578125,
-0.03857421875,
-0.01061248779296875,
0.0022068023681640625,
0.0019121170043945312,
-0.005115509033203125,
-0.006969451904296875,
0.0078125,
-0.03302001953125,
-0.026641845703125,
0.01058197021484375,
-0.03948974609375,
-0.0042572021484375,
-0.0078277587890625,
-0.024322509765625,
-0.026519775390625,
-0.03582763671875,
-0.04803466796875,
0.039794921875,
-0.0015916824340820312,
-0.009063720703125,
0.0088653564453125,
-0.024200439453125,
-0.01413726806640625,
-0.022857666015625,
0.02349853515625,
0.0007486343383789062,
-0.0182037353515625,
0.0161895751953125,
0.018829345703125,
0.0168304443359375,
0.0103302001953125,
0.0235443115234375,
0.01166534423828125,
-0.00984954833984375,
-0.01079559326171875,
-0.0194854736328125,
-0.00946044921875,
0.0190887451171875,
-0.0274658203125,
0.0225067138671875,
0.0289764404296875,
0.021270751953125,
-0.01195526123046875,
0.0123138427734375,
-0.0182952880859375,
-0.033538818359375,
-0.01140594482421875,
0.018829345703125,
0.0030269622802734375,
0.04681396484375,
-0.0156707763671875,
0.00852203369140625,
0.014678955078125,
0.00838470458984375,
0.025421142578125,
-0.001251220703125,
0.01369476318359375,
-0.01163482666015625,
-0.01226806640625,
0.0295257568359375,
0.0020542144775390625,
-0.030029296875,
-0.0037326812744140625,
-0.030975341796875,
-0.0216522216796875,
-0.005489349365234375,
0.0077972412109375,
0.038360595703125,
0.029388427734375,
-0.002605438232421875,
0.0017805099487304688,
0.032257080078125,
-0.0029048919677734375,
-0.0001361370086669922,
0.00675201416015625,
0.0012044906616210938,
-0.01617431640625,
-0.002208709716796875,
-0.0182952880859375,
-0.0026798248291015625,
-0.0229034423828125,
0.014251708984375,
0.033447265625,
0.015045166015625,
0.01018524169921875,
-0.01947021484375,
0.01296234130859375,
-0.01204681396484375,
0.01540374755859375,
-0.001491546630859375,
0.0286407470703125,
0.0105743408203125,
0.062255859375,
0.01288604736328125,
-0.01031494140625,
-0.039459228515625,
0.010833740234375,
0.00580596923828125,
0.007476806640625,
-0.04901123046875,
0.018646240234375,
0.02142333984375,
-0.00958251953125,
0.0139617919921875,
0.003993988037109375,
0.0343017578125,
0.0195770263671875,
0.005443572998046875,
0.020355224609375,
-0.003246307373046875,
0.00897216796875,
-0.00157928466796875,
0.0007576942443847656,
0.01837158203125,
-0.023834228515625,
0.0029773712158203125,
-0.0347900390625,
-0.0117340087890625,
-0.00199127197265625,
0.00021827220916748047,
0.0298004150390625,
0.0084991455078125,
-0.01910400390625,
-0.01035308837890625,
0.028106689453125,
0.01485443115234375,
-0.01108551025390625,
0.00839996337890625,
-0.0301971435546875,
-0.005702972412109375,
0.0045166015625,
0.01531982421875,
-0.0178680419921875,
0.00860595703125,
-0.0018777847290039062,
0.01018524169921875,
-0.01300811767578125,
-0.0204010009765625,
0.0177764892578125,
-0.02532958984375,
-0.0120849609375,
-0.01715087890625,
-0.040802001953125,
-0.0168914794921875,
-0.00896453857421875,
0.005268096923828125,
-0.009857177734375,
0.0013723373413085938,
0.00800323486328125,
0.002002716064453125,
-0.025115966796875,
0.0049896240234375,
-0.0164794921875,
0.002288818359375,
0.014801025390625,
-0.017578125,
0.0340576171875,
-0.003376007080078125,
0.004505157470703125,
0.00209808349609375,
0.0028553009033203125,
0.042510986328125,
-0.004741668701171875,
0.0181427001953125,
0.03277587890625,
-0.004947662353515625,
-0.0220794677734375,
-0.028228759765625,
-0.0235595703125,
0.03564453125,
0.002079010009765625,
-0.0009665489196777344,
0.0313720703125,
0.0224761962890625,
0.0209808349609375,
-0.01262664794921875,
0.004535675048828125,
-0.040771484375,
-0.00286865234375,
-0.01323699951171875,
-0.0523681640625,
-0.00655364990234375,
-0.0305023193359375,
0.0246429443359375,
-0.01251220703125,
-0.022979736328125,
0.0158538818359375,
-0.0202178955078125,
0.01457977294921875,
-0.06658935546875,
0.0306396484375,
-0.01392364501953125,
0.0139617919921875,
0.0264739990234375,
0.0029888153076171875,
0.0146484375,
0.011566162109375,
0.0244598388671875,
-0.039398193359375,
0.02496337890625,
0.0045928955078125,
0.033172607421875,
-0.006450653076171875,
-0.0221099853515625,
0.02813720703125,
-0.0322265625,
0.0098876953125,
-0.0029468536376953125,
0.0070343017578125,
0.0184478759765625,
0.037445068359375,
0.0306396484375,
-0.0070953369140625,
0.023529052734375,
-0.0227508544921875,
0.00949859619140625,
-0.0015821456909179688,
0.0133056640625,
-0.0084228515625,
-0.0177001953125,
-0.0294189453125,
0.0262298583984375,
0.0018520355224609375,
-0.024658203125,
0.0279998779296875,
-0.027587890625,
-0.00588226318359375,
0.031494140625,
-0.009613037109375,
0.009124755859375,
-0.0192413330078125,
-0.006336212158203125,
0.0219268798828125,
0.0143585205078125,
0.0204620361328125,
0.00836181640625,
0.005794525146484375,
0.0162811279296875,
-0.0173492431640625,
-0.0005793571472167969,
0.006191253662109375,
0.006923675537109375,
0.037261962890625,
-0.01381683349609375,
-0.0335693359375,
0.0106353759765625,
-0.0077362060546875,
0.033935546875,
-0.0146026611328125,
-0.0038127899169921875,
0.022369384765625,
0.0440673828125,
-0.0025177001953125,
-0.01055145263671875,
-0.0014734268188476562,
-0.005672454833984375,
-0.0088958740234375,
0.0372314453125,
0.005496978759765625,
0.0157318115234375,
0.037841796875,
0.0389404296875,
-0.006137847900390625,
-0.0232086181640625,
-0.0007495880126953125,
0.0202484130859375,
-0.00891876220703125,
0.0094757080078125,
-0.003936767578125,
0.015106201171875,
-0.00543975830078125,
-0.00728607177734375,
0.009765625,
0.00539398193359375,
-0.0026073455810546875,
-0.01331329345703125,
-0.0120849609375,
0.01186370849609375,
-0.0149078369140625,
0.0169677734375,
-0.01165771484375,
0.014373779296875,
0.0118865966796875,
-0.022979736328125,
-0.00528717041015625,
-0.0026092529296875,
-0.01323699951171875,
0.00878143310546875,
-0.01372528076171875,
0.033538818359375,
0.018768310546875,
-0.004383087158203125,
-0.0101165771484375,
-0.025146484375,
0.00693511962890625,
-0.004024505615234375,
0.00482177734375,
0.01082611083984375,
0.005275726318359375,
0.0016641616821289062,
-0.03271484375,
-0.000274658203125,
0.01441192626953125,
0.02850341796875,
0.018402099609375,
0.005207061767578125,
0.009368896484375,
0.01416778564453125,
-0.03704833984375,
-0.00554656982421875,
-0.05084228515625,
0.03240966796875,
-0.01556396484375,
-0.0156402587890625,
0.0165252685546875,
0.0154266357421875,
-0.003963470458984375,
-0.0237884521484375,
-0.0096282958984375,
0.0109405517578125,
0.0003058910369873047,
-0.0093536376953125,
-0.0016422271728515625,
0.0036907196044921875,
0.00420379638671875,
-0.0214080810546875,
0.00897216796875,
-0.0158233642578125,
0.0045166015625,
-0.01142120361328125,
-0.007480621337890625,
0.01412200927734375,
0.0019178390502929688,
0.0015544891357421875,
-0.002033233642578125,
-0.033721923828125,
-0.0218048095703125,
-0.007568359375,
-0.024261474609375,
0.0328369140625,
-0.01552581787109375,
0.027679443359375,
0.037841796875,
0.00414276123046875,
0.017547607421875,
0.0163116455078125,
0.0154571533203125,
0.024932861328125,
-0.00023746490478515625,
0.0011224746704101562,
-0.032073974609375,
-0.0145721435546875,
0.01410675048828125,
0.0183868408203125,
-0.0017538070678710938,
-0.022430419921875,
0.0040283203125,
-0.03692626953125,
-0.005466461181640625,
-0.0112457275390625,
-0.0102386474609375,
0.0231475830078125,
-0.015289306640625,
-0.0029239654541015625,
0.006824493408203125,
-0.01439666748046875,
-0.006755828857421875,
0.0293426513671875,
-0.00897216796875,
0.0209197998046875,
-0.01398468017578125,
-0.0259552001953125,
-0.01032257080078125,
0.010650634765625,
-0.01629638671875,
-0.01824951171875,
0.00860595703125,
-0.028778076171875,
0.016143798828125,
-0.00901031494140625,
0.003116607666015625,
0.0004982948303222656,
-0.0151214599609375,
-0.00768280029296875,
-0.01276397705078125,
-0.00978851318359375,
0.01397705078125,
-0.0166778564453125,
-0.0162811279296875,
-0.041046142578125,
0.0220794677734375,
0.0034809112548828125,
-0.0253143310546875,
-0.0015459060668945312,
-0.01299285888671875,
0.007358551025390625,
0.0033664703369140625,
0.0158538818359375,
-0.0113372802734375,
-0.03131103515625,
0.01474761962890625,
0.015594482421875,
-0.00624847412109375,
0.001743316650390625,
-0.01032257080078125,
0.032806396484375,
0.0037174224853515625,
-0.0232696533203125,
-0.034820556640625,
-0.0300140380859375,
0.004131317138671875,
0.01171112060546875,
-0.0299835205078125,
-0.0015277862548828125,
-0.0243682861328125,
0.01485443115234375,
-0.03582763671875,
-0.024017333984375,
-0.0212249755859375,
0.01514434814453125,
-0.00040340423583984375,
-0.0283966064453125,
0.0029621124267578125,
0.00995635986328125,
0.02239990234375,
0.0177154541015625,
-0.0278472900390625,
0.015533447265625,
-0.0182647705078125,
-0.02288818359375,
-0.01091766357421875,
0.0255279541015625,
0.01273345947265625,
-0.0014638900756835938,
0.004024505615234375,
-0.055694580078125,
-0.018280029296875,
-0.0199737548828125,
0.010650634765625,
-0.0045318603515625,
0.044921875,
-0.00707244873046875,
-0.006458282470703125,
0.006084442138671875,
0.01216888427734375,
0.023529052734375,
-0.0078277587890625,
0.01995849609375,
0.01094818115234375,
-0.0035190582275390625,
-0.01100921630859375,
0.007366180419921875,
-0.0207672119140625,
-0.029327392578125,
-0.0143585205078125,
0.017791748046875,
0.024749755859375,
0.04486083984375,
0.0036449432373046875,
0.0027904510498046875,
0.0012683868408203125,
-0.01419830322265625,
0.00714874267578125,
0.05255126953125,
0.0134429931640625,
-0.004638671875,
-0.032318115234375,
-0.01180267333984375,
0.004421234130859375,
-0.00409698486328125,
0.03179931640625,
0.0214080810546875,
0.0250244140625,
0.005573272705078125,
0.004825592041015625,
-0.006683349609375,
-0.004634857177734375,
0.0078582763671875,
-0.01219940185546875,
0.039642333984375,
-0.004436492919921875,
-0.017669677734375,
-0.00650787353515625,
-0.0213165283203125,
0.018280029296875,
0.00405120849609375,
0.00128173828125,
-0.0013875961303710938,
0.0309906005859375,
-0.0160980224609375,
0.0125579833984375,
0.02581787109375,
0.0234527587890625,
-0.00048422813415527344,
0.007568359375,
-0.055419921875,
-0.0233306884765625,
-0.027923583984375,
-0.0035495758056640625,
0.020477294921875,
0.02374267578125,
0.00799560546875,
0.003643035888671875,
-0.02349853515625,
-0.018798828125,
0.007343292236328125,
-0.0125732421875,
0.007183074951171875,
0.012420654296875,
-0.020294189453125,
0.01538848876953125,
-0.00406646728515625,
0.0305328369140625,
0.00848388671875,
0.029144287109375,
-0.004421234130859375,
-0.003711700439453125,
-0.01031494140625,
-0.025482177734375,
0.0021457672119140625,
-0.003955841064453125,
-0.0097808837890625,
-0.0053253173828125,
-0.0189971923828125,
0.0013475418090820312,
0.02362060546875,
-0.0232696533203125,
-0.0341796875,
-0.023284912109375,
0.0190887451171875,
0.02508544921875,
-0.01300811767578125,
0.0291290283203125,
-0.00238800048828125,
0.003589630126953125,
-0.02471923828125,
-0.0290985107421875,
0.0106964111328125,
-0.003986358642578125,
0.0233612060546875,
-0.005260467529296875,
0.042144775390625,
0.004505157470703125,
0.009552001953125,
0.005168914794921875,
-0.005496978759765625,
-0.0115814208984375,
-0.0256195068359375,
-0.0175018310546875,
0.01033782958984375,
-0.01416778564453125,
0.00342559814453125,
-0.0090484619140625,
-0.0010366439819335938,
0.01202392578125,
0.0109100341796875,
0.00804901123046875,
-0.00955963134765625,
0.0138092041015625,
0.031707763671875,
-0.00946807861328125,
0.0231475830078125,
-0.0265045166015625,
0.022064208984375,
-0.0212860107421875,
-0.0014019012451171875,
0.0083465576171875,
-0.031890869140625,
-0.017608642578125,
-0.00936126708984375,
-0.007793426513671875,
0.0170135498046875,
0.003841400146484375,
0.0008401870727539062,
-0.0299835205078125,
0.0055389404296875,
0.031097412109375,
-0.0204010009765625,
0.0118255615234375,
0.00027489662170410156,
0.027313232421875,
-0.0400390625,
0.02435302734375,
0.028289794921875,
-0.012542724609375,
-0.0205841064453125,
0.002124786376953125,
-0.00002378225326538086,
-0.004085540771484375,
0.007167816162109375,
-0.033721923828125,
-0.0258941650390625,
0.0188751220703125,
-0.003326416015625,
-0.00576019287109375,
-0.0238189697265625,
0.01241302490234375,
0.008056640625,
0.01522064208984375,
-0.059906005859375,
-0.00527191162109375,
-0.0021877288818359375,
0.01462554931640625,
0.007701873779296875,
-0.0218048095703125,
0.0164031982421875,
-0.01849365234375,
-0.0058746337890625,
0.0018110275268554688,
-0.0277099609375,
-0.0138702392578125,
-0.01136016845703125,
-0.01515960693359375,
-0.026519775390625,
0.0167236328125,
-0.04071044921875,
-0.003383636474609375,
0.0214996337890625,
0.018157958984375,
0.01064300537109375,
-0.034576416015625,
0.005001068115234375,
0.0081329345703125,
-0.00335693359375,
0.033477783203125,
-0.0169219970703125,
0.012786865234375,
-0.00690460205078125,
-0.01169586181640625,
0.0001308917999267578,
0.0247955322265625,
0.019287109375,
-0.0252838134765625,
-0.041839599609375,
0.03741455078125,
-0.004207611083984375,
0.00443267822265625,
-0.0069732666015625,
-0.0092926025390625,
0.00261688232421875,
0.00496673583984375,
0.0006895065307617188,
-0.00904083251953125,
0.00550079345703125,
0.01947021484375,
0.01424407958984375,
-0.0006666183471679688,
0.00102996826171875,
0.006626129150390625,
-0.0301971435546875,
-0.005886077880859375,
-0.0234832763671875,
0.0010128021240234375,
-0.0162811279296875,
0.00399017333984375,
-0.00887298583984375,
0.03515625,
0.0004074573516845703,
-0.021209716796875,
-0.003627777099609375,
-0.00843048095703125,
0.004558563232421875,
0.003841400146484375,
-0.03594970703125,
0.0195465087890625,
0.0230560302734375,
-0.005527496337890625,
-0.0194244384765625,
-0.02069091796875,
-0.019866943359375,
-0.004619598388671875,
0.009552001953125,
-0.0082855224609375,
0.01537322998046875,
-0.03338623046875,
0.0038013458251953125,
0.007221221923828125,
0.0046539306640625,
-0.05059814453125,
0.0199737548828125,
-0.0200653076171875,
0.0240936279296875,
-0.00006693601608276367,
-0.021575927734375,
0.0109100341796875,
0.036102294921875,
-0.0029773712158203125,
-0.0029621124267578125,
-0.06890869140625,
-0.01033782958984375,
-0.0204010009765625,
0.006275177001953125,
0.01432037353515625,
0.0194244384765625,
-0.050262451171875,
-0.036285400390625,
0.0261688232421875,
-0.01000213623046875,
-0.0028972625732421875,
-0.0238494873046875,
0.004985809326171875,
-0.0012493133544921875,
-0.04034423828125,
-0.01201629638671875,
0.0440673828125,
-0.006961822509765625,
-0.007434844970703125,
0.028778076171875,
-0.00144195556640625,
-0.01342010498046875,
0.015869140625,
-0.0189666748046875,
0.0228118896484375,
0.00533294677734375,
-0.0064239501953125,
0.0205078125,
0.01216888427734375,
0.000012636184692382812,
-0.0220947265625,
0.04864501953125,
0.02984619140625,
-0.009613037109375,
-0.01071929931640625,
-0.00008744001388549805,
0.0246124267578125,
0.00933074951171875,
0.010833740234375,
0.005916595458984375,
0.010955810546875,
-0.0128021240234375,
0.01036834716796875,
0.0036468505859375,
0.005218505859375,
-0.003185272216796875,
0.007106781005859375,
-0.004886627197265625,
-0.004474639892578125,
-0.0075531005859375,
0.050079345703125,
-0.032196044921875,
0.00737762451171875,
0.03387451171875,
-0.0002682209014892578,
-0.006195068359375,
-0.00392913818359375,
0.00925445556640625,
0.02801513671875,
0.0010919570922851562,
-0.01247406005859375,
-0.0022754669189453125,
0.00664520263671875,
-0.0125885009765625,
0.01007843017578125,
-0.032867431640625,
0.012176513671875,
0.0159912109375,
-0.021270751953125,
0.051849365234375,
-0.0102386474609375,
0.0002791881561279297,
0.001678466796875,
0.005977630615234375,
-0.0242462158203125,
-0.007259368896484375,
0.02618408203125,
-0.0012559890747070312,
0.025726318359375,
-0.0137176513671875,
0.035308837890625,
-0.007221221923828125,
0.02099609375,
0.0141143798828125,
-0.0291595458984375,
-0.0384521484375,
-0.0105743408203125,
-0.00809478759765625,
0.019500732421875,
-0.0196380615234375,
-0.00498199462890625,
-0.021820068359375,
0.01032257080078125,
-0.006229400634765625,
0.0021381378173828125,
-0.00609588623046875,
-0.0035114288330078125,
-0.0173187255859375,
-0.006122589111328125,
0.01483154296875,
-0.005214691162109375,
0.026519775390625,
0.011810302734375,
-0.0347900390625,
0.023345947265625,
0.007343292236328125,
0.013671875,
-0.0234527587890625,
0.0024585723876953125,
-0.028076171875,
0.00435638427734375,
-0.0149993896484375,
0.0017833709716796875,
0.0257720947265625,
-0.0123291015625,
-0.0004093647003173828,
-0.0143280029296875,
0.031707763671875,
-0.00033402442932128906,
0.0170440673828125,
-0.0239715576171875,
-0.007717132568359375,
-0.011627197265625,
0.008819580078125,
0.0075836181640625,
0.004486083984375,
0.0113372802734375,
-0.02593994140625,
0.00787353515625,
0.0131683349609375,
-0.008819580078125,
0.0193939208984375,
0.0242462158203125,
0.01485443115234375,
0.032623291015625,
-0.04132080078125,
0.010498046875,
-0.0141754150390625,
0.00508880615234375,
0.0228424072265625,
-0.0127105712890625,
-0.001323699951171875,
0.00080108642578125,
-0.0269927978515625,
-0.00511932373046875,
0.0207977294921875,
-0.016693115234375,
-0.0096893310546875,
0.0122222900390625,
0.006221771240234375,
0.004634857177734375,
-0.0147705078125,
0.0140380859375,
0.01461029052734375,
0.042205810546875,
0.055511474609375,
-0.01203155517578125,
0.00843048095703125,
-0.0188751220703125,
-0.015289306640625,
0.0211639404296875,
0.0028362274169921875,
0.0002073049545288086,
0.0018968582153320312,
0.0099334716796875,
0.00928497314453125,
-0.0287933349609375,
-0.01349639892578125,
-0.00862884521484375,
0.0259857177734375,
-0.007358551025390625,
-0.01861572265625,
0.0181427001953125,
-0.037261962890625,
0.0030517578125,
-0.01053619384765625,
0.0164947509765625,
0.04034423828125,
0.0208587646484375,
-0.037322998046875,
0.0233917236328125,
-0.00638580322265625,
0.039154052734375,
0.005672454833984375,
-0.0007109642028808594,
0.005260467529296875,
0.009857177734375,
-0.0003941059112548828,
-0.02691650390625,
-0.01947021484375,
0.0010366439819335938,
-0.0201568603515625,
0.000046253204345703125,
0.0306396484375,
-0.0264892578125,
0.0202178955078125,
-0.006153106689453125,
0.0235137939453125,
-0.01090240478515625,
-0.00736236572265625,
-0.037689208984375,
-0.048919677734375,
-0.0098876953125,
0.0083465576171875,
0.00452423095703125,
-0.014434814453125,
0.002475738525390625,
0.0146026611328125,
-0.0204315185546875,
0.040252685546875,
-0.00922393798828125,
-0.040985107421875,
-0.0114288330078125,
0.01285552978515625,
-0.029144287109375,
-0.02203369140625,
0.0007147789001464844,
-0.01081085205078125,
0.01244354248046875,
-0.00860595703125,
0.003589630126953125,
0.020599365234375,
-0.01023101806640625,
-0.00926971435546875,
-0.017425537109375,
-0.006114959716796875,
0.0013036727905273438,
0.00789642333984375,
0.006565093994140625,
-0.0120391845703125,
0.0159912109375,
0.007183074951171875,
0.0333251953125,
-0.0098419189453125,
0.0164794921875,
0.01776123046875,
-0.0150299072265625,
-0.00334930419921875,
0.005756378173828125,
-0.01910400390625,
0.0213775634765625,
-0.01081085205078125,
-0.00908660888671875,
-0.00223541259765625,
-0.0166015625,
0.01049041748046875,
-0.00914764404296875,
0.0210723876953125,
0.00554656982421875,
0.01012420654296875,
0.005718231201171875,
-0.031768798828125,
0.025146484375,
-0.024749755859375,
-0.027191162109375,
0.012542724609375,
0.0103607177734375,
-0.00695037841796875,
0.004276275634765625,
0.0496826171875,
0.0093841552734375,
0.005123138427734375,
-0.004886627197265625,
0.0026721954345703125,
0.003116607666015625,
0.00885009765625,
0.005474090576171875,
-0.00948333740234375,
-0.02874755859375,
-0.005962371826171875,
-0.005123138427734375,
0.0291900634765625,
-0.015899658203125,
0.002277374267578125,
0.03302001953125,
-0.033905029296875,
0.01349639892578125,
0.0224151611328125,
0.029541015625,
-0.007511138916015625,
0.0002453327178955078,
-0.0168914794921875,
0.0200042724609375,
-0.023529052734375,
-0.01123809814453125,
0.023773193359375,
-0.016693115234375,
-0.0237579345703125,
-0.00609588623046875,
0.0099334716796875,
0.04656982421875,
0.0022830963134765625,
-0.006465911865234375,
-0.0176544189453125,
-0.003940582275390625,
-0.00499725341796875,
-0.0079193115234375,
-0.028076171875,
-0.0048370361328125,
-0.0031147003173828125,
0.01445770263671875,
0.0172882080078125,
0.031951904296875,
0.01381683349609375,
-0.00820159912109375,
0.0196075439453125,
-0.00722503662109375,
0.022247314453125,
-0.01381683349609375,
0.0170440673828125,
0.0264892578125,
0.0053253173828125,
0.0024871826171875,
-0.016204833984375,
-0.0004978179931640625,
-0.0222015380859375,
-0.02239990234375,
0.0185546875,
0.0250244140625,
-0.004909515380859375,
-0.0156402587890625,
-0.00036644935607910156,
-0.004852294921875,
-0.0291748046875,
-0.0006160736083984375,
-0.0021152496337890625,
0.00742340087890625,
0.0183258056640625,
-0.0233306884765625,
0.0140533447265625,
-0.01910400390625,
0.01096343994140625,
0.0002980232238769531,
-0.013916015625,
0.03424072265625,
-0.01209259033203125,
-0.0303802490234375,
-0.005016326904296875,
0.037322998046875,
0.00804901123046875,
-0.0260772705078125,
0.0049896240234375,
-0.03564453125,
-0.0172119140625,
-0.0178985595703125,
0.010528564453125,
0.005279541015625,
-0.0047454833984375,
-0.0235443115234375,
-0.00627899169921875,
-0.0256500244140625,
0.00530242919921875,
-0.01393890380859375,
-0.05889892578125,
-0.0005626678466796875,
-0.00861358642578125,
0.017730712890625,
0.0015802383422851562,
0.0220947265625,
0.004062652587890625,
-0.0175628662109375,
-0.037322998046875,
-0.00429534912109375,
-0.0355224609375,
-0.00772857666015625,
0.0262298583984375,
-0.00766754150390625,
-0.0228271484375,
0.0362548828125,
0.038116455078125,
0.0032329559326171875,
0.0162811279296875,
-0.034881591796875,
0.0036163330078125,
-0.01389312744140625,
-0.04144287109375,
-0.004329681396484375,
-0.0309295654296875,
0.006195068359375,
-0.01340484619140625,
0.0155792236328125,
-0.04351806640625,
-0.017852783203125,
-0.02191162109375,
0.04571533203125,
-0.01611328125,
0.00017547607421875,
-0.0023441314697265625,
0.029693603515625,
-0.0215301513671875,
-0.0249786376953125,
-0.0012693405151367188,
-0.0160675048828125,
0.00846099853515625,
-0.036224365234375,
-0.0035266876220703125,
-0.01078033447265625,
0.0011529922485351562,
-0.0107879638671875,
-0.001789093017578125,
-0.0186920166015625,
-0.00434112548828125,
-0.0050201416015625,
-0.01062774658203125,
0.020538330078125,
-0.00787353515625,
-0.0068206787109375,
-0.006771087646484375,
0.06011962890625,
-0.0063018798828125,
0.00396728515625,
0.00490570068359375,
0.0310516357421875,
-0.0165252685546875,
-0.01125335693359375,
0.05426025390625,
-0.00449371337890625,
0.01552581787109375,
-0.009979248046875,
-0.0225372314453125,
-0.0236358642578125,
0.00525665283203125,
-0.03338623046875,
-0.00882720947265625,
0.005176544189453125,
-0.0213775634765625,
-0.01194000244140625,
-0.0181884765625,
-0.039794921875,
0.0164337158203125,
-0.007110595703125,
-0.01197052001953125,
-0.012725830078125,
0.03314208984375,
-0.003749847412109375,
0.003387451171875,
0.0199737548828125,
-0.0063934326171875,
0.0003209114074707031,
-0.0248870849609375,
-0.03338623046875,
0.016876220703125,
-0.021240234375,
-0.006465911865234375,
-0.0239410400390625,
0.0154571533203125,
0.02105712890625,
-0.0051422119140625,
0.030853271484375,
0.00528717041015625,
-0.0164947509765625,
-0.0017805099487304688,
-0.0311431884765625,
-0.0109100341796875,
-0.0283050537109375,
-0.024658203125,
0.006702423095703125,
-0.0186309814453125,
-0.0145721435546875,
-0.00604248046875,
0.027099609375,
-0.0226287841796875,
-0.032073974609375,
0.009429931640625,
0.00862884521484375,
0.0220489501953125,
0.00777435302734375,
-0.014251708984375,
0.01812744140625,
0.00980377197265625,
0.00397491455078125,
-0.019287109375,
-0.004566192626953125,
-0.0076904296875,
-0.035675048828125,
-0.0026912689208984375,
0.005443572998046875,
0.010528564453125,
-0.02655029296875,
0.004734039306640625,
0.0168609619140625,
-0.0036258697509765625,
-0.036651611328125,
0.0018701553344726562,
-0.0076141357421875,
0.0130767822265625,
0.047210693359375,
-0.00283050537109375,
0.01407623291015625,
0.006145477294921875,
0.0224456787109375,
-0.0220947265625,
-0.0258941650390625,
-0.004119873046875,
0.0244140625,
0.01177215576171875,
0.01885986328125,
-0.0030460357666015625,
-0.0029773712158203125,
0.02178955078125,
-0.0155029296875,
-0.001026153564453125,
0.03839111328125,
0.01560211181640625,
0.029266357421875,
0.0299530029296875,
-0.004093170166015625,
0.0186767578125,
-0.0172271728515625,
-0.0199737548828125,
-0.018463134765625,
-0.023529052734375,
-0.07720947265625,
0.01548004150390625,
-0.003993988037109375,
-0.033935546875,
0.0164337158203125,
-0.010772705078125,
-0.007080078125,
0.0022716522216796875,
0.033203125,
0.03790283203125,
0.00811004638671875,
0.0005292892456054688,
-0.007320404052734375,
0.0280303955078125,
0.00807952880859375,
-0.002429962158203125,
-0.024993896484375,
-0.0082550048828125,
-0.0275726318359375,
0.0265045166015625,
0.0037250518798828125,
0.0177001953125,
-0.05316162109375,
-0.00815582275390625,
-0.02886962890625,
0.041748046875,
0.0029296875,
-0.02032470703125,
-0.0235748291015625,
-0.031829833984375,
-0.0189361572265625,
0.0091094970703125,
0.01276397705078125,
0.01360321044921875,
-0.036773681640625,
0.004772186279296875,
-0.01491546630859375,
0.012420654296875,
-0.017608642578125,
0.0364990234375,
0.0007166862487792969,
-0.0145416259765625,
-0.03216552734375,
0.031005859375,
-0.01413726806640625,
0.0005245208740234375,
-0.0133056640625,
0.015869140625,
0.028778076171875,
0.042510986328125,
-0.01023101806640625,
0.02020263671875,
0.0108642578125,
-0.0350341796875,
-0.0352783203125,
-0.01059722900390625,
0.041259765625,
0.00878143310546875,
-0.0129852294921875,
-0.00768280029296875,
0.0291900634765625,
-0.01538848876953125,
0.01885986328125,
-0.014129638671875,
0.04931640625,
-0.0286407470703125,
0.021331787109375,
-0.0287322998046875,
0.01038360595703125,
0.0117340087890625,
0.016082763671875,
0.006282806396484375,
-0.01375579833984375,
-0.031707763671875,
-0.03057861328125,
-0.00713348388671875,
0.003162384033203125,
0.007389068603515625,
-0.022491455078125,
0.0250701904296875,
0.0172576904296875,
-0.03338623046875,
0.023162841796875,
-0.00746917724609375,
-0.0211944580078125,
0.0262603759765625,
-0.04052734375,
0.0162811279296875,
-0.03204345703125,
0.0252227783203125,
-0.0115966796875,
0.02191162109375,
0.031463623046875,
-0.009246826171875,
-0.0013036727905273438,
0.0204925537109375,
0.01568603515625,
-0.025054931640625,
-0.01233673095703125,
0.000044465065002441406,
-0.011474609375,
-0.0026721954345703125,
-0.046600341796875,
0.006587982177734375,
-0.015716552734375,
0.031463623046875,
0.0220184326171875,
-0.0016508102416992188,
0.0033931732177734375,
-0.004974365234375,
-0.0028362274169921875,
-0.0038928985595703125,
0.0239105224609375,
0.0043792724609375,
-0.0181884765625,
-0.0289764404296875,
0.041259765625,
-0.0140380859375,
-0.015380859375,
0.033050537109375,
0.0017957687377929688,
-0.02996826171875,
-0.0025177001953125,
0.0248260498046875,
0.0007939338684082031,
-0.00868988037109375,
0.00665283203125,
0.00876617431640625,
0.007686614990234375,
-0.01134490966796875,
-0.0036067962646484375,
-0.0204315185546875,
0.01097869873046875,
0.0189208984375,
-0.007232666015625,
-0.004222869873046875,
0.0322265625,
0.02850341796875,
-0.0217132568359375,
0.016815185546875,
-0.027008056640625,
-0.00849151611328125,
0.032257080078125,
-0.0210418701171875,
-0.0195465087890625,
-0.0015659332275390625,
0.025390625,
0.0250701904296875,
-0.03399658203125,
-0.007450103759765625,
-0.00504302978515625,
-0.03509521484375,
-0.00923919677734375,
-0.006549835205078125,
0.00658416748046875,
-0.04327392578125,
-0.0171966552734375,
-0.0177154541015625,
0.0118255615234375,
0.0210723876953125,
0.0143585205078125,
0.0022945404052734375,
0.02392578125,
0.032623291015625,
0.0004858970642089844,
0.0035114288330078125,
0.01293182373046875,
-0.0036563873291015625,
0.006793975830078125,
-0.01447296142578125,
-0.03472900390625,
-0.0299835205078125,
0.0238189697265625,
0.0022716522216796875,
-0.00904083251953125,
0.013763427734375,
0.0267486572265625,
0.021209716796875,
0.00557708740234375,
-0.01561737060546875,
0.002246856689453125,
0.01242828369140625,
0.0022125244140625,
-0.033782958984375,
0.02362060546875,
0.033111572265625,
-0.00899505615234375,
-0.045318603515625,
-0.040679931640625,
-0.00913238525390625,
-0.0224151611328125,
0.037689208984375,
-0.031524658203125,
0.003398895263671875,
-0.0012073516845703125,
-0.0116119384765625,
-0.0123138427734375,
0.031982421875,
-0.02398681640625,
-0.0029888153076171875,
-0.00516510009765625,
0.00719451904296875,
0.0271148681640625,
0.01497650146484375,
-0.016021728515625,
0.0240020751953125,
0.0222625732421875,
-0.0243682861328125,
-0.00913238525390625,
0.0048828125,
0.0138702392578125,
-0.0277252197265625,
-0.0087890625,
-0.006282806396484375,
-0.0059967041015625,
0.0008521080017089844,
0.0008149147033691406,
-0.02178955078125,
0.009368896484375,
-0.0014095306396484375,
0.03216552734375,
0.01297760009765625,
-0.029205322265625,
0.0225677490234375,
0.0053253173828125,
-0.015869140625,
0.0153656005859375,
-0.00485992431640625,
-0.005535125732421875,
0.0086517333984375,
-0.02789306640625,
0.0215911865234375,
0.011871337890625,
0.031036376953125,
0.0338134765625,
-0.03564453125,
0.04595947265625,
-0.0037593841552734375,
-0.007579803466796875,
-0.00951385498046875,
0.02191162109375,
0.012176513671875,
0.0093536376953125,
0.0321044921875,
0.01477813720703125,
0.01287841796875,
0.00571441650390625,
-0.0064849853515625,
-0.00528717041015625,
0.00893402099609375,
-0.0069732666015625,
-0.02178955078125,
0.004642486572265625,
0.032623291015625,
0.0261993408203125,
0.001140594482421875,
0.0018587112426757812,
0.00945281982421875,
-0.026580810546875,
0.00472259521484375,
-0.037506103515625,
0.01666259765625,
0.03466796875,
-0.01534271240234375,
-0.01262664794921875,
0.00016963481903076172,
0.036834716796875,
0.0009403228759765625,
-0.01131439208984375,
-0.032684326171875,
-0.00623321533203125,
0.003238677978515625,
-0.0005846023559570312,
0.0109405517578125,
0.02337646484375,
0.0020313262939453125,
0.0360107421875,
-0.0173797607421875,
0.0162353515625,
0.0262603759765625,
0.0037212371826171875,
-0.022857666015625,
0.024383544921875,
-0.0171966552734375,
0.003025054931640625,
-0.046844482421875,
0.0196380615234375,
-0.01201629638671875,
0.0005202293395996094,
-0.00785064697265625,
-0.0197906494140625,
-0.00469970703125,
0.0010051727294921875,
0.0240936279296875,
-0.005939483642578125,
0.01239013671875,
-0.021575927734375,
0.0014362335205078125,
0.01047515869140625,
-0.005859375,
-0.0160064697265625,
0.0119781494140625,
0.0164337158203125,
0.0005888938903808594,
-0.00732421875,
0.01177978515625,
0.035919189453125,
0.02423095703125,
-0.046875,
-0.022857666015625,
0.008697509765625,
-0.002895355224609375,
0.046234130859375,
-0.0124053955078125,
0.0129241943359375,
-0.0018186569213867188,
0.004669189453125,
0.0294189453125,
0.0032520294189453125,
-0.0014066696166992188,
-0.00894927978515625,
-0.035858154296875,
-0.039703369140625,
0.003662109375,
-0.0156707763671875,
-0.0008707046508789062,
-0.0096588134765625,
0.014923095703125,
-0.0191802978515625,
0.01377105712890625,
-0.004222869873046875,
-0.01265716552734375,
-0.0245513916015625,
0.0188140869140625,
-0.004550933837890625,
0.0051727294921875,
0.040985107421875,
-0.0103302001953125,
-0.014892578125,
-0.0191802978515625,
0.010498046875,
0.01306915283203125,
-0.006923675537109375,
0.0028076171875,
-0.0230560302734375,
-0.0181732177734375,
0.024932861328125,
-0.0179595947265625,
-0.0035572052001953125,
-0.0108642578125,
0.01282501220703125,
0.00853729248046875,
-0.0305633544921875,
0.0243377685546875,
0.0022182464599609375,
-0.007266998291015625,
0.007228851318359375,
0.0229644775390625,
-0.00250244140625,
-0.0024814605712890625,
0.0167999267578125,
-0.01155853271484375,
0.005260467529296875,
-0.00701141357421875,
0.01535797119140625,
-0.027984619140625,
-0.0022296905517578125,
0.0035839080810546875,
-0.033905029296875,
-0.0117340087890625,
-0.0203094482421875,
-0.01525115966796875,
-0.023101806640625,
-0.04193115234375,
0.016845703125,
-0.002506256103515625,
-0.0177459716796875,
0.006160736083984375,
0.02703857421875,
-0.00791168212890625,
0.042633056640625,
0.01493072509765625,
-0.018402099609375,
-0.005878448486328125,
-0.003810882568359375,
-0.0038394927978515625,
0.020172119140625,
0.0196990966796875,
-0.0257415771484375,
0.01126861572265625,
0.0006279945373535156,
-0.0248565673828125,
-0.00048613548278808594,
0.0302581787109375,
0.0013666152954101562,
-0.0057373046875,
-0.021575927734375,
0.01210784912109375,
0.00955963134765625,
0.04840087890625,
-0.0079803466796875,
0.02392578125,
0.0213470458984375,
-0.0080718994140625,
-0.0029659271240234375,
-0.0009984970092773438,
-0.0144500732421875,
0.009063720703125,
0.02166748046875,
0.045684814453125,
-0.0139007568359375,
0.039154052734375,
0.0105133056640625,
0.00396728515625,
0.0193939208984375,
-0.044464111328125,
-0.0010881423950195312,
-0.0238800048828125,
0.051483154296875,
-0.00025153160095214844,
0.00635528564453125,
-0.01149749755859375,
-0.01200103759765625,
0.0218048095703125,
-0.00893402099609375,
-0.0159454345703125,
-0.01282501220703125,
0.0116424560546875,
-0.036834716796875,
-0.02301025390625,
-0.024932861328125,
-0.0160980224609375,
0.019744873046875,
-0.0024089813232421875,
0.0162353515625,
-0.0102691650390625,
0.0220794677734375,
0.026611328125,
-0.0418701171875,
0.007965087890625,
0.00934600830078125,
-0.0007915496826171875,
-0.006320953369140625,
0.01021575927734375,
0.02899169921875,
-0.019378662109375,
-0.0100250244140625,
0.018585205078125,
0.021392822265625,
0.01441192626953125,
0.05670166015625,
0.0036411285400390625,
-0.005458831787109375,
-0.01280975341796875,
0.002651214599609375,
0.0035877227783203125,
-0.037841796875,
-0.00614166259765625,
0.004459381103515625,
0.006092071533203125,
0.0178985595703125,
-0.0013637542724609375,
0.03485107421875,
-0.007663726806640625,
-0.037261962890625,
0.020904541015625,
-0.0012035369873046875,
0.0028476715087890625,
-0.01104736328125,
0.03753662109375,
-0.00838470458984375,
0.01026153564453125,
-0.004150390625,
-0.031982421875,
0.0170135498046875,
0.01136016845703125,
-0.00949859619140625,
0.00238037109375,
-0.0032196044921875,
-0.03692626953125,
0.004627227783203125,
0.006977081298828125,
-0.054229736328125,
-0.0116119384765625,
-0.0338134765625,
0.00399017333984375,
-0.007167816162109375,
-0.0050506591796875,
-0.006076812744140625,
0.0298614501953125,
0.020263671875,
-0.0023193359375,
0.0179595947265625,
-0.00922393798828125,
-0.006465911865234375,
-0.007534027099609375,
-0.01474761962890625,
-0.0220794677734375,
-0.003017425537109375,
-0.0330810546875,
-0.0062408447265625,
-0.010223388671875,
0.0203094482421875,
-0.0196990966796875,
-0.0271453857421875,
0.048248291015625,
0.00225067138671875,
-0.035980224609375,
-0.016448974609375,
-0.0065460205078125,
0.004489898681640625,
-0.00482940673828125,
0.0069122314453125,
-0.0012197494506835938,
-0.03643798828125,
0.0017957687377929688,
-0.01241302490234375,
0.00267791748046875,
0.008453369140625,
-0.0167999267578125,
-0.00841522216796875,
-0.016632080078125,
0.00409698486328125,
-0.00882720947265625,
0.01044464111328125,
-0.024169921875,
-0.030731201171875,
0.0006508827209472656,
-0.01428985595703125,
-0.00882720947265625,
-0.021209716796875,
-0.004119873046875,
-0.032806396484375,
-0.01568603515625,
-0.00572967529296875,
-0.04168701171875,
-0.00823211669921875,
0.047821044921875,
-0.0291290283203125,
-0.00897216796875,
0.00400543212890625,
-0.00609588623046875,
0.016571044921875,
-0.008331298828125,
0.0025959014892578125,
0.043548583984375,
0.01512908935546875,
0.01319122314453125,
-0.00301361083984375,
-0.04718017578125,
-0.042755126953125,
0.004241943359375,
0.00958251953125,
0.030426025390625,
0.020477294921875,
0.0013055801391601562,
0.005565643310546875,
-0.022735595703125,
0.0419921875,
-0.0244293212890625,
0.00420379638671875,
0.00012117624282836914,
-0.01485443115234375,
-0.030487060546875,
-0.0117034912109375,
0.01348114013671875,
0.0018625259399414062,
0.023284912109375,
0.007335662841796875,
-0.004947662353515625,
-0.03509521484375,
-0.03057861328125,
0.01033782958984375,
0.015533447265625,
-0.009246826171875,
0.0168609619140625,
0.01076507568359375,
0.0029544830322265625
] |
ours_535
|
The center of \(\Gamma_{2}\), denoted \(O_{2}\), lies on \(\Gamma_{1}\), denoted \(O_{1}\), because their centers are 2012 apart. Also, \(\angle CO_{1}A = 60^{\circ}\), because \(\angle O_{2}O_{1}A = \angle O_{2}O_{1}B = 60^{\circ}\). Similarly, \(\angle DO_{2}A = 60^{\circ}\). Thus, \(\triangle CO_{1}A\) and \(\triangle DO_{2}A\) are equilateral. This implies that \(CA = DA = 2012\), so \(CD = 4024\).
\(\boxed{4024}\)
|
4024
|
{
"competition": "us_comps",
"dataset": "Ours",
"posts": null,
"source": "OMOSoln2.md"
}
|
Congruent circles \(\Gamma_{1}\) and \(\Gamma_{2}\) have radius 2012, and the center of \(\Gamma_{1}\) lies on \(\Gamma_{2}\). Suppose that \(\Gamma_{1}\) and \(\Gamma_{2}\) intersect at \(A\) and \(B\). The line through \(A\) perpendicular to \(AB\) meets \(\Gamma_{1}\) and \(\Gamma_{2}\) again at \(C\) and \(D\), respectively. Find the length of \(CD\).
|
[
"/Mathematics/Geometry/Distance/Point-PointDistance2-Dimensional",
"/Mathematics/Geometry/GeneralGeometry/Center",
"/Mathematics/Geometry/GeneralGeometry/EuclideanGeometry",
"/Mathematics/Geometry/GeneralGeometry/Geometry",
"/Mathematics/Geometry/PlaneGeometry/Circles/Circle",
"/Mathematics/Geometry/PlaneGeometry/Circles/Circle-CircleIntersection",
"/Mathematics/Geometry/PlaneGeometry/Circles/Radius",
"/Mathematics/Geometry/PlaneGeometry/CircularTriangles",
"/Mathematics/Geometry/PlaneGeometry/Triangles/SpecialTriangles"
] |
Recognize that the centers and an intersection point form an equilateral triangle, giving 60° angles that make the two radii triangles equilateral.
|
[
0.00004869699478149414,
-0.023406982421875,
0.031707763671875,
-0.01244354248046875,
0.00048065185546875,
0.0060272216796875,
-0.0011730194091796875,
0.039093017578125,
0.006526947021484375,
-0.01439666748046875,
-0.00299835205078125,
0.0286102294921875,
-0.005702972412109375,
0.00196075439453125,
-0.02410888671875,
0.0193634033203125,
0.01244354248046875,
-0.017608642578125,
0.0143280029296875,
0.0017147064208984375,
-0.0116424560546875,
0.04180908203125,
-0.08172607421875,
0.003932952880859375,
0.02197265625,
-0.00044083595275878906,
-0.01532745361328125,
-0.04669189453125,
0.02392578125,
0.0341796875,
-0.006427764892578125,
-0.003910064697265625,
0.021881103515625,
-0.019317626953125,
0.0019817352294921875,
0.0164794921875,
-0.01282501220703125,
0.0081634521484375,
-0.01313018798828125,
-0.0171966552734375,
0.005126953125,
0.02337646484375,
-0.0169219970703125,
0.007190704345703125,
-0.0297088623046875,
0.038177490234375,
-0.0075531005859375,
0.01410675048828125,
-0.01457977294921875,
-0.00380706787109375,
0.00606536865234375,
0.017303466796875,
-0.0185089111328125,
0.0018320083618164062,
-0.004688262939453125,
-0.0716552734375,
-0.005565643310546875,
0.0031452178955078125,
-0.019500732421875,
-0.0011577606201171875,
0.004058837890625,
0.0029315948486328125,
0.0005002021789550781,
0.006000518798828125,
-0.0013751983642578125,
0.0017595291137695312,
-0.0014495849609375,
0.0016880035400390625,
-0.0018463134765625,
-0.020538330078125,
0.0174560546875,
-0.013671875,
0.00977325439453125,
-0.005443572998046875,
-0.006603240966796875,
-0.01129913330078125,
0.0021953582763671875,
0.0102996826171875,
-0.0278472900390625,
-0.002368927001953125,
-0.0145263671875,
0.00830841064453125,
0.0259552001953125,
-0.0244140625,
-0.0118408203125,
-0.01171112060546875,
-0.03070068359375,
0.00246429443359375,
0.01346588134765625,
0.0063934326171875,
-0.00597381591796875,
0.0078582763671875,
-0.0175628662109375,
0.010955810546875,
0.00217437744140625,
0.00542449951171875,
0.0021820068359375,
0.0016345977783203125,
-0.016326904296875,
0.00449371337890625,
-0.00958251953125,
-0.005420684814453125,
-0.02520751953125,
-0.0126953125,
-0.011505126953125,
-0.01560211181640625,
-0.00014328956604003906,
-0.00457763671875,
0.001766204833984375,
-0.00902557373046875,
0.0180511474609375,
0.00476837158203125,
0.02960205078125,
0.038482666015625,
-0.0096588134765625,
-0.020965576171875,
0.01181793212890625,
0.0183563232421875,
-0.004405975341796875,
-0.00676727294921875,
-0.0037059783935546875,
0.020751953125,
-0.002017974853515625,
-0.0016345977783203125,
0.002552032470703125,
-0.032623291015625,
0.016357421875,
-0.0198974609375,
-0.023651123046875,
0.0277862548828125,
0.046234130859375,
0.0009388923645019531,
-0.049560546875,
-0.0163421630859375,
0.03021240234375,
-0.019439697265625,
0.020660400390625,
0.00319671630859375,
0.00913238525390625,
0.004405975341796875,
-0.01171875,
-0.01030731201171875,
0.01812744140625,
-0.08050537109375,
0.01450347900390625,
-0.032806396484375,
0.0089263916015625,
-0.01375579833984375,
0.015869140625,
-0.005218505859375,
-0.0204925537109375,
0.00878143310546875,
0.0166015625,
0.00556182861328125,
-0.00989532470703125,
0.0202789306640625,
0.00820159912109375,
0.031982421875,
0.02398681640625,
-0.014923095703125,
0.00396728515625,
-0.00897216796875,
0.0302276611328125,
0.01324462890625,
-0.005016326904296875,
-0.0239410400390625,
0.0271759033203125,
-0.016265869140625,
-0.01435089111328125,
-0.021484375,
-0.00786590576171875,
-0.005279541015625,
0.0091094970703125,
0.0009984970092773438,
-0.0206146240234375,
0.0009098052978515625,
-0.00672149658203125,
-0.01213836669921875,
0.007633209228515625,
0.01209259033203125,
-0.002162933349609375,
-0.0213623046875,
0.0369873046875,
-0.0048675537109375,
0.02813720703125,
0.01036834716796875,
0.005218505859375,
0.0070037841796875,
0.01479339599609375,
0.0009851455688476562,
0.004413604736328125,
-0.036712646484375,
-0.0030841827392578125,
-0.0012350082397460938,
-0.0105133056640625,
-0.0045318603515625,
-0.0205841064453125,
0.01422119140625,
0.01544189453125,
0.0220794677734375,
-0.014434814453125,
-0.03424072265625,
0.0196685791015625,
0.00469970703125,
-0.002468109130859375,
0.007144927978515625,
-0.00008845329284667969,
-0.005657196044921875,
-0.004444122314453125,
0.002117156982421875,
0.0196533203125,
0.02752685546875,
-0.0194549560546875,
0.00615692138671875,
-0.01446533203125,
-0.01800537109375,
-0.01139068603515625,
0.007038116455078125,
0.018310546875,
0.017303466796875,
0.01739501953125,
-0.0116119384765625,
-0.01497650146484375,
0.005001068115234375,
-0.0311737060546875,
-0.006664276123046875,
0.0157928466796875,
-0.01081085205078125,
0.0260162353515625,
0.0030059814453125,
-0.0036678314208984375,
-0.0019931793212890625,
0.000988006591796875,
0.0014371871948242188,
-0.00644683837890625,
-0.004486083984375,
-0.0218048095703125,
0.00832366943359375,
-0.0032520294189453125,
0.03668212890625,
0.031890869140625,
-0.0202484130859375,
0.01406097412109375,
-0.006496429443359375,
0.004604339599609375,
0.0100555419921875,
0.0123291015625,
-0.01047515869140625,
-0.01174163818359375,
-0.01293182373046875,
-0.040283203125,
0.00032448768615722656,
0.00104522705078125,
0.01332855224609375,
-0.00440216064453125,
0.0195465087890625,
-0.0049896240234375,
0.0188140869140625,
0.007770538330078125,
-0.0080108642578125,
-0.020294189453125,
-0.020233154296875,
-0.0027370452880859375,
-0.0211334228515625,
-0.0132598876953125,
0.027862548828125,
-0.03997802734375,
0.0025157928466796875,
0.023193359375,
-0.03424072265625,
0.046478271484375,
-0.005992889404296875,
-0.0111846923828125,
-0.0017871856689453125,
-0.018646240234375,
-0.005733489990234375,
-0.01122283935546875,
0.0283355712890625,
0.0070953369140625,
0.01459503173828125,
-0.0007214546203613281,
0.0005035400390625,
-0.07470703125,
0.02716064453125,
0.0203704833984375,
0.0191192626953125,
0.010406494140625,
-0.0218963623046875,
0.0034122467041015625,
0.0205078125,
-0.00827789306640625,
-0.0189361572265625,
-0.0152435302734375,
-0.0032978057861328125,
0.05706787109375,
0.036163330078125,
-0.017486572265625,
0.02313232421875,
-0.0190582275390625,
-0.0094451904296875,
0.0089263916015625,
-0.016998291015625,
0.00215911865234375,
0.033294677734375,
0.03497314453125,
0.05584716796875,
0.0120697021484375,
-0.01580810546875,
-0.0274658203125,
0.002002716064453125,
0.024993896484375,
-0.000698089599609375,
-0.0164642333984375,
0.00464630126953125,
0.01334381103515625,
-0.03131103515625,
-0.00019943714141845703,
0.0213470458984375,
-0.0017366409301757812,
0.04473876953125,
0.0015726089477539062,
0.022796630859375,
0.0362548828125,
0.0035076141357421875,
0.053802490234375,
-0.0026416778564453125,
0.0372314453125,
-0.01155853271484375,
0.01525115966796875,
0.02374267578125,
0.00922393798828125,
0.00899505615234375,
-0.014190673828125,
-0.0199127197265625,
-0.00992584228515625,
0.002349853515625,
-0.004001617431640625,
-0.00872039794921875,
0.03216552734375,
-0.008087158203125,
-0.0060882568359375,
0.0007081031799316406,
0.036651611328125,
-0.052581787109375,
-0.06292724609375,
0.003509521484375,
-0.0345458984375,
-0.0122833251953125,
-0.06298828125,
-0.011322021484375,
0.0205535888671875,
-0.00023412704467773438,
0.028076171875,
0.00525665283203125,
-0.0220489501953125,
0.007659912109375,
0.01837158203125,
0.01483917236328125,
0.005641937255859375,
0.022857666015625,
0.005130767822265625,
-0.041229248046875,
0.00873565673828125,
-0.004856109619140625,
-0.02874755859375,
-0.0241241455078125,
-0.00310516357421875,
0.016937255859375,
-0.0655517578125,
0.002986907958984375,
0.0015888214111328125,
0.0170135498046875,
-0.0189361572265625,
0.007022857666015625,
0.0123138427734375,
0.01560211181640625,
0.006877899169921875,
0.00556182861328125,
0.002979278564453125,
0.0077972412109375,
0.0080718994140625,
0.01070404052734375,
0.0025424957275390625,
0.0167083740234375,
0.018524169921875,
0.0086517333984375,
0.004093170166015625,
-0.00568389892578125,
-0.005237579345703125,
-0.0021495819091796875,
-0.0131988525390625,
-0.0167388916015625,
-0.0102996826171875,
-0.040924072265625,
-0.052520751953125,
0.016448974609375,
-0.0012674331665039062,
0.00556182861328125,
0.037750244140625,
0.00870513916015625,
-0.03173828125,
-0.0168304443359375,
0.005405426025390625,
0.0235595703125,
-0.01433563232421875,
-0.003688812255859375,
-0.03155517578125,
0.005413055419921875,
0.03466796875,
-0.0233306884765625,
-0.027557373046875,
0.00739288330078125,
0.01309967041015625,
-0.042236328125,
-0.0016918182373046875,
0.03656005859375,
-0.00026798248291015625,
0.018157958984375,
-0.01195526123046875,
-0.0005216598510742188,
0.02215576171875,
-0.0212554931640625,
0.0123748779296875,
-0.016357421875,
0.001880645751953125,
-0.000006616115570068359,
-0.01617431640625,
0.034759521484375,
0.01494598388671875,
-0.0155181884765625,
0.011322021484375,
0.002460479736328125,
-0.00551605224609375,
0.0386962890625,
-0.00959014892578125,
-0.00537109375,
0.060455322265625,
-0.024871826171875,
-0.00928497314453125,
0.0209197998046875,
0.0015411376953125,
-0.0213775634765625,
0.02178955078125,
-0.00786590576171875,
0.0041046142578125,
-0.010040283203125,
0.024688720703125,
-0.01116943359375,
-0.042816162109375,
0.02203369140625,
-0.0167999267578125,
0.03863525390625,
0.02777099609375,
-0.030364990234375,
0.03179931640625,
0.03173828125,
0.00106048583984375,
-0.00457000732421875,
-0.01678466796875,
0.02752685546875,
-0.01544952392578125,
0.00499725341796875,
-0.01000213623046875,
0.0017747879028320312,
-0.0261688232421875,
0.021026611328125,
0.0205535888671875,
0.000980377197265625,
0.0282745361328125,
0.01174163818359375,
0.0130462646484375,
-0.0330810546875,
0.007568359375,
-0.01348876953125,
-0.01045989990234375,
0.02752685546875,
0.01739501953125,
0.0192108154296875,
-0.012176513671875,
0.01424407958984375,
-0.027557373046875,
-0.021728515625,
-0.003368377685546875,
-0.0291290283203125,
-0.0077362060546875,
0.0123291015625,
0.01050567626953125,
-0.01276397705078125,
0.000030159950256347656,
-0.045745849609375,
0.005634307861328125,
0.03955078125,
-0.0214080810546875,
-0.037261962890625,
-0.032257080078125,
-0.021453857421875,
0.0121002197265625,
0.0093994140625,
0.01239013671875,
0.0127105712890625,
0.01018524169921875,
0.004268646240234375,
0.022430419921875,
0.015655517578125,
0.01284027099609375,
-0.0237274169921875,
0.028228759765625,
-0.0159149169921875,
0.022735595703125,
-0.0005331039428710938,
0.002529144287109375,
0.0214691162109375,
0.0212860107421875,
-0.0235443115234375,
0.0328369140625,
-0.034515380859375,
0.013031005859375,
-0.0123748779296875,
-0.003650665283203125,
0.01052093505859375,
-0.0214691162109375,
0.026763916015625,
0.0072479248046875,
-0.025115966796875,
0.005527496337890625,
0.01041412353515625,
-0.0010662078857421875,
-0.03125,
0.0242767333984375,
0.01068115234375,
-0.01904296875,
-0.00595855712890625,
-0.07989501953125,
0.028594970703125,
0.01523590087890625,
0.03521728515625,
-0.007205963134765625,
-0.026123046875,
0.00609588623046875,
-0.01207733154296875,
-0.0218505859375,
0.00039768218994140625,
-0.0086822509765625,
0.01511383056640625,
0.02325439453125,
0.00010353326797485352,
0.0243682861328125,
-0.00565338134765625,
0.00010186433792114258,
0.0010986328125,
0.01103973388671875,
-0.013885498046875,
-0.0204925537109375,
0.01715087890625,
-0.01160430908203125,
0.0118408203125,
-0.03436279296875,
-0.0206146240234375,
-0.0182037353515625,
0.020050048828125,
-0.0020465850830078125,
-0.019744873046875,
0.01233673095703125,
-0.00951385498046875,
-0.00494384765625,
-0.0229644775390625,
0.0140380859375,
0.000568389892578125,
-0.039154052734375,
-0.00672149658203125,
0.00919342041015625,
-0.024200439453125,
-0.023345947265625,
-0.0015611648559570312,
0.0110931396484375,
0.001068115234375,
0.0143585205078125,
0.044677734375,
0.034637451171875,
-0.01113128662109375,
0.02142333984375,
0.00860595703125,
-0.028594970703125,
-0.0225830078125,
0.00841522216796875,
-0.008880615234375,
0.005039215087890625,
-0.00024366378784179688,
0.00968170166015625,
-0.026519775390625,
0.0124053955078125,
0.020050048828125,
0.00551605224609375,
-0.021270751953125,
0.001270294189453125,
0.00421142578125,
0.0287628173828125,
-0.0177154541015625,
0.017547607421875,
-0.00728607177734375,
-0.0108642578125,
-0.001445770263671875,
0.004215240478515625,
-0.007198333740234375,
-0.0234222412109375,
-0.01178741455078125,
-0.007358551025390625,
0.0256805419921875,
-0.010833740234375,
0.004116058349609375,
-0.01337432861328125,
-0.03619384765625,
0.0207061767578125,
0.016845703125,
0.035552978515625,
-0.0333251953125,
-0.0202484130859375,
-0.034027099609375,
0.003650665283203125,
-0.0140838623046875,
-0.0175323486328125,
0.001811981201171875,
-0.005496978759765625,
0.0283660888671875,
0.0212554931640625,
-0.0181884765625,
-0.029998779296875,
-0.031463623046875,
0.012908935546875,
-0.006839752197265625,
-0.049896240234375,
-0.0035800933837890625,
0.0246429443359375,
-0.016845703125,
0.0155029296875,
0.00133514404296875,
0.0012006759643554688,
0.025634765625,
0.032958984375,
0.0289154052734375,
0.01030731201171875,
0.01488494873046875,
0.025634765625,
-0.030059814453125,
-0.0204010009765625,
-0.00948333740234375,
-0.02508544921875,
-0.0148468017578125,
-0.0347900390625,
-0.0028095245361328125,
-0.02227783203125,
0.0206298828125,
-0.003902435302734375,
0.01904296875,
0.0226898193359375,
-0.01392364501953125,
-0.00814056396484375,
-0.005252838134765625,
0.03497314453125,
0.0089111328125,
0.0131683349609375,
0.003932952880859375,
-0.00096893310546875,
-0.002872467041015625,
-0.004913330078125,
-0.0022106170654296875,
-0.02032470703125,
0.0117340087890625,
0.013916015625,
0.04022216796875,
-0.0130462646484375,
0.0243072509765625,
-0.00386810302734375,
-0.032989501953125,
-0.0044403076171875,
-0.005100250244140625,
-0.01003265380859375,
0.01506805419921875,
0.00563812255859375,
-0.0262603759765625,
0.00839996337890625,
-0.00988006591796875,
0.0263671875,
-0.00714111328125,
0.0012083053588867188,
0.031402587890625,
0.01316070556640625,
-0.0034732818603515625,
0.004123687744140625,
0.0000959634780883789,
-0.01251220703125,
0.0278778076171875,
-0.00807952880859375,
-0.017486572265625,
-0.007480621337890625,
-0.006378173828125,
0.0263671875,
-0.0008955001831054688,
-0.005725860595703125,
-0.00882720947265625,
0.01666259765625,
-0.011016845703125,
-0.012664794921875,
0.0202178955078125,
0.0019178390502929688,
-0.0275115966796875,
0.01345062255859375,
0.0242462158203125,
-0.02197265625,
0.009490966796875,
-0.0130462646484375,
-0.044677734375,
0.000060498714447021484,
-0.0270233154296875,
-0.01491546630859375,
-0.02972412109375,
0.01812744140625,
0.01377105712890625,
0.00927734375,
-0.00730133056640625,
0.005645751953125,
0.0124359130859375,
-0.0297393798828125,
-0.033233642578125,
-0.00525665283203125,
0.042388916015625,
0.000026285648345947266,
-0.00655364990234375,
-0.0171661376953125,
-0.004932403564453125,
-0.01141357421875,
0.0016126632690429688,
0.000995635986328125,
0.0077362060546875,
-0.00734710693359375,
0.00913238525390625,
0.0011949539184570312,
-0.037353515625,
-0.00240325927734375,
0.028594970703125,
0.037139892578125,
-0.003635406494140625,
0.0158233642578125,
-0.0218048095703125,
0.016387939453125,
0.00881195068359375,
0.0182952880859375,
0.0186614990234375,
0.004695892333984375,
-0.0163726806640625,
0.0526123046875,
0.005214691162109375,
0.004871368408203125,
-0.04180908203125,
-0.008544921875,
0.0202178955078125,
-0.00916290283203125,
-0.052978515625,
0.00360870361328125,
0.00012135505676269531,
-0.055755615234375,
0.0031337738037109375,
-0.00199127197265625,
0.00791168212890625,
0.01190948486328125,
-0.0064849853515625,
-0.0056915283203125,
-0.01262664794921875,
-0.01303863525390625,
0.022705078125,
0.00923919677734375,
-0.0066375732421875,
0.006557464599609375,
-0.007320404052734375,
0.011993408203125,
0.0106201171875,
-0.032257080078125,
-0.00746917724609375,
0.0143585205078125,
-0.00839996337890625,
-0.002223968505859375,
0.043212890625,
0.007511138916015625,
0.01215362548828125,
-0.0263671875,
-0.0163421630859375,
0.01558685302734375,
0.00689697265625,
-0.0112762451171875,
0.015594482421875,
0.0276641845703125,
0.0247039794921875,
0.0008549690246582031,
-0.054534912109375,
-0.01108551025390625,
0.017333984375,
0.02227783203125,
-0.006801605224609375,
0.00830078125,
-0.036224365234375,
0.007305145263671875,
-0.020111083984375,
0.00473785400390625,
0.01384735107421875,
0.0211639404296875,
0.00684356689453125,
0.0033931732177734375,
-0.0017900466918945312,
0.0037975311279296875,
0.021759033203125,
-0.006191253662109375,
0.00827789306640625,
-0.012481689453125,
-0.01021575927734375,
-0.0010004043579101562,
-0.0034465789794921875,
-0.0216064453125,
0.00763702392578125,
0.0027027130126953125,
0.0087127685546875,
-0.043365478515625,
-0.00399017333984375,
-0.036346435546875,
0.0126800537109375,
-0.0077362060546875,
0.007244110107421875,
-0.0191497802734375,
0.0242462158203125,
-0.0020656585693359375,
0.0026493072509765625,
0.01242828369140625,
0.0377197265625,
-0.01318359375,
-0.003955841064453125,
-0.055572509765625,
0.007801055908203125,
0.0176544189453125,
-0.004871368408203125,
-0.0222320556640625,
-0.02862548828125,
-0.006343841552734375,
-0.042449951171875,
0.03851318359375,
0.00824737548828125,
0.0197906494140625,
-0.004180908203125,
-0.01384735107421875,
0.039642333984375,
0.026611328125,
-0.0064239501953125,
0.0163421630859375,
-0.0196075439453125,
-0.01415252685546875,
-0.004856109619140625,
-0.0102081298828125,
0.016632080078125,
-0.005283355712890625,
0.00759124755859375,
-0.00677490234375,
-0.008148193359375,
0.004009246826171875,
-0.035736083984375,
0.0065765380859375,
-0.009613037109375,
-0.030853271484375,
-0.02099609375,
-0.006465911865234375,
-0.002216339111328125,
0.052978515625,
0.0004534721374511719,
0.0423583984375,
-0.04168701171875,
-0.0006642341613769531,
-0.00775146484375,
0.01824951171875,
0.03253173828125,
-0.02899169921875,
-0.018829345703125,
0.02490234375,
-0.00409698486328125,
0.00579071044921875,
-0.05029296875,
0.01287841796875,
0.0045318603515625,
-0.0137481689453125,
-0.022735595703125,
0.01000213623046875,
0.00177764892578125,
0.011871337890625,
-0.0011081695556640625,
0.00030231475830078125,
-0.01155853271484375,
0.005054473876953125,
-0.0267486572265625,
0.034698486328125,
-0.020538330078125,
0.011138916015625,
-0.050537109375,
0.00921630859375,
-0.0182952880859375,
0.0119171142578125,
0.0062255859375,
0.032135009765625,
0.0133514404296875,
0.005924224853515625,
0.0012531280517578125,
-0.0008907318115234375,
-0.005107879638671875,
0.044891357421875,
0.0313720703125,
-0.003963470458984375,
0.005462646484375,
0.01111602783203125,
-0.004425048828125,
-0.0321044921875,
-0.003871917724609375,
-0.02294921875,
-0.01050567626953125,
-0.007747650146484375,
0.0214996337890625,
0.0086212158203125,
-0.0007123947143554688,
-0.01123809814453125,
-0.020111083984375,
0.0198974609375,
-0.043365478515625,
0.0288848876953125,
-0.00460052490234375,
-0.0292205810546875,
0.031341552734375,
0.02301025390625,
0.034271240234375,
-0.005222320556640625,
0.0306243896484375,
0.016571044921875,
0.0025634765625,
0.0081024169921875,
-0.01209259033203125,
0.004711151123046875,
-0.0035495758056640625,
-0.0008649826049804688,
-0.0078277587890625,
0.00640106201171875,
0.01873779296875,
0.0106964111328125,
-0.0158233642578125,
0.009613037109375,
-0.009857177734375,
0.026763916015625,
0.0283966064453125,
0.03167724609375,
0.011138916015625,
-0.01288604736328125,
0.0006132125854492188,
-0.0035915374755859375,
0.01508331298828125,
-0.004283905029296875,
0.031097412109375,
0.0260009765625,
-0.00344085693359375,
-0.0170745849609375,
-0.0171051025390625,
-0.0222625732421875,
0.01861572265625,
-0.0012378692626953125,
0.039764404296875,
-0.004718780517578125,
-0.0190582275390625,
0.0174102783203125,
-0.0008840560913085938,
0.01393890380859375,
0.01448822021484375,
-0.03192138671875,
-0.0105743408203125,
-0.01678466796875,
0.0237884521484375,
0.0222930908203125,
0.016754150390625,
0.0255889892578125,
-0.0108489990234375,
-0.0243988037109375,
0.03302001953125,
0.01406097412109375,
0.034423828125,
0.0306854248046875,
0.036712646484375,
-0.007366180419921875,
-0.0067291259765625,
0.02972412109375,
-0.02984619140625,
-0.036590576171875,
0.0169830322265625,
-0.0047149658203125,
-0.00537109375,
-0.01454925537109375,
0.02056884765625,
-0.0167236328125,
-0.01983642578125,
-0.0226593017578125,
-0.02130126953125,
-0.0313720703125,
0.0172576904296875,
-0.0174102783203125,
0.00867462158203125,
0.00836181640625,
-0.0031032562255859375,
-0.005283355712890625,
0.0137939453125,
0.026519775390625,
-0.01305389404296875,
-0.02557373046875,
0.0229949951171875,
0.012176513671875,
-0.0006971359252929688,
-0.004016876220703125,
0.0284423828125,
0.030487060546875,
-0.02154541015625,
-0.033721923828125,
0.0038738250732421875,
-0.01123046875,
-0.01200103759765625,
-0.0204010009765625,
-0.0523681640625,
0.0233154296875,
-0.023162841796875,
-0.004489898681640625,
-0.0224609375,
-0.01323699951171875,
0.0318603515625,
-0.00783538818359375,
0.00738525390625,
-0.0159454345703125,
0.0105133056640625,
-0.02093505859375,
-0.016265869140625,
-0.0217132568359375,
-0.00861358642578125,
0.00942230224609375,
0.025238037109375,
-0.0265350341796875,
0.0226287841796875,
0.00047659873962402344,
-0.0026454925537109375,
-0.0016164779663085938,
0.003612518310546875,
0.01181793212890625,
-0.0160064697265625,
-0.0106658935546875,
-0.01097869873046875,
0.0169219970703125,
-0.0277252197265625,
-0.008331298828125,
0.021697998046875,
-0.004177093505859375,
0.0234375,
0.00438690185546875,
-0.0350341796875,
-0.0201416015625,
0.0112762451171875,
-0.0003821849822998047,
-0.03558349609375,
-0.01143646240234375,
-0.007137298583984375,
0.033966064453125,
0.0124969482421875,
-0.01064300537109375,
0.003692626953125,
0.018218994140625,
0.004474639892578125,
-0.01090240478515625,
-0.007633209228515625,
0.005382537841796875,
0.0034427642822265625,
0.006053924560546875,
-0.0157470703125,
0.0172271728515625,
-0.042449951171875,
0.0083160400390625,
-0.044281005859375,
-0.0110626220703125,
0.0009355545043945312,
-0.020294189453125,
-0.00283050537109375,
0.04840087890625,
0.004364013671875,
-0.007354736328125,
-0.026885986328125,
0.028533935546875,
-0.00983428955078125,
0.0033817291259765625,
0.03875732421875,
0.0010318756103515625,
-0.0168914794921875,
-0.0009069442749023438,
-0.0164947509765625,
-0.011505126953125,
0.02386474609375,
0.042327880859375,
0.0255126953125,
0.01715087890625,
-0.006160736083984375,
0.00626373291015625,
-0.0035381317138671875,
-0.0229644775390625,
-0.0213775634765625,
-0.0001323223114013672,
-0.0003833770751953125,
-0.0291900634765625,
-0.01329803466796875,
-0.02862548828125,
-0.00556182861328125,
0.0208892822265625,
0.04266357421875,
-0.01448822021484375,
0.0021266937255859375,
-0.0144500732421875,
-0.041351318359375,
-0.0198211669921875,
-0.032012939453125,
0.045806884765625,
0.01328277587890625,
0.01763916015625,
0.0264434814453125,
-0.007617950439453125,
-0.020751953125,
0.0124969482421875,
0.01560211181640625,
-0.01395416259765625,
0.017303466796875,
-0.042388916015625,
0.00991058349609375,
0.0050811767578125,
-0.0006780624389648438,
-0.00000762939453125,
0.0111541748046875,
-0.00469207763671875,
0.01483917236328125,
0.013458251953125,
-0.006427764892578125,
-0.0034275054931640625,
-0.000025928020477294922,
-0.035186767578125,
-0.0162353515625,
-0.0171966552734375,
-0.017913818359375,
-0.01184844970703125,
-0.0223541259765625,
0.023468017578125,
0.03521728515625,
-0.01861572265625,
-0.007152557373046875,
-0.008392333984375,
0.0030231475830078125,
0.024810791015625,
-0.004573822021484375,
-0.013214111328125,
-0.00240325927734375,
-0.0001398324966430664,
-0.0046844482421875,
-0.009063720703125,
0.020965576171875,
0.02728271484375,
0.042144775390625,
-0.037689208984375,
-0.0158538818359375,
-0.01354217529296875,
-0.00936126708984375,
-0.0024013519287109375,
0.006732940673828125,
-0.005756378173828125,
0.004123687744140625,
0.00902557373046875,
0.01396942138671875,
0.016265869140625,
0.0322265625,
-0.0079498291015625,
-0.0077056884765625,
0.0179595947265625,
0.0068511962890625,
-0.01654052734375,
0.02960205078125,
0.004302978515625,
-0.0211029052734375,
0.01108551025390625,
-0.0195465087890625,
-0.0018177032470703125,
-0.013641357421875,
0.0211029052734375,
-0.0072174072265625,
-0.00811767578125,
-0.002208709716796875,
0.0211334228515625,
0.0011701583862304688,
0.00933074951171875,
-0.03179931640625,
-0.02056884765625,
-0.0030536651611328125,
-0.0025787353515625,
-0.045318603515625,
-0.0010156631469726562,
0.0222625732421875,
-0.0090179443359375,
0.005786895751953125,
0.00525665283203125,
0.016204833984375,
0.01012420654296875,
0.01503753662109375,
-0.006366729736328125,
0.01544952392578125,
-0.00429534912109375,
0.004108428955078125,
0.0212860107421875,
-0.0259552001953125,
0.0303955078125,
-0.0030574798583984375,
-0.003826141357421875,
0.003734588623046875,
0.0032806396484375,
0.00659942626953125,
0.0026111602783203125,
0.0041961669921875,
0.0105743408203125,
-0.003238677978515625,
0.00655364990234375,
0.0028533935546875,
-0.0106658935546875,
0.030853271484375,
0.0062103271484375,
0.031951904296875,
0.01425933837890625,
0.0091400146484375,
-0.0171051025390625,
-0.005634307861328125,
-0.02142333984375,
0.00354766845703125,
-0.00858306884765625,
0.019012451171875,
-0.0109100341796875,
-0.001922607421875,
-0.001926422119140625,
0.01116180419921875,
-0.0216827392578125,
0.0008292198181152344,
0.04473876953125,
0.0130767822265625,
-0.0094451904296875,
0.04278564453125,
-0.0187225341796875,
0.02398681640625,
-0.01076507568359375,
-0.00717926025390625,
-0.0199432373046875,
0.00815582275390625,
-0.01284027099609375,
-0.02337646484375,
0.00693511962890625,
-0.02825927734375,
0.0023479461669921875,
-0.00502777099609375,
-0.007419586181640625,
-0.0278167724609375,
-0.01015472412109375,
-0.019195556640625,
0.0017490386962890625,
-0.01715087890625,
-0.0177001953125,
0.042022705078125,
-0.0090179443359375,
-0.0008645057678222656,
0.0177154541015625,
-0.0175323486328125,
-0.0262451171875,
0.0190582275390625,
0.0005903244018554688,
-0.020965576171875,
-0.0081329345703125,
-0.0340576171875,
0.020599365234375,
0.018585205078125,
-0.030181884765625,
0.002628326416015625,
0.0276336669921875,
-0.0029773712158203125,
-0.0528564453125,
-0.006671905517578125,
-0.0160980224609375,
-0.00974273681640625,
0.01117706298828125,
-0.0027751922607421875,
0.00275421142578125,
0.0256805419921875,
-0.00360107421875,
0.03399658203125,
0.0006866455078125,
0.0186614990234375,
0.00091552734375,
0.016082763671875,
0.005702972412109375,
-0.028778076171875,
-0.0216522216796875,
0.01338958740234375,
-0.008819580078125,
0.01220703125,
-0.0038967132568359375,
-0.021514892578125,
0.0003509521484375,
0.01078033447265625,
-0.0038318634033203125,
-0.01490020751953125,
0.023345947265625,
-0.005462646484375,
-0.0112457275390625,
0.026031494140625,
0.0301971435546875,
0.0254364013671875,
-0.01145172119140625,
-0.01995849609375,
-0.01287078857421875,
-0.0172119140625,
0.05438232421875,
-0.0049285888671875,
-0.032806396484375,
-0.0007295608520507812,
0.03302001953125,
0.00531768798828125,
0.0003902912139892578,
0.001277923583984375,
-0.0220489501953125,
-0.0302581787109375,
-0.025238037109375,
0.00447845458984375,
-0.0210723876953125,
-0.00250244140625,
-0.00982666015625,
0.01385498046875,
0.006298065185546875,
0.0017604827880859375,
-0.0025634765625,
-0.0266265869140625,
-0.0164794921875,
0.0016021728515625,
-0.006687164306640625,
-0.00732421875,
0.0056304931640625,
0.00449371337890625,
-0.031707763671875,
0.008453369140625,
-0.0291290283203125,
0.0027599334716796875,
-0.00440216064453125,
-0.0014619827270507812,
0.01031494140625,
0.0267486572265625,
-0.0269317626953125,
0.0100250244140625,
-0.020233154296875,
0.0197296142578125,
-0.01071929931640625,
0.018218994140625,
0.007495880126953125,
-0.01248931884765625,
0.0350341796875,
0.0135498046875,
-0.0025920867919921875,
0.00591278076171875,
-0.02581787109375,
-0.0195770263671875,
-0.037689208984375,
-0.0198211669921875,
-0.04144287109375,
0.0121002197265625,
0.00800323486328125,
-0.035675048828125,
0.0127410888671875,
-0.00797271728515625,
0.007015228271484375,
-0.01366424560546875,
0.022247314453125,
-0.0032196044921875,
-0.002819061279296875,
-0.01187896728515625,
0.0204010009765625,
-0.03759765625,
-0.000518798828125,
0.0281829833984375,
-0.0235137939453125,
0.00579071044921875,
0.01454925537109375,
-0.0260009765625,
0.029815673828125,
-0.01348876953125,
-0.01180267333984375,
0.01081085205078125,
-0.01103973388671875,
-0.0204010009765625,
0.0277252197265625,
0.0121612548828125,
0.01078033447265625,
-0.0184173583984375,
0.00814056396484375,
0.005859375,
-0.0011262893676757812,
0.01751708984375,
-0.0036869049072265625,
-0.041778564453125,
0.0206146240234375,
0.00383758544921875,
0.023284912109375,
-0.01727294921875,
-0.020050048828125,
-0.0015516281127929688,
-0.019989013671875,
-0.025238037109375,
0.0235748291015625,
-0.033233642578125,
-0.01013946533203125,
-0.01262664794921875,
-0.0391845703125,
0.00611114501953125,
0.0305328369140625,
0.0015439987182617188,
-0.0196380615234375,
0.0182647705078125,
0.034149169921875,
-0.0206146240234375,
-0.0205841064453125,
-0.0016317367553710938,
-0.006439208984375,
-0.01025390625,
0.0005116462707519531,
0.015411376953125,
0.018798828125,
0.01036834716796875,
0.01995849609375,
0.0038852691650390625,
0.042694091796875,
0.01288604736328125,
-0.0138397216796875,
-0.0257110595703125,
-0.00560760498046875,
0.01134490966796875,
0.0386962890625,
-0.0006327629089355469,
0.001422882080078125,
0.018798828125,
-0.0045166015625,
0.019500732421875,
-0.01300048828125,
-0.00531768798828125,
-0.003875732421875,
-0.0256500244140625,
-0.0034503936767578125,
-0.01027679443359375,
0.03448486328125,
0.0012607574462890625,
-0.0288543701171875,
0.05413818359375,
-0.0128631591796875,
-0.0158843994140625,
0.0039215087890625,
0.00598907470703125,
-0.003635406494140625,
0.022705078125,
0.0340576171875,
0.0033721923828125,
0.0009851455688476562,
0.013427734375,
0.043792724609375,
-0.0105743408203125,
-0.01262664794921875,
-0.0214385986328125,
0.0160064697265625,
0.0227813720703125,
0.032684326171875,
-0.024749755859375,
0.023834228515625,
0.00037360191345214844,
0.016021728515625,
0.0010051727294921875,
-0.009521484375,
-0.0261383056640625,
0.0071563720703125,
0.0200958251953125,
0.0228424072265625,
-0.0004825592041015625,
0.011962890625,
0.01922607421875,
-0.0219573974609375,
0.00322723388671875,
-0.0031299591064453125,
-0.0228271484375,
-0.006683349609375,
-0.01192474365234375,
0.0152740478515625,
0.006977081298828125,
-0.020416259765625,
0.0190277099609375,
0.01480865478515625,
-0.02520751953125,
0.03350830078125,
0.013458251953125,
0.04498291015625,
0.037628173828125,
0.0038700103759765625,
-0.00860595703125,
-0.00528717041015625,
-0.0150604248046875,
0.01345062255859375,
-0.0206146240234375,
-0.0021419525146484375,
-0.026275634765625,
0.01031494140625,
0.01421356201171875,
-0.05096435546875,
0.003307342529296875,
-0.0222320556640625,
-0.0006365776062011719,
0.00589752197265625,
-0.0418701171875,
0.03216552734375,
0.0008373260498046875,
-0.005176544189453125,
0.0223236083984375,
-0.0012912750244140625,
-0.0263214111328125,
0.02081298828125,
-0.01015472412109375,
-0.00745391845703125,
-0.0037670135498046875,
0.01031494140625,
-0.020294189453125,
0.01397705078125,
-0.0092620849609375,
-0.0167236328125,
-0.0012445449829101562,
0.0006761550903320312,
-0.007663726806640625,
0.0526123046875,
-0.01375579833984375,
0.003509521484375,
0.0166168212890625,
-0.00530242919921875,
0.02630615234375,
0.004322052001953125,
0.027801513671875,
0.00917816162109375,
0.0251922607421875,
0.040008544921875,
-0.0234222412109375,
0.01177215576171875,
-0.01023101806640625,
-0.0217437744140625,
-0.032257080078125,
0.0010309219360351562,
-0.00971221923828125,
-0.0234222412109375,
0.017974853515625,
-0.01085662841796875,
-0.0206298828125,
-0.0005865097045898438,
0.0275726318359375,
0.005641937255859375,
0.022308349609375,
-0.025115966796875,
-0.046234130859375,
-0.00971221923828125,
-0.01247406005859375,
-0.03436279296875,
0.01428985595703125,
0.01071929931640625,
0.0266876220703125,
-0.039398193359375,
0.0008640289306640625,
0.031890869140625,
0.04296875,
-0.0144195556640625,
-0.007568359375,
0.005107879638671875,
-0.00934600830078125,
-0.0184478759765625,
-0.00043702125549316406,
0.01373291015625,
0.030059814453125,
0.0042266845703125,
-0.00835418701171875,
-0.0167236328125,
0.038330078125,
0.00974273681640625,
-0.025848388671875,
0.0284881591796875,
0.004398345947265625,
-0.0087890625,
-0.017303466796875,
-0.02410888671875,
-0.018463134765625,
0.0015745162963867188,
0.0241851806640625,
0.040283203125,
-0.01177978515625,
0.005077362060546875,
0.0156707763671875,
-0.02301025390625,
-0.00745391845703125,
-0.0016260147094726562,
0.0023708343505859375,
-0.01479339599609375,
0.0235748291015625,
0.0011167526245117188,
0.0020313262939453125,
-0.0251922607421875,
0.004871368408203125,
-0.0206146240234375,
0.0026531219482421875,
0.00501251220703125,
-0.021575927734375,
0.00634002685546875,
0.01369476318359375,
0.00009441375732421875,
-0.0033092498779296875,
0.013031005859375,
-0.0254364013671875,
-0.0147857666015625,
-0.006099700927734375,
0.02935791015625,
0.0269622802734375,
0.027923583984375,
0.02239990234375,
-0.0167388916015625,
-0.023468017578125,
-0.0091552734375,
0.00580596923828125,
-0.006786346435546875,
-0.0021686553955078125,
-0.0123138427734375,
-0.031341552734375,
-0.0107421875,
0.029144287109375,
0.0088043212890625,
0.00835418701171875,
0.014617919921875,
-0.0185394287109375,
0.00542449951171875,
-0.03863525390625,
-0.0184173583984375,
0.012420654296875,
-0.00614166259765625,
0.01456451416015625,
-0.005710601806640625,
-0.005954742431640625,
-0.004688262939453125,
-0.0102081298828125,
0.01155853271484375,
-0.02227783203125,
-0.0035400390625,
-0.01422119140625,
0.016815185546875,
-0.0009589195251464844,
0.004665374755859375,
0.0135345458984375,
0.006206512451171875,
0.035430908203125,
0.03668212890625,
-0.00040340423583984375,
-0.03338623046875,
-0.00971221923828125,
-0.007030487060546875,
-0.0096435546875,
0.003917694091796875,
-0.0275726318359375,
0.006744384765625,
-0.0207061767578125,
0.00307464599609375,
0.0281219482421875,
0.005840301513671875,
-0.014495849609375,
0.004711151123046875,
0.0021877288818359375,
0.01155853271484375,
0.015228271484375,
-0.00649261474609375,
-0.0179595947265625,
0.007022857666015625,
-0.0013742446899414062,
-0.01172637939453125,
-0.042083740234375,
-0.0136566162109375,
0.0068817138671875,
0.005527496337890625,
0.02691650390625,
0.033355712890625,
-0.0286712646484375,
-0.0115203857421875,
0.01222991943359375,
-0.02215576171875,
0.023040771484375,
0.0258941650390625,
-0.0266571044921875,
-0.00966644287109375,
0.006694793701171875,
-0.023223876953125,
0.032928466796875,
0.0287017822265625,
-0.034088134765625,
0.003650665283203125,
-0.00859832763671875,
-0.01534271240234375,
0.0118560791015625,
-0.01169586181640625,
0.004756927490234375,
0.0196533203125,
-0.030364990234375,
0.029632568359375,
0.008331298828125,
-0.01397705078125,
0.03167724609375,
0.005733489990234375,
0.0201416015625,
-0.0067901611328125,
-0.00846099853515625,
0.01369476318359375,
-0.014617919921875,
0.006988525390625,
0.0180206298828125,
-0.001209259033203125,
-0.0116119384765625,
0.00966644287109375,
-0.0269622802734375,
0.00855255126953125,
0.03900146484375,
0.0023956298828125,
0.02166748046875,
-0.00281524658203125,
-0.01291656494140625,
0.00884246826171875,
-0.0152740478515625,
0.0002560615539550781,
0.0027008056640625,
-0.022216796875,
0.0160675048828125,
-0.01464080810546875,
0.024261474609375,
0.01113128662109375,
0.0031909942626953125,
0.006252288818359375,
-0.022003173828125,
-0.00740814208984375,
-0.00605010986328125,
0.013671875,
0.0210723876953125,
-0.006237030029296875,
0.005107879638671875,
0.0099029541015625,
-0.01511383056640625,
-0.037933349609375,
0.012359619140625,
0.02581787109375,
-0.013885498046875,
-0.0123748779296875,
0.0026988983154296875,
-0.01052093505859375,
-0.0458984375,
0.00554656982421875,
-0.017120361328125,
-0.01438140869140625,
0.022125244140625,
-0.0216064453125,
-0.0230560302734375,
0.01033782958984375,
0.00998687744140625,
0.0018062591552734375,
0.022064208984375,
0.0228424072265625,
-0.00438690185546875,
0.0197296142578125,
0.00881195068359375,
0.01812744140625,
-0.0002484321594238281,
-0.03143310546875,
-0.001617431640625,
-0.01235198974609375,
0.01971435546875,
0.026763916015625,
0.02667236328125,
-0.016326904296875,
-0.0022296905517578125,
-0.006320953369140625,
0.0046844482421875,
-0.0143890380859375,
0.0186309814453125,
0.03253173828125,
0.044464111328125,
-0.01739501953125,
-0.0248870849609375,
0.0164794921875,
-0.017852783203125,
-0.005092620849609375,
3.5762786865234375e-7,
0.0002846717834472656,
0.00258636474609375,
-0.01494598388671875,
-0.0276031494140625,
-0.01169586181640625,
-0.007343292236328125,
0.026519775390625,
0.00972747802734375,
-0.047271728515625,
0.0244140625,
0.0202178955078125,
0.0017976760864257812,
0.0230712890625,
-0.031890869140625,
-0.026153564453125,
-0.0113983154296875,
-0.007171630859375,
-0.00653076171875,
-0.005931854248046875,
0.023345947265625,
-0.01503753662109375,
-0.02081298828125,
-0.0088958740234375,
0.009185791015625,
-0.033203125,
-0.00942230224609375,
-0.018341064453125,
-0.007678985595703125,
-0.0035266876220703125,
-0.005279541015625,
-0.0156707763671875,
0.01947021484375,
0.0201416015625,
0.0163726806640625,
-0.0104217529296875,
0.0032978057861328125,
0.01678466796875,
-0.01082611083984375,
-0.016510009765625,
-0.0171051025390625,
-0.0135345458984375,
-0.020233154296875,
0.0296478271484375,
0.02923583984375,
-0.0013093948364257812,
0.0123748779296875,
0.0269012451171875,
-0.00011485815048217773,
0.0005726814270019531,
0.012176513671875,
-0.00487518310546875,
0.00286102294921875,
-0.00789642333984375,
0.01363372802734375,
-0.00920867919921875,
-0.027099609375,
-0.01480865478515625,
0.00292205810546875,
-0.0279388427734375,
0.0270538330078125,
-0.0096893310546875,
-0.006931304931640625,
0.017425537109375,
-0.033538818359375,
-0.005840301513671875,
-0.006305694580078125,
0.011871337890625,
0.01212310791015625,
-0.033416748046875,
-0.0276947021484375,
-0.0037689208984375,
0.01302337646484375,
-0.0017290115356445312,
-0.02789306640625,
0.037139892578125,
0.00527191162109375,
-0.034881591796875,
0.01322174072265625,
-0.00029850006103515625,
0.005908966064453125,
0.0265960693359375,
0.0411376953125,
0.004100799560546875,
0.00001823902130126953,
-0.024322509765625,
0.020477294921875,
0.00522613525390625,
0.0135650634765625,
0.0118865966796875,
0.02264404296875,
0.004985809326171875,
-0.01285552978515625,
0.0127105712890625,
0.018524169921875,
0.0137176513671875,
0.00005513429641723633,
0.035430908203125,
-0.02239990234375,
-0.016357421875,
0.007659912109375,
-0.004375457763671875,
0.00975799560546875,
-0.0105133056640625,
0.00829315185546875,
0.00719451904296875,
0.03448486328125,
-0.0104827880859375,
0.0211029052734375,
-0.00013375282287597656,
-0.01050567626953125,
-0.005462646484375,
-0.0196990966796875,
-0.01396942138671875,
-0.0167388916015625,
0.0017766952514648438,
-0.0169830322265625,
-0.02508544921875,
0.004047393798828125,
-0.026824951171875,
0.036346435546875,
0.01248931884765625,
0.0055389404296875,
-0.0012140274047851562,
0.004833221435546875,
0.0183563232421875,
-0.01154327392578125,
-0.003734588623046875,
-0.0182647705078125,
-0.002201080322265625,
0.008514404296875,
0.0207672119140625,
0.005615234375,
0.0362548828125,
0.0014829635620117188,
-0.00011903047561645508,
0.004970550537109375,
0.0140533447265625,
0.0157928466796875,
0.03155517578125,
-0.0195159912109375,
0.0282440185546875,
-0.00754547119140625,
-0.00872802734375,
0.007232666015625,
-0.001415252685546875,
-0.026580810546875,
-0.005039215087890625,
0.01548004150390625,
0.01058197021484375,
-0.0162353515625,
-0.0017824172973632812,
0.00811004638671875,
-0.01557159423828125,
-0.015838623046875,
-0.0208740234375,
-0.021575927734375,
0.010009765625,
0.0111236572265625,
0.01678466796875,
-0.00336456298828125,
0.0191650390625,
0.011474609375,
-0.03228759765625,
-0.03857421875,
-0.04608154296875,
-0.039642333984375,
0.0195159912109375,
-0.00440216064453125,
0.01629638671875,
-0.01849365234375,
-0.00421142578125,
-0.03289794921875,
-0.0134735107421875,
-0.0265350341796875,
0.018646240234375,
-0.027252197265625,
0.01007843017578125,
0.0013065338134765625,
-0.022186279296875,
0.025238037109375,
0.007076263427734375,
-0.0192718505859375,
-0.0099945068359375,
-0.0195465087890625,
-0.026092529296875,
0.0114898681640625,
0.0278778076171875,
-0.017425537109375,
0.023956298828125,
-0.01253509521484375,
-0.0307769775390625,
0.007595062255859375,
0.040130615234375,
-0.00952911376953125,
-0.0032749176025390625,
-0.0052337646484375,
0.030517578125,
0.02960205078125,
-0.02459716796875,
-0.004669189453125,
0.020904541015625,
-0.0232391357421875,
-0.0278778076171875,
0.023162841796875,
0.032867431640625,
0.0247955322265625,
-0.017425537109375,
-0.027557373046875,
-0.019775390625,
-0.0013189315795898438,
0.00513458251953125,
-0.0147705078125,
0.012115478515625,
-0.03411865234375,
0.0479736328125,
-0.035125732421875,
-0.03131103515625,
0.0372314453125,
-0.004100799560546875,
0.005893707275390625,
-0.01393890380859375,
-0.0290985107421875,
-0.0207061767578125,
0.004611968994140625,
-0.052154541015625,
-0.007568359375,
0.040283203125,
-0.00858306884765625,
-0.002826690673828125,
0.007732391357421875,
-0.0016956329345703125,
0.00954437255859375,
0.033172607421875,
-0.01535797119140625,
0.014007568359375,
0.03729248046875,
0.00733184814453125,
0.001079559326171875,
-0.0251922607421875,
0.041473388671875,
-0.0328369140625,
-0.0016727447509765625,
0.0004715919494628906,
0.0150146484375,
0.00836181640625,
-0.0014896392822265625,
0.008575439453125,
-0.00543212890625,
0.024505615234375,
0.014251708984375,
0.00016105175018310547,
-0.0203094482421875,
0.025787353515625,
-0.0082244873046875,
-0.024261474609375,
-0.0038776397705078125,
0.004550933837890625,
-0.01515960693359375,
-0.02056884765625,
-0.034515380859375,
-0.005519866943359375,
0.0082855224609375,
-0.0023136138916015625,
0.00023734569549560547,
0.0335693359375,
0.020050048828125,
0.0137939453125,
-0.0214691162109375,
-0.000957489013671875,
-0.0024280548095703125,
-0.0031948089599609375,
-0.0034656524658203125,
0.01364898681640625,
0.0193328857421875,
-0.0269775390625,
-0.0206146240234375,
-0.01477813720703125,
0.0149993896484375,
-0.0103302001953125,
-0.0289154052734375,
-0.00024700164794921875,
0.016571044921875,
-0.0265960693359375,
0.0017919540405273438,
-0.008056640625,
0.00557708740234375,
0.0284576416015625,
-0.032012939453125,
0.009307861328125,
0.0248260498046875,
-0.01465606689453125,
-0.00951385498046875,
-0.01140594482421875,
-0.00901031494140625,
-0.007617950439453125,
0.032684326171875,
0.0013608932495117188,
0.01348876953125,
-0.01039886474609375,
0.006725311279296875,
-0.00943756103515625,
0.01314544677734375,
-0.00023055076599121094,
0.00948333740234375,
-0.006206512451171875,
0.0129547119140625,
0.0023593902587890625,
-0.01108551025390625,
0.0218353271484375,
-0.0296630859375,
-0.05462646484375,
-0.0149993896484375,
0.004329681396484375,
0.042388916015625,
0.0097198486328125,
-0.01065826416015625,
0.013427734375,
0.021942138671875,
0.0170135498046875,
-0.0196990966796875,
0.03167724609375,
-0.0010213851928710938,
0.0207977294921875,
0.0223236083984375,
-0.002521514892578125,
-0.00983428955078125,
0.01348876953125,
0.0450439453125,
0.003002166748046875,
-0.0224609375,
0.035064697265625,
-0.0001722574234008789,
-0.0222625732421875,
0.00628662109375,
-0.016876220703125,
-0.0487060546875,
0.0094451904296875,
-0.01233673095703125,
0.00037789344787597656,
-0.0004546642303466797,
-0.020172119140625,
0.017852783203125,
-0.001811981201171875,
0.0081329345703125,
0.0031986236572265625,
0.01226806640625,
0.0006842613220214844,
0.0222320556640625,
0.01345062255859375,
0.02374267578125,
0.038665771484375,
-0.000060558319091796875,
0.030120849609375,
0.0261077880859375,
-0.016357421875,
-0.00937652587890625,
0.051300048828125,
-0.0079498291015625,
0.003627777099609375,
0.003002166748046875,
-0.0233917236328125,
0.046844482421875,
0.01290130615234375,
-0.0130615234375,
-0.0234527587890625,
0.00850677490234375,
0.01320648193359375,
-0.01320648193359375,
-0.036407470703125,
0.004886627197265625,
0.017852783203125,
-0.00342559814453125,
0.0029964447021484375,
0.01142120361328125,
0.0087432861328125,
-0.004730224609375,
0.005390167236328125,
-0.00632476806640625,
0.004055023193359375,
-0.00244140625,
0.0097503662109375,
-0.0278778076171875,
0.0028896331787109375,
0.02850341796875,
-0.031890869140625,
0.0250701904296875,
-0.00007271766662597656,
0.0269927978515625,
0.01480865478515625,
0.027252197265625,
0.026641845703125,
-0.0413818359375,
-0.0007610321044921875,
-0.01519775390625,
0.045562744140625,
0.026275634765625,
0.0036029815673828125,
0.020233154296875,
0.00897216796875,
0.0038089752197265625,
0.002696990966796875,
-0.01152801513671875,
-0.017974853515625,
-0.0209808349609375,
0.00750732421875,
0.0278167724609375,
0.01678466796875,
0.00034618377685546875,
-0.01206207275390625,
0.0004911422729492188,
0.008758544921875,
-0.01428985595703125,
-0.01788330078125,
0.021453857421875,
-0.0042877197265625,
0.0174407958984375,
0.0190887451171875,
-0.0088043212890625,
0.00798797607421875,
0.002384185791015625,
-0.0011768341064453125,
-0.028472900390625,
0.00445556640625,
-0.0161285400390625,
0.032196044921875,
-0.0194854736328125,
0.029815673828125,
-0.0010251998901367188,
-0.012176513671875,
0.02264404296875,
-0.0222015380859375,
0.00757598876953125,
0.017181396484375,
0.029144287109375,
0.00555419921875,
-0.0281829833984375,
0.00650787353515625,
0.0399169921875,
-0.003528594970703125,
0.01788330078125,
-0.018096923828125,
0.0028228759765625,
-0.01154327392578125,
-0.01535797119140625,
-0.0259246826171875,
-0.00023114681243896484,
-0.01100921630859375,
0.006694793701171875,
-0.01088714599609375,
0.0095977783203125,
0.01300811767578125,
-0.00418853759765625,
-0.01329803466796875,
-0.0012197494506835938,
0.01837158203125,
-0.001220703125,
0.0272979736328125,
-0.00046706199645996094,
-0.022125244140625,
-0.0298309326171875,
-0.049957275390625,
-0.0198822021484375,
0.0102996826171875,
-0.00492095947265625,
0.00040149688720703125,
-0.017425537109375,
-0.0193328857421875,
-0.0027027130126953125,
0.01190948486328125,
-0.00045180320739746094,
-0.003711700439453125,
-0.01019287109375,
0.021209716796875,
0.01230621337890625,
-0.0023193359375,
-0.0295562744140625,
-0.00949859619140625,
0.018463134765625,
0.0224609375,
-0.0104217529296875,
0.0018320083618164062,
0.0225372314453125,
0.018829345703125,
0.0010690689086914062,
-0.010467529296875,
-0.00679779052734375,
0.006420135498046875,
0.00179290771484375,
0.0004220008850097656,
0.0024051666259765625,
0.0053253173828125,
-0.00025272369384765625,
-0.01049041748046875,
-0.0049285888671875,
0.015960693359375,
0.0118408203125,
-0.0212860107421875,
0.0016956329345703125,
0.04608154296875,
0.0115966796875,
0.0084686279296875,
0.024139404296875,
0.002208709716796875,
-0.005344390869140625,
0.02587890625,
-0.01104736328125,
-0.0087890625,
-0.0215301513671875,
-0.01250457763671875,
-0.02154541015625,
-0.022918701171875,
0.02825927734375,
0.01953125,
-0.035919189453125,
-0.01468658447265625,
-0.0185394287109375,
-0.035797119140625,
-0.0117340087890625,
-0.009002685546875,
0.033233642578125,
0.0160064697265625,
-0.007144927978515625,
0.01221466064453125,
-0.02374267578125,
-0.0005688667297363281,
0.0152130126953125,
-0.029144287109375,
0.0198974609375,
0.00057220458984375,
-0.00893402099609375,
0.042144775390625,
-0.0211181640625,
0.0160980224609375,
-0.01129150390625,
-0.01091766357421875,
0.0252838134765625,
0.004024505615234375,
0.007701873779296875,
0.031768798828125,
0.024261474609375,
-0.01444244384765625,
0.020050048828125,
-0.0254974365234375,
0.005634307861328125,
-0.0065765380859375,
0.0106201171875,
-0.00467681884765625,
-0.01528167724609375,
-0.0032024383544921875,
-0.037322998046875,
-0.00809478759765625,
-0.01323699951171875,
-0.01020050048828125,
0.00689697265625,
-0.035125732421875,
0.00896453857421875,
-0.0287017822265625,
-0.030548095703125,
-0.00959014892578125,
-0.007068634033203125,
0.0014142990112304688,
-0.0223236083984375,
0.00229644775390625,
0.0216827392578125,
-0.01363372802734375,
-0.004741668701171875,
-0.0086517333984375,
-0.0045318603515625,
0.0010728836059570312,
0.0146484375,
0.01509857177734375,
-0.0006093978881835938,
0.017333984375,
0.00936126708984375,
-0.0207977294921875,
0.020416259765625,
-0.01136016845703125,
0.0147705078125,
-0.016571044921875,
-0.025543212890625,
0.01438140869140625,
0.0070648193359375,
-0.00994110107421875,
0.0234832763671875,
-0.036712646484375,
-0.0012722015380859375,
-0.00804901123046875,
0.0165557861328125,
0.0177001953125,
0.005718231201171875,
0.0285491943359375,
0.0028743743896484375,
0.031768798828125,
0.0323486328125,
-0.01055145263671875,
-0.008514404296875,
-0.01253509521484375,
-0.032867431640625,
0.0038604736328125,
0.0030994415283203125,
-0.0152435302734375,
0.00757598876953125,
0.0262908935546875,
0.054290771484375,
0.018646240234375,
-0.0299530029296875,
-0.02581787109375,
0.02923583984375,
-0.0296783447265625,
0.0053558349609375,
-0.0212860107421875,
0.00091552734375,
0.02447509765625,
0.00032258033752441406,
0.0220184326171875,
0.031890869140625,
-0.035888671875,
-0.0155181884765625,
-0.0182647705078125,
-0.0273284912109375,
-0.0124053955078125,
0.013031005859375,
0.0153656005859375,
0.034820556640625,
-0.0025634765625,
-0.017303466796875,
0.0010137557983398438,
-0.0021724700927734375,
-0.00525665283203125,
0.001216888427734375,
0.002197265625,
-0.004093170166015625,
0.0249481201171875,
-0.013885498046875,
0.0088653564453125,
0.0156402587890625,
0.00691986083984375,
-0.0188140869140625,
0.01194000244140625,
-0.01251983642578125,
0.00970458984375,
0.040313720703125,
0.00969696044921875,
-0.0195465087890625,
0.01314544677734375,
0.0171051025390625,
-0.015869140625,
0.05560302734375,
-0.006282806396484375,
0.029022216796875,
0.011199951171875,
-0.0021686553955078125,
-0.05609130859375,
-0.012298583984375,
-0.034576416015625,
0.019866943359375,
-0.008697509765625,
0.0242919921875,
0.00004887580871582031,
0.0136566162109375,
-0.024627685546875,
-0.0189971923828125,
-0.0180206298828125,
0.00948333740234375,
0.01387786865234375,
0.01078033447265625,
-0.0187530517578125,
0.0196533203125,
-0.009063720703125,
0.061004638671875,
0.00823211669921875,
-0.0303955078125,
0.015716552734375,
-0.0222625732421875,
0.01499176025390625,
0.0169830322265625,
-0.0177001953125,
-0.004482269287109375,
0.0111541748046875,
0.0147247314453125,
0.0017099380493164062,
0.00556182861328125,
-0.01264190673828125,
-0.022308349609375,
-0.0165252685546875,
-0.005825042724609375,
-0.047760009765625,
-0.0093841552734375,
-0.047882080078125,
-0.0143890380859375,
0.0151519775390625,
-0.034637451171875,
-0.01531982421875,
0.0156097412109375,
0.017364501953125,
0.0106964111328125,
-0.0212860107421875,
0.03466796875,
-0.04888916015625,
-0.0401611328125,
-0.000023126602172851562,
0.0069122314453125,
-0.00597381591796875,
-0.049102783203125,
0.0024852752685546875,
0.014007568359375,
0.00489044189453125,
-0.0396728515625,
0.0030918121337890625,
-0.0443115234375,
0.0192108154296875,
-0.00820159912109375,
-0.01276397705078125,
-0.025421142578125,
0.01461029052734375,
-0.022613525390625,
0.00000959634780883789,
-0.004878997802734375,
0.0328369140625,
-0.0095062255859375,
-0.016876220703125,
0.0214996337890625,
-0.022003173828125,
-0.030303955078125,
-0.0010538101196289062,
-0.0001933574676513672,
0.01641845703125,
-0.004119873046875,
0.01102447509765625,
0.00075531005859375,
0.0222320556640625,
-0.0106048583984375,
0.0188446044921875,
0.01568603515625,
-0.0300445556640625,
-0.0178070068359375,
-0.008392333984375,
0.00691986083984375,
0.025238037109375,
-0.0268096923828125,
0.00019121170043945312,
0.0102691650390625,
0.0019283294677734375,
0.0027294158935546875,
-0.0216064453125,
-0.00371551513671875,
-0.0289764404296875,
0.004451751708984375,
0.0105743408203125,
-0.007030487060546875,
0.046234130859375,
0.01078033447265625,
0.0281982421875,
-0.031219482421875,
0.0267486572265625,
-0.0201568603515625,
0.0201873779296875,
-0.00653076171875,
-0.0145416259765625,
0.001720428466796875,
0.00732421875,
0.0024394989013671875
] |
ours_536
|
The answer is \(97654320\).
Because Alice's favorite number is divisible by 180, it must end in a 0. It must also be divisible by 20, so the penultimate digit must be even. The number has decreasing distinct digits, so it must be a 2. Finally, the number must be divisible by 9, which means the sum of the digits must be divisible by 9. The number must contain all the digits from 0 to 9 exactly once except 2 of them, and it is already missing 1. The remaining sum must be 36, so the other missing digit is 8. Thus, the integer is \(97654320\).
\(\boxed{97654320}\)
|
97654320
|
{
"competition": "us_comps",
"dataset": "Ours",
"posts": null,
"source": "OMOSoln2.md"
}
|
Alice's favorite number has the following properties:
- It has 8 distinct digits.
- The digits are decreasing when read from left to right.
- It is divisible by 180.
What is Alice's favorite number?
|
[
"/Mathematics/DiscreteMathematics/Combinatorics/Permutations",
"/Mathematics/DiscreteMathematics/DivisionProblems/SubsetSumProblem",
"/Mathematics/NumberTheory/Arithmetic/GeneralArithmetic",
"/Mathematics/NumberTheory/Divisors/DivisibilityRules",
"/Mathematics/NumberTheory/Divisors/RuleofNines",
"/Mathematics/NumberTheory/GeneralNumberTheory/ElementaryMethods",
"/Mathematics/NumberTheory/GeneralNumberTheory/ElementaryNumberTheory",
"/Mathematics/NumberTheory/GeneralNumberTheory/HigherArithmetic",
"/Mathematics/NumberTheory/GeneralNumberTheory/NumberTheory",
"/Mathematics/NumberTheory/Integers/EvenNumber",
"/Mathematics/NumberTheory/Integers/Integer",
"/Mathematics/NumberTheory/Integers/N",
"/Mathematics/NumberTheory/Integers/NonnegativeInteger",
"/Mathematics/NumberTheory/Integers/PositiveInteger",
"/Mathematics/NumberTheory/Integers/WholeNumber",
"/Mathematics/NumberTheory/Integers/Z",
"/Mathematics/NumberTheory/Integers/Z-Plus",
"/Mathematics/NumberTheory/Numbers",
"/Mathematics/RecreationalMathematics/NumberGuessing",
"/Mathematics/RecreationalMathematics/Puzzles/Puzzle"
] |
Apply the divisibility rules for 180 (ends with 0, penultimate digit even, digit sum multiple of 9) together with decreasing distinct digits to determine the number.
|
[
-0.00007653236389160156,
-0.00024962425231933594,
0.048187255859375,
0.0070343017578125,
-0.0003695487976074219,
0.023040771484375,
0.04461669921875,
0.00824737548828125,
0.005229949951171875,
0.01349639892578125,
-0.00092315673828125,
-0.011260986328125,
-0.00632476806640625,
-0.01497650146484375,
-0.061920166015625,
0.0083770751953125,
0.049530029296875,
0.0288543701171875,
-0.0003349781036376953,
-0.002849578857421875,
-0.0164337158203125,
-0.019500732421875,
-0.01282501220703125,
0.002971649169921875,
-0.034515380859375,
-0.04412841796875,
-0.0237884521484375,
0.00966644287109375,
0.0229339599609375,
-0.030609130859375,
-0.02484130859375,
0.0138702392578125,
0.030029296875,
-0.00772857666015625,
0.00093841552734375,
0.004581451416015625,
0.024688720703125,
-0.0014028549194335938,
0.029388427734375,
-0.00543212890625,
-0.0005359649658203125,
0.01007843017578125,
-0.020233154296875,
0.005970001220703125,
-0.01540374755859375,
0.02215576171875,
-0.0098419189453125,
-0.014068603515625,
-0.00951385498046875,
-0.01470947265625,
-0.00606536865234375,
0.00809478759765625,
-0.032623291015625,
-0.0160064697265625,
-0.04248046875,
-0.0609130859375,
0.01357269287109375,
0.002399444580078125,
-0.0207061767578125,
-0.02130126953125,
0.00768280029296875,
0.02777099609375,
-0.003429412841796875,
-0.0174407958984375,
-0.0006322860717773438,
-0.016265869140625,
-0.01186370849609375,
0.00258636474609375,
-0.005977630615234375,
0.01096343994140625,
-0.0081634521484375,
0.000013947486877441406,
-0.0144500732421875,
0.0084228515625,
-0.009429931640625,
-0.0102996826171875,
-0.01457977294921875,
-0.00400543212890625,
-0.01424407958984375,
0.01873779296875,
0.028167724609375,
0.024017333984375,
-0.0001277923583984375,
0.039276123046875,
0.020599365234375,
-0.01145172119140625,
0.00632476806640625,
0.00017702579498291016,
0.045379638671875,
0.0099029541015625,
-0.004222869873046875,
0.035369873046875,
-0.01806640625,
0.0216217041015625,
-0.006526947021484375,
0.03839111328125,
0.0185699462890625,
-0.016998291015625,
-0.0179595947265625,
0.00240325927734375,
-0.0198974609375,
-0.0259552001953125,
-0.0191192626953125,
0.00322723388671875,
0.006465911865234375,
-0.01172637939453125,
0.00048160552978515625,
-0.01172637939453125,
-0.023101806640625,
-0.0019054412841796875,
0.00917816162109375,
0.004512786865234375,
-0.015777587890625,
-0.0003185272216796875,
0.006771087646484375,
0.00347900390625,
0.004238128662109375,
0.0023365020751953125,
-0.019744873046875,
0.01065826416015625,
0.0247955322265625,
-0.00021457672119140625,
-0.0042266845703125,
0.006511688232421875,
0.0133819580078125,
-0.024627685546875,
-0.024017333984375,
-0.010284423828125,
-0.006977081298828125,
-0.0020885467529296875,
0.04425048828125,
-0.00815582275390625,
-0.00916290283203125,
-0.01381683349609375,
-0.03631591796875,
0.0014085769653320312,
0.0029754638671875,
0.0165557861328125,
-0.014190673828125,
-0.01036834716796875,
0.01303863525390625,
0.0021953582763671875,
0.00890350341796875,
0.0146026611328125,
-0.0056610107421875,
0.00838470458984375,
0.0024662017822265625,
-0.06683349609375,
0.019683837890625,
-0.0011453628540039062,
0.003574371337890625,
-0.00760650634765625,
0.0194854736328125,
0.02386474609375,
0.02239990234375,
0.01108551025390625,
0.0135955810546875,
0.003997802734375,
-0.00450897216796875,
-0.010223388671875,
-0.003681182861328125,
0.0027141571044921875,
-0.00665283203125,
0.029083251953125,
-0.031890869140625,
-0.019775390625,
0.024261474609375,
-0.033782958984375,
-0.01377105712890625,
-0.0020198822021484375,
-0.01299285888671875,
0.00824737548828125,
0.01490020751953125,
-0.0212860107421875,
0.0174102783203125,
-0.0197296142578125,
0.00009769201278686523,
-0.0103607177734375,
-0.0004127025604248047,
0.00626373291015625,
-0.0016298294067382812,
-0.013275146484375,
0.0159149169921875,
0.019012451171875,
0.0238037109375,
0.006496429443359375,
-0.0095977783203125,
-0.01235198974609375,
0.01611328125,
-0.00457763671875,
0.0382080078125,
-0.046234130859375,
0.00664520263671875,
-0.0016765594482421875,
0.0011339187622070312,
-0.020751953125,
0.0010442733764648438,
-0.0027256011962890625,
0.0595703125,
-0.00560760498046875,
-0.0292510986328125,
-0.01132965087890625,
0.004058837890625,
0.0121307373046875,
0.0090179443359375,
0.00870513916015625,
0.00017249584197998047,
0.002399444580078125,
0.003864288330078125,
-0.0121307373046875,
0.0012493133544921875,
-0.05450439453125,
-0.00922393798828125,
-0.0131072998046875,
-0.022796630859375,
-0.0168914794921875,
-0.0017032623291015625,
-0.0095367431640625,
0.0170440673828125,
-0.0238037109375,
0.0271453857421875,
-0.0056915283203125,
-0.00798797607421875,
0.0004417896270751953,
-0.01385498046875,
-0.011566162109375,
-0.0123138427734375,
-0.0015621185302734375,
0.006793975830078125,
0.0060577392578125,
-0.00640869140625,
-0.00359344482421875,
-0.01335906982421875,
0.0001583099365234375,
0.01340484619140625,
0.00376129150390625,
0.0049285888671875,
-0.0200958251953125,
0.0174560546875,
-0.0272979736328125,
0.034576416015625,
-0.01103973388671875,
-0.006443023681640625,
-0.0250396728515625,
0.007266998291015625,
0.0047149658203125,
0.00861358642578125,
0.01259613037109375,
0.01384735107421875,
-0.00537872314453125,
-0.00795745849609375,
0.029052734375,
-0.0020465850830078125,
-0.0166168212890625,
0.0294952392578125,
-0.01279449462890625,
-0.004627227783203125,
0.01074981689453125,
-0.0008783340454101562,
0.00171661376953125,
-0.0009260177612304688,
-0.01019287109375,
-0.0007348060607910156,
-0.00801849365234375,
-0.003101348876953125,
-0.0199432373046875,
0.0131072998046875,
-0.01476287841796875,
0.00958251953125,
0.019134521484375,
0.0185699462890625,
0.0267181396484375,
-0.00727081298828125,
0.0276336669921875,
0.022247314453125,
-0.01186370849609375,
-0.016204833984375,
-0.0165557861328125,
0.004573822021484375,
-0.0232086181640625,
0.01061248779296875,
-0.01509857177734375,
-0.006984710693359375,
0.0007739067077636719,
-0.010009765625,
-0.0177764892578125,
0.0240631103515625,
-0.01018524169921875,
-0.0130462646484375,
0.0258026123046875,
-0.005413055419921875,
-0.0229949951171875,
-0.0217437744140625,
-0.00579071044921875,
0.0288238525390625,
-0.0258026123046875,
-0.007965087890625,
-0.0103302001953125,
0.0160675048828125,
0.0215911865234375,
0.032470703125,
0.0099334716796875,
-0.016021728515625,
0.0084075927734375,
-0.0044097900390625,
0.009674072265625,
0.00310516357421875,
-0.0071563720703125,
-0.05157470703125,
-0.0052947998046875,
-0.01580810546875,
0.0023555755615234375,
0.0305023193359375,
0.006107330322265625,
0.00502777099609375,
0.0025272369384765625,
-0.004520416259765625,
0.029449462890625,
-0.004482269287109375,
-0.015167236328125,
0.036895751953125,
0.0017042160034179688,
-0.0242767333984375,
0.0023021697998046875,
-0.01544952392578125,
0.021881103515625,
-0.00936126708984375,
0.027435302734375,
0.0288238525390625,
0.01107025146484375,
-0.0306854248046875,
0.037353515625,
0.0279998779296875,
-0.013031005859375,
0.0016279220581054688,
0.00982666015625,
0.00478363037109375,
0.029144287109375,
-0.0198211669921875,
-0.013946533203125,
-0.0164031982421875,
0.0078125,
-0.00913238525390625,
0.001399993896484375,
-0.0265350341796875,
0.03411865234375,
-0.03155517578125,
-0.01367950439453125,
-0.0246124267578125,
-0.01447296142578125,
0.005237579345703125,
0.01412200927734375,
-0.0014190673828125,
-0.007293701171875,
-0.0259857177734375,
0.00801849365234375,
-0.0187530517578125,
0.01468658447265625,
0.014373779296875,
0.0177154541015625,
-0.005619049072265625,
-0.00783538818359375,
0.0205841064453125,
0.0200653076171875,
-0.0012865066528320312,
-0.0170135498046875,
-0.006343841552734375,
-0.0004553794860839844,
-0.0307159423828125,
-0.0245513916015625,
0.0027751922607421875,
-0.0079345703125,
-0.01120758056640625,
-0.0001024007797241211,
-0.03509521484375,
0.0104522705078125,
0.0125885009765625,
0.005916595458984375,
-0.022552490234375,
-0.02532958984375,
0.0106353759765625,
0.0275421142578125,
0.007472991943359375,
0.01457977294921875,
-0.0224761962890625,
0.007808685302734375,
0.004840850830078125,
-0.03472900390625,
0.020599365234375,
0.00823974609375,
0.00983428955078125,
0.005828857421875,
-0.0003159046173095703,
-0.02081298828125,
0.004909515380859375,
0.0022735595703125,
-0.00007331371307373047,
0.025177001953125,
0.04766845703125,
0.01605224609375,
0.019561767578125,
-0.0225982666015625,
-0.009979248046875,
0.016632080078125,
0.00901031494140625,
-0.0168914794921875,
-0.018585205078125,
-0.01413726806640625,
0.0023136138916015625,
0.0027484893798828125,
0.032470703125,
0.0016469955444335938,
-0.0075836181640625,
0.01325225830078125,
0.00440216064453125,
0.0096435546875,
0.0277099609375,
-0.0406494140625,
-0.0654296875,
-0.0109100341796875,
0.005290985107421875,
0.005588531494140625,
0.0023860931396484375,
0.0020122528076171875,
0.01299285888671875,
-0.033203125,
-0.035980224609375,
0.01824951171875,
0.06640625,
0.021392822265625,
0.007106781005859375,
-0.01800537109375,
0.0006198883056640625,
0.036865234375,
-0.00768280029296875,
-0.010528564453125,
-0.0183258056640625,
0.00391387939453125,
-0.01568603515625,
0.0174407958984375,
0.0015134811401367188,
0.0038661956787109375,
0.0240936279296875,
-0.018463134765625,
0.017364501953125,
-0.01213836669921875,
0.0122528076171875,
-0.006011962890625,
-0.049407958984375,
0.0283050537109375,
-0.00438690185546875,
-0.0194549560546875,
-0.022552490234375,
-0.029693603515625,
0.0005564689636230469,
-0.0221405029296875,
0.035675048828125,
-0.00086212158203125,
-0.00637054443359375,
-0.046600341796875,
-0.01113128662109375,
-0.016510009765625,
-0.004505157470703125,
-0.0239715576171875,
-0.044097900390625,
-0.0203094482421875,
-0.043914794921875,
0.0198974609375,
0.0218658447265625,
0.01369476318359375,
-0.0011472702026367188,
-0.018768310546875,
-0.003986358642578125,
-0.02581787109375,
-0.0263519287109375,
0.03607177734375,
-0.007354736328125,
0.0249176025390625,
-0.01580810546875,
-0.0021419525146484375,
-0.00812530517578125,
0.0204010009765625,
-0.01715087890625,
-0.005039215087890625,
-0.010955810546875,
-0.00847625732421875,
0.004421234130859375,
0.0003724098205566406,
-0.0474853515625,
-0.0006284713745117188,
0.0079193115234375,
-0.0018405914306640625,
-0.033050537109375,
-0.027740478515625,
-0.0027217864990234375,
-0.005748748779296875,
0.0189666748046875,
-0.0168914794921875,
-0.00017213821411132812,
0.0039215087890625,
0.0128936767578125,
-0.046112060546875,
-0.0122222900390625,
0.0201263427734375,
-0.006877899169921875,
-0.0205078125,
0.00911712646484375,
-0.0186309814453125,
0.03509521484375,
-0.01256561279296875,
0.0343017578125,
0.006061553955078125,
0.0161895751953125,
-0.017242431640625,
-0.0206756591796875,
-0.030242919921875,
0.005199432373046875,
-0.032958984375,
-0.0236053466796875,
0.00998687744140625,
-0.01031494140625,
0.01568603515625,
0.0033588409423828125,
-0.012420654296875,
-0.006130218505859375,
0.02484130859375,
0.02471923828125,
0.005741119384765625,
-0.01062774658203125,
0.0350341796875,
-0.0019292831420898438,
-0.02349853515625,
0.0126495361328125,
0.005947113037109375,
-0.021881103515625,
0.00836944580078125,
0.00922393798828125,
-0.006256103515625,
-0.00595855712890625,
-0.015899658203125,
0.0085601806640625,
-0.007659912109375,
0.02117919921875,
-0.0024261474609375,
0.005664825439453125,
-0.005695343017578125,
-0.0091705322265625,
0.017364501953125,
-0.0015544891357421875,
0.0413818359375,
-0.01001739501953125,
-0.006015777587890625,
-0.006221771240234375,
0.01061248779296875,
-0.01364898681640625,
0.0238494873046875,
0.0172882080078125,
-0.03912353515625,
-0.01482391357421875,
0.004268646240234375,
-0.0183563232421875,
-0.01296234130859375,
0.0172882080078125,
-0.0159149169921875,
0.01490020751953125,
0.0016889572143554688,
-0.01413726806640625,
0.009124755859375,
-0.00469970703125,
-0.0113525390625,
-0.01302337646484375,
-0.00838470458984375,
-0.0182037353515625,
0.01983642578125,
-0.0140533447265625,
-0.000396728515625,
-0.027862548828125,
-0.0125885009765625,
-0.0234375,
-0.01277923583984375,
0.0167236328125,
0.00110626220703125,
0.003314971923828125,
-0.0021209716796875,
0.00542449951171875,
0.0158843994140625,
-0.0280303955078125,
-0.0036716461181640625,
0.0201568603515625,
-0.0184326171875,
-0.029510498046875,
0.01280975341796875,
0.0223846435546875,
0.0218658447265625,
0.0204620361328125,
-0.0246124267578125,
-0.0106048583984375,
-0.0382080078125,
0.026123046875,
-0.006011962890625,
0.057373046875,
-0.0325927734375,
0.005016326904296875,
0.01343536376953125,
0.015533447265625,
-0.034027099609375,
-0.016693115234375,
0.0159759521484375,
-0.0077056884765625,
-0.00913238525390625,
0.031890869140625,
-0.01509857177734375,
0.0001760721206665039,
0.018829345703125,
0.048492431640625,
0.002796173095703125,
-0.0296630859375,
0.0221710205078125,
-0.0066680908203125,
-0.01824951171875,
-0.0104827880859375,
-0.0272369384765625,
-0.02947998046875,
0.022796630859375,
0.018524169921875,
-0.03936767578125,
-0.00028514862060546875,
-0.016143798828125,
0.0181427001953125,
0.019378662109375,
0.00202178955078125,
-0.0384521484375,
-0.013153076171875,
0.01025390625,
0.00927734375,
0.0059051513671875,
0.019622802734375,
0.018310546875,
-0.049560546875,
-0.044677734375,
-0.0018749237060546875,
0.01666259765625,
0.03326416015625,
0.00200653076171875,
0.019866943359375,
0.004474639892578125,
-0.0282135009765625,
0.0221710205078125,
-0.0181732177734375,
0.0095977783203125,
0.01080322265625,
0.0150604248046875,
-0.007053375244140625,
0.0291290283203125,
-0.024078369140625,
0.0250701904296875,
0.00524139404296875,
-0.02996826171875,
0.0160369873046875,
0.0026149749755859375,
0.006443023681640625,
-0.026397705078125,
0.003223419189453125,
-0.0153350830078125,
-0.032989501953125,
-0.01541900634765625,
-0.0004227161407470703,
0.0203094482421875,
0.0239410400390625,
-0.0077056884765625,
-0.00634765625,
-0.053680419921875,
0.04522705078125,
0.023895263671875,
0.0296783447265625,
0.004302978515625,
0.00039076805114746094,
-0.01776123046875,
0.004245758056640625,
-0.004459381103515625,
-0.000713348388671875,
-0.00616455078125,
0.044586181640625,
0.0221710205078125,
0.01123809814453125,
0.034820556640625,
-0.0023670196533203125,
0.0090789794921875,
-0.00675201416015625,
0.035400390625,
0.009063720703125,
-0.0140380859375,
0.0101318359375,
0.037994384765625,
0.006595611572265625,
-0.0004639625549316406,
0.033447265625,
0.0203704833984375,
-0.01349639892578125,
0.0186004638671875,
-0.005687713623046875,
0.0111541748046875,
0.0245208740234375,
-0.023040771484375,
-0.035614013671875,
0.00011682510375976562,
-0.01535797119140625,
0.00905609130859375,
-0.049224853515625,
-0.00662994384765625,
0.0036449432373046875,
-0.03668212890625,
-0.03594970703125,
0.011627197265625,
-0.00604248046875,
0.0298004150390625,
-0.0269012451171875,
-0.01019287109375,
0.004608154296875,
0.0186309814453125,
-0.0023193359375,
0.007175445556640625,
-0.0037593841552734375,
0.0196380615234375,
0.0311737060546875,
-0.002506256103515625,
-0.035797119140625,
-0.00720977783203125,
-0.041412353515625,
-0.01108551025390625,
-0.01459503173828125,
0.0045166015625,
-0.01361083984375,
0.00888824462890625,
-0.034393310546875,
0.006992340087890625,
-0.006855010986328125,
-0.0340576171875,
0.0005898475646972656,
-0.0021762847900390625,
0.00677490234375,
0.002685546875,
0.023834228515625,
0.01097869873046875,
0.0030384063720703125,
0.00971221923828125,
0.02313232421875,
-0.01910400390625,
-0.01079559326171875,
-0.04327392578125,
-0.004955291748046875,
-0.00092315673828125,
0.009063720703125,
-0.0262451171875,
-0.0057373046875,
-0.016510009765625,
0.0216827392578125,
-0.0026302337646484375,
-0.013885498046875,
0.01788330078125,
-0.033172607421875,
0.006198883056640625,
-0.0232086181640625,
-0.030853271484375,
0.0016183853149414062,
-0.007366180419921875,
-0.061798095703125,
0.0016632080078125,
-0.0020389556884765625,
0.0049591064453125,
0.0167999267578125,
0.0031070709228515625,
0.0203399658203125,
0.0172882080078125,
0.0167694091796875,
-0.00775909423828125,
-0.00830078125,
0.007904052734375,
0.030548095703125,
0.0011854171752929688,
0.00820159912109375,
-0.00589752197265625,
-0.01389312744140625,
-0.0042877197265625,
-0.044769287109375,
-0.04766845703125,
-0.02484130859375,
-0.0196380615234375,
0.034881591796875,
-0.004680633544921875,
-0.0167694091796875,
0.0020847320556640625,
-0.0137786865234375,
0.0097198486328125,
-0.034637451171875,
-0.0214080810546875,
-0.0021266937255859375,
0.008056640625,
-0.0408935546875,
0.04266357421875,
0.0016927719116210938,
-0.0192108154296875,
-0.01312255859375,
0.00850677490234375,
0.037567138671875,
-0.01436614990234375,
0.0172882080078125,
-0.00547027587890625,
0.003345489501953125,
0.0295867919921875,
0.01186370849609375,
-0.03277587890625,
-0.0030384063720703125,
-0.032440185546875,
-0.003688812255859375,
-0.0137939453125,
0.013519287109375,
-0.01180267333984375,
0.01104736328125,
0.01419830322265625,
0.01421356201171875,
0.0153350830078125,
-0.0207977294921875,
0.00951385498046875,
-0.02777099609375,
0.0268402099609375,
0.0208282470703125,
-0.02423095703125,
-0.0008974075317382812,
0.0096588134765625,
0.00806427001953125,
0.037811279296875,
-0.015655517578125,
0.0233612060546875,
-0.004337310791015625,
0.0013208389282226562,
-0.0001189112663269043,
-0.013153076171875,
-0.016754150390625,
0.008819580078125,
0.00571441650390625,
0.00646209716796875,
0.038909912109375,
-0.075927734375,
-0.01500701904296875,
0.00357818603515625,
-0.0248565673828125,
-0.007781982421875,
-0.03802490234375,
0.0260162353515625,
0.00824737548828125,
0.0428466796875,
-0.0284271240234375,
0.0118255615234375,
-0.0031948089599609375,
0.00888824462890625,
0.0095977783203125,
-0.01373291015625,
0.006649017333984375,
-0.0102081298828125,
-0.0277099609375,
-0.00907135009765625,
-0.00293731689453125,
-0.013336181640625,
0.03985595703125,
-0.01690673828125,
0.007537841796875,
0.01383209228515625,
-0.01396942138671875,
0.0023670196533203125,
-0.0032634735107421875,
0.054962158203125,
0.0230865478515625,
0.0200653076171875,
0.049346923828125,
0.01123809814453125,
0.0018444061279296875,
-0.003993988037109375,
0.0030536651611328125,
-0.006763458251953125,
0.0007309913635253906,
-0.0419921875,
0.017730712890625,
0.02093505859375,
0.0038852691650390625,
0.02325439453125,
0.0189971923828125,
0.006137847900390625,
0.06549072265625,
-0.0236053466796875,
0.014862060546875,
0.0031566619873046875,
-0.006725311279296875,
-0.02349853515625,
0.0400390625,
0.0213165283203125,
-0.011322021484375,
0.01641845703125,
-0.00942230224609375,
-0.014495849609375,
-0.00360870361328125,
0.0271759033203125,
0.0287628173828125,
0.024993896484375,
0.01030731201171875,
0.01142120361328125,
-0.0025768280029296875,
-0.0184478759765625,
0.0230712890625,
0.004894256591796875,
-0.00606536865234375,
0.0174102783203125,
-0.01059722900390625,
0.005352020263671875,
0.0010509490966796875,
0.0033283233642578125,
0.0024623870849609375,
0.0113525390625,
0.01401519775390625,
-0.02130126953125,
0.0120697021484375,
0.03143310546875,
-0.0233001708984375,
-0.025360107421875,
-0.037841796875,
-0.004032135009765625,
0.00016832351684570312,
0.031463623046875,
0.003726959228515625,
-0.0091552734375,
0.010986328125,
0.049560546875,
-0.01151275634765625,
0.0071563720703125,
0.007083892822265625,
0.00566864013671875,
0.00464630126953125,
-0.0203399658203125,
0.0248260498046875,
-0.03216552734375,
-0.0247039794921875,
0.0038509368896484375,
0.0237579345703125,
-0.0267791748046875,
0.00036525726318359375,
0.02923583984375,
0.010406494140625,
-0.00530242919921875,
0.00994110107421875,
-0.0010967254638671875,
-0.002361297607421875,
0.018035888671875,
0.0217132568359375,
-0.01605224609375,
0.01041412353515625,
0.0175933837890625,
0.00347137451171875,
-0.002460479736328125,
-0.036163330078125,
-0.015716552734375,
0.01476287841796875,
-0.00699615478515625,
-0.03594970703125,
0.0029430389404296875,
-0.018157958984375,
0.030120849609375,
-0.0254669189453125,
-0.00446319580078125,
0.002468109130859375,
-0.002044677734375,
-0.015472412109375,
-0.0165863037109375,
0.00667572021484375,
-0.002429962158203125,
0.02337646484375,
0.019561767578125,
-0.0154571533203125,
0.036834716796875,
0.00862884521484375,
0.0147857666015625,
-0.02789306640625,
0.01324462890625,
-0.0243377685546875,
-0.033905029296875,
-0.01520538330078125,
0.004367828369140625,
0.007358551025390625,
-0.03985595703125,
-0.0036716461181640625,
0.0023822784423828125,
-0.01108551025390625,
0.0211181640625,
-0.00415802001953125,
0.0250091552734375,
-0.01116180419921875,
-0.002002716064453125,
-0.01184844970703125,
0.00579833984375,
0.0214385986328125,
-0.0206298828125,
-0.0313720703125,
-0.00492095947265625,
0.002597808837890625,
0.005474090576171875,
0.0122222900390625,
-0.0139007568359375,
0.007099151611328125,
-0.002132415771484375,
0.0203399658203125,
0.007701873779296875,
0.00276947021484375,
-0.0113067626953125,
-0.021759033203125,
0.0037326812744140625,
-0.014739990234375,
-0.00742340087890625,
0.0277557373046875,
0.0035457611083984375,
-0.031402587890625,
-0.037139892578125,
-0.02490234375,
0.01016998291015625,
-0.0262298583984375,
0.0022411346435546875,
-0.022064208984375,
-0.02301025390625,
-0.0138397216796875,
-0.01166534423828125,
-0.037384033203125,
-0.01556396484375,
0.027435302734375,
-0.018768310546875,
0.007717132568359375,
-0.00681304931640625,
-0.01959228515625,
-0.03424072265625,
-0.0187835693359375,
-0.020355224609375,
0.0139007568359375,
0.007381439208984375,
-0.0335693359375,
0.04034423828125,
0.00682830810546875,
-0.0286102294921875,
-0.029541015625,
-0.01465606689453125,
0.00955963134765625,
0.023712158203125,
-0.01441192626953125,
-0.00908660888671875,
0.0236358642578125,
0.03399658203125,
-0.018524169921875,
-0.01800537109375,
-0.01018524169921875,
0.005138397216796875,
0.0049591064453125,
0.0117950439453125,
-0.03399658203125,
0.005584716796875,
-0.001873016357421875,
0.019134521484375,
0.01393890380859375,
0.031280517578125,
-0.00801849365234375,
-0.0145416259765625,
0.003795623779296875,
-0.0125885009765625,
-0.0092315673828125,
0.0082855224609375,
-0.004230499267578125,
0.00024819374084472656,
0.0247650146484375,
0.018798828125,
0.006710052490234375,
-0.031036376953125,
0.01236724853515625,
-0.00848388671875,
0.015869140625,
0.0111541748046875,
0.012664794921875,
0.0308837890625,
-0.0288848876953125,
0.00783538818359375,
0.00778961181640625,
0.0003955364227294922,
0.0153350830078125,
0.00994110107421875,
0.0012559890747070312,
-0.014892578125,
0.005527496337890625,
-0.00829315185546875,
-0.006305694580078125,
-0.0157318115234375,
-0.016021728515625,
0.003017425537109375,
-0.0197296142578125,
0.031158447265625,
-0.01326751708984375,
-0.04852294921875,
-0.003246307373046875,
0.0010404586791992188,
0.003231048583984375,
0.001186370849609375,
0.007656097412109375,
0.007030487060546875,
-0.01061248779296875,
-0.020965576171875,
0.0240325927734375,
-0.0016994476318359375,
0.013671875,
0.0121917724609375,
-0.0032863616943359375,
-0.0200958251953125,
-0.00472259521484375,
0.0300140380859375,
-0.028594970703125,
-0.01247406005859375,
-0.020751953125,
0.0004124641418457031,
-0.0174102783203125,
0.02435302734375,
-0.010162353515625,
0.042266845703125,
-0.0077056884765625,
-0.001445770263671875,
-0.0147247314453125,
-0.03521728515625,
-0.04400634765625,
-0.00730133056640625,
-0.00136566162109375,
-0.015777587890625,
0.0099029541015625,
-0.032501220703125,
0.0269927978515625,
-0.01406097412109375,
-0.00868988037109375,
-0.032501220703125,
0.0066375732421875,
0.0139617919921875,
-0.002994537353515625,
0.028167724609375,
-0.04052734375,
-0.02081298828125,
-0.0167694091796875,
0.00234222412109375,
-0.01326751708984375,
0.03436279296875,
0.0018491744995117188,
0.00748443603515625,
0.00307464599609375,
-0.0004420280456542969,
0.0044708251953125,
0.03173828125,
0.014068603515625,
0.01378631591796875,
-0.0015707015991210938,
0.006084442138671875,
-0.0123291015625,
0.01055145263671875,
0.01812744140625,
-0.004032135009765625,
-0.007659912109375,
0.00818634033203125,
-0.0134124755859375,
0.013031005859375,
-0.0357666015625,
-0.0059814453125,
-0.0039520263671875,
0.000024497509002685547,
-0.0168914794921875,
-0.0234832763671875,
0.009124755859375,
0.0257415771484375,
0.01381683349609375,
-0.01117706298828125,
0.017120361328125,
0.01458740234375,
0.017730712890625,
0.01415252685546875,
0.00281524658203125,
-0.01204681396484375,
0.0255279541015625,
0.00036835670471191406,
-0.005451202392578125,
-0.00707244873046875,
-0.000946044921875,
-0.0157318115234375,
-0.039703369140625,
-0.0145416259765625,
-0.01557159423828125,
-0.0322265625,
-0.02490234375,
0.006397247314453125,
-0.0185546875,
0.002452850341796875,
-0.017120361328125,
0.0145721435546875,
0.006427764892578125,
-0.019500732421875,
-0.0222015380859375,
0.056884765625,
-0.0159759521484375,
-0.024261474609375,
0.006198883056640625,
-0.00003814697265625,
0.00897979736328125,
0.013916015625,
-0.0178375244140625,
0.01009368896484375,
-0.0265655517578125,
-0.0275726318359375,
0.0145416259765625,
-0.0255279541015625,
-0.0109100341796875,
-0.0019283294677734375,
-0.0031566619873046875,
-0.0002663135528564453,
0.0193328857421875,
-0.01000213623046875,
0.0419921875,
-0.0179290771484375,
0.0015745162963867188,
-0.0061492919921875,
0.01178741455078125,
-0.004039764404296875,
0.0263214111328125,
0.017669677734375,
0.02276611328125,
-0.007061004638671875,
0.007160186767578125,
0.01214599609375,
-0.0102996826171875,
-0.00850677490234375,
-0.01151275634765625,
-0.00005257129669189453,
0.00270843505859375,
0.00273895263671875,
-0.006256103515625,
-0.0153656005859375,
0.0184478759765625,
0.01215362548828125,
0.02130126953125,
-0.00455474853515625,
0.032562255859375,
-0.03143310546875,
-0.0148468017578125,
0.017578125,
-0.0201568603515625,
-0.0001709461212158203,
-0.01110076904296875,
0.007549285888671875,
0.028350830078125,
0.00559234619140625,
0.02386474609375,
-0.01215362548828125,
0.0099029541015625,
-0.0212860107421875,
0.02947998046875,
0.006374359130859375,
0.00284576416015625,
0.035675048828125,
-0.042724609375,
-0.001995086669921875,
0.01319122314453125,
0.002208709716796875,
0.0244140625,
-0.025146484375,
-0.0012941360473632812,
0.0478515625,
0.028564453125,
0.034820556640625,
-0.01354217529296875,
0.045654296875,
0.007114410400390625,
-0.0088348388671875,
-0.00801849365234375,
-0.037933349609375,
-0.004878997802734375,
-0.01415252685546875,
-0.01226806640625,
-0.00215911865234375,
0.01727294921875,
0.0275115966796875,
-0.0162506103515625,
-0.03082275390625,
0.00862884521484375,
-0.009490966796875,
0.0173492431640625,
0.03021240234375,
-0.0177764892578125,
-0.0201568603515625,
-0.002849578857421875,
0.028594970703125,
-0.014007568359375,
0.0190582275390625,
0.00200653076171875,
-0.004302978515625,
-0.02154541015625,
0.0238494873046875,
-0.0164642333984375,
-0.0054168701171875,
0.01036834716796875,
0.00975799560546875,
-0.01306915283203125,
-0.01288604736328125,
0.0244598388671875,
0.0118865966796875,
-0.01806640625,
-0.01294708251953125,
0.0269927978515625,
0.0274200439453125,
0.00530242919921875,
-0.00530242919921875,
0.04486083984375,
-0.015869140625,
-0.04302978515625,
0.0179443359375,
0.00466156005859375,
-0.008209228515625,
-0.02716064453125,
0.023651123046875,
0.0052337646484375,
0.034820556640625,
0.014923095703125,
-0.00217437744140625,
-0.0496826171875,
-0.00926971435546875,
0.0004940032958984375,
0.00615692138671875,
-0.00958251953125,
-0.0005826950073242188,
0.00006788969039916992,
-0.0038661956787109375,
-0.0251922607421875,
-0.0081024169921875,
0.0200347900390625,
-0.01715087890625,
-0.005428314208984375,
-0.0266571044921875,
-0.0142059326171875,
-0.01430511474609375,
-0.00788116455078125,
-0.00649261474609375,
0.0114898681640625,
0.036895751953125,
-0.01220703125,
0.004322052001953125,
-0.0098724365234375,
-0.005462646484375,
0.031829833984375,
0.006938934326171875,
0.007411956787109375,
0.01666259765625,
0.00406646728515625,
-0.033660888671875,
0.035980224609375,
-0.00197601318359375,
0.0025196075439453125,
-0.0190277099609375,
0.00948333740234375,
-0.04815673828125,
-0.038299560546875,
-0.011016845703125,
0.039703369140625,
0.0361328125,
0.01378631591796875,
-0.001495361328125,
-0.004497528076171875,
0.01078033447265625,
-0.023193359375,
-0.020751953125,
0.0260162353515625,
-0.014556884765625,
0.044189453125,
0.0079345703125,
-0.01364898681640625,
0.00035381317138671875,
0.01117706298828125,
-0.0000438690185546875,
-0.0036678314208984375,
-0.0357666015625,
-0.0232086181640625,
0.00447845458984375,
0.00183868408203125,
0.0265960693359375,
-0.0264739990234375,
0.0182342529296875,
-0.005191802978515625,
0.029022216796875,
0.00867462158203125,
0.0241241455078125,
-0.011627197265625,
0.0408935546875,
0.0172119140625,
-0.01107025146484375,
-0.01332855224609375,
0.01061248779296875,
-0.03973388671875,
0.040130615234375,
-0.002349853515625,
0.002506256103515625,
-0.025634765625,
0.00974273681640625,
0.00888824462890625,
-0.00377655029296875,
0.01114654541015625,
-0.00485992431640625,
0.0179443359375,
-0.02349853515625,
0.00311279296875,
-0.005733489990234375,
0.0350341796875,
-0.006122589111328125,
-0.0300445556640625,
-0.04949951171875,
0.039642333984375,
-0.007724761962890625,
-0.0017900466918945312,
-0.02032470703125,
0.01129150390625,
-0.021575927734375,
0.02191162109375,
-0.01409149169921875,
0.022918701171875,
0.00809478759765625,
-0.0125885009765625,
-0.00018322467803955078,
-0.01363372802734375,
-0.00885009765625,
-0.022796630859375,
0.00036072731018066406,
-0.03521728515625,
0.0021724700927734375,
0.0024814605712890625,
0.007549285888671875,
0.005855560302734375,
-0.002925872802734375,
0.0123443603515625,
0.0217132568359375,
-0.017059326171875,
0.0162811279296875,
0.0139312744140625,
0.01541900634765625,
-0.014984130859375,
-0.006439208984375,
-0.01480865478515625,
0.004253387451171875,
0.004505157470703125,
-0.0031299591064453125,
-0.028106689453125,
-0.035125732421875,
0.00238800048828125,
0.014678955078125,
0.0202178955078125,
0.01165771484375,
0.0006151199340820312,
-0.006687164306640625,
0.005619049072265625,
-0.00432586669921875,
-0.058441162109375,
-0.01004791259765625,
-0.0086212158203125,
0.0418701171875,
0.01239013671875,
0.006561279296875,
-0.039825439453125,
0.01898193359375,
-0.005283355712890625,
0.0019626617431640625,
-0.04315185546875,
0.0257568359375,
-0.00804901123046875,
0.004241943359375,
-0.01383209228515625,
-0.005420684814453125,
-0.00925445556640625,
-0.011260986328125,
-0.007007598876953125,
-0.026885986328125,
0.0014371871948242188,
0.01522064208984375,
0.0099945068359375,
-0.011932373046875,
-0.008697509765625,
-0.0122528076171875,
-0.0238494873046875,
0.0070037841796875,
0.0015554428100585938,
-0.0260162353515625,
0.0016498565673828125,
-0.01074981689453125,
-0.00820159912109375,
0.01535797119140625,
0.0195465087890625,
0.013427734375,
-0.007568359375,
-0.0208282470703125,
0.0031223297119140625,
-0.014862060546875,
0.004467010498046875,
-0.0016489028930664062,
0.00710296630859375,
0.016326904296875,
0.0090789794921875,
-0.01358795166015625,
0.01119232177734375,
-0.00971221923828125,
0.0072174072265625,
0.0268402099609375,
-0.016021728515625,
0.00946044921875,
-0.008392333984375,
0.01552581787109375,
0.0006160736083984375,
0.0061798095703125,
0.027801513671875,
-0.0130462646484375,
-0.01348114013671875,
-0.0307159423828125,
0.03717041015625,
0.01270294189453125,
0.006008148193359375,
0.0185546875,
0.005001068115234375,
0.0088043212890625,
-0.0176239013671875,
0.0131072998046875,
0.0076751708984375,
-0.004085540771484375,
0.0291748046875,
0.0137481689453125,
-0.01081085205078125,
-0.007663726806640625,
-0.01727294921875,
-0.031890869140625,
-0.01739501953125,
-0.01490020751953125,
-0.0025386810302734375,
0.018768310546875,
0.01263427734375,
0.022308349609375,
-0.0305938720703125,
-0.007373809814453125,
0.026702880859375,
0.0313720703125,
0.036102294921875,
-0.003742218017578125,
0.0067901611328125,
-0.01279449462890625,
-0.0179901123046875,
0.003726959228515625,
0.0067901611328125,
0.01284027099609375,
-0.0190277099609375,
0.013397216796875,
0.007221221923828125,
0.0032501220703125,
0.0267181396484375,
0.0019321441650390625,
-0.022735595703125,
0.00872039794921875,
-0.030517578125,
0.018035888671875,
-0.0021686553955078125,
-0.00997161865234375,
-0.006679534912109375,
0.0238800048828125,
-0.0211181640625,
-0.040374755859375,
-0.024688720703125,
0.0308837890625,
0.01229095458984375,
-0.0202789306640625,
0.0230560302734375,
0.01383209228515625,
-0.007053375244140625,
-0.002391815185546875,
-0.032135009765625,
-0.00830841064453125,
0.0024013519287109375,
-0.01959228515625,
0.01056671142578125,
-0.0004649162292480469,
-0.004909515380859375,
-0.01055908203125,
-0.010955810546875,
0.0224151611328125,
-0.019805908203125,
-0.01273345947265625,
0.007720947265625,
0.0292816162109375,
-0.00995635986328125,
-0.00852203369140625,
-0.0204925537109375,
0.02764892578125,
0.03253173828125,
0.00850677490234375,
0.01302337646484375,
0.0206451416015625,
0.014007568359375,
0.018096923828125,
0.0127410888671875,
0.020263671875,
-0.0450439453125,
-0.041961669921875,
0.0103607177734375,
-0.0242462158203125,
-0.016510009765625,
0.00601959228515625,
0.0155487060546875,
0.040283203125,
0.006046295166015625,
-0.0018587112426757812,
-0.0128936767578125,
0.0313720703125,
0.0472412109375,
-0.00699615478515625,
0.0209808349609375,
-0.0054931640625,
0.0157928466796875,
0.00033354759216308594,
-0.01000213623046875,
-0.0164642333984375,
0.03753662109375,
-0.00443267822265625,
-0.0211334228515625,
-0.02618408203125,
-0.01256561279296875,
-0.00945281982421875,
-0.01120758056640625,
-0.01509857177734375,
-0.02337646484375,
0.0143890380859375,
-0.0161895751953125,
-0.00690460205078125,
-0.008636474609375,
0.023651123046875,
-0.018280029296875,
0.0465087890625,
-0.01006317138671875,
0.0003495216369628906,
0.00548553466796875,
-0.0297698974609375,
-0.00099945068359375,
0.0096893310546875,
-0.0005426406860351562,
0.0251617431640625,
0.0253753662109375,
-0.0288238525390625,
0.01338958740234375,
0.006664276123046875,
-0.009552001953125,
0.0154571533203125,
-0.02496337890625,
-0.00604248046875,
-0.0297393798828125,
-0.0038700103759765625,
-0.0223388671875,
-0.0177459716796875,
0.00940704345703125,
0.01397705078125,
0.00003844499588012695,
0.045654296875,
0.0036487579345703125,
-0.0063934326171875,
0.007648468017578125,
-0.023406982421875,
-0.01371002197265625,
0.021881103515625,
-0.0166778564453125,
-0.0267333984375,
0.0013427734375,
-0.006290435791015625,
0.0115509033203125,
-0.0146484375,
0.004604339599609375,
0.0179443359375,
-0.0286865234375,
0.0054168701171875,
0.0293121337890625,
-0.0042724609375,
0.007030487060546875,
0.0204620361328125,
-0.0247955322265625,
-0.0112457275390625,
0.007381439208984375,
-0.0167388916015625,
-0.00519561767578125,
-0.015655517578125,
0.00467681884765625,
-0.007488250732421875,
0.009796142578125,
-0.002597808837890625,
0.0006017684936523438,
0.0265350341796875,
-0.0017232894897460938,
-0.0133056640625,
0.0035037994384765625,
-0.0175323486328125,
0.0134429931640625,
0.01343536376953125,
-0.016204833984375,
-0.0360107421875,
-0.0333251953125,
0.009063720703125,
0.047454833984375,
0.003429412841796875,
-0.0032062530517578125,
-0.0249176025390625,
0.01342010498046875,
-0.007694244384765625,
-0.0394287109375,
0.037353515625,
-0.00496673583984375,
-0.0149688720703125,
0.005069732666015625,
0.019989013671875,
0.01416015625,
-0.010498046875,
0.0046234130859375,
0.038116455078125,
0.0159454345703125,
-0.034698486328125,
-0.0019388198852539062,
0.0007901191711425781,
-0.024688720703125,
-0.0162811279296875,
0.02215576171875,
0.003833770751953125,
-0.005146026611328125,
-0.0130462646484375,
-0.0273895263671875,
0.018585205078125,
0.01012420654296875,
0.005733489990234375,
0.0204010009765625,
0.00412750244140625,
-0.0282440185546875,
-0.02947998046875,
0.0014972686767578125,
0.0185089111328125,
-0.03076171875,
-0.009429931640625,
-0.01497650146484375,
-0.0268402099609375,
-0.0018100738525390625,
0.035888671875,
0.016326904296875,
0.018829345703125,
0.0160675048828125,
0.01067352294921875,
0.022705078125,
-0.0306243896484375,
-0.037139892578125,
0.0435791015625,
-0.0104522705078125,
-0.00983428955078125,
0.01113128662109375,
-0.0180206298828125,
-0.00986480712890625,
-0.0467529296875,
-0.005481719970703125,
-0.043853759765625,
0.0213775634765625,
0.004405975341796875,
0.0026607513427734375,
0.01430511474609375,
-0.0028362274169921875,
0.0158233642578125,
0.035552978515625,
0.006500244140625,
0.016845703125,
0.03790283203125,
-0.006404876708984375,
-0.02166748046875,
-0.0014657974243164062,
-0.0123291015625,
-0.01474761962890625,
0.00762176513671875,
-0.012847900390625,
-0.004100799560546875,
0.0130157470703125,
-0.0277862548828125,
-0.0010213851928710938,
0.007724761962890625,
0.005336761474609375,
0.02764892578125,
-0.00949859619140625,
-0.0209503173828125,
-0.00910186767578125,
-0.01277923583984375,
0.0127716064453125,
-0.0283355712890625,
-0.008453369140625,
0.0323486328125,
0.005611419677734375,
0.01250457763671875,
-0.00972747802734375,
0.029327392578125,
-0.002552032470703125,
0.0357666015625,
-0.0157012939453125,
-0.0220794677734375,
0.0147857666015625,
0.0006504058837890625,
0.0131072998046875,
-0.0284423828125,
0.0277099609375,
0.00949859619140625,
0.005977630615234375,
0.031097412109375,
-0.01678466796875,
-0.007099151611328125,
-0.0268402099609375,
0.009033203125,
0.01311492919921875,
-0.01061248779296875,
-0.0015916824340820312,
0.006389617919921875,
-0.01114654541015625,
0.010345458984375,
-0.0322265625,
0.0188140869140625,
0.0024776458740234375,
0.00942230224609375,
0.01824951171875,
0.01763916015625,
0.00047898292541503906,
0.031951904296875,
0.031585693359375,
-0.020599365234375,
-0.01255035400390625,
-0.052825927734375,
-0.01070404052734375,
0.01424407958984375,
0.006744384765625,
-0.028961181640625,
0.0361328125,
-0.00466156005859375,
0.0125579833984375,
0.036102294921875,
0.0205078125,
0.00948333740234375,
0.01971435546875,
-0.036468505859375,
-0.0136871337890625,
0.00586700439453125,
-0.0186767578125,
0.030364990234375,
0.0282440185546875,
-0.0440673828125,
-0.029815673828125,
-0.01068115234375,
-0.0189666748046875,
0.0238189697265625,
-0.0187835693359375,
-0.00011247396469116211,
-0.002552032470703125,
-0.01494598388671875,
0.023895263671875,
-0.03497314453125,
0.0087127685546875,
-0.0013256072998046875,
-0.0247344970703125,
-0.006694793701171875,
-0.00443267822265625,
0.014190673828125,
-0.01477813720703125,
-0.01273345947265625,
0.03057861328125,
0.0078582763671875,
-0.0073394775390625,
-0.006855010986328125,
-0.00753021240234375,
-0.00528717041015625,
0.0281829833984375,
0.01416015625,
0.038055419921875,
-0.030609130859375,
-0.0087890625,
-0.00501251220703125,
0.0288543701171875,
-0.017852783203125,
0.001712799072265625,
0.0092620849609375,
-0.035003662109375,
0.007171630859375,
0.0037174224853515625,
-0.042266845703125,
-0.0233306884765625,
0.01168060302734375,
0.019439697265625,
-0.00513458251953125,
0.0113677978515625,
0.004161834716796875,
0.005016326904296875,
-0.01340484619140625,
-0.0291748046875,
0.011871337890625,
-0.018585205078125,
0.007038116455078125,
-0.032012939453125,
0.032012939453125,
0.0159454345703125,
0.035369873046875,
0.005352020263671875,
-0.039215087890625,
-0.0026645660400390625,
0.005588531494140625,
0.00466156005859375,
-0.00901031494140625,
-0.020050048828125,
-0.0267333984375,
-0.0233154296875,
0.04718017578125,
0.0117950439453125,
0.0191802978515625,
0.005741119384765625,
0.00644683837890625,
-0.006175994873046875,
0.0227203369140625,
-0.033111572265625,
0.0111846923828125,
-0.0166168212890625,
-0.01141357421875,
0.01015472412109375,
0.00962066650390625,
-0.01094818115234375,
-0.003444671630859375,
0.0191497802734375,
0.004962921142578125,
0.0121002197265625,
0.0093231201171875,
0.0059967041015625,
0.038330078125,
-0.01971435546875,
-0.02532958984375,
0.0284881591796875,
0.0132598876953125,
0.00820159912109375,
-0.01355743408203125,
-0.0130462646484375,
-0.0153045654296875,
-0.008575439453125,
-0.0096435546875,
0.032318115234375,
0.021392822265625,
0.0123443603515625,
0.016448974609375,
0.0025730133056640625,
0.01898193359375,
-0.0095367431640625,
-0.01131439208984375,
-0.0657958984375,
0.0161285400390625,
-0.006847381591796875,
0.0013074874877929688,
-0.0008444786071777344,
0.0208740234375,
0.0152130126953125,
0.004634857177734375,
-0.0289306640625,
-0.020477294921875,
-0.0208740234375,
-0.0191192626953125,
0.0277557373046875,
-0.0022754669189453125,
-0.0170440673828125,
-0.01004791259765625,
0.0038394927978515625,
-0.019683837890625,
-0.0168304443359375,
0.04119873046875,
0.030731201171875,
0.00708770751953125,
-0.00933837890625,
0.0235748291015625,
-0.0241241455078125,
-0.023345947265625,
0.0023040771484375,
0.0098114013671875,
-0.00780487060546875,
0.0003757476806640625,
0.0239105224609375,
-0.004669189453125,
0.0135650634765625,
-0.04840087890625,
-0.001644134521484375,
0.00681304931640625,
-0.016448974609375,
0.003482818603515625,
0.01262664794921875,
0.00823974609375,
0.00286865234375,
0.0010824203491210938,
-0.0099945068359375,
0.0295257568359375,
-0.0002777576446533203,
0.0165863037109375,
0.00003844499588012695,
0.0343017578125,
0.01297760009765625,
-0.0482177734375,
-0.0225982666015625,
-0.0177459716796875,
0.00138092041015625,
0.00970458984375,
-0.0015716552734375,
0.01190185546875,
-0.00006341934204101562,
-0.035003662109375,
0.0111541748046875,
0.00020110607147216797,
0.02825927734375,
0.0224609375,
-0.034698486328125,
-0.019256591796875,
0.00030303001403808594,
-0.0144500732421875,
-0.00217437744140625,
-0.0269622802734375,
-0.002040863037109375,
-0.024627685546875,
-0.0056304931640625,
0.028656005859375,
0.00679779052734375,
0.01238250732421875,
-0.003505706787109375,
0.01213836669921875,
-0.017852783203125,
-0.0124359130859375,
0.025604248046875,
0.03240966796875,
-0.01056671142578125,
-0.00136566162109375,
0.0152435302734375,
0.0141143798828125,
0.0166168212890625,
0.00945281982421875,
-0.023895263671875,
-0.01210784912109375,
-0.00547027587890625,
-0.017364501953125,
-0.03460693359375,
-0.01436614990234375,
0.0133209228515625,
-0.03125,
-0.018463134765625,
-0.0099334716796875,
-0.0080108642578125,
0.036376953125,
-0.003124237060546875,
-0.0209808349609375,
-0.005466461181640625,
0.01155853271484375,
-0.0239410400390625,
-0.0010204315185546875,
0.0015687942504882812,
-0.0035343170166015625,
-0.01245880126953125,
0.011474609375,
0.0157928466796875,
-0.0110931396484375,
-0.01222991943359375,
0.0194244384765625,
-0.022674560546875,
0.0004830360412597656,
-0.007190704345703125,
-0.01203155517578125,
-0.05328369140625,
0.01091766357421875,
-0.006855010986328125,
-0.00026345252990722656,
0.045166015625,
-0.0172119140625,
0.007843017578125,
0.020263671875,
0.0038127899169921875,
0.02606201171875,
-0.0097198486328125,
-0.0126953125,
0.020751953125,
0.0254669189453125,
0.00689697265625,
-0.032470703125,
-0.015838623046875,
-0.0005064010620117188,
0.00859832763671875,
0.0013141632080078125,
-0.01424407958984375,
0.00931549072265625,
0.01074981689453125,
0.00705718994140625,
0.0088043212890625,
-0.015838623046875,
-0.0126953125,
-0.00363922119140625,
0.01959228515625,
-0.0330810546875,
-0.01357269287109375,
0.0092315673828125,
0.0272369384765625,
-0.02130126953125,
0.021270751953125,
-0.0132598876953125,
0.0209808349609375,
-0.035247802734375,
-0.01241302490234375,
0.0019512176513671875,
0.0260467529296875,
0.004276275634765625,
-0.0134124755859375,
-0.0016679763793945312,
0.0009312629699707031,
0.0260162353515625,
-0.0061187744140625,
-0.03814697265625,
0.03387451171875,
-0.0008411407470703125,
-0.0036067962646484375,
0.0153045654296875,
-0.00325775146484375,
-0.01568603515625,
-0.007694244384765625,
-0.0160369873046875,
-0.0241851806640625,
0.01495361328125,
-0.00598907470703125,
0.009796142578125,
-0.03173828125,
0.005859375,
-0.030242919921875,
-0.02130126953125,
0.00757598876953125,
0.00455474853515625,
-0.021026611328125,
-0.04388427734375,
-0.01561737060546875,
0.004669189453125,
0.0218658447265625,
-0.0203704833984375,
0.02001953125,
0.00858306884765625,
0.04193115234375,
0.0229644775390625,
-0.001430511474609375,
0.02294921875,
0.02618408203125,
-0.022186279296875,
-0.0029964447021484375,
0.0201568603515625,
-0.0114288330078125,
0.0236663818359375,
0.0083465576171875,
-0.01041412353515625,
0.00804901123046875,
0.0165252685546875,
-0.00009757280349731445,
0.007068634033203125,
0.020416259765625,
-0.036529541015625,
0.00638580322265625,
-0.0057525634765625,
0.000995635986328125,
-0.0190582275390625,
-0.01433563232421875,
-0.003917694091796875,
0.0005064010620117188,
-0.0138397216796875,
0.0008416175842285156,
-0.00986480712890625,
-0.0065155029296875,
0.006237030029296875,
0.00739288330078125,
-0.0016841888427734375,
-0.031158447265625,
-0.00537109375,
-0.0284423828125,
0.00444793701171875,
-0.02130126953125,
0.040557861328125,
0.02288818359375,
0.0124053955078125,
0.01715087890625,
0.0260772705078125,
0.002899169921875,
0.0170135498046875,
0.04736328125,
0.01531982421875,
-0.002216339111328125,
-0.0088958740234375,
0.01027679443359375,
-0.009307861328125,
-0.00991058349609375,
0.0083465576171875,
0.024200439453125,
-0.0177764892578125,
0.0238189697265625,
-0.0008101463317871094,
0.033203125,
0.00884246826171875,
0.00009912252426147461,
0.0015420913696289062,
-0.0237579345703125,
-0.0006003379821777344,
-0.01357269287109375,
-0.025054931640625,
0.01788330078125,
-0.0309295654296875,
0.0027294158935546875,
0.002307891845703125,
-0.03375244140625,
0.01374053955078125,
0.0289764404296875,
0.0003719329833984375,
0.04266357421875,
-0.00046825408935546875,
0.034576416015625,
0.0174560546875,
-0.020660400390625,
0.0036525726318359375,
0.021087646484375,
-0.0294647216796875,
-0.0102081298828125,
-0.00789642333984375,
0.003154754638671875,
-0.00007104873657226562,
-0.005950927734375,
-0.01904296875,
-0.00566864013671875,
-0.0216217041015625,
0.04608154296875,
0.01190948486328125,
0.0174713134765625,
0.004138946533203125,
0.019378662109375,
0.039642333984375,
-0.01247406005859375,
0.0063018798828125,
-0.02325439453125,
-0.007724761962890625,
-0.0203857421875,
-0.064697265625,
-0.007678985595703125,
-0.0139923095703125,
-0.0055694580078125,
-0.0010881423950195312,
-0.01015472412109375,
0.05517578125,
-0.016326904296875,
0.00543975830078125,
-0.0170440673828125,
0.00634765625,
0.003025054931640625,
0.0096282958984375,
-0.008880615234375,
0.0156097412109375,
-0.040985107421875,
0.023162841796875,
-0.001331329345703125,
0.00782012939453125,
-0.0088958740234375,
0.00710296630859375,
-0.0307159423828125,
0.00960540771484375,
-0.00014674663543701172,
-0.023193359375,
-0.0282440185546875,
-0.027069091796875,
0.00946044921875,
-0.0245208740234375,
-0.007442474365234375,
0.004512786865234375,
0.0269317626953125,
0.004093170166015625,
-0.0257415771484375,
-0.0190277099609375,
-0.01203155517578125,
0.017578125,
0.02313232421875,
-0.0301513671875,
0.00748443603515625,
0.01493072509765625,
0.004901885986328125,
-0.031890869140625,
-0.00690460205078125,
0.0145721435546875,
0.001476287841796875,
-0.0157318115234375,
0.01093292236328125,
0.0158538818359375,
-0.00984954833984375,
-0.005626678466796875,
-0.01739501953125,
-0.0006504058837890625,
-0.00252532958984375,
0.004306793212890625,
0.0203704833984375,
-0.010101318359375,
-0.0008993148803710938,
0.004436492919921875,
0.019287109375,
0.0017232894897460938,
-0.0096588134765625,
-0.0016126632690429688,
-0.0223236083984375,
-0.0247344970703125,
-0.0021419525146484375,
0.018768310546875,
-0.004817962646484375,
-0.002864837646484375,
-0.0165863037109375,
0.00516510009765625,
-0.031982421875,
-0.0355224609375,
-0.0054779052734375,
0.028076171875,
0.042724609375,
-0.04534912109375,
-0.004657745361328125,
-0.002315521240234375,
0.0084991455078125,
-0.0177764892578125,
0.0006914138793945312,
-0.0037746429443359375,
-0.001636505126953125,
0.0005288124084472656,
0.01541900634765625,
0.0263519287109375,
0.0142974853515625,
-0.0209197998046875,
-0.00323486328125,
0.017303466796875,
0.00475311279296875,
-0.00988006591796875,
-0.00525665283203125,
-0.0281829833984375,
0.004390716552734375,
0.0279541015625,
-0.0162811279296875,
0.0229339599609375,
0.002040863037109375,
0.00838470458984375,
0.0018291473388671875,
-0.0051422119140625,
-0.0089874267578125,
-0.018096923828125,
0.01177215576171875,
0.02593994140625,
-0.01444244384765625,
-0.026458740234375,
-0.00643157958984375,
0.00555419921875,
-0.0019006729125976562,
-0.039703369140625,
0.033721923828125,
0.003818511962890625,
0.006244659423828125,
-0.01873779296875,
0.016693115234375,
0.0147247314453125,
0.0251617431640625,
0.039825439453125,
0.0062408447265625,
-0.0292816162109375,
0.0162200927734375,
0.0047149658203125,
0.0083770751953125,
0.023040771484375,
-0.005275726318359375,
-0.0208892822265625,
-0.032073974609375,
0.0037899017333984375,
0.006458282470703125,
0.0266876220703125,
0.0609130859375,
-0.002590179443359375,
-0.0204620361328125,
0.004146575927734375,
0.00885009765625,
-0.005916595458984375,
-0.0518798828125,
-0.0089263916015625,
-0.0213470458984375,
0.005939483642578125,
-0.00720977783203125,
-0.006908416748046875,
-0.004428863525390625,
0.043701171875,
-0.01271820068359375,
0.004528045654296875,
-0.007106781005859375,
0.03955078125,
0.030670166015625,
0.00022661685943603516,
-0.0283203125,
-0.00839996337890625,
-0.004669189453125,
0.00335693359375,
0.0199127197265625,
-0.0108795166015625,
0.04681396484375,
-0.0209503173828125,
-0.0195465087890625,
0.01800537109375,
0.035675048828125,
0.029083251953125,
0.0249786376953125,
0.011260986328125,
0.0004596710205078125,
-0.0008444786071777344,
-0.00766754150390625,
-0.0011034011840820312,
-0.01340484619140625,
0.0272369384765625,
0.026519775390625,
-0.00897216796875,
-0.0335693359375,
-0.024200439453125,
-0.0108184814453125,
-0.0245819091796875,
0.00035119056701660156,
0.011505126953125,
0.05023193359375,
-0.01849365234375,
0.035858154296875,
0.010528564453125,
-0.0020618438720703125,
0.0212249755859375,
-0.0105133056640625,
0.020599365234375,
0.033294677734375,
-0.029388427734375,
0.01371002197265625,
-0.01113128662109375,
0.01183319091796875,
0.0161590576171875,
-0.05133056640625,
0.0181884765625,
0.01224517822265625,
-0.0173187255859375,
-0.0294036865234375,
-0.00372314453125,
0.03936767578125,
0.0248870849609375,
-0.035003662109375,
-0.0277252197265625,
0.007373809814453125,
0.022247314453125,
-0.01409149169921875,
0.0032444000244140625,
0.002727508544921875,
0.0228729248046875,
-0.0034732818603515625,
-0.014801025390625,
-0.00992584228515625,
0.0144195556640625,
-0.043701171875,
0.0077972412109375,
-0.0006012916564941406,
-0.00665283203125,
0.0677490234375,
0.0046539306640625,
-0.01776123046875,
0.022003173828125,
-0.0313720703125,
-0.0006284713745117188,
-0.010955810546875,
-0.0181427001953125,
0.0013103485107421875,
-0.019439697265625,
-0.028594970703125,
0.00727081298828125,
-0.0263671875,
0.0130615234375,
-0.017120361328125,
0.005096435546875,
-0.00276947021484375,
0.00208282470703125,
0.03021240234375,
0.006256103515625,
0.021820068359375,
-0.0252227783203125,
-0.002490997314453125,
-0.0377197265625,
-0.0308990478515625,
-0.004169464111328125,
0.00579071044921875,
0.0294647216796875,
0.0041961669921875,
-0.007762908935546875,
0.01136016845703125,
-0.016204833984375,
-0.0085906982421875,
-0.01461029052734375,
-0.033233642578125,
-0.047821044921875,
-0.0021800994873046875,
0.0280609130859375,
0.0128936767578125,
-0.01519012451171875,
-0.008758544921875,
-0.00974273681640625,
-0.02618408203125,
-0.022674560546875,
0.01461029052734375,
-0.01120758056640625,
-0.05126953125,
0.05194091796875,
-0.012725830078125,
-0.0308074951171875,
-0.0248565673828125,
-0.0293426513671875,
0.0098419189453125,
-0.010284423828125,
-0.032623291015625,
-0.00527191162109375,
-0.01433563232421875,
0.03155517578125,
-0.06298828125,
-0.0033931732177734375,
0.01189422607421875,
0.00189208984375,
0.00824737548828125,
-0.034393310546875,
-0.0244903564453125,
-0.016754150390625,
-0.00829315185546875,
-0.0183868408203125,
0.0273284912109375,
0.0023193359375,
-0.0227508544921875,
-0.017120361328125,
-0.0145416259765625,
-0.0219573974609375,
0.005764007568359375,
-0.00942230224609375,
0.01605224609375,
0.00991058349609375,
0.01953125,
-0.003917694091796875,
0.0306243896484375,
-0.005641937255859375,
-0.01226806640625,
-0.0096588134765625,
-0.0117645263671875,
0.006687164306640625,
0.026031494140625,
0.002044677734375,
0.006183624267578125,
-0.00635528564453125,
-0.0032482147216796875,
-0.0212860107421875,
0.0018148422241210938,
0.00518035888671875,
0.0101470947265625,
0.00008434057235717773,
0.0059661865234375,
-0.0017251968383789062
] |
ours_537
|
Call the vertices of the board \(A, B, C, D\) where \(A\) is the vertex on the ground and \(AB\) is the long side of the board. The height of point \(B\), by 30-60-90 triangles, is \(64 \cdot \frac{1}{2} = 32\). The difference in heights of \(C\) and \(B\) is, again by 30-60-90 triangles, \(4 \cdot \frac{\sqrt{3}}{2} = 2\sqrt{3}\). This gives that \(C\) has a height of \(32 + 2\sqrt{3}\). Therefore, the answer is \(32 + 2 + 3 = 37\).
\(\boxed{37}\)
|
37
|
{
"competition": "us_comps",
"dataset": "Ours",
"posts": null,
"source": "OMOSoln2.md"
}
|
A board 64 inches long and 4 inches high is inclined so that the long side of the board makes a 30-degree angle with the ground. The distance from the highest point on the board to the ground can be expressed in the form \(a+b \sqrt{c}\) where \(a, b, c\) are positive integers and \(c\) is not divisible by the square of any prime. What is \(a+b+c\)?
|
[
"/Mathematics/Geometry/Trigonometry/Angles/AcuteAngle",
"/Mathematics/Geometry/Trigonometry/Angles/Angle",
"/Mathematics/Geometry/Trigonometry/GeneralTrigonometry/Trigonometry"
] |
Apply 30‑60‑90 triangle ratios to obtain the vertical components of the 64‑inch side (sin 30°) and the 4‑inch side (sin 60°).
|
[
-0.0002453327178955078,
-0.068115234375,
0.041748046875,
-0.0014753341674804688,
-0.0007576942443847656,
0.0003998279571533203,
0.031646728515625,
0.02020263671875,
0.0018367767333984375,
-0.01837158203125,
-0.043792724609375,
0.0099639892578125,
-0.0043792724609375,
0.025543212890625,
0.0533447265625,
-0.0260009765625,
0.0031948089599609375,
0.01397705078125,
0.05352783203125,
-0.0002758502960205078,
-0.0174560546875,
0.0008144378662109375,
-0.0235137939453125,
-0.0018825531005859375,
-0.027008056640625,
0.01480865478515625,
-0.0196075439453125,
0.01282501220703125,
-0.00664520263671875,
0.0110931396484375,
-0.002685546875,
0.00820159912109375,
-0.029815673828125,
-0.018798828125,
-0.0026721954345703125,
-0.00518035888671875,
0.039764404296875,
0.0016689300537109375,
-0.033172607421875,
-0.046051025390625,
0.004703521728515625,
0.00102996826171875,
-0.006683349609375,
0.0318603515625,
0.004360198974609375,
0.0301971435546875,
-0.01401519775390625,
-0.00984954833984375,
0.01515960693359375,
-0.0171356201171875,
0.001575469970703125,
0.01259613037109375,
-0.03656005859375,
-0.0051727294921875,
-0.00432586669921875,
-0.021942138671875,
-0.01180267333984375,
0.010467529296875,
-0.00347137451171875,
0.006710052490234375,
0.0031566619873046875,
0.0062103271484375,
-0.01776123046875,
0.01309967041015625,
-0.0093231201171875,
-0.006771087646484375,
0.0035152435302734375,
-0.06402587890625,
-0.0032711029052734375,
0.0015840530395507812,
0.0246429443359375,
-0.02532958984375,
0.01132965087890625,
0.0009694099426269531,
-0.007068634033203125,
-0.007274627685546875,
-0.019622802734375,
0.00022780895233154297,
-0.031585693359375,
0.03521728515625,
0.0016155242919921875,
-0.003978729248046875,
0.017913818359375,
-0.04425048828125,
-0.0010776519775390625,
0.002025604248046875,
-0.01556396484375,
0.006473541259765625,
0.0002524852752685547,
-0.00743865966796875,
0.0189971923828125,
0.033172607421875,
-0.02325439453125,
-0.025970458984375,
-0.0027217864990234375,
0.016510009765625,
-0.0201416015625,
-0.01239776611328125,
-0.00675201416015625,
-0.000018656253814697266,
0.00325775146484375,
-0.00481414794921875,
-0.041595458984375,
0.0019969940185546875,
0.017303466796875,
-0.01174163818359375,
-0.01129913330078125,
-0.00971221923828125,
-0.004184722900390625,
0.020050048828125,
0.004688262939453125,
-0.022064208984375,
0.051513671875,
0.00879669189453125,
0.002925872802734375,
0.0093841552734375,
0.0256805419921875,
0.008544921875,
-0.009796142578125,
0.041412353515625,
-0.0011262893676757812,
0.01201629638671875,
-0.0017404556274414062,
0.01537322998046875,
0.006938934326171875,
-0.0028934478759765625,
-0.0170745849609375,
-0.020477294921875,
0.002685546875,
0.0204315185546875,
0.00843048095703125,
-0.01277923583984375,
-0.0172271728515625,
-0.0218048095703125,
0.0142669677734375,
0.018890380859375,
0.0017108917236328125,
0.00006914138793945312,
-0.008270263671875,
-0.00623321533203125,
-0.0017843246459960938,
-0.007373809814453125,
0.00013256072998046875,
-0.0992431640625,
-0.00543212890625,
-0.0083465576171875,
-0.0011749267578125,
-0.00600433349609375,
0.00005418062210083008,
0.002208709716796875,
0.003948211669921875,
-0.01140594482421875,
-0.0123291015625,
0.024627685546875,
0.019439697265625,
0.0031948089599609375,
0.006687164306640625,
0.0186309814453125,
-0.0176849365234375,
0.0010671615600585938,
-0.0262451171875,
-0.0092010498046875,
-0.01114654541015625,
0.037628173828125,
-0.00452423095703125,
-0.0150909423828125,
0.033172607421875,
0.0098114013671875,
-0.017608642578125,
-0.00705718994140625,
-0.0011577606201171875,
0.0079498291015625,
0.00001913309097290039,
-0.0169677734375,
-0.00415802001953125,
0.01209259033203125,
0.002960205078125,
0.004730224609375,
0.00494384765625,
0.0265350341796875,
-0.01551055908203125,
-0.0296783447265625,
0.02423095703125,
-0.01062774658203125,
0.01494598388671875,
0.001552581787109375,
-0.002902984619140625,
-0.0139312744140625,
0.01568603515625,
0.034698486328125,
0.01418304443359375,
-0.0279083251953125,
-0.004329681396484375,
-0.00872802734375,
0.0011692047119140625,
-0.01238250732421875,
-0.030975341796875,
-0.00959014892578125,
0.0280303955078125,
0.00003916025161743164,
-0.0018062591552734375,
-0.0009593963623046875,
0.06280517578125,
-0.0079803466796875,
-0.002429962158203125,
-0.006824493408203125,
-0.00408935546875,
-0.0007495880126953125,
-0.007213592529296875,
0.00714111328125,
-0.0129547119140625,
0.05218505859375,
0.0007128715515136719,
-0.0282440185546875,
-0.0175628662109375,
-0.000896453857421875,
-0.0186614990234375,
-0.0084381103515625,
0.0086517333984375,
0.030548095703125,
0.00481414794921875,
-0.01727294921875,
0.0052490234375,
-0.007171630859375,
-0.00998687744140625,
0.0278778076171875,
-0.00567626953125,
0.0009474754333496094,
0.004581451416015625,
-0.01389312744140625,
0.018798828125,
0.01126861572265625,
-0.0090789794921875,
0.00986480712890625,
-0.021087646484375,
-0.01016998291015625,
-0.0201416015625,
-0.0008311271667480469,
0.0017957687377929688,
-0.01337432861328125,
0.01248931884765625,
-0.0133514404296875,
-0.00299072265625,
-0.00140380859375,
-0.0148773193359375,
-0.006969451904296875,
0.006465911865234375,
-0.0218505859375,
-0.0168304443359375,
-0.01751708984375,
0.0032958984375,
-0.001007080078125,
-0.0108489990234375,
-0.0164337158203125,
-0.018218994140625,
0.0010881423950195312,
0.01715087890625,
0.03936767578125,
-0.01531219482421875,
0.0081634521484375,
-0.009735107421875,
-0.005626678466796875,
-0.0093536376953125,
-0.00870513916015625,
0.00006192922592163086,
-0.00970458984375,
0.00191497802734375,
0.0191802978515625,
0.0124664306640625,
0.01143646240234375,
-0.017242431640625,
0.003299713134765625,
-0.01432037353515625,
0.0135498046875,
-0.0034847259521484375,
-0.007472991943359375,
0.00408935546875,
0.029815673828125,
0.019073486328125,
-0.002033233642578125,
-0.0079498291015625,
0.01160430908203125,
-0.018768310546875,
0.01236724853515625,
-0.0012445449829101562,
-0.03497314453125,
0.0119171142578125,
-0.01294708251953125,
-0.0242156982421875,
0.02789306640625,
0.001773834228515625,
0.0131988525390625,
0.008514404296875,
-0.02484130859375,
0.020294189453125,
0.016754150390625,
0.0200958251953125,
-0.0028533935546875,
-0.023529052734375,
-0.011810302734375,
-0.00519561767578125,
-0.004825592041015625,
0.0093841552734375,
0.004611968994140625,
0.02679443359375,
-0.0099334716796875,
-0.00861358642578125,
0.018157958984375,
-0.025726318359375,
0.02490234375,
0.0201416015625,
0.006259918212890625,
-0.008514404296875,
-0.007717132568359375,
-0.022308349609375,
-0.0289154052734375,
0.01464080810546875,
0.006755828857421875,
-0.02410888671875,
-0.0156707763671875,
0.0169219970703125,
0.00908660888671875,
0.0034332275390625,
-0.0009126663208007812,
0.0089569091796875,
0.0089874267578125,
0.02783203125,
-0.0091705322265625,
-0.0180816650390625,
0.0015621185302734375,
-0.016265869140625,
0.015625,
0.02459716796875,
-0.040496826171875,
-0.00969696044921875,
0.017547607421875,
-0.004291534423828125,
0.0200958251953125,
0.01104736328125,
-0.00133514404296875,
-0.0009832382202148438,
-0.010284423828125,
0.01470184326171875,
-0.06805419921875,
-0.01473236083984375,
0.0087432861328125,
-0.021209716796875,
0.0038852691650390625,
0.00168609619140625,
-0.0193328857421875,
-0.01149749755859375,
-0.01153564453125,
-0.01410675048828125,
-0.0041046142578125,
-0.0164031982421875,
-0.01495361328125,
0.006015777587890625,
0.005916595458984375,
-0.01409912109375,
0.0153961181640625,
0.020782470703125,
-0.00972747802734375,
-0.01287078857421875,
0.01169586181640625,
-0.026123046875,
-0.0015115737915039062,
-0.0193939208984375,
0.018768310546875,
0.031951904296875,
-0.0006594657897949219,
-0.00287628173828125,
-0.0273895263671875,
-0.012451171875,
-0.0132598876953125,
-0.00820159912109375,
0.020233154296875,
0.00836181640625,
-0.012603759765625,
0.0132904052734375,
-0.00447845458984375,
-0.00844573974609375,
0.005970001220703125,
-0.004306793212890625,
0.02099609375,
0.00719451904296875,
0.0100555419921875,
-0.006664276123046875,
-0.03045654296875,
-0.0225372314453125,
0.0246429443359375,
-0.0240020751953125,
0.0025691986083984375,
0.0087127685546875,
-0.00435638427734375,
-0.044952392578125,
-0.017425537109375,
0.0016908645629882812,
0.0007309913635253906,
0.05633544921875,
0.011077880859375,
-0.04925537109375,
0.02044677734375,
-0.013824462890625,
0.01727294921875,
0.0024013519287109375,
-0.00853729248046875,
-0.0085601806640625,
0.04107666015625,
-0.0033245086669921875,
0.01552581787109375,
-0.006107330322265625,
-0.00753021240234375,
0.007770538330078125,
-0.00399017333984375,
-0.059783935546875,
0.0010852813720703125,
0.027435302734375,
-0.047515869140625,
0.003932952880859375,
-0.020843505859375,
-0.0001493692398071289,
0.0016183853149414062,
0.0309600830078125,
-0.00739288330078125,
0.046783447265625,
0.02099609375,
0.006839752197265625,
0.0226287841796875,
-0.0237274169921875,
-0.01611328125,
0.005146026611328125,
-0.012420654296875,
0.006137847900390625,
0.048309326171875,
-0.005176544189453125,
0.010772705078125,
0.0341796875,
0.006870269775390625,
0.0083770751953125,
0.01503753662109375,
0.00954437255859375,
-0.0236053466796875,
-0.01336669921875,
-0.036346435546875,
0.022003173828125,
0.0143890380859375,
-0.005962371826171875,
0.007305145263671875,
0.036529541015625,
-0.006214141845703125,
0.00482940673828125,
-0.01500701904296875,
-0.0166168212890625,
-0.0199737548828125,
-0.02099609375,
-0.0057525634765625,
0.002162933349609375,
-0.03582763671875,
-0.034637451171875,
0.0271453857421875,
-0.02569580078125,
-0.01369476318359375,
0.004024505615234375,
0.011566162109375,
-0.000026345252990722656,
-0.03045654296875,
-0.004734039306640625,
0.0038356781005859375,
-0.039886474609375,
0.002197265625,
0.006237030029296875,
-0.006011962890625,
0.01279449462890625,
0.03460693359375,
-0.016448974609375,
0.011199951171875,
-0.00995635986328125,
0.036468505859375,
-0.006725311279296875,
0.020751953125,
0.00830078125,
0.0160064697265625,
-0.00905609130859375,
0.0299224853515625,
-0.0229949951171875,
0.039886474609375,
0.0090789794921875,
-0.00637054443359375,
0.0101776123046875,
-0.0037059783935546875,
0.01229095458984375,
0.06573486328125,
-0.0200347900390625,
-0.019683837890625,
0.00628662109375,
0.0052032470703125,
-0.002620697021484375,
0.02166748046875,
-0.017852783203125,
-0.0204925537109375,
0.0210723876953125,
-0.020355224609375,
-0.00788116455078125,
0.01708984375,
0.00177764892578125,
-0.02166748046875,
0.047821044921875,
-0.0277862548828125,
0.0147857666015625,
-0.005130767822265625,
0.01367950439453125,
-0.018829345703125,
-0.0190582275390625,
-0.03399658203125,
0.0517578125,
0.006519317626953125,
0.0024509429931640625,
-0.003559112548828125,
0.0071868896484375,
-0.0213470458984375,
-0.003269195556640625,
0.0265655517578125,
0.0011005401611328125,
0.0188751220703125,
-0.0034503936767578125,
0.01465606689453125,
0.0217742919921875,
-0.0301971435546875,
0.012786865234375,
0.00676727294921875,
0.01009368896484375,
-0.0140838623046875,
-0.032135009765625,
0.00920867919921875,
-0.015777587890625,
0.005573272705078125,
0.00028061866760253906,
-0.0096588134765625,
0.02960205078125,
0.030731201171875,
0.003093719482421875,
0.01142120361328125,
-0.0205841064453125,
-0.010528564453125,
0.024322509765625,
0.0234832763671875,
0.011566162109375,
0.0305023193359375,
0.0020427703857421875,
-0.0020999908447265625,
0.005340576171875,
-0.005710601806640625,
0.01953125,
0.0095062255859375,
-0.0309600830078125,
0.01442718505859375,
-0.01233673095703125,
0.03155517578125,
-0.0214080810546875,
0.0144805908203125,
0.004627227783203125,
0.0145111083984375,
0.0160369873046875,
-0.009002685546875,
0.03753662109375,
0.02752685546875,
0.0189971923828125,
-0.0230865478515625,
-0.0238037109375,
-0.0220184326171875,
-0.011505126953125,
-0.004901885986328125,
-0.02642822265625,
0.01406097412109375,
0.01041412353515625,
-0.03729248046875,
0.004238128662109375,
-0.0124969482421875,
0.00925445556640625,
-0.03289794921875,
0.03387451171875,
0.018096923828125,
-0.018707275390625,
-0.0072174072265625,
-0.0161590576171875,
-0.0058441162109375,
0.010009765625,
0.04449462890625,
0.0121612548828125,
0.005176544189453125,
-0.023681640625,
0.037384033203125,
0.01432037353515625,
0.0012722015380859375,
-0.0027027130126953125,
-0.0201873779296875,
-0.01532745361328125,
0.007110595703125,
0.005523681640625,
-0.00229644775390625,
0.0036163330078125,
-0.0022373199462890625,
-0.02862548828125,
0.01239013671875,
0.014923095703125,
0.0146484375,
-0.03936767578125,
0.00841522216796875,
0.024932861328125,
-0.0139923095703125,
-0.004070281982421875,
-0.0059356689453125,
-0.0109710693359375,
0.018157958984375,
0.03131103515625,
0.0091705322265625,
-0.0196380615234375,
-0.00505828857421875,
-0.02239990234375,
0.007808685302734375,
-0.0264129638671875,
0.01305389404296875,
0.020904541015625,
-0.0021839141845703125,
-0.0207061767578125,
-0.02301025390625,
-0.0232086181640625,
-0.00768280029296875,
0.0220489501953125,
0.0072784423828125,
-0.00316619873046875,
-0.0088653564453125,
0.04364013671875,
0.01346588134765625,
-0.0017871856689453125,
-0.04425048828125,
-0.021453857421875,
-0.0143585205078125,
0.0085906982421875,
-0.0306549072265625,
0.003147125244140625,
0.044677734375,
0.019775390625,
-0.049072265625,
-0.0148773193359375,
-0.06341552734375,
-0.0057220458984375,
-0.0330810546875,
-0.0065460205078125,
0.002166748046875,
-0.01419830322265625,
0.03857421875,
-0.0059051513671875,
0.031158447265625,
0.00945281982421875,
-0.00814056396484375,
0.00945281982421875,
-0.0021762847900390625,
0.02923583984375,
0.0228424072265625,
-0.022613525390625,
-0.03143310546875,
-0.020172119140625,
-0.037261962890625,
-0.01354217529296875,
0.00737762451171875,
-0.01035308837890625,
-0.024993896484375,
0.007434844970703125,
0.0153656005859375,
-0.0017976760864257812,
0.005718231201171875,
0.027496337890625,
-0.027984619140625,
-0.016021728515625,
-0.0222930908203125,
-0.04534912109375,
0.01061248779296875,
-0.01227569580078125,
-0.019744873046875,
0.0273590087890625,
0.00920867919921875,
0.0204620361328125,
0.00147247314453125,
0.0118865966796875,
0.026458740234375,
-0.004581451416015625,
0.01409149169921875,
0.004993438720703125,
0.0203094482421875,
-0.0018987655639648438,
0.005023956298828125,
-0.00208282470703125,
0.0380859375,
0.01204681396484375,
0.0161285400390625,
0.011260986328125,
-0.0009088516235351562,
0.0005526542663574219,
-0.003849029541015625,
0.003490447998046875,
0.0011997222900390625,
0.010528564453125,
-0.056243896484375,
-0.033782958984375,
-0.00814056396484375,
-0.00785064697265625,
-0.006908416748046875,
-0.0078582763671875,
0.00788116455078125,
-0.027801513671875,
-0.013946533203125,
-0.020721435546875,
-0.0280303955078125,
-0.0208282470703125,
-0.004344940185546875,
-0.006267547607421875,
-0.047210693359375,
0.0212249755859375,
0.0081634521484375,
0.0572509765625,
-0.002197265625,
-0.0007009506225585938,
-0.01788330078125,
-0.01511383056640625,
0.01456451416015625,
-0.03912353515625,
0.01520538330078125,
-0.024810791015625,
0.0090789794921875,
-0.0029239654541015625,
-0.0243072509765625,
-0.01274871826171875,
-0.0184478759765625,
-0.03741455078125,
-0.0243988037109375,
-0.0195465087890625,
-0.04278564453125,
-0.011383056640625,
0.0033321380615234375,
0.0121002197265625,
-0.00971221923828125,
-0.00269317626953125,
-0.019287109375,
-0.00951385498046875,
0.0032062530517578125,
-0.0275421142578125,
-0.01439666748046875,
0.00278472900390625,
-0.0081024169921875,
-0.01352691650390625,
0.0017766952514648438,
0.005279541015625,
-0.061981201171875,
-0.0209808349609375,
0.0289154052734375,
-0.0203704833984375,
-0.0207061767578125,
-0.0146942138671875,
0.009124755859375,
-0.0290069580078125,
0.04400634765625,
-0.017486572265625,
0.0187530517578125,
-0.0063629150390625,
0.0160369873046875,
-0.00609588623046875,
-0.0032939910888671875,
-0.0111083984375,
-0.0182647705078125,
0.02874755859375,
-0.01537322998046875,
0.0025634765625,
0.0035266876220703125,
-0.0008869171142578125,
0.006999969482421875,
-0.040008544921875,
-0.004123687744140625,
0.032501220703125,
-0.01427459716796875,
0.00811767578125,
-0.0304412841796875,
0.00598907470703125,
0.02496337890625,
-0.0265045166015625,
-0.0027484893798828125,
-0.04345703125,
-0.0299224853515625,
0.023895263671875,
-0.028717041015625,
-0.0001971721649169922,
-0.0173492431640625,
0.00823974609375,
-0.0017261505126953125,
-0.0068206787109375,
-0.00635528564453125,
0.00191497802734375,
-0.01230621337890625,
-0.00946807861328125,
0.020751953125,
-0.0032196044921875,
-0.003391265869140625,
0.020355224609375,
0.038604736328125,
0.04119873046875,
-0.007793426513671875,
-0.00146484375,
0.004634857177734375,
-0.0243682861328125,
0.0023670196533203125,
0.041229248046875,
-0.0113983154296875,
0.01476287841796875,
-0.0249176025390625,
-0.0178070068359375,
0.0014781951904296875,
0.00791168212890625,
-0.0308990478515625,
-0.01082611083984375,
0.0031585693359375,
-0.0225982666015625,
0.036834716796875,
-0.01462554931640625,
-0.00865936279296875,
-0.0148162841796875,
-0.017486572265625,
0.010040283203125,
0.012420654296875,
0.009490966796875,
0.0010461807250976562,
-0.0025691986083984375,
0.00621795654296875,
-0.0084075927734375,
0.0240325927734375,
-0.049285888671875,
0.0196075439453125,
-0.0233917236328125,
-0.007678985595703125,
-0.0106353759765625,
-0.0187530517578125,
0.00830841064453125,
-0.01165008544921875,
0.009765625,
-0.0005407333374023438,
0.0098419189453125,
-0.005306243896484375,
-0.0251007080078125,
-0.0017518997192382812,
0.01265716552734375,
0.011993408203125,
-0.0213775634765625,
0.00594329833984375,
-0.0012102127075195312,
0.014373779296875,
-0.035675048828125,
0.004947662353515625,
-0.001064300537109375,
0.0158538818359375,
-0.018829345703125,
-0.0034275054931640625,
0.0224609375,
-0.004276275634765625,
-0.0222625732421875,
0.0325927734375,
-0.022369384765625,
-0.0287017822265625,
0.0191192626953125,
0.0037860870361328125,
0.015869140625,
-0.027587890625,
0.01389312744140625,
0.00881195068359375,
-0.0050811767578125,
0.00824737548828125,
0.00759124755859375,
-0.030242919921875,
-0.00899505615234375,
0.010986328125,
0.01171875,
0.0198822021484375,
0.0279541015625,
-0.043212890625,
-0.0155181884765625,
0.01320648193359375,
-0.01131439208984375,
0.004619598388671875,
-0.034423828125,
0.017486572265625,
0.005405426025390625,
-0.021697998046875,
0.01776123046875,
-0.006740570068359375,
-0.0203704833984375,
-0.0159454345703125,
0.0107879638671875,
0.006099700927734375,
0.0130615234375,
-0.032958984375,
0.00841522216796875,
-0.0037670135498046875,
0.0036773681640625,
0.039215087890625,
-0.0288848876953125,
-0.0116729736328125,
-0.01132965087890625,
0.00860595703125,
-0.01019287109375,
-0.003604888916015625,
0.013763427734375,
0.040252685546875,
0.0153350830078125,
-0.00439453125,
0.007465362548828125,
0.0129241943359375,
0.0245819091796875,
-0.0295562744140625,
-0.021270751953125,
0.0191802978515625,
-0.01540374755859375,
-0.01776123046875,
0.0008554458618164062,
-0.00408172607421875,
-0.0042877197265625,
-0.0096435546875,
-0.0032558441162109375,
-0.02374267578125,
0.0271148681640625,
-0.0162811279296875,
-0.050018310546875,
-0.0298004150390625,
-0.0164947509765625,
0.024749755859375,
-0.006282806396484375,
0.00293731689453125,
-0.00025081634521484375,
0.008209228515625,
0.00028705596923828125,
-0.013092041015625,
-0.002040863037109375,
0.0037899017333984375,
-0.0242767333984375,
0.042022705078125,
0.006626129150390625,
0.040771484375,
-0.006053924560546875,
0.016632080078125,
-0.014739990234375,
-0.0008249282836914062,
0.01690673828125,
0.00609588623046875,
0.035888671875,
0.00931549072265625,
-0.0087127685546875,
0.040740966796875,
0.0002570152282714844,
-0.0265960693359375,
0.0108642578125,
0.0009236335754394531,
0.0101776123046875,
-0.01091766357421875,
-0.015380859375,
0.01282501220703125,
-0.0184783935546875,
0.01507568359375,
0.00439453125,
-0.0183258056640625,
0.026031494140625,
0.022674560546875,
0.0157012939453125,
-0.00611114501953125,
0.01739501953125,
-0.0252685546875,
0.01467132568359375,
-0.01424407958984375,
-0.023345947265625,
0.02252197265625,
0.0021686553955078125,
0.0175323486328125,
0.01532745361328125,
0.0186004638671875,
-0.0212554931640625,
0.01206207275390625,
0.0291595458984375,
0.01451873779296875,
0.00815582275390625,
-0.0253753662109375,
0.01229095458984375,
-0.0195465087890625,
0.0234527587890625,
-0.00930023193359375,
0.006137847900390625,
0.0335693359375,
-0.0247802734375,
0.01398468017578125,
0.01166534423828125,
0.0185394287109375,
0.0009393692016601562,
0.0000028014183044433594,
0.005046844482421875,
-0.032562255859375,
-0.015655517578125,
-0.009979248046875,
0.0204010009765625,
-0.038360595703125,
-0.01020050048828125,
-0.0311737060546875,
0.0020732879638671875,
0.0322265625,
0.0037288665771484375,
0.0094757080078125,
-0.0283050537109375,
0.00672149658203125,
-0.00571441650390625,
-0.00891876220703125,
-0.002155303955078125,
0.0743408203125,
0.01123809814453125,
-0.0022335052490234375,
-0.045440673828125,
0.01641845703125,
-0.011199951171875,
-0.0260162353515625,
-0.00199127197265625,
-0.015289306640625,
-0.003726959228515625,
-0.05963134765625,
0.01052093505859375,
0.023468017578125,
0.01523590087890625,
0.05828857421875,
-0.020050048828125,
0.003086090087890625,
-0.020965576171875,
-0.01544189453125,
-0.0022068023681640625,
-0.0115203857421875,
-0.01396942138671875,
-0.02825927734375,
-0.0022792816162109375,
0.0340576171875,
-0.018890380859375,
-0.009368896484375,
0.0227203369140625,
-0.02117919921875,
-0.01213836669921875,
-0.0274658203125,
0.0089263916015625,
0.01282501220703125,
-0.047332763671875,
-0.006801605224609375,
-0.0019321441650390625,
0.0180511474609375,
-0.00821685791015625,
-0.00232696533203125,
0.0018596649169921875,
-0.0061492919921875,
0.0106658935546875,
-0.005199432373046875,
0.01458740234375,
0.0118560791015625,
-0.0153350830078125,
0.007781982421875,
-0.048370361328125,
-0.020843505859375,
0.00667572021484375,
0.0210418701171875,
-0.020660400390625,
-0.0170440673828125,
0.02764892578125,
0.0032196044921875,
-0.04217529296875,
0.01390838623046875,
-0.0030994415283203125,
0.038787841796875,
0.009033203125,
0.0023899078369140625,
-0.004650115966796875,
-0.0016727447509765625,
-0.0083160400390625,
-0.03485107421875,
0.0172119140625,
-0.00079345703125,
-0.010223388671875,
0.0290985107421875,
0.0278472900390625,
0.0156402587890625,
-0.005168914794921875,
-0.0036296844482421875,
-0.01082611083984375,
0.018707275390625,
0.018585205078125,
0.018310546875,
-0.007663726806640625,
-0.0216522216796875,
0.01412200927734375,
-0.02056884765625,
-0.000492095947265625,
0.0081787109375,
0.00257110595703125,
0.0108642578125,
0.00695037841796875,
0.022796630859375,
0.027313232421875,
0.019073486328125,
0.0091400146484375,
-0.00506591796875,
-0.011138916015625,
0.0270538330078125,
0.00681304931640625,
-0.0182647705078125,
-0.04779052734375,
-0.0011653900146484375,
0.039764404296875,
0.00643157958984375,
-0.00634765625,
-0.025115966796875,
-0.030487060546875,
-0.0072479248046875,
-0.00020933151245117188,
-0.0096282958984375,
0.0243988037109375,
0.01023101806640625,
-0.0176239013671875,
0.0137939453125,
0.0253753662109375,
0.0245819091796875,
0.005542755126953125,
-0.01439666748046875,
0.002689361572265625,
0.01873779296875,
-0.01348114013671875,
0.0341796875,
-0.00994873046875,
0.0004837512969970703,
0.01617431640625,
0.03082275390625,
0.00977325439453125,
-0.015045166015625,
-0.0017337799072265625,
-0.0031795501708984375,
-0.0231781005859375,
-0.0152130126953125,
0.0001366138458251953,
-0.0309295654296875,
-0.0131988525390625,
0.0297698974609375,
0.01113128662109375,
0.0107879638671875,
0.051849365234375,
-0.0038928985595703125,
-0.010894775390625,
-0.00482940673828125,
-0.03717041015625,
0.0258026123046875,
-0.016937255859375,
0.003864288330078125,
0.02044677734375,
-0.0189361572265625,
0.0141448974609375,
0.0126190185546875,
0.019317626953125,
-0.0239715576171875,
0.01412200927734375,
0.0193023681640625,
0.01195526123046875,
0.00860595703125,
-0.01122283935546875,
0.0261077880859375,
-0.02093505859375,
-0.00957489013671875,
-0.004001617431640625,
-0.029083251953125,
0.0269927978515625,
-0.0035400390625,
0.0004413127899169922,
0.023956298828125,
-0.0005822181701660156,
-0.0158843994140625,
-0.012786865234375,
-0.046417236328125,
0.0159759521484375,
0.0190887451171875,
0.0128631591796875,
-0.0034084320068359375,
-0.0097808837890625,
-0.003978729248046875,
0.03021240234375,
-0.031951904296875,
-0.038970947265625,
-0.0233306884765625,
0.01324462890625,
-0.033782958984375,
-0.0355224609375,
-0.004947662353515625,
0.01126861572265625,
0.00527191162109375,
-0.00554656982421875,
0.0163726806640625,
-0.0152587890625,
-0.0269622802734375,
0.01047515869140625,
-0.0136260986328125,
-0.017303466796875,
-0.015838623046875,
-0.008331298828125,
0.0080108642578125,
-0.001934051513671875,
0.02972412109375,
-0.02923583984375,
0.00855255126953125,
0.00015532970428466797,
0.0022830963134765625,
0.0236053466796875,
-0.01163482666015625,
-0.0014324188232421875,
-0.01092529296875,
0.02996826171875,
0.003993988037109375,
0.00959014892578125,
0.0132598876953125,
0.01337432861328125,
0.0121917724609375,
-0.0007772445678710938,
-0.0152587890625,
0.0186004638671875,
0.0004892349243164062,
0.0224761962890625,
0.03472900390625,
0.049041748046875,
-0.005222320556640625,
0.005893707275390625,
0.0189666748046875,
-0.0154571533203125,
0.024139404296875,
-0.028045654296875,
0.0077056884765625,
-0.0157623291015625,
0.0035915374755859375,
-0.0009241104125976562,
0.045501708984375,
0.00402069091796875,
0.003383636474609375,
0.0161590576171875,
-0.01357269287109375,
0.03778076171875,
-0.045257568359375,
-0.016021728515625,
0.01473236083984375,
-0.01019287109375,
0.013397216796875,
0.00832366943359375,
0.0201263427734375,
-0.019561767578125,
0.0145263671875,
0.002780914306640625,
0.0122222900390625,
0.0246429443359375,
0.0097198486328125,
-0.00951385498046875,
-0.027099609375,
-0.01617431640625,
0.0036258697509765625,
0.0125579833984375,
-0.030609130859375,
0.00926971435546875,
0.0086822509765625,
-0.004520416259765625,
0.0255126953125,
-0.0176239013671875,
0.00940704345703125,
0.0015687942504882812,
0.04913330078125,
-0.018646240234375,
0.04241943359375,
0.00981903076171875,
0.000461578369140625,
0.0228729248046875,
-0.0227203369140625,
-0.00952911376953125,
0.0266876220703125,
-0.030609130859375,
0.0113067626953125,
0.01346588134765625,
-0.047119140625,
0.0010528564453125,
-0.038177490234375,
-0.003757476806640625,
0.0180511474609375,
0.02685546875,
-0.017547607421875,
0.012603759765625,
0.030059814453125,
-0.01123809814453125,
0.02362060546875,
-0.00272369384765625,
0.00400543212890625,
-0.00010830163955688477,
-0.0167236328125,
-0.01084136962890625,
0.0258636474609375,
-0.0014934539794921875,
0.015594482421875,
0.00548553466796875,
-0.0455322265625,
0.0031604766845703125,
-0.006317138671875,
0.04083251953125,
0.005645751953125,
-0.03253173828125,
0.0250701904296875,
-0.0007519721984863281,
-0.0140838623046875,
-0.0075225830078125,
0.0157623291015625,
-0.006381988525390625,
-0.016693115234375,
0.00824737548828125,
-0.0015268325805664062,
-0.019500732421875,
0.0306396484375,
0.0110015869140625,
0.006237030029296875,
-0.0005340576171875,
-0.0154266357421875,
0.0009341239929199219,
-0.0230865478515625,
-0.0201873779296875,
0.0004298686981201172,
-0.026397705078125,
0.003082275390625,
-0.021575927734375,
0.0046234130859375,
-0.033538818359375,
0.01806640625,
-0.01515960693359375,
0.007442474365234375,
-0.01068115234375,
0.01439666748046875,
0.004726409912109375,
-0.01953125,
-0.00449371337890625,
0.007015228271484375,
-0.0091705322265625,
-0.0169525146484375,
0.0225677490234375,
0.0261993408203125,
-0.04302978515625,
-0.0124359130859375,
0.046356201171875,
-0.0203399658203125,
0.0295257568359375,
-0.0330810546875,
0.01220703125,
0.0301971435546875,
-0.005458831787109375,
-0.01360321044921875,
0.021942138671875,
0.0101165771484375,
0.0199127197265625,
0.00019288063049316406,
0.031982421875,
0.0268096923828125,
0.02301025390625,
0.01239013671875,
-0.032196044921875,
0.035858154296875,
0.01467132568359375,
0.019866943359375,
-0.006435394287109375,
0.01003265380859375,
-0.01395416259765625,
0.00176239013671875,
0.010589599609375,
0.004703521728515625,
0.0195159912109375,
0.00019216537475585938,
-0.01146697998046875,
-0.005474090576171875,
-0.02972412109375,
-0.048065185546875,
-0.0082855224609375,
-0.018463134765625,
0.0167388916015625,
-0.01727294921875,
0.030609130859375,
0.01229095458984375,
-0.0135650634765625,
0.0028972625732421875,
0.02789306640625,
-0.0004363059997558594,
-0.018798828125,
-0.01540374755859375,
-0.0243072509765625,
0.0282745361328125,
0.027008056640625,
-0.00036215782165527344,
-0.006195068359375,
-0.040374755859375,
-0.007587432861328125,
0.03460693359375,
0.03131103515625,
-0.007610321044921875,
-0.02850341796875,
-0.0318603515625,
0.04107666015625,
-0.0070037841796875,
0.00010675191879272461,
-0.0146484375,
-0.010986328125,
-0.032196044921875,
-0.0017633438110351562,
0.00444793701171875,
0.0142364501953125,
-0.0255279541015625,
-0.01123809814453125,
0.00582122802734375,
0.010711669921875,
-0.0173797607421875,
0.01403045654296875,
0.034027099609375,
0.033966064453125,
0.020172119140625,
0.0003387928009033203,
0.02313232421875,
-0.00015485286712646484,
-0.01551055908203125,
0.00951385498046875,
-0.031646728515625,
0.004001617431640625,
-0.00849151611328125,
-0.01018524169921875,
-0.0142364501953125,
-0.0218963623046875,
0.02130126953125,
0.014007568359375,
0.008880615234375,
0.040679931640625,
0.006275177001953125,
0.026397705078125,
0.056060791015625,
-0.0166473388671875,
0.0199737548828125,
0.0107269287109375,
0.03497314453125,
-0.0099639892578125,
-0.0031833648681640625,
-0.00821685791015625,
0.0025787353515625,
-0.01055908203125,
0.019805908203125,
-0.0193023681640625,
-0.033477783203125,
-0.001728057861328125,
-0.01432037353515625,
0.0204315185546875,
-0.00588226318359375,
0.034149169921875,
0.01456451416015625,
0.0014562606811523438,
0.00708770751953125,
-0.01312255859375,
0.004970550537109375,
0.0017538070678710938,
0.032318115234375,
-0.0208740234375,
0.0152740478515625,
0.00601959228515625,
0.020355224609375,
0.016693115234375,
-0.00708770751953125,
0.0131072998046875,
0.005756378173828125,
-0.0013380050659179688,
-0.0242462158203125,
0.031707763671875,
-0.00254058837890625,
-0.0121002197265625,
-0.0284271240234375,
0.01537322998046875,
-0.0014600753784179688,
0.00518798828125,
-0.0278167724609375,
0.0362548828125,
0.0040283203125,
-0.019012451171875,
0.0178070068359375,
0.0059661865234375,
0.0102996826171875,
0.004444122314453125,
-0.026397705078125,
-0.0311431884765625,
-0.01556396484375,
-0.00030112266540527344,
0.00017893314361572266,
0.041839599609375,
-0.01425933837890625,
-0.01110076904296875,
0.0194549560546875,
-0.00788116455078125,
-0.01348876953125,
0.0217742919921875,
0.0186920166015625,
0.0369873046875,
0.002391815185546875,
0.0023441314697265625,
-0.027191162109375,
0.01465606689453125,
0.010467529296875,
0.01296234130859375,
-0.01226043701171875,
-0.03289794921875,
-0.00568389892578125,
-0.00804901123046875,
0.0204925537109375,
-0.045318603515625,
-0.01026153564453125,
0.00717926025390625,
-0.0183258056640625,
-0.033905029296875,
-0.007755279541015625,
0.0248260498046875,
-0.0225677490234375,
-0.01276397705078125,
0.0003941059112548828,
0.0260009765625,
-0.022186279296875,
0.0186004638671875,
0.0033111572265625,
-0.01995849609375,
0.027984619140625,
-0.02435302734375,
-0.0057830810546875,
-0.0020847320556640625,
-0.005992889404296875,
-0.0084075927734375,
0.0267181396484375,
-0.00042939186096191406,
-0.0183868408203125,
0.00450897216796875,
-0.006786346435546875,
-0.01132965087890625,
0.0170745849609375,
-0.0146484375,
0.0280303955078125,
0.0265350341796875,
0.0033245086669921875,
-0.00904083251953125,
0.0140380859375,
0.0212249755859375,
0.005535125732421875,
-0.0159759521484375,
0.01024627685546875,
-0.00463104248046875,
0.036895751953125,
-0.0305023193359375,
0.0175018310546875,
-0.0014095306396484375,
0.001220703125,
-0.0259552001953125,
-0.0289154052734375,
0.00652313232421875,
0.003520965576171875,
-0.0269622802734375,
-0.0032291412353515625,
0.01050567626953125,
-0.0287017822265625,
0.02362060546875,
0.01629638671875,
0.012176513671875,
-0.005054473876953125,
-0.00445556640625,
0.03558349609375,
-0.00015604496002197266,
-0.04302978515625,
0.00897216796875,
0.0201263427734375,
-0.016571044921875,
-0.00966644287109375,
-0.01377105712890625,
0.0182952880859375,
0.00260162353515625,
0.01230621337890625,
0.0260162353515625,
0.00250244140625,
-0.01206207275390625,
0.003566741943359375,
-0.013153076171875,
0.04278564453125,
0.0162353515625,
-0.0303955078125,
-0.0003151893615722656,
0.013275146484375,
-0.0032176971435546875,
-0.005584716796875,
0.0110015869140625,
0.0018644332885742188,
0.0185546875,
0.01122283935546875,
0.0283050537109375,
-0.0294647216796875,
0.0013875961303710938,
0.00911712646484375,
-0.0224761962890625,
0.0134429931640625,
-0.031585693359375,
0.007770538330078125,
0.00923919677734375,
-0.02545166015625,
-0.006259918212890625,
0.0011682510375976562,
0.01384735107421875,
0.0203399658203125,
0.0233154296875,
0.035980224609375,
0.017120361328125,
0.005718231201171875,
-0.00905609130859375,
0.048095703125,
0.03363037109375,
0.0028972625732421875,
0.024749755859375,
0.04119873046875,
-0.00818634033203125,
-0.0020313262939453125,
0.007404327392578125,
-0.003284454345703125,
0.024688720703125,
-0.039581298828125,
-0.00377655029296875,
-0.0187530517578125,
0.0008401870727539062,
0.0235748291015625,
0.0027103424072265625,
-0.0014944076538085938,
-0.047943115234375,
-0.0151519775390625,
-0.0178985595703125,
0.01432037353515625,
-0.04852294921875,
0.017791748046875,
-0.00586700439453125,
0.0014543533325195312,
0.016693115234375,
-0.0268096923828125,
-0.020233154296875,
0.0189666748046875,
-0.037353515625,
0.00839996337890625,
0.00959014892578125,
-0.004901885986328125,
-0.01983642578125,
0.0167083740234375,
0.01439666748046875,
0.0192413330078125,
-0.02947998046875,
0.009857177734375,
-0.019561767578125,
-0.033355712890625,
0.0018939971923828125,
-0.0036029815673828125,
-0.007587432861328125,
0.0246124267578125,
0.0256500244140625,
-0.0014829635620117188,
0.0005297660827636719,
0.0007781982421875,
0.0080413818359375,
-0.0080413818359375,
-0.0074005126953125,
0.0034122467041015625,
0.016082763671875,
-0.0220947265625,
-0.01441192626953125,
0.0078125,
-0.0025081634521484375,
-0.0013370513916015625,
0.004100799560546875,
0.032257080078125,
-0.0089111328125,
-0.031585693359375,
0.0011844635009765625,
-0.036712646484375,
0.00252532958984375,
0.04248046875,
-0.01483154296875,
0.012237548828125,
0.0252838134765625,
-0.01003265380859375,
0.022674560546875,
0.0252838134765625,
0.038482666015625,
-0.0302734375,
-0.026031494140625,
0.0177154541015625,
0.017181396484375,
0.05316162109375,
0.005657196044921875,
-0.0020923614501953125,
-0.0299224853515625,
0.0099029541015625,
0.004817962646484375,
-0.0117034912109375,
0.0172576904296875,
-0.026336669921875,
0.00934600830078125,
0.028411865234375,
-0.04827880859375,
-0.010955810546875,
-0.0269317626953125,
0.02215576171875,
0.010009765625,
-0.0221405029296875,
-0.0218048095703125,
0.035369873046875,
0.0240478515625,
-0.0176544189453125,
0.03704833984375,
0.021270751953125,
0.00962066650390625,
0.0037097930908203125,
-0.026123046875,
-0.0106201171875,
-0.0044097900390625,
-0.01245880126953125,
0.006328582763671875,
-0.0218353271484375,
0.01273345947265625,
-0.005931854248046875,
-0.0029468536376953125,
0.02545166015625,
0.0110015869140625,
0.0147705078125,
0.00795745849609375,
-0.0102386474609375,
0.002010345458984375,
-0.01119232177734375,
0.0225830078125,
0.005390167236328125,
0.00428009033203125,
0.01351165771484375,
-0.006099700927734375,
-0.0091552734375,
0.003582000732421875,
0.0227508544921875,
0.003185272216796875,
0.0146636962890625,
-0.0301666259765625,
-0.018707275390625,
0.033599853515625,
0.03192138671875,
-0.005344390869140625,
-0.01177215576171875,
-0.0225677490234375,
-0.01444244384765625,
-0.0165252685546875,
0.0239105224609375,
-0.00650787353515625,
-0.0272369384765625,
0.01047515869140625,
-0.004055023193359375,
0.0189971923828125,
-0.0219268798828125,
0.002288818359375,
-0.04376220703125,
0.00821685791015625,
-0.004138946533203125,
-0.007221221923828125,
0.00914764404296875,
-0.00914764404296875,
0.014373779296875,
0.00241851806640625,
0.0235443115234375,
0.0291900634765625,
-0.00612640380859375,
-0.01067352294921875,
-0.013763427734375,
0.01025390625,
0.003452301025390625,
-0.01114654541015625,
-0.0082550048828125,
-0.0208587646484375,
-0.0021152496337890625,
-0.004489898681640625,
0.004077911376953125,
0.0214691162109375,
-0.005290985107421875,
0.01593017578125,
-0.02398681640625,
-0.018951416015625,
-0.003223419189453125,
-0.00565338134765625,
0.01177978515625,
0.0030193328857421875,
-0.0295257568359375,
-0.007755279541015625,
0.002956390380859375,
-0.0227203369140625,
0.011627197265625,
-0.0118865966796875,
0.0273284912109375,
-0.01532745361328125,
-0.0014181137084960938,
-0.0173187255859375,
0.001556396484375,
0.01129150390625,
0.02740478515625,
0.028411865234375,
0.00022912025451660156,
0.035552978515625,
-0.0261688232421875,
0.0107879638671875,
-0.00885772705078125,
0.0180511474609375,
-0.007457733154296875,
-0.0144805908203125,
-0.0338134765625,
-0.004146575927734375,
0.01401519775390625,
-0.03302001953125,
-0.006931304931640625,
0.01494598388671875,
-0.00302886962890625,
-0.01580810546875,
-0.01544952392578125,
-0.0098876953125,
-0.0019989013671875,
0.0034008026123046875,
-0.0117340087890625,
-0.0419921875,
-0.0098114013671875,
0.042572021484375,
-0.005100250244140625,
0.01103973388671875,
-0.0309600830078125,
0.02099609375,
0.0026607513427734375,
0.006572723388671875,
-0.03662109375,
-0.005687713623046875,
-0.03411865234375,
-0.00238037109375,
0.0216827392578125,
-0.00452423095703125,
0.03790283203125,
0.0121612548828125,
-0.003665924072265625,
0.018829345703125,
-0.0017070770263671875,
-0.0199127197265625,
-0.000032901763916015625,
0.0024127960205078125,
-0.00750732421875,
-0.01617431640625,
-0.00023889541625976562,
-0.00412750244140625,
0.0072479248046875,
0.03729248046875,
-0.00962066650390625,
0.0177154541015625,
0.0010232925415039062,
0.0249176025390625,
-0.03472900390625,
0.02557373046875,
-0.0269622802734375,
0.0019054412841796875,
0.033538818359375,
-0.0202484130859375,
-0.0273590087890625,
-0.01091766357421875,
0.00765228271484375,
0.0181732177734375,
-0.01236724853515625,
-0.0140228271484375,
-0.036712646484375,
0.0178680419921875,
0.02777099609375,
0.005535125732421875,
0.00472259521484375,
-0.008697509765625,
0.003780364990234375,
-0.0171356201171875,
0.020355224609375,
0.027557373046875,
-0.00963592529296875,
-0.01477813720703125,
-0.0105438232421875,
0.01398468017578125,
0.02862548828125,
0.032928466796875,
-0.007709503173828125,
0.004039764404296875,
0.0189208984375,
-0.0001405477523803711,
0.010650634765625,
0.018707275390625,
0.019989013671875,
-0.0243988037109375,
0.01177215576171875,
-0.01165008544921875,
0.00331878662109375,
-0.01141357421875,
-0.01125335693359375,
0.01117706298828125,
0.01186370849609375,
0.0142364501953125,
-0.014495849609375,
-0.005664825439453125,
-0.0099639892578125,
-0.00894927978515625,
0.0283355712890625,
0.0027484893798828125,
-0.02178955078125,
-0.003116607666015625,
-0.03009033203125,
-0.02337646484375,
0.01161956787109375,
-0.0173492431640625,
0.023101806640625,
-0.0023288726806640625,
-0.0157012939453125,
0.0243988037109375,
0.0009107589721679688,
0.0012369155883789062,
-0.004520416259765625,
-0.0158538818359375,
-0.0133056640625,
0.004039764404296875,
-0.021148681640625,
-0.001308441162109375,
-0.0160980224609375,
0.00916290283203125,
-0.035369873046875,
0.035980224609375,
-0.033416748046875,
-0.0013027191162109375,
-0.0182647705078125,
-0.00838470458984375,
-0.0283203125,
0.005558013916015625,
-0.025665283203125,
0.0036334991455078125,
-0.004886627197265625,
-0.045257568359375,
-0.0008683204650878906,
0.005153656005859375,
-0.002147674560546875,
-0.00531768798828125,
-0.034515380859375,
-0.0004343986511230469,
-0.0261383056640625,
0.0097198486328125,
-0.007717132568359375,
0.006137847900390625,
0.0108642578125,
-0.024688720703125,
0.0217437744140625,
0.0001913309097290039,
-0.0033092498779296875,
0.0292510986328125,
-0.01050567626953125,
0.0010614395141601562,
0.000919342041015625,
-0.02618408203125,
-0.0169830322265625,
-0.00894927978515625,
-0.0006055831909179688,
-0.006439208984375,
-0.0250396728515625,
-0.01371002197265625,
0.0014781951904296875,
-0.023223876953125,
0.01483154296875,
-0.03802490234375,
-0.0016412734985351562,
0.0036983489990234375,
0.007686614990234375,
0.0260467529296875,
0.0254364013671875,
-0.03070068359375,
-0.0343017578125,
0.00322723388671875,
0.008026123046875,
0.002017974853515625,
-0.00968170166015625,
0.016937255859375,
-0.00632476806640625,
0.003993988037109375,
-0.01123046875,
0.03692626953125,
0.0204620361328125,
0.01436614990234375,
-0.00676727294921875,
-0.0075836181640625,
0.0211181640625,
0.0303497314453125,
-0.0006856918334960938,
-0.0170745849609375,
0.021392822265625,
-0.0027523040771484375,
-0.0251312255859375,
-0.03167724609375,
0.0250701904296875,
0.03271484375,
0.0010890960693359375,
-0.01331329345703125,
-0.01556396484375,
-0.0231475830078125,
-0.0206451416015625,
-0.025909423828125,
-0.046051025390625,
-0.00899505615234375,
-0.01324462890625,
0.0190277099609375,
-0.0256500244140625,
-0.0258941650390625,
-0.01555633544921875,
-0.0228271484375,
-0.0016870498657226562,
0.002925872802734375,
-0.015167236328125,
0.00785064697265625,
-0.00994110107421875,
-0.0304107666015625,
-0.0142822265625,
-0.045166015625,
-0.014801025390625,
-0.00896453857421875,
0.046173095703125,
-0.0029754638671875,
0.0093536376953125,
0.01195526123046875,
-0.0012292861938476562,
0.033538818359375,
0.028106689453125,
-0.01212310791015625,
0.01331329345703125,
-0.032745361328125,
-0.00986480712890625,
0.004596710205078125,
-0.015106201171875,
0.01898193359375,
-0.0008873939514160156,
0.03265380859375,
0.02490234375,
0.01148223876953125,
0.0137786865234375,
0.03375244140625,
0.021392822265625,
0.0086212158203125,
-0.0000871419906616211,
-0.027587890625,
-0.01275634765625,
-0.006046295166015625,
0.011322021484375,
0.0011882781982421875,
-0.01197052001953125,
0.002582550048828125,
-0.0234222412109375,
0.0167694091796875,
0.0280609130859375,
0.0004112720489501953,
0.00838470458984375,
0.029205322265625,
-0.022430419921875,
-0.00962066650390625,
0.005176544189453125,
-0.038970947265625,
0.0007719993591308594,
-0.0029735565185546875,
-0.0275115966796875,
-0.004669189453125,
-0.004283905029296875,
-0.0210723876953125,
0.01580810546875,
-0.01395416259765625,
0.034027099609375,
-0.0038967132568359375,
0.0036487579345703125,
0.0014524459838867188,
0.016571044921875,
0.003711700439453125,
-0.0026340484619140625,
0.060211181640625,
0.00888824462890625,
-0.002811431884765625,
-0.0170440673828125,
-0.0286865234375,
-0.0168609619140625,
-0.0188140869140625,
-0.00824737548828125,
-0.0275421142578125,
-0.02392578125,
0.01654052734375,
0.022918701171875,
-0.01456451416015625,
0.00991058349609375,
0.006389617919921875,
-0.004364013671875,
-0.00656890869140625,
0.002399444580078125,
0.0306396484375,
0.00672149658203125,
-0.01328277587890625,
-0.007175445556640625,
-0.008392333984375,
-0.0019025802612304688,
0.035186767578125,
-0.01448822021484375,
0.019744873046875,
0.0001481771469116211,
-0.019287109375,
-0.01519012451171875,
-0.0167999267578125,
0.0168609619140625,
0.0260162353515625,
0.0298309326171875,
0.001323699951171875,
-0.0200042724609375,
0.01953125,
0.01323699951171875,
-0.0159149169921875,
-0.017913818359375,
-0.016143798828125,
-0.0199432373046875,
-0.0062408447265625,
0.03570556640625,
-0.00945281982421875,
-0.017303466796875,
0.01236724853515625,
0.02752685546875,
-0.0101318359375,
0.00922393798828125,
-0.00621795654296875,
0.00312042236328125,
-0.021270751953125,
-0.0204315185546875,
0.01474761962890625,
0.006328582763671875,
-0.01328277587890625,
-0.007755279541015625,
0.01751708984375,
-0.02154541015625,
0.01081085205078125,
0.00836181640625,
0.002166748046875,
0.0012340545654296875,
0.0236358642578125,
-0.0114898681640625,
0.034698486328125,
-0.0182037353515625,
0.017364501953125,
0.0153961181640625,
-0.03350830078125,
-0.0097808837890625,
0.03369140625,
-0.014404296875,
0.0379638671875,
0.0193939208984375,
0.00183868408203125,
-0.03570556640625,
0.002899169921875,
-0.0008425712585449219,
-0.0287933349609375,
0.0133056640625,
-0.03240966796875,
-0.022857666015625,
-0.0181427001953125,
-0.0101318359375,
0.00836944580078125,
0.0005774497985839844,
0.0163116455078125,
-0.0030269622802734375,
0.0077362060546875,
-0.0168609619140625,
0.023345947265625,
-0.01177978515625,
0.0093994140625,
0.03717041015625,
0.01425933837890625,
0.0031719207763671875,
-0.035369873046875,
0.0097198486328125,
0.00971221923828125,
0.01702880859375,
0.0167388916015625,
-0.0018129348754882812,
-0.0245819091796875,
0.016357421875,
0.0146636962890625,
0.0240478515625,
0.00691986083984375,
-0.0011138916015625,
0.045440673828125,
0.00644683837890625,
-0.00731658935546875,
0.049713134765625,
0.044830322265625,
-0.0040283203125,
-0.02874755859375,
-0.033355712890625,
-0.0011758804321289062,
-0.0023136138916015625,
-0.00432586669921875,
0.024871826171875,
0.0033893585205078125,
-0.0225677490234375,
-0.006519317626953125,
-0.0052337646484375,
-0.005382537841796875,
-0.0007600784301757812,
-0.00839996337890625,
0.0061187744140625,
-0.028594970703125,
-0.00930023193359375,
-0.0166168212890625,
-0.007305145263671875,
-0.00615692138671875,
0.002140045166015625,
0.0191650390625,
-0.00853729248046875,
-0.0278472900390625,
0.0091552734375,
0.04217529296875,
0.00254058837890625,
-0.01116180419921875,
-0.03936767578125,
0.03106689453125,
0.01039886474609375,
-0.026885986328125,
0.0007138252258300781,
-0.020782470703125,
0.01227569580078125,
0.038604736328125,
0.0029964447021484375,
0.00011175870895385742,
0.031402587890625,
-0.0262603759765625,
-0.009063720703125,
-0.05267333984375,
-0.00984954833984375,
0.01959228515625,
0.0003750324249267578,
-0.0290679931640625,
0.0263519287109375,
0.01284027099609375,
-0.0067291259765625,
-0.01258087158203125,
-0.0248870849609375,
0.0014123916625976562,
-0.0075225830078125,
-0.01629638671875,
0.0214996337890625,
-0.01617431640625,
0.035125732421875,
-0.026153564453125,
0.00823974609375,
-0.01349639892578125,
0.0246734619140625,
-0.018463134765625,
0.034423828125,
-0.003932952880859375,
0.0152130126953125,
0.005443572998046875,
0.0130157470703125,
-0.0223236083984375,
0.016632080078125,
0.0143890380859375,
-0.0021991729736328125,
0.01006317138671875,
0.001445770263671875,
0.00881195068359375,
-0.0014362335205078125,
0.0021572113037109375,
-0.0233612060546875,
0.00838470458984375,
0.011932373046875,
-0.00022554397583007812,
-0.0199432373046875,
-0.0011434555053710938,
0.01548004150390625,
-0.004474639892578125,
-0.00934600830078125,
-0.0091552734375,
-0.00616455078125,
0.0259552001953125,
-0.0216522216796875,
-0.01317596435546875,
-0.037506103515625,
0.0193634033203125,
-0.003543853759765625,
0.017486572265625,
0.01485443115234375,
-0.009735107421875,
0.004962921142578125,
0.004970550537109375,
0.029998779296875,
0.033905029296875,
0.01409912109375,
0.021270751953125,
0.021087646484375,
-0.0030498504638671875,
0.0011472702026367188,
0.00975799560546875,
-0.0263671875,
0.004764556884765625,
-0.02923583984375,
-0.004459381103515625,
-0.0289306640625,
-0.0137481689453125,
0.0191802978515625,
-0.0045928955078125,
-0.037841796875,
0.004241943359375,
-0.0193939208984375,
-0.048858642578125,
-0.00624847412109375,
0.00276947021484375,
0.0135650634765625,
0.011810302734375,
0.004619598388671875,
0.004383087158203125,
-0.0193939208984375,
-0.01177215576171875,
0.0109405517578125,
-0.036285400390625,
-0.0008907318115234375,
0.0253143310546875,
0.027862548828125,
0.014190673828125,
-0.01465606689453125,
-0.0187225341796875,
-0.00836181640625,
-0.01407623291015625,
0.0204925537109375,
-0.0272979736328125,
-0.024993896484375,
-0.005138397216796875,
0.0213623046875,
-0.0006375312805175781,
0.0254974365234375,
-0.03594970703125,
-0.0157318115234375,
0.0236358642578125,
-0.0209197998046875,
0.01226043701171875,
-0.015625,
-0.026641845703125,
0.0155792236328125,
0.012237548828125,
-0.003360748291015625,
-0.02667236328125,
-0.005641937255859375,
0.0220947265625,
-0.00373077392578125,
-0.0151824951171875,
-0.00981903076171875,
-0.00316619873046875,
-0.0234527587890625,
-0.01125335693359375,
0.0015306472778320312,
0.02130126953125,
0.01336669921875,
-0.0059814453125,
0.036834716796875,
-0.021728515625,
-0.0113372802734375,
-0.035491943359375,
-0.017730712890625,
0.005298614501953125,
0.0226898193359375,
0.034423828125,
0.036407470703125,
-0.0101470947265625,
-0.006351470947265625,
-0.0180206298828125,
0.01215362548828125,
0.022216796875,
-0.04730224609375,
0.009979248046875,
0.0216217041015625,
0.019073486328125,
0.0038604736328125,
-0.0273590087890625,
0.01348114013671875,
0.0183563232421875,
0.00457763671875,
-0.027191162109375,
-0.045867919921875,
0.0015077590942382812,
0.004322052001953125,
-0.0009598731994628906,
0.016448974609375,
-0.006427764892578125,
-0.00955963134765625,
0.00911712646484375,
-0.007305145263671875,
-0.0007882118225097656,
0.00513458251953125,
0.0226898193359375,
0.0191497802734375,
0.018280029296875,
-0.0176849365234375,
0.0186920166015625,
-0.004364013671875,
-0.037017822265625,
0.0223388671875,
0.0036754608154296875,
0.017669677734375,
0.0207061767578125,
-0.004482269287109375,
0.018646240234375,
0.003582000732421875,
-0.0631103515625,
0.0307159423828125,
-0.02325439453125,
-0.006500244140625,
0.0238494873046875,
-0.0103759765625,
-0.00498199462890625,
-0.032012939453125,
0.0254364013671875,
-0.012969970703125,
-0.0010175704956054688,
0.00830841064453125,
0.02117919921875,
0.0020084381103515625,
-0.018829345703125,
0.029815673828125,
-0.019012451171875,
-0.01367950439453125,
-0.0148468017578125,
0.007709503173828125,
0.033203125,
-0.02789306640625,
0.0037670135498046875,
-0.0202178955078125,
0.01413726806640625,
0.0239105224609375,
-0.0296783447265625,
-0.001800537109375,
0.0197601318359375,
-0.013031005859375,
0.017669677734375,
0.00467681884765625,
0.00995635986328125,
0.0411376953125,
-0.034454345703125,
0.0164947509765625,
-0.0011653900146484375,
-0.0024814605712890625,
-0.030303955078125,
0.004787445068359375,
-0.0175323486328125,
0.001308441162109375,
-0.0132598876953125,
0.002124786376953125,
0.026763916015625,
0.006656646728515625,
-0.0164947509765625,
-0.003536224365234375,
0.0226287841796875,
0.042999267578125,
0.01331329345703125,
0.0159149169921875,
-0.00865936279296875,
-0.0128936767578125,
-0.00786590576171875,
0.0165252685546875,
-0.014434814453125,
-0.023162841796875,
0.014617919921875,
0.01363372802734375,
-0.0011749267578125,
0.008880615234375,
-0.01316070556640625,
-0.035003662109375,
-0.006992340087890625,
0.0200653076171875,
-0.0007557868957519531,
0.004222869873046875,
0.0187530517578125,
0.0287933349609375,
-0.016998291015625,
-0.01629638671875,
-0.006195068359375,
-0.003002166748046875,
-0.005939483642578125,
-0.019683837890625,
0.0139617919921875,
-0.0276641845703125,
-0.01031494140625,
-0.00295257568359375,
0.021392822265625,
0.025421142578125,
-0.00975799560546875,
-0.01381683349609375,
0.0098876953125,
-0.01358795166015625,
-0.0169830322265625,
0.01526641845703125,
0.00623321533203125,
-0.01403045654296875,
-0.034393310546875,
-0.01497650146484375,
0.009674072265625,
-0.00531005859375,
-0.0132293701171875,
-0.02783203125,
0.048187255859375,
0.00806427001953125,
-0.005527496337890625,
-0.01311492919921875,
-0.0289459228515625,
-0.0200347900390625,
-0.024017333984375,
0.045166015625,
-0.00687408447265625,
-0.03839111328125,
-0.01372528076171875,
0.0246734619140625,
-0.0369873046875,
0.032501220703125,
0.00211334228515625,
0.00318145751953125,
-0.014190673828125,
0.0179901123046875,
-0.0167388916015625,
0.00958251953125,
-0.01556396484375,
-0.00704193115234375,
-0.0057220458984375,
0.0249481201171875,
-0.00872802734375,
0.0118255615234375,
0.0312347412109375,
0.0211334228515625,
0.040374755859375,
-0.03912353515625,
0.0254669189453125,
0.038604736328125,
0.0258026123046875,
0.0129547119140625,
0.0002930164337158203,
-0.0223236083984375,
-0.00342559814453125,
0.00415802001953125,
0.00007140636444091797,
-0.0257720947265625,
0.023681640625,
-0.0005002021789550781,
0.006622314453125,
-0.0200347900390625,
0.0138702392578125,
0.0188140869140625,
0.0233154296875,
-0.003650665283203125,
-0.0194091796875,
0.002048492431640625,
0.037628173828125,
0.01068115234375
] |
ours_538
|
The answer is \(56\).
The blue faces and red faces meet at 8 edges. Each edge has 8 cubes. The 8 vertices are each counted twice, so our final answer is \(8 \cdot 8 - 8 = 56\).
\(\boxed{56}\)
|
56
|
{
"competition": "us_comps",
"dataset": "Ours",
"posts": null,
"source": "OMOSoln2.md"
}
|
An \(8 \times 8 \times 8\) cube is painted red on 3 faces and blue on 3 faces such that no corner is surrounded by three faces of the same color. The cube is then cut into 512 unit cubes. How many of these cubes contain both red and blue paint on at least one of their faces?
|
[
"/Mathematics/DiscreteMathematics/Combinatorics/Enumeration",
"/Mathematics/DiscreteMathematics/Combinatorics/GeneralCombinatorics",
"/Mathematics/DiscreteMathematics/GeneralDiscreteMathematics/DiscreteMath",
"/Mathematics/DiscreteMathematics/GeneralDiscreteMathematics/DiscreteMathematics",
"/Mathematics/DiscreteMathematics/GeneralDiscreteMathematics/FiniteMathematics",
"/Mathematics/Geometry/CombinatorialGeometry",
"/Mathematics/Geometry/Dissection/CubeDissection",
"/Mathematics/Geometry/SolidGeometry/GeneralSolidGeometry/SolidGeometry",
"/Mathematics/Geometry/SolidGeometry/Polyhedra/Cubes",
"/Mathematics/Geometry/SolidGeometry/Polyhedra/Hexahedra",
"/Mathematics/Geometry/SolidGeometry/Polyhedra/PlatonicSolids",
"/Mathematics/RecreationalMathematics/Puzzles/Puzzle"
] |
Count the unit cubes on edges where red and blue faces meet, then subtract the vertices counted twice.
|
[
0.00006389617919921875,
-0.028228759765625,
0.01132965087890625,
0.0104827880859375,
0.0001150965690612793,
0.0146331787109375,
-0.01947021484375,
-0.0333251953125,
0.00762176513671875,
-0.0042572021484375,
-0.0254364013671875,
0.01378631591796875,
-0.0014657974243164062,
-0.01296234130859375,
-0.01617431640625,
-0.04583740234375,
-0.018829345703125,
0.0016002655029296875,
-0.0166015625,
-0.0038318634033203125,
-0.01204681396484375,
0.0163726806640625,
-0.035888671875,
-0.007183074951171875,
0.042572021484375,
-0.038818359375,
-0.0183868408203125,
0.013641357421875,
0.0128021240234375,
-0.02484130859375,
-0.00881195068359375,
-0.035888671875,
0.0213470458984375,
-0.0225982666015625,
0.0007390975952148438,
-0.01508331298828125,
0.00360107421875,
0.00011968612670898438,
0.005252838134765625,
-0.0489501953125,
-0.00838470458984375,
0.00205230712890625,
0.01006317138671875,
0.00673675537109375,
0.0159759521484375,
0.00527191162109375,
0.0054931640625,
-0.00826263427734375,
-0.0283355712890625,
0.009552001953125,
0.004070281982421875,
0.01995849609375,
-0.01141357421875,
-0.0151214599609375,
0.006557464599609375,
-0.035003662109375,
-0.01398468017578125,
0.003856658935546875,
-0.013763427734375,
-0.00988006591796875,
-0.002483367919921875,
0.01224517822265625,
0.01137542724609375,
-0.026214599609375,
0.0023632049560546875,
0.004299163818359375,
0.002227783203125,
0.0202789306640625,
0.0037822723388671875,
-0.0187530517578125,
0.0220947265625,
0.017669677734375,
0.02197265625,
0.01934814453125,
0.058349609375,
-0.0100860595703125,
-0.004428863525390625,
0.0216064453125,
0.0435791015625,
0.0158233642578125,
0.0143280029296875,
-0.00609588623046875,
-0.0120086669921875,
-0.007144927978515625,
0.02886962890625,
0.02081298828125,
0.0187835693359375,
-0.00902557373046875,
-0.0107269287109375,
-0.00940704345703125,
0.0156707763671875,
0.02056884765625,
-0.00949859619140625,
0.0271759033203125,
0.01018524169921875,
-0.00646209716796875,
-0.00414276123046875,
0.0029544830322265625,
0.0101470947265625,
0.0098724365234375,
-0.017333984375,
-0.007061004638671875,
0.01548004150390625,
-0.00701141357421875,
-0.0263519287109375,
-0.00794219970703125,
-0.00897216796875,
0.007770538330078125,
0.00893402099609375,
-0.0084991455078125,
-0.0019626617431640625,
-0.0018796920776367188,
0.0129547119140625,
0.005252838134765625,
0.005832672119140625,
0.002658843994140625,
0.0094451904296875,
-0.01312255859375,
0.00920867919921875,
0.0146484375,
-0.0123291015625,
0.0164337158203125,
0.00449371337890625,
0.0007958412170410156,
0.005184173583984375,
-0.037567138671875,
0.0029621124267578125,
-0.0006527900695800781,
0.0184478759765625,
-0.00019311904907226562,
0.01435089111328125,
0.0029582977294921875,
0.0283355712890625,
0.006397247314453125,
-0.00873565673828125,
-0.005443572998046875,
0.02325439453125,
-0.0050201416015625,
-0.01023101806640625,
-0.00823211669921875,
0.017364501953125,
0.0010976791381835938,
-0.0016260147094726562,
0.0127410888671875,
0.0157012939453125,
0.027374267578125,
0.0259246826171875,
-0.0361328125,
0.01409912109375,
0.00725555419921875,
-0.0035724639892578125,
-0.020111083984375,
0.0136871337890625,
-0.005886077880859375,
-0.0198974609375,
-0.00029587745666503906,
-0.018280029296875,
0.037994384765625,
0.0057220458984375,
0.00946807861328125,
-0.006855010986328125,
0.001949310302734375,
0.00901031494140625,
0.0268707275390625,
-0.0045166015625,
0.005725860595703125,
0.0137176513671875,
0.005916595458984375,
-0.0059051513671875,
0.038787841796875,
-0.01084136962890625,
-0.032806396484375,
0.00372314453125,
0.0011606216430664062,
-0.01311492919921875,
-0.0156402587890625,
-0.015655517578125,
0.0147247314453125,
-0.00951385498046875,
0.01279449462890625,
0.0048675537109375,
-0.01105499267578125,
0.0297698974609375,
-0.00449371337890625,
0.003566741943359375,
-0.008544921875,
0.006435394287109375,
0.0189666748046875,
0.01108551025390625,
0.01132965087890625,
-0.03387451171875,
-0.00464630126953125,
-0.01483154296875,
0.0015859603881835938,
-0.01476287841796875,
-0.006866455078125,
-0.00484466552734375,
0.0194549560546875,
0.037353515625,
0.0014925003051757812,
0.0025634765625,
-0.036712646484375,
0.048828125,
0.01464080810546875,
0.00644683837890625,
0.00263214111328125,
0.0226287841796875,
-0.0102996826171875,
-0.004863739013671875,
-0.00571441650390625,
-0.007171630859375,
-0.0110626220703125,
-0.00601959228515625,
-0.041351318359375,
-0.0197601318359375,
-0.01041412353515625,
-0.032135009765625,
0.0038280487060546875,
0.0015821456909179688,
-0.036407470703125,
0.01483917236328125,
0.00878143310546875,
-0.00254058837890625,
0.00620269775390625,
-0.0243377685546875,
-0.0009484291076660156,
0.00695037841796875,
0.005733489990234375,
-0.0009436607360839844,
-0.0159759521484375,
0.0177154541015625,
0.00726318359375,
-0.0174102783203125,
-0.01708984375,
-0.005886077880859375,
0.002414703369140625,
-0.0462646484375,
-0.03497314453125,
-0.0237274169921875,
0.009063720703125,
0.0784912109375,
-0.00972747802734375,
0.0028591156005859375,
0.01129913330078125,
0.00495147705078125,
-0.007137298583984375,
0.00774383544921875,
0.01424407958984375,
-0.023529052734375,
-0.01016998291015625,
-0.016021728515625,
-0.002452850341796875,
0.005809783935546875,
-0.0196990966796875,
-0.01445770263671875,
-0.031341552734375,
0.0137176513671875,
0.025115966796875,
-0.00955963134765625,
-0.031646728515625,
0.0095672607421875,
0.0155181884765625,
-0.003833770751953125,
-0.0133056640625,
-0.00807952880859375,
0.00037169456481933594,
0.031982421875,
-0.01229095458984375,
0.0198211669921875,
-0.00530242919921875,
0.03802490234375,
-0.0019550323486328125,
-0.00585174560546875,
-0.005397796630859375,
0.00542449951171875,
-0.007640838623046875,
-0.0044403076171875,
0.0005941390991210938,
-0.00008112192153930664,
0.0155029296875,
0.01175689697265625,
-0.0252227783203125,
-0.0257110595703125,
0.007686614990234375,
-0.008758544921875,
-0.00418853759765625,
0.037811279296875,
-0.0198516845703125,
-0.0121917724609375,
0.00878143310546875,
-0.0021457672119140625,
0.032623291015625,
-0.012603759765625,
-0.008209228515625,
0.029754638671875,
-0.01316070556640625,
-0.0222015380859375,
-0.0089111328125,
0.001506805419921875,
-0.002765655517578125,
-0.01139068603515625,
-0.0111846923828125,
-0.0085296630859375,
0.053619384765625,
0.01812744140625,
0.0218963623046875,
-0.00377655029296875,
0.00884246826171875,
0.01561737060546875,
0.02569580078125,
0.00201416015625,
-0.0175018310546875,
-0.0220794677734375,
0.0122528076171875,
-0.0052947998046875,
-0.050323486328125,
0.013763427734375,
0.0030307769775390625,
0.01129150390625,
-0.0282440185546875,
0.013397216796875,
-0.023193359375,
-0.03070068359375,
-0.0029544830322265625,
0.01531219482421875,
-0.023193359375,
0.008514404296875,
0.001842498779296875,
-0.0093994140625,
-0.022216796875,
-0.005359649658203125,
0.04010009765625,
-0.00673675537109375,
0.01371002197265625,
-0.0222015380859375,
0.0158538818359375,
0.00846099853515625,
0.0191497802734375,
-0.005229949951171875,
-0.005809783935546875,
-0.024017333984375,
0.0268402099609375,
0.01458740234375,
-0.027130126953125,
0.0185394287109375,
0.0005054473876953125,
0.0447998046875,
0.0062255859375,
-0.0133819580078125,
-0.003650665283203125,
-0.00907135009765625,
-0.0005483627319335938,
-0.00757598876953125,
-0.005924224853515625,
-0.0029888153076171875,
-0.0252227783203125,
0.0014657974243164062,
0.0024662017822265625,
-0.007472991943359375,
0.00009959936141967773,
-0.01434326171875,
0.000415802001953125,
0.0223388671875,
0.01091766357421875,
-0.006641387939453125,
-0.01922607421875,
0.0006084442138671875,
0.0296478271484375,
-0.00890350341796875,
-0.047576904296875,
-0.0019168853759765625,
0.01099395751953125,
-0.015716552734375,
-0.003963470458984375,
0.01329803466796875,
0.0010919570922851562,
0.0130157470703125,
0.0087127685546875,
-0.014404296875,
-0.0113983154296875,
-0.0177764892578125,
-0.0028228759765625,
-0.0157318115234375,
0.04083251953125,
0.01172637939453125,
0.0011310577392578125,
0.0010890960693359375,
0.0374755859375,
-0.0211334228515625,
0.011505126953125,
0.041778564453125,
0.0170440673828125,
-0.0294952392578125,
-0.007785797119140625,
0.006755828857421875,
-0.023651123046875,
-0.0002579689025878906,
0.018402099609375,
0.032501220703125,
-0.003631591796875,
-0.034698486328125,
-0.0090179443359375,
-0.0218963623046875,
-0.01313018798828125,
-0.00839996337890625,
0.0214080810546875,
0.006786346435546875,
0.029815673828125,
0.01152801513671875,
0.022308349609375,
0.02496337890625,
-0.040618896484375,
0.0131683349609375,
0.0035724639892578125,
-0.0259552001953125,
-0.00865936279296875,
-0.0034122467041015625,
-0.0216064453125,
-0.021759033203125,
0.001522064208984375,
0.01485443115234375,
-0.028076171875,
-0.001926422119140625,
0.0001704692840576172,
0.0005178451538085938,
0.0090484619140625,
-0.041168212890625,
0.0032405853271484375,
0.011474609375,
-0.00875091552734375,
-0.00814056396484375,
-0.0049285888671875,
0.0009655952453613281,
0.021820068359375,
0.0165863037109375,
0.0210723876953125,
0.0099945068359375,
0.02813720703125,
-0.009307861328125,
-0.00574493408203125,
-0.00959014892578125,
-0.037353515625,
-0.0233917236328125,
-0.0316162109375,
0.0010700225830078125,
-0.0015811920166015625,
0.007465362548828125,
0.0269622802734375,
-0.0166473388671875,
-0.0207672119140625,
-0.0026111602783203125,
0.0058441162109375,
0.0228729248046875,
-0.0209808349609375,
-0.02032470703125,
0.01483917236328125,
-0.003330230712890625,
-0.040557861328125,
0.0207672119140625,
-0.0256805419921875,
-0.0057220458984375,
0.0550537109375,
-0.006412506103515625,
0.00933074951171875,
0.0029354095458984375,
-0.004871368408203125,
-0.021636962890625,
-0.0166015625,
0.024261474609375,
0.0240020751953125,
-0.01357269287109375,
-0.026123046875,
-0.0208892822265625,
-0.00559234619140625,
-0.0239105224609375,
0.0086822509765625,
-0.0007967948913574219,
0.0283966064453125,
-0.006023406982421875,
-0.03619384765625,
0.029083251953125,
0.0013246536254882812,
0.003070831298828125,
0.04608154296875,
0.00044918060302734375,
-0.00753021240234375,
0.02154541015625,
0.015380859375,
-0.0187530517578125,
-0.00830841064453125,
0.051513671875,
0.0621337890625,
-0.0298614501953125,
0.0014257431030273438,
-0.0173492431640625,
0.00201416015625,
0.01245880126953125,
0.00489044189453125,
0.0224151611328125,
-0.0202484130859375,
0.0022830963134765625,
-0.01096343994140625,
0.0093994140625,
-0.0048980712890625,
0.0213165283203125,
0.0181427001953125,
0.06207275390625,
-0.053680419921875,
0.0120086669921875,
-0.00981903076171875,
-0.0018482208251953125,
0.00262451171875,
0.0257568359375,
-0.0221710205078125,
0.032318115234375,
0.0212554931640625,
0.0197906494140625,
-0.04052734375,
0.01337432861328125,
0.034210205078125,
-0.0214385986328125,
-0.0060577392578125,
0.00777435302734375,
-0.0093231201171875,
0.006664276123046875,
0.0250091552734375,
0.0265960693359375,
-0.0164642333984375,
-0.0165557861328125,
0.0225677490234375,
0.00569915771484375,
0.0114898681640625,
0.0211944580078125,
-0.016571044921875,
-0.04888916015625,
-0.0256805419921875,
0.006103515625,
-0.00882720947265625,
0.007053375244140625,
0.0192413330078125,
0.003871917724609375,
-0.038299560546875,
0.037261962890625,
-0.0018358230590820312,
-0.01007080078125,
-0.0215301513671875,
0.00977325439453125,
0.00910186767578125,
-0.0068359375,
0.0171356201171875,
-0.01357269287109375,
-0.00890350341796875,
-0.040802001953125,
-0.01776123046875,
-0.006931304931640625,
0.0246124267578125,
-0.0201873779296875,
0.0025196075439453125,
0.00954437255859375,
0.007274627685546875,
-0.0022830963134765625,
-0.006641387939453125,
-0.00997161865234375,
0.048004150390625,
0.00829315185546875,
-0.016204833984375,
-0.01209259033203125,
-0.0211181640625,
-0.01253509521484375,
-0.012939453125,
-0.0016126632690429688,
-0.0238494873046875,
-0.001583099365234375,
-0.011016845703125,
0.0252227783203125,
0.0037441253662109375,
-0.045928955078125,
-0.0129241943359375,
-0.01776123046875,
-0.012939453125,
0.0152740478515625,
0.00904083251953125,
0.00875091552734375,
0.015411376953125,
0.0188446044921875,
-0.0156402587890625,
0.0106964111328125,
0.04229736328125,
0.01409912109375,
0.0072479248046875,
-0.016448974609375,
0.007266998291015625,
0.01300811767578125,
0.0082550048828125,
-0.004177093505859375,
-0.00762939453125,
-0.00450897216796875,
0.0015697479248046875,
-0.0212860107421875,
0.0208587646484375,
-0.004245758056640625,
-0.0242919921875,
-0.003086090087890625,
0.0609130859375,
0.004795074462890625,
-0.0202178955078125,
0.03131103515625,
-0.017974853515625,
0.025543212890625,
-0.01049041748046875,
0.00618743896484375,
0.01495361328125,
-0.0051727294921875,
-0.0180206298828125,
-0.0140380859375,
-0.0083465576171875,
-0.004337310791015625,
0.005039215087890625,
0.0007224082946777344,
-0.0008325576782226562,
-0.00833892822265625,
0.031951904296875,
0.0439453125,
-0.018646240234375,
0.0109710693359375,
-0.00930023193359375,
0.049072265625,
-0.01690673828125,
0.0096893310546875,
-0.0239410400390625,
0.0036907196044921875,
-0.0036754608154296875,
0.005626678466796875,
0.0205230712890625,
0.0158538818359375,
0.03826904296875,
0.0168914794921875,
0.01465606689453125,
-0.057342529296875,
-0.0017995834350585938,
-0.004161834716796875,
0.021881103515625,
0.006252288818359375,
-0.032440185546875,
-0.01611328125,
0.01245880126953125,
0.014434814453125,
0.0202789306640625,
0.0195159912109375,
0.018463134765625,
-0.0208282470703125,
0.01396942138671875,
-0.01446533203125,
-0.0174560546875,
0.0242919921875,
-0.0142059326171875,
0.03759765625,
-0.02099609375,
-0.024383544921875,
-0.0244293212890625,
0.030792236328125,
0.00508880615234375,
0.0112152099609375,
0.019500732421875,
-0.041900634765625,
-0.0120697021484375,
0.010345458984375,
-0.00531005859375,
-0.00440216064453125,
-0.0267333984375,
0.0049285888671875,
0.03173828125,
-0.03387451171875,
-0.0285797119140625,
-0.032989501953125,
-0.0156707763671875,
-0.01806640625,
0.01849365234375,
0.03912353515625,
0.0125732421875,
0.007152557373046875,
0.025665283203125,
0.0355224609375,
-0.0309600830078125,
0.016632080078125,
-0.01123809814453125,
0.00860595703125,
0.0289154052734375,
0.04974365234375,
0.0106353759765625,
0.01079559326171875,
-0.02880859375,
0.0130767822265625,
0.051849365234375,
-0.02435302734375,
-0.0218505859375,
0.016815185546875,
0.003002166748046875,
-0.013153076171875,
-0.021728515625,
0.0400390625,
-0.003330230712890625,
0.034942626953125,
0.00653839111328125,
-0.0275421142578125,
0.01629638671875,
0.005466461181640625,
-0.00936126708984375,
0.006885528564453125,
-0.00604248046875,
-0.01180267333984375,
-0.0159454345703125,
0.0089263916015625,
0.0296783447265625,
-0.005329132080078125,
-0.014495849609375,
0.0014944076538085938,
-0.0092315673828125,
0.015899658203125,
-0.00731658935546875,
0.0161285400390625,
0.04681396484375,
-0.01448822021484375,
0.0086517333984375,
0.002056121826171875,
0.003787994384765625,
-0.0175323486328125,
-0.01119232177734375,
-0.0196533203125,
-0.0106201171875,
-0.0013322830200195312,
-0.004993438720703125,
0.01222991943359375,
0.01462554931640625,
-0.04315185546875,
-0.033660888671875,
-0.0185699462890625,
-0.03253173828125,
-0.049652099609375,
-0.01556396484375,
0.02813720703125,
0.0253448486328125,
0.03424072265625,
0.0138092041015625,
-0.0200347900390625,
0.0179595947265625,
-0.026336669921875,
-0.019775390625,
-0.006320953369140625,
-0.0230865478515625,
0.033447265625,
-0.0013885498046875,
0.0222930908203125,
-0.019866943359375,
-0.00008124113082885742,
0.0196075439453125,
0.044921875,
0.016265869140625,
0.004749298095703125,
0.0189056396484375,
-0.0295867919921875,
-0.00841522216796875,
-0.01236724853515625,
-0.03704833984375,
-0.0111846923828125,
-0.019439697265625,
0.039154052734375,
-0.0007061958312988281,
-0.0116119384765625,
0.0174102783203125,
-0.0236358642578125,
-0.003147125244140625,
0.00952911376953125,
0.01393890380859375,
0.032623291015625,
-0.05096435546875,
-0.04705810546875,
-0.0006842613220214844,
0.00733184814453125,
-0.043304443359375,
-0.0175323486328125,
-0.006511688232421875,
-0.025421142578125,
-0.0173797607421875,
-0.01508331298828125,
-0.004913330078125,
-0.01346588134765625,
0.0031261444091796875,
-0.0069122314453125,
-0.01012420654296875,
0.027801513671875,
0.017578125,
0.01238250732421875,
0.002346038818359375,
0.0106964111328125,
0.01392364501953125,
0.0163726806640625,
-0.033721923828125,
0.0035305023193359375,
-0.0274505615234375,
-0.006275177001953125,
-0.0037441253662109375,
-0.00923919677734375,
0.040283203125,
0.01007843017578125,
0.016998291015625,
0.0140380859375,
0.01273345947265625,
-0.0017070770263671875,
0.032135009765625,
0.022552490234375,
-0.01490020751953125,
-0.010528564453125,
-0.008453369140625,
-0.005878448486328125,
0.01482391357421875,
-0.00592041015625,
-0.034271240234375,
0.0237884521484375,
0.047637939453125,
-0.0184173583984375,
0.05120849609375,
-0.0026302337646484375,
-0.0172271728515625,
-0.0032176971435546875,
-0.014129638671875,
0.025970458984375,
0.006175994873046875,
-0.0073699951171875,
0.011505126953125,
0.02581787109375,
0.01003265380859375,
-0.0249176025390625,
-0.0012922286987304688,
-0.0182647705078125,
0.011016845703125,
0.01425933837890625,
-0.039215087890625,
-0.0233154296875,
-0.04022216796875,
-0.031707763671875,
0.0011816024780273438,
-0.01055145263671875,
0.009002685546875,
0.02532958984375,
-0.00870513916015625,
-0.0223388671875,
-0.0017690658569335938,
0.01027679443359375,
0.0065460205078125,
0.0086669921875,
0.0022220611572265625,
-0.0229949951171875,
-0.0195159912109375,
0.02996826171875,
-0.001934051513671875,
-0.00522613525390625,
-0.009307861328125,
0.0228271484375,
0.007293701171875,
-0.00855255126953125,
-0.00971221923828125,
0.032196044921875,
-0.0104217529296875,
0.00710296630859375,
-0.00799560546875,
-0.0014219284057617188,
0.00014710426330566406,
0.0167388916015625,
-0.003505706787109375,
0.03240966796875,
0.0163726806640625,
0.01319122314453125,
-0.0008502006530761719,
0.044525146484375,
0.015777587890625,
-0.02142333984375,
0.0019683837890625,
-0.00179290771484375,
0.006053924560546875,
0.0145721435546875,
-0.035919189453125,
-0.029205322265625,
0.00614166259765625,
-0.0277099609375,
0.0003254413604736328,
-0.0238037109375,
-0.021240234375,
-0.018218994140625,
-0.0389404296875,
-0.0231170654296875,
0.017303466796875,
0.0085296630859375,
-0.007495880126953125,
0.00522613525390625,
-0.016571044921875,
0.0158538818359375,
-0.0200347900390625,
-0.007274627685546875,
-0.041656494140625,
-0.0260009765625,
0.01485443115234375,
0.02008056640625,
-0.00975799560546875,
-0.0034999847412109375,
-0.0020389556884765625,
-0.0208892822265625,
-0.01409149169921875,
0.03192138671875,
0.005092620849609375,
0.002674102783203125,
0.010528564453125,
-0.01006317138671875,
0.059600830078125,
-0.021759033203125,
0.00495147705078125,
0.0040283203125,
0.032440185546875,
0.00739288330078125,
-0.0018281936645507812,
0.01381683349609375,
0.0261688232421875,
-0.04376220703125,
-0.03240966796875,
0.01385498046875,
-0.0345458984375,
-0.0207672119140625,
-0.0160980224609375,
-0.0264739990234375,
-0.01202392578125,
-0.0185546875,
0.0171661376953125,
-0.01155853271484375,
0.02264404296875,
0.00189208984375,
-0.006938934326171875,
-0.00995635986328125,
-0.00963592529296875,
-0.0156402587890625,
0.005535125732421875,
-0.00798797607421875,
0.017547607421875,
-0.03167724609375,
0.033721923828125,
0.0074615478515625,
-0.015899658203125,
-0.01102447509765625,
-0.030975341796875,
-0.025299072265625,
-0.0202789306640625,
0.059783935546875,
-0.01654052734375,
-0.0091400146484375,
0.0053253173828125,
-0.028350830078125,
-0.00415802001953125,
0.02978515625,
-0.028106689453125,
0.006374359130859375,
0.00518035888671875,
-0.0009555816650390625,
0.03741455078125,
-0.00658416748046875,
0.0122222900390625,
-0.0033588409423828125,
-0.0145721435546875,
0.0007534027099609375,
0.017333984375,
0.006378173828125,
-0.0147247314453125,
-0.02001953125,
0.00939178466796875,
0.0172882080078125,
-0.0147857666015625,
-0.015869140625,
-0.0156707763671875,
-0.00701904296875,
0.0274810791015625,
0.0350341796875,
-0.01264190673828125,
-0.036834716796875,
-0.0152435302734375,
-0.0100250244140625,
-0.01168060302734375,
-0.03326416015625,
-0.040008544921875,
0.019500732421875,
-0.027130126953125,
-0.01285552978515625,
-0.00020754337310791016,
0.0277862548828125,
0.0208587646484375,
0.0014858245849609375,
-0.011566162109375,
-0.032470703125,
-0.0095367431640625,
0.01016998291015625,
0.000965118408203125,
0.0391845703125,
-0.005832672119140625,
-0.0147247314453125,
0.0257415771484375,
-0.02520751953125,
-0.0042724609375,
0.036590576171875,
-0.0013971328735351562,
0.00726318359375,
-0.0350341796875,
0.044219970703125,
-0.007137298583984375,
-0.0228118896484375,
-0.01690673828125,
0.01068115234375,
0.00012564659118652344,
-0.0241851806640625,
0.0209808349609375,
-0.0012912750244140625,
-0.004337310791015625,
-0.002696990966796875,
0.0190277099609375,
0.041229248046875,
0.0019369125366210938,
-0.0262298583984375,
0.015716552734375,
-0.004657745361328125,
0.008331298828125,
0.01104736328125,
0.0185699462890625,
0.0098114013671875,
0.02703857421875,
-0.0051727294921875,
0.0079498291015625,
-0.00786590576171875,
-0.0082244873046875,
-0.00402069091796875,
-0.02703857421875,
0.0022716522216796875,
-0.0222625732421875,
0.0077972412109375,
0.0020732879638671875,
0.00818634033203125,
0.0180816650390625,
-0.00936126708984375,
-0.01042938232421875,
0.0129241943359375,
-0.0178680419921875,
0.017059326171875,
-0.0012979507446289062,
-0.01488494873046875,
0.00394439697265625,
0.0235748291015625,
0.0004487037658691406,
0.0203399658203125,
0.0029544830322265625,
-0.00018990039825439453,
-0.01678466796875,
0.0007295608520507812,
-0.005580902099609375,
0.00640869140625,
-0.01282501220703125,
0.0121917724609375,
-0.01287078857421875,
-0.006984710693359375,
-0.0113983154296875,
-0.019805908203125,
-0.0069580078125,
-0.037261962890625,
-0.01337432861328125,
0.0286102294921875,
0.026947021484375,
0.0093536376953125,
0.0194854736328125,
-0.0160064697265625,
0.001918792724609375,
0.0113525390625,
-0.035736083984375,
-0.00225830078125,
-0.0209808349609375,
-0.04168701171875,
0.0244903564453125,
0.0281524658203125,
0.0205078125,
-0.01641845703125,
0.0156097412109375,
-0.0153961181640625,
-0.0206756591796875,
0.007350921630859375,
0.0014190673828125,
0.0027256011962890625,
0.00852203369140625,
-0.0037784576416015625,
-0.01483917236328125,
-0.001354217529296875,
0.022979736328125,
-0.0006399154663085938,
0.004497528076171875,
-0.007297515869140625,
0.006824493408203125,
0.006580352783203125,
0.04144287109375,
0.0221405029296875,
-0.0147247314453125,
-0.0284271240234375,
-0.058258056640625,
-0.0230255126953125,
-0.005107879638671875,
0.0262298583984375,
0.0292205810546875,
-0.004138946533203125,
-0.00942230224609375,
0.01441192626953125,
0.01039886474609375,
0.007354736328125,
-0.0011157989501953125,
-0.0088348388671875,
-0.008056640625,
-0.0305938720703125,
-0.0226593017578125,
-0.0254364013671875,
-0.00022208690643310547,
-0.01485443115234375,
0.031097412109375,
0.005100250244140625,
0.0528564453125,
-0.0083770751953125,
0.0075836181640625,
0.004543304443359375,
0.01070404052734375,
-0.046173095703125,
-0.0043182373046875,
-0.01328277587890625,
-0.0230712890625,
0.00328826904296875,
-0.0045623779296875,
0.0205841064453125,
0.0191497802734375,
-0.01214599609375,
0.0169219970703125,
0.04534912109375,
-0.01371002197265625,
-0.0014801025390625,
0.0193634033203125,
-0.015106201171875,
-0.025604248046875,
0.02838134765625,
-0.0043792724609375,
-0.043121337890625,
0.0214080810546875,
-0.0150604248046875,
-0.0105438232421875,
-0.00307464599609375,
0.0129852294921875,
-0.0025177001953125,
0.007415771484375,
0.011199951171875,
0.00138092041015625,
-0.009979248046875,
0.00402069091796875,
0.01033782958984375,
0.0310516357421875,
-0.016448974609375,
-0.0303497314453125,
0.03131103515625,
-0.0013904571533203125,
-0.0244903564453125,
0.01027679443359375,
-0.0142364501953125,
-0.0012350082397460938,
-0.02978515625,
0.023895263671875,
0.004077911376953125,
-0.0179901123046875,
0.0253448486328125,
0.01690673828125,
-0.03546142578125,
-0.009002685546875,
0.005199432373046875,
0.005329132080078125,
-0.00675201416015625,
-0.01446533203125,
-0.0203094482421875,
0.00020074844360351562,
-0.00841522216796875,
0.00902557373046875,
-0.00469207763671875,
0.03411865234375,
-0.01006317138671875,
0.0033931732177734375,
-0.01201629638671875,
-0.002086639404296875,
0.01288604736328125,
-0.0139312744140625,
0.04486083984375,
-0.0321044921875,
-0.024322509765625,
-0.0097503662109375,
-0.0006122589111328125,
0.00839996337890625,
-0.0187225341796875,
-0.0260162353515625,
0.0165252685546875,
-0.007720947265625,
0.01287841796875,
-0.0160064697265625,
0.0103302001953125,
-0.005474090576171875,
-0.01045989990234375,
-0.0010690689086914062,
0.0008950233459472656,
0.0185089111328125,
-0.0204315185546875,
-0.035308837890625,
0.025665283203125,
-0.0037899017333984375,
0.0160369873046875,
-0.01500701904296875,
0.0221099853515625,
-0.0005588531494140625,
0.003887176513671875,
0.023590087890625,
-0.01678466796875,
-0.0152740478515625,
-0.0119171142578125,
0.01326751708984375,
-0.0117950439453125,
0.024139404296875,
-0.01715087890625,
-0.019378662109375,
-0.0015993118286132812,
-0.00023496150970458984,
0.022308349609375,
0.037933349609375,
0.00615692138671875,
-0.023193359375,
-0.01168060302734375,
-0.0196533203125,
0.0254974365234375,
-0.0108642578125,
-0.00099945068359375,
-0.0273284912109375,
-0.0312042236328125,
-0.004734039306640625,
0.016448974609375,
0.01277923583984375,
0.0041961669921875,
0.016387939453125,
0.01442718505859375,
0.005008697509765625,
-0.031646728515625,
0.01068115234375,
0.00443267822265625,
0.049774169921875,
-0.01480865478515625,
0.00939178466796875,
0.00882720947265625,
-0.0236663818359375,
-0.0007891654968261719,
-0.022674560546875,
-0.004596710205078125,
0.0009198188781738281,
-0.01092529296875,
-0.0016546249389648438,
-0.03472900390625,
0.0014467239379882812,
0.004093170166015625,
-0.019195556640625,
0.007221221923828125,
0.0181884765625,
0.006725311279296875,
0.0231475830078125,
-0.018768310546875,
-0.01180267333984375,
0.005035400390625,
-0.020416259765625,
0.0180816650390625,
-0.02490234375,
-0.029266357421875,
-0.010986328125,
-0.001857757568359375,
0.01488494873046875,
-0.01441192626953125,
0.02313232421875,
0.02093505859375,
0.014892578125,
-0.0226898193359375,
-0.0221710205078125,
0.000186920166015625,
0.0205841064453125,
-0.00243377685546875,
0.00771331787109375,
0.004558563232421875,
-0.0013761520385742188,
-0.016998291015625,
0.005565643310546875,
0.0152740478515625,
0.01032257080078125,
0.00592803955078125,
0.047698974609375,
0.00598907470703125,
0.00848388671875,
0.02227783203125,
0.0120086669921875,
-0.0223388671875,
-0.00814056396484375,
-0.010955810546875,
-0.035003662109375,
0.016326904296875,
0.0216827392578125,
0.0003933906555175781,
-0.0071868896484375,
0.0267486572265625,
0.008575439453125,
0.002635955810546875,
0.004978179931640625,
0.0131683349609375,
-0.0149383544921875,
0.0109710693359375,
0.02484130859375,
-0.01239013671875,
-0.004428863525390625,
-0.03045654296875,
0.018798828125,
-0.027587890625,
-0.006160736083984375,
-0.00955963134765625,
-0.0118865966796875,
0.00640869140625,
0.01513671875,
0.0130462646484375,
0.0024890899658203125,
0.016632080078125,
-0.0022296905517578125,
-0.0209503173828125,
-0.0074310302734375,
0.016571044921875,
0.040283203125,
0.007083892822265625,
0.00677490234375,
-0.025360107421875,
-0.01560211181640625,
-0.00614166259765625,
0.00516510009765625,
-0.0133514404296875,
-0.0240020751953125,
0.00220489501953125,
0.0205078125,
-0.00234222412109375,
0.010711669921875,
-0.004695892333984375,
-0.0408935546875,
0.0028171539306640625,
0.01824951171875,
0.00421905517578125,
0.004711151123046875,
-0.02239990234375,
0.00487518310546875,
-0.01348876953125,
-0.007965087890625,
0.0003261566162109375,
-0.0198516845703125,
0.021636962890625,
-0.00849151611328125,
-0.034576416015625,
-0.033599853515625,
0.01297760009765625,
0.03607177734375,
0.01107025146484375,
0.005100250244140625,
0.024566650390625,
0.021728515625,
-0.0272979736328125,
-0.0090484619140625,
-0.0011005401611328125,
-0.01486968994140625,
0.04095458984375,
-0.003017425537109375,
-0.00978851318359375,
-0.01276397705078125,
-0.0029354095458984375,
-0.00806427001953125,
0.0005307197570800781,
-0.019287109375,
-0.02001953125,
-0.022735595703125,
-0.005283355712890625,
0.0243377685546875,
-0.011016845703125,
-0.0016527175903320312,
0.01404571533203125,
-0.0095367431640625,
-0.019439697265625,
0.0154571533203125,
-0.034698486328125,
0.0101776123046875,
0.005916595458984375,
-0.0204620361328125,
-0.0201873779296875,
-0.007175445556640625,
-0.036407470703125,
0.017120361328125,
-0.01226043701171875,
0.036529541015625,
-0.038330078125,
0.007389068603515625,
0.005161285400390625,
-0.01108551025390625,
0.0019197463989257812,
-0.027618408203125,
-0.0278778076171875,
-0.0245208740234375,
-0.00374603271484375,
0.01934814453125,
-0.00644683837890625,
-0.02020263671875,
0.0004715919494628906,
-0.003528594970703125,
0.0091094970703125,
0.01324462890625,
-0.046051025390625,
-0.01357269287109375,
-0.0190582275390625,
0.0007600784301757812,
-0.0184783935546875,
-0.02056884765625,
0.01221466064453125,
-0.01058197021484375,
0.05181884765625,
-0.0209808349609375,
0.02801513671875,
-0.03204345703125,
0.017333984375,
-0.021728515625,
-0.031280517578125,
0.0019197463989257812,
0.0178070068359375,
0.017578125,
0.025543212890625,
0.017059326171875,
0.0210113525390625,
0.028656005859375,
-0.00699615478515625,
-0.00001341104507446289,
0.0137786865234375,
0.0237579345703125,
0.005157470703125,
-0.023406982421875,
0.0164794921875,
-0.030731201171875,
-0.029571533203125,
0.0306549072265625,
0.0010480880737304688,
0.003437042236328125,
-0.0189361572265625,
-0.016632080078125,
0.0219573974609375,
0.01522064208984375,
-0.01099395751953125,
0.00823974609375,
0.01242828369140625,
-0.01617431640625,
-0.0245819091796875,
0.0171051025390625,
0.0163116455078125,
0.03802490234375,
0.0147247314453125,
-0.0187225341796875,
-0.031707763671875,
0.018218994140625,
-0.00884246826171875,
-0.0219879150390625,
0.025360107421875,
-0.004055023193359375,
-0.01274871826171875,
-0.0022735595703125,
0.0098419189453125,
-0.018157958984375,
-0.01515960693359375,
0.020843505859375,
0.055999755859375,
0.0064239501953125,
0.00948333740234375,
0.0026760101318359375,
0.0255126953125,
-0.010101318359375,
-0.0121307373046875,
-0.0241546630859375,
0.0175018310546875,
-0.00641632080078125,
0.037445068359375,
-0.04296875,
-0.0213165283203125,
-0.004169464111328125,
-0.0002498626708984375,
-0.0050811767578125,
0.00907135009765625,
-0.0027313232421875,
0.00846099853515625,
-0.00812530517578125,
-0.01438140869140625,
-0.040679931640625,
0.0173797607421875,
-0.0012063980102539062,
0.005847930908203125,
0.00872039794921875,
-0.00244903564453125,
-0.0484619140625,
0.039886474609375,
-0.004039764404296875,
0.028564453125,
-0.01236724853515625,
-0.01410675048828125,
0.00787353515625,
0.04217529296875,
-0.007419586181640625,
-0.045806884765625,
0.0076751708984375,
0.0068511962890625,
-0.00800323486328125,
-0.017425537109375,
0.002460479736328125,
0.0184783935546875,
0.0137786865234375,
-0.023712158203125,
-0.004119873046875,
0.005016326904296875,
0.0140380859375,
0.0297698974609375,
0.012969970703125,
-0.03094482421875,
0.004230499267578125,
-0.017486572265625,
0.0009555816650390625,
0.0265045166015625,
0.011138916015625,
-0.0007424354553222656,
0.007732391357421875,
0.0222625732421875,
-0.002918243408203125,
-0.000339508056640625,
-0.00896453857421875,
-0.00734710693359375,
0.0259857177734375,
0.0276031494140625,
0.037445068359375,
0.01030731201171875,
0.0033721923828125,
0.0209503173828125,
0.018951416015625,
0.0018644332885742188,
-0.032684326171875,
0.0215606689453125,
-0.0154876708984375,
-0.01507568359375,
-0.01140594482421875,
-0.02783203125,
-0.01605224609375,
0.0150604248046875,
-0.0209197998046875,
0.003246307373046875,
-0.0297698974609375,
0.002674102783203125,
0.0291290283203125,
-0.0151519775390625,
-0.0088348388671875,
0.0126190185546875,
-0.007312774658203125,
0.01299285888671875,
-0.00881195068359375,
-0.00829315185546875,
-0.0014867782592773438,
0.0118865966796875,
-0.019012451171875,
0.01508331298828125,
0.0099639892578125,
0.01238250732421875,
-0.0024471282958984375,
0.0244140625,
0.0034122467041015625,
0.00787353515625,
0.01290130615234375,
0.00923919677734375,
-0.0177001953125,
0.02203369140625,
0.002521514892578125,
0.0212554931640625,
-0.006343841552734375,
-0.0040435791015625,
-0.0225677490234375,
-0.006805419921875,
-0.00788116455078125,
0.0257415771484375,
0.00860595703125,
0.0017557144165039062,
0.03076171875,
-0.00574493408203125,
-0.0212554931640625,
0.043304443359375,
0.0007963180541992188,
0.0200653076171875,
0.006927490234375,
-0.0084381103515625,
-0.0127716064453125,
0.0245513916015625,
-0.00035500526428222656,
-0.0222930908203125,
-0.04180908203125,
0.00914764404296875,
-0.0460205078125,
-0.0113372802734375,
-0.003177642822265625,
0.003963470458984375,
0.0288238525390625,
0.01482391357421875,
0.0078125,
-0.020233154296875,
0.03277587890625,
0.019256591796875,
0.01302337646484375,
-0.006320953369140625,
0.01265716552734375,
0.03179931640625,
0.003223419189453125,
0.0011997222900390625,
-0.00800323486328125,
0.031005859375,
0.0172271728515625,
-0.00295257568359375,
0.0160064697265625,
-0.0014667510986328125,
0.0340576171875,
0.0157470703125,
-0.00014388561248779297,
-0.0112762451171875,
0.02911376953125,
0.0223236083984375,
-0.0546875,
0.018585205078125,
0.0231475830078125,
-0.0290374755859375,
0.00036835670471191406,
0.0243988037109375,
-0.004123687744140625,
-0.002819061279296875,
-0.0303955078125,
-0.01161956787109375,
-0.0120849609375,
0.018646240234375,
0.0027828216552734375,
-0.0028533935546875,
-0.00843048095703125,
-0.001331329345703125,
0.0081024169921875,
0.0226898193359375,
-0.009613037109375,
0.0157928466796875,
0.03192138671875,
-0.0088958740234375,
0.0019521713256835938,
0.0189971923828125,
0.004730224609375,
0.032257080078125,
-0.002140045166015625,
0.0060577392578125,
0.0165557861328125,
-0.002750396728515625,
0.01306915283203125,
0.00974273681640625,
-0.0127105712890625,
-0.020751953125,
0.00574493408203125,
0.01514434814453125,
0.01092529296875,
-0.0247650146484375,
0.00687408447265625,
-0.01332855224609375,
0.0031185150146484375,
-0.00646209716796875,
0.028778076171875,
-0.0195770263671875,
-0.007129669189453125,
0.017425537109375,
-0.0330810546875,
0.0035724639892578125,
0.0357666015625,
0.0198516845703125,
0.0007958412170410156,
0.0166778564453125,
0.0247650146484375,
0.004810333251953125,
-0.0171966552734375,
-0.0098114013671875,
-0.0013265609741210938,
-0.00771331787109375,
-0.009796142578125,
-0.00933074951171875,
0.00574493408203125,
0.0294189453125,
-0.007160186767578125,
-0.032623291015625,
0.0129241943359375,
0.00495147705078125,
0.01806640625,
-0.013519287109375,
-0.0028533935546875,
0.0018444061279296875,
0.031036376953125,
-0.0121917724609375,
-0.026641845703125,
-0.021759033203125,
0.0006060600280761719,
0.015777587890625,
-0.007663726806640625,
-0.047760009765625,
0.00928497314453125,
0.00945281982421875,
0.004764556884765625,
0.0009274482727050781,
-0.0209808349609375,
0.0218353271484375,
-0.006805419921875,
0.007373809814453125,
0.0194091796875,
0.028167724609375,
-0.01441192626953125,
0.0205078125,
0.02667236328125,
-0.022430419921875,
-0.003753662109375,
0.01702880859375,
0.01325225830078125,
0.035858154296875,
0.0394287109375,
-0.01385498046875,
0.01349639892578125,
0.0260162353515625,
-0.0158233642578125,
0.0110931396484375,
-0.042694091796875,
-0.0274810791015625,
0.01424407958984375,
-0.0030651092529296875,
-0.003963470458984375,
-0.01169586181640625,
0.023284912109375,
0.0098114013671875,
-0.00997161865234375,
-0.0280914306640625,
0.034088134765625,
0.018035888671875,
0.00467681884765625,
0.008880615234375,
-0.00862884521484375,
-0.0024166107177734375,
-0.0261688232421875,
-0.0212249755859375,
-0.0175933837890625,
-0.0063629150390625,
-0.003711700439453125,
-0.01245880126953125,
-0.00860595703125,
0.0157470703125,
-0.0160064697265625,
0.0017385482788085938,
-0.032684326171875,
-0.0026836395263671875,
-0.0006628036499023438,
-0.020263671875,
-0.016265869140625,
-0.025421142578125,
0.0272216796875,
0.0247650146484375,
0.00603485107421875,
0.025360107421875,
0.015625,
0.0142974853515625,
-0.0186920166015625,
-0.0140533447265625,
0.0099334716796875,
-0.00959014892578125,
0.0213775634765625,
-0.003997802734375,
0.007289886474609375,
0.0057525634765625,
-0.01450347900390625,
-0.00534820556640625,
0.0012149810791015625,
-0.020233154296875,
-0.01267242431640625,
-0.0208282470703125,
0.004913330078125,
-0.0279083251953125,
-0.0015039443969726562,
0.0247344970703125,
-0.00144195556640625,
-0.003448486328125,
0.01531982421875,
-0.014007568359375,
0.0103759765625,
-0.0246429443359375,
0.040924072265625,
-0.01374053955078125,
0.0101776123046875,
0.00806427001953125,
-0.0611572265625,
0.02679443359375,
0.00630950927734375,
-0.033599853515625,
-0.0239410400390625,
0.02642822265625,
-0.017608642578125,
-0.0064544677734375,
-0.01044464111328125,
0.003307342529296875,
0.01393890380859375,
-0.056182861328125,
0.02398681640625,
0.007354736328125,
-0.02435302734375,
-0.05377197265625,
0.040283203125,
0.00742340087890625,
0.001644134521484375,
-0.032012939453125,
0.002040863037109375,
0.0142364501953125,
-0.00598907470703125,
0.032928466796875,
-0.01849365234375,
-0.0439453125,
0.035614013671875,
-0.022979736328125,
0.007572174072265625,
-0.0367431640625,
-0.0509033203125,
0.0257720947265625,
0.007659912109375,
0.01271820068359375,
-0.032073974609375,
0.0230560302734375,
-0.033233642578125,
-0.022552490234375,
-0.01129913330078125,
0.003177642822265625,
0.0196990966796875,
0.0018148422241210938,
-0.01519775390625,
0.000423431396484375,
-0.0036144256591796875,
0.0296173095703125,
0.0030841827392578125,
-0.00693511962890625,
-0.049591064453125,
-0.02099609375,
0.0013017654418945312,
0.006649017333984375,
-0.007572174072265625,
0.03265380859375,
0.00475311279296875,
-0.017547607421875,
0.0109710693359375,
-0.018341064453125,
-0.01155853271484375,
0.0061492919921875,
-0.0101165771484375,
0.01480865478515625,
-0.04547119140625,
-0.0063629150390625,
0.019134521484375,
0.00414276123046875,
-0.0196380615234375,
0.01064300537109375,
-0.0236663818359375,
0.0006060600280761719,
0.0123443603515625,
0.0146484375,
0.0114593505859375,
0.02081298828125,
0.00945281982421875,
0.0240020751953125,
-0.0031032562255859375,
0.04150390625,
-0.010772705078125,
-0.005268096923828125,
-0.0032749176025390625,
0.01081085205078125,
0.01265716552734375,
0.0067291259765625,
0.0240631103515625,
0.0006265640258789062,
-0.0263824462890625,
0.007595062255859375,
-0.019073486328125,
-0.0145111083984375,
0.0236053466796875,
0.00957489013671875,
-0.00722503662109375,
0.0176544189453125,
0.0180816650390625,
0.01427459716796875,
0.0304412841796875,
-0.0091400146484375,
0.009429931640625,
-0.043182373046875,
-0.0166168212890625,
0.01137542724609375,
0.00899505615234375,
0.0032405853271484375,
-0.029449462890625,
-0.0148468017578125,
0.025909423828125,
0.006916046142578125,
0.0218658447265625,
0.0038318634033203125,
0.0026397705078125,
-0.0372314453125,
0.00936126708984375,
-0.01224517822265625,
0.0290374755859375,
-0.004978179931640625,
-0.03668212890625,
0.007007598876953125,
-0.0372314453125,
0.017303466796875,
0.0018911361694335938,
0.0225830078125,
-0.01129150390625,
-0.0024280548095703125,
0.0122833251953125,
-0.004161834716796875,
0.0047454833984375,
0.00716400146484375,
-0.00672149658203125,
0.0015115737915039062,
-0.0151519775390625,
-0.02325439453125,
0.01904296875,
0.00386810302734375,
0.029632568359375,
0.0026874542236328125,
0.00688934326171875,
-0.0105133056640625,
0.004161834716796875,
-0.043060302734375,
-0.0078277587890625,
0.0005540847778320312,
-0.033172607421875,
0.0276641845703125,
-0.0166015625,
0.00783538818359375,
0.0298004150390625,
-0.01042938232421875,
-0.004482269287109375,
-0.0294952392578125,
0.005725860595703125,
-0.00025653839111328125,
-0.007129669189453125,
0.016937255859375,
0.003704071044921875,
0.0145111083984375,
0.0205078125,
0.007717132568359375,
-0.00080108642578125,
-0.033843994140625,
-0.00005251169204711914,
-0.01366424560546875,
0.025177001953125,
0.0288543701171875,
-0.06842041015625,
0.01202392578125,
0.0007300376892089844,
0.004947662353515625,
0.0115203857421875,
0.0158843994140625,
0.00994873046875,
-0.000022172927856445312,
0.00806427001953125,
-0.0046234130859375,
0.01158905029296875,
-0.0286712646484375,
-0.02655029296875,
0.009857177734375,
0.0128936767578125,
-0.0249176025390625,
-0.0039005279541015625,
0.038818359375,
-0.0341796875,
0.0209808349609375,
0.0214385986328125,
0.00896453857421875,
-0.0146484375,
0.003173828125,
0.01085662841796875,
0.055816650390625,
0.007843017578125,
-0.00522613525390625,
-0.0245513916015625,
0.0635986328125,
0.0216522216796875,
0.0092315673828125,
-0.0251922607421875,
-0.03900146484375,
0.016448974609375,
0.0216522216796875,
0.041534423828125,
-0.01294708251953125,
0.000012099742889404297,
0.00011265277862548828,
-0.027099609375,
0.01020050048828125,
-0.01047515869140625,
0.034393310546875,
-0.036224365234375,
0.015045166015625,
0.00667572021484375,
-0.01360321044921875,
-0.0145416259765625,
-0.002178192138671875,
-0.002742767333984375,
-0.0081329345703125,
0.0021991729736328125,
0.0256500244140625,
-0.017181396484375,
0.0077362060546875,
0.003047943115234375,
0.0178375244140625,
-0.0225830078125,
0.0107879638671875,
0.0312042236328125,
-0.01108551025390625,
0.01222991943359375,
0.0214080810546875,
0.02423095703125,
0.006801605224609375,
0.006855010986328125,
-0.02032470703125,
-0.0177459716796875,
-0.0181121826171875,
-0.0031414031982421875,
-0.029937744140625,
-0.01274871826171875,
0.0286102294921875,
0.01580810546875,
-0.005794525146484375,
0.0166168212890625,
-0.015350341796875,
-0.019561767578125,
-0.01238250732421875,
0.00013065338134765625,
-0.0124359130859375,
-0.0166168212890625,
-0.0088043212890625,
0.030548095703125,
0.0026187896728515625,
0.0177459716796875,
0.0169677734375,
0.005573272705078125,
-0.0120849609375,
-0.028411865234375,
0.031005859375,
0.01319122314453125,
0.0183563232421875,
0.01104736328125,
-0.01389312744140625,
-0.0306243896484375,
0.007617950439453125,
0.00959014892578125,
-0.05364990234375,
0.0007586479187011719,
0.0028095245361328125,
0.0131378173828125,
0.016815185546875,
-0.00005996227264404297,
-0.011138916015625,
-0.0140380859375,
0.006404876708984375,
-0.022857666015625,
-0.03167724609375,
0.032928466796875,
0.01531982421875,
0.0271759033203125,
-0.0026645660400390625,
0.01190948486328125,
0.01483917236328125,
0.06597900390625,
0.00760650634765625,
-0.01727294921875,
0.0136260986328125,
-0.0255279541015625,
-0.0148773193359375,
-0.024871826171875,
0.0022373199462890625,
0.0211181640625,
0.01317596435546875,
-0.0196990966796875,
0.01419830322265625,
-0.046875,
0.044708251953125,
0.0007538795471191406,
0.0008554458618164062,
0.0062713623046875,
-0.00377655029296875,
0.00991058349609375,
0.0121612548828125,
0.01544952392578125,
0.00743865966796875,
-0.01288604736328125,
-0.03558349609375,
-0.01519775390625,
-0.0025424957275390625,
0.01116943359375,
0.00487518310546875,
-0.002544403076171875,
0.01366424560546875,
0.00848388671875,
0.029571533203125,
0.00963592529296875,
-0.00653076171875,
-0.01446533203125,
0.00872039794921875,
0.0157623291015625,
0.039276123046875,
-0.0166168212890625,
-0.00896453857421875,
0.02789306640625,
-0.00943756103515625,
0.045501708984375,
0.0022487640380859375,
0.010772705078125,
-0.01221466064453125,
-0.00540924072265625,
-0.025787353515625,
0.032745361328125,
0.03143310546875,
-0.026947021484375,
-0.0199737548828125,
0.0206146240234375,
0.035400390625,
0.0035381317138671875,
-0.01287078857421875,
-0.0297698974609375,
0.0308074951171875,
0.01084136962890625,
-0.002147674560546875,
-0.0086822509765625,
0.003696441650390625,
0.004150390625,
-0.0117034912109375,
0.0537109375,
0.00653076171875,
-0.004482269287109375,
0.0010595321655273438,
0.01041412353515625,
0.004138946533203125,
-0.037933349609375,
0.0032806396484375,
0.0017824172973632812,
-0.012298583984375,
-0.0175628662109375,
-0.0015354156494140625,
0.0133056640625,
0.0411376953125,
-0.00998687744140625,
0.017242431640625,
0.008056640625,
0.0106964111328125,
0.0141143798828125,
-0.029266357421875,
0.005954742431640625,
0.0179595947265625,
-0.01824951171875,
0.0156707763671875,
-0.009246826171875,
-0.0294189453125,
0.01499176025390625,
0.01293182373046875,
0.005626678466796875,
-0.00997161865234375,
0.02996826171875,
-0.0010881423950195312,
-0.01148223876953125,
-0.007411956787109375,
0.0254669189453125,
-0.05096435546875,
0.006458282470703125,
0.01751708984375,
0.0189056396484375,
-0.0305938720703125,
0.0290985107421875,
0.0014944076538085938,
-0.0037822723388671875,
0.0210418701171875,
-0.0008749961853027344,
0.01172637939453125,
-0.0072174072265625,
0.016082763671875,
0.0009589195251464844,
0.0129241943359375,
-0.0066680908203125,
-0.0177154541015625,
-0.027008056640625,
0.025115966796875,
-0.0015649795532226562,
0.01406097412109375,
-0.023284912109375,
-0.018768310546875,
-0.0121307373046875,
0.009368896484375,
0.0189056396484375,
0.0023212432861328125,
0.005542755126953125,
-0.016326904296875,
0.005706787109375,
-0.056640625,
-0.0064697265625,
-0.040679931640625,
-0.0183258056640625,
0.01512908935546875,
-0.0479736328125,
-0.001049041748046875,
0.006488800048828125,
-0.0252532958984375,
0.020843505859375,
0.0018739700317382812,
-0.00838470458984375,
0.040985107421875,
-0.0110015869140625,
0.024505615234375,
-0.007541656494140625,
0.00405120849609375,
0.01053619384765625,
0.0060272216796875,
0.0240631103515625,
0.00022804737091064453,
0.0100250244140625,
-0.0107879638671875,
0.04705810546875,
0.004390716552734375,
0.01468658447265625,
-0.027984619140625,
-0.0033092498779296875,
-0.02008056640625,
-0.005535125732421875,
-0.0279541015625,
0.002361297607421875,
-0.01137542724609375,
-0.0261383056640625,
0.0029449462890625,
-0.0002586841583251953,
0.00725555419921875,
0.020782470703125,
-0.01253509521484375,
-0.0054779052734375,
-0.053009033203125,
-0.0091400146484375,
0.018524169921875,
0.01172637939453125,
-0.020782470703125,
0.01021575927734375,
-0.0259552001953125,
-0.0164642333984375,
-0.0187225341796875,
0.026123046875,
0.001354217529296875,
0.0423583984375,
-0.0007119178771972656,
0.0157470703125,
0.0240936279296875,
-0.0268402099609375,
-0.00933837890625,
0.000006496906280517578,
-0.00372314453125,
-0.003292083740234375,
0.038787841796875,
0.0014390945434570312,
-0.0077972412109375,
-0.006900787353515625,
-0.00396728515625,
-0.026458740234375,
-0.00626373291015625,
-0.014678955078125,
0.0124359130859375,
0.01947021484375,
-0.0025959014892578125,
-0.0311737060546875,
0.0203094482421875,
-0.00832366943359375,
-0.040374755859375,
-0.002246856689453125,
-0.0026226043701171875,
-0.00016164779663085938,
-0.01543426513671875,
-0.007038116455078125,
-0.0006971359252929688,
0.01219940185546875,
0.0111083984375,
-0.00402069091796875,
0.0277862548828125,
-0.06298828125,
0.002658843994140625,
-0.038604736328125,
0.01526641845703125,
0.0175323486328125,
0.0241546630859375,
-0.00897979736328125,
-0.0172119140625,
-0.027557373046875,
-0.00004786252975463867,
-0.01556396484375,
0.014251708984375,
0.0225677490234375,
-0.0289459228515625,
0.0071868896484375,
0.012725830078125,
0.006725311279296875,
-0.0313720703125,
-0.00992584228515625,
0.01302337646484375,
0.035369873046875,
0.03643798828125,
0.015777587890625,
0.01580810546875,
0.015869140625,
-0.0202178955078125,
0.03045654296875,
0.005313873291015625,
0.01381683349609375,
-0.005512237548828125,
-0.00997161865234375,
0.0184783935546875,
-0.006259918212890625,
0.004974365234375,
-0.0284423828125,
-0.018096923828125,
0.0029315948486328125,
-0.0131072998046875,
-0.01418304443359375,
-0.01373291015625,
-0.00931549072265625,
-0.0253753662109375,
0.015960693359375,
-0.0149993896484375,
-0.003276824951171875,
-0.020294189453125,
-0.006610870361328125,
0.0091705322265625,
0.01349639892578125,
-0.00469207763671875,
-0.00870513916015625,
-0.02276611328125,
0.0018758773803710938,
-0.0259857177734375,
0.00550079345703125,
-0.00035500526428222656,
0.0041961669921875,
-0.01178741455078125,
-0.004024505615234375,
0.03192138671875,
0.004528045654296875,
-0.01690673828125,
0.007732391357421875,
0.008636474609375,
0.007114410400390625,
0.00576019287109375,
0.02545166015625,
-0.01177978515625,
-0.01041412353515625,
0.00521087646484375,
-0.0019474029541015625,
0.0007867813110351562,
0.0284881591796875,
-0.0034313201904296875,
0.03692626953125,
0.0036468505859375,
0.0287933349609375,
0.0140228271484375,
-0.0037059783935546875,
-0.006633758544921875,
-0.025299072265625,
-0.0032672882080078125,
0.0207672119140625,
0.0220184326171875,
0.015594482421875,
-0.051910400390625,
0.01953125,
0.01319122314453125,
-0.0013408660888671875,
0.045074462890625,
0.0010013580322265625,
0.005184173583984375,
-0.0020503997802734375,
0.00787353515625,
-0.025604248046875,
-0.02691650390625,
-0.00020766258239746094,
0.0206451416015625,
-0.0201568603515625,
-0.03765869140625,
-0.0224456787109375,
-0.0222930908203125,
0.033233642578125,
0.021881103515625,
-0.0107269287109375,
-0.00252532958984375,
-0.035980224609375,
-0.02435302734375,
-0.0016412734985351562,
-0.00820159912109375,
0.007534027099609375,
0.0328369140625,
-0.03521728515625,
-0.004611968994140625,
0.0094146728515625,
-0.0025043487548828125,
0.0253143310546875,
-0.007335662841796875,
-0.00743865966796875,
-0.011627197265625,
0.018829345703125,
-0.016143798828125,
-0.01154327392578125,
-0.02752685546875,
-0.047515869140625,
0.01220703125,
0.015594482421875,
0.007617950439453125,
0.0098876953125,
-0.002590179443359375,
0.0146331787109375,
0.0016469955444335938,
-0.0190887451171875,
-0.00463104248046875,
-0.03289794921875,
0.029571533203125,
-0.005191802978515625,
-0.0160675048828125,
0.0020198822021484375,
0.02825927734375,
-0.0150299072265625,
-0.0059814453125,
-0.01934814453125,
-0.004055023193359375,
0.0241851806640625,
0.0282440185546875,
-0.03863525390625,
0.0190277099609375,
0.04443359375,
-0.0209503173828125,
0.004283905029296875,
0.01490020751953125,
0.027099609375,
-0.006580352783203125,
-0.019256591796875,
0.04327392578125,
-0.01329803466796875,
0.0014190673828125,
0.0019893646240234375,
0.0286865234375,
-0.0065155029296875,
0.03070068359375,
0.0026378631591796875,
0.0164794921875,
0.005268096923828125,
0.0157470703125,
-0.00708770751953125,
-0.01219940185546875,
0.0145263671875,
-0.0263671875,
-0.0247650146484375,
-0.0155029296875,
-0.02032470703125,
0.027435302734375,
0.00414276123046875,
-0.04718017578125,
-0.0173797607421875,
-0.021331787109375,
-0.0106658935546875,
0.0361328125,
0.00266265869140625,
0.0156707763671875,
0.02239990234375,
-0.00432586669921875,
0.01375579833984375,
0.004177093505859375,
0.01270294189453125,
0.0228729248046875,
-0.01102447509765625,
-0.0303802490234375,
-0.028839111328125,
0.033782958984375,
0.002101898193359375,
-0.034759521484375,
0.0007915496826171875,
-0.0179290771484375,
0.01412200927734375,
0.034271240234375,
-0.0116424560546875,
-0.0247344970703125,
-0.0245819091796875,
0.00894927978515625,
0.00836181640625,
0.02642822265625,
-0.0260467529296875,
-0.0018510818481445312,
-0.040740966796875,
0.0160980224609375,
-0.01500701904296875,
0.0035991668701171875,
-0.045562744140625,
-0.019073486328125,
-0.0023250579833984375,
-0.0006890296936035156,
0.00705718994140625,
0.006214141845703125,
-0.03350830078125,
-0.0024585723876953125,
0.0096435546875,
0.004241943359375,
0.005157470703125,
-0.0031604766845703125,
0.037841796875,
0.0131072998046875,
-0.006069183349609375,
0.02313232421875,
-0.01210784912109375,
-0.01432037353515625,
0.01409912109375,
0.0195159912109375,
-0.0205535888671875,
0.0037555694580078125,
0.00878143310546875,
0.0090179443359375,
-0.005527496337890625,
-0.0112762451171875,
0.01024627685546875,
0.00042510032653808594,
0.0152587890625,
-0.04705810546875,
-0.02520751953125,
0.003963470458984375,
0.016143798828125,
0.00232696533203125,
0.005329132080078125,
0.01021575927734375,
-0.00772857666015625,
0.01166534423828125,
0.002864837646484375,
0.0018415451049804688,
0.01393890380859375,
0.03125,
-0.0238800048828125,
-0.01476287841796875,
0.00392913818359375,
-0.024627685546875,
0.01401519775390625,
-0.005748748779296875,
0.0035381317138671875,
-0.0260009765625,
0.0015306472778320312,
-0.0023784637451171875,
0.01806640625
] |
ours_539
|
The number of cookies must be a multiple of $13$. It is easy to see that $13, 26, 39$ are all impossible to form using boxes of $10$ and $21$. However, $52 = 2 \times 21 + 10$, which is a multiple of $13$. Therefore, the minimum positive number of cookies that can be split evenly among $13$ people is \(\boxed{52}\).
|
52
|
{
"competition": "us_comps",
"dataset": "Ours",
"posts": null,
"source": "OMOSoln2.md"
}
|
At a certain grocery store, cookies may be bought in boxes of $10$ or $21$. What is the minimum positive number of cookies that must be bought so that the cookies may be split evenly among $13$ people?
|
[
"/Mathematics/NumberTheory/Arithmetic/GeneralArithmetic",
"/Mathematics/NumberTheory/DiophantineEquations/CoinProblem",
"/Mathematics/NumberTheory/DiophantineEquations/Diophantine",
"/Mathematics/NumberTheory/DiophantineEquations/DiophantineEquation",
"/Mathematics/NumberTheory/DiophantineEquations/FrobeniusCoinProblem",
"/Mathematics/NumberTheory/DiophantineEquations/FrobeniusNumber",
"/Mathematics/NumberTheory/DiophantineEquations/FrobeniusPostageStampProblem",
"/Mathematics/NumberTheory/DiophantineEquations/FrobeniusProblem",
"/Mathematics/NumberTheory/DiophantineEquations/PostageStampProblem",
"/Mathematics/NumberTheory/GeneralNumberTheory/AdditiveNumberTheory",
"/Mathematics/NumberTheory/GeneralNumberTheory/ElementaryNumberTheory",
"/Mathematics/NumberTheory/GeneralNumberTheory/NumberTheory",
"/Mathematics/NumberTheory/Integers/Integer",
"/Mathematics/NumberTheory/Integers/N",
"/Mathematics/NumberTheory/Integers/PositiveInteger",
"/Mathematics/NumberTheory/Integers/WholeNumber",
"/Mathematics/NumberTheory/Integers/Z",
"/Mathematics/NumberTheory/Integers/Z-Plus"
] |
Find the smallest multiple of 13 that can be expressed as a combination of 10 and 21 using modular arithmetic.
|
[
0.00008875131607055664,
-0.0341796875,
0.031158447265625,
-0.03118896484375,
-0.0000014901161193847656,
0.0198974609375,
0.01311492919921875,
-0.0289306640625,
0.0167388916015625,
0.01611328125,
-0.0258026123046875,
-0.0168914794921875,
-0.0019397735595703125,
-0.0238800048828125,
-0.040283203125,
0.0150604248046875,
-0.0020503997802734375,
-0.009674072265625,
0.0273895263671875,
-0.0003902912139892578,
-0.01390838623046875,
0.01358795166015625,
0.033905029296875,
-0.035919189453125,
0.004901885986328125,
-0.0225677490234375,
-0.0221099853515625,
0.0350341796875,
0.014007568359375,
0.00997161865234375,
-0.00833892822265625,
-0.0280609130859375,
0.02008056640625,
-0.047698974609375,
-0.005649566650390625,
0.0164031982421875,
0.0228424072265625,
0.0064697265625,
-0.019439697265625,
-0.036346435546875,
-0.01512908935546875,
0.020355224609375,
-0.008941650390625,
0.00528717041015625,
-0.02569580078125,
0.0175628662109375,
-0.007904052734375,
0.0367431640625,
0.0010461807250976562,
-0.0162506103515625,
-0.002658843994140625,
0.018798828125,
0.02325439453125,
0.007244110107421875,
0.0101776123046875,
-0.052001953125,
0.0557861328125,
0.004116058349609375,
-0.019622802734375,
0.02099609375,
-0.006923675537109375,
-0.0180816650390625,
0.0204620361328125,
0.0092620849609375,
-0.006397247314453125,
-0.004688262939453125,
-0.021026611328125,
-0.019378662109375,
-0.000774383544921875,
-0.014801025390625,
0.015777587890625,
0.0290374755859375,
-0.0152587890625,
0.0109710693359375,
0.01403045654296875,
-0.0163421630859375,
-0.010650634765625,
0.00861358642578125,
-0.00020802021026611328,
0.01226043701171875,
0.04754638671875,
0.0204925537109375,
-0.011505126953125,
0.00684356689453125,
-0.003963470458984375,
-0.06268310546875,
0.0153656005859375,
0.01059722900390625,
0.032012939453125,
-0.00766754150390625,
0.0008516311645507812,
0.0016088485717773438,
-0.007183074951171875,
0.025054931640625,
-0.0016317367553710938,
-0.004276275634765625,
-0.005321502685546875,
-0.003528594970703125,
-0.0111236572265625,
0.00611114501953125,
-0.0119476318359375,
0.01438140869140625,
0.0445556640625,
-0.01148223876953125,
-0.03131103515625,
-0.01500701904296875,
-0.0308685302734375,
-0.0124664306640625,
-0.018157958984375,
-0.01213836669921875,
-0.006710052490234375,
-0.0005116462707519531,
-0.0098724365234375,
0.00009363889694213867,
-0.005138397216796875,
-0.01044464111328125,
0.005817413330078125,
-0.00762939453125,
-0.0223236083984375,
0.002422332763671875,
-0.0052032470703125,
0.0028553009033203125,
-0.01296234130859375,
0.01593017578125,
-0.006378173828125,
-0.0165557861328125,
-0.010894775390625,
-0.020843505859375,
-0.03204345703125,
0.0037250518798828125,
0.031219482421875,
-0.01123046875,
-0.0229034423828125,
-0.0179443359375,
-0.0149688720703125,
0.0155181884765625,
0.0020313262939453125,
-0.018035888671875,
-0.005893707275390625,
0.00475311279296875,
0.0070953369140625,
-0.0015239715576171875,
-0.0021839141845703125,
0.00980377197265625,
-0.01190185546875,
0.0117950439453125,
0.0022754669189453125,
-0.050445556640625,
0.0186920166015625,
-0.0135955810546875,
0.01520538330078125,
0.00518798828125,
-0.01551055908203125,
-0.00283050537109375,
-0.0106658935546875,
0.0255584716796875,
0.006763458251953125,
0.00948333740234375,
0.0154876708984375,
0.00948333740234375,
-0.005275726318359375,
0.0148468017578125,
-0.01439666748046875,
0.04046630859375,
-0.01334381103515625,
0.01244354248046875,
-0.0178070068359375,
-0.0166015625,
-0.0115814208984375,
-0.00460052490234375,
0.0088043212890625,
-0.0153350830078125,
-0.0026988983154296875,
-0.00180816650390625,
0.0009918212890625,
-0.006877899169921875,
-0.014434814453125,
-0.004604339599609375,
-0.0144500732421875,
0.00510406494140625,
-0.0025920867919921875,
-0.0020542144775390625,
0.026092529296875,
-0.0218353271484375,
0.00930023193359375,
0.001422882080078125,
-0.0101470947265625,
0.0009584426879882812,
0.03009033203125,
0.0222015380859375,
-0.01331329345703125,
-0.03924560546875,
-0.01305389404296875,
-0.0119781494140625,
-0.017120361328125,
-0.0070648193359375,
-0.029327392578125,
-0.01094818115234375,
0.00521087646484375,
0.00992584228515625,
0.01436614990234375,
-0.01279449462890625,
-0.0293426513671875,
-0.0037212371826171875,
0.00272369384765625,
-0.02294921875,
-0.002010345458984375,
-0.0020771026611328125,
-0.01763916015625,
0.00550079345703125,
-0.0017871856689453125,
0.0192413330078125,
-0.018310546875,
-0.034698486328125,
-0.006038665771484375,
-0.01904296875,
-0.00005906820297241211,
-0.01190185546875,
-0.006992340087890625,
-0.023651123046875,
-0.01009368896484375,
0.01378631591796875,
0.0006279945373535156,
-0.01189422607421875,
-0.032440185546875,
0.00795745849609375,
0.007251739501953125,
-0.00664520263671875,
0.00878143310546875,
0.006011962890625,
0.052154541015625,
0.0011262893676757812,
-0.017181396484375,
0.005977630615234375,
-0.005016326904296875,
0.007354736328125,
-0.0130157470703125,
0.0024204254150390625,
-0.00771331787109375,
-0.0163726806640625,
0.0284423828125,
-0.02099609375,
0.00933074951171875,
-0.0080413818359375,
-0.0262603759765625,
-0.0110321044921875,
-0.00789642333984375,
-0.01922607421875,
0.00948333740234375,
-0.00458526611328125,
-0.016693115234375,
0.004405975341796875,
-0.0012445449829101562,
-0.0169677734375,
0.0186309814453125,
0.0032367706298828125,
0.0031108856201171875,
0.02239990234375,
-0.0185089111328125,
-0.00695037841796875,
-0.01354217529296875,
-0.056915283203125,
-0.01123809814453125,
-0.019805908203125,
0.00637054443359375,
-0.0264892578125,
0.00033211708068847656,
-0.0009908676147460938,
0.00424957275390625,
-0.008392333984375,
-0.0165863037109375,
-0.01100921630859375,
-0.01971435546875,
-0.0025634765625,
0.0084075927734375,
-0.005344390869140625,
0.0043182373046875,
0.0068511962890625,
-0.00043129920959472656,
0.01358795166015625,
-0.001415252685546875,
-0.0103912353515625,
-0.02734375,
0.022796630859375,
-0.00830078125,
-0.015106201171875,
0.027587890625,
-0.0065155029296875,
-0.0261077880859375,
0.00677490234375,
0.0084075927734375,
-0.04656982421875,
0.0139617919921875,
-0.004001617431640625,
0.01425933837890625,
-0.046356201171875,
0.0093841552734375,
0.00453948974609375,
0.008819580078125,
-0.007289886474609375,
0.006855010986328125,
0.0023403167724609375,
0.008392333984375,
-0.0168304443359375,
-0.00954437255859375,
0.0236968994140625,
-0.00777435302734375,
0.0013837814331054688,
0.016265869140625,
-0.028228759765625,
0.004985809326171875,
-0.0005741119384765625,
-0.01201629638671875,
0.0182037353515625,
-0.01271820068359375,
-0.0430908203125,
0.0103302001953125,
-0.00815582275390625,
-0.006343841552734375,
0.0206756591796875,
0.004055023193359375,
0.005279541015625,
-0.027923583984375,
0.0037288665771484375,
-0.00677490234375,
-0.003749847412109375,
0.0186614990234375,
0.0018110275268554688,
-0.027618408203125,
0.03240966796875,
-0.059783935546875,
0.023773193359375,
-0.00844573974609375,
-0.051055908203125,
-0.0163116455078125,
0.03216552734375,
0.0034008026123046875,
0.0228729248046875,
0.0005154609680175781,
0.0106353759765625,
0.00818634033203125,
-0.005462646484375,
-0.0094757080078125,
0.044097900390625,
-0.01568603515625,
-0.00609588623046875,
-0.00749969482421875,
0.02154541015625,
0.0462646484375,
0.00818634033203125,
0.0010595321655273438,
-0.005924224853515625,
0.010711669921875,
-0.005290985107421875,
-0.0260772705078125,
-0.01080322265625,
-0.01062774658203125,
0.0009431838989257812,
0.0004699230194091797,
0.017181396484375,
0.01297760009765625,
0.008392333984375,
-0.0002276897430419922,
0.010498046875,
-0.01107025146484375,
-0.0007109642028808594,
0.0003783702850341797,
0.0173797607421875,
-0.00920867919921875,
-0.036407470703125,
-0.002864837646484375,
-0.002582550048828125,
0.0131072998046875,
-0.0200042724609375,
-0.006511688232421875,
-0.002109527587890625,
-0.0222625732421875,
0.00733184814453125,
0.0222015380859375,
0.008758544921875,
0.0220489501953125,
0.0031795501708984375,
-0.00339508056640625,
0.034637451171875,
0.0163421630859375,
-0.004703521728515625,
0.0149688720703125,
-0.00457000732421875,
0.0028209686279296875,
0.039520263671875,
-0.00962066650390625,
0.0113067626953125,
-0.01076507568359375,
-0.018585205078125,
-0.01082611083984375,
-0.0333251953125,
-0.0000845193862915039,
0.0088958740234375,
0.036651611328125,
-0.0019426345825195312,
-0.007106781005859375,
0.00966644287109375,
-0.033294677734375,
0.01175689697265625,
0.0181884765625,
-0.0023708343505859375,
-0.00952911376953125,
0.008056640625,
0.00011402368545532227,
-0.015472412109375,
-0.0193634033203125,
-0.005176544189453125,
-0.0205841064453125,
-0.01141357421875,
-0.01099395751953125,
-0.004558563232421875,
0.01197052001953125,
-0.03875732421875,
-0.055145263671875,
-0.009429931640625,
0.015625,
-0.043426513671875,
-0.00431060791015625,
-0.01361083984375,
0.0245361328125,
0.0286865234375,
-0.00667572021484375,
0.018646240234375,
0.00617218017578125,
0.0003571510314941406,
0.010589599609375,
-0.02056884765625,
0.044586181640625,
0.03826904296875,
0.0030879974365234375,
0.039886474609375,
-0.025146484375,
0.00925445556640625,
-0.00963592529296875,
0.01031494140625,
0.02886962890625,
-0.0098876953125,
0.0134429931640625,
-0.028778076171875,
-0.0115966796875,
0.0045928955078125,
0.00977325439453125,
0.0115203857421875,
-0.035675048828125,
0.0106048583984375,
0.004474639892578125,
0.0150604248046875,
-0.0147705078125,
-0.005069732666015625,
-0.0328369140625,
0.0399169921875,
0.01340484619140625,
0.0234375,
-0.0289154052734375,
-0.0177764892578125,
-0.0310516357421875,
-0.010406494140625,
-0.0008449554443359375,
-0.01800537109375,
0.0024280548095703125,
-0.01116943359375,
-0.0125274658203125,
-0.005413055419921875,
0.0219879150390625,
0.005207061767578125,
-0.0163726806640625,
-0.04376220703125,
0.0176544189453125,
-0.0174713134765625,
-0.04498291015625,
0.0062103271484375,
-0.023101806640625,
0.0114593505859375,
-0.02923583984375,
-0.0025539398193359375,
-0.041748046875,
-0.0174560546875,
-0.019622802734375,
0.0114593505859375,
-0.0102996826171875,
0.0298919677734375,
0.0289306640625,
0.0005464553833007812,
-0.00634002685546875,
0.01568603515625,
0.002353668212890625,
0.05328369140625,
-0.02020263671875,
-0.043701171875,
0.0108795166015625,
-0.01139068603515625,
-0.026214599609375,
-0.00312042236328125,
-0.004665374755859375,
0.01690673828125,
0.01446533203125,
-0.041748046875,
-0.01097869873046875,
-0.0192718505859375,
0.021728515625,
0.01416015625,
0.01409149169921875,
-0.04425048828125,
-0.006565093994140625,
-0.0187835693359375,
0.021728515625,
0.017181396484375,
-0.00019228458404541016,
-0.042510986328125,
0.005828857421875,
-0.047027587890625,
0.0266265869140625,
-0.01467132568359375,
0.01551055908203125,
0.03466796875,
-0.0098724365234375,
0.01491546630859375,
0.0290985107421875,
-0.00504302978515625,
-0.002544403076171875,
0.009063720703125,
-0.00904083251953125,
-0.0216827392578125,
0.025726318359375,
-0.01666259765625,
-0.0201263427734375,
-0.0289154052734375,
0.033233642578125,
0.01369476318359375,
-0.02801513671875,
0.0096588134765625,
0.03570556640625,
0.05242919921875,
-0.0111846923828125,
0.00891876220703125,
-0.03204345703125,
-0.0010900497436523438,
0.00904083251953125,
-0.01216888427734375,
0.01126861572265625,
-0.049713134765625,
0.0189056396484375,
-0.011627197265625,
0.002063751220703125,
0.01213836669921875,
0.019683837890625,
-0.00659942626953125,
0.0218658447265625,
-0.01285552978515625,
-0.0099334716796875,
0.0094451904296875,
-0.01302337646484375,
0.0102386474609375,
-0.0023975372314453125,
-0.003437042236328125,
-0.021087646484375,
-0.0200347900390625,
0.0160369873046875,
0.0015974044799804688,
0.0030651092529296875,
-0.01561737060546875,
-0.0117645263671875,
0.01123046875,
0.007381439208984375,
-0.0254364013671875,
0.000476837158203125,
0.0078277587890625,
-0.011383056640625,
0.0092620849609375,
-0.006488800048828125,
-0.0170440673828125,
-0.0196075439453125,
0.0017080307006835938,
0.01238250732421875,
-0.019256591796875,
-0.00731658935546875,
0.00975799560546875,
-0.0019121170043945312,
0.01076507568359375,
-0.01198577880859375,
0.0082550048828125,
0.0199127197265625,
0.01551055908203125,
0.007843017578125,
-0.004299163818359375,
-0.036285400390625,
0.01190948486328125,
0.0214385986328125,
0.024658203125,
-0.0408935546875,
-0.054962158203125,
0.0259552001953125,
-0.01776123046875,
0.01468658447265625,
0.0016336441040039062,
0.0046539306640625,
-0.0055389404296875,
0.01212310791015625,
0.0262298583984375,
0.0044097900390625,
-0.0121307373046875,
-0.0251617431640625,
0.0191497802734375,
-0.00333404541015625,
-0.002773284912109375,
-0.01219940185546875,
-0.02423095703125,
0.0205078125,
0.018035888671875,
0.03692626953125,
0.043853759765625,
-0.0167694091796875,
-0.021209716796875,
-0.0107879638671875,
-0.0271148681640625,
-0.01181793212890625,
-0.033111572265625,
-0.01611328125,
-0.0043182373046875,
0.004444122314453125,
0.007579803466796875,
-0.0041351318359375,
-0.0206756591796875,
-0.0007419586181640625,
-0.004314422607421875,
-0.006160736083984375,
-0.0199432373046875,
0.0152740478515625,
-0.0165863037109375,
0.0164031982421875,
-0.0245513916015625,
-0.034088134765625,
-0.00780487060546875,
-0.0034389495849609375,
-0.012054443359375,
-0.007511138916015625,
0.0195159912109375,
-0.0015859603881835938,
-0.04638671875,
-0.00691986083984375,
-0.006710052490234375,
-0.041107177734375,
-0.007289886474609375,
-0.062286376953125,
-0.00592041015625,
-0.03851318359375,
-0.018463134765625,
-0.015472412109375,
0.02117919921875,
-0.02117919921875,
-0.0035457611083984375,
0.0171661376953125,
-0.046051025390625,
0.0009326934814453125,
-0.031890869140625,
0.0087127685546875,
-0.02191162109375,
-0.0110931396484375,
0.004230499267578125,
-0.033660888671875,
0.004291534423828125,
0.0242462158203125,
0.037261962890625,
0.0128173828125,
-0.02362060546875,
-0.0200958251953125,
-0.027252197265625,
0.04376220703125,
-0.006343841552734375,
-0.0202178955078125,
-0.0301971435546875,
0.0079803466796875,
-0.03460693359375,
0.042327880859375,
0.035003662109375,
-0.0104827880859375,
-0.005344390869140625,
0.04107666015625,
-0.0252227783203125,
0.004894256591796875,
0.0171051025390625,
-0.0176544189453125,
-0.03619384765625,
-0.00849151611328125,
0.0038661956787109375,
0.007144927978515625,
0.0072479248046875,
-0.0217742919921875,
0.01366424560546875,
-0.00786590576171875,
-0.0298614501953125,
0.01340484619140625,
-0.003345489501953125,
-0.004665374755859375,
0.005664825439453125,
0.03460693359375,
0.0029315948486328125,
0.047332763671875,
-0.014007568359375,
-0.00466156005859375,
0.0146942138671875,
-0.0206756591796875,
-0.00881195068359375,
-0.0054779052734375,
0.01654052734375,
-0.01206207275390625,
-0.00586700439453125,
-0.045562744140625,
0.0009756088256835938,
0.0220184326171875,
-0.00449371337890625,
-0.005523681640625,
-0.0198211669921875,
-0.000652313232421875,
-0.027923583984375,
0.004863739013671875,
-0.0159149169921875,
-0.020294189453125,
0.01390838623046875,
-0.0026264190673828125,
0.02056884765625,
-0.01462554931640625,
-0.0511474609375,
0.00751495361328125,
-0.0005841255187988281,
-0.01517486572265625,
0.01788330078125,
-0.00716400146484375,
0.018585205078125,
-0.059814453125,
-0.01617431640625,
0.0088958740234375,
-0.0292510986328125,
0.0307464599609375,
0.0003383159637451172,
0.0270538330078125,
-0.027252197265625,
0.018341064453125,
-0.012481689453125,
-0.0173797607421875,
0.01458740234375,
0.0260162353515625,
-0.0316162109375,
-0.013671875,
-0.0247039794921875,
0.02032470703125,
0.0091400146484375,
-0.0104827880859375,
-0.00797271728515625,
-0.028717041015625,
0.01375579833984375,
0.0050048828125,
-0.003322601318359375,
0.0016088485717773438,
-0.0011777877807617188,
-0.01776123046875,
-0.0169219970703125,
-0.016937255859375,
0.0013742446899414062,
0.017974853515625,
-0.049407958984375,
-0.01097869873046875,
0.0083160400390625,
-0.03765869140625,
0.037078857421875,
-0.015472412109375,
0.01171112060546875,
0.0048370361328125,
-0.004001617431640625,
-0.004703521728515625,
0.00731658935546875,
-0.0751953125,
-0.0178070068359375,
0.02886962890625,
0.00823974609375,
-0.021514892578125,
0.0040130615234375,
0.022125244140625,
0.0087127685546875,
-0.019622802734375,
-0.0137939453125,
0.0006155967712402344,
-0.00878143310546875,
0.0100860595703125,
-0.00634765625,
0.0156097412109375,
0.0165252685546875,
-0.0235443115234375,
-0.0191192626953125,
0.006916046142578125,
0.010406494140625,
0.00786590576171875,
-0.00940704345703125,
-0.01476287841796875,
0.0003807544708251953,
-0.00215911865234375,
-0.00862884521484375,
-0.010589599609375,
0.018310546875,
0.0094757080078125,
0.0016689300537109375,
0.0038013458251953125,
-0.00879669189453125,
0.007686614990234375,
-0.0025310516357421875,
-0.0167999267578125,
-0.0301513671875,
-0.01983642578125,
0.01364898681640625,
0.0233917236328125,
-0.0061187744140625,
0.009307861328125,
-0.035675048828125,
-0.0016126632690429688,
0.039825439453125,
0.00646209716796875,
0.0489501953125,
0.00624847412109375,
-0.00799560546875,
-0.0128173828125,
0.00567626953125,
0.0015554428100585938,
-0.0116729736328125,
0.039886474609375,
-0.0055084228515625,
-0.0026702880859375,
0.00249481201171875,
-0.01885986328125,
0.003673553466796875,
-0.0009541511535644531,
-0.0235137939453125,
0.00287628173828125,
-0.01235198974609375,
-0.0310516357421875,
-0.0196685791015625,
-0.0036487579345703125,
-0.0372314453125,
0.012420654296875,
0.005229949951171875,
-0.00749969482421875,
0.00354766845703125,
-0.0197601318359375,
0.01183319091796875,
-0.0095672607421875,
0.00335693359375,
0.0041046142578125,
0.046295166015625,
0.00865936279296875,
-0.0013027191162109375,
-0.024322509765625,
0.027435302734375,
-0.004711151123046875,
-0.0226898193359375,
-0.0181884765625,
0.0015649795532226562,
-0.013031005859375,
0.0031147003173828125,
-0.0268402099609375,
-0.03375244140625,
-0.014434814453125,
-0.01186370849609375,
0.0009202957153320312,
0.0312347412109375,
-0.0117645263671875,
0.004070281982421875,
-0.0086669921875,
0.00943756103515625,
0.012969970703125,
0.00241851806640625,
0.003238677978515625,
0.00931549072265625,
-0.01215362548828125,
0.0153656005859375,
0.037445068359375,
-0.0238494873046875,
0.0157623291015625,
-0.03741455078125,
0.01092529296875,
0.03460693359375,
-0.034576416015625,
-0.00461578369140625,
-0.0020885467529296875,
0.0176849365234375,
-0.039398193359375,
-0.03173828125,
0.0059051513671875,
0.0019969940185546875,
0.01078033447265625,
-0.0169219970703125,
-0.0004107952117919922,
-0.01174163818359375,
-0.0026702880859375,
-0.027313232421875,
0.0264892578125,
0.005344390869140625,
-0.0240020751953125,
0.01129150390625,
0.0308380126953125,
0.056610107421875,
-0.0103912353515625,
-0.0157623291015625,
-0.0018625259399414062,
-0.0031890869140625,
-0.001644134521484375,
0.020233154296875,
-0.01497650146484375,
-0.0030689239501953125,
0.0201873779296875,
0.019012451171875,
-0.032562255859375,
0.0159149169921875,
0.0244293212890625,
-0.0256805419921875,
0.039459228515625,
-0.007564544677734375,
0.004871368408203125,
-0.00824737548828125,
-0.0004978179931640625,
-0.01375579833984375,
-0.0018415451049804688,
0.0016422271728515625,
0.01514434814453125,
0.0030536651611328125,
-0.0675048828125,
0.003635406494140625,
-0.020416259765625,
0.0200958251953125,
-0.0131378173828125,
0.0207366943359375,
0.0157012939453125,
-0.0014495849609375,
-0.004451751708984375,
0.00923919677734375,
0.02685546875,
0.00494384765625,
-0.0015888214111328125,
0.006061553955078125,
0.004169464111328125,
0.02691650390625,
0.008270263671875,
0.00499725341796875,
0.002735137939453125,
0.019500732421875,
-0.0016298294067382812,
-0.014617919921875,
-0.030426025390625,
0.005413055419921875,
-0.0193634033203125,
0.036346435546875,
-0.0164642333984375,
0.004901885986328125,
0.0024242401123046875,
0.00630950927734375,
-0.01457977294921875,
-0.03302001953125,
0.0188446044921875,
-0.00142669677734375,
-0.0277099609375,
-0.0020465850830078125,
0.01488494873046875,
0.039703369140625,
-0.0010805130004882812,
0.0264129638671875,
0.0226287841796875,
0.0035419464111328125,
-0.029205322265625,
-0.02215576171875,
-0.0112457275390625,
-0.0423583984375,
0.00881195068359375,
0.01367950439453125,
-0.0311279296875,
0.029510498046875,
0.035400390625,
-0.01593017578125,
-0.056549072265625,
0.006885528564453125,
-0.0109100341796875,
-0.01136016845703125,
-0.000008702278137207031,
-0.00959014892578125,
0.00609588623046875,
-0.04132080078125,
-0.01082611083984375,
-0.021759033203125,
-0.0059814453125,
0.014251708984375,
0.003932952880859375,
-0.0305023193359375,
0.019012451171875,
0.0305633544921875,
-0.00998687744140625,
-0.016204833984375,
-0.0059051513671875,
0.008026123046875,
-0.040435791015625,
0.035003662109375,
0.022369384765625,
-0.0182952880859375,
-0.00814056396484375,
-0.033416748046875,
0.030731201171875,
0.012725830078125,
-0.007587432861328125,
0.015960693359375,
-0.00862884521484375,
0.00765228271484375,
0.005649566650390625,
-0.014678955078125,
-0.02716064453125,
0.01456451416015625,
-0.01261138916015625,
0.010955810546875,
-0.037750244140625,
0.01617431640625,
0.00023984909057617188,
-0.038330078125,
-0.04339599609375,
-0.0094451904296875,
-0.01044464111328125,
-0.0165557861328125,
-0.00849151611328125,
0.0134735107421875,
0.0017070770263671875,
0.0032176971435546875,
-0.006595611572265625,
-0.0036220550537109375,
0.035919189453125,
-0.0197296142578125,
-0.0224456787109375,
-0.0116424560546875,
0.01512908935546875,
-0.02178955078125,
-0.00028061866760253906,
0.0205078125,
-0.0005254745483398438,
-0.00951385498046875,
-0.005626678466796875,
0.00713348388671875,
0.02099609375,
0.00982666015625,
-0.0140380859375,
0.01239013671875,
-0.022247314453125,
0.00835418701171875,
-0.01183319091796875,
-0.0189056396484375,
0.015716552734375,
-0.0226593017578125,
0.005504608154296875,
0.00576019287109375,
0.002895355224609375,
-0.0159759521484375,
-0.0017004013061523438,
0.0265045166015625,
0.0193328857421875,
-0.00850677490234375,
-0.01226043701171875,
0.0208282470703125,
-0.00682830810546875,
-0.00811767578125,
-0.039825439453125,
0.021484375,
-0.01690673828125,
0.01419830322265625,
-0.0401611328125,
-0.013153076171875,
0.03411865234375,
0.022247314453125,
0.044219970703125,
0.00685882568359375,
0.01751708984375,
-0.019744873046875,
-0.0252532958984375,
-0.031707763671875,
-0.0098876953125,
0.0035152435302734375,
-0.0135345458984375,
-0.0007829666137695312,
-0.0028076171875,
0.023284912109375,
-0.00640869140625,
-0.029022216796875,
-0.0065765380859375,
-0.010833740234375,
-0.00241851806640625,
0.036102294921875,
0.0049285888671875,
-0.01056671142578125,
0.0379638671875,
-0.02197265625,
-0.01215362548828125,
-0.0037250518798828125,
-0.00811767578125,
0.01284027099609375,
0.0011663436889648438,
0.057586669921875,
-0.0200042724609375,
0.007785797119140625,
-0.02227783203125,
0.01068115234375,
-0.0128173828125,
0.00719451904296875,
-0.0026416778564453125,
-0.0017728805541992188,
-0.00783538818359375,
0.01479339599609375,
0.0213165283203125,
-0.01708984375,
-0.0235137939453125,
-0.006526947021484375,
-0.05218505859375,
-0.015838623046875,
-0.0350341796875,
-0.0253143310546875,
-0.01334381103515625,
0.0263824462890625,
-0.049102783203125,
0.019927978515625,
0.00835418701171875,
0.00025177001953125,
0.032623291015625,
0.0251007080078125,
-0.01541900634765625,
-0.0162811279296875,
-0.0223541259765625,
-0.0031261444091796875,
-0.0230560302734375,
-0.007434844970703125,
0.0287017822265625,
-0.01335906982421875,
0.01268768310546875,
-0.0080108642578125,
0.01404571533203125,
-0.0138092041015625,
0.007404327392578125,
0.01557159423828125,
-0.0170135498046875,
-0.039337158203125,
-0.004787445068359375,
0.01184844970703125,
-0.003475189208984375,
0.00434112548828125,
0.038604736328125,
-0.002559661865234375,
0.002460479736328125,
0.0287933349609375,
-0.0305328369140625,
0.0258331298828125,
-0.01381683349609375,
0.041900634765625,
-0.0009794235229492188,
-0.027191162109375,
0.0031299591064453125,
0.016326904296875,
-0.0088043212890625,
-0.01470184326171875,
0.024658203125,
0.0083770751953125,
-0.0254974365234375,
0.0007867813110351562,
-0.027252197265625,
0.0104217529296875,
-0.03179931640625,
0.03350830078125,
-0.0182952880859375,
-0.0177459716796875,
0.03094482421875,
0.0239105224609375,
-0.01470947265625,
0.0174713134765625,
0.00736236572265625,
-0.004241943359375,
-0.0096588134765625,
0.007778167724609375,
-0.01312255859375,
0.0237884521484375,
0.03228759765625,
-0.0103759765625,
0.01806640625,
-0.0197601318359375,
0.024810791015625,
-0.041900634765625,
-0.031280517578125,
-0.00469207763671875,
0.035400390625,
-0.04022216796875,
-0.01166534423828125,
-0.007427215576171875,
0.0137939453125,
0.006778717041015625,
-0.0206298828125,
0.010162353515625,
-0.004734039306640625,
-0.0007567405700683594,
-0.015380859375,
-0.0016336441040039062,
-0.0322265625,
-0.007450103759765625,
0.0311126708984375,
-0.00821685791015625,
-0.0088653564453125,
0.0015506744384765625,
0.009429931640625,
0.0014133453369140625,
0.01015472412109375,
-0.0167388916015625,
0.0137786865234375,
0.033538818359375,
0.0137481689453125,
-0.0064544677734375,
0.0291748046875,
0.0038318634033203125,
-0.0011148452758789062,
0.0141754150390625,
0.0188446044921875,
-0.0013208389282226562,
0.0104217529296875,
-0.005573272705078125,
0.023101806640625,
-0.00885009765625,
-0.0184478759765625,
0.0246124267578125,
0.022064208984375,
-0.00033283233642578125,
0.01323699951171875,
-0.01922607421875,
0.006145477294921875,
0.01503753662109375,
-0.01654052734375,
-0.01377105712890625,
0.01300048828125,
-0.002941131591796875,
0.037261962890625,
0.0247955322265625,
0.0037364959716796875,
0.02557373046875,
0.041290283203125,
0.0007843971252441406,
0.0477294921875,
-0.0169525146484375,
-0.021240234375,
-0.0221405029296875,
0.017059326171875,
0.007198333740234375,
-0.01318359375,
0.027374267578125,
0.005245208740234375,
0.0034503936767578125,
-0.0197296142578125,
-0.03204345703125,
-0.0012531280517578125,
-0.01837158203125,
-0.01433563232421875,
-0.0113372802734375,
0.00628662109375,
0.0201568603515625,
-0.0171356201171875,
0.04486083984375,
-0.00737762451171875,
-0.01031494140625,
0.0180206298828125,
-0.0038051605224609375,
-0.00748443603515625,
0.0031681060791015625,
-0.00821685791015625,
-0.0064697265625,
-0.0023479461669921875,
0.051605224609375,
0.00897216796875,
-0.016204833984375,
0.0022296905517578125,
-0.01336669921875,
-0.0179595947265625,
0.0011768341064453125,
-0.03375244140625,
0.0111083984375,
0.024658203125,
-0.0185699462890625,
-0.0216522216796875,
0.005596160888671875,
0.007259368896484375,
-0.01108551025390625,
-0.0237274169921875,
-0.0114898681640625,
0.0185546875,
-0.00931549072265625,
0.004322052001953125,
0.035369873046875,
-0.003452301025390625,
0.0060577392578125,
-0.001750946044921875,
0.0252227783203125,
-0.0008182525634765625,
-0.005764007568359375,
-0.00179290771484375,
-0.03118896484375,
0.01407623291015625,
0.00785064697265625,
-0.0229034423828125,
0.00856781005859375,
0.0301666259765625,
0.005779266357421875,
-0.0289764404296875,
0.0279083251953125,
0.0035190582275390625,
0.0040130615234375,
0.01355743408203125,
0.0159454345703125,
0.005207061767578125,
-0.01258087158203125,
-0.00933837890625,
-0.0009140968322753906,
-0.029632568359375,
0.00335693359375,
-0.01012420654296875,
0.01129913330078125,
0.005596160888671875,
0.03240966796875,
0.0242919921875,
-0.00266265869140625,
-0.04937744140625,
0.004100799560546875,
-0.0120849609375,
-0.019256591796875,
-0.0018129348754882812,
-0.01042938232421875,
-0.01751708984375,
0.007556915283203125,
-0.0245819091796875,
0.02728271484375,
0.009033203125,
-0.01456451416015625,
0.01096343994140625,
0.00031304359436035156,
0.0082550048828125,
0.03546142578125,
0.016265869140625,
-0.006816864013671875,
-0.0021648406982421875,
0.008880615234375,
-0.01511383056640625,
-0.002162933349609375,
0.038421630859375,
-0.0230560302734375,
0.007720947265625,
0.02655029296875,
0.01134490966796875,
0.04412841796875,
-0.011749267578125,
-0.04962158203125,
0.006664276123046875,
-0.01143646240234375,
0.01763916015625,
-0.01763916015625,
0.0341796875,
-0.024322509765625,
0.0196075439453125,
0.0209808349609375,
0.025054931640625,
0.0291290283203125,
-0.0111236572265625,
0.00684356689453125,
-0.015838623046875,
-0.0005030632019042969,
-0.01861572265625,
-0.0248565673828125,
-0.0115203857421875,
-0.005466461181640625,
0.01080322265625,
-0.0090484619140625,
-0.0079803466796875,
-0.03173828125,
-0.0261993408203125,
-0.00830841064453125,
0.00027942657470703125,
-0.03424072265625,
-0.0194549560546875,
-0.0174407958984375,
-0.0121307373046875,
0.026397705078125,
-0.00724029541015625,
-0.0008978843688964844,
-0.01337432861328125,
-0.029327392578125,
0.00206756591796875,
0.0185394287109375,
-0.026275634765625,
0.01050567626953125,
0.0013055801391601562,
-0.002391815185546875,
0.01349639892578125,
-0.0009360313415527344,
-0.004970550537109375,
0.020843505859375,
0.037933349609375,
-0.01000213623046875,
0.002834320068359375,
-0.007049560546875,
-0.0081787109375,
0.00522613525390625,
0.01465606689453125,
-0.0203399658203125,
0.0200347900390625,
-0.001373291015625,
0.004688262939453125,
0.01412200927734375,
0.001979827880859375,
-0.0173797607421875,
0.009765625,
-0.02349853515625,
-0.0008826255798339844,
-0.0295562744140625,
0.0106201171875,
-0.02191162109375,
0.0206146240234375,
-0.006839752197265625,
-0.01678466796875,
0.0022678375244140625,
0.01190185546875,
0.006122589111328125,
-0.0187225341796875,
0.001499176025390625,
-0.0274200439453125,
-0.031951904296875,
-0.010589599609375,
-0.050872802734375,
-0.0301055908203125,
-0.022186279296875,
-0.0311126708984375,
-0.02215576171875,
0.0020084381103515625,
0.007503509521484375,
0.0296173095703125,
0.022247314453125,
-0.0236358642578125,
-0.00372314453125,
-0.005496978759765625,
0.012542724609375,
-0.006473541259765625,
0.00041365623474121094,
-0.01265716552734375,
-0.004535675048828125,
-0.01160430908203125,
-0.005096435546875,
-0.0230865478515625,
-0.0152130126953125,
-0.0166168212890625,
-0.01146697998046875,
0.0192718505859375,
0.0009188652038574219,
0.007335662841796875,
-0.00909423828125,
0.0144500732421875,
-0.006206512451171875,
-0.01375579833984375,
-0.0035343170166015625,
0.006099700927734375,
0.00849151611328125,
0.04595947265625,
-0.0222625732421875,
-0.01091766357421875,
-0.0170135498046875,
0.017303466796875,
-0.027130126953125,
0.0166473388671875,
-0.037628173828125,
-0.024139404296875,
-0.02294921875,
0.018402099609375,
-0.0005502700805664062,
0.029205322265625,
0.00004875659942626953,
-0.002422332763671875,
-0.0245361328125,
-0.024658203125,
-0.005035400390625,
0.04766845703125,
0.0205841064453125,
-0.0567626953125,
-0.040771484375,
0.0171356201171875,
-0.0153656005859375,
-0.022796630859375,
0.003948211669921875,
0.0035305023193359375,
-0.0232391357421875,
-0.01032257080078125,
0.0229034423828125,
0.0229644775390625,
-0.0193023681640625,
-0.0007205009460449219,
0.0224609375,
0.0301055908203125,
-0.00638580322265625,
0.005084991455078125,
0.0156097412109375,
-0.005092620849609375,
0.0014238357543945312,
-0.0114593505859375,
-0.005748748779296875,
0.00539398193359375,
-0.0219573974609375,
0.0099639892578125,
0.006969451904296875,
0.0251312255859375,
0.0036334991455078125,
0.01617431640625,
0.0023097991943359375,
-0.0203704833984375,
0.017181396484375,
-0.01296234130859375,
-0.0057525634765625,
-0.004276275634765625,
-0.0034198760986328125,
-0.0012769699096679688,
0.006622314453125,
-0.01227569580078125,
-0.0298919677734375,
0.01947021484375,
-0.02239990234375,
0.006664276123046875,
0.006328582763671875,
-0.01055908203125,
0.01390838623046875,
0.0147705078125,
-0.017578125,
-0.01126861572265625,
0.0311431884765625,
0.0160675048828125,
-0.005397796630859375,
0.009918212890625,
-0.00489044189453125,
0.02508544921875,
-0.0013065338134765625,
-0.0230255126953125,
0.0221099853515625,
-0.0195770263671875,
0.01849365234375,
-0.007640838623046875,
0.004222869873046875,
0.004856109619140625,
0.03033447265625,
-0.00405120849609375,
-0.0151214599609375,
0.014984130859375,
0.0003159046173095703,
0.0150146484375,
-0.0006237030029296875,
-0.0391845703125,
0.0170135498046875,
0.029754638671875,
0.0357666015625,
-0.0188446044921875,
-0.0018949508666992188,
0.0017948150634765625,
0.01256561279296875,
-0.037261962890625,
0.020782470703125,
0.0025463104248046875,
0.0151824951171875,
0.0028247833251953125,
0.01351165771484375,
0.0118255615234375,
0.01373291015625,
0.036712646484375,
0.0156707763671875,
-0.01247406005859375,
-0.0091552734375,
0.0084991455078125,
0.03912353515625,
0.0178985595703125,
-0.0119781494140625,
0.0267181396484375,
0.057708740234375,
-0.0137939453125,
-0.03472900390625,
-0.0101318359375,
-0.005123138427734375,
-0.0074005126953125,
0.005352020263671875,
0.0115203857421875,
0.03955078125,
-0.00725555419921875,
-0.01396942138671875,
0.0020694732666015625,
0.0274810791015625,
-0.01495361328125,
0.020294189453125,
-0.017791748046875,
0.0054779052734375,
0.0035266876220703125,
0.000013053417205810547,
0.0008225440979003906,
0.0032196044921875,
-0.005413055419921875,
0.0181732177734375,
-0.002445220947265625,
0.0251922607421875,
0.0224761962890625,
-0.0190887451171875,
-0.0010805130004882812,
-0.0203857421875,
-0.005641937255859375,
0.01776123046875,
0.01311492919921875,
-0.01435089111328125,
0.015838623046875,
0.0034160614013671875,
-0.0022525787353515625,
-0.004535675048828125,
0.0021114349365234375,
0.04229736328125,
0.0440673828125,
0.005947113037109375,
0.04986572265625,
0.01433563232421875,
0.0141448974609375,
-0.0054779052734375,
0.0360107421875,
0.01078033447265625,
-0.03338623046875,
-0.0284576416015625,
0.00075531005859375,
0.0273895263671875,
-0.01397705078125,
0.0133056640625,
-0.0043182373046875,
0.038909912109375,
-0.0003609657287597656,
-0.01485443115234375,
-0.007686614990234375,
0.03271484375,
-0.00841522216796875,
0.01776123046875,
-0.005893707275390625,
0.0017461776733398438,
0.0014476776123046875,
-0.0316162109375,
-0.00833892822265625,
0.0211334228515625,
-0.01519775390625,
0.0006189346313476562,
0.028961181640625,
-0.0123138427734375,
0.0174713134765625,
-0.0044403076171875,
0.0260009765625,
0.005916595458984375,
-0.00811767578125,
-0.016632080078125,
0.0033245086669921875,
0.013336181640625,
0.007625579833984375,
-0.0011730194091796875,
-0.0207672119140625,
0.0149383544921875,
0.0265350341796875,
-0.006122589111328125,
-0.0186767578125,
0.022979736328125,
0.01070404052734375,
-0.0011835098266601562,
-0.02325439453125,
-0.019317626953125,
-0.0190582275390625,
-0.0294952392578125,
-0.03826904296875,
0.0013799667358398438,
-0.006977081298828125,
0.00012934207916259766,
-0.0313720703125,
0.03125,
0.0146026611328125,
-0.0210113525390625,
-0.001434326171875,
-0.052001953125,
-0.000017404556274414062,
-0.01084136962890625,
0.0200042724609375,
-0.034698486328125,
0.01349639892578125,
-0.00583648681640625,
-0.00835418701171875,
-0.0146942138671875,
-0.003795623779296875,
-0.0011644363403320312,
0.01678466796875,
0.0310211181640625,
0.00019097328186035156,
0.00946044921875,
0.0196685791015625,
0.00794219970703125,
-0.01139068603515625,
0.022613525390625,
0.0015802383422851562,
0.024658203125,
0.01114654541015625,
-0.0090789794921875,
0.0055999755859375,
0.0288848876953125,
0.01194000244140625,
0.0003020763397216797,
-0.0257110595703125,
-0.035064697265625,
0.0313720703125,
-0.04034423828125,
-0.003292083740234375,
0.039306640625,
0.0037078857421875,
0.00690460205078125,
0.0282135009765625,
0.02813720703125,
-0.007526397705078125,
-0.023651123046875,
-0.0036487579345703125,
-0.01349639892578125,
0.01213836669921875,
-0.020782470703125,
0.041961669921875,
-0.0206756591796875,
0.00019407272338867188,
-0.008514404296875,
0.051483154296875,
-0.02362060546875,
-0.0003628730773925781,
-0.032379150390625,
0.002948760986328125,
0.0025005340576171875,
0.019195556640625,
-0.0026035308837890625,
0.01519012451171875,
0.00009924173355102539,
-0.017486572265625,
-0.0011844635009765625,
-0.0012598037719726562,
-0.00412750244140625,
-0.0290374755859375,
-0.01666259765625,
0.0203857421875,
-0.01503753662109375,
-0.036041259765625,
0.005771636962890625,
0.0288543701171875,
0.01389312744140625,
-0.0150909423828125,
-0.02777099609375,
0.0228271484375,
-0.021209716796875,
-0.031494140625,
-0.01421356201171875,
0.017547607421875,
-0.0173797607421875,
-0.011383056640625,
0.0038051605224609375,
0.006160736083984375,
-0.009918212890625,
0.01346588134765625,
0.0269927978515625,
0.0149078369140625,
0.0183258056640625,
-0.0119781494140625,
0.024322509765625,
-0.0124969482421875,
-0.01554107666015625,
0.01000213623046875,
-0.01025390625,
0.0299835205078125,
0.033050537109375,
0.0242767333984375,
0.002529144287109375,
0.0197906494140625,
0.0179290771484375,
-0.00823211669921875,
-0.01277923583984375,
0.0097503662109375,
0.030548095703125,
0.0233917236328125,
0.01287841796875,
0.0298614501953125,
-0.00560760498046875,
0.01053619384765625,
-0.00414276123046875,
0.01519775390625,
-0.00698089599609375,
-0.006504058837890625,
-0.008941650390625,
0.0113983154296875,
0.0055084228515625,
-0.02996826171875,
0.022125244140625,
-0.01010894775390625,
-0.0081024169921875,
0.00921630859375,
0.003795623779296875,
-0.01229095458984375,
0.0022068023681640625,
-0.0159912109375,
-0.0277557373046875,
-0.00916290283203125,
0.01427459716796875,
-0.008697509765625,
0.0035152435302734375,
0.041961669921875,
0.021209716796875,
0.0478515625,
0.03460693359375,
0.000865936279296875,
-0.0203399658203125,
-0.0252532958984375,
0.004150390625,
-0.002658843994140625,
-0.0034427642822265625,
-0.043914794921875,
-0.0399169921875,
-0.01441192626953125,
-0.0013036727905273438,
-0.004878997802734375,
-0.0019779205322265625,
-0.0007719993591308594,
-0.0001919269561767578,
0.0125579833984375,
0.02337646484375,
-0.02301025390625,
0.03125,
0.040313720703125,
0.00897979736328125,
-0.03350830078125,
-0.0289306640625,
-0.02435302734375,
0.002208709716796875,
-0.0205841064453125,
-0.031402587890625,
-0.03466796875,
0.00458526611328125,
-0.01611328125,
0.026092529296875,
0.019195556640625,
0.03521728515625,
0.039276123046875,
-0.014892578125,
0.0177001953125,
-0.01128387451171875,
-0.041107177734375,
0.010406494140625,
0.032073974609375,
-0.0419921875,
0.0105133056640625,
0.026275634765625,
0.002292633056640625,
-0.008026123046875,
-0.007266998291015625,
0.032379150390625,
-0.0006890296936035156,
0.0083465576171875,
-0.009552001953125,
-0.00751495361328125,
0.00400543212890625,
-0.039031982421875,
-0.01271820068359375,
0.0107269287109375,
-0.007602691650390625,
0.014892578125,
-0.005237579345703125,
0.002590179443359375,
0.0204925537109375,
-0.00977325439453125,
0.001148223876953125,
-0.007965087890625,
-0.0207061767578125,
0.0064239501953125,
0.00963592529296875,
-0.018646240234375,
0.042694091796875,
-0.0024433135986328125,
-0.01158905029296875,
0.0141754150390625,
0.01849365234375,
-0.0285797119140625,
0.03277587890625,
0.00873565673828125,
0.012786865234375,
0.017120361328125,
-0.02423095703125,
0.0031280517578125,
-0.020599365234375,
0.0008244514465332031,
0.0157928466796875,
-0.033203125,
0.022064208984375,
-0.0116424560546875,
0.01224517822265625,
0.0015420913696289062,
-0.028839111328125,
0.0159759521484375,
-0.007354736328125,
0.000308990478515625,
-0.00899505615234375,
-0.00960540771484375,
-0.00977325439453125,
-0.0008749961853027344,
-0.005229949951171875,
-0.0129852294921875,
-0.0355224609375,
0.029052734375,
0.01678466796875,
-0.0008769035339355469,
-0.01102447509765625,
-0.015289306640625,
-0.020263671875,
0.0192413330078125,
0.01380157470703125,
0.01495361328125,
-0.00310516357421875,
-0.00010281801223754883,
0.01214599609375,
-0.031494140625,
0.027587890625,
-0.006290435791015625,
-0.01442718505859375,
0.01265716552734375,
-0.00667572021484375,
0.00695037841796875,
-0.0213165283203125,
-0.01465606689453125,
-0.00994873046875,
0.0117034912109375,
-0.00853729248046875,
-0.003902435302734375,
0.0101470947265625,
-0.0185699462890625,
0.01158905029296875,
0.015533447265625,
0.0164642333984375,
-0.0138702392578125,
-0.029937744140625,
0.005496978759765625,
0.01153564453125,
-0.035186767578125,
-0.01461029052734375,
0.0176239013671875,
0.007205963134765625,
-0.009185791015625,
0.0136566162109375,
-0.0019502639770507812,
-0.0307464599609375,
-0.020721435546875,
-0.005939483642578125,
-0.0155029296875,
-0.00982666015625,
-0.0028896331787109375,
0.0046844482421875,
-0.005023956298828125,
-0.01403045654296875,
0.004154205322265625,
0.0002048015594482422,
-0.019073486328125,
-0.014007568359375,
-0.0304412841796875,
0.0040740966796875,
0.006641387939453125,
0.036163330078125,
-0.02703857421875,
-0.0164794921875,
-0.0200958251953125,
-0.0197601318359375,
-0.00717926025390625,
-0.00894927978515625,
0.02703857421875,
0.02691650390625,
-0.01531219482421875,
-0.004116058349609375,
0.0260772705078125,
0.0194244384765625,
-0.056915283203125,
-0.01163482666015625,
-0.02728271484375,
-0.0301055908203125,
0.00798797607421875,
0.004302978515625,
-0.019683837890625,
0.0304718017578125,
0.0004780292510986328,
0.00643157958984375,
0.02490234375,
-0.0148773193359375,
-0.0325927734375,
-0.0007328987121582031,
-0.0161590576171875,
0.003818511962890625,
0.0006175041198730469,
0.023406982421875,
-0.016632080078125,
0.0167083740234375,
-0.0127410888671875,
-0.03692626953125,
0.004222869873046875,
0.06475830078125,
0.00214385986328125,
0.01517486572265625,
-0.01168060302734375,
0.00376129150390625,
-0.0007524490356445312,
0.0185699462890625,
-0.0159454345703125,
-0.00229644775390625,
-0.0233306884765625,
0.034271240234375,
0.00200653076171875,
-0.017913818359375,
0.0003075599670410156,
0.00780487060546875,
-0.0006985664367675781,
-0.00673675537109375,
-0.00768280029296875,
0.0121002197265625,
-0.00797271728515625,
-0.00525665283203125,
-0.02020263671875,
-0.0305633544921875,
0.0251922607421875,
-0.002162933349609375,
-0.0157470703125,
0.01082611083984375,
0.00041103363037109375,
0.025360107421875,
-0.00012218952178955078,
0.067138671875,
0.0157012939453125,
-0.034637451171875,
0.0015115737915039062,
0.0028171539306640625,
0.01983642578125,
0.0003275871276855469,
0.0001691579818725586,
0.0081787109375,
-0.01519012451171875,
0.00667572021484375,
0.006290435791015625,
-0.019287109375,
-0.0015420913696289062,
0.0112457275390625,
-0.026885986328125,
-0.0218963623046875,
0.02288818359375,
-0.01009368896484375,
0.03399658203125,
0.007080078125,
-0.002651214599609375,
-0.01161956787109375,
-0.017486572265625,
0.01132965087890625,
0.00568389892578125,
-0.00856781005859375,
0.01849365234375,
0.01210784912109375,
0.0190582275390625,
0.00759124755859375,
-0.00850677490234375,
-0.0023651123046875,
0.0245513916015625,
-0.042999267578125,
0.0121307373046875,
0.00707244873046875,
-0.0024852752685546875,
-0.032867431640625,
0.0158233642578125,
-0.0093994140625,
0.01448822021484375,
0.00653839111328125,
0.0205078125,
-0.0292205810546875,
0.0192413330078125,
-0.0015506744384765625,
-0.00963592529296875,
-0.0048675537109375,
0.007305145263671875,
0.0104217529296875,
-0.01302337646484375,
-0.0021076202392578125,
-0.04248046875,
-0.024078369140625,
0.0192718505859375,
0.002849578857421875,
0.0087127685546875,
-0.0230712890625,
-0.0199737548828125,
0.00817108154296875,
0.01366424560546875,
0.0019502639770507812,
0.02008056640625,
0.0002071857452392578,
-0.0180511474609375,
0.038116455078125,
-0.03656005859375,
0.0022563934326171875,
0.041107177734375,
-0.0089874267578125,
-0.0013742446899414062,
-0.0022258758544921875,
-0.01125335693359375,
-0.0205841064453125,
-0.0060272216796875,
-0.01288604736328125,
-0.006153106689453125,
0.00661468505859375,
0.011138916015625,
0.04248046875,
0.01557159423828125,
0.02020263671875,
-0.027679443359375,
-0.010772705078125,
0.003101348876953125,
-0.00670623779296875,
0.0020503997802734375,
0.01236724853515625,
-0.0184173583984375,
-0.0203704833984375,
-0.0167694091796875,
0.0088653564453125,
-0.0197296142578125,
0.0012969970703125,
0.025543212890625,
-0.00823211669921875,
0.034576416015625,
-0.0487060546875,
0.00022029876708984375,
0.0021648406982421875,
-0.0004115104675292969,
-0.0043487548828125,
-0.016204833984375,
0.00919342041015625,
-0.00765228271484375,
-0.0088043212890625,
0.0290374755859375,
0.0012722015380859375,
-0.007801055908203125,
0.016204833984375,
-0.0187225341796875,
0.0088348388671875,
-0.0058746337890625,
-0.0219268798828125,
0.01058197021484375,
-0.00897216796875,
-0.0064849853515625,
-0.004314422607421875,
-0.0015468597412109375,
-0.005924224853515625,
0.002849578857421875,
0.00327301025390625,
0.004039764404296875,
0.026123046875,
0.0233612060546875,
0.00557708740234375,
0.0085296630859375,
0.006168365478515625,
-0.012786865234375,
0.00226593017578125,
0.033477783203125,
0.0033969879150390625,
-0.009765625,
-0.0251922607421875,
-0.0173797607421875,
0.004924774169921875,
0.0217742919921875,
0.004123687744140625,
0.00959014892578125,
-0.01255035400390625,
0.0233154296875,
0.0220794677734375,
-0.017364501953125,
-0.0203094482421875,
0.052276611328125,
-0.019805908203125,
0.0028591156005859375,
-0.0017242431640625,
0.04888916015625,
-0.0285797119140625,
0.029876708984375,
-0.0112762451171875,
0.010498046875,
0.0009679794311523438,
0.0474853515625,
0.0051727294921875,
0.0196685791015625,
0.004230499267578125,
0.0116119384765625,
0.00955963134765625,
0.018035888671875,
-0.01181793212890625,
-0.004276275634765625,
0.00923919677734375,
-0.0180511474609375,
-0.031829833984375,
-0.0477294921875,
0.034027099609375,
0.01033782958984375,
-0.0041351318359375,
0.0224456787109375,
0.00055694580078125,
-0.00984954833984375,
-0.03497314453125,
-0.01384735107421875,
0.0272216796875,
0.00479888916015625,
0.02545166015625,
0.032806396484375,
-0.0361328125,
0.006412506103515625,
0.0236053466796875,
-0.0004432201385498047,
0.0238189697265625,
0.00986480712890625,
0.0288848876953125,
-0.0160675048828125,
-0.01605224609375,
-0.01192474365234375,
0.0222320556640625,
0.007503509521484375,
-0.00276947021484375,
-0.033782958984375,
-0.00745391845703125,
-0.00618743896484375,
-0.005931854248046875,
-0.004596710205078125,
-0.004283905029296875,
0.0009369850158691406,
0.021270751953125,
-0.0177154541015625,
-0.0005440711975097656,
0.0020771026611328125,
-0.01096343994140625,
0.042633056640625,
-0.006195068359375,
0.0189208984375,
-0.0219573974609375,
0.01454925537109375,
-0.0386962890625,
0.013092041015625,
-0.0245361328125,
-0.033599853515625,
-0.0235748291015625,
-0.004169464111328125,
-0.0002536773681640625,
-0.03741455078125,
-0.037933349609375,
-0.007587432861328125,
-0.0433349609375,
0.01015472412109375,
0.046539306640625,
0.005374908447265625,
-0.007122039794921875,
-0.01910400390625,
0.01200103759765625,
-0.0030155181884765625,
0.0084228515625,
0.00830841064453125,
0.031951904296875,
-0.00217437744140625,
0.0182342529296875,
0.00689697265625,
0.00988006591796875,
0.00406646728515625,
0.023651123046875,
-0.0012683868408203125,
-0.019927978515625,
-0.04925537109375,
0.00247955322265625,
0.0244598388671875,
0.0207061767578125,
-0.0180511474609375,
-0.0101318359375,
-0.00841522216796875,
0.005268096923828125,
0.006183624267578125,
-0.001621246337890625,
-0.0284881591796875,
-0.004993438720703125,
-0.0165557861328125,
0.020660400390625,
-0.01479339599609375,
0.0165863037109375,
-0.012237548828125,
0.02154541015625,
-0.0149993896484375,
-0.0191497802734375,
-0.03277587890625,
0.00487518310546875,
-0.0163421630859375,
0.0017271041870117188,
0.0027103424072265625,
-0.010498046875,
-0.00423431396484375,
-0.033203125,
0.030487060546875,
0.004138946533203125,
0.0021648406982421875,
0.0214080810546875,
-0.0321044921875,
-0.01207733154296875,
-0.0166778564453125,
-0.03765869140625,
-0.026519775390625,
0.01947021484375,
0.038330078125,
-0.0014553070068359375,
-0.010223388671875,
0.020263671875,
-0.025299072265625,
-0.034942626953125,
-0.0210418701171875,
-0.01548004150390625,
0.0260009765625,
0.0007681846618652344,
-0.019500732421875,
0.0035648345947265625,
0.00887298583984375,
0.00469207763671875,
-0.0093994140625,
-0.00591278076171875,
0.0265045166015625,
-0.0009131431579589844,
-0.025634765625,
-0.0154876708984375,
-0.0262451171875,
0.0149993896484375,
-0.026275634765625,
0.0130767822265625,
-0.01058197021484375,
-0.026824951171875,
-0.0168304443359375,
0.007266998291015625,
-0.040283203125,
0.032867431640625,
0.0097503662109375,
-0.0201873779296875,
-0.00540924072265625,
-0.0159912109375,
-0.012847900390625,
0.0023593902587890625,
-0.032958984375,
-0.00878143310546875,
0.02069091796875,
0.0114898681640625,
-0.004131317138671875,
-0.01204681396484375,
-0.0234222412109375,
-0.0290679931640625,
-0.00847625732421875,
-0.00919342041015625,
-0.041229248046875,
-0.00820159912109375,
-0.018890380859375,
-0.01313018798828125,
0.017822265625,
-0.0018978118896484375,
0.007236480712890625,
0.0220184326171875,
0.004833221435546875,
-0.025604248046875,
0.01363372802734375,
0.020233154296875,
0.00670623779296875,
-0.0261688232421875,
-0.030303955078125,
-0.036895751953125,
0.025848388671875,
-0.0226287841796875,
0.016021728515625,
-0.0168304443359375,
-0.003795623779296875,
0.03802490234375,
-0.037109375,
0.019775390625,
-0.0032405853271484375,
0.047760009765625,
0.0076751708984375,
-0.03802490234375,
0.0029544830322265625,
-0.02752685546875,
0.01300811767578125,
-0.01403045654296875,
-0.0036029815673828125,
-0.0021533966064453125,
0.01467132568359375,
0.0015592575073242188,
0.041900634765625,
0.0093536376953125,
0.01366424560546875,
-0.017364501953125,
-0.0111083984375,
0.0290679931640625,
-0.007526397705078125,
-0.0011444091796875,
0.0160064697265625,
0.02117919921875,
0.03143310546875,
-0.005199432373046875,
-0.0272369384765625,
-0.0164337158203125,
0.028900146484375,
-0.02276611328125,
0.004547119140625,
0.01119232177734375,
-0.03302001953125,
-0.039794921875,
0.0078887939453125,
-0.018463134765625,
0.006458282470703125,
0.003337860107421875,
-0.0018892288208007812,
-0.00952911376953125,
-0.00995635986328125,
-0.015106201171875,
0.0269775390625,
0.0290985107421875,
-0.01171112060546875,
-0.0200347900390625,
0.023529052734375,
-0.0018472671508789062,
0.0006132125854492188,
-0.00730133056640625,
0.015289306640625,
-0.0221710205078125,
-0.0252227783203125,
0.016204833984375,
0.022003173828125,
0.0267333984375,
-0.035491943359375,
-0.0188140869140625,
-0.020477294921875,
0.0276336669921875,
0.0182037353515625,
-0.037872314453125,
-0.014617919921875,
0.0182952880859375,
-0.008270263671875,
0.023345947265625,
-0.01078033447265625,
0.02178955078125,
0.047027587890625,
-0.01016998291015625,
0.0145416259765625,
0.0142822265625,
0.055572509765625,
-0.021087646484375,
-0.010345458984375,
-0.0239410400390625,
0.00910186767578125,
0.0594482421875,
0.016632080078125,
0.0029354095458984375,
0.01444244384765625,
-0.004947662353515625,
-0.0165557861328125,
0.0305023193359375,
-0.007381439208984375,
0.018951416015625,
-0.0128631591796875,
-0.0301055908203125,
-0.0196533203125,
-0.0261688232421875,
0.0239105224609375,
-0.01277923583984375,
-0.01158905029296875,
0.01436614990234375,
-0.006572723388671875,
-0.0092315673828125,
0.02349853515625,
-0.052276611328125,
0.0013742446899414062,
0.0004093647003173828,
-0.0033359527587890625,
-0.013946533203125,
0.00809478759765625,
-0.007686614990234375,
-0.0187530517578125,
-0.0021495819091796875,
0.0257720947265625,
-0.0033740997314453125,
-0.0357666015625,
-0.038482666015625,
0.0296478271484375,
0.0185394287109375,
-0.0175933837890625,
-0.025543212890625,
-0.0210113525390625,
0.00946044921875,
-0.00270843505859375,
0.0088348388671875,
-0.01806640625,
-0.01036834716796875,
-0.0165252685546875,
-0.0160064697265625,
-0.015655517578125,
-0.0057830810546875,
-0.0195770263671875,
0.0004341602325439453,
0.01079559326171875,
0.02783203125,
-0.043426513671875,
0.0284423828125,
0.023040771484375,
-0.00830841064453125,
0.01345062255859375,
-0.0253753662109375,
-0.00650787353515625,
-0.0288238525390625,
-0.006984710693359375,
0.01605224609375,
-0.0156097412109375,
-0.02520751953125,
-0.004150390625,
-0.00868988037109375,
0.01486968994140625,
-0.00040268898010253906,
-0.0123748779296875,
-0.0216827392578125,
0.0294647216796875,
0.01540374755859375,
0.01181793212890625,
0.0173187255859375,
0.010101318359375,
-0.01149749755859375,
0.01253509521484375,
-0.0008053779602050781,
0.0023021697998046875,
-0.014617919921875,
0.025543212890625,
0.0008378028869628906,
0.01446533203125,
-0.01471710205078125,
-0.0202484130859375,
-0.0167999267578125,
0.0130462646484375,
0.0167999267578125,
0.010040283203125,
0.0184173583984375,
0.005092620849609375,
-0.006343841552734375,
-0.00580596923828125,
0.01007080078125,
0.012115478515625,
0.0217132568359375,
0.004985809326171875,
0.007354736328125,
0.0027027130126953125,
0.0401611328125,
0.0313720703125,
0.019317626953125,
-0.01366424560546875,
0.00765228271484375,
0.007503509521484375,
0.022430419921875,
0.0008668899536132812
] |
ours_540
|
There are 5 ways to choose a pair, then 8 ways to choose the remaining sock, giving a probability of
\[
\frac{5 \cdot 8}{\binom{10}{3}} = \frac{1}{3}
\]
Thus, the answer is \(1 + 3 = 4\). Therefore, \(m+n = 4\).
\(\boxed{4}\)
|
4
|
{
"competition": "us_comps",
"dataset": "Ours",
"posts": null,
"source": "OMOSoln2.md"
}
|
A drawer has 5 pairs of socks. Three socks are chosen at random. If the probability that there is a pair among the three is \(\frac{m}{n}\), where \(m\) and \(n\) are relatively prime positive integers, what is \(m+n\)?
|
[
"/Mathematics/DiscreteMathematics/Combinatorics/BinomialCoefficients",
"/Mathematics/DiscreteMathematics/Combinatorics/Enumeration",
"/Mathematics/DiscreteMathematics/Combinatorics/GeneralCombinatorics",
"/Mathematics/DiscreteMathematics/GeneralDiscreteMathematics/ConcreteMath",
"/Mathematics/DiscreteMathematics/GeneralDiscreteMathematics/ConcreteMathematics",
"/Mathematics/DiscreteMathematics/GeneralDiscreteMathematics/DiscreteMath",
"/Mathematics/DiscreteMathematics/GeneralDiscreteMathematics/DiscreteMathematics",
"/Mathematics/DiscreteMathematics/GeneralDiscreteMathematics/FiniteMathematics",
"/Mathematics/ProbabilityandStatistics/Probability"
] |
Count favourable 3‑sock selections by picking which pair occurs (5 ways) and then any third sock (8 ways), then divide by total combinations.
|
[
0.00007408857345581055,
-0.0257415771484375,
0.052093505859375,
-0.0256805419921875,
0.0006837844848632812,
-0.00443267822265625,
0.056243896484375,
-0.033966064453125,
0.00775146484375,
-0.0033168792724609375,
-0.017303466796875,
-0.0209503173828125,
-0.004077911376953125,
-0.061553955078125,
-0.0226287841796875,
-0.0195770263671875,
0.0279541015625,
0.021942138671875,
-0.018218994140625,
0.0018129348754882812,
-0.0093231201171875,
-0.02313232421875,
-0.013275146484375,
0.0124053955078125,
-0.0216217041015625,
-0.01137542724609375,
-0.0141448974609375,
0.0308685302734375,
-0.007038116455078125,
-0.002590179443359375,
-0.02276611328125,
-0.0223541259765625,
0.0150299072265625,
-0.0266571044921875,
-0.0028972625732421875,
0.0116424560546875,
0.01202392578125,
-0.00047278404235839844,
0.01006317138671875,
-0.025848388671875,
0.00457000732421875,
0.03155517578125,
0.00247955322265625,
0.0163726806640625,
0.01120758056640625,
-0.009552001953125,
-0.00044465065002441406,
0.01149749755859375,
0.007404327392578125,
-0.002468109130859375,
-0.0079498291015625,
0.005008697509765625,
-0.03564453125,
-0.0014200210571289062,
0.0178070068359375,
-0.0814208984375,
0.0109405517578125,
-0.004974365234375,
-0.01291656494140625,
-0.026031494140625,
-0.0017633438110351562,
-0.0264434814453125,
0.027252197265625,
-0.01192474365234375,
-0.0023345947265625,
-0.008514404296875,
0.0116119384765625,
-0.039276123046875,
0.01297760009765625,
-0.022247314453125,
0.00992584228515625,
0.015960693359375,
-0.0205535888671875,
0.032562255859375,
0.058868408203125,
-0.0056915283203125,
-0.003749847412109375,
0.00693511962890625,
-0.00518035888671875,
0.0248870849609375,
0.01499176025390625,
0.00907135009765625,
-0.0060882568359375,
0.0246429443359375,
0.02459716796875,
0.009765625,
0.00222015380859375,
-0.0023975372314453125,
0.040924072265625,
-0.0031681060791015625,
0.006572723388671875,
0.0211181640625,
-0.01184844970703125,
0.01322174072265625,
-0.004489898681640625,
-0.01102447509765625,
-0.005596160888671875,
-0.0017442703247070312,
-0.0172576904296875,
0.008270263671875,
-0.01294708251953125,
-0.00022518634796142578,
0.058807373046875,
-0.0029506683349609375,
-0.04058837890625,
-0.005802154541015625,
-0.02099609375,
0.01403045654296875,
-0.0155181884765625,
0.0212554931640625,
0.0048370361328125,
0.010772705078125,
0.005161285400390625,
0.00937652587890625,
0.0237884521484375,
0.03271484375,
0.01324462890625,
0.0031223297119140625,
-0.023834228515625,
-0.004150390625,
0.007320404052734375,
0.004032135009765625,
-0.0118865966796875,
0.0016632080078125,
0.00025391578674316406,
0.0384521484375,
-0.004150390625,
-0.02093505859375,
0.0101165771484375,
0.019439697265625,
0.021270751953125,
0.0004508495330810547,
-0.013671875,
-0.004489898681640625,
-0.030731201171875,
0.01549530029296875,
0.00701141357421875,
0.0102386474609375,
-0.0130767822265625,
-0.004169464111328125,
0.012725830078125,
-0.004421234130859375,
-0.0020503997802734375,
-0.0095062255859375,
-0.012176513671875,
0.0213470458984375,
-0.01409912109375,
-0.0272216796875,
-0.0006070137023925781,
0.0009946823120117188,
0.0010213851928710938,
-0.01461029052734375,
-0.00597381591796875,
0.001422882080078125,
-0.0251312255859375,
-0.00125885009765625,
0.0239410400390625,
-0.005435943603515625,
-0.001514434814453125,
0.0035343170166015625,
-0.016754150390625,
-0.0010042190551757812,
0.0202789306640625,
0.0305938720703125,
0.004749298095703125,
0.015350341796875,
-0.0345458984375,
0.018280029296875,
-0.0159454345703125,
0.040740966796875,
0.001323699951171875,
-0.0029010772705078125,
-0.01123046875,
0.001262664794921875,
-0.0086822509765625,
-0.0125732421875,
-0.010711669921875,
0.0196685791015625,
-0.01324462890625,
0.041473388671875,
0.004650115966796875,
-0.023681640625,
0.0131378173828125,
-0.005100250244140625,
0.006549835205078125,
-0.00537872314453125,
-0.0023193359375,
0.0188751220703125,
0.01299285888671875,
0.00665283203125,
-0.042236328125,
-0.045166015625,
-0.01392364501953125,
0.00266265869140625,
-0.00838470458984375,
-0.0217132568359375,
-0.0088958740234375,
-0.004505157470703125,
0.033721923828125,
0.0142974853515625,
0.0301513671875,
-0.00807952880859375,
-0.0103302001953125,
0.0036869049072265625,
0.0006918907165527344,
-0.01172637939453125,
0.00991058349609375,
-0.0011472702026367188,
-0.0000012516975402832031,
0.01004791259765625,
-0.018341064453125,
0.004642486572265625,
-0.01181793212890625,
-0.012176513671875,
-0.00785064697265625,
-0.0017290115356445312,
-0.00832366943359375,
-0.00983428955078125,
0.0011196136474609375,
-0.059967041015625,
-0.01349639892578125,
0.010833740234375,
0.0079193115234375,
-0.0093994140625,
0.006595611572265625,
-0.0123291015625,
0.0003948211669921875,
-0.0011072158813476562,
-0.002307891845703125,
-0.015655517578125,
0.0072174072265625,
-0.0022869110107421875,
0.011993408203125,
0.0010395050048828125,
-0.0008873939514160156,
-0.003986358642578125,
-0.023101806640625,
-0.0281982421875,
0.02874755859375,
-0.00814056396484375,
0.0517578125,
-0.005558013916015625,
-0.0016326904296875,
-0.0150146484375,
-0.0105133056640625,
-0.0014219284057617188,
-0.004657745361328125,
-0.01506805419921875,
0.019073486328125,
-0.0186309814453125,
-0.007476806640625,
0.01250457763671875,
0.0034046173095703125,
-0.0173187255859375,
0.0119476318359375,
-0.00012034177780151367,
0.006710052490234375,
0.0107421875,
-0.00992584228515625,
-0.014617919921875,
-0.01183319091796875,
-0.040863037109375,
-0.0081329345703125,
-0.00836944580078125,
0.0233001708984375,
0.042510986328125,
0.043304443359375,
-0.0008025169372558594,
0.01751708984375,
-0.01171112060546875,
-0.01270294189453125,
-0.0016765594482421875,
-0.00559234619140625,
0.0159759521484375,
-0.012847900390625,
0.0037403106689453125,
0.0010128021240234375,
0.01222991943359375,
0.0126953125,
0.00200653076171875,
-0.0024585723876953125,
0.0164794921875,
-0.0266571044921875,
0.006893157958984375,
0.01690673828125,
0.005580902099609375,
-0.0067596435546875,
-0.0103912353515625,
-0.0281982421875,
-0.00007909536361694336,
0.0091552734375,
0.00998687744140625,
0.0013341903686523438,
-0.005916595458984375,
0.002223968505859375,
-0.0460205078125,
0.0020618438720703125,
-0.0006036758422851562,
0.0222930908203125,
0.0068817138671875,
0.02301025390625,
-0.0100860595703125,
0.003932952880859375,
0.035675048828125,
-0.040435791015625,
0.0138702392578125,
0.00740814208984375,
-0.0276031494140625,
0.050140380859375,
-0.037322998046875,
0.00045800209045410156,
0.0156707763671875,
0.018402099609375,
0.00917816162109375,
0.018096923828125,
-0.03399658203125,
-0.0004982948303222656,
0.0052947998046875,
-0.00887298583984375,
0.041656494140625,
-0.00499725341796875,
-0.040557861328125,
-0.02362060546875,
-0.00815582275390625,
0.058135986328125,
-0.01047515869140625,
-0.004520416259765625,
0.039306640625,
-0.038726806640625,
-0.01033782958984375,
0.016632080078125,
0.02734375,
0.000980377197265625,
-0.0207977294921875,
0.002651214599609375,
0.0286712646484375,
0.0019483566284179688,
0.0275115966796875,
-0.012725830078125,
0.0140228271484375,
-0.01549530029296875,
0.0078582763671875,
0.0190277099609375,
0.015838623046875,
-0.0019626617431640625,
0.01483154296875,
0.00150299072265625,
0.00980377197265625,
0.006328582763671875,
-0.0333251953125,
-0.04962158203125,
0.01361846923828125,
0.045440673828125,
0.006412506103515625,
-0.0160064697265625,
-0.008880615234375,
0.00664520263671875,
-0.003448486328125,
0.0047149658203125,
0.020904541015625,
0.0263824462890625,
-0.0194549560546875,
-0.0130615234375,
-0.00914764404296875,
0.0382080078125,
-0.0333251953125,
0.019805908203125,
0.01136016845703125,
-0.042449951171875,
-0.03094482421875,
-0.0263519287109375,
0.01629638671875,
-0.00345611572265625,
-0.0033473968505859375,
0.009674072265625,
0.0002892017364501953,
0.0093994140625,
-0.00502777099609375,
-0.01052093505859375,
0.00429534912109375,
0.00301361083984375,
0.017059326171875,
0.00536346435546875,
0.0278472900390625,
-0.032867431640625,
-0.01422882080078125,
0.03692626953125,
-0.013702392578125,
-0.012359619140625,
-0.000010907649993896484,
-0.007503509521484375,
0.00669097900390625,
0.0023441314697265625,
-0.027252197265625,
0.0281219482421875,
-0.048614501953125,
0.0012540817260742188,
-0.00858306884765625,
0.050384521484375,
-0.023590087890625,
0.0204010009765625,
0.0180511474609375,
-0.017547607421875,
-0.00466156005859375,
-0.00003141164779663086,
-0.01166534423828125,
-0.006053924560546875,
0.001499176025390625,
0.00543975830078125,
-0.0172271728515625,
-0.02899169921875,
0.0122528076171875,
-0.034271240234375,
0.0190887451171875,
-0.038238525390625,
0.0006971359252929688,
-0.008026123046875,
0.0007615089416503906,
-0.01165771484375,
-0.022369384765625,
-0.0268707275390625,
0.0017728805541992188,
-0.032135009765625,
-0.005138397216796875,
0.03564453125,
0.03363037109375,
-0.01296234130859375,
0.002300262451171875,
-0.025115966796875,
-0.0050506591796875,
-0.0009064674377441406,
0.01178741455078125,
0.0120391845703125,
0.0147705078125,
-0.00310516357421875,
0.030914306640625,
0.02978515625,
-0.005840301513671875,
0.0015783309936523438,
0.00554656982421875,
0.010650634765625,
-0.0009374618530273438,
-0.015289306640625,
-0.0185699462890625,
0.0178680419921875,
0.0244598388671875,
-0.008636474609375,
-0.00555419921875,
-0.01593017578125,
-0.01071929931640625,
-0.013824462890625,
-0.02813720703125,
0.0013971328735351562,
-0.033966064453125,
-0.016204833984375,
0.013916015625,
0.0045013427734375,
-0.0286407470703125,
-0.005168914794921875,
-0.0250091552734375,
-0.0100860595703125,
0.0120697021484375,
-0.0004372596740722656,
-0.0216522216796875,
0.0169830322265625,
0.021881103515625,
-0.0241546630859375,
0.004734039306640625,
-0.01142120361328125,
0.057403564453125,
-0.007568359375,
-0.0264892578125,
-0.0014333724975585938,
0.00424957275390625,
-0.0338134765625,
0.033538818359375,
0.0197906494140625,
0.0275115966796875,
-0.0249481201171875,
-0.01434326171875,
-0.018096923828125,
0.009521484375,
-0.0198211669921875,
0.033294677734375,
0.0198822021484375,
-0.01255035400390625,
0.01617431640625,
0.0213623046875,
-0.00516510009765625,
-0.040283203125,
-0.01216888427734375,
0.018096923828125,
-0.053436279296875,
-0.02667236328125,
-0.00730133056640625,
0.0025691986083984375,
-0.004364013671875,
-0.0011806488037109375,
-0.00853729248046875,
0.0033550262451171875,
0.01540374755859375,
-0.0035228729248046875,
0.0283050537109375,
0.01195526123046875,
0.0007762908935546875,
0.02056884765625,
0.0450439453125,
-0.0039825439453125,
-0.0303955078125,
0.0077362060546875,
-0.00803375244140625,
0.02783203125,
0.0159759521484375,
-0.01092529296875,
0.0013675689697265625,
0.012420654296875,
0.019805908203125,
-0.018951416015625,
0.0291595458984375,
0.038482666015625,
-0.03729248046875,
0.00946044921875,
0.0186767578125,
0.00589752197265625,
-0.004100799560546875,
0.0260162353515625,
0.0167236328125,
-0.00040435791015625,
-0.03997802734375,
-0.0106658935546875,
-0.01383209228515625,
-0.0031299591064453125,
0.0207672119140625,
-0.033599853515625,
-0.038116455078125,
0.0087738037109375,
-0.006786346435546875,
-0.015655517578125,
0.03271484375,
0.0198211669921875,
0.00937652587890625,
-0.0196380615234375,
0.006175994873046875,
-0.036376953125,
-0.0191192626953125,
-0.02923583984375,
-0.009429931640625,
0.01132965087890625,
-0.0115509033203125,
-0.01097869873046875,
0.004352569580078125,
0.0089569091796875,
0.0037841796875,
-0.0019664764404296875,
-0.007038116455078125,
-0.020782470703125,
0.00823211669921875,
0.00833892822265625,
-0.0079803466796875,
-0.01971435546875,
0.015167236328125,
-0.00011831521987915039,
-0.0298614501953125,
0.00213623046875,
0.01293182373046875,
0.01751708984375,
-0.020233154296875,
-0.0017080307006835938,
0.0169830322265625,
-0.05474853515625,
0.030303955078125,
0.00778961181640625,
0.03631591796875,
-0.0015573501586914062,
0.03729248046875,
0.00278472900390625,
-0.007232666015625,
-0.0009937286376953125,
0.051300048828125,
-0.0220947265625,
0.0021953582763671875,
-0.0018825531005859375,
0.018096923828125,
0.038665771484375,
0.0244903564453125,
0.01275634765625,
0.0029811859130859375,
0.01873779296875,
0.0220489501953125,
0.0186004638671875,
-0.007770538330078125,
0.005035400390625,
0.01065826416015625,
0.0033817291259765625,
0.01422119140625,
-0.03399658203125,
0.0122528076171875,
-0.01898193359375,
-0.0313720703125,
-0.001842498779296875,
0.0006246566772460938,
-0.003017425537109375,
-0.036041259765625,
0.0161285400390625,
-0.0009937286376953125,
0.022247314453125,
0.006618499755859375,
0.00992584228515625,
0.03729248046875,
0.0134429931640625,
0.02838134765625,
-0.01514434814453125,
-0.037353515625,
0.0186920166015625,
0.0232391357421875,
-0.004337310791015625,
-0.0243377685546875,
-0.00392913818359375,
-0.0225067138671875,
-0.00438690185546875,
0.011505126953125,
0.026458740234375,
-0.002460479736328125,
-0.0285797119140625,
-0.019866943359375,
-0.0051727294921875,
-0.0006532669067382812,
-0.0172576904296875,
-0.0173187255859375,
0.002681732177734375,
0.00510406494140625,
-0.0295562744140625,
0.04205322265625,
0.00824737548828125,
0.01027679443359375,
-0.0181121826171875,
-0.01407623291015625,
0.0029773712158203125,
-0.0048828125,
0.010833740234375,
-0.01511383056640625,
0.0274658203125,
0.037109375,
-0.030120849609375,
-0.003757476806640625,
0.0214996337890625,
0.01491546630859375,
0.02392578125,
-0.0247955322265625,
0.01232147216796875,
-0.009307861328125,
0.0226898193359375,
-0.028961181640625,
0.0225830078125,
0.0055694580078125,
-0.007476806640625,
-0.003902435302734375,
-0.0181427001953125,
0.01343536376953125,
-0.0162200927734375,
0.0124664306640625,
-0.00403594970703125,
0.02587890625,
0.0117645263671875,
-0.01462554931640625,
-0.018829345703125,
0.032867431640625,
-0.028594970703125,
0.03143310546875,
-0.01788330078125,
-0.01776123046875,
-0.0001500844955444336,
0.005603790283203125,
-0.011688232421875,
0.0245819091796875,
-0.035308837890625,
-0.00792694091796875,
-0.007648468017578125,
-0.004535675048828125,
0.0165252685546875,
-0.041259765625,
-0.001956939697265625,
0.018768310546875,
-0.045166015625,
-0.00897216796875,
0.04815673828125,
0.01071929931640625,
-0.0032749176025390625,
0.034149169921875,
0.0238494873046875,
0.005558013916015625,
-0.0019626617431640625,
0.00792694091796875,
0.019134521484375,
0.01248931884765625,
-0.009765625,
-0.0194091796875,
-0.0014820098876953125,
-0.0172882080078125,
-0.034759521484375,
0.0000909566879272461,
0.007183074951171875,
-0.0017852783203125,
0.01666259765625,
-0.0075225830078125,
-0.00495147705078125,
0.005641937255859375,
-0.022308349609375,
0.0013799667358398438,
0.0131072998046875,
-0.0252532958984375,
0.01288604736328125,
-0.014892578125,
0.001384735107421875,
-0.0020904541015625,
-0.04412841796875,
0.01216888427734375,
0.004730224609375,
0.007015228271484375,
0.005462646484375,
-0.00937652587890625,
0.0025348663330078125,
-0.027862548828125,
0.0016689300537109375,
0.0034770965576171875,
0.00627899169921875,
-0.01629638671875,
-0.03741455078125,
-0.0036983489990234375,
0.0119476318359375,
-0.0086517333984375,
-0.0166473388671875,
-0.006107330322265625,
-0.019500732421875,
-0.0200653076171875,
-0.027069091796875,
0.01318359375,
-0.037322998046875,
0.022735595703125,
-0.0267486572265625,
0.0238037109375,
-0.0275726318359375,
0.009979248046875,
0.007518768310546875,
-0.019775390625,
-0.004085540771484375,
-0.0005044937133789062,
0.00438690185546875,
0.0263824462890625,
0.0148468017578125,
0.007904052734375,
-0.0193023681640625,
-0.01861572265625,
0.008636474609375,
-0.03436279296875,
0.0186920166015625,
0.0211029052734375,
0.00920867919921875,
-0.0087432861328125,
-0.003391265869140625,
0.00974273681640625,
-0.002960205078125,
0.01004791259765625,
-0.020263671875,
0.0285491943359375,
0.0056915283203125,
-0.00931549072265625,
0.01959228515625,
-0.0173492431640625,
0.013397216796875,
-0.023651123046875,
0.0152435302734375,
0.00042891502380371094,
-0.0101776123046875,
0.0004551410675048828,
0.0022487640380859375,
-0.056396484375,
-0.007762908935546875,
0.01309967041015625,
-0.021728515625,
-0.007488250732421875,
-0.039398193359375,
0.025146484375,
-0.0191650390625,
0.0276947021484375,
-0.0235443115234375,
-0.0211639404296875,
0.005100250244140625,
-0.0163421630859375,
-0.002696990966796875,
0.051544189453125,
-0.0027370452880859375,
0.0178070068359375,
0.005840301513671875,
-0.00385284423828125,
-0.04547119140625,
-0.028472900390625,
-0.01432037353515625,
0.01145172119140625,
0.0004901885986328125,
-0.0218353271484375,
-0.037689208984375,
0.0001729726791381836,
-0.0022220611572265625,
0.023681640625,
-0.020660400390625,
-0.005970001220703125,
0.00421142578125,
-0.01079559326171875,
0.0279388427734375,
0.0116119384765625,
0.0083160400390625,
-0.025970458984375,
-0.0031719207763671875,
-0.0139312744140625,
-0.009490966796875,
-0.0059967041015625,
0.01081085205078125,
0.0081787109375,
0.00214385986328125,
-0.006206512451171875,
0.08782958984375,
0.00890350341796875,
-0.002323150634765625,
-0.0245208740234375,
-0.00788116455078125,
-0.01488494873046875,
-0.01377105712890625,
0.00830078125,
-0.007549285888671875,
0.0026721954345703125,
-0.0194244384765625,
-0.0635986328125,
0.0008649826049804688,
0.00910186767578125,
-0.0017032623291015625,
-0.01448822021484375,
0.037384033203125,
-0.0013322830200195312,
-0.0224609375,
0.0100555419921875,
0.00476837158203125,
0.018096923828125,
0.0003097057342529297,
0.01337432861328125,
-0.0090484619140625,
-0.0083770751953125,
-0.037261962890625,
0.0020771026611328125,
0.01219940185546875,
0.0245819091796875,
0.0042266845703125,
0.006374359130859375,
0.0221405029296875,
0.0240478515625,
-0.0042572021484375,
0.0219268798828125,
-0.01561737060546875,
-0.001354217529296875,
0.023895263671875,
0.0185089111328125,
-0.01708984375,
0.0086517333984375,
-0.01166534423828125,
0.0032939910888671875,
0.0025691986083984375,
0.020355224609375,
0.0030689239501953125,
0.03619384765625,
-0.0172882080078125,
0.022979736328125,
-0.008209228515625,
0.039794921875,
0.0279388427734375,
0.0134429931640625,
0.047882080078125,
0.0009584426879882812,
0.0219268798828125,
-0.0003154277801513672,
-0.01120758056640625,
0.038482666015625,
-0.005832672119140625,
-0.0005717277526855469,
0.023834228515625,
-0.0164947509765625,
-0.0226593017578125,
0.0252227783203125,
0.001140594482421875,
-0.00579833984375,
-0.0120849609375,
-0.01375579833984375,
-0.007656097412109375,
-0.01265716552734375,
-0.009490966796875,
-0.00028514862060546875,
-0.0124053955078125,
-0.01308441162109375,
-0.0164337158203125,
-0.013275146484375,
0.0112457275390625,
-0.006134033203125,
-0.0128326416015625,
-0.0114898681640625,
0.045013427734375,
-0.0181884765625,
-0.01528167724609375,
-0.0284576416015625,
0.0028781890869140625,
-0.006595611572265625,
-0.00254058837890625,
-0.0219573974609375,
0.044891357421875,
0.002460479736328125,
0.011077880859375,
-0.0011615753173828125,
-0.0223236083984375,
-0.0011034011840820312,
0.0175933837890625,
-0.00496673583984375,
0.01044464111328125,
0.03265380859375,
0.02789306640625,
0.015380859375,
-0.00811767578125,
-0.0037708282470703125,
-0.0173187255859375,
-0.0013494491577148438,
0.003368377685546875,
-0.037841796875,
-0.0010061264038085938,
-0.004703521728515625,
0.0286407470703125,
-0.0207977294921875,
0.0007982254028320312,
-0.0384521484375,
-0.00551605224609375,
-0.053070068359375,
-0.0129547119140625,
0.0100555419921875,
0.0428466796875,
-0.0188446044921875,
0.0157470703125,
-0.06695556640625,
0.026885986328125,
0.01422882080078125,
-0.01727294921875,
0.005298614501953125,
0.00888824462890625,
-0.006622314453125,
-0.0084686279296875,
-0.0226593017578125,
-0.01093292236328125,
-0.00713348388671875,
-0.01435089111328125,
0.00870513916015625,
-0.0287628173828125,
-0.0052490234375,
-0.007373809814453125,
-0.01019287109375,
-0.032684326171875,
0.0194854736328125,
0.01031494140625,
-0.001865386962890625,
-0.02105712890625,
0.0283355712890625,
-0.00634002685546875,
0.02008056640625,
-0.0013303756713867188,
-0.01207733154296875,
0.00844573974609375,
0.0050201416015625,
-0.0088653564453125,
-0.020355224609375,
-0.040618896484375,
-0.0026721954345703125,
-0.01275634765625,
0.01434326171875,
0.0191192626953125,
0.010040283203125,
-0.00916290283203125,
-0.05926513671875,
-0.0000705718994140625,
0.0308380126953125,
-0.025909423828125,
-0.00812530517578125,
0.0029926300048828125,
-0.01070404052734375,
-0.0179443359375,
-0.015106201171875,
-0.059539794921875,
0.0182342529296875,
0.02099609375,
0.004329681396484375,
-0.0294952392578125,
-0.01062774658203125,
0.0312347412109375,
0.005756378173828125,
-0.026275634765625,
-0.006908416748046875,
0.0229644775390625,
-0.0101165771484375,
0.0157012939453125,
0.01995849609375,
-0.0153656005859375,
0.044342041015625,
0.015472412109375,
0.00144195556640625,
-0.0097808837890625,
-0.0024204254150390625,
-0.007297515869140625,
-0.0068359375,
0.0220947265625,
-0.0207977294921875,
-0.0013875961303710938,
-0.0024929046630859375,
-0.0215301513671875,
-0.005126953125,
0.0210418701171875,
-0.061309814453125,
-0.005390167236328125,
0.007648468017578125,
-0.0438232421875,
-0.00708770751953125,
-0.0119781494140625,
-0.02972412109375,
-0.01479339599609375,
-0.0167388916015625,
-0.0256805419921875,
0.021453857421875,
-0.01560211181640625,
0.028717041015625,
-0.0162506103515625,
0.006000518798828125,
0.03021240234375,
0.007495880126953125,
0.01270294189453125,
-0.00756072998046875,
-0.0299835205078125,
0.020782470703125,
-0.031951904296875,
0.0034027099609375,
-0.00017714500427246094,
0.0096282958984375,
-0.03155517578125,
0.0303497314453125,
-0.01038360595703125,
-0.013092041015625,
0.0024013519287109375,
-0.0249481201171875,
0.01143646240234375,
-0.003818511962890625,
0.0300750732421875,
-0.025634765625,
-0.042633056640625,
-0.01885986328125,
0.0172882080078125,
-0.0149383544921875,
0.02313232421875,
0.007526397705078125,
0.011962890625,
0.003719329833984375,
-0.0030422210693359375,
-0.008941650390625,
-0.03515625,
-0.01502227783203125,
0.01171112060546875,
-0.008514404296875,
-0.06488037109375,
-0.011505126953125,
0.029144287109375,
-0.04412841796875,
0.00792694091796875,
0.01100921630859375,
0.0027713775634765625,
-0.0252532958984375,
-0.0197906494140625,
-0.0034084320068359375,
-0.002056121826171875,
0.0124664306640625,
0.0204925537109375,
-0.00909423828125,
0.0269775390625,
-0.030059814453125,
0.0222015380859375,
-0.019500732421875,
0.027191162109375,
0.017608642578125,
-0.00177001953125,
-0.00559234619140625,
0.0010271072387695312,
-0.00809478759765625,
-0.012451171875,
-0.0155181884765625,
-0.01398468017578125,
0.0086669921875,
-0.0008711814880371094,
0.017486572265625,
-0.00726318359375,
-0.0035953521728515625,
-0.008270263671875,
-0.00403594970703125,
0.0305633544921875,
-0.032745361328125,
0.03271484375,
-0.00982666015625,
-0.0013189315795898438,
0.010284423828125,
0.043243408203125,
0.0242767333984375,
-0.008941650390625,
-0.0058135986328125,
0.011322021484375,
0.01251220703125,
0.060302734375,
-0.006977081298828125,
-0.031097412109375,
-0.01396942138671875,
-0.0166015625,
0.003910064697265625,
-0.01549530029296875,
-0.0106201171875,
0.01183319091796875,
-0.0220489501953125,
0.0200042724609375,
0.00974273681640625,
0.02862548828125,
0.04052734375,
0.0084991455078125,
-0.010589599609375,
-0.0247344970703125,
-0.020538330078125,
-0.00812530517578125,
-0.022369384765625,
-0.007274627685546875,
0.013336181640625,
0.025146484375,
-0.004268646240234375,
0.0263214111328125,
0.00542449951171875,
-0.023773193359375,
-0.0017499923706054688,
0.0264739990234375,
0.0004055500030517578,
-0.0253143310546875,
0.0024929046630859375,
-0.0159149169921875,
0.00434112548828125,
0.033538818359375,
0.023681640625,
-0.004486083984375,
-0.012298583984375,
-0.006500244140625,
-0.016448974609375,
0.047576904296875,
-0.0002796649932861328,
-0.031585693359375,
-0.01268768310546875,
-0.016815185546875,
-0.0308837890625,
0.028167724609375,
0.0129547119140625,
0.014739990234375,
0.02496337890625,
-0.027069091796875,
-0.005413055419921875,
0.0080108642578125,
0.01094818115234375,
0.00247955322265625,
0.0022106170654296875,
0.05828857421875,
-0.01947021484375,
0.0015573501586914062,
0.024932861328125,
0.03497314453125,
0.00756072998046875,
0.002071380615234375,
-0.003986358642578125,
-0.0217437744140625,
-0.00992584228515625,
-0.0122833251953125,
-0.01331329345703125,
0.02471923828125,
0.0302734375,
0.006011962890625,
0.010833740234375,
0.0140533447265625,
0.01439666748046875,
-0.021392822265625,
-0.03753662109375,
-0.049530029296875,
-0.041229248046875,
0.0013055801391601562,
0.00437164306640625,
-0.044952392578125,
0.0076904296875,
0.0019702911376953125,
-0.022674560546875,
-0.027099609375,
-0.00428009033203125,
-0.00031065940856933594,
0.004138946533203125,
-0.003925323486328125,
0.00933837890625,
-0.01284027099609375,
-0.00011456012725830078,
0.0197906494140625,
0.00435638427734375,
0.04522705078125,
0.006908416748046875,
0.003421783447265625,
-0.0186920166015625,
0.01165771484375,
-0.01160430908203125,
0.0211334228515625,
0.03570556640625,
-0.0260162353515625,
0.02459716796875,
0.0000559687614440918,
-0.0184326171875,
0.019134521484375,
0.00035881996154785156,
0.018310546875,
0.018707275390625,
0.013946533203125,
-0.023162841796875,
-0.022308349609375,
-0.01259613037109375,
0.0015726089477539062,
0.00803375244140625,
0.0006799697875976562,
0.039306640625,
-0.0298919677734375,
-0.0128021240234375,
0.0214385986328125,
-0.011871337890625,
-0.03289794921875,
0.0029773712158203125,
-0.00019121170043945312,
-0.01247406005859375,
0.028961181640625,
-0.012939453125,
0.03369140625,
0.01513671875,
0.0248260498046875,
0.048095703125,
-0.050506591796875,
-0.007465362548828125,
0.004917144775390625,
0.0088348388671875,
0.0205841064453125,
0.001285552978515625,
0.02374267578125,
0.0254669189453125,
-0.006465911865234375,
0.01947021484375,
-0.023468017578125,
-0.01103973388671875,
-0.01690673828125,
0.01297760009765625,
-0.0160980224609375,
0.006038665771484375,
0.01959228515625,
-0.01483917236328125,
0.031646728515625,
-0.01018524169921875,
0.01340484619140625,
0.023529052734375,
0.004253387451171875,
0.005634307861328125,
0.01456451416015625,
0.0081634521484375,
-0.00470733642578125,
-0.0016765594482421875,
0.0188446044921875,
0.047882080078125,
-0.0224761962890625,
-0.021270751953125,
-0.006786346435546875,
-0.037139892578125,
0.0145721435546875,
-0.031707763671875,
0.033447265625,
0.005481719970703125,
0.0036411285400390625,
-0.01172637939453125,
0.0035552978515625,
0.0093536376953125,
0.0288543701171875,
-0.002880096435546875,
0.0009937286376953125,
0.01019287109375,
0.004436492919921875,
0.01264190673828125,
0.021820068359375,
0.006816864013671875,
-0.02825927734375,
0.02197265625,
-0.01462554931640625,
0.021026611328125,
0.01235198974609375,
0.0179901123046875,
0.002475738525390625,
0.01483917236328125,
-0.0021991729736328125,
-0.00702667236328125,
-0.03228759765625,
0.021759033203125,
-0.0166015625,
0.031036376953125,
-0.0272979736328125,
0.01239013671875,
0.017730712890625,
0.0305633544921875,
-0.01548004150390625,
0.01396942138671875,
-0.04486083984375,
0.0113067626953125,
-0.005527496337890625,
-0.0206451416015625,
-0.02215576171875,
-0.0010986328125,
0.04095458984375,
-0.01171875,
-0.00748443603515625,
0.0009436607360839844,
-0.01007843017578125,
-0.0288848876953125,
0.004810333251953125,
0.044952392578125,
0.016082763671875,
0.0106964111328125,
-0.0003802776336669922,
-0.0204315185546875,
-0.0238800048828125,
0.001277923583984375,
-0.003017425537109375,
-0.01245880126953125,
0.0035762786865234375,
0.0119476318359375,
-0.027557373046875,
0.028076171875,
0.00934600830078125,
-0.0014286041259765625,
-0.008331298828125,
0.0012273788452148438,
0.031646728515625,
-0.054962158203125,
-0.002025604248046875,
0.01486968994140625,
-0.042816162109375,
0.0100555419921875,
0.005168914794921875,
-0.010650634765625,
0.034942626953125,
-0.01971435546875,
-0.0149383544921875,
0.0159454345703125,
-0.0149078369140625,
-0.0167999267578125,
0.006317138671875,
0.062286376953125,
-0.023468017578125,
-0.03857421875,
-0.01309967041015625,
0.01399993896484375,
-0.0025959014892578125,
0.0238037109375,
0.024261474609375,
0.008514404296875,
0.00325775146484375,
-0.025390625,
-0.0015277862548828125,
-0.035491943359375,
0.03411865234375,
0.0177764892578125,
0.004863739013671875,
0.0307159423828125,
-0.038604736328125,
-0.03765869140625,
0.0028972625732421875,
-0.01476287841796875,
-0.007022857666015625,
-0.006458282470703125,
-0.0177459716796875,
-0.00481414794921875,
0.007732391357421875,
-0.0156402587890625,
-0.019805908203125,
0.004955291748046875,
0.004730224609375,
0.0014057159423828125,
0.0010986328125,
-0.01436614990234375,
0.0020160675048828125,
0.0010271072387695312,
0.005016326904296875,
0.016204833984375,
0.005588531494140625,
0.00019490718841552734,
-0.019439697265625,
-0.00980377197265625,
-0.0233001708984375,
0.0150909423828125,
-0.01290130615234375,
-0.01959228515625,
-0.0013370513916015625,
0.00811767578125,
0.00262451171875,
-0.006076812744140625,
0.007457733154296875,
-0.0030670166015625,
-0.00634002685546875,
-0.027801513671875,
-0.0226898193359375,
-0.00890350341796875,
-0.025360107421875,
-0.01062774658203125,
-0.007171630859375,
0.0120391845703125,
-0.0084228515625,
0.0239105224609375,
0.0029888153076171875,
-0.041046142578125,
0.013916015625,
-0.027374267578125,
-0.02496337890625,
0.0028076171875,
0.032867431640625,
0.0015544891357421875,
-0.00029850006103515625,
0.010589599609375,
-0.047821044921875,
-0.060455322265625,
-0.0214691162109375,
0.01403045654296875,
-0.0050811767578125,
0.01474761962890625,
-0.0223541259765625,
0.006793975830078125,
0.037353515625,
0.0050506591796875,
-0.0261688232421875,
-0.0038509368896484375,
0.03533935546875,
0.0053558349609375,
-0.0027446746826171875,
0.037078857421875,
-0.0013408660888671875,
0.00823211669921875,
-0.0065460205078125,
-0.0246429443359375,
0.0100250244140625,
-0.01934814453125,
-0.0010480880737304688,
0.034271240234375,
-0.0200042724609375,
0.029205322265625,
-0.016143798828125,
-0.00951385498046875,
-0.003875732421875,
-0.03961181640625,
-0.004787445068359375,
-0.0038089752197265625,
-0.006191253662109375,
-0.008026123046875,
-0.0308837890625,
-0.0161590576171875,
0.0111083984375,
-0.02777099609375,
0.0016469955444335938,
-0.005550384521484375,
-0.0031299591064453125,
0.0120849609375,
0.005435943603515625,
-0.01296234130859375,
0.0010881423950195312,
0.014801025390625,
-0.00675201416015625,
0.02276611328125,
0.0011262893676757812,
0.0064697265625,
0.010009765625,
0.029541015625,
-0.007717132568359375,
-0.0226898193359375,
-0.0021114349365234375,
0.03851318359375,
0.01348114013671875,
0.0170135498046875,
-0.0169677734375,
-0.0006151199340820312,
-0.01837158203125,
0.01690673828125,
-0.01027679443359375,
0.01030731201171875,
0.0143280029296875,
-0.00788116455078125,
-0.0236053466796875,
-0.0038623809814453125,
-0.0088348388671875,
0.0022640228271484375,
-0.01427459716796875,
0.004566192626953125,
0.002071380615234375,
-0.001224517822265625,
-0.01207733154296875,
0.00989532470703125,
-0.025390625,
0.006267547607421875,
-0.0029144287109375,
0.00710296630859375,
-0.005550384521484375,
0.01020050048828125,
0.01617431640625,
-0.0236968994140625,
-0.00437164306640625,
-0.0026702880859375,
-0.019256591796875,
-0.007740020751953125,
-0.004528045654296875,
-0.0171966552734375,
0.0088043212890625,
-0.017303466796875,
-0.00269317626953125,
-0.00371551513671875,
-0.05078125,
0.0166168212890625,
0.01503753662109375,
0.007617950439453125,
0.00020742416381835938,
-0.0206451416015625,
-0.0078887939453125,
0.0231475830078125,
-0.0224456787109375,
0.01837158203125,
-0.0234222412109375,
0.00910186767578125,
-0.00406646728515625,
-0.00936126708984375,
0.0015459060668945312,
-0.0164337158203125,
0.025543212890625,
0.0439453125,
0.011260986328125,
-0.00289154052734375,
-0.037689208984375,
0.010345458984375,
0.00943756103515625,
0.00250244140625,
-0.01432037353515625,
0.0196685791015625,
-0.041229248046875,
-0.0109100341796875,
0.0157318115234375,
-0.01335906982421875,
0.007457733154296875,
-0.004886627197265625,
0.019775390625,
0.019775390625,
-0.0223846435546875,
0.0152740478515625,
0.043365478515625,
-0.052459716796875,
0.0074310302734375,
0.019500732421875,
-0.00868988037109375,
-0.022369384765625,
-0.0030994415283203125,
0.0185546875,
-0.0007138252258300781,
0.01953125,
0.0198516845703125,
0.02789306640625,
-0.001102447509765625,
-0.032684326171875,
0.024169921875,
0.016815185546875,
0.0031948089599609375,
0.017730712890625,
0.0223846435546875,
0.0254669189453125,
-0.035125732421875,
0.005168914794921875,
-0.00891876220703125,
0.005191802978515625,
0.006488800048828125,
-0.00632476806640625,
-0.00458526611328125,
-0.01308441162109375,
0.018829345703125,
-0.0150604248046875,
0.016815185546875,
0.00930023193359375,
0.00966644287109375,
0.0030117034912109375,
0.00913238525390625,
0.01312255859375,
0.00910186767578125,
0.0177154541015625,
-0.016510009765625,
-0.007587432861328125,
0.0024967193603515625,
0.0167694091796875,
0.0361328125,
-0.01531982421875,
-0.0160980224609375,
-0.00493621826171875,
-0.045379638671875,
-0.0045166015625,
-0.015655517578125,
0.01219940185546875,
-0.004039764404296875,
0.022552490234375,
0.008026123046875,
0.002597808837890625,
-0.0020294189453125,
0.002185821533203125,
0.044342041015625,
0.032379150390625,
0.0178680419921875,
0.03338623046875,
-0.007526397705078125,
0.0196075439453125,
-0.012451171875,
-0.0024127960205078125,
0.038299560546875,
-0.018035888671875,
-0.00582122802734375,
0.01090240478515625,
-0.0120086669921875,
-0.004528045654296875,
-0.00949859619140625,
0.0201416015625,
0.022705078125,
-0.0017118453979492188,
-0.0325927734375,
-0.030364990234375,
0.01360321044921875,
-0.00882720947265625,
0.016510009765625,
0.0033626556396484375,
-0.01434326171875,
-0.006389617919921875,
-0.0191802978515625,
-0.01367950439453125,
0.0079498291015625,
-0.0024890899658203125,
-0.01045989990234375,
-0.00018537044525146484,
-0.0071258544921875,
-0.0024433135986328125,
0.00537872314453125,
-0.007450103759765625,
-0.00405120849609375,
0.043212890625,
0.0161590576171875,
-0.01971435546875,
-0.0022335052490234375,
-0.0186004638671875,
-0.029083251953125,
0.0010242462158203125,
0.03216552734375,
-0.01271820068359375,
-0.0006380081176757812,
-0.00722503662109375,
0.0264434814453125,
0.002048492431640625,
-0.00952911376953125,
-0.0187530517578125,
0.04547119140625,
-0.01165008544921875,
-0.01551055908203125,
0.00858306884765625,
0.0019140243530273438,
-0.0003898143768310547,
-0.037017822265625,
-0.0002148151397705078,
0.0225982666015625,
0.0037555694580078125,
-0.017730712890625,
0.023468017578125,
-0.007045745849609375,
-0.01015472412109375,
0.0289459228515625,
-0.03082275390625,
0.0084381103515625,
0.017486572265625,
-0.025604248046875,
0.00659942626953125,
-0.01416778564453125,
0.005870819091796875,
0.0008587837219238281,
0.0011882781982421875,
0.0029811859130859375,
0.029541015625,
0.0176849365234375,
0.0277099609375,
0.0231781005859375,
0.00717926025390625,
0.039031982421875,
0.0036144256591796875,
0.00041961669921875,
0.0168609619140625,
-0.000995635986328125,
-0.0174560546875,
0.026641845703125,
-0.0212554931640625,
-0.023773193359375,
0.00376129150390625,
-0.016571044921875,
0.0675048828125,
-0.0120086669921875,
-0.00608062744140625,
0.0163116455078125,
0.00223541259765625,
0.007305145263671875,
0.0191497802734375,
-0.010772705078125,
-0.01421356201171875,
-0.036590576171875,
0.0107269287109375,
-0.006717681884765625,
0.006374359130859375,
-0.01204681396484375,
0.01178741455078125,
-0.0299530029296875,
0.00016105175018310547,
0.01432037353515625,
0.03643798828125,
0.03985595703125,
-0.0194854736328125,
-0.00019276142120361328,
-0.0045013427734375,
-0.0200042724609375,
0.0311737060546875,
-0.01088714599609375,
0.0095977783203125,
-0.0268707275390625,
-0.025726318359375,
-0.004352569580078125,
-0.01456451416015625,
-0.005893707275390625,
-0.046417236328125,
0.00951385498046875,
-0.005420684814453125,
-0.01116943359375,
0.04901123046875,
0.0003466606140136719,
-0.001895904541015625,
-0.0026912689208984375,
-0.01421356201171875,
-0.0090484619140625,
0.00104522705078125,
-0.011627197265625,
-0.035736083984375,
0.013458251953125,
-0.01000213623046875,
0.0178985595703125,
-0.01824951171875,
0.0048065185546875,
0.035247802734375,
-0.01204681396484375,
-0.012603759765625,
0.006191253662109375,
-0.0270233154296875,
-0.0104522705078125,
-0.004974365234375,
-0.00189208984375,
-0.009613037109375,
-0.005748748779296875,
-0.02001953125,
-0.0112762451171875,
0.025421142578125,
0.0224609375,
0.005550384521484375,
0.00724029541015625,
0.029815673828125,
0.007110595703125,
0.01033782958984375,
0.004367828369140625,
-0.0088653564453125,
-0.01113128662109375,
0.005390167236328125,
0.005352020263671875,
0.01983642578125,
-0.006927490234375,
0.0011548995971679688,
0.005153656005859375,
0.004367828369140625,
-0.042022705078125,
-0.014068603515625,
-0.016815185546875,
-0.0024509429931640625,
-0.021209716796875,
0.00565338134765625,
-0.01160430908203125,
-0.021881103515625,
-0.03839111328125,
0.0224151611328125,
0.0171661376953125,
-0.0159454345703125,
0.035400390625,
-0.043243408203125,
-0.03900146484375,
0.007801055908203125,
0.0177001953125,
-0.0154876708984375,
-0.016326904296875,
0.0099945068359375,
-0.039093017578125,
-0.02093505859375,
-0.021636962890625,
-0.0030612945556640625,
0.012298583984375,
-0.01293182373046875,
-0.001708984375,
0.03082275390625,
-0.01462554931640625,
-0.0199432373046875,
0.01071929931640625,
-0.008392333984375,
0.0233917236328125,
0.0016450881958007812,
0.01013946533203125,
0.02508544921875,
0.0198516845703125,
0.0160675048828125,
0.0052642822265625,
-0.01480865478515625,
0.0217437744140625,
0.01273345947265625,
0.0170440673828125,
-0.024627685546875,
-0.032745361328125,
-0.00899505615234375,
-0.018310546875,
-0.0160675048828125,
0.01343536376953125,
-0.023040771484375,
-0.0229644775390625,
0.00021708011627197266,
0.01561737060546875,
0.0208587646484375,
0.00850677490234375,
0.0192413330078125,
0.01971435546875,
0.0247955322265625,
-0.00905609130859375,
-0.006572723388671875,
-0.01462554931640625,
0.0170440673828125,
-0.01751708984375,
0.032928466796875,
0.01251220703125,
0.0006723403930664062,
-0.003810882568359375,
0.003826141357421875,
-0.002101898193359375,
0.0077362060546875,
0.0199127197265625,
-0.01378631591796875,
-0.019866943359375,
0.0210113525390625,
-0.010345458984375,
0.004932403564453125,
-0.0207977294921875,
-0.0016536712646484375,
0.02532958984375,
0.0118255615234375,
-0.032806396484375,
0.04156494140625,
-0.02435302734375,
-0.0286407470703125,
-0.028961181640625,
-0.007465362548828125,
0.0236358642578125,
-0.015411376953125,
0.005390167236328125,
0.01995849609375,
-0.021209716796875,
0.0235137939453125,
0.0018587112426757812,
0.01096343994140625,
-0.0026569366455078125,
0.008056640625,
-0.0159912109375,
0.01226806640625,
0.044677734375,
0.025238037109375,
-0.033538818359375,
-0.008087158203125,
-0.013336181640625,
-0.011962890625,
0.0185089111328125,
0.0227203369140625,
-0.0016803741455078125,
-0.0035648345947265625,
0.01525115966796875,
0.0028781890869140625,
0.0169525146484375,
0.0031681060791015625,
0.009552001953125,
0.005336761474609375,
0.019317626953125,
-0.00441741943359375,
0.0121917724609375,
-0.0303802490234375,
-0.001804351806640625,
-0.05010986328125,
0.004528045654296875,
0.019775390625,
0.003841400146484375,
-0.02386474609375,
-0.0241241455078125,
-0.02520751953125,
-0.004791259765625,
0.006927490234375,
0.034271240234375,
-0.032501220703125,
0.00701904296875,
-0.016937255859375,
-0.0312042236328125,
0.00974273681640625,
0.0020618438720703125,
0.0204620361328125,
-0.011138916015625,
0.000057756900787353516,
0.01580810546875,
0.00505828857421875,
-0.0168609619140625,
-0.016326904296875,
-0.017486572265625,
-0.0166168212890625,
0.0020122528076171875,
-0.002960205078125,
0.0166778564453125,
-0.029083251953125,
0.035888671875,
-0.00030159950256347656,
0.004878997802734375,
-0.03240966796875,
-0.0121612548828125,
0.00609588623046875,
-0.0074920654296875,
0.004009246826171875,
0.009521484375,
0.0210723876953125,
0.007091522216796875,
0.00031876564025878906,
0.016815185546875,
-0.0206146240234375,
-0.035675048828125,
-0.0234832763671875,
-0.043670654296875,
0.003383636474609375,
-0.03411865234375,
-0.006305694580078125,
0.0090484619140625,
-0.0053253173828125,
0.0236358642578125,
-0.0189208984375,
-0.0198822021484375,
-0.0249176025390625,
-0.00988006591796875,
-0.03106689453125,
0.01202392578125,
-0.0118408203125,
-0.007049560546875,
0.01548004150390625,
0.0055999755859375,
0.006256103515625,
-0.005580902099609375,
0.0033054351806640625,
0.05072021484375,
0.0060882568359375,
0.0247802734375,
-0.017974853515625,
0.0014972686767578125,
-0.000012814998626708984,
-0.012054443359375,
-0.02685546875,
-0.0202789306640625,
0.005889892578125,
0.0031147003173828125,
0.0205078125,
0.0016651153564453125,
0.0050506591796875,
0.0013647079467773438,
-0.022369384765625,
0.0203857421875,
0.0020465850830078125,
-0.024017333984375,
-0.034759521484375,
0.0106201171875,
-0.0131683349609375,
0.03631591796875,
0.023040771484375,
-0.020172119140625,
-0.01255035400390625,
-0.029998779296875,
-0.0209197998046875,
-0.004421234130859375,
0.026702880859375,
0.0176239013671875,
0.0187835693359375,
0.0228424072265625,
0.006378173828125,
0.0100860595703125,
0.0006761550903320312,
-0.003864288330078125,
-0.0306549072265625,
0.021331787109375,
0.00974273681640625,
-0.00815582275390625,
0.006519317626953125,
0.0125579833984375,
0.0214691162109375,
-0.004566192626953125,
-0.00916290283203125,
-0.0253753662109375,
0.00891876220703125,
-0.0081024169921875,
0.00580596923828125,
-0.0206451416015625,
-0.044403076171875,
0.000461578369140625,
0.012054443359375,
0.0165557861328125,
0.0199737548828125,
-0.0100555419921875,
0.020416259765625,
-0.0024242401123046875,
0.00930023193359375,
0.00588226318359375,
-0.00678253173828125,
-0.0037937164306640625,
0.0292205810546875,
-0.0180206298828125,
0.007110595703125,
-0.011810302734375,
0.057373046875,
-0.006999969482421875,
-0.022003173828125,
0.007595062255859375,
-0.0196380615234375,
-0.0032672882080078125,
0.014892578125,
-0.0004730224609375,
0.005962371826171875,
0.0172576904296875,
-0.01015472412109375,
0.0020904541015625,
0.0374755859375,
0.0024318695068359375,
0.004131317138671875,
0.007171630859375,
0.009552001953125,
0.007843017578125,
-0.004901885986328125,
0.000038743019104003906,
0.024261474609375,
0.02154541015625,
-0.018768310546875,
-0.0057373046875,
0.0018815994262695312,
0.02520751953125,
-0.04132080078125,
0.00913238525390625,
-0.030914306640625,
-0.0009965896606445312,
-0.01312255859375,
0.030517578125,
0.0235137939453125,
-0.0182647705078125,
0.02197265625,
-0.0183563232421875,
-0.0253753662109375,
0.042816162109375,
0.007686614990234375,
-0.003665924072265625,
0.02008056640625,
0.0123138427734375,
-0.00885009765625,
0.021636962890625,
-0.029083251953125,
-0.006450653076171875,
0.00440216064453125,
-0.008270263671875,
0.00038433074951171875,
-0.01165771484375,
-0.026519775390625,
-0.015960693359375,
-0.00846099853515625,
-0.00382232666015625,
-0.0023555755615234375,
-0.032073974609375,
-0.00033545494079589844,
0.016998291015625,
0.00273895263671875,
-0.00582122802734375,
-0.0023975372314453125,
0.03662109375,
0.0035915374755859375,
-0.007015228271484375,
-0.003749847412109375,
0.00989532470703125,
0.022430419921875,
-0.05523681640625,
0.0109100341796875,
-0.01202392578125,
0.006008148193359375,
-0.00995635986328125,
-0.007480621337890625,
-0.0278472900390625,
0.00363922119140625,
-0.02142333984375,
0.0129241943359375,
-0.028717041015625,
0.01262664794921875,
0.005619049072265625,
0.0164947509765625,
0.01202392578125,
0.00160980224609375,
0.00934600830078125,
0.0098114013671875,
-0.00572967529296875,
0.001171112060546875,
0.0184326171875,
-0.00641632080078125,
0.0162200927734375,
-0.0171661376953125,
-0.01303863525390625,
-0.00887298583984375,
-0.0298614501953125,
-0.009124755859375,
-0.0271453857421875,
0.060821533203125,
-0.0211944580078125,
-0.0287628173828125,
0.0186767578125,
0.01195526123046875,
0.021392822265625,
-0.01617431640625,
0.0016736984252929688,
-0.0014543533325195312,
-0.03363037109375,
0.01523590087890625,
0.0139007568359375,
0.0161895751953125,
-0.010528564453125,
0.0010042190551757812,
0.0030422210693359375,
-0.00043845176696777344,
0.0068817138671875,
0.030120849609375,
-0.030242919921875,
0.01209259033203125,
0.0158538818359375,
-0.005672454833984375,
0.0030269622802734375,
0.04400634765625,
-0.0277557373046875,
0.01470184326171875,
-0.0098876953125,
0.0258636474609375,
0.031768798828125,
-0.03240966796875,
-0.042572021484375,
-0.007965087890625,
0.00555419921875,
-0.0179290771484375,
0.0005102157592773438,
-0.015777587890625,
-0.004070281982421875,
0.0019426345825195312,
-0.027435302734375,
-0.0167083740234375,
0.0273895263671875,
-0.0197296142578125,
-0.0122528076171875,
-0.0100250244140625,
0.0107269287109375,
-0.0189666748046875,
0.01049041748046875,
-0.01534271240234375,
0.0039825439453125,
0.0027942657470703125,
0.040924072265625,
-0.005962371826171875,
-0.018768310546875,
0.00867462158203125,
-0.03558349609375,
0.005420684814453125,
-0.0234222412109375,
0.01456451416015625,
0.016571044921875,
-0.008758544921875,
-0.04876708984375,
-0.003231048583984375,
-0.040863037109375,
-0.005279541015625,
0.015533447265625,
-0.061065673828125,
-0.0030994415283203125,
0.0021457672119140625,
-0.009552001953125,
0.007236480712890625,
-0.0117950439453125,
-0.0200042724609375,
-0.00971221923828125,
0.0102081298828125,
0.004917144775390625,
-0.005229949951171875,
-0.014404296875,
-0.011505126953125,
-0.005100250244140625,
0.01383209228515625,
-0.01372528076171875,
0.00891876220703125,
0.017333984375,
-0.00311279296875,
-0.01526641845703125,
-0.01174163818359375,
-0.0165863037109375,
-0.0146942138671875,
-0.0003826618194580078,
0.00949859619140625,
-0.004150390625,
0.004642486572265625,
0.025390625,
-0.00926971435546875,
-0.016387939453125,
0.009674072265625,
0.0243072509765625,
0.01174163818359375,
0.025543212890625,
-0.00711822509765625,
0.0020351409912109375,
-0.00896453857421875,
-0.01500701904296875,
-0.02386474609375,
0.041259765625,
0.003665924072265625,
0.01873779296875,
-0.001678466796875,
-0.03753662109375,
0.001125335693359375,
0.002681732177734375,
-0.01467132568359375,
0.045684814453125,
-0.00916290283203125,
0.0277557373046875,
-0.0288543701171875,
-0.01500701904296875,
-0.0165557861328125,
0.0108642578125,
-0.00775909423828125,
-0.00672149658203125,
-0.044219970703125,
-0.0033721923828125,
0.01428985595703125,
-0.00827789306640625,
0.03851318359375,
-0.034912109375,
-0.0207366943359375,
0.0272674560546875,
0.01134490966796875,
-0.03924560546875,
0.00540924072265625,
-0.0012302398681640625,
-0.0236053466796875,
-0.0288543701171875,
-0.0089111328125,
-0.006603240966796875,
0.01258087158203125,
0.01294708251953125,
-0.019134521484375,
0.005603790283203125,
-0.004001617431640625,
0.0010251998901367188,
0.0273590087890625,
0.007472991943359375,
0.0165252685546875,
-0.01316070556640625,
0.019378662109375,
0.01145172119140625,
-0.0171051025390625,
0.03143310546875,
0.03472900390625,
0.0224456787109375,
0.01308441162109375,
-0.01558685302734375,
-0.0007953643798828125,
0.01190185546875,
0.0160369873046875,
0.0107269287109375,
-0.00872039794921875,
0.0036182403564453125,
0.034088134765625,
-0.00817108154296875,
0.010650634765625,
0.021820068359375,
0.02874755859375,
0.020721435546875,
0.01180267333984375,
-0.0159149169921875,
-0.04229736328125,
-0.00894927978515625,
0.0128936767578125,
0.01160430908203125,
-0.0036869049072265625,
-0.04180908203125,
-0.0006756782531738281,
-0.0179290771484375,
0.02069091796875,
0.002948760986328125,
-0.0168914794921875,
0.0141754150390625,
-0.010009765625,
-0.022552490234375,
0.0057830810546875,
0.019927978515625,
-0.01055145263671875,
0.022308349609375,
-0.00878143310546875,
-0.03057861328125,
-0.006458282470703125,
0.0191650390625,
-0.00824737548828125,
-0.00795745849609375,
0.02996826171875,
-0.005634307861328125,
0.0082244873046875,
0.01502227783203125,
0.01038360595703125,
0.01568603515625,
-0.01456451416015625,
-0.0078582763671875,
0.0008893013000488281,
0.00946807861328125,
0.0017290115356445312,
0.00130462646484375,
0.00554656982421875,
0.0012302398681640625,
0.01157379150390625,
0.002288818359375,
0.01308441162109375,
0.004657745361328125,
-0.004878997802734375,
-0.0142822265625,
-0.0265960693359375,
-0.0029449462890625,
-0.00537872314453125,
-0.01436614990234375,
0.0000998377799987793,
0.0184478759765625,
-0.0020198822021484375,
-0.007137298583984375,
-0.018707275390625,
0.036895751953125,
0.01543426513671875,
0.01091766357421875,
-0.04052734375,
0.008270263671875,
-0.041900634765625,
0.004756927490234375,
0.0250701904296875,
0.025543212890625,
0.0267486572265625,
-0.01030731201171875,
0.034088134765625,
0.0018529891967773438,
-0.035888671875,
0.01447296142578125,
0.016937255859375,
-0.004428863525390625,
0.0360107421875,
-0.0242462158203125,
0.0263519287109375,
0.01806640625,
0.02313232421875,
0.015960693359375,
-0.0257568359375,
0.00498199462890625,
0.00864410400390625,
-0.022369384765625,
0.0028743743896484375,
0.0158843994140625,
0.038421630859375,
0.01123809814453125,
-0.016845703125,
-0.017547607421875,
0.019775390625,
0.00518798828125,
-0.0231475830078125,
-0.008453369140625,
-0.00792694091796875,
-0.0044097900390625,
0.00004100799560546875,
0.00084686279296875,
0.01427459716796875,
-0.0157012939453125,
-0.007778167724609375,
-0.0121002197265625,
-0.02239990234375,
0.007137298583984375,
-0.00719451904296875,
-0.0027370452880859375,
0.019989013671875,
-0.003925323486328125,
-0.01088714599609375,
0.016876220703125,
-0.039306640625,
0.0144805908203125,
-0.03515625,
-0.03131103515625,
-0.0165557861328125,
0.0274810791015625,
-0.0249176025390625,
0.0197906494140625,
0.0562744140625,
-0.0043487548828125,
-0.0030803680419921875,
0.0038852691650390625,
-0.000270843505859375,
-0.033050537109375,
-0.0181121826171875,
0.004322052001953125,
-0.0186614990234375,
-0.006137847900390625,
0.04937744140625,
-0.0034122467041015625,
0.040496826171875,
0.01192474365234375,
-0.0011768341064453125,
0.0052947998046875,
0.0121307373046875,
-0.008453369140625,
-0.03411865234375,
-0.0190887451171875,
-0.006793975830078125,
0.0075531005859375,
0.00972747802734375,
0.0199432373046875,
-0.00521087646484375,
0.006992340087890625,
-0.020721435546875,
0.0128936767578125,
0.04132080078125,
0.0075531005859375,
0.006069183349609375,
0.0034084320068359375,
0.0177154541015625,
0.0006589889526367188,
0.000006020069122314453,
0.025390625,
0.006343841552734375,
-0.0015392303466796875,
0.0160369873046875,
0.005825042724609375,
0.0281219482421875,
0.0161285400390625,
0.007259368896484375,
0.02728271484375,
-0.039642333984375,
-0.011932373046875,
-0.0183563232421875,
0.015228271484375,
-0.0264434814453125,
-0.020294189453125,
0.03790283203125,
0.00202178955078125,
0.0034275054931640625,
-0.0322265625,
-0.030792236328125,
0.006488800048828125,
0.0281829833984375,
-0.00988006591796875,
-0.0028400421142578125,
0.0038356781005859375,
0.006084442138671875,
-0.01097869873046875,
-0.0125885009765625,
0.005565643310546875,
-0.01348114013671875,
-0.00031185150146484375,
-0.00913238525390625,
-0.00778961181640625,
-0.014373779296875,
-0.01071929931640625,
-0.0274200439453125,
-0.032012939453125,
-0.02252197265625,
-0.020843505859375,
0.0205230712890625,
-0.0293426513671875,
-0.005619049072265625,
0.015167236328125,
0.008453369140625,
0.03228759765625,
0.0218658447265625,
-0.0106964111328125,
-0.006744384765625,
0.0240325927734375,
0.030731201171875,
-0.01317596435546875,
-0.025146484375,
-0.00930023193359375,
0.00638580322265625,
-0.01328277587890625,
0.0175628662109375,
0.0341796875,
0.01910400390625,
-0.0086669921875,
0.0360107421875,
-0.00730133056640625,
-0.0194854736328125,
-0.01073455810546875,
0.0206298828125,
-0.0161590576171875,
-0.0135650634765625,
0.01459503173828125,
0.0029010772705078125,
-0.0126800537109375,
-0.0167694091796875,
0.0123748779296875,
0.019256591796875,
-0.006927490234375,
0.0213470458984375,
-0.0269012451171875,
0.0025157928466796875,
0.0250244140625,
-0.03643798828125,
-0.0138702392578125,
0.0162353515625,
0.00586700439453125,
-0.011810302734375,
-0.020111083984375,
0.021697998046875,
-0.01995849609375,
0.032012939453125,
0.00408935546875,
0.013641357421875,
0.01080322265625,
0.006866455078125,
-0.011077880859375,
-0.018890380859375,
0.0098724365234375,
0.00424957275390625,
-0.0270538330078125,
-0.00884246826171875,
0.017486572265625,
0.0278472900390625,
0.01227569580078125,
0.0170745849609375,
0.00746917724609375,
0.01020050048828125,
0.00687408447265625,
0.0340576171875,
0.0243072509765625
] |
ours_541
|
This is a geometric series:
$$
\frac{1}{x}+\frac{1}{2 x^{2}}+\frac{1}{4 x^{3}}+\frac{1}{8 x^{4}}+\frac{1}{16 x^{5}}+\cdots=\frac{\frac{1}{x}}{1-\frac{1}{2x}}=\frac{1}{64}.
$$
Solving the equation:
\[
\frac{1/x}{1-1/(2x)} = \frac{1}{64} \implies \frac{2}{2x-1} = \frac{1}{64}
\]
Cross-multiplying gives:
\[
128 = 2x - 1 \implies 2x = 129 \implies x = \frac{129}{2}
\]
Thus, \(m = 129\) and \(n = 2\), so \(m+n = 129 + 2 = 131\).
\(\boxed{131}\)
|
131
|
{
"competition": "us_comps",
"dataset": "Ours",
"posts": null,
"source": "OMOSoln2.md"
}
|
If
$$
\frac{1}{x}+\frac{1}{2 x^{2}}+\frac{1}{4 x^{3}}+\frac{1}{8 x^{4}}+\frac{1}{16 x^{5}}+\cdots=\frac{1}{64}
$$
and \(x\) can be expressed in the form \(\frac{m}{n}\), where \(m, n\) are relatively prime positive integers, find \(m+n\).
|
[
"/Mathematics/Algebra/AlgebraicEquations/AlgebraicEquation",
"/Mathematics/Algebra/AlgebraicEquations/AlgebraicExpression",
"/Mathematics/Algebra/AlgebraicEquations/LinearEquation",
"/Mathematics/Algebra/GeneralAlgebra/Algebra",
"/Mathematics/Algebra/Sums/PartialSum",
"/Mathematics/Algebra/Sums/Sum"
] |
Recognize the infinite sum as a geometric series and apply the formula S = a/(1−r).
|
[
-0.00010961294174194336,
-0.003093719482421875,
0.0115814208984375,
0.044403076171875,
-0.0001590251922607422,
0.0100860595703125,
-0.0020389556884765625,
-0.0237274169921875,
0.002574920654296875,
-0.0278167724609375,
0.019805908203125,
-0.04266357421875,
-0.0003921985626220703,
0.0177764892578125,
-0.0153350830078125,
-0.00801849365234375,
0.00812530517578125,
-0.00264739990234375,
0.06768798828125,
0.0016889572143554688,
-0.003498077392578125,
-0.0265960693359375,
-0.0318603515625,
0.00799560546875,
-0.05157470703125,
0.00348663330078125,
-0.015289306640625,
-0.01457977294921875,
-0.004974365234375,
0.01078033447265625,
-0.00693511962890625,
-0.007198333740234375,
-0.0107574462890625,
-0.022064208984375,
0.0010805130004882812,
-0.004596710205078125,
0.015716552734375,
-0.0034313201904296875,
-0.040557861328125,
-0.004032135009765625,
0.0199127197265625,
0.001129150390625,
-0.0054168701171875,
0.0007719993591308594,
-0.01081085205078125,
-0.0020294189453125,
-0.0069427490234375,
-0.026214599609375,
-0.01043701171875,
0.00928497314453125,
-0.0027313232421875,
-0.00019824504852294922,
0.007568359375,
-0.004436492919921875,
-0.0305633544921875,
-0.058624267578125,
-0.002132415771484375,
-0.00635528564453125,
-0.0189971923828125,
-0.003173828125,
0.01155853271484375,
0.01171875,
-0.00565338134765625,
-0.01806640625,
-0.0023899078369140625,
-0.01541900634765625,
0.0022296905517578125,
-0.037689208984375,
-0.0111541748046875,
0.0010881423950195312,
-0.013916015625,
-0.01177978515625,
-0.005115509033203125,
0.019805908203125,
0.023468017578125,
-0.00762176513671875,
-0.0188446044921875,
0.0208282470703125,
0.01496124267578125,
0.0024871826171875,
0.005336761474609375,
0.0014905929565429688,
0.0106353759765625,
-0.01175689697265625,
0.008636474609375,
0.03875732421875,
-0.04937744140625,
0.0094146728515625,
0.0223236083984375,
-0.0208892822265625,
0.009368896484375,
0.0589599609375,
-0.00020444393157958984,
-0.073486328125,
-0.0027446746826171875,
-0.00201416015625,
-0.01189422607421875,
-0.0068511962890625,
-0.02362060546875,
0.0078582763671875,
0.001239776611328125,
-0.009002685546875,
-0.022613525390625,
0.0031414031982421875,
-0.056396484375,
-0.007701873779296875,
-0.01474761962890625,
0.0112457275390625,
0.0004868507385253906,
0.017974853515625,
0.01519012451171875,
-0.003475189208984375,
0.031280517578125,
0.025726318359375,
-0.0282135009765625,
0.021240234375,
0.0174102783203125,
0.01611328125,
-0.020050048828125,
0.01509857177734375,
0.0205230712890625,
0.01666259765625,
-0.0251617431640625,
-0.0211944580078125,
-0.00313568115234375,
0.016632080078125,
0.005664825439453125,
-0.0126495361328125,
0.0265655517578125,
0.044921875,
-0.00733184814453125,
-0.0160675048828125,
-0.03167724609375,
-0.02197265625,
-0.063720703125,
0.01129150390625,
-0.02740478515625,
-0.0101165771484375,
-0.0165252685546875,
-0.01898193359375,
-0.00411224365234375,
-0.013763427734375,
0.0211639404296875,
-0.00530242919921875,
-0.0244293212890625,
0.03326416015625,
0.005748748779296875,
-0.0238800048828125,
0.0121917724609375,
0.004016876220703125,
0.01555633544921875,
-0.021697998046875,
0.018463134765625,
0.0038433074951171875,
-0.005489349365234375,
0.0012845993041992188,
0.00719451904296875,
0.004741668701171875,
-0.00635528564453125,
0.0179595947265625,
0.0126953125,
-0.01238250732421875,
-0.011138916015625,
0.030670166015625,
-0.0038356781005859375,
-0.0061187744140625,
-0.0380859375,
0.0119781494140625,
-0.009063720703125,
0.001918792724609375,
-0.016937255859375,
-0.0133056640625,
-0.0146026611328125,
-0.0190277099609375,
0.007297515869140625,
0.006801605224609375,
-0.0267791748046875,
-0.0047149658203125,
-0.005176544189453125,
0.0090484619140625,
0.0028171539306640625,
-0.03289794921875,
-0.0118560791015625,
-0.0015811920166015625,
0.0307464599609375,
-0.0033702850341796875,
0.01129913330078125,
-0.004665374755859375,
0.01441192626953125,
0.012237548828125,
-0.0028362274169921875,
-0.01678466796875,
-0.0015478134155273438,
-0.01428985595703125,
-0.016998291015625,
0.00018739700317382812,
-0.0018138885498046875,
-0.008697509765625,
0.00989532470703125,
-0.00543975830078125,
0.0055389404296875,
0.0052490234375,
0.0171966552734375,
0.01207733154296875,
0.006320953369140625,
-0.0013418197631835938,
0.0050506591796875,
-0.0023708343505859375,
-0.00795745849609375,
0.0165863037109375,
0.0234832763671875,
0.01291656494140625,
-0.016571044921875,
-0.03839111328125,
-0.0298614501953125,
0.019683837890625,
-0.015228271484375,
0.0007905960083007812,
0.02191162109375,
0.021484375,
0.02764892578125,
0.020233154296875,
0.0225982666015625,
-0.0193939208984375,
-0.01464080810546875,
-0.002498626708984375,
0.00970458984375,
-0.0104217529296875,
0.0024852752685546875,
-0.0033817291259765625,
0.0205535888671875,
0.0091705322265625,
-0.0245361328125,
-0.0219879150390625,
-0.01236724853515625,
0.0012083053588867188,
-0.0302734375,
-0.0158843994140625,
0.01419830322265625,
0.013275146484375,
0.0157928466796875,
-0.005634307861328125,
0.0216217041015625,
0.0157318115234375,
0.0160064697265625,
-0.003063201904296875,
-0.00028896331787109375,
-0.01097869873046875,
0.007724761962890625,
-0.0012464523315429688,
0.0020904541015625,
-0.00676727294921875,
-0.00971221923828125,
-0.0172882080078125,
-0.0286865234375,
0.006664276123046875,
0.0006928443908691406,
-0.0149993896484375,
-0.024688720703125,
0.036895751953125,
-0.004474639892578125,
-0.01291656494140625,
-0.006877899169921875,
0.00673675537109375,
-0.0030307769775390625,
0.0212554931640625,
-0.007671356201171875,
-0.01280975341796875,
0.007659912109375,
0.001800537109375,
0.050567626953125,
0.00208282470703125,
-0.01403045654296875,
0.0037174224853515625,
-0.0075836181640625,
-0.01788330078125,
0.0041961669921875,
0.022430419921875,
0.01303863525390625,
-0.016754150390625,
0.01253509521484375,
-0.02545166015625,
-0.051788330078125,
0.007656097412109375,
0.0015821456909179688,
-0.004611968994140625,
0.054840087890625,
-0.00850677490234375,
-0.0218963623046875,
0.0062103271484375,
-0.0167236328125,
-0.0214385986328125,
-0.0184173583984375,
-0.00704193115234375,
0.061798095703125,
-0.0273895263671875,
0.0032863616943359375,
-0.0007476806640625,
-0.0194244384765625,
-0.01143646240234375,
0.046478271484375,
-0.002811431884765625,
0.0019197463989257812,
-0.00464630126953125,
0.038055419921875,
0.0084381103515625,
-0.005458831787109375,
0.007049560546875,
-0.02783203125,
-0.006938934326171875,
0.007259368896484375,
-0.009979248046875,
0.002231597900390625,
-0.0184783935546875,
-0.005474090576171875,
-0.0217742919921875,
0.01116180419921875,
0.01885986328125,
-0.029876708984375,
0.0237884521484375,
-0.0037021636962890625,
0.0029659271240234375,
-0.01409912109375,
0.0049285888671875,
0.03515625,
-0.002971649169921875,
0.016326904296875,
-0.0030727386474609375,
-0.0098419189453125,
-0.005641937255859375,
-0.053070068359375,
0.0240631103515625,
0.03106689453125,
-0.0217132568359375,
0.0037479400634765625,
0.0075225830078125,
-0.02069091796875,
-0.00792694091796875,
0.008819580078125,
0.020233154296875,
-0.002452850341796875,
0.0018968582153320312,
-0.007167816162109375,
0.0023708343505859375,
-0.01268768310546875,
-0.0011262893676757812,
0.00266265869140625,
0.005176544189453125,
0.01300811767578125,
0.003894805908203125,
0.00579071044921875,
-0.0087127685546875,
0.002017974853515625,
-0.01544952392578125,
-0.0467529296875,
0.033966064453125,
0.01258087158203125,
-0.0178375244140625,
0.005695343017578125,
0.0259857177734375,
-0.0032215118408203125,
-0.01451873779296875,
-0.005878448486328125,
-0.0231475830078125,
0.025390625,
-0.0241851806640625,
-0.01013946533203125,
0.0044403076171875,
-0.040069580078125,
-0.004032135009765625,
-0.007049560546875,
-0.03814697265625,
-0.006710052490234375,
0.0008993148803710938,
0.01456451416015625,
0.0146942138671875,
0.0251617431640625,
0.0003407001495361328,
0.021392822265625,
0.0032520294189453125,
-0.0111541748046875,
0.01157379150390625,
-0.0152435302734375,
0.009735107421875,
-0.0044708251953125,
-0.00133514404296875,
-0.016021728515625,
-0.024688720703125,
-0.03851318359375,
-0.004413604736328125,
-0.01020050048828125,
-0.0135650634765625,
0.0034942626953125,
-0.00037860870361328125,
-0.0297088623046875,
0.024627685546875,
-0.00522613525390625,
-0.0135498046875,
0.037017822265625,
-0.009429931640625,
-0.0030536651611328125,
0.005352020263671875,
-0.043792724609375,
-0.00814056396484375,
0.0086669921875,
0.003345489501953125,
0.0041046142578125,
-0.01140594482421875,
-0.036376953125,
0.017059326171875,
-0.00545501708984375,
0.01047515869140625,
-0.01131439208984375,
0.006977081298828125,
-0.0391845703125,
0.014404296875,
0.018646240234375,
-0.0181427001953125,
-0.0010690689086914062,
0.007099151611328125,
-0.0103302001953125,
0.006298065185546875,
0.0248260498046875,
0.034454345703125,
0.031982421875,
0.001556396484375,
-0.030364990234375,
0.036956787109375,
-0.0202178955078125,
-0.02587890625,
-0.01050567626953125,
0.010223388671875,
0.01568603515625,
-0.002140045166015625,
0.018707275390625,
-0.034759521484375,
0.007633209228515625,
0.01428985595703125,
-0.0194091796875,
-0.0018596649169921875,
-0.0276336669921875,
-0.01058197021484375,
-0.0172882080078125,
-0.0182952880859375,
-0.035614013671875,
-0.021514892578125,
0.0301055908203125,
0.027313232421875,
-0.0216827392578125,
0.022247314453125,
-0.006587982177734375,
-0.02154541015625,
-0.034576416015625,
0.01184844970703125,
-0.013336181640625,
0.0155181884765625,
0.037353515625,
0.013214111328125,
0.01239776611328125,
0.00550079345703125,
-0.02252197265625,
-0.001659393310546875,
-0.023834228515625,
-0.006519317626953125,
-0.030609130859375,
0.0177764892578125,
-0.0166168212890625,
0.00771331787109375,
-0.0017099380493164062,
0.0016489028930664062,
0.009307861328125,
-0.0091094970703125,
0.005397796630859375,
-0.0303802490234375,
0.0015926361083984375,
0.04937744140625,
0.0041351318359375,
0.0108489990234375,
-0.008392333984375,
-0.0149993896484375,
0.0372314453125,
0.037872314453125,
-0.003307342529296875,
-0.02410888671875,
0.0074615478515625,
0.027313232421875,
0.0309906005859375,
0.01497650146484375,
0.00016641616821289062,
-0.007343292236328125,
0.01641845703125,
0.055572509765625,
-0.01666259765625,
-0.0253143310546875,
-0.0207672119140625,
-0.00655364990234375,
-0.006134033203125,
0.00408172607421875,
-0.022857666015625,
-0.006771087646484375,
0.033599853515625,
-0.00971221923828125,
-0.0175628662109375,
0.02728271484375,
0.03765869140625,
-0.002315521240234375,
0.031890869140625,
0.018310546875,
0.0338134765625,
-0.0038509368896484375,
0.0279693603515625,
0.01092529296875,
0.026458740234375,
-0.0104217529296875,
0.00789642333984375,
0.01120758056640625,
0.026611328125,
-0.027099609375,
-0.0016508102416992188,
-0.030548095703125,
-0.01276397705078125,
0.0225067138671875,
0.0243072509765625,
-0.0008769035339355469,
0.0064697265625,
-0.007480621337890625,
0.00710296630859375,
0.0160980224609375,
-0.01033782958984375,
-0.0033740997314453125,
-0.004924774169921875,
-0.030731201171875,
0.01236724853515625,
0.020050048828125,
-0.0283203125,
0.00458526611328125,
0.0175018310546875,
0.01160430908203125,
-0.0143890380859375,
0.011871337890625,
0.00273895263671875,
-0.0252838134765625,
-0.01348114013671875,
-0.023468017578125,
-0.0287933349609375,
-0.04864501953125,
-0.0081024169921875,
0.0234832763671875,
-0.027801513671875,
0.0184478759765625,
0.0271453857421875,
-0.0010728836059570312,
0.0223846435546875,
-0.0187835693359375,
-0.02801513671875,
0.028228759765625,
0.0218048095703125,
-0.00560760498046875,
-0.01751708984375,
0.0077362060546875,
0.03399658203125,
0.020751953125,
0.0251312255859375,
0.01110076904296875,
0.00904083251953125,
-0.011566162109375,
-0.0019989013671875,
0.01410675048828125,
-0.00688934326171875,
-0.03436279296875,
0.000015795230865478516,
-0.008331298828125,
-0.008758544921875,
0.01280975341796875,
-0.0226593017578125,
-0.0301055908203125,
-0.025848388671875,
0.0038166046142578125,
-0.0054931640625,
-0.035736083984375,
0.033477783203125,
0.0193939208984375,
-0.0094146728515625,
-0.0082244873046875,
-0.0036163330078125,
-0.01088714599609375,
0.043060302734375,
-0.02642822265625,
0.0096282958984375,
0.01021575927734375,
-0.0281982421875,
0.00946807861328125,
-0.0157318115234375,
-0.023284912109375,
-0.00997161865234375,
-0.0258331298828125,
0.0175323486328125,
-0.017669677734375,
-0.0128326416015625,
-0.0234832763671875,
0.0322265625,
-0.021514892578125,
0.0091552734375,
0.0014896392822265625,
-0.02471923828125,
-0.00841522216796875,
-0.0023479461669921875,
0.0031757354736328125,
0.0026912689208984375,
0.0080413818359375,
0.012237548828125,
0.0005049705505371094,
-0.04327392578125,
0.019500732421875,
0.0024547576904296875,
0.0023479461669921875,
-0.00936126708984375,
-0.006710052490234375,
0.016632080078125,
0.0257568359375,
0.00821685791015625,
0.01012420654296875,
-0.00861358642578125,
0.01690673828125,
0.0095062255859375,
-0.0145416259765625,
0.0220184326171875,
0.0060577392578125,
0.01300048828125,
0.02947998046875,
-0.005977630615234375,
-0.030792236328125,
0.050537109375,
0.00457763671875,
-0.0022525787353515625,
-0.01214599609375,
-0.014495849609375,
-0.0015811920166015625,
-0.0179443359375,
0.0009984970092773438,
0.01299285888671875,
-0.00490570068359375,
0.033477783203125,
-0.046661376953125,
0.006877899169921875,
-0.01198577880859375,
0.003025054931640625,
0.023223876953125,
-0.0343017578125,
0.019317626953125,
-0.006359100341796875,
0.01551055908203125,
0.0276031494140625,
0.003082275390625,
0.01149749755859375,
-0.00567626953125,
-0.0015287399291992188,
0.0008845329284667969,
0.017974853515625,
0.01375579833984375,
0.00923919677734375,
0.029388427734375,
-0.0013751983642578125,
-0.0171661376953125,
-0.038055419921875,
-0.028961181640625,
0.0026798248291015625,
-0.0092315673828125,
0.046417236328125,
0.0025463104248046875,
0.007049560546875,
0.02093505859375,
0.006313323974609375,
-0.0154876708984375,
0.00632476806640625,
-0.0106658935546875,
-0.0084075927734375,
-0.008544921875,
0.0116729736328125,
-0.00145721435546875,
0.01392364501953125,
0.016021728515625,
0.04150390625,
0.003406524658203125,
0.004962921142578125,
0.0037212371826171875,
-0.0260009765625,
0.027496337890625,
0.0350341796875,
-0.0094451904296875,
0.0002319812774658203,
-0.0120849609375,
-0.0025005340576171875,
0.0014848709106445312,
0.0090179443359375,
-0.008087158203125,
0.0232391357421875,
0.0018596649169921875,
-0.026947021484375,
-0.004726409912109375,
-0.0171966552734375,
-0.00612640380859375,
0.0186614990234375,
-0.024688720703125,
0.0167999267578125,
-0.00705718994140625,
0.034759521484375,
0.006298065185546875,
-0.0013599395751953125,
-0.0081787109375,
-0.035430908203125,
0.0098876953125,
-0.0090179443359375,
-0.0200958251953125,
-0.0199127197265625,
0.0027866363525390625,
-0.005153656005859375,
0.00023174285888671875,
0.009033203125,
0.004428863525390625,
-0.0231475830078125,
0.0165863037109375,
-0.007904052734375,
-0.025665283203125,
0.034210205078125,
-0.0011577606201171875,
-0.029510498046875,
-0.0186309814453125,
-0.03875732421875,
0.02154541015625,
-0.002079010009765625,
-0.0009326934814453125,
0.0129241943359375,
-0.01277923583984375,
0.003841400146484375,
-0.0034847259521484375,
0.01320648193359375,
0.0003502368927001953,
-0.002391815185546875,
-0.00548553466796875,
0.036773681640625,
-0.0164947509765625,
0.0294647216796875,
-0.019287109375,
-0.01251983642578125,
0.0181884765625,
-0.0090484619140625,
0.006809234619140625,
-0.006404876708984375,
-0.0031280517578125,
0.0035400390625,
0.0146942138671875,
0.00008654594421386719,
-0.04522705078125,
-0.00763702392578125,
-0.00016057491302490234,
0.005908966064453125,
-0.0222625732421875,
-0.0162353515625,
0.017974853515625,
-0.036376953125,
-0.01654052734375,
-0.04644775390625,
0.0033397674560546875,
-0.006740570068359375,
0.00565338134765625,
-0.0184783935546875,
-0.00817108154296875,
0.035614013671875,
-0.003726959228515625,
-0.0105743408203125,
-0.000377655029296875,
-0.032379150390625,
-0.007694244384765625,
0.022979736328125,
0.006343841552734375,
-0.04681396484375,
-0.00791168212890625,
0.0222930908203125,
-0.00844573974609375,
0.0462646484375,
0.006732940673828125,
-0.00408935546875,
-0.0038433074951171875,
-0.0030670166015625,
-0.0003361701965332031,
-0.00954437255859375,
-0.01508331298828125,
0.0153045654296875,
0.0036182403564453125,
0.0142059326171875,
-0.0003514289855957031,
0.0248260498046875,
-0.00933837890625,
0.0001220703125,
-0.00096893310546875,
0.005489349365234375,
-0.0091705322265625,
-0.0019092559814453125,
0.004150390625,
-0.00904083251953125,
-0.01320648193359375,
0.0016260147094726562,
0.03106689453125,
0.009002685546875,
-0.01018524169921875,
0.0176849365234375,
0.00910186767578125,
-0.01387786865234375,
0.031829833984375,
0.00897216796875,
-0.021392822265625,
-0.0022602081298828125,
-0.01039886474609375,
-0.01114654541015625,
0.00933074951171875,
-0.0018787384033203125,
-0.00376129150390625,
-0.0010824203491210938,
0.02105712890625,
0.006458282470703125,
0.01534271240234375,
-0.0151824951171875,
-0.009552001953125,
-0.002838134765625,
-0.0007252693176269531,
0.01338958740234375,
0.04071044921875,
0.0224456787109375,
0.0025691986083984375,
0.0159912109375,
-0.0301971435546875,
-0.0312347412109375,
0.0347900390625,
-0.028533935546875,
0.0286865234375,
0.00533294677734375,
0.00975799560546875,
-0.026641845703125,
0.023834228515625,
0.006366729736328125,
0.030670166015625,
0.0010366439819335938,
0.0103607177734375,
0.025177001953125,
0.0255889892578125,
-0.0234375,
-0.01171875,
0.02734375,
0.027069091796875,
0.0019474029541015625,
0.021392822265625,
-0.004779815673828125,
0.03076171875,
-0.006504058837890625,
0.01007843017578125,
0.0113372802734375,
0.017181396484375,
-0.0254669189453125,
-0.00939178466796875,
0.0214080810546875,
-0.04156494140625,
-0.005558013916015625,
0.0036869049072265625,
0.00940704345703125,
0.0162506103515625,
-0.010833740234375,
-0.05584716796875,
0.028350830078125,
0.0175628662109375,
0.0193634033203125,
-0.00907135009765625,
0.0277099609375,
0.0138397216796875,
0.0015869140625,
-0.0009984970092773438,
-0.0127410888671875,
0.0235748291015625,
0.044036865234375,
0.002101898193359375,
-0.0189666748046875,
-0.00336456298828125,
-0.016357421875,
-0.01690673828125,
-0.007568359375,
-0.01161956787109375,
-0.0121612548828125,
0.0400390625,
0.005741119384765625,
-0.0310211181640625,
-0.0228424072265625,
-0.00860595703125,
-0.031768798828125,
-0.0027294158935546875,
0.0296783447265625,
-0.0141754150390625,
-0.00982666015625,
-0.005306243896484375,
0.0128173828125,
-0.046417236328125,
0.001926422119140625,
0.0023097991943359375,
0.0019817352294921875,
0.01885986328125,
-0.044677734375,
-0.0197601318359375,
0.0088348388671875,
0.003528594970703125,
0.00004124641418457031,
0.016387939453125,
-0.0146636962890625,
0.01861572265625,
-0.00957489013671875,
0.0194244384765625,
-0.017791748046875,
0.0020198822021484375,
0.0120391845703125,
-0.0145263671875,
-0.005771636962890625,
0.0296783447265625,
-0.02630615234375,
-0.0017528533935546875,
-0.031463623046875,
0.004367828369140625,
0.0165252685546875,
-0.0088653564453125,
-0.0236663818359375,
-0.0003731250762939453,
0.000058591365814208984,
0.01285552978515625,
-0.0290374755859375,
0.007129669189453125,
-0.007297515869140625,
-0.038604736328125,
0.015411376953125,
-0.01262664794921875,
-0.011566162109375,
-0.01177215576171875,
0.003597259521484375,
-0.004108428955078125,
-0.022796630859375,
-0.019927978515625,
0.0237274169921875,
0.040924072265625,
-0.0095062255859375,
0.02130126953125,
0.0137176513671875,
0.0029850006103515625,
-0.00868988037109375,
-0.0188446044921875,
0.01151275634765625,
0.00980377197265625,
-0.0188446044921875,
0.048492431640625,
0.0010595321655273438,
-0.01375579833984375,
0.0032444000244140625,
-0.02154541015625,
0.0206146240234375,
-0.0330810546875,
-0.01525115966796875,
0.003162384033203125,
-0.0200042724609375,
-0.042572021484375,
0.0020275115966796875,
-0.006587982177734375,
0.0226287841796875,
0.0109100341796875,
0.007648468017578125,
0.00409698486328125,
0.0200653076171875,
-0.0177001953125,
-0.052398681640625,
-0.0127410888671875,
-0.028228759765625,
0.01505279541015625,
0.0238037109375,
0.0078582763671875,
0.004726409912109375,
0.01727294921875,
-0.055694580078125,
0.037109375,
-0.005275726318359375,
-0.0235595703125,
-0.0307159423828125,
-0.02239990234375,
0.00766754150390625,
-0.031707763671875,
0.035369873046875,
-0.0241241455078125,
-0.02679443359375,
0.038299560546875,
0.009521484375,
0.042694091796875,
-0.00890350341796875,
0.00847625732421875,
-0.0025653839111328125,
-0.0184173583984375,
0.046417236328125,
0.02734375,
0.001903533935546875,
0.00033402442932128906,
-0.003620147705078125,
-0.0007548332214355469,
0.032135009765625,
-0.00539398193359375,
0.01302337646484375,
0.00586700439453125,
-0.0028228759765625,
-0.0143890380859375,
-0.024566650390625,
0.00939178466796875,
0.006114959716796875,
-0.000743865966796875,
-0.033966064453125,
0.03509521484375,
0.0034122467041015625,
0.00791168212890625,
-0.0556640625,
-0.024993896484375,
0.0274200439453125,
0.00017964839935302734,
-0.035430908203125,
-0.016754150390625,
0.006938934326171875,
0.001361846923828125,
-0.0129241943359375,
0.055206298828125,
0.02587890625,
0.029998779296875,
0.01291656494140625,
-0.00897979736328125,
0.0117950439453125,
-0.00878143310546875,
0.00487518310546875,
-0.040618896484375,
-0.00647735595703125,
-0.00754547119140625,
0.01284027099609375,
0.006999969482421875,
-0.0117340087890625,
0.00293731689453125,
0.015838623046875,
-0.010955810546875,
0.013092041015625,
0.0214996337890625,
-0.008575439453125,
0.03179931640625,
-0.021331787109375,
0.0181121826171875,
0.0074005126953125,
0.0132904052734375,
-0.050933837890625,
-0.01021575927734375,
-0.02557373046875,
-0.0014200210571289062,
0.01275634765625,
-0.029052734375,
0.022064208984375,
0.02764892578125,
0.011138916015625,
-0.01934814453125,
-0.024261474609375,
-0.02435302734375,
-0.02374267578125,
-0.01389312744140625,
-0.02093505859375,
-0.0196380615234375,
0.0206298828125,
0.032470703125,
-0.016265869140625,
0.0258941650390625,
0.0188140869140625,
0.005126953125,
0.02008056640625,
-0.007266998291015625,
0.0135498046875,
-0.0092010498046875,
-0.0024166107177734375,
-0.01104736328125,
0.00214385986328125,
-0.0004665851593017578,
-0.036651611328125,
0.026031494140625,
0.0256805419921875,
0.006923675537109375,
-0.0124053955078125,
0.031768798828125,
0.0291748046875,
0.0017881393432617188,
0.0106964111328125,
0.0241241455078125,
-0.019256591796875,
-0.01544952392578125,
-0.00424957275390625,
-0.0250701904296875,
0.02923583984375,
-0.0095062255859375,
0.037078857421875,
-0.0089263916015625,
0.0234222412109375,
0.036529541015625,
-0.01216888427734375,
-0.018157958984375,
-0.002872467041015625,
0.0017757415771484375,
0.007511138916015625,
0.0252532958984375,
0.007293701171875,
-0.002338409423828125,
0.00020933151245117188,
0.0186309814453125,
0.018218994140625,
0.02911376953125,
0.01904296875,
-0.005828857421875,
-0.0287017822265625,
-0.0074615478515625,
0.001239776611328125,
-0.0235137939453125,
0.00746917724609375,
0.01561737060546875,
0.0177764892578125,
-0.01358795166015625,
0.010650634765625,
-0.0340576171875,
-0.003997802734375,
-0.00891876220703125,
-0.01824951171875,
0.00605010986328125,
0.013641357421875,
0.0276336669921875,
0.00036144256591796875,
-0.0207672119140625,
0.002170562744140625,
0.00787353515625,
0.0158233642578125,
-0.011383056640625,
0.0150909423828125,
0.00521087646484375,
0.01084136962890625,
-0.0006165504455566406,
0.0016412734985351562,
0.001529693603515625,
-0.0181121826171875,
0.01947021484375,
-0.00202178955078125,
-0.0029201507568359375,
0.0151519775390625,
0.00015532970428466797,
-0.003299713134765625,
0.0051422119140625,
-0.0077972412109375,
0.021514892578125,
-0.019866943359375,
-0.000690460205078125,
-0.01153564453125,
0.002567291259765625,
0.005077362060546875,
0.0032024383544921875,
-0.00788116455078125,
-0.015960693359375,
-0.0169677734375,
-0.00838470458984375,
-0.0112152099609375,
0.00905609130859375,
-0.0316162109375,
0.0242462158203125,
-0.055908203125,
-0.0137939453125,
-0.044647216796875,
-0.0296783447265625,
-0.00038743019104003906,
-0.016845703125,
-0.0160369873046875,
0.0204925537109375,
0.015777587890625,
-0.03179931640625,
-0.040496826171875,
-0.01227569580078125,
-0.01181793212890625,
0.033935546875,
-0.0144195556640625,
-0.0277099609375,
-0.006298065185546875,
-0.035491943359375,
-0.005580902099609375,
-0.0147247314453125,
0.0007939338684082031,
0.0149688720703125,
0.0156707763671875,
-0.04052734375,
-0.034027099609375,
-0.01482391357421875,
-0.007541656494140625,
0.020294189453125,
-0.0202484130859375,
-0.0235443115234375,
0.0296783447265625,
0.0008540153503417969,
-0.00890350341796875,
0.01146697998046875,
-0.00930023193359375,
0.003658294677734375,
-0.007049560546875,
0.0178375244140625,
-0.00553131103515625,
0.0205535888671875,
0.013824462890625,
0.00618743896484375,
-0.01538848876953125,
-0.0019197463989257812,
0.0124053955078125,
-0.050048828125,
0.0264434814453125,
-0.01250457763671875,
0.01248931884765625,
-0.0158233642578125,
-0.0369873046875,
-0.0119171142578125,
0.0215911865234375,
0.0171356201171875,
0.0215301513671875,
-0.022003173828125,
0.0024700164794921875,
0.039520263671875,
-0.0209197998046875,
0.05615234375,
-0.01201629638671875,
0.01496124267578125,
0.00820159912109375,
0.0272979736328125,
0.00652313232421875,
0.0240631103515625,
-0.06243896484375,
0.0005083084106445312,
-0.035736083984375,
0.0225982666015625,
-0.017242431640625,
0.035888671875,
-0.01227569580078125,
-0.0014791488647460938,
-0.0228118896484375,
0.0089111328125,
0.01885986328125,
-0.0162811279296875,
-0.0069122314453125,
0.023406982421875,
-0.046539306640625,
0.0015106201171875,
0.01477813720703125,
0.007122039794921875,
-0.0105438232421875,
0.01702880859375,
-0.01264190673828125,
-0.01776123046875,
0.00376129150390625,
-0.00205230712890625,
-0.005779266357421875,
0.00420379638671875,
-0.0251007080078125,
-0.00102996826171875,
0.0023632049560546875,
-0.005268096923828125,
-0.0085296630859375,
0.0010156631469726562,
-0.00635528564453125,
0.01434326171875,
-0.0243682861328125,
-0.01036834716796875,
0.01116943359375,
-0.004177093505859375,
-0.029815673828125,
0.0297698974609375,
0.0009927749633789062,
0.0310821533203125,
0.00653839111328125,
-0.0211029052734375,
-0.01861572265625,
0.004764556884765625,
-0.00978851318359375,
0.0016050338745117188,
0.0193634033203125,
-0.0183868408203125,
-0.024383544921875,
-0.003940582275390625,
-0.01422119140625,
0.0169219970703125,
-0.005077362060546875,
0.002948760986328125,
-0.0009918212890625,
0.0240020751953125,
-0.01486968994140625,
0.01204681396484375,
0.00771331787109375,
-0.005672454833984375,
0.005435943603515625,
-0.0080413818359375,
-0.0172576904296875,
-0.029144287109375,
0.0005035400390625,
-0.0312347412109375,
0.016357421875,
-0.024200439453125,
-0.0101165771484375,
-0.012237548828125,
0.0380859375,
0.004680633544921875,
0.01239776611328125,
-0.0140533447265625,
0.0056304931640625,
-0.0151214599609375,
0.045501708984375,
0.019256591796875,
0.015716552734375,
-0.01015472412109375,
0.005237579345703125,
-0.0008678436279296875,
-0.0190277099609375,
-0.0181884765625,
0.002841949462890625,
0.034515380859375,
-0.01316070556640625,
0.00872802734375,
0.0171051025390625,
-0.0227203369140625,
-0.0276336669921875,
-0.0274505615234375,
-0.0210723876953125,
-0.010955810546875,
0.010986328125,
0.01482391357421875,
-0.004486083984375,
0.0099945068359375,
0.01544189453125,
0.03948974609375,
-0.0217437744140625,
0.0007739067077636719,
0.04541015625,
-0.04901123046875,
0.0040740966796875,
-0.0019235610961914062,
-0.00048089027404785156,
-0.0168609619140625,
0.007717132568359375,
0.005764007568359375,
-0.020599365234375,
0.0164031982421875,
0.0122833251953125,
-0.031585693359375,
-0.01143646240234375,
0.00640106201171875,
0.009552001953125,
0.0036907196044921875,
-0.034027099609375,
0.0160369873046875,
0.0163421630859375,
0.0210723876953125,
0.00839996337890625,
0.0223388671875,
0.0032329559326171875,
-0.0106048583984375,
0.054107666015625,
-0.023040771484375,
0.0282135009765625,
-0.002521514892578125,
-0.016357421875,
0.016632080078125,
-0.0265960693359375,
0.0014133453369140625,
-0.0043182373046875,
-0.0218505859375,
-0.01507568359375,
-0.0036563873291015625,
-0.0119476318359375,
0.0080108642578125,
-0.0243072509765625,
0.004566192626953125,
-0.013946533203125,
0.034393310546875,
-0.00811767578125,
-0.042724609375,
-0.009674072265625,
-0.004039764404296875,
0.035247802734375,
0.01312255859375,
-0.01593017578125,
0.0170135498046875,
0.035125732421875,
-0.022064208984375,
0.025115966796875,
0.0007543563842773438,
-0.0299835205078125,
0.026214599609375,
0.011749267578125,
-0.00769805908203125,
0.006481170654296875,
-0.023834228515625,
-0.004627227783203125,
0.03302001953125,
0.039886474609375,
0.0021152496337890625,
0.0038890838623046875,
0.01137542724609375,
0.01181793212890625,
-0.0033893585205078125,
0.00598907470703125,
-0.00811004638671875,
0.0128326416015625,
-0.0288238525390625,
-0.0098114013671875,
-0.0033245086669921875,
-0.0019216537475585938,
-0.0269622802734375,
0.0264892578125,
-0.01318359375,
0.008697509765625,
-0.0016374588012695312,
0.02301025390625,
-0.01207733154296875,
0.03057861328125,
0.0076904296875,
-0.025970458984375,
-0.0037364959716796875,
-0.0273284912109375,
-0.005191802978515625,
-0.0007476806640625,
-0.01413726806640625,
-0.0144500732421875,
-0.01331329345703125,
-0.040802001953125,
-0.007297515869140625,
-0.022125244140625,
-0.0469970703125,
-0.0087432861328125,
0.02447509765625,
0.00897979736328125,
0.02435302734375,
0.0440673828125,
0.037078857421875,
0.00142669677734375,
0.01454925537109375,
-0.015655517578125,
-0.002964019775390625,
-0.029815673828125,
0.0382080078125,
-0.017578125,
0.01116943359375,
0.01450347900390625,
0.0018968582153320312,
-0.0197906494140625,
-0.036376953125,
0.0293426513671875,
0.031463623046875,
0.0095672607421875,
0.00818634033203125,
0.00494384765625,
0.034393310546875,
0.021270751953125,
-0.04144287109375,
-0.038421630859375,
-0.00862884521484375,
0.0060272216796875,
0.0367431640625,
0.0311279296875,
-0.00777435302734375,
-0.032867431640625,
0.032440185546875,
0.005794525146484375,
-0.0003814697265625,
-0.01119232177734375,
0.0013036727905273438,
0.005504608154296875,
-0.0209197998046875,
-0.0146942138671875,
-0.019927978515625,
0.0302886962890625,
0.0012102127075195312,
0.01560211181640625,
-0.03155517578125,
0.00618743896484375,
0.031158447265625,
-0.00917816162109375,
-0.0298614501953125,
-0.01291656494140625,
-0.00954437255859375,
0.01885986328125,
-0.0185394287109375,
-0.00475311279296875,
-0.00817108154296875,
0.0015544891357421875,
-0.006500244140625,
-0.0004177093505859375,
-0.0038776397705078125,
0.05218505859375,
-0.024505615234375,
-0.0213775634765625,
0.01261138916015625,
-0.0170440673828125,
-0.00595855712890625,
0.0222320556640625,
0.0205078125,
0.0155029296875,
-0.0116729736328125,
0.031982421875,
-0.00795745849609375,
0.01166534423828125,
0.041015625,
-0.0036144256591796875,
-0.01416778564453125,
-0.0154876708984375,
-0.01678466796875,
0.005443572998046875,
0.0209808349609375,
-0.0435791015625,
-0.01113128662109375,
-0.020233154296875,
-0.0037326812744140625,
-0.0134735107421875,
-0.041595458984375,
0.00949859619140625,
0.00525665283203125,
-0.00409698486328125,
0.02655029296875,
-0.0028858184814453125,
-0.06231689453125,
0.008880615234375,
-0.0063018798828125,
0.0273590087890625,
0.019775390625,
0.0026340484619140625,
-0.017364501953125,
-0.0004627704620361328,
0.00743865966796875,
-0.0185546875,
-0.01100921630859375,
-0.0122833251953125,
0.04022216796875,
-0.0109405517578125,
-0.00780487060546875,
-0.0155792236328125,
-0.0297393798828125,
-0.014404296875,
-0.013336181640625,
-0.0236663818359375,
-0.00959014892578125,
0.00865936279296875,
0.0218048095703125,
0.025665283203125,
-0.00424957275390625,
0.01538848876953125,
-0.00444793701171875,
-0.018798828125,
0.0146331787109375,
-0.00875091552734375,
-0.0019054412841796875,
-0.0010137557983398438,
0.027099609375,
-0.008056640625,
-0.01381683349609375,
0.01197052001953125,
-0.003459930419921875,
-0.0035076141357421875,
0.007312774658203125,
-0.0224456787109375,
0.005496978759765625,
0.00685882568359375,
0.0192108154296875,
0.0167388916015625,
-0.0131988525390625,
0.005126953125,
0.0287933349609375,
-0.0038509368896484375,
-0.0171966552734375,
0.015716552734375,
0.0250396728515625,
0.00975799560546875,
-0.007686614990234375,
-0.00585174560546875,
-0.0030117034912109375,
-0.01169586181640625,
-0.0157928466796875,
0.035247802734375,
0.005420684814453125,
0.01328277587890625,
0.03887939453125,
-0.00696563720703125,
0.062744140625,
0.00011783838272094727,
0.0023345947265625,
0.032623291015625,
-0.005802154541015625,
0.002056121826171875,
-0.0118560791015625,
0.005168914794921875,
-0.0269622802734375,
0.0183258056640625,
-0.013153076171875,
0.01727294921875,
0.033935546875,
-0.01355743408203125,
-0.01134490966796875,
-0.0234375,
-0.00789642333984375,
-0.0111083984375,
0.007678985595703125,
0.029083251953125,
-0.0162506103515625,
0.0159912109375,
-0.01043701171875,
0.01727294921875,
0.005062103271484375,
-0.006683349609375,
-0.026092529296875,
0.0017728805541992188,
0.04901123046875,
0.007843017578125,
0.01418304443359375,
-0.004291534423828125,
-0.01177215576171875,
0.022003173828125,
0.046600341796875,
-0.01079559326171875,
-0.0175018310546875,
0.0462646484375,
0.0024356842041015625,
0.0173187255859375,
-0.004299163818359375,
-0.0030460357666015625,
-0.0200653076171875,
0.0156402587890625,
-0.030548095703125,
-0.0081787109375,
0.020660400390625,
-0.023162841796875,
-0.0133056640625,
-0.024871826171875,
0.0007228851318359375,
-0.0308837890625,
0.01285552978515625,
-0.0297393798828125,
0.002735137939453125,
0.0181884765625,
-0.0548095703125,
-0.006740570068359375,
-0.015045166015625,
-0.01800537109375,
-0.0108642578125,
-0.0007028579711914062,
-0.00711822509765625,
-0.0006208419799804688,
0.0276641845703125,
0.0159759521484375,
0.0003228187561035156,
0.016510009765625,
-0.0138397216796875,
0.0092620849609375,
-0.00247955322265625,
-0.060211181640625,
0.0038700103759765625,
-0.0018062591552734375,
0.0152130126953125,
0.0396728515625,
0.0127410888671875,
0.01168060302734375,
-0.00244903564453125,
-0.00487518310546875,
0.024261474609375,
-0.0311431884765625,
-0.00030493736267089844,
0.005641937255859375,
-0.00485992431640625,
0.005702972412109375,
0.0098419189453125,
0.00872039794921875,
-0.0328369140625,
-0.0028076171875,
0.006580352783203125,
0.0023403167724609375,
-0.0095062255859375,
0.020233154296875,
-0.026336669921875,
0.004077911376953125,
0.0210723876953125,
-0.0110626220703125,
-0.0031223297119140625,
0.042266845703125,
0.0137176513671875,
0.0242462158203125,
0.04571533203125,
0.0282745361328125,
-0.0222320556640625,
-0.020172119140625,
0.0260772705078125,
0.0216064453125,
0.039215087890625,
-0.01009368896484375,
0.0207672119140625,
-0.0170440673828125,
0.00531768798828125,
0.00075531005859375,
-0.0018100738525390625,
-0.01418304443359375,
-0.0240936279296875,
0.0269927978515625,
0.00505828857421875,
-0.0430908203125,
0.0003566741943359375,
-0.0005631446838378906,
0.005908966064453125,
-0.0013895034790039062,
0.01186370849609375,
-0.006832122802734375,
-0.0008082389831542969,
0.006122589111328125,
0.00797271728515625,
0.01554107666015625,
0.0177154541015625,
0.0023288726806640625,
-0.036041259765625,
-0.00504302978515625,
-0.0020847320556640625,
0.013671875,
0.00926971435546875,
0.0322265625,
-0.0032958984375,
-0.003528594970703125,
-0.01360321044921875,
-0.0189361572265625,
0.040191650390625,
-0.023529052734375,
0.003871917724609375,
0.0133819580078125,
-0.039794921875,
0.035858154296875,
-0.0029888153076171875,
0.0236663818359375,
-0.02044677734375,
-0.019989013671875,
-0.017852783203125,
0.0126800537109375,
0.00870513916015625,
-0.01206207275390625,
-0.01532745361328125,
-0.01406097412109375,
-0.0006809234619140625,
0.0128326416015625,
0.007049560546875,
0.03558349609375,
-0.0245819091796875,
0.01025390625,
-0.0302734375,
0.0275421142578125,
0.01110076904296875,
-0.0233612060546875,
0.01513671875,
-0.005939483642578125,
-0.02716064453125,
-0.0174102783203125,
0.0284271240234375,
-0.0038204193115234375,
-0.027435302734375,
0.0093231201171875,
-0.0094146728515625,
0.0014247894287109375,
-0.023162841796875,
0.026519775390625,
0.0176849365234375,
-0.0178375244140625,
0.01371002197265625,
-0.0163421630859375,
0.0200042724609375,
0.0122528076171875,
-0.03826904296875,
0.0247955322265625,
-0.0174560546875,
0.045623779296875,
-0.011993408203125,
-0.01424407958984375,
0.01192474365234375,
-0.007762908935546875,
0.01227569580078125,
0.0022296905517578125,
-0.00783538818359375,
0.01250457763671875,
0.033905029296875,
0.0009565353393554688,
-0.00707244873046875,
-0.0233154296875,
-0.0017757415771484375,
0.007572174072265625,
-0.01422119140625,
0.01461029052734375,
0.00606536865234375,
0.020355224609375,
-0.015838623046875,
-0.031829833984375,
-0.0302581787109375,
-0.000027894973754882812,
0.01036834716796875,
0.0043487548828125,
-0.00807952880859375,
0.00804901123046875,
0.00708770751953125,
0.01031494140625,
-0.00530242919921875,
-0.039886474609375,
0.00421905517578125,
0.0186920166015625,
-0.0268096923828125,
0.011077880859375,
0.03155517578125,
0.0020732879638671875,
0.018524169921875,
0.01331329345703125,
0.0086822509765625,
0.01409149169921875,
0.0014362335205078125,
-0.020904541015625,
-0.0012655258178710938,
-0.0007495880126953125,
0.016082763671875,
0.0022182464599609375,
-0.03448486328125,
-0.003383636474609375,
-0.022979736328125,
-0.0111083984375,
-0.02166748046875,
-0.019927978515625,
0.011688232421875,
0.03192138671875,
0.0261993408203125,
-0.01232147216796875,
-0.020294189453125,
0.0369873046875,
0.00994873046875,
-0.0133056640625,
-0.01021575927734375,
-0.0005559921264648438,
0.00885009765625,
-0.003902435302734375,
0.01312255859375,
-0.01837158203125,
0.0018205642700195312,
0.01519775390625,
-0.018646240234375,
0.010833740234375,
-0.00972747802734375,
-0.031005859375,
-0.002483367919921875,
-0.0164947509765625,
-0.00852203369140625,
-0.0284881591796875,
-0.00568389892578125,
-0.026275634765625,
0.005596160888671875,
0.000675201416015625,
0.0013189315795898438,
0.00803375244140625,
0.01519775390625,
0.0205841064453125,
-0.004840850830078125,
-0.029571533203125,
0.007122039794921875,
0.0153045654296875,
-0.00015819072723388672,
0.0043792724609375,
-0.0100250244140625,
0.00608062744140625,
-0.0003337860107421875,
0.005008697509765625,
0.0178985595703125,
-0.006771087646484375,
-0.028411865234375,
0.0024433135986328125,
0.0169219970703125,
-0.0236053466796875,
0.00115203857421875,
0.0227813720703125,
0.0212249755859375,
0.0157012939453125,
0.0022735595703125,
0.0131072998046875,
0.0286712646484375,
-0.0111236572265625,
0.01497650146484375,
0.0198516845703125,
0.01373291015625,
-0.0123443603515625,
0.023468017578125,
0.0025005340576171875,
0.046356201171875,
0.031402587890625,
-0.01354217529296875,
0.013702392578125,
-0.02496337890625,
-0.0197601318359375,
0.0201416015625,
0.016937255859375,
-0.0035343170166015625,
-0.006763458251953125,
-0.00583648681640625,
0.0037860870361328125,
-0.00852203369140625,
-0.005565643310546875,
0.005859375,
-0.0057525634765625,
-0.010284423828125,
0.0198516845703125,
-0.029144287109375,
0.00727081298828125,
0.000019371509552001953,
-0.04986572265625,
-0.036163330078125,
-0.0007739067077636719,
0.05633544921875,
0.0030307769775390625,
-0.0161285400390625,
-0.0285186767578125,
-0.0007243156433105469,
-0.016448974609375,
-0.0082244873046875,
0.003948211669921875,
0.01043701171875,
0.0010786056518554688,
0.01537322998046875,
-0.021514892578125,
-0.02520751953125,
-0.00917816162109375,
0.0006909370422363281,
0.0267486572265625,
-0.006412506103515625,
0.0007867813110351562,
-0.00588226318359375,
0.005390167236328125,
-0.0042724609375,
-0.0006451606750488281,
-0.00499725341796875,
0.01268768310546875,
-0.033172607421875,
0.01459503173828125,
0.0003910064697265625,
0.00902557373046875,
0.005161285400390625,
-0.030120849609375,
-0.027557373046875,
-0.00926971435546875,
-0.0018253326416015625,
0.0199737548828125,
-0.01114654541015625,
-0.002140045166015625,
-0.0024929046630859375,
0.005290985107421875,
-0.03564453125,
0.02545166015625,
0.0001989603042602539,
0.0177154541015625,
-0.0213623046875,
0.0254364013671875,
-0.010955810546875,
-0.00714874267578125,
0.00127410888671875,
-0.018951416015625,
-0.048248291015625,
-0.008392333984375,
0.00998687744140625,
0.0182952880859375,
-0.02728271484375,
-0.000005245208740234375,
-0.0150909423828125,
0.00899505615234375,
0.002613067626953125,
0.016021728515625,
0.0232696533203125,
0.023345947265625,
-0.01279449462890625,
-0.007564544677734375,
0.0017671585083007812,
0.005168914794921875,
-0.0211334228515625,
-0.01285552978515625,
-0.0188446044921875,
0.007537841796875,
-0.018280029296875,
0.01049041748046875,
-0.016693115234375,
0.0032978057861328125,
-0.00905609130859375,
0.00711822509765625,
0.03656005859375,
0.029449462890625,
0.0016260147094726562,
0.007534027099609375,
-0.0230560302734375,
-0.0027141571044921875,
-0.0166168212890625,
0.004779815673828125,
0.02398681640625,
0.0025310516357421875,
-0.03338623046875,
0.00882720947265625,
0.02301025390625,
0.005550384521484375,
-0.0265045166015625,
0.0019779205322265625,
0.032806396484375,
-0.00801849365234375,
0.03759765625,
-0.0033416748046875,
0.00344085693359375,
-0.007144927978515625,
-0.03216552734375,
0.001476287841796875,
-0.023590087890625,
-0.00009518861770629883,
0.00818634033203125,
-0.0209808349609375,
-0.003387451171875,
-0.005443572998046875,
-0.0012378692626953125,
-0.04168701171875,
-0.01184844970703125,
0.026885986328125,
-0.020843505859375,
0.01291656494140625,
0.0273895263671875,
0.0165557861328125,
-0.0028934478759765625,
0.0280914306640625,
-0.0037784576416015625,
-0.01702880859375,
0.011993408203125,
-0.00034546852111816406,
0.03240966796875,
0.0205078125,
0.028656005859375,
-0.0010957717895507812,
0.01374053955078125,
0.03350830078125,
-0.01300048828125,
0.01287841796875,
0.0025577545166015625,
-0.0012483596801757812,
0.00146484375,
-0.00390625,
-0.008087158203125,
0.04083251953125,
0.0386962890625,
0.01313018798828125,
0.034393310546875,
-0.0018100738525390625,
-0.007747650146484375,
0.004398345947265625,
-0.0262298583984375,
-0.010040283203125,
-0.047637939453125,
0.035614013671875,
-0.007579803466796875,
0.0039043426513671875,
0.0195465087890625,
0.0050201416015625,
-0.0306243896484375,
0.038177490234375,
-0.0062713623046875,
0.0164642333984375,
0.028472900390625,
-0.0250091552734375,
-0.0242462158203125,
0.000812530517578125,
-0.0012912750244140625,
-0.0015840530395507812,
0.0465087890625,
-0.03125,
0.02117919921875,
0.0129547119140625,
0.019378662109375,
0.02716064453125,
0.0260162353515625,
-0.025115966796875,
-0.01268768310546875,
-0.0218353271484375,
0.01554107666015625,
0.0116729736328125,
0.04095458984375,
0.038970947265625,
0.012054443359375,
-0.04888916015625,
-0.0223236083984375,
-0.01258087158203125,
-0.00858306884765625,
-0.056610107421875,
0.0177459716796875,
-0.020660400390625,
0.02752685546875,
0.02374267578125,
-0.0269927978515625,
0.01053619384765625,
-0.008880615234375,
0.0062103271484375,
-0.0224456787109375,
0.003391265869140625,
0.0265655517578125,
0.012298583984375,
-0.0182342529296875,
0.03363037109375,
0.01739501953125,
0.00966644287109375,
0.00670623779296875,
-0.004688262939453125,
0.00475311279296875,
0.005397796630859375,
-0.01708984375,
0.00862884521484375,
0.00028777122497558594,
0.022979736328125,
0.0078277587890625,
-0.0200653076171875,
-0.0394287109375,
0.0214996337890625,
0.0127716064453125,
0.01445770263671875,
-0.0308685302734375,
-0.01517486572265625,
0.0189361572265625,
-0.01336669921875,
-0.00616455078125,
-0.0220794677734375,
-0.01090240478515625,
0.006317138671875,
0.016937255859375,
0.0059051513671875,
0.01523590087890625,
0.0012502670288085938,
-0.01508331298828125,
-0.0129547119140625,
-0.0019741058349609375,
0.0240936279296875,
-0.0017642974853515625,
-0.014007568359375,
-0.01209259033203125,
-0.003200531005859375,
0.0200347900390625,
0.0269317626953125,
0.0080413818359375,
0.0002949237823486328,
-0.0004696846008300781,
-0.019866943359375,
-0.0128021240234375,
0.031982421875,
0.008270263671875,
-0.0031890869140625,
0.01187896728515625,
0.0003979206085205078,
0.006244659423828125,
-0.0000743865966796875,
0.00102996826171875,
0.05145263671875,
-0.0310821533203125,
-0.0212249755859375,
0.0003428459167480469,
-0.006633758544921875,
-0.0208740234375,
-0.061309814453125,
0.0171051025390625,
0.006591796875,
-0.0225982666015625,
0.009124755859375,
-0.006389617919921875,
-0.002460479736328125,
0.01104736328125,
0.0053558349609375,
-0.0171051025390625,
-0.01294708251953125,
0.006092071533203125,
0.0164947509765625,
-0.004486083984375,
-0.0245819091796875,
0.00614166259765625,
-0.007503509521484375,
-0.004322052001953125,
0.01421356201171875,
-0.00263214111328125,
-0.06695556640625,
0.01971435546875,
0.014068603515625,
-0.00905609130859375,
0.014312744140625,
0.0028705596923828125,
0.002941131591796875,
-0.00788116455078125,
0.00841522216796875,
-0.01397705078125,
0.03765869140625,
0.01343536376953125,
-0.024871826171875,
-0.0195159912109375,
-0.0009150505065917969,
0.0015783309936523438,
-0.032470703125,
0.0002932548522949219,
-0.0161895751953125,
0.00518035888671875,
-0.0284576416015625,
-0.00698089599609375,
-0.025177001953125,
-0.0123291015625,
-0.03326416015625,
-0.01265716552734375,
-0.024261474609375,
0.01519775390625,
-0.010955810546875,
0.020751953125,
-0.028533935546875,
0.0196990966796875,
0.0261383056640625,
-0.0125274658203125,
-0.001773834228515625,
0.0166015625,
-0.0097198486328125,
-0.0038299560546875,
-0.0206146240234375,
0.00766754150390625,
0.005062103271484375,
0.04107666015625,
0.0091400146484375,
0.006038665771484375,
0.03857421875,
0.035369873046875,
-0.021575927734375,
0.00861358642578125,
0.00794219970703125,
0.0030803680419921875,
0.016876220703125,
0.0016937255859375,
0.00408935546875,
0.00601959228515625,
0.0215301513671875,
-0.0182647705078125,
-0.01190948486328125,
-0.003993988037109375,
0.00865936279296875,
-0.000007033348083496094,
-0.03277587890625,
-0.0003311634063720703,
0.007541656494140625,
-0.0113525390625,
0.005584716796875,
-0.0120391845703125,
-0.01111602783203125,
0.01971435546875,
-0.025390625,
-0.0279541015625,
-0.01210784912109375,
-0.0186004638671875,
0.0026416778564453125,
-0.020263671875,
0.0013322830200195312,
-0.0002486705780029297,
-0.027862548828125,
0.007598876953125,
0.0189971923828125,
0.038177490234375,
-0.0027256011962890625,
-0.00833892822265625,
-0.018402099609375,
0.0238037109375,
0.0124359130859375,
0.015960693359375,
-0.0328369140625,
-0.004642486572265625,
0.01629638671875,
0.018280029296875,
-0.02349853515625,
0.00022923946380615234,
-0.01343536376953125,
0.0236358642578125,
-0.0023193359375,
-0.00466156005859375,
-0.05133056640625,
0.03875732421875,
-0.0028018951416015625,
-0.01197052001953125,
-0.019622802734375,
0.00864410400390625,
0.01485443115234375,
-0.004543304443359375,
-0.016998291015625,
0.005649566650390625,
0.0211181640625,
0.01433563232421875,
0.01190948486328125,
-0.010772705078125,
-0.01047515869140625,
0.00917816162109375,
0.0083770751953125,
-0.006404876708984375,
0.0284271240234375,
-0.0087738037109375,
0.0269775390625,
0.0192108154296875,
0.0521240234375,
-0.0264129638671875,
0.01666259765625,
0.00553131103515625,
-0.0081787109375,
-0.038238525390625,
-0.019805908203125,
-0.01146697998046875,
0.0022716522216796875,
0.047821044921875,
0.006053924560546875,
0.025543212890625,
0.018646240234375,
-0.00428009033203125,
-0.03424072265625,
-0.0318603515625,
0.02886962890625,
0.01314544677734375,
-0.013641357421875,
-0.013336181640625,
-0.0245361328125,
-0.03839111328125,
0.02197265625,
0.006053924560546875,
-0.0244598388671875,
-0.01528167724609375,
-0.0175018310546875,
-0.0214385986328125,
-0.003116607666015625,
-0.016571044921875,
-0.0240478515625,
-0.00909423828125,
-0.008514404296875,
0.0041046142578125,
-0.043670654296875,
-0.01065826416015625,
-0.008880615234375,
-0.0064849853515625,
-0.005237579345703125,
0.046875,
-0.00913238525390625,
-0.006130218505859375,
0.0002777576446533203,
-0.0018825531005859375,
0.0138397216796875,
0.00850677490234375,
-0.014495849609375,
-0.005584716796875,
-0.0128021240234375,
-0.03204345703125,
-0.0114593505859375,
-0.0015735626220703125,
0.01165771484375,
0.0029468536376953125,
-0.0182037353515625,
-0.0188140869140625,
-0.0199127197265625,
-0.0173797607421875,
-0.01290130615234375,
-0.020599365234375,
-0.0205078125,
-0.0013303756713867188,
-0.00673675537109375,
-0.0008068084716796875,
0.0179443359375,
0.0155029296875,
0.006450653076171875,
-0.00543975830078125,
-0.0005197525024414062,
0.0105133056640625,
0.005107879638671875,
0.027069091796875,
-0.00921630859375,
-0.02081298828125,
0.0195770263671875,
0.04803466796875,
0.044708251953125,
-0.0460205078125,
0.03021240234375,
-0.004337310791015625,
0.01934814453125,
0.031890869140625,
0.00984954833984375,
0.029022216796875,
-0.005168914794921875,
-0.006252288818359375,
-0.021942138671875,
0.0021648406982421875,
0.006046295166015625,
0.002765655517578125,
0.00887298583984375,
0.0139923095703125,
-0.0132904052734375,
-0.0143585205078125,
0.016937255859375,
0.01421356201171875,
-0.01030731201171875,
-0.00261688232421875,
0.0194854736328125,
0.014739990234375,
0.044189453125,
-0.0215911865234375,
0.01360321044921875,
-0.0007371902465820312,
-0.0301971435546875,
0.004367828369140625,
0.024017333984375,
0.01308441162109375,
-0.0071563720703125,
0.00705718994140625,
0.046630859375,
0.0018072128295898438,
-0.05572509765625,
-0.00266265869140625,
0.016571044921875,
0.019622802734375,
0.0193634033203125,
-0.0175628662109375,
-0.02813720703125,
0.0005121231079101562,
0.02984619140625,
-0.0185089111328125,
0.00152587890625,
0.016387939453125,
-0.039031982421875,
-0.005619049072265625,
-0.0096282958984375,
-0.0162811279296875,
-0.0018329620361328125,
0.0031871795654296875,
0.016998291015625,
-0.0021572113037109375,
0.0050201416015625,
0.003803253173828125,
0.01654052734375,
0.005889892578125,
0.01270294189453125,
-0.03338623046875,
0.0009164810180664062,
0.01654052734375,
-0.006931304931640625,
-0.007537841796875,
0.01175689697265625,
-0.01229095458984375,
0.0254974365234375,
0.00012230873107910156,
-0.004726409912109375,
0.0081634521484375,
-0.006591796875,
0.02392578125,
0.006267547607421875,
-0.00824737548828125,
-0.006160736083984375,
0.0284881591796875,
0.011077880859375,
-0.031005859375,
-0.00829315185546875,
0.0287933349609375,
-0.0182952880859375,
0.03759765625,
0.0006647109985351562,
-0.01331329345703125,
0.0235595703125,
-0.0103759765625,
-0.0212249755859375,
-0.03521728515625,
0.0006237030029296875,
0.0269622802734375,
-0.02142333984375,
-0.003814697265625,
-0.00113677978515625,
0.01441192626953125,
-0.0066375732421875,
-0.010711669921875,
-0.0362548828125,
-0.03509521484375,
0.0121917724609375,
-0.020721435546875,
0.0037288665771484375,
0.01318359375,
-0.006046295166015625,
0.0195465087890625,
-0.0200958251953125,
0.020172119140625,
-0.026702880859375,
-0.03192138671875,
-0.02606201171875,
0.0303192138671875,
-0.01172637939453125,
-0.060546875,
-0.0048370361328125,
-0.028076171875,
-0.03424072265625,
-0.011474609375,
0.040924072265625,
-0.00833892822265625,
-0.021484375,
-0.00215911865234375,
-0.035369873046875,
0.0109100341796875,
0.0034236907958984375,
-0.0272674560546875,
-0.004669189453125,
-0.01230621337890625,
-0.00843048095703125,
0.00815582275390625,
0.0010519027709960938,
0.00431060791015625,
0.016357421875,
-0.006999969482421875,
0.0074005126953125,
-0.0243988037109375,
-0.038909912109375,
0.015472412109375,
0.003963470458984375,
-0.0268402099609375,
0.0286712646484375,
-0.004840850830078125,
-0.0192108154296875,
0.03668212890625,
-0.031768798828125,
0.01451873779296875,
-0.035858154296875,
-0.034027099609375,
-0.0157928466796875,
0.00511932373046875,
-0.0012044906616210938,
0.005939483642578125,
-0.0205841064453125,
0.01509857177734375,
0.0074310302734375,
0.012725830078125,
-0.051605224609375,
-0.0150909423828125,
0.034942626953125,
0.0208892822265625,
0.005237579345703125,
0.0155181884765625,
0.00637054443359375,
0.013336181640625,
-0.01515960693359375,
0.0037250518798828125,
0.01776123046875,
-0.01505279541015625,
-0.005279541015625,
-0.0060272216796875,
0.0237579345703125,
0.00030684471130371094,
0.0244293212890625,
-0.01194000244140625,
-0.008819580078125,
-0.017852783203125,
-0.0174407958984375,
0.0059967041015625,
0.0123291015625,
0.0020580291748046875,
0.005191802978515625,
-0.022613525390625,
0.016082763671875,
0.033721923828125
] |
ours_542
|
The answer is \( 250 \). The calculation is \( 100 \cdot \frac{5}{2} = 250 \).
\(\boxed{250}\)
|
250
|
{
"competition": "us_comps",
"dataset": "Ours",
"posts": null,
"source": "OMOSoln2.md"
}
|
A cross-pentomino is a shape that consists of a unit square and four other unit squares each sharing a different edge with the first square. If a cross-pentomino is inscribed in a circle of radius \( R \), what is \( 100 R^{2} \)?
|
[
"/Mathematics/Geometry/PlaneGeometry/Circles/Circle",
"/Mathematics/Geometry/PlaneGeometry/Circles/Radius"
] |
Place the cross-pentomino on a coordinate grid, locate its center, and use the distance from the center to an outer corner to find the radius.
|
[
0.000007033348083496094,
-0.0206451416015625,
0.0194244384765625,
0.025482177734375,
-0.00021255016326904297,
0.010772705078125,
0.0474853515625,
0.008544921875,
0.01082611083984375,
0.036529541015625,
-0.0267181396484375,
-0.009063720703125,
-0.006153106689453125,
0.0144195556640625,
0.0030765533447265625,
-0.00563812255859375,
0.0135498046875,
-0.037994384765625,
0.00984954833984375,
-0.0008521080017089844,
-0.0088043212890625,
-0.006649017333984375,
-0.053741455078125,
0.0284271240234375,
-0.0364990234375,
-0.003082275390625,
-0.0233154296875,
-0.03271484375,
0.02581787109375,
-0.01444244384765625,
-0.035186767578125,
-0.033782958984375,
0.0216522216796875,
0.004596710205078125,
-0.0008635520935058594,
0.008575439453125,
0.00952911376953125,
-0.006591796875,
-0.043243408203125,
-0.06475830078125,
0.004344940185546875,
0.00823211669921875,
-0.00882720947265625,
0.0035266876220703125,
-0.01290130615234375,
0.006359100341796875,
-0.006328582763671875,
0.01227569580078125,
-0.0015468597412109375,
0.00482177734375,
0.002197265625,
0.01454925537109375,
-0.053955078125,
-0.0006327629089355469,
-0.026092529296875,
-0.0262298583984375,
-0.0177154541015625,
-0.006107330322265625,
-0.017303466796875,
0.0037097930908203125,
0.007747650146484375,
0.0030002593994140625,
-0.01477813720703125,
-0.00858306884765625,
-0.0002968311309814453,
-0.005855560302734375,
0.035247802734375,
-0.0201416015625,
-0.00800323486328125,
-0.01360321044921875,
-0.01233673095703125,
-0.01416778564453125,
0.0019207000732421875,
0.010101318359375,
0.02520751953125,
-0.02587890625,
-0.01239776611328125,
0.01129150390625,
-0.00008666515350341797,
0.019073486328125,
0.01493072509765625,
0.0094757080078125,
0.00004780292510986328,
-0.01393890380859375,
0.0013628005981445312,
-0.000820159912109375,
0.020751953125,
0.0016536712646484375,
0.0340576171875,
-0.0158233642578125,
0.0031108856201171875,
0.024658203125,
0.00376129150390625,
-0.01465606689453125,
0.0160369873046875,
-0.0018033981323242188,
-0.0035915374755859375,
-0.007965087890625,
-0.0224151611328125,
0.00655364990234375,
-0.02276611328125,
-0.0099945068359375,
-0.0106201171875,
-0.0131072998046875,
0.0128173828125,
-0.0100555419921875,
-0.0259246826171875,
0.017486572265625,
0.009979248046875,
-0.0055694580078125,
0.01163482666015625,
0.0006837844848632812,
0.00024199485778808594,
0.021240234375,
-0.005374908447265625,
0.00934600830078125,
0.0290679931640625,
-0.01094818115234375,
-0.0159912109375,
-0.023529052734375,
0.006755828857421875,
0.01154327392578125,
0.007495880126953125,
-0.0012044906616210938,
0.0205078125,
-0.05706787109375,
-0.0009126663208007812,
0.0062255859375,
-0.0234222412109375,
0.0306396484375,
0.019866943359375,
-0.0157470703125,
-0.0220794677734375,
-0.004444122314453125,
-0.016204833984375,
-0.018798828125,
-0.00386810302734375,
-0.01323699951171875,
-0.00408935546875,
0.0030002593994140625,
0.0081634521484375,
-0.01239776611328125,
0.009063720703125,
-0.07830810546875,
-0.0031566619873046875,
0.00724029541015625,
-0.005367279052734375,
-0.03924560546875,
0.01515960693359375,
0.0195159912109375,
0.005413055419921875,
-0.01030731201171875,
0.01436614990234375,
0.02374267578125,
-0.0120849609375,
0.009124755859375,
-0.0007152557373046875,
0.032440185546875,
0.019073486328125,
0.00669097900390625,
0.00286865234375,
-0.008697509765625,
0.01467132568359375,
0.047210693359375,
0.0005860328674316406,
-0.0203704833984375,
-0.00525665283203125,
-0.010101318359375,
0.0019588470458984375,
-0.0027561187744140625,
0.0009427070617675781,
-0.01219940185546875,
-0.006023406982421875,
-0.003948211669921875,
-0.01229095458984375,
0.0004684925079345703,
-0.0219268798828125,
0.01110076904296875,
-0.006618499755859375,
0.0089569091796875,
0.001678466796875,
0.00493621826171875,
0.039337158203125,
-0.01528167724609375,
-0.002140045166015625,
0.017608642578125,
0.00930023193359375,
0.01190185546875,
0.0022220611572265625,
0.013702392578125,
0.002086639404296875,
-0.041961669921875,
0.01509857177734375,
0.00518798828125,
0.0029392242431640625,
-0.0017805099487304688,
0.0063934326171875,
-0.0062103271484375,
0.01351165771484375,
0.01268768310546875,
-0.0055084228515625,
0.00911712646484375,
0.0295257568359375,
0.028106689453125,
0.005489349365234375,
-0.0006966590881347656,
0.00618743896484375,
-0.01435089111328125,
-0.005176544189453125,
0.0080108642578125,
-0.002292633056640625,
-0.0158538818359375,
-0.005435943603515625,
0.00804901123046875,
-0.01171112060546875,
0.0025920867919921875,
-0.0016260147094726562,
0.003482818603515625,
0.0296630859375,
-0.014434814453125,
0.01971435546875,
-0.0011434555053710938,
0.00334930419921875,
-0.007534027099609375,
-0.02618408203125,
-0.00748443603515625,
0.00949859619140625,
-0.013671875,
0.009429931640625,
0.0030059814453125,
0.01190185546875,
0.0187225341796875,
0.0043182373046875,
0.0004825592041015625,
-0.0038509368896484375,
0.02166748046875,
-0.037933349609375,
0.00954437255859375,
0.01073455810546875,
-0.00707244873046875,
0.0283355712890625,
-0.0177764892578125,
-0.00010544061660766602,
0.020599365234375,
0.0176849365234375,
0.0012826919555664062,
0.004276275634765625,
-0.00389862060546875,
0.00485992431640625,
-0.002338409423828125,
-0.0297088623046875,
0.00799560546875,
0.004726409912109375,
-0.0133209228515625,
-0.01078033447265625,
-0.0158538818359375,
0.00551605224609375,
-0.0181884765625,
-0.00978851318359375,
-0.007965087890625,
-0.006130218505859375,
-0.0151519775390625,
-0.0028247833251953125,
-0.01094818115234375,
-0.01419830322265625,
-0.03204345703125,
-0.0002925395965576172,
0.00689697265625,
0.004421234130859375,
-0.006694793701171875,
0.042572021484375,
-0.0185394287109375,
-0.0151824951171875,
0.004039764404296875,
-0.0157470703125,
-0.024169921875,
-0.0052947998046875,
0.012603759765625,
0.0281829833984375,
0.012847900390625,
-0.00417327880859375,
-0.01922607421875,
-0.0210113525390625,
-0.0020503997802734375,
0.00782012939453125,
-0.0003635883331298828,
0.00415802001953125,
-0.0169830322265625,
-0.0095977783203125,
0.006694793701171875,
-0.00025177001953125,
0.01136016845703125,
-0.00469207763671875,
-0.0088348388671875,
0.036834716796875,
-0.0355224609375,
-0.01335906982421875,
0.0108795166015625,
0.0110931396484375,
-0.0153045654296875,
0.0132598876953125,
-0.0097808837890625,
0.00567626953125,
0.0496826171875,
0.0271759033203125,
0.0285797119140625,
0.01038360595703125,
-0.0065460205078125,
-0.038726806640625,
-0.0014028549194335938,
0.03790283203125,
0.0102386474609375,
-0.0024871826171875,
-0.007656097412109375,
0.01117706298828125,
-0.050048828125,
-0.000019311904907226562,
0.0262603759765625,
-0.00640106201171875,
-0.0018396377563476562,
-0.002979278564453125,
-0.002017974853515625,
0.0006818771362304688,
0.0021991729736328125,
0.02606201171875,
-0.01081085205078125,
0.0200347900390625,
-0.0003638267517089844,
0.006267547607421875,
0.00785064697265625,
-0.0287933349609375,
0.0283050537109375,
0.0122833251953125,
-0.0260009765625,
-0.00962066650390625,
-0.00865936279296875,
-0.021575927734375,
0.0169525146484375,
0.01486968994140625,
0.0231781005859375,
-0.0208740234375,
0.0083160400390625,
0.0104217529296875,
-0.034393310546875,
0.00281524658203125,
-0.00020599365234375,
-0.004253387451171875,
0.0216217041015625,
-0.018768310546875,
-0.01241302490234375,
-0.0457763671875,
0.00012576580047607422,
0.0023937225341796875,
-0.020965576171875,
-0.0396728515625,
0.0308990478515625,
0.0042724609375,
0.04107666015625,
-0.0214385986328125,
0.0007381439208984375,
0.00897979736328125,
-0.0060577392578125,
-0.0198974609375,
-0.005359649658203125,
-0.010101318359375,
-0.035186767578125,
-0.01287841796875,
0.0209197998046875,
0.01187896728515625,
-0.03570556640625,
-0.0103302001953125,
-0.02850341796875,
-0.005252838134765625,
-0.00957489013671875,
0.0206756591796875,
0.012542724609375,
0.006565093994140625,
0.0227813720703125,
-0.0248870849609375,
0.002384185791015625,
0.0012722015380859375,
0.0276336669921875,
0.01453399658203125,
0.01435089111328125,
0.00809478759765625,
0.0270843505859375,
-0.0013523101806640625,
-0.006641387939453125,
-0.0243988037109375,
-0.0007767677307128906,
0.0038661956787109375,
-0.012939453125,
-0.0043487548828125,
-0.0004222393035888672,
-0.0114288330078125,
0.01094818115234375,
0.0012025833129882812,
-0.0081024169921875,
0.0274505615234375,
0.006862640380859375,
-0.041961669921875,
-0.00783538818359375,
0.0016450881958007812,
0.0236053466796875,
-0.0030040740966796875,
-0.0050811767578125,
-0.0014104843139648438,
0.0300750732421875,
0.00372314453125,
-0.007396697998046875,
-0.01003265380859375,
0.006954193115234375,
0.006900787353515625,
-0.0273284912109375,
-0.0169219970703125,
0.0283355712890625,
-0.00164031982421875,
0.0143585205078125,
0.010772705078125,
-0.0079193115234375,
0.01296234130859375,
0.010162353515625,
0.02215576171875,
0.00702667236328125,
0.013671875,
0.035858154296875,
-0.00344085693359375,
0.04498291015625,
0.0219573974609375,
0.0034236907958984375,
0.0101776123046875,
0.00643157958984375,
0.0032138824462890625,
0.059112548828125,
0.01448822021484375,
0.01505279541015625,
0.016357421875,
-0.0130157470703125,
-0.0173187255859375,
-0.0174407958984375,
-0.01690673828125,
-0.0116729736328125,
-0.0003943443298339844,
-0.0298614501953125,
-0.00614166259765625,
-0.0039215087890625,
0.006435394287109375,
-0.01111602783203125,
0.02862548828125,
-0.007293701171875,
-0.0153350830078125,
0.0199127197265625,
0.003875732421875,
-0.0175323486328125,
-0.0098419189453125,
-0.004390716552734375,
0.0150909423828125,
-0.0196380615234375,
-0.000033795833587646484,
0.00690460205078125,
-0.004119873046875,
-0.0006589889526367188,
0.0091400146484375,
0.01165008544921875,
-0.0262908935546875,
-0.02032470703125,
0.005702972412109375,
0.0094757080078125,
0.01739501953125,
0.016693115234375,
-0.006404876708984375,
-0.03143310546875,
0.0276336669921875,
-0.040802001953125,
0.005100250244140625,
0.038299560546875,
0.03887939453125,
0.0149078369140625,
0.00620269775390625,
0.0034122467041015625,
-0.01480865478515625,
0.00885772705078125,
0.01509857177734375,
0.0181884765625,
-0.01837158203125,
0.003726959228515625,
-0.00022494792938232422,
0.0186920166015625,
-0.045806884765625,
-0.01422882080078125,
-0.0092315673828125,
0.03948974609375,
-0.0203857421875,
-0.0396728515625,
-0.01424407958984375,
-0.00397491455078125,
0.021759033203125,
0.006694793701171875,
0.01393890380859375,
0.0136566162109375,
-0.0265045166015625,
-0.01128387451171875,
-0.0087738037109375,
-0.003997802734375,
0.03106689453125,
-0.01053619384765625,
0.046356201171875,
-0.00278472900390625,
0.0185394287109375,
-0.004425048828125,
0.00948333740234375,
0.01373291015625,
0.009307861328125,
-0.066162109375,
0.0275421142578125,
-0.0225830078125,
0.0278472900390625,
-0.0335693359375,
0.0305633544921875,
0.0200042724609375,
-0.01479339599609375,
0.011474609375,
0.031219482421875,
0.011810302734375,
0.01514434814453125,
0.0310211181640625,
0.017730712890625,
0.0032806396484375,
-0.01300811767578125,
0.0135345458984375,
-0.0299072265625,
-0.0162200927734375,
-0.046142578125,
0.0233612060546875,
-0.02911376953125,
0.00473785400390625,
-0.002460479736328125,
0.0200958251953125,
-0.019378662109375,
-0.005100250244140625,
-0.00798797607421875,
0.021759033203125,
0.0421142578125,
-0.0176239013671875,
0.0258026123046875,
-0.033477783203125,
0.0027980804443359375,
0.0289764404296875,
-0.0007338523864746094,
0.03326416015625,
0.0206146240234375,
0.038299560546875,
-0.0300750732421875,
0.005077362060546875,
-0.02264404296875,
-0.0056915283203125,
-0.015869140625,
-0.00922393798828125,
-0.01509857177734375,
0.029541015625,
0.006374359130859375,
-0.004146575927734375,
0.00524139404296875,
0.018890380859375,
0.0248565673828125,
-0.02276611328125,
0.0078125,
-0.0009765625,
-0.028472900390625,
-0.0400390625,
-0.01175689697265625,
0.0384521484375,
0.00878143310546875,
0.007579803466796875,
0.011199951171875,
-0.0034198760986328125,
-0.0087738037109375,
0.0007672309875488281,
0.032928466796875,
-0.011627197265625,
0.0165863037109375,
0.01611328125,
-0.01074981689453125,
-0.0097808837890625,
0.009796142578125,
-0.03369140625,
0.0224151611328125,
0.0029964447021484375,
0.031280517578125,
0.003932952880859375,
-0.029449462890625,
0.01922607421875,
0.0390625,
-0.02178955078125,
-0.0017948150634765625,
-0.00655364990234375,
0.001300811767578125,
-0.0264892578125,
-0.0010328292846679688,
0.0369873046875,
0.00934600830078125,
-0.00461578369140625,
-0.00569915771484375,
0.0133056640625,
-0.00879669189453125,
-0.045806884765625,
0.0181884765625,
0.01983642578125,
-0.0015926361083984375,
-0.0185394287109375,
-0.034454345703125,
-0.004146575927734375,
-0.00966644287109375,
0.0227813720703125,
0.0184173583984375,
-0.0290069580078125,
-0.0021228790283203125,
-0.02496337890625,
0.004749298095703125,
-0.0032939910888671875,
-0.0161895751953125,
0.0023097991943359375,
-0.0216522216796875,
0.026123046875,
0.02996826171875,
0.002166748046875,
-0.0032176971435546875,
-0.0022907257080078125,
-0.0016613006591796875,
-0.0095672607421875,
-0.06378173828125,
0.0211639404296875,
0.01446533203125,
-0.0191192626953125,
-0.0036754608154296875,
0.0223846435546875,
-0.0030422210693359375,
0.01324462890625,
0.006011962890625,
0.041961669921875,
-0.01110076904296875,
-0.002925872802734375,
0.05828857421875,
-0.0426025390625,
-0.0034198760986328125,
0.02130126953125,
0.01364898681640625,
0.0155181884765625,
-0.037567138671875,
0.019927978515625,
-0.039276123046875,
-0.005184173583984375,
-0.020538330078125,
-0.00371551513671875,
0.01297760009765625,
-0.0237274169921875,
-0.005558013916015625,
-0.015625,
0.039825439453125,
0.0005168914794921875,
0.006755828857421875,
0.0045166015625,
0.01125335693359375,
-0.006969451904296875,
-0.041839599609375,
-0.016387939453125,
-0.0172271728515625,
-0.01448822021484375,
0.0204315185546875,
0.0211944580078125,
-0.0516357421875,
0.02301025390625,
-0.0201873779296875,
-0.0211334228515625,
0.040557861328125,
0.0059814453125,
-0.037384033203125,
0.01157379150390625,
0.024688720703125,
-0.01091766357421875,
-0.0343017578125,
-0.00519561767578125,
0.0261077880859375,
-0.0019626617431640625,
-0.0087432861328125,
-0.0195159912109375,
0.0190582275390625,
0.020782470703125,
0.00452423095703125,
0.01486968994140625,
-0.00231170654296875,
0.016021728515625,
0.019561767578125,
0.0010671615600585938,
-0.034515380859375,
-0.004364013671875,
0.0177001953125,
-0.00032520294189453125,
0.0025997161865234375,
-0.01538848876953125,
-0.0155181884765625,
-0.006328582763671875,
0.038848876953125,
0.0113525390625,
-0.025421142578125,
-0.055633544921875,
0.01605224609375,
0.01111602783203125,
-0.037994384765625,
0.02203369140625,
-0.00415802001953125,
-0.02496337890625,
0.0193634033203125,
-0.0223388671875,
0.0082244873046875,
-0.037139892578125,
-0.0283660888671875,
-0.006267547607421875,
-0.01152801513671875,
-0.02001953125,
0.0073394775390625,
0.00894927978515625,
-0.02703857421875,
0.00244903564453125,
0.018798828125,
0.048370361328125,
0.005214691162109375,
-0.02398681640625,
-0.041168212890625,
0.0294036865234375,
0.0247955322265625,
-0.01715087890625,
-0.008880615234375,
0.0095062255859375,
-0.01107025146484375,
-0.0011835098266601562,
0.005279541015625,
-0.0258636474609375,
-0.0283050537109375,
0.00952911376953125,
0.0175628662109375,
-0.00862884521484375,
0.0018863677978515625,
-0.0099639892578125,
0.0047454833984375,
0.004566192626953125,
-0.01438140869140625,
0.01329803466796875,
0.004547119140625,
0.00807952880859375,
0.017913818359375,
0.01263427734375,
0.0278167724609375,
-0.0224151611328125,
-0.0265350341796875,
0.008392333984375,
0.00011086463928222656,
0.00616455078125,
-0.00998687744140625,
-0.0006651878356933594,
-0.03955078125,
0.000583648681640625,
0.0014133453369140625,
0.02044677734375,
0.0231781005859375,
-0.00952911376953125,
0.0231781005859375,
-0.0279998779296875,
0.00116729736328125,
0.0162200927734375,
-0.0037364959716796875,
-0.0272216796875,
0.039794921875,
0.0284271240234375,
-0.0007987022399902344,
0.036346435546875,
-0.04864501953125,
-0.0199432373046875,
0.0249786376953125,
-0.0379638671875,
0.029266357421875,
0.0051727294921875,
-0.028961181640625,
0.003757476806640625,
-0.0423583984375,
-0.0062255859375,
-0.004619598388671875,
-0.00004112720489501953,
0.03173828125,
0.0213470458984375,
0.029205322265625,
-0.003711700439453125,
-0.007366180419921875,
-0.0091094970703125,
0.00525665283203125,
0.01082611083984375,
0.007205963134765625,
-0.018157958984375,
0.00643157958984375,
-0.007099151611328125,
0.00775909423828125,
-0.0188140869140625,
-0.0011959075927734375,
0.0335693359375,
0.033050537109375,
-0.0294342041015625,
-0.01206207275390625,
0.016845703125,
-0.003986358642578125,
0.0208587646484375,
0.0181427001953125,
-0.0225067138671875,
-0.01136016845703125,
0.0034732818603515625,
-0.0184326171875,
-0.0002639293670654297,
-0.001476287841796875,
-0.0145721435546875,
0.0243988037109375,
0.0096588134765625,
0.0064544677734375,
0.037445068359375,
-0.03460693359375,
0.00974273681640625,
-0.00714874267578125,
-0.00775909423828125,
-0.03564453125,
-0.03656005859375,
-0.0091094970703125,
0.03363037109375,
0.033203125,
0.004741668701171875,
0.009918212890625,
0.01013946533203125,
-0.0213470458984375,
0.0014247894287109375,
0.01218414306640625,
-0.01468658447265625,
-0.01476287841796875,
-0.0175323486328125,
0.005523681640625,
0.0285186767578125,
0.0232086181640625,
0.00905609130859375,
0.012908935546875,
-0.0086822509765625,
-0.0261077880859375,
0.00742340087890625,
0.01119232177734375,
0.0225372314453125,
-0.00595855712890625,
0.00940704345703125,
0.0012054443359375,
0.029937744140625,
-0.0027332305908203125,
-0.0007443428039550781,
-0.004695892333984375,
-0.0164337158203125,
-0.000591278076171875,
0.00787353515625,
0.013031005859375,
-0.01473236083984375,
0.006954193115234375,
-0.0013294219970703125,
-0.0086822509765625,
-0.015716552734375,
-0.00951385498046875,
-0.02874755859375,
0.0299835205078125,
-0.0169219970703125,
0.0107879638671875,
-0.0235748291015625,
0.012542724609375,
0.004123687744140625,
0.0439453125,
0.021240234375,
-0.008209228515625,
-0.0147552490234375,
0.03778076171875,
-0.0231475830078125,
-0.011688232421875,
-0.029022216796875,
0.006313323974609375,
-0.001834869384765625,
0.00698089599609375,
-0.0279083251953125,
0.0264129638671875,
0.00894927978515625,
0.0445556640625,
0.001644134521484375,
0.023223876953125,
-0.0164642333984375,
-0.0330810546875,
-0.0037841796875,
0.0099639892578125,
-0.0060272216796875,
0.01678466796875,
-0.04888916015625,
0.0084686279296875,
-0.0121002197265625,
-0.0190887451171875,
0.02099609375,
0.00972747802734375,
0.00829315185546875,
0.0206146240234375,
-0.01910400390625,
-0.0009756088256835938,
0.0102386474609375,
0.01363372802734375,
0.01708984375,
-0.007781982421875,
-0.00925445556640625,
0.01959228515625,
-0.0265350341796875,
-0.0271148681640625,
-0.010711669921875,
0.0198974609375,
-0.017120361328125,
0.006412506103515625,
-0.0184326171875,
0.00797271728515625,
-0.0258331298828125,
0.0179290771484375,
-0.01166534423828125,
0.013916015625,
-0.0247955322265625,
-0.041015625,
-0.0110626220703125,
-0.0138702392578125,
0.050811767578125,
-0.036041259765625,
-0.00262451171875,
-0.01336669921875,
-0.00881195068359375,
-0.01287841796875,
0.00036787986755371094,
0.00004476308822631836,
-0.007171630859375,
0.03369140625,
-0.0438232421875,
-0.02618408203125,
0.00046515464782714844,
0.05120849609375,
0.01351165771484375,
-0.00722503662109375,
-0.01010894775390625,
0.0235137939453125,
0.01226043701171875,
0.0145721435546875,
-0.0152130126953125,
0.0182647705078125,
-0.00457763671875,
-0.020599365234375,
0.01215362548828125,
-0.017913818359375,
0.0022792816162109375,
0.022003173828125,
0.01064300537109375,
0.0238037109375,
-0.0011796951293945312,
-0.002193450927734375,
-0.0149993896484375,
0.01136016845703125,
0.0015993118286132812,
0.0107879638671875,
0.01465606689453125,
0.0217742919921875,
0.0079345703125,
0.01168060302734375,
-0.002201080322265625,
-0.0017719268798828125,
-0.018890380859375,
-0.021881103515625,
-0.0031147003173828125,
-0.0255126953125,
0.038330078125,
-0.01110076904296875,
0.009490966796875,
0.0220947265625,
-0.00234222412109375,
-0.0155181884765625,
0.0303497314453125,
0.01490020751953125,
-0.047515869140625,
-0.0035247802734375,
0.0179901123046875,
-0.024749755859375,
-0.008453369140625,
0.0272674560546875,
-0.00939178466796875,
-0.0322265625,
0.03277587890625,
-0.004207611083984375,
0.038604736328125,
0.01198577880859375,
0.0231475830078125,
-0.0252685546875,
-0.002742767333984375,
0.0212554931640625,
0.02630615234375,
-0.031158447265625,
0.019989013671875,
0.01494598388671875,
-0.0254669189453125,
-0.0216217041015625,
-0.023040771484375,
0.007755279541015625,
0.0136566162109375,
0.0445556640625,
-0.01456451416015625,
-0.01435089111328125,
0.01097869873046875,
0.012725830078125,
-0.021881103515625,
-0.0031414031982421875,
0.0092010498046875,
-0.0007042884826660156,
0.0212554931640625,
-0.007259368896484375,
0.030853271484375,
0.038055419921875,
0.00417327880859375,
-0.0303955078125,
0.0008020401000976562,
0.0020351409912109375,
-0.0035247802734375,
-0.028533935546875,
0.006317138671875,
0.002300262451171875,
0.0170135498046875,
0.0148468017578125,
-0.0187530517578125,
0.01061248779296875,
0.005664825439453125,
0.00649261474609375,
-0.028717041015625,
-0.007030487060546875,
-0.00628662109375,
-0.022247314453125,
0.0111083984375,
0.0118560791015625,
-0.00885772705078125,
0.011688232421875,
-0.00994110107421875,
-0.04290771484375,
-0.01274871826171875,
0.0083770751953125,
-0.012847900390625,
-0.008026123046875,
-0.0240631103515625,
0.029327392578125,
0.0229644775390625,
0.00922393798828125,
0.0016908645629882812,
0.01324462890625,
0.02618408203125,
0.0208282470703125,
0.01023101806640625,
-0.031951904296875,
-0.006603240966796875,
0.002696990966796875,
-0.039276123046875,
0.003124237060546875,
-0.017364501953125,
-0.01419830322265625,
-0.0275115966796875,
-0.02288818359375,
0.006420135498046875,
-0.01983642578125,
0.0283355712890625,
-0.02642822265625,
-0.0075836181640625,
-0.00469970703125,
-0.0283050537109375,
-0.0157470703125,
-0.006740570068359375,
0.023162841796875,
-0.0205535888671875,
0.0026912689208984375,
-0.0028533935546875,
-0.018463134765625,
-0.0018644332885742188,
-0.0298614501953125,
0.0010089874267578125,
0.01419830322265625,
-0.00771331787109375,
0.0309906005859375,
-0.0170135498046875,
-0.0142059326171875,
-0.018463134765625,
0.0230712890625,
-0.0143585205078125,
-0.019439697265625,
0.01800537109375,
0.00754547119140625,
-0.00981903076171875,
0.0183258056640625,
0.006946563720703125,
0.0265960693359375,
-0.0259246826171875,
0.01288604736328125,
0.007659912109375,
0.006641387939453125,
0.00624847412109375,
-0.003620147705078125,
-0.0212249755859375,
-0.031341552734375,
0.0017156600952148438,
0.028839111328125,
-0.025604248046875,
-0.03680419921875,
-0.011810302734375,
0.00315093994140625,
0.0142669677734375,
-0.005207061767578125,
0.018707275390625,
-0.0215911865234375,
-0.0242767333984375,
-0.007434844970703125,
-0.003520965576171875,
0.033233642578125,
0.003314971923828125,
-0.002288818359375,
0.01470947265625,
-0.0088043212890625,
-0.019866943359375,
0.01273345947265625,
0.01849365234375,
-0.0159454345703125,
-0.0036411285400390625,
0.01256561279296875,
-0.0010423660278320312,
0.0030059814453125,
0.00732421875,
-0.00887298583984375,
0.004730224609375,
0.00556182861328125,
0.0034923553466796875,
0.021728515625,
-0.0193328857421875,
-0.0030384063720703125,
0.0208282470703125,
-0.00815582275390625,
-0.0016374588012695312,
-0.0215606689453125,
0.0274505615234375,
-0.0049896240234375,
-0.01177978515625,
0.027008056640625,
-0.0080718994140625,
-0.03955078125,
0.0164794921875,
-0.0264739990234375,
-0.01288604736328125,
0.01120758056640625,
-0.0166778564453125,
-0.03704833984375,
0.007343292236328125,
0.0099945068359375,
0.005855560302734375,
-0.0042877197265625,
0.0164794921875,
-0.01010894775390625,
0.00460052490234375,
0.01349639892578125,
-0.025909423828125,
-0.016845703125,
0.00814056396484375,
-0.039276123046875,
-0.0100860595703125,
-0.0200042724609375,
-0.01552581787109375,
0.0012149810791015625,
0.00421142578125,
-0.003948211669921875,
0.0247650146484375,
0.00386810302734375,
-0.0069122314453125,
0.0211639404296875,
0.00931549072265625,
0.006984710693359375,
0.006748199462890625,
0.00894927978515625,
-0.003108978271484375,
0.0083160400390625,
-0.033050537109375,
-0.0011043548583984375,
0.006435394287109375,
0.0239105224609375,
0.013031005859375,
0.0089569091796875,
-0.04412841796875,
-0.0037174224853515625,
-0.026824951171875,
0.02130126953125,
-0.0192413330078125,
0.01122283935546875,
-0.00829315185546875,
0.0178070068359375,
-0.0150909423828125,
-0.00905609130859375,
-0.00774383544921875,
-0.0091552734375,
0.0016632080078125,
-0.0009517669677734375,
0.0169219970703125,
0.01467132568359375,
0.01110076904296875,
-0.0162353515625,
0.016845703125,
0.01053619384765625,
0.0014142990112304688,
0.00952911376953125,
0.0264129638671875,
0.04107666015625,
0.005527496337890625,
0.020904541015625,
-0.0147552490234375,
-0.01407623291015625,
-0.04974365234375,
0.0011510848999023438,
0.03369140625,
0.00438690185546875,
-0.0225067138671875,
-0.0275115966796875,
0.0155792236328125,
-0.019256591796875,
0.014190673828125,
-0.01262664794921875,
0.006015777587890625,
0.032012939453125,
0.013458251953125,
0.0203094482421875,
0.01180267333984375,
-0.043487548828125,
-0.0022525787353515625,
-0.00788116455078125,
0.03460693359375,
-0.009765625,
0.0164794921875,
-0.008270263671875,
0.0236053466796875,
-0.0162811279296875,
-0.0142364501953125,
-0.00359344482421875,
-0.005542755126953125,
-0.025634765625,
0.019073486328125,
-0.044708251953125,
-0.00943756103515625,
-0.030517578125,
0.0273590087890625,
0.017059326171875,
-0.04742431640625,
-0.0198822021484375,
0.0010433197021484375,
-0.004894256591796875,
0.0147857666015625,
-0.0166168212890625,
-0.01076507568359375,
-0.006404876708984375,
-0.00917816162109375,
0.022857666015625,
-0.0267181396484375,
-0.0152130126953125,
-0.0246429443359375,
-0.001369476318359375,
0.0255584716796875,
0.0059814453125,
-0.026763916015625,
-0.00592041015625,
-0.00641632080078125,
-0.0230712890625,
0.03289794921875,
0.018646240234375,
0.0176239013671875,
-0.00836181640625,
-0.0196685791015625,
0.01313018798828125,
-0.0038967132568359375,
-0.00716400146484375,
0.0193634033203125,
0.015411376953125,
-0.021148681640625,
-0.0089263916015625,
-0.007503509521484375,
-0.00844573974609375,
0.01428985595703125,
0.02960205078125,
-0.04351806640625,
0.0140228271484375,
0.0222625732421875,
-0.006500244140625,
0.020904541015625,
0.0196380615234375,
0.031524658203125,
0.0036945343017578125,
-0.0016841888427734375,
-0.0064544677734375,
0.01055145263671875,
-0.0004172325134277344,
0.007297515869140625,
0.0037841796875,
0.003421783447265625,
-0.006168365478515625,
-0.017791748046875,
0.02032470703125,
0.0406494140625,
0.0066375732421875,
-0.004726409912109375,
-0.00609588623046875,
-0.0245513916015625,
0.00022101402282714844,
-0.007358551025390625,
0.0251922607421875,
-0.03070068359375,
-0.0057830810546875,
-0.041168212890625,
0.01081085205078125,
-0.005146026611328125,
-0.0179595947265625,
-0.01441192626953125,
-0.00690460205078125,
0.0076904296875,
0.0274200439453125,
-0.0202178955078125,
0.0014009475708007812,
0.0078582763671875,
-0.0435791015625,
-0.0174560546875,
0.0196533203125,
0.00942230224609375,
0.001194000244140625,
0.01593017578125,
-0.0022830963134765625,
-0.01377105712890625,
0.0158538818359375,
0.033416748046875,
-0.0017824172973632812,
-0.01294708251953125,
-0.044464111328125,
0.01322174072265625,
-0.037017822265625,
0.0250396728515625,
0.0197601318359375,
0.0156707763671875,
-0.0075531005859375,
-0.0139617919921875,
0.0035610198974609375,
0.0050811767578125,
0.0034465789794921875,
-0.0076141357421875,
-0.003612518310546875,
0.0112762451171875,
-0.049957275390625,
-0.01102447509765625,
0.01404571533203125,
0.0303497314453125,
0.007373809814453125,
0.0121612548828125,
0.01256561279296875,
0.0154876708984375,
0.0123291015625,
-0.0013675689697265625,
0.0186767578125,
-0.0115966796875,
0.0085296630859375,
-0.0115814208984375,
-0.0022296905517578125,
0.0098419189453125,
-0.001659393310546875,
0.022216796875,
-0.0260009765625,
-0.01558685302734375,
0.01297760009765625,
0.01392364501953125,
-0.0130157470703125,
-0.0024089813232421875,
0.0204620361328125,
-0.0133514404296875,
-0.005680084228515625,
-0.0191497802734375,
0.005573272705078125,
-0.039031982421875,
0.041168212890625,
0.0221099853515625,
-0.023101806640625,
0.0118255615234375,
0.0139007568359375,
-0.01372528076171875,
0.01064300537109375,
0.0009775161743164062,
-0.044464111328125,
0.007598876953125,
0.0175933837890625,
-0.022247314453125,
0.0166778564453125,
0.0172882080078125,
-0.030914306640625,
0.002849578857421875,
0.0102996826171875,
0.00737762451171875,
-0.0176239013671875,
0.0269775390625,
0.01085662841796875,
-0.0009331703186035156,
-0.036285400390625,
-0.006656646728515625,
0.0268096923828125,
-0.0116729736328125,
-0.00882720947265625,
0.00720977783203125,
0.009857177734375,
-0.0173187255859375,
0.0197601318359375,
-0.03778076171875,
0.0165252685546875,
0.0202789306640625,
-0.0024852752685546875,
-0.0103607177734375,
-0.011077880859375,
0.00496673583984375,
-0.017364501953125,
-0.0016202926635742188,
0.00299072265625,
-0.0009851455688476562,
0.00731658935546875,
-0.035430908203125,
-0.002166748046875,
-0.0216522216796875,
0.0216064453125,
0.00466156005859375,
-0.0184326171875,
-0.0260467529296875,
0.01108551025390625,
0.0158843994140625,
0.0103607177734375,
0.0050811767578125,
0.03582763671875,
0.0119171142578125,
0.019012451171875,
-0.0045013427734375,
-0.00464630126953125,
0.00743865966796875,
-0.0213470458984375,
0.01253509521484375,
-0.0048980712890625,
0.010498046875,
0.00234222412109375,
-0.0196990966796875,
-0.0213775634765625,
-0.0286865234375,
-0.0030765533447265625,
0.003925323486328125,
0.0134429931640625,
0.01255035400390625,
-0.03619384765625,
-0.0014142990112304688,
0.0238494873046875,
-0.0152587890625,
-0.0180816650390625,
0.021697998046875,
-0.0020999908447265625,
0.01505279541015625,
0.03582763671875,
-0.00841522216796875,
-0.02349853515625,
-0.0243682861328125,
0.0086517333984375,
-0.01540374755859375,
0.029998779296875,
-0.04443359375,
0.0140533447265625,
0.02581787109375,
-0.01812744140625,
-0.028411865234375,
-0.018798828125,
0.00537872314453125,
0.027984619140625,
-0.0419921875,
-0.01076507568359375,
-0.027069091796875,
0.025146484375,
-0.0008645057678222656,
-0.0039215087890625,
-0.01065826416015625,
0.0008654594421386719,
0.0244598388671875,
-0.003871917724609375,
-0.0130157470703125,
0.0014619827270507812,
-0.014923095703125,
-0.01151275634765625,
0.00972747802734375,
0.033203125,
0.0026607513427734375,
-0.00023877620697021484,
-0.00914764404296875,
0.00403594970703125,
-0.0107421875,
0.01267242431640625,
0.0002906322479248047,
0.003055572509765625,
0.03363037109375,
-0.0030117034912109375,
-0.00836944580078125,
-0.017791748046875,
-0.0169525146484375,
0.021453857421875,
-0.0274658203125,
-0.0177154541015625,
-0.003692626953125,
-0.011749267578125,
0.0184478759765625,
-0.04217529296875,
-0.005321502685546875,
-0.043304443359375,
-0.004482269287109375,
0.003978729248046875,
-0.0076904296875,
0.0235748291015625,
0.0152130126953125,
-0.0165252685546875,
0.00666046142578125,
0.01303863525390625,
-0.00311279296875,
0.0352783203125,
0.0026798248291015625,
0.0161285400390625,
0.000522613525390625,
-0.006870269775390625,
-0.0092620849609375,
-0.0069122314453125,
-0.0254669189453125,
0.00628662109375,
0.0102081298828125,
0.02313232421875,
0.026885986328125,
0.0169219970703125,
-0.00891876220703125,
0.0164794921875,
0.0182952880859375,
-0.0203704833984375,
-0.0032806396484375,
-0.005184173583984375,
-0.0057220458984375,
-0.0183563232421875,
0.036041259765625,
0.029052734375,
0.0031642913818359375,
0.03619384765625,
-0.011627197265625,
0.01019287109375,
-0.0066070556640625,
-0.028289794921875,
0.00415802001953125,
0.0089263916015625,
0.03070068359375,
-0.01383209228515625,
-0.0169525146484375,
-0.0009441375732421875,
0.0538330078125,
0.0014400482177734375,
-0.0011377334594726562,
-0.023956298828125,
-0.0306549072265625,
-0.0367431640625,
-0.0274200439453125,
-0.023590087890625,
0.0030803680419921875,
0.01264190673828125,
-0.022125244140625,
0.021240234375,
0.010650634765625,
0.004322052001953125,
0.032928466796875,
0.006015777587890625,
0.004482269287109375,
0.0279541015625,
0.00373077392578125,
-0.005153656005859375,
-0.0097808837890625,
-0.016204833984375,
0.02191162109375,
0.0295867919921875,
0.02838134765625,
0.0068359375,
0.03289794921875,
-0.007785797119140625,
-0.00885772705078125,
0.03289794921875,
0.00867462158203125,
0.00434112548828125,
-0.0003459453582763672,
-0.009613037109375,
-0.004985809326171875,
0.0251617431640625,
0.0310211181640625,
0.0211334228515625,
0.0294342041015625,
0.01261138916015625,
-0.04339599609375,
0.00673675537109375,
0.0286102294921875,
0.0157012939453125,
-0.048370361328125,
-0.002079010009765625,
0.00312042236328125,
0.00492095947265625,
0.007022857666015625,
0.0036220550537109375,
-0.01141357421875,
0.00490570068359375,
0.00936126708984375,
0.01480865478515625,
-0.02203369140625,
0.0157928466796875,
0.053009033203125,
-0.0187835693359375,
0.001697540283203125,
0.01457977294921875,
-0.0182342529296875,
0.0002541542053222656,
-0.0377197265625,
0.01380157470703125,
0.0305633544921875,
0.0234527587890625,
0.0286407470703125,
-0.01013946533203125,
-0.00032138824462890625,
-0.0022640228271484375,
0.004909515380859375,
-0.005950927734375,
-0.0091552734375,
-0.006343841552734375,
-0.0208587646484375,
-0.0025539398193359375,
0.0263214111328125,
-0.018280029296875,
0.06939697265625,
-0.00812530517578125,
-0.0030155181884765625,
-0.0031871795654296875,
0.0004906654357910156,
-0.01332855224609375,
-0.0069732666015625,
-0.03363037109375,
-0.01302337646484375,
-0.01091766357421875,
-0.031768798828125,
0.0256500244140625,
0.0226287841796875,
0.0235443115234375,
0.01068878173828125,
0.00165557861328125,
0.0158233642578125,
0.00803375244140625,
-0.050201416015625,
-0.005184173583984375,
-0.0161895751953125,
0.00626373291015625,
0.00426483154296875,
0.005706787109375,
0.006366729736328125,
-0.01430511474609375,
-0.00565338134765625,
0.0211639404296875,
0.0072021484375,
-0.0164337158203125,
0.023284912109375,
-0.01800537109375,
-0.03363037109375,
0.021697998046875,
0.035675048828125,
0.00473785400390625,
0.0179443359375,
-0.004779815673828125,
0.031768798828125,
0.005615234375,
-0.0235748291015625,
-0.02197265625,
-0.023590087890625,
-0.00348663330078125,
0.03125,
-0.00531005859375,
-0.042755126953125,
0.014434814453125,
0.006153106689453125,
-0.0037288665771484375,
-0.01031494140625,
0.021209716796875,
-0.01436614990234375,
-0.0183868408203125,
0.0176239013671875,
0.00916290283203125,
0.01137542724609375,
0.0292205810546875,
-0.00276947021484375,
-0.0126953125,
-0.02978515625,
0.007076263427734375,
0.007671356201171875,
-0.00408172607421875,
0.0025577545166015625,
-0.0025501251220703125,
0.02679443359375,
-0.043914794921875,
0.03009033203125,
-0.0296173095703125,
-0.0067291259765625,
0.01236724853515625,
-0.036163330078125,
0.0082855224609375,
-0.02886962890625,
0.0303802490234375,
0.00988006591796875,
0.00916290283203125,
0.00231170654296875,
0.01070404052734375,
-0.00717926025390625,
-0.022613525390625,
0.01416015625,
0.0013055801391601562,
0.0158233642578125,
0.00868988037109375,
0.005462646484375,
0.0137939453125,
-0.0067901611328125,
0.027496337890625,
0.018341064453125,
0.01462554931640625,
0.005641937255859375,
-0.0175933837890625,
-0.046112060546875,
0.00917816162109375,
-0.0234375,
0.01369476318359375,
-0.0073699951171875,
-0.0185699462890625,
0.0248565673828125,
0.01201629638671875,
-0.007617950439453125,
-0.002864837646484375,
-0.006786346435546875,
0.0237579345703125,
0.0023899078369140625,
0.0157470703125,
0.003185272216796875,
-0.01788330078125,
0.00262451171875,
-0.0005335807800292969,
0.036285400390625,
-0.0123443603515625,
-0.021881103515625,
-0.0186920166015625,
0.010650634765625,
0.00743865966796875,
0.00919342041015625,
-0.014312744140625,
0.0021495819091796875,
0.03668212890625,
-0.02215576171875,
-0.01134490966796875,
-0.024078369140625,
-0.037353515625,
0.01003265380859375,
-0.02435302734375,
0.01464080810546875,
-0.021270751953125,
-0.0160675048828125,
0.01025390625,
0.0188140869140625,
0.028778076171875,
-0.007572174072265625,
0.0094146728515625,
-0.0240325927734375,
0.04150390625,
0.0196533203125,
-0.027099609375,
-0.027099609375,
-0.0150604248046875,
-0.0294952392578125,
0.00862884521484375,
-0.00281524658203125,
0.01165771484375,
0.00009334087371826172,
-0.0012254714965820312,
0.008575439453125,
-0.027801513671875,
-0.0022144317626953125,
-0.007701873779296875,
0.00251007080078125,
-0.006786346435546875,
-0.031524658203125,
0.0243988037109375,
-0.027984619140625,
0.0002288818359375,
-0.0138397216796875,
-0.0234527587890625,
0.03717041015625,
-0.025390625,
-0.0258331298828125,
-0.0018339157104492188,
-0.0232086181640625,
0.045196533203125,
-0.00896453857421875,
-0.041778564453125,
0.044189453125,
0.03271484375,
0.0290985107421875,
-0.003185272216796875,
0.0396728515625,
0.0151824951171875,
0.01580810546875,
0.002681732177734375,
-0.0022525787353515625,
0.0123291015625,
-0.0109710693359375,
-0.0238494873046875,
-0.0270233154296875,
-0.01739501953125,
0.006824493408203125,
0.0019207000732421875,
-0.0194244384765625,
-0.0023288726806640625,
-0.0222320556640625,
0.0028285980224609375,
-0.015655517578125,
-0.0152435302734375,
0.018768310546875,
0.0007381439208984375,
0.0111236572265625,
-0.040985107421875,
-0.01485443115234375,
0.02471923828125,
-0.0218963623046875,
-0.01227569580078125,
-0.034515380859375,
0.0170135498046875,
-0.04144287109375,
0.01233673095703125,
0.01238250732421875,
0.0027561187744140625,
0.00711822509765625,
0.021270751953125,
-0.032012939453125,
0.0018053054809570312,
0.0207977294921875,
0.0196075439453125,
0.009033203125,
-0.0081939697265625,
-0.024932861328125,
0.0031032562255859375,
-0.01116943359375,
-0.048980712890625,
0.006626129150390625,
0.0021648406982421875,
0.0222320556640625,
0.00251007080078125,
0.0271148681640625,
0.0179443359375,
-0.03826904296875,
-0.010528564453125,
-0.0247955322265625,
0.0237579345703125,
0.0152740478515625,
-0.01157379150390625,
-0.037322998046875,
-0.016387939453125,
0.0005693435668945312,
-0.009368896484375,
-0.042236328125,
0.00881195068359375,
0.01168060302734375,
-0.01338958740234375,
0.027496337890625,
0.0037822723388671875,
-0.007747650146484375,
0.046875,
0.01377105712890625,
0.031982421875,
0.023101806640625,
0.0207061767578125,
0.026824951171875,
0.02484130859375,
-0.029571533203125,
-0.009857177734375,
0.0355224609375,
0.0023403167724609375,
-0.014312744140625,
-0.00504302978515625,
0.03436279296875,
0.0010585784912109375,
-0.023712158203125,
0.04193115234375,
-0.00568389892578125,
-0.032806396484375,
0.01824951171875,
-0.01410675048828125,
0.021881103515625,
-0.01055908203125,
-0.009124755859375,
0.0104217529296875,
0.008575439453125,
-0.00370025634765625,
0.0330810546875,
0.0233917236328125,
-0.01336669921875,
-0.00638580322265625,
-0.0001785755157470703,
0.007537841796875,
0.0017566680908203125,
-0.03448486328125,
-0.0236358642578125,
-0.041717529296875,
0.034393310546875,
0.007282257080078125,
0.036834716796875,
0.04327392578125,
0.00827789306640625,
-0.007381439208984375,
-0.01139068603515625,
0.04248046875,
0.00823211669921875,
0.0198211669921875,
-0.01177215576171875,
0.006137847900390625,
0.0234832763671875,
-0.01274871826171875,
0.00936126708984375,
0.0214996337890625,
-0.00021135807037353516,
0.0241241455078125,
-0.0302276611328125,
0.0038585662841796875,
0.039459228515625,
-0.0010900497436523438,
0.0035686492919921875,
0.023040771484375,
0.0132904052734375,
0.0234527587890625,
0.0028076171875,
-0.02874755859375,
-0.001651763916015625,
0.005046844482421875,
0.0212860107421875,
0.006744384765625,
-0.0010967254638671875,
0.0132904052734375,
0.026092529296875,
0.018035888671875,
-0.045684814453125,
-0.02203369140625,
0.0005917549133300781,
-0.006786346435546875,
0.0015048980712890625,
0.03619384765625,
-0.0009646415710449219,
0.005214691162109375,
0.0049285888671875,
-0.00325775146484375,
-0.01291656494140625,
-0.033172607421875,
0.007236480712890625,
0.00569915771484375,
0.05059814453125,
0.0175933837890625,
-0.044708251953125,
-0.01654052734375,
-0.0297698974609375,
0.0203399658203125,
0.02899169921875,
0.00968170166015625,
0.01273345947265625,
0.030914306640625,
-0.004726409912109375,
-0.03204345703125,
0.0237884521484375,
-0.0162200927734375,
-0.033050537109375,
0.0012607574462890625,
-0.0197296142578125,
-0.026580810546875,
-0.006519317626953125,
0.00966644287109375,
-0.05718994140625,
0.0130767822265625,
-0.01904296875,
-0.03778076171875,
0.019500732421875,
0.013458251953125,
0.005367279052734375,
0.0029697418212890625,
-0.01036834716796875,
0.014862060546875,
-0.0035037994384765625,
0.0008597373962402344,
0.00878143310546875,
-0.0138702392578125,
-0.015899658203125,
-0.032806396484375,
0.029815673828125,
0.0308837890625,
0.019805908203125,
-0.0167388916015625,
-0.004978179931640625,
0.0262603759765625,
0.0189208984375,
0.004444122314453125,
-0.01268768310546875,
-0.00293731689453125,
-0.05419921875,
0.023773193359375,
-0.035888671875,
-0.0406494140625,
0.004314422607421875,
-0.0006580352783203125,
0.0013685226440429688,
-0.00009638071060180664,
-0.007801055908203125,
-0.0291900634765625,
0.0075531005859375,
0.0152435302734375,
-0.040130615234375,
0.009613037109375,
-0.0107269287109375,
-0.00978851318359375,
0.01457977294921875,
0.0236663818359375,
-0.00948333740234375,
0.01776123046875,
-0.0113525390625,
0.0263824462890625,
0.0167236328125,
-0.0288543701171875,
0.013916015625,
-0.0167999267578125,
-0.00933074951171875,
0.0109100341796875,
-0.01079559326171875,
0.008392333984375,
0.021759033203125,
-0.019866943359375,
0.0215606689453125,
0.005008697509765625,
-0.02386474609375,
0.047637939453125,
0.01177215576171875,
-0.00891876220703125,
-0.002681732177734375,
-0.01806640625,
-0.00614166259765625,
-0.01214599609375,
-0.0072174072265625,
-0.0214385986328125,
-0.01580810546875,
0.004974365234375,
-0.026947021484375,
0.01049041748046875,
0.0019397735595703125,
0.0164337158203125,
0.035614013671875,
0.0423583984375,
-0.0201263427734375,
0.0095977783203125,
-0.0128021240234375,
-0.0030803680419921875,
0.004398345947265625,
0.0012998580932617188,
0.0089111328125,
0.0176239013671875,
0.0181121826171875,
0.0017881393432617188,
-0.0023441314697265625,
0.0171966552734375,
-0.00244903564453125,
-0.0236358642578125,
-0.0125579833984375,
-0.016204833984375,
0.0014324188232421875,
-0.0266571044921875,
-0.0289306640625,
0.035980224609375,
0.0262908935546875,
0.0308837890625,
-0.0330810546875,
-0.0141143798828125,
-0.004535675048828125,
-0.039337158203125,
-0.03875732421875,
-0.01468658447265625,
0.014495849609375,
0.0166168212890625,
-0.0022144317626953125,
0.0261688232421875,
0.027618408203125,
-0.0026302337646484375,
-0.01168060302734375,
0.0006399154663085938,
-0.006122589111328125,
-0.0271759033203125,
-0.004276275634765625,
-0.0066070556640625,
-0.004665374755859375,
0.020843505859375,
0.0115966796875,
0.00965118408203125,
-0.00254058837890625,
-0.022430419921875,
-0.01224517822265625,
-0.0206756591796875,
0.004779815673828125,
0.00030231475830078125,
0.018524169921875,
0.0153656005859375,
-0.015106201171875,
-0.0293121337890625,
-0.0261993408203125,
0.032623291015625,
-0.01007843017578125,
0.00041985511779785156,
0.004261016845703125,
0.0026874542236328125,
-0.0150146484375,
0.0179290771484375,
-0.0033435821533203125,
-0.0071563720703125,
-0.017059326171875,
0.0020275115966796875,
-0.004444122314453125,
-0.0025806427001953125,
0.0140380859375,
-0.02508544921875,
-0.03656005859375,
0.00879669189453125,
0.0015306472778320312,
0.0034122467041015625,
-0.01375579833984375,
-0.01277923583984375,
-0.0248565673828125,
-0.00909423828125,
-0.005222320556640625,
-0.00691986083984375,
0.01690673828125,
0.03460693359375,
0.01201629638671875,
0.0276336669921875,
0.02630615234375,
0.023712158203125,
-0.0018739700317382812,
0.01629638671875,
0.033477783203125,
-0.0017671585083007812,
0.0013208389282226562,
0.037506103515625,
0.0007634162902832031,
0.0167999267578125,
-0.014251708984375,
-0.0112152099609375,
0.01378631591796875,
0.00380706787109375,
-0.0089111328125,
-0.032196044921875,
-0.0015459060668945312,
0.0328369140625,
0.0005631446838378906,
-0.027587890625,
-0.01067352294921875,
-0.03662109375,
-0.00536346435546875,
-0.0168304443359375,
-0.00124359130859375,
-0.01108551025390625,
0.0261688232421875,
-0.0011358261108398438,
-0.01265716552734375,
-0.022674560546875,
0.0159149169921875,
0.0110931396484375,
-0.0110321044921875,
-0.0279998779296875,
-0.001201629638671875,
-0.031951904296875,
0.031219482421875,
0.0027484893798828125,
-0.023284912109375,
0.0077362060546875,
0.03564453125,
0.031097412109375,
0.01551055908203125,
-0.0124969482421875,
-0.020050048828125,
0.0180511474609375,
0.0087738037109375,
-0.03985595703125,
0.03656005859375,
0.054779052734375,
-0.007205963134765625,
0.0166168212890625,
0.03857421875,
0.013458251953125,
-0.015228271484375,
0.0038051605224609375,
-0.0223541259765625,
0.00899505615234375,
-0.013641357421875,
-0.0165252685546875,
0.004886627197265625,
0.030303955078125,
-0.00795745849609375,
-0.01348876953125,
0.0122528076171875,
-0.0241546630859375,
0.034515380859375,
-0.00720977783203125,
-0.0185699462890625,
0.015350341796875,
0.0009860992431640625,
-0.01306915283203125,
0.0062713623046875,
0.01085662841796875,
0.005615234375,
0.0186309814453125,
-0.0107574462890625,
0.0242919921875,
0.0101318359375,
0.0204315185546875,
0.008453369140625,
0.0042266845703125,
-0.0036754608154296875,
0.00879669189453125,
0.00392913818359375,
0.037384033203125,
-0.050445556640625,
0.037567138671875,
0.00237274169921875,
-0.023895263671875,
0.023773193359375,
-0.004306793212890625,
-0.0013914108276367188,
-0.0106048583984375,
-0.0207977294921875,
-0.004856109619140625,
0.002689361572265625,
-0.00931549072265625,
-0.01491546630859375,
0.006626129150390625,
0.019866943359375,
-0.00530242919921875,
0.0253143310546875,
-0.01151275634765625,
-0.00942230224609375,
-0.0040435791015625,
0.024688720703125,
-0.00423431396484375,
-0.0097808837890625,
0.0272674560546875,
-0.0066680908203125,
0.006664276123046875,
0.00696563720703125,
-0.0006022453308105469,
0.03143310546875,
0.0036220550537109375,
0.00008124113082885742,
-0.009033203125,
0.020416259765625,
0.03076171875,
0.00841522216796875,
-0.057098388671875,
-0.029541015625,
-0.01003265380859375,
0.0400390625,
-0.0205230712890625,
0.0018205642700195312,
-0.004169464111328125,
0.038482666015625,
-0.0177154541015625,
-0.00443267822265625,
0.0186004638671875,
0.00829315185546875,
-0.00806427001953125,
0.007389068603515625,
-0.002223968505859375,
-0.0126190185546875,
-0.0003116130828857422,
0.033203125,
-0.02056884765625,
-0.0019321441650390625,
-0.0119171142578125,
-0.00438690185546875,
-0.040130615234375,
-0.0084381103515625,
0.005496978759765625,
0.03253173828125,
0.0177764892578125,
0.01100921630859375,
0.056884765625,
-0.00667572021484375,
-0.02447509765625,
0.03985595703125,
0.018890380859375,
0.0015916824340820312,
0.026641845703125,
0.01097869873046875,
0.01397705078125,
-0.0210723876953125,
-0.0190582275390625,
-0.042694091796875,
0.002197265625,
0.037017822265625,
-0.0006055831909179688,
-0.0200958251953125,
-0.0197296142578125,
-0.00998687744140625,
-0.029541015625,
0.00704193115234375,
-0.00447845458984375,
0.01111602783203125,
-0.0038242340087890625,
-0.0231475830078125,
0.0128631591796875,
-0.002445220947265625,
0.00101470947265625,
0.01134490966796875,
-0.00567626953125,
0.0157012939453125,
0.0292510986328125,
0.0149993896484375,
0.04986572265625,
-0.0252227783203125,
0.0004322528839111328,
0.01861572265625,
-0.01482391357421875,
0.04742431640625,
-0.050506591796875,
0.008697509765625,
0.006595611572265625,
-0.00948333740234375,
-0.01294708251953125,
-0.0010728836059570312,
-0.00608062744140625,
0.0034046173095703125,
-0.005245208740234375,
0.0024547576904296875,
-0.0036373138427734375,
-0.006679534912109375,
-0.004673004150390625,
0.03863525390625,
0.0002961158752441406,
-0.01253509521484375,
-0.0012722015380859375,
-0.0172576904296875,
-0.03472900390625,
-0.0199432373046875,
-0.004756927490234375,
0.0002772808074951172,
-0.01104736328125,
-0.0024166107177734375,
0.004329681396484375,
-0.03399658203125,
-0.0010786056518554688,
0.03466796875,
-0.0177764892578125,
-0.0258331298828125,
0.0030517578125,
0.00994110107421875,
-0.0037822723388671875,
0.01800537109375,
0.0004260540008544922,
-0.026580810546875,
-0.00406646728515625,
0.01371002197265625,
-0.0036792755126953125,
0.0015401840209960938,
-0.024139404296875,
0.014984130859375,
0.0171356201171875,
-0.0290374755859375,
0.0270843505859375,
0.030029296875,
0.0258026123046875,
0.0389404296875,
-0.016082763671875,
-0.0206146240234375,
-0.002742767333984375,
-0.03472900390625,
-0.005397796630859375,
-0.0034465789794921875,
0.01605224609375,
-0.0060882568359375,
-0.020477294921875,
0.033966064453125,
0.0241851806640625,
0.013397216796875,
0.036041259765625,
-0.005748748779296875,
-0.017120361328125,
-0.0111083984375,
-0.01568603515625,
0.0416259765625,
0.050628662109375,
-0.0022373199462890625,
-0.0241546630859375,
-0.02618408203125,
-0.005496978759765625,
0.03009033203125,
-0.0251922607421875,
0.0193328857421875,
-0.0211944580078125,
-0.02923583984375,
0.01806640625,
-0.0281982421875,
-0.02557373046875,
0.0024013519287109375,
-0.0196685791015625,
0.00339508056640625,
0.01177215576171875,
-0.0071868896484375,
0.0122222900390625,
-0.0023059844970703125,
-0.0043182373046875,
0.01471710205078125,
0.01297760009765625,
0.00394439697265625,
-0.0031414031982421875,
-0.031524658203125,
0.0005745887756347656,
-0.007419586181640625,
0.020843505859375,
-0.007778167724609375,
0.007709503173828125,
-0.0202484130859375,
0.02362060546875,
-0.00732421875,
0.02520751953125,
-0.0130767822265625,
0.022369384765625,
-0.0146942138671875,
0.0003275871276855469,
-0.00914764404296875,
0.00022232532501220703,
0.00617218017578125,
0.0231170654296875,
-0.01006317138671875,
-0.0007491111755371094,
0.0362548828125,
-0.03369140625,
0.003368377685546875,
-0.023468017578125,
0.0272216796875,
-0.00653076171875,
0.009033203125,
-0.032562255859375,
0.03289794921875,
0.00870513916015625,
0.0146331787109375,
0.0008344650268554688,
-0.01238250732421875,
0.01318359375,
0.0146636962890625,
-0.00930023193359375,
0.002773284912109375,
0.0218658447265625,
0.0150299072265625,
-0.03155517578125,
-0.005016326904296875,
0.020233154296875,
0.040435791015625,
-0.006771087646484375,
0.00006693601608276367,
-0.009552001953125,
0.002529144287109375,
0.0131378173828125,
-0.00933074951171875,
-0.031890869140625,
0.0188446044921875,
0.0093231201171875,
-0.016998291015625,
0.0543212890625,
0.0128936767578125,
0.0165863037109375,
-0.011077880859375,
-0.01279449462890625,
0.01727294921875,
-0.006954193115234375,
-0.0209197998046875,
-0.036651611328125,
-0.00036978721618652344,
0.01312255859375,
-0.0394287109375,
-0.022552490234375,
0.01267242431640625,
-0.00034809112548828125,
-0.00901031494140625,
0.0174102783203125,
0.01413726806640625,
-0.04937744140625,
-0.0294952392578125,
-0.001865386962890625,
0.03387451171875,
0.006870269775390625,
-0.0012187957763671875,
-0.002895355224609375,
-0.0269775390625,
-0.0313720703125,
-0.03009033203125,
-0.0015764236450195312,
-0.028778076171875,
0.004268646240234375,
0.0018987655639648438,
0.023712158203125,
0.0145721435546875,
0.0006575584411621094,
0.0121917724609375,
-0.01959228515625,
-0.00003045797348022461,
0.0039005279541015625,
0.002227783203125,
0.0176849365234375,
0.012725830078125,
-0.0228424072265625,
0.0119171142578125,
-0.00122833251953125,
-0.00838470458984375,
-0.0087738037109375,
0.0108489990234375,
0.005107879638671875,
0.0173492431640625,
0.0132293701171875,
-0.0185089111328125,
-0.01507568359375,
-0.01145172119140625,
-0.027862548828125,
-0.01050567626953125,
-0.00038886070251464844,
-0.0155792236328125,
0.0201416015625,
-0.003383636474609375,
-0.0015630722045898438,
0.0014390945434570312,
0.00914764404296875,
0.01284027099609375,
-0.01004791259765625,
-0.0114593505859375,
-0.0086517333984375,
0.003162384033203125,
-0.002452850341796875,
0.02764892578125,
0.04388427734375,
0.0009398460388183594,
0.0058135986328125,
0.00939178466796875,
-0.0377197265625,
-0.005420684814453125,
0.0306854248046875,
-0.01477813720703125,
-0.00043392181396484375,
0.0007848739624023438,
0.03717041015625,
0.001781463623046875
] |
ours_543
|
The answer is \(135\).
Our strategy is to first find \(\angle BDE\) and \(\angle BED\), then subtract their sum from \(180\) to get the desired answer.
Note that \(\triangle BOC\) is equilateral, so \(\angle BOC = 60^\circ\) and \(\angle BOA = 30^\circ\). By inscribed angles, \(\angle BDE\) is half of \(\angle BOA\), or \(15^\circ\). Now examine \(\triangle ABO\). \(\angle ABO\) is right since \(AB\) is a tangent, and \(\angle BOA = 30^\circ\), so \(\angle BAO = 60^\circ\). Therefore, \(\angle BED = 30^\circ\) by inscribed angles, and the answer is \(180^\circ - 30^\circ - 15^\circ = 135^\circ\).
\(\boxed{135}\)
|
135
|
{
"competition": "us_comps",
"dataset": "Ours",
"posts": null,
"source": "OMOSoln2.md"
}
|
A circle \(\omega\) has center \(O\) and radius \(r\). A chord \(BC\) of \(\omega\) also has length \(r\), and the tangents to \(\omega\) at \(B\) and \(C\) meet at \(A\). Ray \(AO\) meets \(\omega\) at \(D\) past \(O\), and ray \(OA\) meets the circle centered at \(A\) with radius \(AB\) at \(E\) past \(A\). Compute the degree measure of \(\angle DBE\).
|
[
"/Mathematics/Geometry/GeneralGeometry/EuclideanGeometry",
"/Mathematics/Geometry/GeneralGeometry/Geometry",
"/Mathematics/Geometry/PlaneGeometry/Circles/Circle",
"/Mathematics/Geometry/PlaneGeometry/Circles/CircleTangentLine",
"/Mathematics/Geometry/PlaneGeometry/CircularTriangles/CircularTriangle",
"/Mathematics/RecreationalMathematics/Puzzles/Puzzle"
] |
Use that the chord length equals the radius, making triangle BOC equilateral and fixing central angles, then apply the inscribed angle theorem.
|
[
-0.00013113021850585938,
-0.0114288330078125,
0.004688262939453125,
-0.00984954833984375,
0.00003743171691894531,
0.0401611328125,
-0.0014848709106445312,
0.0275726318359375,
0.0016908645629882812,
-0.0161895751953125,
-0.0015611648559570312,
0.04351806640625,
0.0007967948913574219,
0.01995849609375,
-0.037750244140625,
0.001667022705078125,
0.011627197265625,
0.020751953125,
0.031890869140625,
0.002391815185546875,
-0.005535125732421875,
-0.004810333251953125,
-0.053497314453125,
-0.0021228790283203125,
0.0133514404296875,
-0.01641845703125,
-0.0178985595703125,
0.0210418701171875,
-0.0192413330078125,
0.0264892578125,
0.0157012939453125,
-0.0050506591796875,
0.00054931640625,
-0.01348114013671875,
0.0003707408905029297,
0.00397491455078125,
-0.00018453598022460938,
-0.0029735565185546875,
-0.01525115966796875,
-0.0274658203125,
0.0179290771484375,
0.0026836395263671875,
-0.0211639404296875,
0.01348114013671875,
0.011016845703125,
0.0197296142578125,
0.00044155120849609375,
-0.0181121826171875,
-0.00971221923828125,
-0.01488494873046875,
0.009063720703125,
0.01416015625,
-0.050750732421875,
-0.003673553466796875,
-0.0182342529296875,
-0.055938720703125,
-0.037811279296875,
-0.0007143020629882812,
-0.038421630859375,
-0.02081298828125,
0.00440216064453125,
0.0333251953125,
-0.01102447509765625,
-0.031158447265625,
-0.0021915435791015625,
-0.0006251335144042969,
-0.03472900390625,
-0.00809478759765625,
0.006145477294921875,
0.00785064697265625,
-0.012115478515625,
-0.0360107421875,
0.016845703125,
0.039581298828125,
-0.01490020751953125,
-0.0116424560546875,
-0.01004791259765625,
0.01080322265625,
-0.01065826416015625,
0.0146942138671875,
0.01947021484375,
0.005168914794921875,
0.006809234619140625,
-0.035614013671875,
0.0253143310546875,
-0.01861572265625,
-0.0460205078125,
0.00658416748046875,
0.02227783203125,
-0.00446319580078125,
-0.01145172119140625,
0.01328277587890625,
-0.053192138671875,
0.0055999755859375,
-0.00832366943359375,
0.0027179718017578125,
0.01447296142578125,
-0.021881103515625,
-0.01561737060546875,
0.003734588623046875,
-0.0238189697265625,
-0.0054779052734375,
-0.0238037109375,
-0.01393890380859375,
-0.0026111602783203125,
-0.01666259765625,
0.0039825439453125,
0.0014791488647460938,
-0.0177764892578125,
-0.00934600830078125,
0.000043451786041259766,
-0.00844573974609375,
-0.0012836456298828125,
0.0179290771484375,
-0.0039215087890625,
-0.0032806396484375,
0.0009822845458984375,
0.019744873046875,
-0.024078369140625,
-0.0145416259765625,
0.01904296875,
0.012298583984375,
-0.0234832763671875,
0.004032135009765625,
0.0043182373046875,
-0.00826263427734375,
-0.00861358642578125,
-0.0201568603515625,
-0.034027099609375,
0.01403045654296875,
0.0240020751953125,
-0.0021343231201171875,
-0.044403076171875,
-0.039520263671875,
0.004367828369140625,
-0.01177978515625,
-0.006534576416015625,
0.00412750244140625,
0.0079498291015625,
0.00789642333984375,
-0.005031585693359375,
0.00027871131896972656,
0.00933074951171875,
-0.1004638671875,
0.00586700439453125,
-0.040740966796875,
0.004791259765625,
0.0072784423828125,
0.0066375732421875,
0.005504608154296875,
0.0016803741455078125,
-0.0010576248168945312,
0.02032470703125,
0.0022907257080078125,
0.00817108154296875,
0.002887725830078125,
-0.00374603271484375,
0.0290985107421875,
0.0034847259521484375,
0.0103302001953125,
-0.00930023193359375,
-0.0064849853515625,
0.0157928466796875,
0.001522064208984375,
-0.002910614013671875,
-0.011322021484375,
-0.003936767578125,
0.0067291259765625,
-0.029144287109375,
0.01398468017578125,
-0.01035308837890625,
0.0083770751953125,
0.018402099609375,
-0.007328033447265625,
-0.005260467529296875,
0.009063720703125,
-0.00518798828125,
-0.002483367919921875,
-0.02728271484375,
0.00528717041015625,
0.01198577880859375,
-0.032928466796875,
0.0240631103515625,
0.0008978843688964844,
0.0367431640625,
0.0176849365234375,
0.00949859619140625,
0.0199127197265625,
0.007244110107421875,
0.00786590576171875,
-0.01010894775390625,
-0.03973388671875,
0.01136016845703125,
-0.00644683837890625,
0.00862884521484375,
-0.0015935897827148438,
-0.024627685546875,
0.0244140625,
0.03143310546875,
-0.0010461807250976562,
-0.03533935546875,
-0.01300811767578125,
0.01213836669921875,
0.020233154296875,
-0.004375457763671875,
0.0010013580322265625,
-0.0053253173828125,
-0.00412750244140625,
-0.004947662353515625,
-0.00713348388671875,
-0.0007052421569824219,
-0.004833221435546875,
-0.0245208740234375,
-0.0305023193359375,
-0.0024013519287109375,
-0.0229644775390625,
-0.0159912109375,
0.01059722900390625,
-0.005832672119140625,
0.031280517578125,
-0.0008020401000976562,
-0.02362060546875,
0.00989532470703125,
-0.0189666748046875,
-0.03387451171875,
0.0004734992980957031,
0.00366973876953125,
-0.01401519775390625,
-0.015838623046875,
0.0026721954345703125,
-0.0160675048828125,
0.004573822021484375,
-0.01094818115234375,
0.0177001953125,
0.0030002593994140625,
-0.0078887939453125,
-0.0307159423828125,
-0.0168609619140625,
-0.00884246826171875,
0.00881195068359375,
0.031524658203125,
-0.01331329345703125,
-0.01239013671875,
-0.0201416015625,
-0.00289154052734375,
0.0030574798583984375,
0.01117706298828125,
-0.00992584228515625,
0.0108795166015625,
-0.014404296875,
-0.04107666015625,
0.03875732421875,
0.017059326171875,
-0.00969696044921875,
0.00616455078125,
0.0224151611328125,
0.0007433891296386719,
0.03289794921875,
-0.0091094970703125,
0.0122222900390625,
-0.0159912109375,
0.014068603515625,
0.01451873779296875,
-0.0193328857421875,
-0.002353668212890625,
0.0311126708984375,
-0.00382232666015625,
0.0101165771484375,
0.017669677734375,
0.0089263916015625,
0.031219482421875,
-0.0112457275390625,
-0.01006317138671875,
0.008148193359375,
-0.0278472900390625,
0.007686614990234375,
-0.0053863525390625,
0.03057861328125,
0.006595611572265625,
0.0015230178833007812,
0.0067138671875,
-0.0208740234375,
-0.03900146484375,
0.0092620849609375,
0.00423431396484375,
-0.0199432373046875,
0.0016431808471679688,
-0.003108978271484375,
0.00472259521484375,
0.00794219970703125,
-0.00045371055603027344,
-0.0196075439453125,
-0.003551483154296875,
-0.0193939208984375,
0.03814697265625,
0.00531768798828125,
0.0032100677490234375,
0.01317596435546875,
0.006076812744140625,
0.004573822021484375,
0.023590087890625,
-0.0186767578125,
0.004856109619140625,
0.01035308837890625,
0.0241851806640625,
0.0121307373046875,
0.006549835205078125,
0.019012451171875,
-0.038177490234375,
0.0086212158203125,
0.0267181396484375,
0.00873565673828125,
-0.01537322998046875,
-0.004756927490234375,
-0.00010776519775390625,
-0.03814697265625,
0.007640838623046875,
-0.009857177734375,
-0.0094757080078125,
0.0219573974609375,
0.00958251953125,
0.009552001953125,
0.04083251953125,
0.00003147125244140625,
0.0533447265625,
-0.028900146484375,
0.0110931396484375,
0.0029888153076171875,
0.0217742919921875,
0.0290985107421875,
-0.0252227783203125,
0.01953125,
0.00809478759765625,
-0.0020885467529296875,
0.0179443359375,
0.00789642333984375,
-0.0125579833984375,
0.01837158203125,
0.00865936279296875,
0.00730133056640625,
0.0020084381103515625,
0.0222930908203125,
0.05352783203125,
-0.05340576171875,
-0.056121826171875,
0.0110015869140625,
-0.048187255859375,
0.0089111328125,
-0.01873779296875,
-0.04052734375,
-0.0005903244018554688,
-0.00043773651123046875,
0.002651214599609375,
-0.00952911376953125,
-0.0270538330078125,
-0.0162200927734375,
0.00998687744140625,
0.014251708984375,
-0.00608062744140625,
0.039093017578125,
0.0191497802734375,
-0.034515380859375,
0.002349853515625,
0.02227783203125,
-0.02264404296875,
0.00930023193359375,
-0.0158843994140625,
-0.003948211669921875,
-0.048309326171875,
-0.00016689300537109375,
0.0002982616424560547,
-0.038818359375,
0.0338134765625,
0.00794219970703125,
0.0265655517578125,
0.0098876953125,
-0.003795623779296875,
0.00849151611328125,
-0.0096282958984375,
-0.01308441162109375,
0.003040313720703125,
-0.00630950927734375,
-0.00946807861328125,
0.016632080078125,
0.001865386962890625,
-0.002117156982421875,
0.01149749755859375,
-0.00882720947265625,
0.0201873779296875,
0.011871337890625,
-0.01263427734375,
0.0082244873046875,
0.00962066650390625,
-0.035675048828125,
-0.0189056396484375,
0.02398681640625,
0.001895904541015625,
-0.023651123046875,
0.0467529296875,
0.01247406005859375,
-0.018951416015625,
0.00806427001953125,
0.0010747909545898438,
-0.0218658447265625,
0.01018524169921875,
0.006122589111328125,
-0.00406646728515625,
0.006801605224609375,
0.004360198974609375,
0.0099639892578125,
-0.02569580078125,
-0.01030731201171875,
-0.019287109375,
-0.027923583984375,
-0.0005359649658203125,
0.0271759033203125,
-0.0004825592041015625,
0.01279449462890625,
-0.005474090576171875,
-0.00452423095703125,
0.0265045166015625,
-0.0017118453979492188,
0.0262451171875,
0.004390716552734375,
0.03326416015625,
-0.004688262939453125,
-0.01515960693359375,
0.0160369873046875,
0.013580322265625,
-0.022674560546875,
0.01849365234375,
-0.02471923828125,
-0.01381683349609375,
0.019561767578125,
-0.01200103759765625,
-0.02191162109375,
0.031402587890625,
0.00958251953125,
-0.0255279541015625,
0.002170562744140625,
0.03387451171875,
0.0030059814453125,
-0.00394439697265625,
-0.0031719207763671875,
0.0209808349609375,
-0.0108642578125,
-0.007434844970703125,
0.004817962646484375,
0.0157012939453125,
0.0132904052734375,
-0.004146575927734375,
-0.0163116455078125,
-0.0026035308837890625,
-0.020233154296875,
0.0283660888671875,
0.0128631591796875,
0.042724609375,
-0.020263671875,
-0.031707763671875,
0.043365478515625,
-0.023651123046875,
0.004863739013671875,
-0.02886962890625,
0.005023956298828125,
-0.008575439453125,
-0.00843048095703125,
-0.008392333984375,
0.015350341796875,
0.006298065185546875,
-0.0318603515625,
0.00872802734375,
-0.034881591796875,
-0.0278472900390625,
-0.00893402099609375,
-0.027984619140625,
0.017791748046875,
0.01331329345703125,
0.00595855712890625,
0.0099334716796875,
0.034149169921875,
-0.0166778564453125,
-0.00539398193359375,
-0.016632080078125,
-0.00830841064453125,
-0.01053619384765625,
0.001956939697265625,
0.0279388427734375,
0.00830841064453125,
-0.004192352294921875,
-0.0143890380859375,
-0.01123809814453125,
0.0254058837890625,
-0.0211334228515625,
-0.0304412841796875,
-0.0208282470703125,
-0.040069580078125,
0.0202178955078125,
0.0012664794921875,
0.0154876708984375,
-0.01000213623046875,
0.0199127197265625,
-0.024322509765625,
-0.0182647705078125,
0.017608642578125,
0.00302886962890625,
-0.04913330078125,
0.0384521484375,
-0.014923095703125,
0.0186767578125,
0.0204010009765625,
-0.00260162353515625,
0.0214691162109375,
0.0172119140625,
-0.031402587890625,
0.015899658203125,
-0.0006299018859863281,
0.02532958984375,
-0.02960205078125,
0.041900634765625,
0.042083740234375,
-0.0035343170166015625,
0.049468994140625,
-0.01080322265625,
0.0167236328125,
-0.0046539306640625,
0.0199432373046875,
0.004749298095703125,
0.004634857177734375,
0.0201416015625,
-0.001033782958984375,
0.0146636962890625,
-0.0106201171875,
-0.047637939453125,
0.006427764892578125,
-0.0023746490478515625,
0.002086639404296875,
0.007442474365234375,
-0.002506256103515625,
-0.002918243408203125,
0.01171875,
-0.01010894775390625,
0.01361083984375,
-0.0084075927734375,
-0.0155029296875,
-0.007099151611328125,
-0.0010156631469726562,
-0.0276641845703125,
0.006561279296875,
-0.017578125,
0.042999267578125,
-0.008148193359375,
0.0248565673828125,
-0.03546142578125,
0.00420379638671875,
0.0125732421875,
-0.0036602020263671875,
-0.03826904296875,
0.00986480712890625,
0.01369476318359375,
0.006744384765625,
0.01062774658203125,
-0.0129547119140625,
0.0372314453125,
0.007129669189453125,
-0.0263671875,
-0.0005249977111816406,
0.007114410400390625,
0.0309600830078125,
-0.01073455810546875,
-0.02581787109375,
0.0012149810791015625,
-0.0201568603515625,
0.00609588623046875,
-0.01038360595703125,
0.036712646484375,
-0.027374267578125,
0.0169219970703125,
-0.015838623046875,
-0.0025005340576171875,
-0.005741119384765625,
0.01178741455078125,
0.057891845703125,
-0.0047454833984375,
-0.02142333984375,
0.005725860595703125,
0.003536224365234375,
-0.01320648193359375,
0.024169921875,
0.011993408203125,
-0.0221405029296875,
0.0255126953125,
0.004375457763671875,
0.025115966796875,
-0.01432037353515625,
-0.0054168701171875,
-0.019927978515625,
0.0357666015625,
-0.0282745361328125,
0.0221710205078125,
0.023590087890625,
-0.01505279541015625,
-0.003261566162109375,
0.01552581787109375,
0.019622802734375,
-0.01367950439453125,
0.01311492919921875,
0.0087890625,
0.0022068023681640625,
0.036346435546875,
0.03424072265625,
-0.029510498046875,
0.022918701171875,
-0.0164337158203125,
0.0116729736328125,
0.034027099609375,
0.0063323974609375,
-0.025299072265625,
0.00274658203125,
-0.007656097412109375,
-0.01294708251953125,
-0.017486572265625,
-0.003124237060546875,
0.0120391845703125,
0.039520263671875,
-0.0007815361022949219,
-0.0173492431640625,
-0.0253143310546875,
-0.05657958984375,
0.0140838623046875,
-0.0216522216796875,
-0.02398681640625,
0.005458831787109375,
0.00893402099609375,
0.01096343994140625,
-0.0163421630859375,
-0.00019788742065429688,
0.0155792236328125,
0.0158233642578125,
0.01288604736328125,
-0.00417327880859375,
0.035308837890625,
0.016815185546875,
0.0103759765625,
-0.042633056640625,
0.005535125732421875,
-0.0143890380859375,
0.004764556884765625,
0.01355743408203125,
0.005352020263671875,
0.010986328125,
0.0012712478637695312,
-0.00402069091796875,
0.01377105712890625,
0.024932861328125,
-0.01183319091796875,
-0.03253173828125,
0.0016450881958007812,
-0.0132598876953125,
0.033477783203125,
0.0104827880859375,
0.015594482421875,
-0.033111572265625,
-0.00989532470703125,
-0.0152130126953125,
0.01502227783203125,
-0.010589599609375,
-0.03387451171875,
-0.044036865234375,
-0.01296234130859375,
0.040740966796875,
-0.0142822265625,
-0.01497650146484375,
0.0310516357421875,
-0.0272979736328125,
-0.0196533203125,
0.0001430511474609375,
-0.0306854248046875,
0.021484375,
0.004180908203125,
0.01617431640625,
0.02032470703125,
0.027130126953125,
0.04840087890625,
0.018280029296875,
0.01386260986328125,
0.052520751953125,
0.0301055908203125,
-0.01079559326171875,
-0.0072174072265625,
-0.00893402099609375,
-0.0012340545654296875,
0.027862548828125,
-0.00395965576171875,
-0.00884246826171875,
-0.001407623291015625,
-0.01255035400390625,
0.02349853515625,
0.0144195556640625,
0.0176544189453125,
-0.015838623046875,
-0.0160369873046875,
-0.0174407958984375,
0.00534820556640625,
-0.038482666015625,
0.00811767578125,
-0.0299530029296875,
0.0154876708984375,
0.046630859375,
-0.01326751708984375,
0.0098724365234375,
-0.0003185272216796875,
-0.03192138671875,
0.0009732246398925781,
0.002471923828125,
-0.03582763671875,
-0.0264129638671875,
-0.0270233154296875,
0.01983642578125,
-0.01430511474609375,
0.00930023193359375,
-0.019073486328125,
-0.0257720947265625,
0.0034275054931640625,
-0.0103607177734375,
0.0084686279296875,
0.0024089813232421875,
-0.0218353271484375,
-0.0284881591796875,
-0.006412506103515625,
0.045074462890625,
0.0222930908203125,
-0.0011053085327148438,
-0.0259857177734375,
0.0102691650390625,
-0.025634765625,
0.01328277587890625,
-0.0166778564453125,
-0.000263214111328125,
-0.031341552734375,
0.00397491455078125,
0.02972412109375,
-0.01177215576171875,
-0.003704071044921875,
-0.007617950439453125,
-0.0035228729248046875,
-0.010589599609375,
-0.0172119140625,
-0.037567138671875,
0.0235595703125,
0.0124053955078125,
0.037872314453125,
-0.0032787322998046875,
-0.00238800048828125,
-0.0118865966796875,
-0.00849151611328125,
0.00707244873046875,
-0.0037288665771484375,
-0.00009673833847045898,
0.01258087158203125,
-0.025115966796875,
-0.048583984375,
0.0070037841796875,
0.00778961181640625,
-0.0086517333984375,
-0.0035381317138671875,
0.00691986083984375,
-0.0010538101196289062,
-0.0070037841796875,
-0.0117645263671875,
-0.00370025634765625,
0.0088348388671875,
0.004215240478515625,
0.0223236083984375,
-0.0176544189453125,
0.017242431640625,
0.0025310516357421875,
-0.041595458984375,
-0.0153656005859375,
-0.0308074951171875,
-0.00323486328125,
0.02783203125,
0.0207977294921875,
-0.0426025390625,
0.0482177734375,
-0.00856781005859375,
-0.0069122314453125,
-0.01546478271484375,
0.00997161865234375,
0.0195770263671875,
-0.026397705078125,
0.019744873046875,
0.00986480712890625,
-0.006282806396484375,
-0.0083465576171875,
0.018463134765625,
-0.0204620361328125,
0.006988525390625,
-0.019195556640625,
0.0010976791381835938,
0.0169830322265625,
-0.006664276123046875,
-0.0399169921875,
0.004528045654296875,
0.0151519775390625,
0.00821685791015625,
0.0002758502960205078,
0.0059356689453125,
-0.0243377685546875,
-0.01354217529296875,
0.0013427734375,
0.000476837158203125,
-0.0225677490234375,
0.0032501220703125,
0.02734375,
-0.022369384765625,
0.017578125,
-0.0132293701171875,
-0.01873779296875,
0.0024166107177734375,
-0.0190887451171875,
-0.004505157470703125,
-0.0083770751953125,
-0.01377105712890625,
0.017730712890625,
-0.028472900390625,
-0.0001552104949951172,
-0.00811004638671875,
-0.0189666748046875,
0.00888824462890625,
0.0157928466796875,
-0.0062713623046875,
-0.004230499267578125,
-0.037445068359375,
0.000047206878662109375,
-0.033905029296875,
-0.0171966552734375,
0.00897216796875,
0.0009622573852539062,
-0.0186614990234375,
-0.01776123046875,
0.002239227294921875,
-0.027557373046875,
0.038818359375,
-0.00395965576171875,
0.035858154296875,
-0.0107574462890625,
-0.038543701171875,
0.021392822265625,
0.0222320556640625,
0.0087738037109375,
0.0025081634521484375,
0.019195556640625,
-0.01708984375,
0.01727294921875,
-0.027740478515625,
0.004268646240234375,
-0.0025005340576171875,
0.00958251953125,
0.0267486572265625,
-0.0185394287109375,
0.0279693603515625,
-0.01137542724609375,
-0.0021152496337890625,
0.0022869110107421875,
0.00951385498046875,
-0.01514434814453125,
-0.03662109375,
0.0006766319274902344,
0.0675048828125,
0.002101898193359375,
0.0210113525390625,
0.004528045654296875,
-0.0014696121215820312,
-0.0168304443359375,
0.0026702880859375,
0.032562255859375,
0.015380859375,
-0.025146484375,
0.036468505859375,
0.0010004043579101562,
0.048370361328125,
-0.0179443359375,
0.0296783447265625,
0.00357818603515625,
-0.00806427001953125,
-0.00524139404296875,
0.0166015625,
-0.004119873046875,
0.017059326171875,
0.007137298583984375,
0.0102996826171875,
-0.036163330078125,
-0.01258087158203125,
-0.027008056640625,
0.047698974609375,
-0.01273345947265625,
0.0011415481567382812,
-0.016082763671875,
0.0156402587890625,
-0.0101318359375,
0.01525115966796875,
0.019561767578125,
0.00736236572265625,
0.011932373046875,
0.0005121231079101562,
-0.002643585205078125,
-0.01067352294921875,
-0.0186767578125,
0.027191162109375,
0.0175933837890625,
0.00823974609375,
0.005268096923828125,
0.0247039794921875,
0.004978179931640625,
-0.01751708984375,
0.003917694091796875,
-0.04522705078125,
0.00606536865234375,
-0.0120849609375,
-0.00876617431640625,
0.0086212158203125,
0.0209808349609375,
-0.0258636474609375,
0.01268768310546875,
-0.0251922607421875,
-0.001537322998046875,
0.041748046875,
-0.037353515625,
-0.03265380859375,
-0.0174102783203125,
0.0018854141235351562,
0.0166778564453125,
0.00510406494140625,
0.01568603515625,
-0.02392578125,
-0.0009522438049316406,
0.01525115966796875,
-0.027313232421875,
0.0023212432861328125,
-0.0103302001953125,
-0.0279693603515625,
-0.0027637481689453125,
0.0328369140625,
0.0269622802734375,
0.01458740234375,
-0.003345489501953125,
-0.005157470703125,
-0.01099395751953125,
0.0297088623046875,
0.0032596588134765625,
0.007640838623046875,
0.00556182861328125,
0.01505279541015625,
-0.00016808509826660156,
-0.0186767578125,
0.0166778564453125,
0.004817962646484375,
0.0129241943359375,
0.0097808837890625,
-0.0253753662109375,
-0.002262115478515625,
0.00870513916015625,
0.01506805419921875,
0.0017070770263671875,
-0.01337432861328125,
-0.0088043212890625,
0.015899658203125,
0.005641937255859375,
-0.0217132568359375,
0.029327392578125,
0.03131103515625,
-0.0004668235778808594,
-0.0206146240234375,
-0.0115509033203125,
0.0062713623046875,
0.0029754638671875,
-0.00688934326171875,
0.007678985595703125,
0.0379638671875,
-0.003208160400390625,
-0.0229949951171875,
0.02313232421875,
0.00202178955078125,
0.014129638671875,
0.00368499755859375,
0.0010852813720703125,
0.0038776397705078125,
-0.0174102783203125,
0.034088134765625,
-0.004261016845703125,
-0.01160430908203125,
0.053924560546875,
-0.0222320556640625,
0.011627197265625,
-0.0003237724304199219,
0.028289794921875,
-0.01122283935546875,
-0.0220184326171875,
-0.00865936279296875,
-0.01233673095703125,
0.0220947265625,
0.007663726806640625,
0.0259857177734375,
0.0081787109375,
-0.00786590576171875,
0.00004464387893676758,
-0.0167236328125,
0.0020198822021484375,
0.01227569580078125,
0.012664794921875,
-0.032958984375,
-0.00319671630859375,
-0.0078887939453125,
0.007663726806640625,
-0.00556182861328125,
0.024993896484375,
0.0109710693359375,
0.016571044921875,
-0.05096435546875,
0.0182342529296875,
0.0175933837890625,
0.0092620849609375,
-0.04290771484375,
-0.0513916015625,
0.00991058349609375,
-0.044036865234375,
0.0004329681396484375,
-0.003383636474609375,
-0.01702880859375,
0.00492095947265625,
-0.022857666015625,
0.01206207275390625,
-0.0440673828125,
0.0259857177734375,
-0.0196533203125,
0.004146575927734375,
-0.0177154541015625,
-0.033355712890625,
-0.003940582275390625,
0.0261383056640625,
-0.0361328125,
0.03057861328125,
-0.00408172607421875,
-0.051055908203125,
-0.008087158203125,
0.01476287841796875,
0.0003764629364013672,
0.005558013916015625,
0.019561767578125,
0.0307464599609375,
0.014129638671875,
0.020904541015625,
-0.012298583984375,
-0.0012197494506835938,
0.02069091796875,
0.011138916015625,
-0.0225372314453125,
-0.03204345703125,
-0.01031494140625,
0.0157318115234375,
0.019866943359375,
-0.044464111328125,
0.01174163818359375,
-0.00848388671875,
0.025238037109375,
0.006031036376953125,
0.006649017333984375,
-0.0031757354736328125,
-0.01806640625,
0.01540374755859375,
-0.04608154296875,
-0.01605224609375,
-0.0005850791931152344,
-0.0007319450378417969,
-0.02325439453125,
-0.01435089111328125,
0.005229949951171875,
-0.016082763671875,
-0.01727294921875,
0.0018463134765625,
-0.01468658447265625,
0.0236358642578125,
-0.005832672119140625,
0.003917694091796875,
0.048828125,
-0.00933837890625,
-0.0203094482421875,
-0.0267486572265625,
0.01561737060546875,
0.0077972412109375,
0.03692626953125,
0.024871826171875,
-0.0088043212890625,
-0.006763458251953125,
-0.0089263916015625,
-0.0027027130126953125,
0.005252838134765625,
0.036285400390625,
0.031524658203125,
-0.0056915283203125,
-0.005859375,
0.0355224609375,
0.015869140625,
0.00571441650390625,
0.00247955322265625,
0.0118560791015625,
-0.046142578125,
0.00943756103515625,
0.005970001220703125,
-0.0137481689453125,
-0.00681304931640625,
-0.0131988525390625,
0.0012350082397460938,
-0.00424957275390625,
-0.004306793212890625,
-0.0166015625,
-0.0265350341796875,
-0.019775390625,
0.02349853515625,
-0.004199981689453125,
0.006671905517578125,
0.00986480712890625,
0.0164642333984375,
0.0153961181640625,
-0.0189971923828125,
-0.0098876953125,
0.01387786865234375,
0.036163330078125,
-0.0211181640625,
0.0102691650390625,
-0.029266357421875,
-0.0036106109619140625,
-0.0254974365234375,
-0.01312255859375,
-0.025146484375,
0.02362060546875,
0.0214691162109375,
-0.0282135009765625,
-0.0167388916015625,
0.0080718994140625,
0.0032100677490234375,
0.0171356201171875,
-0.0043182373046875,
-0.0521240234375,
-0.032928466796875,
-0.03216552734375,
0.0102386474609375,
0.01068878173828125,
0.00472259521484375,
0.01348876953125,
-0.035125732421875,
0.0289306640625,
0.0025348663330078125,
-0.003917694091796875,
-0.016082763671875,
-0.0167694091796875,
-0.0406494140625,
-0.0005545616149902344,
0.0007824897766113281,
0.015350341796875,
0.007472991943359375,
-0.006793975830078125,
0.035552978515625,
0.0079345703125,
-0.004878997802734375,
0.01084136962890625,
0.0161895751953125,
0.0264739990234375,
-0.0233306884765625,
-0.00010842084884643555,
-0.015228271484375,
-0.0005192756652832031,
0.00691986083984375,
0.01556396484375,
-0.011322021484375,
0.026214599609375,
-0.001186370849609375,
-0.0369873046875,
-0.01837158203125,
-0.00739288330078125,
-0.034271240234375,
0.0264892578125,
0.01534271240234375,
0.021209716796875,
0.002838134765625,
0.005924224853515625,
-0.005279541015625,
-0.01253509521484375,
-0.038482666015625,
0.006336212158203125,
-0.01473236083984375,
-0.0033435821533203125,
-0.042999267578125,
0.01305389404296875,
0.01276397705078125,
-0.015899658203125,
-0.0229034423828125,
-0.01120758056640625,
-0.00965118408203125,
-0.0251617431640625,
-0.01288604736328125,
0.002941131591796875,
-0.0162506103515625,
-0.021209716796875,
-0.00806427001953125,
0.01534271240234375,
-0.00266265869140625,
0.03460693359375,
0.01435089111328125,
0.036376953125,
-0.0222015380859375,
-0.01419830322265625,
0.0188446044921875,
-0.00623321533203125,
0.0001342296600341797,
-0.01325225830078125,
0.0016908645629882812,
0.016998291015625,
0.01055908203125,
0.007415771484375,
-0.0005598068237304688,
0.031890869140625,
0.0010223388671875,
-0.007259368896484375,
-0.00542449951171875,
0.005046844482421875,
-0.007610321044921875,
0.031585693359375,
0.00983428955078125,
0.016021728515625,
0.0181427001953125,
0.00844573974609375,
-0.0148162841796875,
-0.0085601806640625,
-0.034698486328125,
-0.0252532958984375,
0.006504058837890625,
0.00957489013671875,
0.01543426513671875,
-0.01239013671875,
0.01418304443359375,
0.00902557373046875,
-0.005279541015625,
-0.0292816162109375,
0.019500732421875,
-0.031982421875,
-0.01039886474609375,
0.0178070068359375,
-0.0181732177734375,
0.0182037353515625,
-0.00930023193359375,
0.03948974609375,
-0.015899658203125,
0.003673553466796875,
0.0019683837890625,
0.0198516845703125,
-0.006626129150390625,
-0.0038852691650390625,
-0.00371551513671875,
-0.0012979507446289062,
-0.024169921875,
0.007724761962890625,
0.012176513671875,
-0.000995635986328125,
-0.004207611083984375,
0.00882720947265625,
-0.0078582763671875,
0.0408935546875,
0.0252685546875,
0.0023555755615234375,
0.0281982421875,
0.026519775390625,
-0.005847930908203125,
0.0307159423828125,
0.023834228515625,
-0.016448974609375,
-0.000499725341796875,
-0.060394287109375,
0.00835418701171875,
0.00855255126953125,
0.0027713775634765625,
0.01050567626953125,
0.044281005859375,
-0.01230621337890625,
-0.01465606689453125,
-0.0026416778564453125,
-0.01213836669921875,
-0.00809478759765625,
0.022125244140625,
0.002368927001953125,
-0.004489898681640625,
0.01227569580078125,
0.0006809234619140625,
0.00881195068359375,
0.00286102294921875,
-0.009613037109375,
-0.01535797119140625,
0.0025539398193359375,
0.03253173828125,
-0.01143646240234375,
-0.001953125,
0.00591278076171875,
-0.01428985595703125,
-0.011474609375,
-0.007568359375,
-0.014862060546875,
0.0011873245239257812,
0.0046844482421875,
0.009429931640625,
-0.025604248046875,
0.02496337890625,
0.004871368408203125,
-0.006717681884765625,
0.0323486328125,
0.0186309814453125,
0.00838470458984375,
-0.0005326271057128906,
-0.011444091796875,
-0.0005955696105957031,
-0.00495147705078125,
0.013519287109375,
0.0288543701171875,
-0.04241943359375,
-0.01201629638671875,
-0.0300445556640625,
-0.01678466796875,
0.0036182403564453125,
-0.0301361083984375,
0.005596160888671875,
0.005588531494140625,
0.0108795166015625,
0.003376007080078125,
-0.02593994140625,
0.006137847900390625,
-0.0082855224609375,
0.00386810302734375,
0.0019683837890625,
-0.0274658203125,
-0.01861572265625,
0.0263214111328125,
-0.021759033203125,
0.0052490234375,
-0.024932861328125,
-0.0025844573974609375,
0.010650634765625,
-0.00762176513671875,
-0.044342041015625,
0.017425537109375,
0.019744873046875,
0.0062103271484375,
0.026123046875,
-0.0151214599609375,
0.006183624267578125,
0.01010894775390625,
-0.050994873046875,
0.0007452964782714844,
0.01546478271484375,
0.036346435546875,
-0.007904052734375,
0.01068878173828125,
0.028472900390625,
-0.0014543533325195312,
0.0413818359375,
0.0036106109619140625,
0.02264404296875,
-0.002613067626953125,
0.0227508544921875,
-0.0294342041015625,
0.0136871337890625,
-0.02459716796875,
-0.00603485107421875,
0.0189056396484375,
0.010589599609375,
-0.0153350830078125,
0.0208282470703125,
-0.0084991455078125,
-0.00001919269561767578,
-0.044830322265625,
-0.0007548332214355469,
-0.0049285888671875,
-0.00449371337890625,
0.008453369140625,
0.0188446044921875,
-0.0122222900390625,
0.0160675048828125,
0.005298614501953125,
-0.0010385513305664062,
-0.0173492431640625,
0.006195068359375,
-0.0031147003173828125,
0.036407470703125,
0.007129669189453125,
-0.00353240966796875,
-0.0163726806640625,
0.01294708251953125,
-0.032196044921875,
0.0229644775390625,
-0.0322265625,
-0.01522064208984375,
0.00919342041015625,
-0.00027561187744140625,
-0.0287933349609375,
-0.004428863525390625,
0.031951904296875,
0.037078857421875,
-0.0205230712890625,
-0.006389617919921875,
-0.0207672119140625,
0.01324462890625,
0.034271240234375,
-0.01385498046875,
0.01442718505859375,
0.016387939453125,
0.0004425048828125,
-0.02496337890625,
-0.01004791259765625,
-0.022735595703125,
-0.0194549560546875,
-0.0247039794921875,
-0.0200958251953125,
0.02587890625,
0.0224151611328125,
-0.0198822021484375,
0.00548553466796875,
0.0245208740234375,
-0.0225372314453125,
0.0035114288330078125,
-0.0170135498046875,
-0.0156707763671875,
-0.004047393798828125,
-0.03857421875,
-0.01446533203125,
-0.0036792755126953125,
-0.00098419189453125,
-0.025634765625,
0.006458282470703125,
0.0198974609375,
0.00431060791015625,
-0.00498199462890625,
-0.017669677734375,
-0.0117034912109375,
0.01458740234375,
0.01271820068359375,
-0.0084686279296875,
-0.005535125732421875,
-0.0185546875,
0.017974853515625,
0.015228271484375,
-0.005550384521484375,
0.0023365020751953125,
0.00940704345703125,
-0.0234527587890625,
-0.03875732421875,
-0.01293182373046875,
0.0226593017578125,
-0.01776123046875,
-0.00775909423828125,
0.00945281982421875,
0.01509857177734375,
-0.0266265869140625,
-0.019622802734375,
-0.0027904510498046875,
-0.01013946533203125,
0.007785797119140625,
-0.009613037109375,
0.009033203125,
0.0066986083984375,
0.051300048828125,
0.012420654296875,
0.0030059814453125,
-0.01953125,
-0.01812744140625,
-0.002063751220703125,
0.0242156982421875,
-0.009735107421875,
0.0263214111328125,
0.034088134765625,
0.01448822021484375,
0.0218505859375,
-0.0101470947265625,
-0.0105438232421875,
0.01091766357421875,
-0.006866455078125,
0.017120361328125,
-0.040557861328125,
0.0033245086669921875,
0.008209228515625,
0.035125732421875,
-0.0131683349609375,
-0.023193359375,
0.0133514404296875,
-0.0010805130004882812,
0.047088623046875,
-0.004756927490234375,
0.02996826171875,
0.00614166259765625,
-0.005947113037109375,
-0.0256805419921875,
0.0016393661499023438,
-0.037109375,
0.017242431640625,
0.0245208740234375,
0.0428466796875,
0.016693115234375,
0.0262298583984375,
-0.023590087890625,
-0.00028228759765625,
-0.00887298583984375,
0.02783203125,
-0.017364501953125,
0.0123138427734375,
-0.01177978515625,
-0.00753021240234375,
0.0268402099609375,
-0.04168701171875,
0.01690673828125,
-0.018707275390625,
-0.0164031982421875,
-0.005329132080078125,
-0.0225982666015625,
0.00701141357421875,
-0.00030612945556640625,
0.000331878662109375,
0.01488494873046875,
0.0312042236328125,
-0.0273590087890625,
0.006374359130859375,
-0.003971099853515625,
-0.0243072509765625,
0.0101318359375,
0.01483154296875,
-0.03765869140625,
0.00809478759765625,
0.01556396484375,
-0.0032672882080078125,
-0.01012420654296875,
-0.005512237548828125,
-0.004344940185546875,
0.0202484130859375,
-0.0166015625,
0.00855255126953125,
-0.00365447998046875,
0.0030956268310546875,
0.0164947509765625,
-0.011260986328125,
-0.0113525390625,
-0.0005965232849121094,
0.032379150390625,
0.0236968994140625,
0.0180206298828125,
0.029937744140625,
-0.0077667236328125,
0.005069732666015625,
-0.0022182464599609375,
0.022613525390625,
0.01082611083984375,
-0.0131988525390625,
0.040313720703125,
0.003955841064453125,
-0.0255889892578125,
-0.00247955322265625,
0.03070068359375,
-0.0369873046875,
0.0280609130859375,
-0.0213165283203125,
-0.0258026123046875,
-0.005268096923828125,
-0.0041046142578125,
-0.01202392578125,
-0.01175689697265625,
0.0231475830078125,
0.00856781005859375,
-0.023712158203125,
-0.0232086181640625,
-0.00791168212890625,
0.0250091552734375,
-0.03265380859375,
0.0181732177734375,
-0.00955963134765625,
-0.0003859996795654297,
0.00673675537109375,
-0.002895355224609375,
0.01776123046875,
0.01177978515625,
0.040008544921875,
-0.0120849609375,
0.00994873046875,
0.0157470703125,
-0.0168914794921875,
-0.006992340087890625,
0.044281005859375,
0.00429534912109375,
0.024017333984375,
0.0087432861328125,
-0.0162506103515625,
-0.01224517822265625,
0.005970001220703125,
0.005462646484375,
0.05438232421875,
-0.0017862319946289062,
-0.00742340087890625,
-0.004299163818359375,
0.0036945343017578125,
0.01568603515625,
0.00299072265625,
-0.03399658203125,
-0.004947662353515625,
-0.0058746337890625,
-0.000476837158203125,
-0.007389068603515625,
-0.02398681640625,
-0.0013904571533203125,
0.005645751953125,
0.02569580078125,
-0.0006346702575683594,
0.01280975341796875,
-0.0110626220703125,
0.01580810546875,
-0.00958251953125,
-0.0014476776123046875,
-0.0201416015625,
-0.02850341796875,
-0.033721923828125,
0.01195526123046875,
0.01459503173828125,
0.009307861328125,
0.00624847412109375,
-0.024658203125,
-0.01641845703125,
-0.01407623291015625,
-0.006916046142578125,
0.00933837890625,
-0.0031719207763671875,
0.0021877288818359375,
-0.0183258056640625,
-0.0257568359375,
-0.0030460357666015625,
0.02020263671875,
-0.0037078857421875,
-0.0048370361328125,
-0.01187896728515625,
-0.0269775390625,
0.0270843505859375,
-0.04388427734375,
-0.0062408447265625,
0.0037250518798828125,
-0.01519012451171875,
0.01552581787109375,
0.01219940185546875,
-0.033477783203125,
-0.002841949462890625,
0.0102081298828125,
0.0367431640625,
0.0246429443359375,
0.0210418701171875,
-0.0291290283203125,
0.035064697265625,
-0.01029205322265625,
-0.0217437744140625,
0.008209228515625,
-0.0105438232421875,
-0.004047393798828125,
0.01299285888671875,
0.016143798828125,
-0.0289459228515625,
-0.0106201171875,
0.0064849853515625,
0.0036487579345703125,
0.002208709716796875,
-0.03985595703125,
-0.0006737709045410156,
-0.0276947021484375,
0.006320953369140625,
0.0111846923828125,
-0.0254058837890625,
-0.040802001953125,
-0.0005168914794921875,
0.0160064697265625,
-0.0111846923828125,
-0.00807952880859375,
0.021240234375,
-0.032958984375,
0.00940704345703125,
0.0160675048828125,
0.00765228271484375,
-0.030914306640625,
0.01323699951171875,
0.0030307769775390625,
0.00696563720703125,
-0.005962371826171875,
-0.004367828369140625,
0.01329803466796875,
-0.0206756591796875,
0.0219573974609375,
0.008941650390625,
0.034454345703125,
0.010955810546875,
0.0057373046875,
-0.032684326171875,
0.030975341796875,
-0.01242828369140625,
0.0012693405151367188,
0.04071044921875,
-0.0253448486328125,
0.007274627685546875,
0.013671875,
-0.0210418701171875,
-0.0498046875,
-0.0341796875,
-0.030487060546875,
0.0491943359375,
-0.009368896484375,
-0.040252685546875,
0.006832122802734375,
-0.031463623046875,
0.0174407958984375,
0.01934814453125,
0.033477783203125,
-0.01168060302734375,
-0.029266357421875,
0.0109100341796875,
-0.0129852294921875,
0.01229095458984375,
0.0360107421875,
-0.00737762451171875,
-0.0048980712890625,
0.0238037109375,
-0.0286712646484375,
-0.004116058349609375,
0.0198211669921875,
-0.00110626220703125,
0.00927734375,
-0.0195465087890625,
-0.025970458984375,
0.004856109619140625,
-0.00975799560546875,
0.032958984375,
-0.0031337738037109375,
0.00047469139099121094,
0.03497314453125,
-0.007366180419921875,
0.02313232421875,
0.03912353515625,
0.0117645263671875,
-0.00763702392578125,
0.0183868408203125,
-0.0230865478515625,
0.02337646484375,
-0.00429534912109375,
0.0123291015625,
-0.001499176025390625,
0.0255584716796875,
0.032440185546875,
-0.0008788108825683594,
-0.024749755859375,
0.0113677978515625,
-0.00351715087890625,
0.0010013580322265625,
-0.00983428955078125,
-0.017669677734375,
0.027679443359375,
-0.0357666015625,
0.0194854736328125,
0.01837158203125,
0.00766754150390625,
-0.0156707763671875,
0.010650634765625,
-0.0218658447265625,
-0.0087738037109375,
0.01169586181640625,
-0.0284423828125,
0.0285797119140625,
0.016021728515625,
-0.005214691162109375,
0.01947021484375,
0.01309967041015625,
0.0053253173828125,
-0.00292205810546875,
-0.0181884765625,
-0.00806427001953125,
-0.0023956298828125,
-0.011016845703125,
-0.0011548995971679688,
-0.01045989990234375,
0.01258087158203125,
0.041961669921875,
-0.02874755859375,
-0.0321044921875,
0.0004222393035888672,
-0.025726318359375,
0.0164794921875,
0.01085662841796875,
-0.00746917724609375,
-0.03436279296875,
-0.0001264810562133789,
0.0005402565002441406,
0.0091400146484375,
-0.0305023193359375,
-0.0032825469970703125,
0.0168914794921875,
-0.001148223876953125,
-0.00748443603515625,
-0.006988525390625,
-0.00225830078125,
0.033599853515625,
-0.0000013709068298339844,
-0.00007218122482299805,
0.0105743408203125,
0.0221405029296875,
0.00026679039001464844,
-0.005069732666015625,
-0.00511932373046875,
0.00787353515625,
-0.0009255409240722656,
-0.0283966064453125,
0.0096588134765625,
-0.001995086669921875,
0.0117645263671875,
-0.01033782958984375,
0.00902557373046875,
0.017242431640625,
-0.003482818603515625,
-0.0372314453125,
-0.0096893310546875,
-0.0008516311645507812,
-0.005046844482421875,
0.00081634521484375,
-0.002513885498046875,
0.00255584716796875,
-0.00786590576171875,
0.05096435546875,
-0.0030422210693359375,
-0.035369873046875,
-0.008026123046875,
0.02960205078125,
0.0108795166015625,
0.004627227783203125,
-0.0254364013671875,
0.036102294921875,
0.01557159423828125,
0.0276641845703125,
0.01238250732421875,
-0.019134521484375,
0.032562255859375,
0.027618408203125,
0.006771087646484375,
-0.004337310791015625,
0.0233306884765625,
-0.0104827880859375,
0.033355712890625,
0.001132965087890625,
-0.004207611083984375,
-0.0159149169921875,
0.0218658447265625,
0.010223388671875,
-0.00463104248046875,
-0.017974853515625,
-0.010589599609375,
0.0077972412109375,
-0.017059326171875,
0.02447509765625,
-0.016143798828125,
0.028472900390625,
0.0062408447265625,
-0.0125579833984375,
0.0169525146484375,
-0.017059326171875,
-0.0114593505859375,
-0.01030731201171875,
0.0221405029296875,
-0.020172119140625,
-0.0194244384765625,
0.00933074951171875,
-0.0204010009765625,
-0.0107421875,
0.018157958984375,
-0.0033359527587890625,
0.021820068359375,
0.01432037353515625,
0.028533935546875,
-0.006195068359375,
-0.00438690185546875,
-0.005336761474609375,
0.016265869140625,
-0.01364898681640625,
0.033233642578125,
-0.00447845458984375,
-0.00841522216796875,
0.06292724609375,
0.0044708251953125,
-0.004680633544921875,
-0.004741668701171875,
0.007755279541015625,
-0.007297515869140625,
0.0035915374755859375,
-0.0009603500366210938,
-0.0135345458984375,
0.0307159423828125,
-0.006649017333984375,
0.040679931640625,
-0.0085906982421875,
-0.004150390625,
0.022308349609375,
0.0207672119140625,
0.0178680419921875,
0.019805908203125,
-0.00853729248046875,
-0.01403045654296875,
-0.00457763671875,
0.0104827880859375,
-0.004791259765625,
-0.0227813720703125,
-0.0085601806640625,
-0.003925323486328125,
-0.018280029296875,
0.017578125,
0.0008363723754882812,
0.03662109375,
-0.0022735595703125,
0.027923583984375,
0.01198577880859375,
0.0185699462890625,
0.00806427001953125,
-0.015594482421875,
0.01142120361328125,
-0.0015764236450195312,
-0.0119171142578125,
-0.035125732421875,
0.01043701171875,
-0.00447845458984375,
0.023956298828125,
-0.006275177001953125,
0.0445556640625,
-0.03924560546875,
0.01100921630859375,
0.034271240234375,
-0.0150909423828125,
0.0155487060546875,
0.00920867919921875,
-0.01342010498046875,
-0.00859832763671875,
0.008758544921875,
0.00031256675720214844,
-0.007709503173828125,
-0.002101898193359375,
-0.00537872314453125,
-0.0023822784423828125,
-0.00017261505126953125,
-0.003917694091796875,
-0.00519561767578125,
-0.001922607421875,
-0.01043701171875,
-0.002536773681640625,
-0.0140380859375,
-0.0266876220703125,
0.008758544921875,
0.0000152587890625,
0.032958984375,
0.01325225830078125,
0.0122833251953125,
0.00385284423828125,
-0.0160369873046875,
-0.0287322998046875,
-0.02032470703125,
-0.032318115234375,
-0.0194091796875,
-0.0201873779296875,
-0.0087432861328125,
0.0054779052734375,
0.002796173095703125,
-0.014556884765625,
-0.00234222412109375,
-0.02392578125,
0.006633758544921875,
0.02001953125,
0.030670166015625,
0.007228851318359375,
0.041778564453125,
-0.006351470947265625,
-0.04962158203125,
-0.03131103515625,
0.007335662841796875,
-0.0223846435546875,
0.0158538818359375,
0.00018787384033203125,
-0.035369873046875,
0.028533935546875,
-0.0203399658203125,
-0.00838470458984375,
-0.01184844970703125,
0.0157012939453125,
-0.000019490718841552734,
-0.0033893585205078125,
0.0285186767578125,
-0.01239013671875,
0.03857421875,
0.00753021240234375,
0.01198577880859375,
0.0015211105346679688,
-0.00449371337890625,
-0.045867919921875,
0.0165252685546875,
0.038482666015625,
0.004436492919921875,
0.00751495361328125,
0.0106658935546875,
-0.036590576171875,
0.0259246826171875,
-0.0017461776733398438,
0.0138702392578125,
-0.01548004150390625,
-0.01509857177734375,
0.038665771484375,
0.0088348388671875,
0.00722503662109375,
0.046722412109375,
-0.03277587890625,
-0.01404571533203125,
0.0290374755859375,
-0.0224456787109375,
-0.031768798828125,
-0.0146942138671875,
-0.003505706787109375,
-0.0019502639770507812,
0.003452301025390625,
-0.02239990234375,
-0.02215576171875,
0.007320404052734375,
-0.00640106201171875,
-0.007724761962890625,
0.01477813720703125,
-0.037689208984375,
0.0284881591796875,
0.0004363059997558594,
0.0308074951171875,
0.0167083740234375,
-0.00000864267349243164,
0.005306243896484375,
0.025604248046875,
-0.0095367431640625,
0.0236663818359375,
-0.01001739501953125,
-0.00034546852111816406,
0.035308837890625,
0.017181396484375,
-0.01212310791015625,
0.0159454345703125,
-0.004543304443359375,
-0.0279693603515625,
0.01458740234375,
0.018798828125,
-0.000001430511474609375,
-0.03594970703125,
-0.02508544921875,
-0.01367950439453125,
-0.0183868408203125,
0.0016736984252929688,
-0.007221221923828125,
-0.019989013671875,
0.0026912689208984375,
-0.0005474090576171875,
0.0115509033203125,
0.025238037109375,
-0.005054473876953125,
0.006153106689453125,
-0.0196533203125,
-0.002620697021484375,
-0.0004878044128417969,
0.00917816162109375,
0.040130615234375,
-0.029876708984375,
-0.0000476837158203125,
-0.055206298828125,
-0.01126861572265625,
0.0020427703857421875,
0.0287017822265625,
0.007404327392578125,
-0.0269317626953125,
-0.021697998046875,
0.03271484375,
-0.046661376953125,
0.04168701171875,
0.004314422607421875,
0.032470703125,
0.0318603515625,
-0.0360107421875,
-0.019744873046875,
0.0191802978515625,
-0.0400390625,
0.002819061279296875,
-0.0153656005859375,
-0.0197601318359375,
-0.00013017654418945312,
-0.0011529922485351562,
-0.00856781005859375,
-0.002094268798828125,
0.0009183883666992188,
0.01080322265625,
0.0133056640625,
-0.008453369140625,
0.00408172607421875,
-0.01056671142578125,
0.0047149658203125,
-0.01019287109375,
-0.006175994873046875,
0.00867462158203125,
0.01084136962890625,
-0.0092315673828125,
-0.041046142578125,
-0.00634002685546875,
-0.01457977294921875,
0.027191162109375,
0.009033203125,
-0.007686614990234375,
0.0287017822265625,
0.0277099609375,
0.0159759521484375,
-0.006824493408203125,
0.054534912109375,
-0.00041937828063964844,
0.00885772705078125,
0.00803375244140625,
-0.0182952880859375,
0.01435089111328125,
0.0006966590881347656,
0.0178070068359375,
0.0087890625,
-0.005840301513671875,
0.0236968994140625,
0.0057220458984375,
-0.0274505615234375,
-0.0012969970703125,
-0.01032257080078125,
-0.0296478271484375,
0.006755828857421875,
-0.020355224609375,
0.0164947509765625,
-0.02191162109375,
0.009796142578125,
0.0308685302734375,
0.03228759765625,
-0.0211029052734375,
0.020050048828125,
0.004482269287109375,
0.01678466796875,
-0.0017299652099609375,
0.0265045166015625,
0.0242462158203125,
0.045074462890625,
-0.018218994140625,
-0.00264739990234375,
0.039703369140625,
-0.0293121337890625,
-0.00521087646484375,
0.0290069580078125,
-0.0513916015625,
0.003204345703125,
-0.01708984375,
-0.01763916015625,
0.0130615234375,
0.015960693359375,
-0.016021728515625,
-0.020660400390625,
0.017547607421875,
0.0144195556640625,
-0.043609619140625,
-0.042388916015625,
-0.000621795654296875,
0.0308685302734375,
0.01366424560546875,
-0.005603790283203125,
-0.00347137451171875,
0.00365447998046875,
-0.003864288330078125,
0.018402099609375,
-0.01041412353515625,
0.0247955322265625,
0.00211334228515625,
-0.004650115966796875,
-0.04217529296875,
0.0316162109375,
0.0278472900390625,
-0.026336669921875,
0.0307769775390625,
-0.02008056640625,
0.0308990478515625,
-0.0036067962646484375,
0.005222320556640625,
0.0286712646484375,
0.003467559814453125,
0.0078277587890625,
-0.028594970703125,
0.022705078125,
0.0198974609375,
-0.00502777099609375,
0.032501220703125,
-0.00921630859375,
-0.01080322265625,
0.00205230712890625,
0.001132965087890625,
0.0008969306945800781,
-0.01238250732421875,
-0.004451751708984375,
0.0142974853515625,
-0.0143585205078125,
-0.0294036865234375,
-0.0293426513671875,
0.0235443115234375,
-0.0205841064453125,
-0.0174713134765625,
-0.01751708984375,
0.0008401870727539062,
-0.0181884765625,
0.018951416015625,
0.02105712890625,
-0.0270538330078125,
0.01219940185546875,
0.0030727386474609375,
-0.008026123046875,
0.004947662353515625,
-0.018951416015625,
-0.0206298828125,
0.035308837890625,
-0.03424072265625,
0.00971221923828125,
-0.015350341796875,
0.00815582275390625,
0.01044464111328125,
0.00594329833984375,
0.0150146484375,
-0.0189361572265625,
0.0243682861328125,
-0.005695343017578125,
0.004451751708984375,
-0.01739501953125,
0.0167694091796875,
-0.014373779296875,
0.035858154296875,
-0.01171112060546875,
0.0258331298828125,
-0.004467010498046875,
-0.00592803955078125,
-0.037109375,
0.0012874603271484375,
0.0211944580078125,
-0.0294189453125,
-0.0085601806640625,
-0.0018186569213867188,
0.0164642333984375,
0.01483917236328125,
-0.0258636474609375,
-0.00550079345703125,
0.003452301025390625,
-0.023712158203125,
0.007251739501953125,
-0.02386474609375,
-0.01027679443359375,
0.0050811767578125,
-0.039306640625,
-0.01204681396484375,
0.01088714599609375,
-0.0083160400390625,
-0.022216796875,
0.0031719207763671875,
-0.00986480712890625,
-0.020751953125,
0.00865936279296875,
-0.01082611083984375,
-0.01824951171875,
-0.0322265625,
-0.0157928466796875,
0.031982421875,
0.03570556640625,
-0.026947021484375,
0.0011911392211914062,
0.0066680908203125,
0.03369140625,
-0.01491546630859375,
-0.00691986083984375,
0.0057525634765625,
-0.0018138885498046875,
0.003940582275390625,
-0.005565643310546875,
0.0161285400390625,
0.02325439453125,
-0.00540924072265625,
-0.0247039794921875,
0.0061798095703125,
0.0018310546875,
-0.0227508544921875,
0.01519012451171875,
-0.007049560546875,
0.02008056640625,
-0.01378631591796875,
-0.004150390625,
0.029022216796875,
-0.004802703857421875,
0.0234832763671875,
0.00792694091796875,
0.05816650390625,
-0.0007138252258300781,
0.0183258056640625,
0.018280029296875,
-0.04925537109375,
0.0116729736328125,
0.019073486328125,
0.0007867813110351562,
-0.052215576171875,
-0.0272064208984375,
0.00455474853515625,
0.0169219970703125,
-0.01458740234375,
0.0280914306640625,
-0.00554656982421875,
-0.02740478515625,
-0.01317596435546875,
-0.0193328857421875,
-0.007480621337890625,
0.0106048583984375,
0.00560760498046875,
-0.002880096435546875,
-0.01494598388671875,
0.002643585205078125,
-0.004924774169921875,
-0.00992584228515625,
-0.011077880859375,
-0.004833221435546875,
0.0010538101196289062,
-0.0031414031982421875,
-0.01291656494140625,
0.0258331298828125,
0.018463134765625,
-0.0017175674438476562,
0.01435089111328125,
0.01110076904296875,
-0.00637054443359375,
0.00890350341796875,
-0.006534576416015625,
-0.01111602783203125,
0.00057220458984375,
-0.0361328125,
-0.031494140625,
0.0248565673828125,
0.00621795654296875,
0.0280914306640625,
-0.005512237548828125,
-0.003063201904296875,
-0.008453369140625,
0.00865936279296875,
0.0082550048828125,
-0.01503753662109375,
0.004512786865234375,
-0.03265380859375,
0.02484130859375,
-0.037689208984375,
-0.0301361083984375,
-0.0085296630859375,
-0.0020599365234375,
-0.0021209716796875,
0.001983642578125,
0.004489898681640625,
0.006744384765625,
-0.006988525390625,
0.0025634765625,
-0.01251983642578125,
-0.007129669189453125,
0.0068817138671875,
-0.008636474609375,
0.038299560546875,
0.02618408203125,
0.0310821533203125,
0.033416748046875,
-0.032684326171875,
0.0167083740234375,
0.025390625,
0.01389312744140625,
0.00789642333984375,
0.006565093994140625,
-0.007198333740234375,
0.01232147216796875,
0.00417327880859375,
0.00897216796875,
-0.03411865234375,
0.01483917236328125,
0.00814056396484375,
0.0002048015594482422,
-0.01439666748046875,
-0.043365478515625,
0.006587982177734375,
0.00823211669921875,
0.00879669189453125,
0.0261383056640625,
0.01617431640625,
0.03533935546875,
-0.0124053955078125,
-0.018951416015625,
-0.005809783935546875,
-0.006500244140625,
-0.0133514404296875,
-0.01177978515625,
0.0174713134765625,
-0.00336456298828125,
0.01007843017578125,
-0.0090179443359375,
-0.0106201171875,
0.023773193359375,
-0.01160430908203125,
0.005237579345703125,
0.017791748046875,
-0.0089111328125,
0.01256561279296875,
-0.00485992431640625,
-0.0289154052734375,
0.005992889404296875,
-0.0007171630859375,
-0.012054443359375,
0.000598907470703125,
-0.00785064697265625,
-0.008575439453125,
-0.01520538330078125,
0.00433349609375,
0.0004420280456542969,
-0.0294952392578125,
-0.0007171630859375,
0.005382537841796875,
0.007228851318359375,
0.046112060546875,
0.0221405029296875,
-0.00516510009765625,
0.00858306884765625,
0.0246124267578125,
0.010986328125,
0.0106048583984375,
-0.0028247833251953125,
-0.00321197509765625,
-0.0055694580078125,
0.0247955322265625,
0.0247039794921875,
-0.0066680908203125,
0.0105133056640625,
0.0198516845703125,
0.0251922607421875,
-0.0211181640625,
-0.0018110275268554688,
0.019256591796875,
0.0418701171875,
-0.0273590087890625,
0.0041961669921875,
-0.0186614990234375,
0.0110015869140625,
-0.06414794921875,
-0.00505828857421875,
-0.005390167236328125,
0.0264129638671875,
-0.0021419525146484375,
-0.0034942626953125,
0.0214080810546875,
-0.0289764404296875,
0.011810302734375,
-0.0185089111328125,
0.032928466796875,
-0.01439666748046875,
-0.01253509521484375,
-0.00733184814453125,
-0.001544952392578125,
0.0180816650390625,
0.0012998580932617188,
0.038421630859375,
-0.00807952880859375,
-0.01259613037109375,
0.024505615234375,
-0.0009870529174804688,
0.01503753662109375,
-0.024505615234375,
-0.03253173828125,
-0.017303466796875,
0.0253143310546875,
-0.0167083740234375,
0.003612518310546875,
0.024566650390625,
-0.021728515625,
-0.023681640625,
0.0064239501953125,
-0.0081634521484375,
0.00418853759765625,
0.01395416259765625,
-0.03759765625,
0.01885986328125,
0.04132080078125,
-0.01983642578125,
0.0032672882080078125,
-0.036041259765625,
0.036285400390625,
0.006549835205078125,
-0.0234222412109375,
0.02667236328125,
-0.049346923828125,
-0.031951904296875,
0.0134429931640625,
0.019195556640625,
-0.0265045166015625,
-0.03070068359375,
0.0037078857421875,
-0.01849365234375,
0.01085662841796875,
-0.004970550537109375,
0.0059967041015625,
-0.0299072265625,
0.021331787109375,
0.017059326171875,
0.0036220550537109375,
-0.0196533203125,
-0.009521484375,
-0.027008056640625,
-0.020599365234375,
-0.016845703125,
0.0259246826171875,
-0.03997802734375,
0.008331298828125,
0.0150299072265625,
-0.0235748291015625,
-0.015960693359375,
0.00550079345703125,
-0.00010943412780761719,
-0.018157958984375,
-0.01428985595703125,
0.025115966796875,
-0.00650787353515625,
0.0220489501953125,
-0.0194244384765625,
-0.0011348724365234375,
0.032958984375,
-0.0213470458984375,
-0.0199127197265625,
0.004241943359375,
-0.005035400390625,
0.0177154541015625,
-0.0196990966796875,
-0.0045166015625,
0.0100250244140625,
0.018280029296875,
-0.004955291748046875,
-0.0119781494140625,
-0.0027217864990234375,
-0.007205963134765625,
-0.00244903564453125,
-0.00783538818359375,
-0.005771636962890625,
-0.01953125,
-0.0048370361328125,
0.005504608154296875,
0.023193359375,
0.0020923614501953125,
0.00397491455078125,
0.00608062744140625,
0.0179595947265625,
-0.026214599609375,
-0.032440185546875,
0.018218994140625,
0.0303497314453125
] |
ours_544
|
Let \( s = 1 + 2 + \cdots + 2010 + 2011 \). If the sum \( S \) told is larger than \( s+1 \), then the integers could be either \( 1, 2, \ldots, 2009, 2010, 2011+S-s \), or \( 1, 2, \ldots, 2009, 2011, 2010+S-s \). Clearly, the sum is at least \( s \), so the only possibilities are \( s \) and \( s+1 \). Therefore, the number of possible sums is \(\boxed{2}\).
|
2
|
{
"competition": "us_comps",
"dataset": "Ours",
"posts": null,
"source": "OMOSoln2.md"
}
|
Al told Bob that he was thinking of 2011 distinct positive integers. He also told Bob the sum of those integers. From this information, Bob was able to determine all 2011 integers. How many possible sums could Al have told Bob?
|
[
"/Mathematics/DiscreteMathematics/Combinatorics/Enumeration",
"/Mathematics/DiscreteMathematics/Combinatorics/GeneralCombinatorics",
"/Mathematics/DiscreteMathematics/GeneralDiscreteMathematics/DiscreteMath",
"/Mathematics/DiscreteMathematics/GeneralDiscreteMathematics/DiscreteMathematics",
"/Mathematics/RecreationalMathematics/NumberGuessing",
"/Mathematics/RecreationalMathematics/Puzzles/Puzzle"
] |
Recognize that the smallest possible sum is the sum of the first 2011 integers, and any larger sum creates a swap ambiguity between the two largest numbers, so only sums s and s+1 yield a unique set.
|
[
-0.00011873245239257812,
-0.004367828369140625,
0.034423828125,
0.038330078125,
-0.00077056884765625,
0.01268768310546875,
0.0301055908203125,
-0.0254669189453125,
0.00557708740234375,
-0.0126953125,
0.00119781494140625,
-0.06689453125,
-0.00254058837890625,
-0.0160369873046875,
-0.0347900390625,
-0.0119476318359375,
0.0457763671875,
0.024017333984375,
0.0086517333984375,
-0.006336212158203125,
-0.01026153564453125,
0.01214599609375,
-0.01910400390625,
0.0404052734375,
-0.0102996826171875,
-0.05010986328125,
-0.0260162353515625,
-0.0016918182373046875,
0.054840087890625,
0.0219268798828125,
-0.0196533203125,
-0.027618408203125,
0.0299224853515625,
-0.0452880859375,
0.0011272430419921875,
0.0128173828125,
0.006549835205078125,
-0.0128631591796875,
-0.0048828125,
-0.0253753662109375,
-0.006359100341796875,
-0.00759124755859375,
0.0068511962890625,
0.00018644332885742188,
-0.0303955078125,
-0.005462646484375,
-0.00342559814453125,
0.03228759765625,
-0.003856658935546875,
-0.00426483154296875,
-0.0032634735107421875,
0.01213836669921875,
-0.0159454345703125,
-0.01490020751953125,
-0.03741455078125,
-0.05401611328125,
0.00970458984375,
-0.00321197509765625,
-0.0269622802734375,
0.00272369384765625,
0.001194000244140625,
0.006610870361328125,
0.01311492919921875,
-0.00316619873046875,
0.0012531280517578125,
-0.0160369873046875,
0.006755828857421875,
-0.03662109375,
0.01041412353515625,
-0.00696563720703125,
0.0171661376953125,
-0.004657745361328125,
-0.01519012451171875,
0.041290283203125,
0.033721923828125,
-0.0190277099609375,
-0.00885772705078125,
0.00836181640625,
0.0243988037109375,
0.005950927734375,
0.0262908935546875,
0.0206451416015625,
0.004222869873046875,
0.035430908203125,
0.013214111328125,
0.0079803466796875,
-0.00099945068359375,
-0.0030078887939453125,
0.01044464111328125,
-0.0273895263671875,
0.00811767578125,
0.03302001953125,
0.00875091552734375,
0.005039215087890625,
-0.0057830810546875,
0.00777435302734375,
0.01513671875,
-0.021087646484375,
-0.018585205078125,
0.01425933837890625,
-0.016998291015625,
0.007183074951171875,
0.023345947265625,
-0.0070953369140625,
-0.049957275390625,
-0.01169586181640625,
-0.0250396728515625,
0.00812530517578125,
-0.0181427001953125,
-0.005283355712890625,
0.016754150390625,
0.01450347900390625,
0.0011911392211914062,
0.005275726318359375,
-0.0255889892578125,
0.0210418701171875,
-0.0030765533447265625,
0.0004851818084716797,
-0.018218994140625,
-0.01349639892578125,
0.0044403076171875,
0.024383544921875,
-0.00156402587890625,
0.006839752197265625,
0.0022487640380859375,
-0.0206451416015625,
-0.00351715087890625,
-0.0087738037109375,
0.010009765625,
-0.007904052734375,
0.0298614501953125,
-0.003814697265625,
-0.0450439453125,
-0.0207061767578125,
-0.0697021484375,
0.0042266845703125,
0.005664825439453125,
-0.0121307373046875,
0.006099700927734375,
-0.01129150390625,
0.01352691650390625,
-0.01207733154296875,
0.0029506683349609375,
0.020538330078125,
0.0019435882568359375,
0.0155487060546875,
0.0052032470703125,
-0.067626953125,
0.01812744140625,
0.0013990402221679688,
0.015777587890625,
-0.0004267692565917969,
0.00044846534729003906,
0.01471710205078125,
-0.004566192626953125,
0.033477783203125,
-0.0084991455078125,
0.0036563873291015625,
0.0008258819580078125,
0.00275421142578125,
0.0005178451538085938,
-0.0056304931640625,
-0.046356201171875,
0.04217529296875,
-0.00823211669921875,
0.0055084228515625,
0.0097503662109375,
-0.0169830322265625,
-0.0142974853515625,
-0.001743316650390625,
-0.00855255126953125,
0.01212310791015625,
0.00493621826171875,
-0.0198974609375,
-0.022918701171875,
0.0144805908203125,
-0.01406097412109375,
0.0158538818359375,
0.002445220947265625,
0.0275421142578125,
-0.01151275634765625,
-0.05731201171875,
-0.0026798248291015625,
-0.00763702392578125,
0.028411865234375,
0.00020241737365722656,
-0.004245758056640625,
-0.0012826919555664062,
0.0172882080078125,
0.013275146484375,
0.0093994140625,
-0.0004508495330810547,
-0.0105438232421875,
-0.01044464111328125,
-0.00727081298828125,
-0.0226593017578125,
-0.014404296875,
0.004688262939453125,
0.0214080810546875,
0.01430511474609375,
0.0057525634765625,
0.0027713775634765625,
0.0322265625,
-0.0015048980712890625,
-0.0027332305908203125,
-0.0203857421875,
0.003047943115234375,
-0.0021190643310546875,
0.004482269287109375,
0.007122039794921875,
0.0002925395965576172,
-0.0168304443359375,
-0.006999969482421875,
-0.00511932373046875,
-0.00897979736328125,
-0.009521484375,
-0.0188140869140625,
-0.003543853759765625,
-0.0008764266967773438,
-0.05181884765625,
0.0063323974609375,
0.0070953369140625,
-0.0059814453125,
-0.0261383056640625,
-0.031219482421875,
-0.0041351318359375,
0.0164947509765625,
-0.00550079345703125,
-0.02520751953125,
0.00714874267578125,
0.01702880859375,
-0.004688262939453125,
-0.00641632080078125,
-0.0078582763671875,
-0.0009016990661621094,
0.027313232421875,
-0.025634765625,
-0.00730133056640625,
0.0106201171875,
-0.022186279296875,
0.0229034423828125,
-0.000457763671875,
0.0208282470703125,
-0.00508880615234375,
-0.01181793212890625,
-0.0059661865234375,
0.004581451416015625,
-0.0183868408203125,
0.004169464111328125,
-0.0306243896484375,
-0.00604248046875,
0.0126495361328125,
-0.0253753662109375,
-0.005664825439453125,
0.0086669921875,
-0.006366729736328125,
0.005229949951171875,
-0.0246429443359375,
-0.000186920166015625,
-0.0173797607421875,
0.005619049072265625,
-0.0382080078125,
-0.01413726806640625,
0.0007605552673339844,
-0.007965087890625,
0.038055419921875,
0.01016998291015625,
-0.01043701171875,
0.017303466796875,
-0.0012731552124023438,
0.00201416015625,
-0.0035953521728515625,
-0.0175933837890625,
0.004810333251953125,
0.0059814453125,
0.0019445419311523438,
-0.01395416259765625,
-0.0063934326171875,
-0.01227569580078125,
0.008514404296875,
-0.012969970703125,
0.002696990966796875,
0.004302978515625,
0.00804901123046875,
0.0032520294189453125,
-0.0035114288330078125,
-0.004802703857421875,
-0.0038814544677734375,
-0.01995849609375,
-0.00102996826171875,
0.00923919677734375,
-0.0176239013671875,
-0.01215362548828125,
-0.013427734375,
-0.0032901763916015625,
-0.05267333984375,
0.01438140869140625,
0.0031604766845703125,
0.018157958984375,
-0.0038814544677734375,
0.027923583984375,
-0.0191497802734375,
0.006591796875,
0.032470703125,
-0.00803375244140625,
0.0195465087890625,
0.0070953369140625,
0.0106658935546875,
-0.0179443359375,
-0.03265380859375,
-0.01126861572265625,
0.01047515869140625,
-0.0132904052734375,
-0.0008363723754882812,
0.0209808349609375,
-0.048492431640625,
-0.00666046142578125,
0.01247406005859375,
-0.000015079975128173828,
-0.0161895751953125,
0.0230865478515625,
-0.00888824462890625,
0.0311126708984375,
0.01513671875,
0.0139312744140625,
0.0092010498046875,
0.0235748291015625,
0.0260772705078125,
-0.023895263671875,
0.043304443359375,
-0.06170654296875,
0.036865234375,
-0.002979278564453125,
-0.0254364013671875,
-0.01047515869140625,
0.0138397216796875,
-0.01561737060546875,
0.03741455078125,
-0.0077972412109375,
0.002685546875,
0.0093536376953125,
-0.0087890625,
-0.01031494140625,
0.060699462890625,
-0.01482391357421875,
0.0030002593994140625,
-0.0272216796875,
-0.01715087890625,
-0.025390625,
-0.038848876953125,
-0.0000902414321899414,
0.00794219970703125,
0.02581787109375,
-0.012054443359375,
-0.047637939453125,
0.0262603759765625,
-0.0189056396484375,
-0.0030803680419921875,
0.004528045654296875,
0.005573272705078125,
0.01239776611328125,
-0.015167236328125,
-0.00527191162109375,
0.02301025390625,
-0.00732421875,
-0.033538818359375,
-0.019256591796875,
0.006206512451171875,
-0.006130218505859375,
-0.0243682861328125,
0.00246429443359375,
-0.032135009765625,
0.0114288330078125,
-0.04229736328125,
-0.0400390625,
0.00753021240234375,
-0.0023441314697265625,
-0.003326416015625,
-0.012542724609375,
0.0201568603515625,
0.004238128662109375,
0.021697998046875,
-0.00801849365234375,
0.0177764892578125,
-0.0087432861328125,
-0.0020580291748046875,
0.0047607421875,
-0.0254058837890625,
-0.0142669677734375,
0.01438140869140625,
-0.0150299072265625,
0.0180511474609375,
0.00627899169921875,
-0.00936126708984375,
0.01175689697265625,
-0.041748046875,
0.003215789794921875,
0.0115966796875,
0.038604736328125,
-0.02545166015625,
-0.0074005126953125,
-0.0290679931640625,
-0.0188446044921875,
0.01424407958984375,
-0.0205078125,
0.0097503662109375,
0.0010843276977539062,
-0.00850677490234375,
0.007904052734375,
-0.0108795166015625,
0.048126220703125,
0.0309906005859375,
-0.00506591796875,
-0.006923675537109375,
0.03179931640625,
-0.0081634521484375,
0.0372314453125,
-0.022216796875,
-0.04278564453125,
-0.017333984375,
0.042266845703125,
-0.0219268798828125,
0.006649017333984375,
0.0038909912109375,
0.0457763671875,
0.004268646240234375,
-0.0172119140625,
0.041534423828125,
0.036224365234375,
0.0007038116455078125,
0.029693603515625,
-0.0257568359375,
-0.00795745849609375,
0.003597259521484375,
-0.0169830322265625,
0.031707763671875,
0.01328277587890625,
0.01007843017578125,
-0.0004858970642089844,
-0.0184173583984375,
0.0231781005859375,
0.0017375946044921875,
-0.002147674560546875,
0.00395965576171875,
-0.007740020751953125,
0.00429534912109375,
-0.0053863525390625,
0.01108551025390625,
-0.0297393798828125,
0.0173187255859375,
-0.02435302734375,
-0.0017223358154296875,
-0.0306549072265625,
0.00611114501953125,
-0.0643310546875,
0.0191497802734375,
0.028900146484375,
-0.0248260498046875,
-0.01459503173828125,
-0.05914306640625,
-0.0025234222412109375,
-0.0156707763671875,
-0.0011768341064453125,
0.0030364990234375,
-0.02557373046875,
-0.017333984375,
-0.0182037353515625,
0.0085906982421875,
0.0362548828125,
0.0037975311279296875,
0.004093170166015625,
-0.0195770263671875,
0.0098876953125,
-0.037200927734375,
-0.0316162109375,
0.036468505859375,
0.000637054443359375,
0.0269012451171875,
-0.01454925537109375,
-0.0257415771484375,
-0.0252532958984375,
0.0216522216796875,
-0.021331787109375,
0.06451416015625,
0.00992584228515625,
0.03143310546875,
0.0421142578125,
0.01500701904296875,
-0.010009765625,
-0.0129852294921875,
0.03155517578125,
0.0230560302734375,
-0.0224761962890625,
-0.031890869140625,
-0.01128387451171875,
-0.049896240234375,
0.006122589111328125,
-0.0253753662109375,
0.0064544677734375,
0.00023937225341796875,
0.01006317138671875,
-0.04022216796875,
0.0299224853515625,
0.0185089111328125,
0.006256103515625,
0.0004367828369140625,
0.01390838623046875,
-0.034637451171875,
0.0134735107421875,
0.0075225830078125,
0.007251739501953125,
0.0106048583984375,
0.007259368896484375,
-0.040130615234375,
-0.0136566162109375,
0.009613037109375,
0.016998291015625,
-0.0384521484375,
-0.020355224609375,
0.01276397705078125,
-0.01482391357421875,
0.019317626953125,
0.033172607421875,
0.0025272369384765625,
-0.002948760986328125,
0.0229644775390625,
-0.01169586181640625,
-0.0235137939453125,
-0.0013895034790039062,
0.01345062255859375,
0.0044097900390625,
-0.037078857421875,
0.0214385986328125,
0.037872314453125,
-0.031280517578125,
0.0007801055908203125,
0.01183319091796875,
-0.00537109375,
-0.003963470458984375,
0.0116729736328125,
-0.0051727294921875,
0.0007829666137695312,
-0.006916046142578125,
0.01073455810546875,
-0.0017232894897460938,
-0.05291748046875,
0.007534027099609375,
-0.0016641616821289062,
-0.01416015625,
0.013946533203125,
-0.0012111663818359375,
0.010833740234375,
0.022552490234375,
-0.002590179443359375,
-0.002986907958984375,
0.0182037353515625,
0.02496337890625,
0.033538818359375,
0.0018825531005859375,
-0.004123687744140625,
-0.00640869140625,
0.006031036376953125,
0.0139617919921875,
0.006839752197265625,
0.006885528564453125,
-0.0043182373046875,
-0.004180908203125,
0.01482391357421875,
-0.0217742919921875,
-0.036590576171875,
0.0103912353515625,
0.00228118896484375,
0.006633758544921875,
-0.01129150390625,
-0.01343536376953125,
-0.035125732421875,
-0.03497314453125,
0.01033782958984375,
-0.006954193115234375,
-0.01456451416015625,
0.005130767822265625,
0.021575927734375,
-0.034210205078125,
0.0214691162109375,
0.0154876708984375,
-0.01611328125,
-0.0022983551025390625,
0.0082244873046875,
0.0114593505859375,
-0.0013856887817382812,
-0.043243408203125,
-0.00006371736526489258,
0.0192718505859375,
-0.0004127025604248047,
-0.0221405029296875,
-0.035980224609375,
0.0229034423828125,
-0.034271240234375,
0.0196685791015625,
-0.00472259521484375,
0.030426025390625,
0.0062255859375,
-0.0105133056640625,
0.0259246826171875,
0.00537872314453125,
-0.01371002197265625,
0.0021648406982421875,
0.02630615234375,
-0.01015472412109375,
0.0211029052734375,
0.015289306640625,
-0.01129150390625,
-0.0063934326171875,
0.018585205078125,
0.0227508544921875,
0.006221771240234375,
-0.0390625,
-0.00252532958984375,
0.0180511474609375,
0.002712249755859375,
-0.01528167724609375,
-0.005828857421875,
-0.0083465576171875,
-0.0021495819091796875,
-0.0154876708984375,
-0.048370361328125,
-0.0017490386962890625,
-0.0269317626953125,
0.00885772705078125,
-0.014678955078125,
-0.0040283203125,
-0.03564453125,
0.021331787109375,
0.0011854171752929688,
-0.002262115478515625,
-0.0181884765625,
-0.043792724609375,
0.00620269775390625,
0.00044608116149902344,
0.002704620361328125,
0.01265716552734375,
0.01226043701171875,
-0.0022182464599609375,
-0.056854248046875,
0.00838470458984375,
0.03594970703125,
-0.0060882568359375,
0.0243682861328125,
0.00911712646484375,
0.0291748046875,
0.006214141845703125,
0.01190185546875,
-0.004306793212890625,
0.005878448486328125,
0.0204315185546875,
0.03448486328125,
0.020294189453125,
0.0008158683776855469,
0.04736328125,
-0.006622314453125,
0.0203094482421875,
-0.019287109375,
0.03912353515625,
0.01485443115234375,
-0.004241943359375,
-0.015655517578125,
0.00604248046875,
-0.0135498046875,
0.005702972412109375,
-0.02215576171875,
-0.00659942626953125,
-0.01499176025390625,
0.00308990478515625,
0.01548004150390625,
0.030792236328125,
-0.0079193115234375,
-0.004177093505859375,
-0.016937255859375,
0.029449462890625,
0.02117919921875,
-0.00772857666015625,
0.007396697998046875,
0.0177459716796875,
-0.0016946792602539062,
0.0164031982421875,
-0.00620269775390625,
-0.0133514404296875,
0.009521484375,
0.0281524658203125,
0.005329132080078125,
-0.0020904541015625,
-0.021484375,
-0.007534027099609375,
0.018707275390625,
0.008758544921875,
-0.049774169921875,
0.036376953125,
-0.0165252685546875,
-0.0027141571044921875,
-0.0086822509765625,
0.0323486328125,
-0.01129150390625,
0.0271453857421875,
0.019073486328125,
0.004669189453125,
0.00043511390686035156,
-0.0178680419921875,
0.02496337890625,
-0.026092529296875,
0.01393890380859375,
-0.0235748291015625,
-0.0204010009765625,
-0.034271240234375,
0.00646209716796875,
-0.0196533203125,
0.0190582275390625,
-0.0033702850341796875,
-0.012420654296875,
-0.00267791748046875,
-0.00012695789337158203,
-0.0106048583984375,
-0.0014371871948242188,
-0.02862548828125,
-0.0186767578125,
0.0059051513671875,
-0.00029468536376953125,
-0.031036376953125,
-0.0261077880859375,
-0.00982666015625,
0.00623321533203125,
-0.007411956787109375,
-0.01446533203125,
-0.00036215782165527344,
0.0009570121765136719,
-0.0249786376953125,
-0.0092620849609375,
0.0255279541015625,
-0.0472412109375,
0.0250091552734375,
-0.03082275390625,
0.0241241455078125,
-0.01154327392578125,
0.0139923095703125,
-0.00010591745376586914,
0.00200653076171875,
-0.015655517578125,
0.0016574859619140625,
-0.0275726318359375,
-0.0129241943359375,
-0.03839111328125,
0.0159149169921875,
-0.0029315948486328125,
0.0276336669921875,
-0.0305633544921875,
-0.051727294921875,
-0.0083465576171875,
0.028533935546875,
0.0013866424560546875,
-0.036346435546875,
-0.00601959228515625,
-0.027740478515625,
0.0220794677734375,
-0.0284271240234375,
-0.018310546875,
-0.007701873779296875,
-0.01169586181640625,
-0.03814697265625,
-0.017303466796875,
-0.031585693359375,
0.0310211181640625,
-0.04736328125,
0.025482177734375,
0.01422882080078125,
0.0256195068359375,
0.0185089111328125,
0.004451751708984375,
-0.0211334228515625,
-0.0005431175231933594,
0.01457977294921875,
-0.00859832763671875,
0.0063629150390625,
0.00588226318359375,
0.02838134765625,
0.01163482666015625,
-0.033172607421875,
-0.0010356903076171875,
0.0006279945373535156,
-0.002590179443359375,
0.0276947021484375,
-0.0023479461669921875,
0.0016641616821289062,
0.0043792724609375,
0.00348663330078125,
-0.0022716522216796875,
-0.0128173828125,
-0.01055145263671875,
0.01042938232421875,
-0.0218353271484375,
0.013153076171875,
-0.004833221435546875,
0.0224456787109375,
-0.03619384765625,
-0.0224456787109375,
0.04791259765625,
0.042633056640625,
-0.028350830078125,
-0.0009641647338867188,
-0.01178741455078125,
-0.005321502685546875,
0.035980224609375,
0.00466156005859375,
-0.00594329833984375,
-0.0057525634765625,
-0.014556884765625,
-0.004436492919921875,
-0.0362548828125,
-0.006862640380859375,
0.004077911376953125,
0.0014238357543945312,
0.019317626953125,
0.0004949569702148438,
0.0007996559143066406,
0.0006098747253417969,
-0.00550079345703125,
0.00875091552734375,
-0.0115509033203125,
-0.007038116455078125,
-0.00928497314453125,
0.0089111328125,
0.01100921630859375,
-0.0290985107421875,
-0.00913238525390625,
-0.02008056640625,
0.0238800048828125,
-0.007244110107421875,
0.0113677978515625,
-0.0141143798828125,
-0.0027313232421875,
-0.036224365234375,
-0.02679443359375,
0.045867919921875,
0.0240020751953125,
0.0186004638671875,
-0.0311126708984375,
0.0007677078247070312,
-0.033233642578125,
-0.01641845703125,
-0.00626373291015625,
-0.0130462646484375,
0.0000852346420288086,
0.004421234130859375,
0.047698974609375,
-0.01708984375,
0.02862548828125,
-0.02459716796875,
0.0224456787109375,
0.00954437255859375,
-0.01418304443359375,
0.00424957275390625,
0.003208160400390625,
-0.01242828369140625,
-0.042449951171875,
-0.01471710205078125,
0.00882720947265625,
0.012359619140625,
-0.0152587890625,
0.0038433074951171875,
-0.002315521240234375,
0.01491546630859375,
-0.0028285980224609375,
0.020416259765625,
0.01020050048828125,
0.0100555419921875,
-0.008270263671875,
0.03582763671875,
0.0105133056640625,
-0.00882720947265625,
0.006072998046875,
0.0247955322265625,
-0.011505126953125,
0.02667236328125,
-0.05133056640625,
0.006114959716796875,
0.01462554931640625,
-0.021514892578125,
0.0008478164672851562,
0.05010986328125,
0.01361846923828125,
-0.0091094970703125,
-0.023895263671875,
0.00665283203125,
-0.006961822509765625,
0.0158843994140625,
0.0173797607421875,
-0.0148773193359375,
-0.0021991729736328125,
0.01544189453125,
-0.01096343994140625,
-0.0107421875,
-0.049102783203125,
-0.00853729248046875,
0.003017425537109375,
0.0120697021484375,
0.0209197998046875,
-0.04248046875,
0.000003159046173095703,
-0.00119781494140625,
-0.0012350082397460938,
-0.015533447265625,
0.0268707275390625,
-0.0094451904296875,
0.002796173095703125,
0.0277099609375,
0.029754638671875,
-0.051239013671875,
0.0232696533203125,
0.0010471343994140625,
0.02655029296875,
0.007358551025390625,
0.0025196075439453125,
0.00170135498046875,
-0.011627197265625,
-0.0290679931640625,
-0.0154266357421875,
0.0299835205078125,
-0.03375244140625,
-0.00800323486328125,
-0.00815582275390625,
-0.00498199462890625,
-0.0157318115234375,
-0.0103759765625,
0.035003662109375,
-0.04693603515625,
-0.0034236907958984375,
-0.0017452239990234375,
0.02056884765625,
0.0030364990234375,
0.01412200927734375,
0.0178070068359375,
0.007122039794921875,
-0.020538330078125,
-0.0176849365234375,
-0.02142333984375,
0.01032257080078125,
0.00702667236328125,
-0.0014019012451171875,
0.0070953369140625,
0.039825439453125,
-0.0210113525390625,
0.0010471343994140625,
-0.0086822509765625,
0.02105712890625,
0.0237274169921875,
0.004726409912109375,
-0.002712249755859375,
-0.0049896240234375,
0.01280975341796875,
-0.0014066696166992188,
-0.02215576171875,
-0.040191650390625,
0.025482177734375,
-0.00891876220703125,
-0.05291748046875,
0.01517486572265625,
-0.001674652099609375,
0.0273284912109375,
-0.00226593017578125,
0.0262908935546875,
-0.00217437744140625,
0.0016937255859375,
-0.04937744140625,
0.0164947509765625,
-0.00977325439453125,
-0.040740966796875,
0.0021572113037109375,
-0.0014410018920898438,
0.0001010894775390625,
0.01348876953125,
0.0253143310546875,
-0.01482391357421875,
-0.030548095703125,
0.00826263427734375,
0.0093536376953125,
-0.01605224609375,
-0.0159759521484375,
0.0220947265625,
0.018768310546875,
-0.0150909423828125,
0.008453369140625,
-0.02764892578125,
-0.0161285400390625,
0.0177764892578125,
0.006500244140625,
0.0172119140625,
-0.0076446533203125,
0.00753021240234375,
-0.0323486328125,
0.003429412841796875,
0.0257568359375,
0.031707763671875,
-0.0194244384765625,
0.00946807861328125,
-0.0167999267578125,
-0.031982421875,
0.024169921875,
0.006549835205078125,
0.0173492431640625,
-0.001163482666015625,
0.01629638671875,
0.0212249755859375,
-0.0010786056518554688,
0.008392333984375,
-0.029266357421875,
0.0006051063537597656,
-0.047698974609375,
0.0229644775390625,
0.0007958412170410156,
-0.005374908447265625,
-0.05108642578125,
0.0184173583984375,
0.01849365234375,
0.00975799560546875,
-0.0174713134765625,
-0.0172882080078125,
-0.0028076171875,
-0.00847625732421875,
-0.003170013427734375,
0.01207733154296875,
0.0164947509765625,
0.0214996337890625,
-0.006298065185546875,
-0.00344085693359375,
0.037384033203125,
-0.0251617431640625,
0.03314208984375,
-0.0259246826171875,
0.0178375244140625,
-0.02996826171875,
0.01007843017578125,
-0.004993438720703125,
-0.0291748046875,
0.015960693359375,
0.028564453125,
-0.035980224609375,
-0.02252197265625,
-0.033660888671875,
0.004512786865234375,
0.00403594970703125,
-0.039215087890625,
-0.0245361328125,
-0.00421905517578125,
0.0255889892578125,
-0.02301025390625,
-0.01666259765625,
0.01371002197265625,
0.0097198486328125,
0.0034122467041015625,
0.019439697265625,
0.014190673828125,
0.050750732421875,
0.01486968994140625,
-0.01303863525390625,
0.0189361572265625,
-0.0218048095703125,
-0.01386260986328125,
0.01214599609375,
-0.0294342041015625,
0.0172576904296875,
0.00695037841796875,
0.0128021240234375,
-0.0194091796875,
0.0170440673828125,
0.01500701904296875,
-0.046478271484375,
0.033477783203125,
-0.005702972412109375,
0.0054779052734375,
0.00516510009765625,
0.0180816650390625,
0.004436492919921875,
-0.0013980865478515625,
0.0185394287109375,
-0.033294677734375,
0.0144500732421875,
0.01203155517578125,
0.0014562606811523438,
-0.01276397705078125,
-0.0010194778442382812,
-0.0005998611450195312,
-0.00453948974609375,
-0.0148773193359375,
0.009490966796875,
0.011199951171875,
-0.0086822509765625,
0.033477783203125,
-0.01215362548828125,
0.01287841796875,
0.0237884521484375,
0.006168365478515625,
0.005558013916015625,
-0.00505828857421875,
0.026397705078125,
-0.030670166015625,
0.01088714599609375,
-0.006809234619140625,
-0.0213470458984375,
-0.037872314453125,
0.01861572265625,
0.0038433074951171875,
0.01374053955078125,
-0.037322998046875,
0.0180511474609375,
-0.00533294677734375,
0.0245819091796875,
-0.006938934326171875,
-0.0019464492797851562,
-0.041748046875,
-0.0328369140625,
-0.00335693359375,
-0.018096923828125,
-0.004657745361328125,
0.05767822265625,
-0.0009303092956542969,
0.0009512901306152344,
0.0162353515625,
0.007144927978515625,
0.000980377197265625,
0.003482818603515625,
-0.0030040740966796875,
0.031494140625,
0.00263214111328125,
0.012847900390625,
-0.018402099609375,
0.004364013671875,
0.0120391845703125,
-0.0214691162109375,
0.011993408203125,
-0.018768310546875,
0.04193115234375,
-0.050140380859375,
-0.02203369140625,
0.0218963623046875,
-0.045623779296875,
-0.046905517578125,
-0.01317596435546875,
0.03662109375,
-0.024078369140625,
0.02374267578125,
0.0225677490234375,
-0.0024852752685546875,
-0.0306243896484375,
0.03485107421875,
0.0011653900146484375,
0.0078887939453125,
-0.0162506103515625,
0.001529693603515625,
-0.002338409423828125,
0.00571441650390625,
0.018524169921875,
0.02008056640625,
0.01541900634765625,
-0.0289459228515625,
0.0258026123046875,
0.0146026611328125,
-0.0304718017578125,
0.00756072998046875,
-0.02606201171875,
0.0032482147216796875,
-0.0131988525390625,
0.03448486328125,
-0.011810302734375,
-0.03131103515625,
-0.005096435546875,
-0.015380859375,
-0.0020351409912109375,
-0.01168060302734375,
0.0256500244140625,
-0.0083770751953125,
-0.0002434253692626953,
-0.00789642333984375,
-0.01033782958984375,
0.01068115234375,
0.00730133056640625,
-0.0132598876953125,
-0.0294647216796875,
-0.017486572265625,
0.00644683837890625,
-0.00606536865234375,
-0.0323486328125,
-0.01366424560546875,
0.0125274658203125,
-0.012359619140625,
-0.01209259033203125,
-0.0009851455688476562,
-0.01369476318359375,
-0.01049041748046875,
-0.0298309326171875,
0.0072021484375,
-0.005016326904296875,
0.006328582763671875,
0.0072021484375,
0.03271484375,
-0.035247802734375,
-0.00803375244140625,
-0.00504302978515625,
-0.01605224609375,
0.01056671142578125,
0.0256195068359375,
0.017578125,
0.00568389892578125,
-0.0018606185913085938,
-0.033843994140625,
-0.003459930419921875,
-0.003284454345703125,
0.0025691986083984375,
0.0038509368896484375,
0.0450439453125,
-0.00315093994140625,
-0.0016698837280273438,
-0.0275726318359375,
-0.0187225341796875,
-0.030120849609375,
-0.010345458984375,
0.00505828857421875,
0.0116119384765625,
0.005069732666015625,
-0.01654052734375,
0.0310516357421875,
-0.00015175342559814453,
0.0264892578125,
0.016387939453125,
-0.0028476715087890625,
-0.016448974609375,
0.05194091796875,
0.002590179443359375,
-0.007801055908203125,
0.007205963134765625,
0.011688232421875,
-0.0018672943115234375,
0.02569580078125,
-0.00844573974609375,
0.022308349609375,
0.0243072509765625,
0.00830841064453125,
0.028961181640625,
-0.0149383544921875,
-0.039794921875,
0.0219268798828125,
-0.0187835693359375,
0.006740570068359375,
0.002166748046875,
0.01447296142578125,
0.0158843994140625,
-0.027099609375,
-0.00792694091796875,
-0.0278472900390625,
0.010833740234375,
-0.01132965087890625,
0.0210113525390625,
0.004413604736328125,
0.007320404052734375,
0.01380157470703125,
0.000030934810638427734,
-0.0014591217041015625,
0.0079193115234375,
-0.0179290771484375,
0.0170745849609375,
0.0156707763671875,
0.004718780517578125,
0.022491455078125,
0.0107421875,
0.005550384521484375,
-0.007717132568359375,
0.055267333984375,
0.0129547119140625,
-0.002716064453125,
-0.0272674560546875,
-0.027008056640625,
-0.01165008544921875,
-0.0152435302734375,
-0.0211944580078125,
0.02764892578125,
0.018157958984375,
-0.032989501953125,
0.003276824951171875,
-0.0255126953125,
-0.01171875,
0.01227569580078125,
-0.0019235610961914062,
0.00637054443359375,
-0.00202178955078125,
0.0000064373016357421875,
-0.00856781005859375,
0.0259857177734375,
0.01105499267578125,
-0.0171661376953125,
0.0160369873046875,
-0.0122528076171875,
0.010955810546875,
-0.00725555419921875,
-0.009185791015625,
-0.0005278587341308594,
-0.0097503662109375,
-0.0105743408203125,
-0.01168060302734375,
-0.019256591796875,
0.01448822021484375,
0.0130615234375,
-0.019256591796875,
-0.014068603515625,
0.0222930908203125,
0.0008544921875,
0.01233673095703125,
-0.003879547119140625,
0.051116943359375,
-0.01039886474609375,
0.009368896484375,
-0.00007927417755126953,
-0.0192413330078125,
-0.01096343994140625,
-0.0024261474609375,
0.0016298294067382812,
-0.01161956787109375,
0.01043701171875,
0.00804901123046875,
0.0053558349609375,
-0.01496124267578125,
0.00017690658569335938,
-0.0171966552734375,
0.004364013671875,
0.00592803955078125,
0.021026611328125,
-0.0281982421875,
-0.0169830322265625,
0.00939178466796875,
0.035552978515625,
0.00933837890625,
0.01140594482421875,
0.0233612060546875,
-0.0106353759765625,
-0.01213836669921875,
0.0297698974609375,
-0.01218414306640625,
0.00934600830078125,
-0.02606201171875,
0.00931549072265625,
-0.0150299072265625,
-0.008270263671875,
0.01515960693359375,
-0.035491943359375,
0.03192138671875,
0.0228424072265625,
0.004161834716796875,
0.003116607666015625,
-0.02569580078125,
-0.019195556640625,
0.00988006591796875,
-0.019287109375,
0.021575927734375,
-0.0214080810546875,
0.02978515625,
-0.025726318359375,
-0.0015954971313476562,
-0.025909423828125,
0.02532958984375,
0.0273590087890625,
0.01104736328125,
-0.01378631591796875,
-0.007373809814453125,
-0.028839111328125,
-0.00052642822265625,
-0.0054779052734375,
-0.0160369873046875,
-0.012054443359375,
0.020111083984375,
-0.0170440673828125,
-0.02203369140625,
0.0031566619873046875,
-0.005779266357421875,
0.0187530517578125,
-0.0164642333984375,
-0.01413726806640625,
-0.00899505615234375,
-0.01033782958984375,
0.004150390625,
0.0341796875,
-0.02313232421875,
0.0271759033203125,
-0.0029659271240234375,
-0.00569915771484375,
0.022796630859375,
-0.016143798828125,
0.0009241104125976562,
0.00791168212890625,
-0.0014734268188476562,
-0.053436279296875,
0.00017917156219482422,
-0.0173797607421875,
-0.0285491943359375,
0.016387939453125,
0.034820556640625,
-0.004657745361328125,
0.01366424560546875,
-0.0003058910369873047,
0.00981903076171875,
-0.036712646484375,
0.0118408203125,
-0.01087188720703125,
0.019073486328125,
-0.0078582763671875,
-0.0134124755859375,
0.01042938232421875,
0.002197265625,
-0.01299285888671875,
0.01361846923828125,
-0.012786865234375,
0.0173492431640625,
-0.027557373046875,
-0.02294921875,
-0.004367828369140625,
0.03509521484375,
0.0183258056640625,
-0.006099700927734375,
0.00848388671875,
-0.009368896484375,
0.00728607177734375,
0.0017547607421875,
-0.0177154541015625,
-0.00543212890625,
-0.009246826171875,
0.0186767578125,
-0.047210693359375,
-0.0284576416015625,
-0.00481414794921875,
-0.0064697265625,
-0.004871368408203125,
0.0195159912109375,
0.00040912628173828125,
0.045745849609375,
0.002346038818359375,
-0.0235595703125,
-0.001552581787109375,
0.00856781005859375,
0.00988006591796875,
-0.0153656005859375,
-0.01351165771484375,
0.01837158203125,
-0.033782958984375,
-0.026123046875,
-0.0129852294921875,
-0.0149078369140625,
-0.00893402099609375,
-0.01320648193359375,
0.0088348388671875,
0.035980224609375,
0.01605224609375,
-0.045013427734375,
0.01259613037109375,
-0.0124969482421875,
0.011566162109375,
-0.05072021484375,
0.016815185546875,
0.0039825439453125,
0.014312744140625,
0.0205078125,
-0.0137176513671875,
-0.048187255859375,
0.019439697265625,
0.009979248046875,
-0.0246734619140625,
0.01412200927734375,
-0.0094451904296875,
-0.0125732421875,
-0.004367828369140625,
0.0035305023193359375,
-0.00821685791015625,
0.01357269287109375,
-0.0195770263671875,
0.006076812744140625,
-0.053680419921875,
-0.021148681640625,
0.0308685302734375,
0.0207977294921875,
0.005710601806640625,
-0.034332275390625,
-0.01226806640625,
-0.0005135536193847656,
0.0242767333984375,
0.01168060302734375,
0.007293701171875,
-0.008544921875,
-0.025726318359375,
-0.0008640289306640625,
0.02325439453125,
0.044403076171875,
-0.01186370849609375,
0.002727508544921875,
-0.006313323974609375,
-0.01263427734375,
-0.003936767578125,
-0.0062408447265625,
0.006195068359375,
0.00799560546875,
-0.015869140625,
0.0204925537109375,
-0.01708984375,
-0.038360595703125,
0.0112457275390625,
0.00910186767578125,
-0.01351165771484375,
-0.00922393798828125,
-0.0188446044921875,
-0.00439453125,
-0.00420379638671875,
-0.03045654296875,
-0.004058837890625,
-0.0057373046875,
0.0012750625610351562,
-0.0227203369140625,
-0.0092926025390625,
0.0260162353515625,
-0.0215606689453125,
-0.01557159423828125,
-0.0005154609680175781,
-0.004852294921875,
-0.01557159423828125,
-0.0019893646240234375,
0.006008148193359375,
-0.0055694580078125,
0.0220794677734375,
0.02728271484375,
-0.006099700927734375,
-0.0184326171875,
0.0026950836181640625,
0.03729248046875,
-0.026397705078125,
-0.0290374755859375,
0.0215301513671875,
0.0246124267578125,
-0.000438690185546875,
-0.003627777099609375,
0.0126800537109375,
-0.0157470703125,
-0.018524169921875,
0.019622802734375,
-0.0030460357666015625,
0.017730712890625,
0.04205322265625,
-0.00406646728515625,
-0.0101776123046875,
0.01190948486328125,
0.00658416748046875,
0.016632080078125,
-0.01239013671875,
-0.0295867919921875,
-0.01235198974609375,
-0.01934814453125,
0.0260162353515625,
0.00902557373046875,
0.0177001953125,
-0.0018367767333984375,
-0.00527191162109375,
-0.020294189453125,
0.01250457763671875,
0.002887725830078125,
0.005054473876953125,
-0.005687713623046875,
0.0264129638671875,
0.0029888153076171875,
-0.033538818359375,
0.0038623809814453125,
0.0247039794921875,
-0.007801055908203125,
0.0181121826171875,
-0.005962371826171875,
0.0014219284057617188,
0.0237884521484375,
-0.0035266876220703125,
0.0250091552734375,
0.03466796875,
-0.00983428955078125,
-0.00662994384765625,
-0.003757476806640625,
-0.004726409912109375,
0.023345947265625,
-0.037017822265625,
0.0025482177734375,
0.01197052001953125,
-0.00528717041015625,
-0.0290679931640625,
-0.0031299591064453125,
0.0012102127075195312,
-0.0040283203125,
-0.0216217041015625,
-0.0007801055908203125,
-0.003910064697265625,
0.0173492431640625,
0.00789642333984375,
0.0045318603515625,
0.01473236083984375,
-0.0220489501953125,
0.031646728515625,
-0.0016956329345703125,
0.01073455810546875,
0.0046539306640625,
0.0151519775390625,
0.012298583984375,
-0.01293182373046875,
0.004199981689453125,
0.0095062255859375,
0.01197052001953125,
0.0129241943359375,
0.0161895751953125,
-0.00550079345703125,
0.015960693359375,
-0.004169464111328125,
0.00677490234375,
0.04510498046875,
0.026947021484375,
0.0030536651611328125,
0.0145721435546875,
-0.020355224609375,
-0.0083160400390625,
-0.01526641845703125,
0.0124053955078125,
0.020477294921875,
-0.0255126953125,
-0.0111541748046875,
0.00032591819763183594,
-0.0255279541015625,
0.03582763671875,
-0.00936126708984375,
-0.0019521713256835938,
0.0256805419921875,
-0.0149688720703125,
-0.031646728515625,
-0.0130615234375,
0.038818359375,
-0.00537872314453125,
0.008544921875,
0.002246856689453125,
-0.001953125,
0.02093505859375,
-0.0224151611328125,
-0.025421142578125,
0.015838623046875,
-0.0241241455078125,
-0.002719879150390625,
0.00440216064453125,
-0.0374755859375,
0.01715087890625,
-0.0224761962890625,
0.00904083251953125,
0.01947021484375,
-0.0162811279296875,
-0.0207366943359375,
-0.00799560546875,
-0.01316070556640625,
0.0128173828125,
-0.0137176513671875,
0.0012722015380859375,
-0.006160736083984375,
0.036407470703125,
-0.0036754608154296875,
-0.0020465850830078125,
-0.0001424551010131836,
-0.006473541259765625,
-0.00562286376953125,
0.00965118408203125,
0.004489898681640625,
-0.0185089111328125,
-0.0291290283203125,
-0.0193939208984375,
0.0185699462890625,
0.0086517333984375,
-0.005970001220703125,
-0.0012369155883789062,
0.02166748046875,
0.000637054443359375,
-0.03460693359375,
0.0144195556640625,
0.005580902099609375,
-0.0024814605712890625,
0.0193634033203125,
-0.0191802978515625,
-0.029266357421875,
0.01180267333984375,
-0.00641632080078125,
-0.00994110107421875,
-0.00919342041015625,
0.0445556640625,
0.010040283203125,
0.003597259521484375,
0.006702423095703125,
0.02777099609375,
0.01126861572265625,
0.010711669921875,
-0.0175323486328125,
-0.0226287841796875,
0.005260467529296875,
-0.003871917724609375,
0.028839111328125,
-0.007602691650390625,
-0.01319122314453125,
0.016693115234375,
0.04052734375,
-0.03424072265625,
-0.0101776123046875,
-0.02532958984375,
-0.0161590576171875,
0.002307891845703125,
-0.0268402099609375,
-0.0275726318359375,
0.027313232421875,
-0.0012063980102539062,
0.0090789794921875,
0.035308837890625,
0.012603759765625,
0.002231597900390625,
-0.04962158203125,
0.035614013671875,
0.0028400421142578125,
0.00580596923828125,
-0.03070068359375,
0.004970550537109375,
0.006458282470703125,
-0.0012426376342773438,
-0.02618408203125,
-0.0117645263671875,
0.00913238525390625,
-0.004268646240234375,
0.0194091796875,
-0.0107269287109375,
-0.00899505615234375,
0.014251708984375,
-0.041351318359375,
0.00881195068359375,
-0.01255035400390625,
-0.0283660888671875,
0.0006895065307617188,
0.0093231201171875,
0.0033588409423828125,
-0.0193939208984375,
-0.005229949951171875,
0.0011987686157226562,
0.00390625,
-0.00846099853515625,
0.0220947265625,
0.027099609375,
-0.0013074874877929688,
0.0016679763793945312,
-0.015899658203125,
0.00988006591796875,
-0.015411376953125,
-0.0247650146484375,
0.004520416259765625,
-0.01285552978515625,
-0.01496124267578125,
-0.0019311904907226562,
0.0019779205322265625,
0.02154541015625,
-0.03448486328125,
-0.01151275634765625,
-0.0250244140625,
-0.0103607177734375,
-0.0022335052490234375,
-0.004608154296875,
-0.025177001953125,
-0.04254150390625,
0.00835418701171875,
0.012847900390625,
0.01535797119140625,
0.0281219482421875,
0.0217742919921875,
0.005390167236328125,
-0.023468017578125,
0.02410888671875,
0.0304107666015625,
-0.034881591796875,
0.01380157470703125,
-0.01342010498046875,
0.004093170166015625,
0.024017333984375,
-0.01502227783203125,
0.017242431640625,
0.0010995864868164062,
-0.02557373046875,
0.0018024444580078125,
0.0079498291015625,
-0.031402587890625,
-0.0087738037109375,
0.0164947509765625,
0.0012521743774414062,
0.006763458251953125,
-0.00745391845703125,
-0.0122528076171875,
-0.019439697265625,
-0.003223419189453125,
-0.0015649795532226562,
0.044097900390625,
-0.00847625732421875,
0.005588531494140625,
0.0025234222412109375,
-0.00811767578125,
0.0345458984375,
0.0081634521484375,
-0.01178741455078125,
-0.0009369850158691406,
0.025634765625,
-0.003284454345703125,
-0.002010345458984375,
0.035064697265625,
0.0031890869140625,
-0.027374267578125,
-0.022064208984375,
-0.0124664306640625,
0.026519775390625,
0.007709503173828125,
-0.036651611328125,
-0.0312042236328125,
0.0035457611083984375,
0.01276397705078125,
-0.004436492919921875,
-0.0003807544708251953,
-0.01062774658203125,
-0.0030155181884765625,
0.0254364013671875,
-0.01812744140625,
-0.02508544921875,
0.035797119140625,
0.002216339111328125,
0.0029315948486328125,
-0.00006341934204101562,
-0.0186309814453125,
0.026336669921875,
-0.0249786376953125,
-0.00002568960189819336,
-0.03289794921875,
-0.01143646240234375,
-0.01198577880859375,
0.0141448974609375,
-0.0001493692398071289,
0.004932403564453125,
0.0090179443359375,
0.0165557861328125,
-0.0200347900390625,
-0.003269195556640625,
0.0228271484375,
-0.0228424072265625,
0.0157318115234375,
0.000507354736328125,
-0.033599853515625,
-0.00572967529296875,
0.0152435302734375,
-0.0223541259765625,
-0.0232391357421875,
0.0220489501953125,
-0.0015239715576171875,
-0.01068115234375,
0.00504302978515625,
-0.01436614990234375,
-0.019134521484375,
0.01224517822265625,
-0.0102996826171875,
-0.0294952392578125,
0.01898193359375,
0.045623779296875,
-0.007244110107421875,
0.0084075927734375,
0.01398468017578125,
0.0125579833984375,
0.0033245086669921875,
-0.04986572265625,
0.0010423660278320312,
-0.0005507469177246094,
0.0258636474609375,
0.00817108154296875,
0.005107879638671875,
0.0287017822265625,
0.0009226799011230469,
0.0178375244140625,
0.01068878173828125,
0.039520263671875,
-0.0122833251953125,
-0.01326751708984375,
0.01476287841796875,
0.01160430908203125,
0.031463623046875,
0.005123138427734375,
0.005199432373046875,
-0.0278472900390625,
-0.0081787109375,
0.039398193359375,
-0.004222869873046875,
0.0015773773193359375,
-0.023345947265625,
0.0066986083984375,
-0.007030487060546875,
-0.0235748291015625,
0.01125335693359375,
-0.01215362548828125,
0.04327392578125,
-0.038848876953125,
0.02789306640625,
-0.018768310546875,
0.0117950439453125,
0.007701873779296875,
-0.01904296875,
-0.0287933349609375,
0.0224609375,
0.02197265625,
-0.0188140869140625,
-0.01386260986328125,
-0.022796630859375,
-0.0081329345703125,
0.047515869140625,
0.0196075439453125,
0.0094451904296875,
-0.00981903076171875,
0.01006317138671875,
-0.00356292724609375,
-0.01465606689453125,
0.013275146484375,
-0.00785064697265625,
0.007724761962890625,
0.0185394287109375,
0.003696441650390625,
-0.007335662841796875,
0.008819580078125,
-0.044464111328125,
-0.0019063949584960938,
0.0038585662841796875,
-0.00238037109375,
-0.00861358642578125,
-0.006374359130859375,
0.01357269287109375,
-0.0164642333984375,
0.0113525390625,
0.027191162109375,
0.0024089813232421875,
0.001247406005859375,
-0.048095703125,
-0.02001953125,
-0.00325775146484375,
0.0061798095703125,
-0.02020263671875,
-0.0035953521728515625,
-0.0031280517578125,
0.0013227462768554688,
0.0022373199462890625,
-0.006717681884765625,
-0.021270751953125,
0.01006317138671875,
-0.00746917724609375,
0.007511138916015625,
0.03326416015625,
0.02777099609375,
0.005634307861328125,
-0.01617431640625,
0.01442718505859375,
-0.004169464111328125,
-0.0237274169921875,
0.00467681884765625,
-0.0220184326171875,
-0.0146331787109375,
-0.016357421875,
0.033935546875,
-0.02001953125,
-0.0205841064453125,
-0.024627685546875,
0.020721435546875,
-0.0012559890747070312,
0.006683349609375,
0.01861572265625,
0.01319122314453125,
0.005611419677734375,
-0.0295867919921875,
-0.00531005859375,
-0.00039958953857421875,
-0.0031757354736328125,
-0.005252838134765625,
-0.0298004150390625,
-0.047393798828125,
-0.023406982421875,
0.013641357421875,
-0.04644775390625,
0.046478271484375,
-0.02093505859375,
-0.0287933349609375,
0.01910400390625,
-0.0081024169921875,
-0.007671356201171875,
-0.016571044921875,
0.00487518310546875,
0.024658203125,
0.0187835693359375,
0.0129852294921875,
-0.0025539398193359375,
0.01520538330078125,
-0.01523590087890625,
-0.01204681396484375,
0.0202178955078125,
0.0452880859375,
0.00371551513671875,
-0.0153350830078125,
0.0170135498046875,
0.0197296142578125,
0.037750244140625,
-0.01012420654296875,
0.0004291534423828125,
0.005847930908203125,
-0.0304412841796875,
-0.004314422607421875,
0.0025501251220703125,
-0.0172271728515625,
0.0282745361328125,
0.017486572265625,
-0.021331787109375,
0.01322174072265625,
0.03826904296875,
-0.0025501251220703125,
-0.02178955078125,
-0.006320953369140625,
-0.03466796875,
-0.007045745849609375,
0.02069091796875,
0.007080078125,
0.0189971923828125,
-0.003902435302734375,
0.0009965896606445312,
-0.0007395744323730469,
0.01031494140625,
0.02105712890625,
0.0257110595703125,
0.0072479248046875,
0.00614166259765625,
-0.004421234130859375,
-0.0162200927734375,
-0.0085906982421875,
-0.006374359130859375,
-0.006214141845703125,
0.01447296142578125,
-0.01214599609375,
0.0273590087890625,
0.004913330078125,
-0.00865936279296875,
0.005889892578125,
-0.0271148681640625,
-0.037353515625,
0.029388427734375,
0.0143585205078125,
0.0088653564453125,
-0.01184844970703125,
-0.00946044921875,
0.0014142990112304688,
0.005435943603515625,
-0.002140045166015625,
-0.01319122314453125,
-0.019805908203125,
0.00321197509765625,
-0.024993896484375,
0.032562255859375,
0.01227569580078125,
-0.0214080810546875,
-0.00876617431640625,
0.03778076171875,
-0.0048980712890625,
0.0086822509765625,
-0.00968170166015625,
0.01543426513671875,
-0.0011873245239257812,
0.03369140625,
-0.0037364959716796875,
-0.0003552436828613281,
0.0243988037109375,
-0.0169677734375,
-0.019134521484375,
0.0308990478515625,
0.00018012523651123047,
0.01424407958984375,
-0.0016069412231445312,
0.0213775634765625,
0.039794921875,
0.04345703125,
-0.024322509765625,
0.0001283884048461914,
-0.03509521484375,
0.00322723388671875,
0.015960693359375,
-0.00273895263671875,
-0.0301513671875,
0.032562255859375,
-0.0132598876953125,
-0.0042572021484375,
0.037689208984375,
-0.0020084381103515625,
0.0185394287109375,
-0.016815185546875,
0.028839111328125,
-0.01348114013671875,
-0.0091552734375,
0.034454345703125,
0.00807952880859375,
-0.001064300537109375,
-0.0016698837280273438,
0.020294189453125,
-0.01373291015625,
-0.0261993408203125,
0.0178985595703125,
-0.016754150390625,
0.012969970703125,
-0.004322052001953125,
-0.0016021728515625,
0.015228271484375,
0.0200347900390625,
0.0177459716796875,
0.0003674030303955078,
-0.0115814208984375,
0.00824737548828125,
0.0009336471557617188,
-0.01184844970703125,
0.014984130859375,
-0.00872802734375,
0.0008716583251953125,
-0.01473236083984375,
0.0016603469848632812,
0.0092010498046875,
0.0027942657470703125,
-0.024658203125,
0.0003247261047363281,
-0.0384521484375,
0.03277587890625,
0.006725311279296875,
-0.0230865478515625,
-0.0163726806640625,
-0.0169677734375,
0.01557159423828125,
-0.0321044921875,
-0.0276031494140625,
0.0115203857421875,
-0.0304107666015625,
-0.00569915771484375,
0.020843505859375,
0.0009441375732421875,
0.017333984375,
-0.01340484619140625,
0.007411956787109375,
0.01021575927734375,
-0.01416015625,
0.0176239013671875,
0.00897216796875,
0.0015611648559570312,
-0.032623291015625,
-0.032501220703125,
0.03955078125,
-0.005176544189453125,
-0.0036163330078125,
-0.00351715087890625,
0.008544921875,
0.00669097900390625,
0.00411224365234375,
-0.0200042724609375,
-0.023101806640625,
-0.0382080078125,
-0.007778167724609375,
-0.01593017578125,
-0.006847381591796875,
-0.0249786376953125,
0.003940582275390625,
-0.0106048583984375,
0.0126190185546875,
-0.0064849853515625,
-0.0008106231689453125,
0.0219268798828125,
0.00069427490234375,
0.003582000732421875,
-0.0261383056640625,
0.02386474609375,
-0.0162811279296875,
-0.00041103363037109375,
-0.01215362548828125,
0.0311126708984375,
-0.02703857421875,
0.04058837890625,
0.040618896484375,
0.01084136962890625,
0.026336669921875,
0.005794525146484375,
0.045440673828125,
0.0142364501953125,
0.0014514923095703125,
-0.04034423828125,
0.04376220703125,
0.005405426025390625,
-0.0185089111328125,
-0.003376007080078125,
0.01837158203125,
0.0008106231689453125,
-0.03302001953125,
-0.016021728515625,
0.03875732421875,
0.0036640167236328125,
-0.0231170654296875,
0.01505279541015625,
-0.0173492431640625,
0.00586700439453125,
-0.0055084228515625,
-0.05047607421875,
-0.00787353515625,
-0.00382232666015625,
-0.0153350830078125,
0.021514892578125,
-0.0292510986328125,
0.00901031494140625,
0.0049285888671875,
0.01320648193359375,
0.0218658447265625,
0.0195770263671875,
0.020477294921875,
-0.0022640228271484375,
-0.0263214111328125,
-0.0150146484375,
0.004634857177734375,
-0.03765869140625,
0.0287017822265625,
-0.00592041015625,
-0.00618743896484375,
0.0194091796875,
-0.01100921630859375,
-0.0084381103515625,
-0.008209228515625,
-0.0078887939453125,
0.0253753662109375,
0.003376007080078125,
0.000011563301086425781,
0.0198211669921875,
-0.0095977783203125,
0.02734375,
-0.00934600830078125,
-0.0015687942504882812,
-0.008331298828125,
-0.01702880859375,
-0.0281829833984375,
-0.016448974609375,
-0.000675201416015625,
-0.034210205078125,
0.0178070068359375,
0.01837158203125,
0.014862060546875,
0.003040313720703125,
-0.018707275390625,
0.01342010498046875,
-0.01006317138671875,
0.0073089599609375,
0.0063934326171875,
-0.010833740234375,
0.0125732421875,
0.0014896392822265625,
-0.014892578125,
-0.0097198486328125,
0.01290130615234375,
0.03369140625,
0.02410888671875,
0.007328033447265625,
-0.0251617431640625,
0.0206146240234375,
-0.00270843505859375,
-0.01372528076171875,
-0.001983642578125,
-0.01873779296875,
-0.03057861328125,
-0.0296173095703125,
0.0156707763671875,
0.004222869873046875,
0.025787353515625,
0.00722503662109375,
-0.0030078887939453125,
-0.0210113525390625,
-0.006565093994140625,
-0.0015811920166015625,
-0.003265380859375,
-0.01332855224609375,
-0.0169830322265625,
-0.01580810546875,
0.037811279296875,
-0.00228118896484375,
-0.020782470703125,
-0.0149688720703125,
0.0175933837890625,
-0.0032939910888671875,
-0.013153076171875,
0.00852203369140625,
0.0240020751953125,
0.0092315673828125,
0.0011014938354492188,
0.0302886962890625,
0.026275634765625,
0.019317626953125,
0.025604248046875,
0.027313232421875,
0.045166015625,
0.004955291748046875,
0.0178070068359375,
0.0004715919494628906,
-0.0146331787109375,
0.0048370361328125,
-0.0175933837890625,
-0.0248260498046875,
0.0022125244140625,
0.0034618377685546875,
0.0149078369140625,
-0.0304718017578125,
0.017120361328125,
-0.013031005859375,
-0.02508544921875,
0.01177215576171875,
-0.0236968994140625,
0.025787353515625,
0.017791748046875,
-0.00952911376953125,
-0.0264739990234375,
-0.00881195068359375,
0.034637451171875,
0.0063323974609375,
-0.0194854736328125,
-0.018157958984375,
0.0066070556640625,
0.00319671630859375,
-0.0024509429931640625,
-0.0029087066650390625,
0.004787445068359375,
-0.00862884521484375,
-0.00908660888671875,
-0.009857177734375,
-0.017608642578125,
0.006015777587890625,
0.006664276123046875,
-0.0159759521484375,
0.0064849853515625,
0.036590576171875,
-0.0289154052734375,
0.0017299652099609375,
-0.0216217041015625,
-0.0192718505859375,
0.0220489501953125,
0.0182037353515625,
-0.006145477294921875,
-0.0282440185546875,
0.00862884521484375,
-0.006336212158203125,
-0.0111541748046875,
-0.00923919677734375,
-0.015960693359375,
-0.001590728759765625,
-0.0290679931640625,
-0.0175628662109375,
-0.0195770263671875,
-0.0137176513671875,
0.005218505859375,
-0.012603759765625,
-0.0009737014770507812,
0.0223388671875,
0.03594970703125,
0.0285491943359375,
-0.0295867919921875,
-0.01824951171875,
0.02288818359375,
0.002635955810546875,
-0.00539398193359375,
-0.0020999908447265625,
0.03594970703125,
0.041107177734375,
-0.02899169921875,
-0.00018644332885742188,
0.00560760498046875,
-0.00606536865234375,
0.0191802978515625,
-0.0253143310546875,
0.032012939453125,
0.011871337890625,
0.0277862548828125,
0.04559326171875,
-0.022857666015625,
0.0007596015930175781,
-0.01288604736328125,
0.0030384063720703125,
0.036163330078125,
-0.0016689300537109375,
-0.0185394287109375,
0.0176849365234375,
0.008941650390625,
0.0005450248718261719,
-0.018218994140625,
0.0321044921875,
0.0174560546875,
0.0176544189453125,
-0.0090484619140625,
0.033294677734375,
-0.0222320556640625,
0.0255889892578125,
0.0350341796875,
-0.01093292236328125,
0.0330810546875,
-0.0489501953125,
-0.0021228790283203125,
-0.0087738037109375,
0.0030956268310546875,
0.0477294921875,
0.004222869873046875,
-0.0063629150390625,
0.00017011165618896484,
0.034515380859375,
-0.0232086181640625,
0.0251922607421875,
0.0034275054931640625,
0.0010366439819335938,
-0.00010573863983154297,
0.00261688232421875,
-0.015838623046875,
0.0275421142578125,
0.0198822021484375,
-0.02044677734375,
-0.0102996826171875,
0.0088348388671875,
0.0249786376953125,
-0.02813720703125,
-0.00682830810546875,
-0.004390716552734375,
-0.01407623291015625,
0.0029697418212890625,
-0.012908935546875,
0.0083465576171875,
0.01702880859375,
-0.01213836669921875,
0.00495147705078125,
-0.0205841064453125,
0.0224456787109375,
-0.0252838134765625,
-0.0250244140625,
0.00872039794921875,
0.01009368896484375,
-0.020172119140625,
0.0184173583984375,
0.003559112548828125,
-0.0276031494140625,
0.0126495361328125,
0.030181884765625,
-0.01372528076171875,
0.0276031494140625,
0.03485107421875,
-0.0008115768432617188,
0.01076507568359375,
0.0006842613220214844,
0.02197265625,
-0.0200042724609375,
-0.049163818359375,
-0.004581451416015625,
0.01010894775390625,
-0.0168304443359375,
0.0195770263671875,
-0.028167724609375,
0.016845703125,
0.01580810546875,
0.0172119140625,
-0.0236663818359375,
0.00673675537109375,
-0.022125244140625,
0.029327392578125,
-0.01551055908203125,
-0.000621795654296875,
-0.00891876220703125,
-0.0052642822265625,
-0.007534027099609375,
0.007152557373046875,
-0.0540771484375,
-0.0401611328125,
0.035491943359375,
-0.007724761962890625,
0.0014276504516601562,
0.032135009765625,
-0.0010232925415039062,
0.0222930908203125,
-0.01605224609375,
0.005588531494140625,
-0.0105438232421875,
-0.035552978515625,
-0.0261688232421875,
-0.0119781494140625,
0.022918701171875,
-0.00901031494140625,
0.0133209228515625,
-0.01045989990234375,
0.0186920166015625,
0.0017833709716796875,
0.017669677734375,
-0.0082244873046875,
-0.04644775390625,
-0.0135040283203125,
-0.006488800048828125,
0.02630615234375,
-0.006687164306640625,
-0.0246124267578125,
0.0006170272827148438,
-0.0074005126953125,
-0.00926971435546875,
-0.012176513671875,
0.017913818359375,
0.01099395751953125,
0.004421234130859375,
0.0017957687377929688,
0.005710601806640625,
0.004634857177734375,
0.0005383491516113281,
-0.0112762451171875,
-0.031280517578125,
0.0034637451171875,
0.01526641845703125,
-0.02349853515625,
0.01432037353515625,
0.0218353271484375,
-0.023590087890625,
0.0034961700439453125,
0.0014162063598632812,
-0.0175933837890625,
-0.02960205078125,
-0.05267333984375,
0.0242156982421875,
0.04058837890625,
-0.01812744140625,
0.0006012916564941406,
0.01331329345703125,
0.0007176399230957031,
-0.01326751708984375,
-0.0037899017333984375,
0.0047760009765625,
-0.005084991455078125,
0.0158233642578125,
0.00870513916015625,
-0.007656097412109375,
-0.00876617431640625,
0.021148681640625,
0.007534027099609375,
0.0271759033203125,
-0.004390716552734375,
0.0004825592041015625,
-0.033538818359375,
0.007434844970703125,
0.005466461181640625,
0.0214385986328125,
-0.01163482666015625,
0.0034656524658203125,
-0.00616455078125,
-0.00797271728515625,
0.0129547119140625,
0.02947998046875,
0.00971221923828125,
-0.01654052734375,
-0.00914764404296875,
-0.0026721954345703125,
-0.01373291015625
] |
ours_545
|
Let the time of the fastest bricklayer be \( t \). To minimize \( t \), assume the other 4 workers each take 36 hours. Let the total work be 1 unit. Using the formula \( D = R \times T \), we have:
\[
\frac{1}{\frac{1}{36} + \frac{1}{36} + \frac{1}{36} + \frac{1}{36} + \frac{1}{t}} = 3
\]
Simplifying, we get:
\[
\frac{1}{t} + \frac{1}{9} = \frac{1}{3}
\]
Solving for \( t \), we find:
\[
\frac{1}{t} = \frac{1}{3} - \frac{1}{9} = \frac{2}{9}
\]
Thus, \( t = \frac{9}{2} \) hours, which is 270 minutes.
\(\boxed{270}\)
|
270
|
{
"competition": "us_comps",
"dataset": "Ours",
"posts": null,
"source": "OMOSoln2.md"
}
|
Five bricklayers working together finish a job in 3 hours. Working alone, each bricklayer takes at most 36 hours to finish the job. What is the smallest number of minutes it could take the fastest bricklayer to complete the job alone?
|
[
"/Mathematics/Algebra/AlgebraicEquations/LinearEquation",
"/Mathematics/Algebra/RateProblems"
] |
Assume the other four bricklayers work at their slowest (36 h) to minimize the fastest's time, then apply the additive work‑rate formula.
|
[
0.000019311904907226562,
-0.063232421875,
0.033905029296875,
0.0026073455810546875,
0.00009703636169433594,
0.04241943359375,
0.03765869140625,
-0.0193939208984375,
0.006011962890625,
-0.006313323974609375,
-0.03924560546875,
-0.0347900390625,
0.0018949508666992188,
-0.029266357421875,
0.020660400390625,
-0.00769805908203125,
-0.01177215576171875,
0.053955078125,
0.00522613525390625,
0.003231048583984375,
-0.00740814208984375,
0.00942230224609375,
0.0048828125,
-0.01206207275390625,
0.013031005859375,
-0.0013637542724609375,
-0.023162841796875,
0.01348114013671875,
-0.0246429443359375,
0.022613525390625,
-0.01099395751953125,
-0.007549285888671875,
-0.021575927734375,
-0.0390625,
-0.003940582275390625,
0.0089874267578125,
-0.0009183883666992188,
0.0099029541015625,
-0.0023593902587890625,
-0.04608154296875,
-0.0081329345703125,
-0.034698486328125,
-0.027679443359375,
-0.00608062744140625,
-0.05560302734375,
0.0231170654296875,
-0.00212860107421875,
0.0022373199462890625,
-0.006954193115234375,
-0.0139617919921875,
-0.00036263465881347656,
-0.00267791748046875,
0.0287933349609375,
0.003971099853515625,
0.00396728515625,
-0.0297088623046875,
0.060791015625,
0.001338958740234375,
0.0052947998046875,
0.01209259033203125,
0.0029144287109375,
0.00855255126953125,
0.03741455078125,
0.0171661376953125,
-0.0079193115234375,
-0.0080108642578125,
0.0203399658203125,
-0.030670166015625,
0.0015497207641601562,
-0.0210418701171875,
0.03466796875,
-0.0167388916015625,
0.00421905517578125,
0.02764892578125,
0.0380859375,
-0.00705718994140625,
-0.0023174285888671875,
-0.003818511962890625,
-0.0183258056640625,
0.0215301513671875,
0.006206512451171875,
0.0293731689453125,
0.00878143310546875,
0.034271240234375,
0.00438690185546875,
-0.049530029296875,
0.01131439208984375,
-0.002399444580078125,
-0.00537109375,
-0.01218414306640625,
0.00876617431640625,
0.0077667236328125,
0.0005869865417480469,
0.00949859619140625,
0.004302978515625,
0.006519317626953125,
-0.0002779960632324219,
-0.005443572998046875,
-0.004428863525390625,
0.010040283203125,
0.0036773681640625,
-0.007480621337890625,
0.0279693603515625,
-0.01535797119140625,
-0.034423828125,
-0.00405120849609375,
-0.026153564453125,
-0.0037670135498046875,
-0.000247955322265625,
0.001312255859375,
0.01436614990234375,
0.0031147003173828125,
0.0384521484375,
0.039031982421875,
-0.0005197525024414062,
0.00011444091796875,
0.00505828857421875,
-0.0042877197265625,
0.004863739013671875,
0.012908935546875,
-0.0001266002655029297,
-0.0011653900146484375,
-0.023834228515625,
-0.0021209716796875,
0.005138397216796875,
-0.0164642333984375,
-0.004100799560546875,
0.007568359375,
-0.01512908935546875,
0.0153656005859375,
-0.01284027099609375,
-0.00274658203125,
-0.031890869140625,
0.0012378692626953125,
-0.037841796875,
0.016632080078125,
0.0298309326171875,
0.0157928466796875,
-0.033294677734375,
-0.0217132568359375,
0.0103912353515625,
-0.01154327392578125,
-0.00672149658203125,
0.01476287841796875,
-0.0226593017578125,
0.0252227783203125,
0.0040740966796875,
-0.040802001953125,
0.012420654296875,
-0.00362396240234375,
0.0270843505859375,
-0.004215240478515625,
0.00472259521484375,
0.009796142578125,
-0.01287078857421875,
0.0254974365234375,
-0.0009207725524902344,
0.006160736083984375,
0.00571441650390625,
-0.004886627197265625,
0.01204681396484375,
-0.00836181640625,
-0.01331329345703125,
0.01123809814453125,
0.00684356689453125,
0.006256103515625,
-0.00710296630859375,
-0.01074981689453125,
-0.0245513916015625,
0.01458740234375,
0.01071929931640625,
0.004810333251953125,
0.00005251169204711914,
-0.00571441650390625,
0.007022857666015625,
-0.0166168212890625,
-0.01181793212890625,
0.00518035888671875,
0.00217437744140625,
0.00821685791015625,
0.0118408203125,
0.018798828125,
0.035125732421875,
0.0092010498046875,
0.029693603515625,
0.012786865234375,
-0.011444091796875,
-0.00751495361328125,
0.0207977294921875,
0.01418304443359375,
0.004299163818359375,
-0.026580810546875,
-0.00920867919921875,
-0.0231170654296875,
0.032745361328125,
-0.006748199462890625,
-0.0162506103515625,
-0.00984954833984375,
0.0292510986328125,
0.0254669189453125,
0.025115966796875,
-0.01236724853515625,
-0.01030731201171875,
-0.0011081695556640625,
-0.0012769699096679688,
-0.00875091552734375,
-0.007137298583984375,
-0.006252288818359375,
0.004154205322265625,
0.01043701171875,
0.00455474853515625,
0.017852783203125,
-0.01953125,
0.004184722900390625,
-0.0002522468566894531,
0.00485992431640625,
-0.00872802734375,
-0.01396942138671875,
0.006023406982421875,
-0.01006317138671875,
0.00380706787109375,
-0.0028934478759765625,
0.019073486328125,
-0.00005918741226196289,
-0.004550933837890625,
-0.0108489990234375,
-0.0135345458984375,
-0.0099639892578125,
-0.00418853759765625,
-0.009246826171875,
0.034088134765625,
0.0068511962890625,
0.00988006591796875,
0.005161285400390625,
-0.012969970703125,
-0.0001500844955444336,
0.0003883838653564453,
-0.004058837890625,
0.0164947509765625,
0.0150299072265625,
0.0794677734375,
-0.01181793212890625,
0.0019207000732421875,
0.0030918121337890625,
-0.0200347900390625,
0.0030059814453125,
0.0008440017700195312,
-0.0276947021484375,
-0.00954437255859375,
-0.01506805419921875,
0.012420654296875,
-0.00650787353515625,
0.0148773193359375,
-0.025604248046875,
0.010223388671875,
0.0020751953125,
0.01751708984375,
0.006099700927734375,
-0.0298614501953125,
0.00008213520050048828,
0.0004124641418457031,
-0.0262908935546875,
-0.00405120849609375,
0.00531005859375,
0.006801605224609375,
-0.01409149169921875,
0.020538330078125,
-0.0037784576416015625,
-0.01110076904296875,
-0.0093994140625,
0.0491943359375,
-0.01320648193359375,
-0.0108184814453125,
0.01995849609375,
0.0013265609741210938,
-0.0014562606811523438,
0.013397216796875,
0.0017833709716796875,
-0.018218994140625,
0.00006109476089477539,
0.015228271484375,
-0.00203704833984375,
0.0026035308837890625,
0.0045318603515625,
-0.005199432373046875,
-0.01971435546875,
0.023193359375,
0.0032634735107421875,
-0.00897979736328125,
0.01293182373046875,
-0.0002732276916503906,
-0.0190582275390625,
-0.0006241798400878906,
-0.001277923583984375,
0.0269012451171875,
-0.0307159423828125,
-0.0068511962890625,
-0.0028839111328125,
0.03448486328125,
-0.002445220947265625,
0.01012420654296875,
-0.0247802734375,
-0.0054168701171875,
-0.047210693359375,
-0.0225067138671875,
0.0031986236572265625,
-0.00878143310546875,
-0.00435638427734375,
0.053741455078125,
-0.01055908203125,
-0.026947021484375,
-0.007022857666015625,
-0.0007863044738769531,
0.00013875961303710938,
0.01529693603515625,
-0.02996826171875,
0.00646209716796875,
0.0121307373046875,
-0.013763427734375,
-0.00008577108383178711,
0.0070037841796875,
-0.02386474609375,
-0.01221466064453125,
0.001995086669921875,
0.0169525146484375,
0.0032062530517578125,
-0.0012760162353515625,
0.0263214111328125,
-0.026824951171875,
0.0174102783203125,
-0.01207733154296875,
0.01953125,
-0.028350830078125,
0.006053924560546875,
-0.010528564453125,
0.017242431640625,
-0.00846099853515625,
0.0302886962890625,
-0.00537109375,
0.021392822265625,
0.00994110107421875,
0.006923675537109375,
0.052337646484375,
0.0174713134765625,
-0.0155487060546875,
0.0034198760986328125,
-0.00916290283203125,
0.024139404296875,
0.041351318359375,
-0.00812530517578125,
0.02197265625,
-0.01352691650390625,
0.035552978515625,
-0.015960693359375,
0.0007162094116210938,
-0.019073486328125,
0.006900787353515625,
-0.000759124755859375,
0.006122589111328125,
0.03192138671875,
0.015869140625,
-0.04254150390625,
-0.0244903564453125,
-0.01367950439453125,
-0.0027904510498046875,
-0.034210205078125,
-0.0162506103515625,
0.016571044921875,
0.003936767578125,
-0.0169830322265625,
-0.0103607177734375,
-0.0030002593994140625,
0.01416778564453125,
-0.058074951171875,
-0.020751953125,
-0.01183319091796875,
-0.0169219970703125,
0.00047516822814941406,
0.0025691986083984375,
0.01023101806640625,
0.002811431884765625,
0.01222991943359375,
-0.01174163818359375,
0.0162200927734375,
-0.0027942657470703125,
0.0089263916015625,
-0.0028533935546875,
-0.004878997802734375,
-0.0276641845703125,
0.00608062744140625,
0.0004303455352783203,
-0.0170135498046875,
-0.005847930908203125,
-0.04498291015625,
0.0022373199462890625,
-0.036651611328125,
0.0036830902099609375,
0.01342010498046875,
0.0443115234375,
-0.023223876953125,
-0.019744873046875,
0.0204315185546875,
-0.0277252197265625,
-0.010223388671875,
0.008575439453125,
0.027740478515625,
0.0017385482788085938,
0.051239013671875,
0.01163482666015625,
0.0006818771362304688,
0.0039215087890625,
0.00937652587890625,
-0.0179901123046875,
0.018310546875,
-0.006969451904296875,
0.0020313262939453125,
0.0070037841796875,
-0.0169677734375,
-0.01531219482421875,
0.005809783935546875,
0.01042938232421875,
-0.005634307861328125,
-0.003818511962890625,
-0.031585693359375,
0.006351470947265625,
0.0102386474609375,
0.008880615234375,
0.0278472900390625,
0.02813720703125,
-0.0144805908203125,
0.003063201904296875,
0.00550079345703125,
0.00957489013671875,
0.0212860107421875,
0.00836944580078125,
0.0025310516357421875,
-0.0117340087890625,
0.0008306503295898438,
-0.0180206298828125,
0.0019502639770507812,
0.03179931640625,
-0.0267333984375,
-0.003673553466796875,
-0.015960693359375,
0.01384735107421875,
0.02801513671875,
0.018707275390625,
0.00582122802734375,
-0.0060577392578125,
-0.020416259765625,
0.0004811286926269531,
-0.032440185546875,
-0.0248565673828125,
-0.006336212158203125,
0.0025806427001953125,
0.02606201171875,
0.00904083251953125,
0.034912109375,
-0.00461578369140625,
-0.0404052734375,
-0.018524169921875,
0.01100921630859375,
-0.025787353515625,
0.005344390869140625,
0.0228424072265625,
0.0015583038330078125,
-0.004947662353515625,
0.017181396484375,
-0.0213623046875,
0.0192413330078125,
0.00290679931640625,
-0.0186004638671875,
0.01369476318359375,
0.007770538330078125,
-0.032012939453125,
0.0020961761474609375,
-0.001697540283203125,
0.029205322265625,
0.006793975830078125,
0.0019989013671875,
-0.007305145263671875,
0.0090789794921875,
0.01192474365234375,
-0.001979827880859375,
0.0194244384765625,
0.029754638671875,
0.01058197021484375,
0.017578125,
-0.0162506103515625,
-0.01163482666015625,
0.020721435546875,
0.033416748046875,
-0.046173095703125,
-0.03985595703125,
-0.0199737548828125,
0.0263519287109375,
-0.0030879974365234375,
-0.0266265869140625,
0.00012695789337158203,
0.016845703125,
0.01395416259765625,
-0.00896453857421875,
-0.0196685791015625,
-0.0183258056640625,
0.01360321044921875,
-0.0235595703125,
-0.026611328125,
-0.04425048828125,
0.0018024444580078125,
-0.000949859619140625,
0.0302276611328125,
-0.00209808349609375,
-0.004146575927734375,
-0.01367950439453125,
0.02313232421875,
0.027496337890625,
-0.00020945072174072266,
-0.021942138671875,
0.0222320556640625,
-0.005191802978515625,
-0.0220184326171875,
0.0277862548828125,
0.047119140625,
0.0227813720703125,
0.011810302734375,
0.024505615234375,
0.0213775634765625,
-0.0012140274047851562,
-0.007106781005859375,
-0.019378662109375,
-0.01023101806640625,
0.00037479400634765625,
0.007297515869140625,
0.022125244140625,
-0.050201416015625,
0.0242462158203125,
0.0283966064453125,
0.049285888671875,
-0.01024627685546875,
0.0190887451171875,
0.0291595458984375,
-0.00579833984375,
0.01169586181640625,
-0.0245208740234375,
-0.0007567405700683594,
-0.03778076171875,
-0.0274200439453125,
-0.0261077880859375,
0.01122283935546875,
0.0224456787109375,
0.00508880615234375,
0.0301361083984375,
-0.01446533203125,
0.0026760101318359375,
0.0185394287109375,
0.0066375732421875,
0.0282135009765625,
0.0238037109375,
-0.0030670166015625,
-0.00510406494140625,
-0.002201080322265625,
-0.031219482421875,
0.00696563720703125,
0.0293121337890625,
0.031341552734375,
-0.006267547607421875,
0.01605224609375,
-0.00403594970703125,
0.0116119384765625,
-0.024078369140625,
0.0030002593994140625,
0.00466156005859375,
0.0189056396484375,
-0.01079559326171875,
-0.0106201171875,
-0.0099639892578125,
-0.0265960693359375,
0.00975799560546875,
-0.003936767578125,
-0.0205841064453125,
0.0174713134765625,
0.00009393692016601562,
-0.01018524169921875,
-0.0278167724609375,
-0.011627197265625,
0.00019180774688720703,
-0.0295562744140625,
0.0029201507568359375,
0.00862884521484375,
-0.0040740966796875,
0.0006766319274902344,
0.00982666015625,
0.031768798828125,
0.01800537109375,
-0.015777587890625,
-0.031036376953125,
-0.015380859375,
-0.01397705078125,
0.0149078369140625,
0.0090789794921875,
0.0328369140625,
0.0012273788452148438,
0.0083770751953125,
0.02142333984375,
0.01515960693359375,
0.002719879150390625,
0.0052490234375,
0.0242919921875,
0.034149169921875,
0.01097869873046875,
-0.0221710205078125,
-0.03875732421875,
-0.037322998046875,
0.00951385498046875,
0.0229339599609375,
0.0008416175842285156,
-0.0140380859375,
0.0036754608154296875,
-0.0194549560546875,
-0.00707244873046875,
-0.00942230224609375,
0.0059051513671875,
-0.0124664306640625,
0.02862548828125,
0.00821685791015625,
-0.0509033203125,
-0.023681640625,
-0.024688720703125,
-0.0244903564453125,
0.0087432861328125,
-0.0015974044799804688,
-0.06005859375,
0.0277252197265625,
0.0196380615234375,
-0.027435302734375,
-0.035858154296875,
-0.026275634765625,
-0.01314544677734375,
-0.0299835205078125,
0.0200347900390625,
0.025482177734375,
0.00466156005859375,
0.0194549560546875,
-0.046966552734375,
0.0008139610290527344,
0.0206298828125,
-0.01605224609375,
0.02203369140625,
-0.00125885009765625,
-0.01177215576171875,
0.0003104209899902344,
-0.015838623046875,
-0.0027923583984375,
0.03631591796875,
0.02947998046875,
-0.0173187255859375,
-0.0154571533203125,
-0.054534912109375,
0.006244659423828125,
0.037750244140625,
-0.0017004013061523438,
-0.00460052490234375,
0.02789306640625,
0.03546142578125,
-0.01213836669921875,
-0.0036716461181640625,
0.00557708740234375,
0.043914794921875,
0.019775390625,
-0.0343017578125,
-0.048095703125,
-0.011474609375,
0.00887298583984375,
-0.00677490234375,
0.0177764892578125,
0.03350830078125,
-0.03704833984375,
-0.00833892822265625,
0.043914794921875,
-0.0247802734375,
0.006252288818359375,
0.0070343017578125,
0.015777587890625,
-0.035736083984375,
-0.0095977783203125,
0.00909423828125,
-0.040924072265625,
-0.0243682861328125,
0.0300750732421875,
0.0252838134765625,
0.019866943359375,
0.005573272705078125,
-0.0222015380859375,
0.024505615234375,
-0.01556396484375,
-0.0134735107421875,
0.0124969482421875,
-0.010467529296875,
-0.0325927734375,
-0.006259918212890625,
0.005390167236328125,
0.022613525390625,
0.04052734375,
-0.0100250244140625,
-0.0102691650390625,
-0.0167236328125,
0.0034732818603515625,
0.0172271728515625,
-0.02716064453125,
0.021728515625,
-0.01194000244140625,
0.0159454345703125,
0.0112762451171875,
-0.0026416778564453125,
0.0008673667907714844,
0.00753021240234375,
-0.039825439453125,
0.01403045654296875,
0.025390625,
-0.00614166259765625,
0.0138397216796875,
-0.00839996337890625,
-0.009552001953125,
0.00878143310546875,
0.00519561767578125,
0.01763916015625,
-0.0084075927734375,
-0.0261383056640625,
-0.0186309814453125,
-0.00029277801513671875,
0.0292816162109375,
0.005786895751953125,
0.00911712646484375,
0.0018157958984375,
-0.00466156005859375,
0.0024776458740234375,
0.0012760162353515625,
-0.013916015625,
0.007411956787109375,
0.006626129150390625,
0.038299560546875,
-0.0278472900390625,
-0.01372528076171875,
0.01409149169921875,
-0.0294952392578125,
-0.0004596710205078125,
-0.0256195068359375,
0.006988525390625,
-0.02020263671875,
-0.026458740234375,
-0.01070404052734375,
-0.0140228271484375,
0.03106689453125,
-0.051513671875,
-0.0186767578125,
0.0245819091796875,
0.02642822265625,
-0.01116943359375,
-0.03436279296875,
-0.01386260986328125,
0.0034084320068359375,
-0.0184478759765625,
-0.00659942626953125,
0.01447296142578125,
-0.00860595703125,
-0.040863037109375,
-0.02545166015625,
0.008514404296875,
-0.0161895751953125,
-0.00376129150390625,
-0.02801513671875,
0.0269775390625,
0.0077056884765625,
0.00458526611328125,
-0.0006990432739257812,
0.01081085205078125,
-0.02655029296875,
-0.021484375,
0.0038661956787109375,
-0.0220947265625,
0.016571044921875,
-0.0177764892578125,
-0.0092926025390625,
0.030853271484375,
-0.0106048583984375,
-0.0305328369140625,
0.001216888427734375,
0.0261383056640625,
0.0310821533203125,
-0.0294189453125,
0.0128936767578125,
0.0041961669921875,
0.00521087646484375,
0.013916015625,
-0.0019311904907226562,
-0.024627685546875,
0.00965118408203125,
0.0017042160034179688,
0.04736328125,
0.020751953125,
-0.0139007568359375,
-0.0143890380859375,
-0.00705718994140625,
0.025665283203125,
0.0011148452758789062,
-0.0330810546875,
-0.018524169921875,
0.0196685791015625,
0.010345458984375,
0.036468505859375,
0.04400634765625,
-0.0168304443359375,
-0.0083465576171875,
-0.0191192626953125,
0.003055572509765625,
-0.0005192756652832031,
0.01446533203125,
-0.0323486328125,
0.027984619140625,
0.0146636962890625,
0.037506103515625,
0.0225677490234375,
-0.01264190673828125,
-0.006458282470703125,
-0.0026531219482421875,
0.01073455810546875,
-0.0341796875,
-0.0140380859375,
0.0163726806640625,
0.02685546875,
-0.04339599609375,
-0.00815582275390625,
-0.0175018310546875,
0.0219268798828125,
-0.00678253173828125,
-0.0016756057739257812,
-0.02557373046875,
-0.029510498046875,
-0.046875,
0.04876708984375,
0.0252838134765625,
0.01178741455078125,
0.00423431396484375,
0.0241241455078125,
0.0147552490234375,
-0.004886627197265625,
0.015899658203125,
0.0161590576171875,
-0.0143585205078125,
0.03546142578125,
0.015960693359375,
0.0239105224609375,
-0.0355224609375,
0.0205841064453125,
-0.0240478515625,
0.04034423828125,
0.0252685546875,
0.007251739501953125,
0.01294708251953125,
0.03582763671875,
-0.020904541015625,
-0.01454925537109375,
0.0156097412109375,
-0.005420684814453125,
0.01432037353515625,
-0.040191650390625,
0.048065185546875,
0.042388916015625,
-0.0060577392578125,
-0.019012451171875,
0.0098724365234375,
0.0231170654296875,
-0.007801055908203125,
0.031982421875,
0.02581787109375,
0.0027713775634765625,
-0.039154052734375,
0.0222015380859375,
0.0069122314453125,
-0.034576416015625,
0.0277252197265625,
-0.010650634765625,
0.0111541748046875,
0.015899658203125,
-0.011962890625,
-0.008331298828125,
0.0109405517578125,
0.0089569091796875,
-0.00801849365234375,
-0.010345458984375,
-0.0000502467155456543,
0.0186309814453125,
0.006977081298828125,
-0.007259368896484375,
0.0084991455078125,
-0.0223236083984375,
0.0201568603515625,
-0.01459503173828125,
0.01155853271484375,
0.0024623870849609375,
-0.0260009765625,
0.0190582275390625,
0.007579803466796875,
0.0357666015625,
-0.00276947021484375,
-0.00330352783203125,
-0.027496337890625,
0.0246429443359375,
0.0009021759033203125,
0.027099609375,
-0.002826690673828125,
0.01483917236328125,
0.0019588470458984375,
0.0257568359375,
-0.00814056396484375,
-0.01447296142578125,
-0.025634765625,
0.00826263427734375,
0.0008697509765625,
-0.0170135498046875,
-0.0157623291015625,
-0.02685546875,
-0.0147552490234375,
0.01430511474609375,
-0.0306243896484375,
-0.006084442138671875,
0.0102386474609375,
0.01081085205078125,
-0.0036830902099609375,
-0.00934600830078125,
-0.031585693359375,
0.0182647705078125,
-0.004058837890625,
0.01087188720703125,
0.0009717941284179688,
0.0187530517578125,
0.00012612342834472656,
0.0390625,
0.044891357421875,
-0.0136260986328125,
-0.0308990478515625,
-0.01038360595703125,
0.01885986328125,
0.022735595703125,
0.0021343231201171875,
-0.01540374755859375,
-0.0012731552124023438,
0.02349853515625,
-0.017974853515625,
0.038818359375,
-0.0228118896484375,
0.0243377685546875,
-0.0012636184692382812,
-0.00015056133270263672,
-0.0085906982421875,
-0.0262908935546875,
-0.021209716796875,
0.0189361572265625,
0.0192108154296875,
-0.0136871337890625,
-0.006778717041015625,
0.011810302734375,
-0.047637939453125,
-0.01432037353515625,
0.01251220703125,
0.00554656982421875,
0.0228118896484375,
0.0009579658508300781,
0.009429931640625,
0.0008759498596191406,
-0.00714111328125,
0.0382080078125,
-0.012603759765625,
-0.0215911865234375,
-0.03326416015625,
-0.026336669921875,
-0.0193634033203125,
0.0171051025390625,
0.0213775634765625,
0.0137176513671875,
-0.019378662109375,
0.0273895263671875,
0.00173187255859375,
-0.0197296142578125,
0.001285552978515625,
-0.014068603515625,
0.0157623291015625,
0.0014848709106445312,
0.002895355224609375,
0.00811767578125,
0.006381988525390625,
0.0223388671875,
0.00673675537109375,
-0.0034885406494140625,
0.004596710205078125,
0.0299072265625,
-0.0302734375,
-0.01111602783203125,
0.033447265625,
0.006481170654296875,
-0.0145416259765625,
0.01186370849609375,
-0.00591278076171875,
-0.01190948486328125,
0.058380126953125,
-0.0086517333984375,
0.020904541015625,
-0.041290283203125,
0.00524139404296875,
0.01401519775390625,
0.0248870849609375,
-0.01508331298828125,
-0.0020771026611328125,
-0.0013027191162109375,
-0.0252532958984375,
0.0151214599609375,
-0.0347900390625,
0.025482177734375,
-0.0297698974609375,
0.017425537109375,
0.010955810546875,
-0.0172119140625,
-0.0135345458984375,
0.01837158203125,
-0.040679931640625,
-0.00545501708984375,
-0.03302001953125,
0.017333984375,
0.00811767578125,
-0.01519775390625,
0.014923095703125,
-0.02899169921875,
0.00745391845703125,
-0.0295562744140625,
-0.007843017578125,
-0.0206451416015625,
0.01457977294921875,
-0.039398193359375,
0.004787445068359375,
0.0022830963134765625,
-0.00695037841796875,
0.00800323486328125,
0.062042236328125,
-0.0258941650390625,
0.01390838623046875,
0.0038890838623046875,
0.007793426513671875,
-0.01157379150390625,
-0.018798828125,
0.01409149169921875,
0.01351165771484375,
0.026275634765625,
-0.01419830322265625,
0.0012311935424804688,
0.002170562744140625,
-0.005580902099609375,
0.0386962890625,
0.00502777099609375,
-0.0214385986328125,
0.02557373046875,
-0.007137298583984375,
-0.0241546630859375,
-0.0247344970703125,
0.00782012939453125,
0.01328277587890625,
0.028961181640625,
-0.031005859375,
-0.00977325439453125,
-0.0304718017578125,
0.0311126708984375,
0.004638671875,
0.033538818359375,
0.0233154296875,
0.004428863525390625,
0.0018672943115234375,
0.01415252685546875,
0.00896453857421875,
0.00464630126953125,
0.0101318359375,
-0.012237548828125,
-0.00830841064453125,
0.04400634765625,
-0.022003173828125,
0.0235748291015625,
-0.0186309814453125,
0.039154052734375,
-0.02239990234375,
-0.0080413818359375,
-0.031280517578125,
-0.007328033447265625,
0.0012483596801757812,
0.006664276123046875,
-0.00588226318359375,
-0.02374267578125,
0.01043701171875,
0.02276611328125,
-0.0152587890625,
-0.0011749267578125,
-0.053558349609375,
0.007450103759765625,
0.0070037841796875,
0.036712646484375,
0.0274810791015625,
0.00269317626953125,
-0.0274658203125,
0.0129241943359375,
-0.006404876708984375,
0.02581787109375,
-0.021148681640625,
0.012054443359375,
-0.01399993896484375,
-0.00495147705078125,
0.0005474090576171875,
0.0038814544677734375,
0.0210113525390625,
-0.007781982421875,
-0.02850341796875,
-0.025360107421875,
0.006084442138671875,
-0.014862060546875,
0.01407623291015625,
0.032196044921875,
-0.00620269775390625,
0.00925445556640625,
0.00472259521484375,
-0.026885986328125,
0.01074981689453125,
0.0004184246063232422,
0.0269775390625,
-0.009033203125,
-0.034027099609375,
-0.0103607177734375,
0.0243072509765625,
-0.049346923828125,
0.025054931640625,
0.042266845703125,
-0.002300262451171875,
-0.0220794677734375,
-0.00441741943359375,
-0.0174102783203125,
0.00138092041015625,
0.006649017333984375,
-0.0238189697265625,
-0.01030731201171875,
-0.0335693359375,
0.0019855499267578125,
-0.031829833984375,
0.037139892578125,
0.0235595703125,
0.0175628662109375,
0.0207977294921875,
0.0362548828125,
0.0176849365234375,
0.015289306640625,
-0.0084686279296875,
0.016632080078125,
0.01363372802734375,
-0.0243988037109375,
-0.023956298828125,
0.00951385498046875,
0.003559112548828125,
-0.0169830322265625,
-0.00600433349609375,
-0.018585205078125,
-0.016815185546875,
0.020660400390625,
-0.0171051025390625,
0.01282501220703125,
-0.026031494140625,
0.023040771484375,
-0.003559112548828125,
-0.052703857421875,
0.004993438720703125,
0.004001617431640625,
-0.00341033935546875,
0.04071044921875,
0.012298583984375,
0.0188751220703125,
0.0089263916015625,
-0.02301025390625,
-0.01611328125,
-0.001251220703125,
0.0250701904296875,
-0.032745361328125,
0.0362548828125,
-0.0308380126953125,
0.01378631591796875,
-0.0193023681640625,
-0.044647216796875,
-0.03216552734375,
0.01508331298828125,
-0.0108795166015625,
0.0052337646484375,
-0.01517486572265625,
-0.008056640625,
-0.00940704345703125,
-0.004444122314453125,
0.00812530517578125,
-0.035308837890625,
0.006595611572265625,
0.007534027099609375,
-0.01012420654296875,
0.004657745361328125,
0.0080108642578125,
0.037567138671875,
-0.015655517578125,
0.0008006095886230469,
0.043121337890625,
-0.0292205810546875,
-0.0013179779052734375,
0.0299072265625,
0.00811767578125,
0.03216552734375,
0.0244598388671875,
0.0245361328125,
-0.020660400390625,
0.0215301513671875,
0.0013608932495117188,
0.0023479461669921875,
-0.01309967041015625,
0.0080108642578125,
-0.0026836395263671875,
0.019866943359375,
-0.02679443359375,
-0.0018835067749023438,
-0.0260162353515625,
-0.0288238525390625,
0.02349853515625,
-0.01084136962890625,
-0.0078277587890625,
0.034942626953125,
0.00040340423583984375,
0.00389862060546875,
-0.0153350830078125,
-0.00003331899642944336,
0.021240234375,
0.0287017822265625,
-0.0061492919921875,
0.030517578125,
0.0079803466796875,
-0.010955810546875,
0.01910400390625,
0.007328033447265625,
-0.0061798095703125,
0.0443115234375,
-0.006862640380859375,
-0.0259857177734375,
0.01064300537109375,
0.0215911865234375,
-0.0236358642578125,
0.01226806640625,
0.0246429443359375,
0.0029163360595703125,
-0.014862060546875,
0.0013275146484375,
-0.0288238525390625,
-0.0189208984375,
0.0157012939453125,
-0.01134490966796875,
0.011810302734375,
-0.021697998046875,
0.00991058349609375,
0.01111602783203125,
0.01239776611328125,
0.0018749237060546875,
0.0194854736328125,
0.02276611328125,
-0.003032684326171875,
0.034698486328125,
0.004589080810546875,
-0.0167999267578125,
-0.01044464111328125,
-0.0081634521484375,
0.01708984375,
0.013580322265625,
-0.00304412841796875,
-0.00754547119140625,
-0.020965576171875,
0.0084991455078125,
0.018035888671875,
-0.026763916015625,
0.0165252685546875,
0.0120391845703125,
-0.0309906005859375,
-0.028289794921875,
0.0180816650390625,
-0.0019893646240234375,
0.01367950439453125,
0.041229248046875,
-0.01290130615234375,
0.01532745361328125,
-0.0005846023559570312,
0.0014066696166992188,
0.0252685546875,
-0.0113677978515625,
0.0335693359375,
0.00421905517578125,
-0.0204925537109375,
0.002223968505859375,
0.0293731689453125,
0.00786590576171875,
0.01141357421875,
0.0135345458984375,
0.01025390625,
-0.011993408203125,
-0.0160980224609375,
0.01605224609375,
0.0136566162109375,
0.024169921875,
-0.0036067962646484375,
-0.01508331298828125,
-0.00963592529296875,
0.0294952392578125,
0.003856658935546875,
-0.0140533447265625,
-0.040283203125,
-0.012542724609375,
-0.026214599609375,
-0.02276611328125,
0.01430511474609375,
0.0077972412109375,
-0.001331329345703125,
-0.002765655517578125,
0.018280029296875,
0.0242767333984375,
-0.005950927734375,
-0.03265380859375,
-0.016937255859375,
0.0011615753173828125,
-0.0038814544677734375,
0.005329132080078125,
0.004852294921875,
-0.0330810546875,
-0.00011396408081054688,
-0.01300048828125,
0.00560760498046875,
0.017181396484375,
-0.0236053466796875,
0.012939453125,
-0.017730712890625,
0.0135498046875,
0.034698486328125,
0.005535125732421875,
-0.0008535385131835938,
-0.0264892578125,
0.046051025390625,
-0.01499176025390625,
-0.0302581787109375,
0.01617431640625,
-0.004894256591796875,
0.0182342529296875,
0.00653076171875,
-0.0106201171875,
0.005405426025390625,
-0.01384735107421875,
-0.024261474609375,
0.046844482421875,
0.007411956787109375,
0.002593994140625,
-0.022430419921875,
0.0772705078125,
0.0021266937255859375,
-0.0313720703125,
-0.00341033935546875,
0.046661376953125,
0.02001953125,
0.01496124267578125,
0.0234527587890625,
-0.0011157989501953125,
-0.0201568603515625,
-0.001171112060546875,
-0.0085906982421875,
-0.019683837890625,
0.0094757080078125,
-0.01190948486328125,
0.021636962890625,
-0.0011606216430664062,
-0.01174163818359375,
-0.04571533203125,
0.03125,
-0.0160064697265625,
-0.044097900390625,
0.01071929931640625,
-0.0031261444091796875,
-0.0012226104736328125,
0.007320404052734375,
-0.0101318359375,
0.01323699951171875,
-0.021759033203125,
0.002197265625,
-0.0173187255859375,
0.0188140869140625,
-0.01435089111328125,
0.0216217041015625,
0.015838623046875,
0.00702667236328125,
0.0028514862060546875,
-0.00984954833984375,
-0.0024166107177734375,
0.01153564453125,
0.01232147216796875,
-0.0270843505859375,
-0.005279541015625,
0.01161956787109375,
-0.00689697265625,
0.003589630126953125,
0.00038051605224609375,
0.0117034912109375,
-0.004497528076171875,
0.007450103759765625,
0.0210418701171875,
-0.0052642822265625,
-0.004222869873046875,
-0.010528564453125,
-0.0008416175842285156,
0.01434326171875,
-0.0121917724609375,
-0.02545166015625,
-0.0063323974609375,
0.0025691986083984375,
-0.0038166046142578125,
-0.0236663818359375,
-0.039337158203125,
-0.00021219253540039062,
-0.017059326171875,
-0.016021728515625,
-0.0037174224853515625,
-0.0312042236328125,
-0.0100555419921875,
0.0168304443359375,
0.0038509368896484375,
-0.034454345703125,
0.002777099609375,
-0.0248870849609375,
-0.0115203857421875,
-0.0164031982421875,
0.026123046875,
0.0149383544921875,
0.0012054443359375,
0.0161590576171875,
-0.01517486572265625,
0.01345062255859375,
-0.007099151611328125,
0.021392822265625,
0.019378662109375,
0.00527191162109375,
-0.0002999305725097656,
-0.04547119140625,
0.016326904296875,
0.005184173583984375,
-0.017913818359375,
-0.019256591796875,
-0.0035419464111328125,
-0.0027637481689453125,
0.027374267578125,
-0.0140380859375,
0.01358795166015625,
0.00695037841796875,
-0.0241241455078125,
-0.0156402587890625,
-0.06494140625,
0.00800323486328125,
-0.005924224853515625,
0.01322174072265625,
0.043548583984375,
-0.00968170166015625,
-0.02764892578125,
-0.00923919677734375,
0.003902435302734375,
-0.033233642578125,
0.043365478515625,
0.0291900634765625,
-0.00601959228515625,
-0.0210723876953125,
0.012664794921875,
-0.0201568603515625,
0.023040771484375,
0.01305389404296875,
-0.00130462646484375,
-0.0084228515625,
-0.016632080078125,
-0.0157012939453125,
0.020050048828125,
-0.0034923553466796875,
-0.0083465576171875,
-0.01311492919921875,
0.0144195556640625,
-0.003814697265625,
-0.027069091796875,
-0.0054779052734375,
-0.01116180419921875,
-0.03009033203125,
0.00542449951171875,
-0.015106201171875,
0.0211334228515625,
0.00989532470703125,
0.0021114349365234375,
0.0092010498046875,
0.01155853271484375,
-0.02301025390625,
0.03167724609375,
0.000476837158203125,
0.0172271728515625,
-0.01050567626953125,
0.01366424560546875,
-0.02203369140625,
0.005374908447265625,
-0.01166534423828125,
0.0257568359375,
-0.002422332763671875,
-0.0097503662109375,
0.00438690185546875,
-0.02984619140625,
-0.0005731582641601562,
-0.025604248046875,
0.0009851455688476562,
-0.03814697265625,
-0.0250091552734375,
0.02734375,
0.006435394287109375,
-0.008148193359375,
0.018798828125,
-0.02691650390625,
-0.0207366943359375,
0.0304412841796875,
0.047210693359375,
0.0010204315185546875,
-0.001125335693359375,
0.015869140625,
0.00984954833984375,
0.0147857666015625,
0.0272369384765625,
0.0147857666015625,
0.024017333984375,
-0.01129150390625,
0.011138916015625,
-0.0088958740234375,
0.0227203369140625,
0.013824462890625,
-0.005523681640625,
0.0103759765625,
-0.0022373199462890625,
-0.01483154296875,
-0.007053375244140625,
0.033538818359375,
0.01137542724609375,
-0.0002658367156982422,
0.00665283203125,
0.011138916015625,
-0.039306640625,
-0.00925445556640625,
0.01058197021484375,
0.024322509765625,
-0.0224609375,
-0.00897979736328125,
0.00559234619140625,
-0.0010852813720703125,
0.01497650146484375,
0.0218963623046875,
0.0005054473876953125,
-0.01678466796875,
0.0206146240234375,
-0.028594970703125,
0.0361328125,
0.03997802734375,
0.021392822265625,
-0.02630615234375,
-0.0049591064453125,
-0.00189208984375,
-0.01169586181640625,
-0.007808685302734375,
-0.00856781005859375,
-0.01081085205078125,
0.01384735107421875,
-0.0206146240234375,
0.022430419921875,
-0.007537841796875,
0.006107330322265625,
-0.0120086669921875,
0.024444580078125,
-0.007511138916015625,
0.004070281982421875,
0.0195159912109375,
-0.03497314453125,
0.0113067626953125,
0.01529693603515625,
-0.002750396728515625,
0.01216888427734375,
-0.00395965576171875,
-0.01418304443359375,
-0.037445068359375,
0.008941650390625,
0.02020263671875,
0.009124755859375,
0.0189666748046875,
0.0016736984252929688,
0.0233154296875,
0.0035457611083984375,
-0.007175445556640625,
0.021484375,
-0.01454925537109375,
-0.010772705078125,
-0.0196533203125,
0.0257415771484375,
0.0036525726318359375,
-0.0257720947265625,
0.00464630126953125,
-0.0019931793212890625,
0.0242462158203125,
-0.0081329345703125,
0.0313720703125,
0.0202484130859375,
0.0279083251953125,
-0.007320404052734375,
-0.0049285888671875,
0.037322998046875,
-0.0086517333984375,
0.05810546875,
0.021575927734375,
0.0132598876953125,
0.022674560546875,
-0.001781463623046875,
0.034881591796875,
-0.00867462158203125,
0.0227508544921875,
0.033966064453125,
-0.01123809814453125,
-0.003509521484375,
0.0228118896484375,
0.010894775390625,
0.00847625732421875,
0.0203094482421875,
0.0161285400390625,
0.047332763671875,
0.0027523040771484375,
-0.016815185546875,
0.01308441162109375,
0.032928466796875,
-0.0316162109375,
0.0259857177734375,
0.0177154541015625,
0.023712158203125,
0.034454345703125,
-0.023834228515625,
-0.031829833984375,
0.0128021240234375,
-0.0137176513671875,
0.0237884521484375,
0.00832366943359375,
-0.0185699462890625,
0.0076751708984375,
0.031494140625,
0.024261474609375,
0.002593994140625,
-0.0022640228271484375,
0.0003304481506347656,
-0.03240966796875,
-0.036102294921875,
0.007049560546875,
-0.001873016357421875,
0.00531768798828125,
0.005580902099609375,
0.0280914306640625,
0.0259857177734375,
0.0101318359375,
0.0160064697265625,
-0.0285186767578125,
-0.0167388916015625,
-0.0106353759765625,
0.0029392242431640625,
-0.02642822265625,
-0.007015228271484375,
-0.016998291015625,
-0.004390716552734375,
0.0225677490234375,
-0.0245208740234375,
0.021820068359375,
0.01194000244140625,
0.0030193328857421875,
-0.019378662109375,
-0.004398345947265625,
-0.0247650146484375,
0.00231170654296875,
0.0308990478515625,
-0.002471923828125,
-0.026092529296875,
0.04156494140625,
-0.005283355712890625,
0.0146331787109375,
0.01381683349609375,
0.0168609619140625,
0.0014390945434570312,
0.0280914306640625,
-0.00406646728515625,
0.0211029052734375,
0.0116729736328125,
-0.0007109642028808594,
0.0135498046875,
-0.01433563232421875,
0.02655029296875,
0.0202178955078125,
0.006839752197265625,
-0.0276031494140625,
-0.0264434814453125,
-0.042510986328125,
-0.0017309188842773438,
0.005008697509765625,
0.028350830078125,
-0.001346588134765625,
0.026641845703125,
0.0164031982421875,
-0.0318603515625,
-0.0285797119140625,
0.009033203125,
0.0162200927734375,
-0.016754150390625,
0.027587890625,
0.004119873046875,
0.0323486328125,
-0.041412353515625,
-0.01116180419921875,
0.01016998291015625,
-0.01334381103515625,
-0.02008056640625,
0.0005464553833007812,
0.0174713134765625,
0.0239105224609375,
0.0246734619140625,
0.01018524169921875,
0.012786865234375,
-0.00881195068359375,
-0.0052337646484375,
-0.001689910888671875,
0.0271759033203125,
0.008514404296875,
0.0289459228515625,
0.057525634765625,
-0.0120849609375,
-0.0164947509765625,
-0.004123687744140625,
-0.02301025390625,
-0.0087890625,
-0.00229644775390625,
0.0172576904296875,
-0.01328277587890625,
-0.0202789306640625,
-0.0025348663330078125,
-0.0005259513854980469,
0.019927978515625,
0.00675201416015625,
-0.0204010009765625,
-0.030975341796875,
0.0242462158203125,
-0.0170745849609375,
-0.0059814453125,
0.014373779296875,
-0.0009560585021972656,
0.010833740234375,
-0.007476806640625,
0.0035724639892578125,
-0.00952911376953125,
-0.0153350830078125,
-0.0165557861328125,
0.01004791259765625,
-0.0194854736328125,
-0.0242767333984375,
-0.01873779296875,
-0.0037364959716796875,
-0.044189453125,
0.003093719482421875,
0.0061798095703125,
0.01031494140625,
0.0041046142578125,
0.0308837890625,
-0.005977630615234375,
0.01418304443359375,
-0.0030670166015625,
0.01462554931640625,
-0.0455322265625,
-0.01114654541015625,
0.009033203125,
0.018035888671875,
0.01308441162109375,
0.0019817352294921875,
-0.0008578300476074219,
0.0026702880859375,
0.0236358642578125,
0.0032024383544921875,
-0.0151214599609375,
-0.006931304931640625,
-0.0008001327514648438,
-0.0265045166015625,
-0.01061248779296875,
0.016693115234375,
-0.01558685302734375,
-0.0026073455810546875,
-0.024444580078125,
-0.00933074951171875,
0.0205841064453125,
0.016357421875,
-0.0180511474609375,
0.0232391357421875,
-0.009033203125,
0.015655517578125,
0.0037403106689453125,
-0.0220489501953125,
0.00011169910430908203,
-0.024810791015625,
0.0234527587890625,
-0.00786590576171875,
0.02825927734375,
0.05419921875,
-0.00015151500701904297,
-0.033355712890625,
-0.01324462890625,
-0.006374359130859375,
-0.01369476318359375,
0.00730133056640625,
-0.0221405029296875,
-0.015411376953125,
0.01303863525390625,
0.00989532470703125,
-0.0116424560546875,
0.009552001953125,
-0.006927490234375,
-0.00846099853515625,
-0.0046234130859375,
-0.0023517608642578125,
-0.028533935546875,
0.0153656005859375,
0.01494598388671875,
-0.04052734375,
-0.01464080810546875,
-0.00782012939453125,
0.0157623291015625,
0.0033779144287109375,
0.002349853515625,
-0.0304107666015625,
-0.0066680908203125,
-0.00595855712890625,
-0.0006647109985351562,
-0.007568359375,
0.018096923828125,
0.039215087890625,
-0.0123291015625,
-0.00543975830078125,
0.0092620849609375,
-0.040252685546875,
-0.000453948974609375,
-0.0148773193359375,
-0.0084075927734375,
-0.0269622802734375,
0.008392333984375,
0.0081024169921875,
-0.00128173828125,
-0.006175994873046875,
-0.019561767578125,
0.018035888671875,
0.019134521484375,
-0.0005006790161132812,
-0.017303466796875,
-0.031890869140625,
0.019012451171875,
-0.0210723876953125,
-0.04083251953125,
-0.0018253326416015625,
0.01151275634765625,
-0.01410675048828125,
-0.01039886474609375,
-0.016204833984375,
-0.0163116455078125,
0.0012617111206054688,
0.0064849853515625,
0.01389312744140625,
-0.016815185546875,
0.03387451171875,
-0.00594329833984375,
0.0013017654418945312,
0.00585174560546875,
-0.016876220703125,
0.0231170654296875,
0.006443023681640625,
0.0244903564453125,
-0.002838134765625,
-0.0002942085266113281,
-0.015228271484375,
0.0079803466796875,
0.0218963623046875,
0.01861572265625,
-0.002254486083984375,
0.005741119384765625,
-0.004169464111328125,
-0.01027679443359375,
0.01119232177734375,
-0.003337860107421875,
-0.0261688232421875,
0.019805908203125,
0.00861358642578125,
0.009307861328125,
0.0135650634765625,
-0.0335693359375,
0.00746917724609375,
-0.0037288665771484375,
0.0297698974609375,
-0.00820159912109375,
0.002712249755859375,
-0.007801055908203125,
-0.031585693359375,
-0.040985107421875,
-0.00859832763671875,
-0.0230712890625,
-0.0187530517578125,
-0.012115478515625,
-0.0227203369140625,
-0.0396728515625,
0.034912109375,
0.016204833984375,
0.0606689453125,
-0.02630615234375,
-0.015472412109375,
-0.0140533447265625,
-0.032806396484375,
0.0240478515625,
-0.00392913818359375,
-0.02734375,
0.0160369873046875,
0.015838623046875,
-0.007572174072265625,
0.00563812255859375,
-0.02362060546875,
0.00959014892578125,
0.0220947265625,
0.005290985107421875,
-0.03326416015625,
-0.010467529296875,
0.027984619140625,
-0.0244903564453125,
0.0006661415100097656,
0.0088958740234375,
-0.0190887451171875,
-0.002223968505859375,
-0.020904541015625,
-0.0012826919555664062,
0.026519775390625,
-0.020294189453125,
-0.01445770263671875,
0.0026721954345703125,
0.007175445556640625,
-0.011810302734375,
0.0016126632690429688,
-0.01447296142578125,
-0.01001739501953125,
-0.01806640625,
-0.0119781494140625,
-0.0017213821411132812,
0.00823974609375,
-0.00988006591796875,
-0.005840301513671875,
-0.00592803955078125,
0.03192138671875,
-0.00157928466796875,
0.00884246826171875,
-0.015716552734375,
-0.0033092498779296875,
-0.0015134811401367188,
-0.002017974853515625,
-0.01435089111328125,
-0.031341552734375,
-0.017364501953125,
0.004100799560546875,
0.016632080078125,
0.047882080078125,
-0.00798797607421875,
0.056365966796875,
0.0229949951171875,
0.0045166015625,
-0.0205535888671875,
0.0239410400390625,
0.01410675048828125,
-0.032012939453125,
-0.01947021484375,
0.0006866455078125,
0.0029544830322265625,
-0.00848388671875,
0.0251922607421875,
-0.0102691650390625,
0.01142120361328125,
-0.00806427001953125,
-0.0433349609375,
-0.006465911865234375,
0.00601959228515625,
0.01366424560546875,
-0.0109710693359375,
0.0129547119140625,
-0.0069122314453125,
0.002254486083984375,
0.0113983154296875,
-0.01043701171875,
0.0108184814453125,
-0.0108642578125,
-0.01432037353515625,
-0.0007534027099609375,
0.0278778076171875,
0.0028285980224609375,
0.007415771484375,
-0.0237884521484375,
0.002216339111328125,
0.00453948974609375,
0.004474639892578125,
-0.019927978515625,
-0.0022182464599609375,
-0.0197296142578125,
0.00444793701171875,
0.00457763671875,
0.00738525390625,
0.0377197265625,
-0.001720428466796875,
-0.0265655517578125,
-0.0022335052490234375,
0.0205535888671875,
0.0316162109375,
-0.0333251953125,
0.025115966796875,
-0.03070068359375,
-0.0145721435546875,
0.0295257568359375,
0.0011539459228515625,
0.0034542083740234375,
0.0222625732421875,
-0.001964569091796875,
0.019256591796875,
0.0021610260009765625,
0.0247344970703125,
-0.0222015380859375,
0.0010938644409179688,
-0.004852294921875,
0.020904541015625,
-0.0009822845458984375,
-0.00959014892578125,
-0.0025768280029296875,
0.020294189453125,
0.013763427734375,
0.019775390625,
-0.0115966796875,
0.014434814453125,
0.0012359619140625,
-0.009368896484375,
-0.0007905960083007812,
-0.00942230224609375,
0.025482177734375,
0.0167236328125,
0.004436492919921875,
-0.0184478759765625,
-0.001125335693359375,
0.00933074951171875,
0.03173828125,
-0.0054931640625,
0.01313018798828125,
-0.017333984375,
-0.0014190673828125,
-0.006237030029296875,
0.018310546875,
0.01544189453125,
-0.004161834716796875,
0.0269775390625,
0.0294342041015625,
-0.0306396484375,
-0.0016422271728515625,
0.0177001953125,
-0.0088653564453125,
-0.048828125,
-0.0142059326171875,
-0.0126953125,
0.000705718994140625,
0.0239105224609375,
-0.006893157958984375,
0.0154876708984375,
0.0325927734375,
-0.00598907470703125,
-0.0005321502685546875,
0.0146636962890625,
-0.006717681884765625,
0.03228759765625,
0.0059661865234375,
0.01267242431640625,
0.020751953125,
-0.023651123046875,
0.004299163818359375,
-0.0167388916015625,
0.00699615478515625,
-0.03973388671875,
-0.03448486328125,
-0.021484375,
0.0231475830078125,
0.0026092529296875,
-0.00135040283203125,
0.0136566162109375,
0.01395416259765625,
0.0266876220703125,
-0.005130767822265625,
0.00063323974609375,
0.0245361328125,
0.007587432861328125,
-0.0104217529296875,
0.0200042724609375,
0.0112762451171875,
-0.006214141845703125,
-0.0284423828125,
0.00946044921875,
-0.00502777099609375,
0.01502227783203125,
0.0044403076171875,
0.016265869140625,
0.01389312744140625,
-0.0010280609130859375,
0.0020580291748046875,
-0.00972747802734375,
-0.00856781005859375,
0.0176849365234375,
0.0250396728515625,
0.003177642822265625,
0.0196990966796875,
-0.0238037109375,
-0.022735595703125,
-0.0191192626953125,
0.003070831298828125,
0.00682830810546875,
-0.01031494140625,
-0.0006170272827148438,
-0.0185394287109375,
-0.017486572265625,
0.00830841064453125,
0.0092926025390625,
-0.0233612060546875,
-0.015045166015625,
-0.0141754150390625,
0.0467529296875,
-0.02606201171875,
-0.006229400634765625,
0.024200439453125,
-0.0145263671875,
-0.0094757080078125,
0.007511138916015625,
0.0120849609375,
0.0203094482421875,
0.0020961761474609375,
0.0245513916015625,
0.00177001953125,
-0.00868988037109375,
-0.0152587890625,
0.01445770263671875,
0.012359619140625,
-0.0169525146484375,
-0.006824493408203125,
0.034912109375,
-0.01033782958984375,
0.02593994140625,
0.002254486083984375,
-0.0014009475708007812,
-0.01013946533203125,
-0.0035572052001953125,
-0.05712890625,
-0.00274658203125,
0.005096435546875,
0.003818511962890625,
0.00823211669921875,
-0.01314544677734375,
-0.0245361328125,
0.007610321044921875,
0.00603485107421875,
0.0015287399291992188,
-0.0211334228515625,
-0.00942230224609375,
0.0229339599609375,
-0.0017671585083007812,
0.0009169578552246094,
0.0256500244140625,
0.0271759033203125,
-0.01152801513671875,
0.01119232177734375,
-0.0257720947265625,
0.006168365478515625,
-0.01800537109375,
0.0020542144775390625,
0.012420654296875,
0.0025577545166015625,
0.00872039794921875,
0.006626129150390625,
0.031890869140625,
0.004009246826171875,
-0.037567138671875,
-0.015838623046875,
0.00508880615234375,
0.01116180419921875,
0.002727508544921875,
0.01007080078125,
0.0182037353515625,
-0.0013341903686523438,
-0.037628173828125,
0.00955963134765625,
0.033843994140625,
0.002330780029296875,
-0.01267242431640625,
0.00783538818359375,
-0.00634765625,
-0.0046539306640625,
0.01409149169921875,
0.0004401206970214844,
0.01071929931640625,
-0.0155792236328125,
0.0271453857421875,
0.020050048828125,
-0.0149383544921875,
0.0029850006103515625,
-0.003086090087890625,
-0.00395965576171875,
0.032379150390625,
0.02447509765625,
0.0179443359375,
-0.0144195556640625,
-0.03851318359375,
0.01678466796875,
0.044891357421875,
-0.006031036376953125,
0.01543426513671875,
0.01227569580078125,
0.0002696514129638672,
-0.0088653564453125,
0.0160675048828125,
0.00007683038711547852,
0.0084686279296875,
-0.003742218017578125,
0.0161590576171875,
0.015380859375,
0.00023472309112548828,
-0.0296630859375,
0.0252838134765625,
0.01331329345703125,
0.0274658203125,
-0.010162353515625,
-0.009124755859375,
0.004673004150390625,
-0.0246734619140625,
0.0023345947265625,
0.015655517578125,
0.0128326416015625,
0.0018987655639648438,
-0.017974853515625,
-0.021942138671875,
0.010833740234375,
-0.018035888671875,
0.020233154296875,
0.0006117820739746094,
0.0282745361328125,
-0.0233306884765625,
0.007106781005859375,
-0.0186920166015625,
0.0163116455078125,
-0.014251708984375,
0.00446319580078125,
-0.013153076171875,
0.011810302734375,
0.03082275390625,
0.006053924560546875,
-0.060394287109375,
0.0199432373046875,
0.00025725364685058594,
0.01425933837890625,
-0.001865386962890625,
-0.0130767822265625,
0.0178070068359375,
0.0014028549194335938,
0.006366729736328125,
-0.01125335693359375,
0.0027942657470703125,
-0.0015430450439453125,
0.00774383544921875,
0.0028839111328125,
-0.010772705078125,
0.0057373046875,
0.005458831787109375,
-0.0011911392211914062,
-0.0171661376953125,
-0.032470703125,
0.00580596923828125,
-0.01468658447265625,
0.00452423095703125,
-0.0004949569702148438,
0.033477783203125,
0.00470733642578125,
0.001861572265625,
0.0017023086547851562,
0.006511688232421875,
0.01416015625,
-0.050689697265625,
0.025634765625,
0.032012939453125,
-0.0020618438720703125,
-0.0239105224609375,
0.0117340087890625,
0.0545654296875,
0.01224517822265625,
0.0183258056640625,
0.017791748046875,
-0.03857421875,
-0.040740966796875,
-0.032928466796875,
-0.0031642913818359375,
0.0048675537109375,
0.04638671875,
-0.0017223358154296875,
-0.01560211181640625,
0.01192474365234375,
-0.0089111328125,
-0.02728271484375,
-0.0185089111328125,
-0.0258941650390625,
0.0257720947265625,
0.003993988037109375,
0.013458251953125,
0.0175628662109375,
0.00220489501953125,
-0.005451202392578125,
-0.02117919921875,
-0.01181793212890625,
0.01763916015625,
-0.0016450881958007812,
0.006359100341796875,
0.017120361328125,
-0.056060791015625,
0.005832672119140625,
0.0011539459228515625,
-0.00661468505859375,
0.0020503997802734375,
-0.0298309326171875,
0.002105712890625,
0.0019588470458984375,
-0.035888671875,
0.02618408203125,
0.01059722900390625,
0.0024509429931640625,
-0.0280609130859375,
0.00731658935546875,
-0.0274810791015625,
-0.00974273681640625,
-0.0257568359375,
-0.0374755859375,
0.02520751953125,
0.0189056396484375,
0.0072784423828125,
-0.01361846923828125,
-0.0225677490234375,
-0.0164947509765625,
0.02154541015625,
-0.00461578369140625,
0.0028057098388671875,
0.0020427703857421875,
0.0081634521484375,
0.0225372314453125,
-0.0019683837890625,
-0.004856109619140625,
0.0172271728515625,
0.0229339599609375,
0.033721923828125,
-0.03887939453125,
-0.0095062255859375,
0.024383544921875,
-0.0182342529296875,
-0.007396697998046875,
0.026275634765625,
0.022003173828125,
-0.01309967041015625,
0.00360870361328125,
-0.004985809326171875,
0.0018157958984375,
0.005645751953125,
0.0357666015625,
-0.0206298828125,
0.007625579833984375,
-0.0015430450439453125,
0.00951385498046875,
0.0133514404296875,
-0.0419921875,
-0.0067596435546875,
0.006381988525390625,
-0.0035076141357421875,
-0.03204345703125,
-0.006969451904296875,
0.0019121170043945312,
0.0221710205078125,
0.0012845993041992188,
0.0077667236328125,
-0.0176239013671875,
-0.00626373291015625,
0.0196075439453125,
-0.0150909423828125,
-0.0054473876953125,
0.01329803466796875,
0.003559112548828125,
0.01515960693359375,
0.0109100341796875,
0.00714874267578125,
-0.01898193359375,
-0.00638580322265625,
-0.042205810546875,
0.038482666015625,
-0.0085296630859375,
0.029815673828125,
0.01241302490234375,
-0.002407073974609375,
0.0029449462890625,
0.0295867919921875,
-0.014495849609375,
-0.00968170166015625,
-0.01169586181640625,
0.00006407499313354492,
-0.0036754608154296875,
-0.01238250732421875,
-0.01433563232421875,
0.004146575927734375,
0.011260986328125,
-0.04705810546875,
-0.0117034912109375,
-0.0030422210693359375,
0.04766845703125,
0.012786865234375,
-0.0226898193359375,
-0.0037822723388671875,
-0.01313018798828125,
-0.007328033447265625,
-0.01270294189453125,
0.016021728515625,
0.04986572265625,
-0.0186004638671875,
0.0268707275390625,
-0.0175018310546875,
0.057159423828125,
0.017242431640625,
-0.03662109375,
0.0225372314453125,
0.0225830078125,
-0.0230255126953125,
0.007518768310546875,
-0.008819580078125,
-0.0203094482421875,
0.007274627685546875,
-0.01495361328125,
-0.0263519287109375,
-0.00007015466690063477,
0.0140838623046875,
0.0003116130828857422,
-0.0091094970703125,
0.0014476776123046875,
0.01320648193359375,
-0.004825592041015625,
-0.0031032562255859375,
-0.016204833984375,
0.015472412109375,
-0.010528564453125,
-0.0031280517578125,
0.03955078125,
0.0292205810546875,
0.04052734375,
-0.0185089111328125,
0.0033817291259765625,
-0.00521087646484375,
-0.029144287109375,
0.0124664306640625,
-0.022430419921875,
0.0007686614990234375,
-0.00943756103515625,
0.02447509765625,
0.0218505859375,
0.01325225830078125,
-0.05169677734375,
-0.0036640167236328125,
0.0167694091796875,
0.0097503662109375,
0.0013408660888671875,
-0.0180511474609375,
-0.013427734375,
0.046112060546875,
-0.01091766357421875,
-0.00043964385986328125,
-0.01148223876953125,
-0.028106689453125,
-0.02899169921875,
0.027252197265625,
0.024932861328125,
-0.035125732421875,
0.0007524490356445312,
-0.048431396484375,
0.00420379638671875,
-0.00461578369140625,
0.0086822509765625,
-0.0033702850341796875,
-0.056427001953125,
-0.004974365234375,
-0.0191650390625,
0.0203704833984375,
0.0030498504638671875,
0.00800323486328125,
0.0010509490966796875,
0.015533447265625,
-0.0019378662109375,
-0.038421630859375,
0.0088348388671875,
-0.00630950927734375,
0.008453369140625,
0.0028285980224609375,
0.007328033447265625,
0.01910400390625,
-0.030181884765625,
-0.005939483642578125,
-0.004154205322265625,
-0.002880096435546875,
0.0006089210510253906,
0.0215911865234375,
-0.00464630126953125,
0.0207672119140625,
-0.00567626953125,
-0.006542205810546875,
0.004039764404296875,
0.00412750244140625,
-0.0208282470703125,
-0.01580810546875,
-0.007602691650390625,
-0.0094757080078125,
0.0096435546875,
-0.0002396106719970703,
-0.01397705078125,
0.06451416015625,
-0.02392578125,
0.002201080322265625,
-0.0016326904296875,
0.023590087890625,
-0.008544921875,
-0.005077362060546875,
0.01274871826171875,
0.0017910003662109375,
-0.017822265625,
-0.00492095947265625,
0.021759033203125,
-0.020111083984375,
-0.0212554931640625,
-0.020416259765625,
0.01210784912109375,
-0.018157958984375,
0.049468994140625,
-0.00598907470703125,
-0.0005950927734375,
0.033538818359375,
0.01015472412109375,
0.041290283203125,
0.00020134449005126953,
-0.0037784576416015625,
0.0027370452880859375,
0.026214599609375,
-0.019927978515625,
-0.0167694091796875
] |
ours_546
|
The solid's surface area consists of 5 unit squares and 4 isosceles triangles. The base of each triangle is 1, and the height is \(\sqrt{(1/2)^2 + 1^2} = \sqrt{5}/2\). Therefore, the area of each triangle is \(\sqrt{5}/4\), and for 4 triangles, the total area of the triangles is \(\sqrt{5}\). The total surface area is \(5 + \sqrt{5}\), so \(a + b = 10\).
\(\boxed{10}\)
|
10
|
{
"competition": "us_comps",
"dataset": "Ours",
"posts": null,
"source": "OMOSoln2.md"
}
|
Let \( A_{1} B_{1} C_{1} D_{1} A_{2} B_{2} C_{2} D_{2} \) be a unit cube, with \( A_{1} B_{1} C_{1} D_{1} \) and \( A_{2} B_{2} C_{2} D_{2} \) opposite square faces, and let \( M \) be the center of face \( A_{2} B_{2} C_{2} D_{2} \). Rectangular pyramid \( M A_{1} B_{1} C_{1} D_{1} \) is cut out of the cube. If the surface area of the remaining solid can be expressed in the form \( a+\sqrt{b} \), where \( a \) and \( b \) are positive integers and \( b \) is not divisible by the square of any prime, find \( a+b \).
|
[
"/Mathematics/Geometry/MultidimensionalGeometry/Polytopes/Hypercube",
"/Mathematics/Geometry/MultidimensionalGeometry/Polytopes/Orthotope",
"/Mathematics/Geometry/MultidimensionalGeometry/Polytopes/Parallelotope",
"/Mathematics/Geometry/SolidGeometry/GeneralSolidGeometry/SlantHeight",
"/Mathematics/Geometry/SolidGeometry/GeneralSolidGeometry/Solid",
"/Mathematics/Geometry/SolidGeometry/GeneralSolidGeometry/SolidGeometry",
"/Mathematics/Geometry/SolidGeometry/Polyhedra/Cubes",
"/Mathematics/Geometry/SolidGeometry/Polyhedra/Pyramids",
"/Mathematics/Geometry/Surfaces/SurfaceProperties"
] |
Identify the four congruent triangular faces created by the cut and use the Pythagorean theorem to find their height for area calculation.
|
[
0.00011599063873291016,
-0.0242156982421875,
0.006687164306640625,
-0.0198974609375,
0.0005388259887695312,
-0.00467681884765625,
-0.024566650390625,
-0.0301055908203125,
0.011322021484375,
-0.01264190673828125,
-0.04931640625,
-0.00009649991989135742,
-0.002826690673828125,
0.03863525390625,
0.00803375244140625,
-0.01462554931640625,
0.0081787109375,
-0.00867462158203125,
0.03021240234375,
-0.0026531219482421875,
-0.0240478515625,
-0.0016393661499023438,
-0.035491943359375,
0.0006995201110839844,
0.01465606689453125,
-0.04547119140625,
-0.01534271240234375,
-0.0014286041259765625,
0.00611114501953125,
-0.0439453125,
-0.041900634765625,
-0.034332275390625,
0.08502197265625,
-0.0157318115234375,
-0.0005521774291992188,
-0.02130126953125,
0.04901123046875,
-0.0012531280517578125,
-0.0209197998046875,
-0.05133056640625,
0.005168914794921875,
-0.0136260986328125,
0.00243377685546875,
-0.0115509033203125,
0.0284423828125,
0.0157318115234375,
-0.0036792755126953125,
-0.02783203125,
0.006591796875,
-0.005603790283203125,
-0.0032672882080078125,
0.014312744140625,
0.005977630615234375,
-0.0111846923828125,
-0.0237274169921875,
-0.0264739990234375,
-0.026885986328125,
0.003246307373046875,
-0.0028934478759765625,
-0.0211181640625,
-0.01116180419921875,
0.0020923614501953125,
-0.0072784423828125,
-0.0238800048828125,
-0.00084686279296875,
-0.01436614990234375,
0.03179931640625,
-0.0271148681640625,
0.0005464553833007812,
0.004528045654296875,
0.046539306640625,
-0.00518798828125,
0.011871337890625,
0.006763458251953125,
0.0029201507568359375,
-0.01207733154296875,
-0.0012006759643554688,
-0.0013790130615234375,
-0.0006542205810546875,
-0.003925323486328125,
0.0122833251953125,
-0.021575927734375,
-0.0067291259765625,
-0.028961181640625,
0.01158905029296875,
-0.0025424957275390625,
0.00656890869140625,
0.007099151611328125,
0.0657958984375,
-0.0399169921875,
0.00144195556640625,
0.0149993896484375,
0.00830078125,
-0.004650115966796875,
0.0132293701171875,
0.0027027130126953125,
0.0226287841796875,
0.00337982177734375,
0.0005974769592285156,
0.005588531494140625,
-0.015472412109375,
-0.0053558349609375,
0.00630950927734375,
-0.002262115478515625,
0.0013427734375,
-0.0006184577941894531,
-0.01081085205078125,
-0.003490447998046875,
0.00762176513671875,
0.0169219970703125,
-0.0032958984375,
0.00635528564453125,
-0.021209716796875,
0.005825042724609375,
-0.00026988983154296875,
-0.00582122802734375,
0.0243072509765625,
0.0347900390625,
0.00872802734375,
0.0204620361328125,
-0.004001617431640625,
0.0012483596801757812,
0.0172119140625,
0.02520751953125,
-0.0116729736328125,
-0.005596160888671875,
-0.0017833709716796875,
-0.02886962890625,
-0.01557159423828125,
0.004878997802734375,
-0.016632080078125,
0.00554656982421875,
-0.0095062255859375,
-0.0117340087890625,
-0.0321044921875,
0.02001953125,
0.00031375885009765625,
-0.0161590576171875,
0.01525115966796875,
-0.0251922607421875,
0.01113128662109375,
-0.00722503662109375,
-0.0105438232421875,
-0.034393310546875,
0.0210113525390625,
-0.00431060791015625,
0.0166778564453125,
-0.04168701171875,
0.0179595947265625,
0.0035839080810546875,
0.01055145263671875,
0.002223968505859375,
0.013946533203125,
0.0113983154296875,
-0.0237579345703125,
0.00017178058624267578,
-0.0018720626831054688,
0.013397216796875,
0.005016326904296875,
0.0052337646484375,
0.00945281982421875,
0.0027942657470703125,
-0.015472412109375,
0.035980224609375,
0.008026123046875,
-0.0024890899658203125,
0.004520416259765625,
0.0198516845703125,
-0.0015583038330078125,
0.00846099853515625,
0.016143798828125,
-0.003147125244140625,
-0.0017118453979492188,
-0.01061248779296875,
-0.01568603515625,
-0.002071380615234375,
-0.00792694091796875,
-0.0055999755859375,
0.00240325927734375,
0.00896453857421875,
0.006801605224609375,
-0.005336761474609375,
0.025634765625,
-0.01461029052734375,
0.026580810546875,
-0.0106658935546875,
0.012725830078125,
-0.00360107421875,
0.029571533203125,
0.013214111328125,
-0.014251708984375,
-0.01116943359375,
-0.01239013671875,
0.00592041015625,
-0.04754638671875,
-0.019287109375,
-0.0230865478515625,
-0.016845703125,
0.01416778564453125,
0.020660400390625,
0.0072784423828125,
-0.0035572052001953125,
0.04815673828125,
0.0185394287109375,
0.030792236328125,
-0.00363922119140625,
0.002651214599609375,
-0.003070831298828125,
-0.005512237548828125,
-0.00457000732421875,
0.00356292724609375,
-0.0086669921875,
-0.004913330078125,
-0.00861358642578125,
-0.0101776123046875,
-0.0020923614501953125,
-0.009765625,
-0.0013761520385742188,
0.006275177001953125,
0.0140380859375,
0.006809234619140625,
0.0034637451171875,
0.00025272369384765625,
-0.006107330322265625,
-0.00862884521484375,
-0.007080078125,
-0.003223419189453125,
-0.0036869049072265625,
-0.003948211669921875,
-0.0048675537109375,
0.0054473876953125,
0.0015811920166015625,
-0.004703521728515625,
-0.0164947509765625,
-0.00461578369140625,
-0.00009763240814208984,
-0.085693359375,
-0.01186370849609375,
-0.006206512451171875,
-0.029510498046875,
0.00714111328125,
-0.029632568359375,
0.00852203369140625,
0.00215911865234375,
0.005550384521484375,
0.000022113323211669922,
0.0171356201171875,
0.020538330078125,
-0.0020122528076171875,
0.004177093505859375,
0.0141143798828125,
-0.0002720355987548828,
-0.0169525146484375,
-0.0186920166015625,
-0.05462646484375,
-0.004573822021484375,
-0.001987457275390625,
-0.0037364959716796875,
-0.01410675048828125,
-0.0071258544921875,
0.0009407997131347656,
0.018798828125,
-0.004215240478515625,
-0.0018062591552734375,
-0.01580810546875,
-0.04010009765625,
0.0033550262451171875,
0.0020236968994140625,
0.007442474365234375,
-0.01337432861328125,
-0.0191802978515625,
-0.01507568359375,
-0.00598907470703125,
0.0014543533325195312,
-0.0165557861328125,
-0.0233306884765625,
-0.00617218017578125,
0.0276947021484375,
-0.0006928443908691406,
0.00823974609375,
-0.036468505859375,
-0.00177001953125,
-0.0284881591796875,
0.0181884765625,
-0.0025119781494140625,
0.0237579345703125,
0.040771484375,
-0.01873779296875,
0.00701141357421875,
0.0215301513671875,
0.007755279541015625,
0.01263427734375,
-0.00252532958984375,
-0.004405975341796875,
0.02923583984375,
-0.029083251953125,
0.00469970703125,
-0.01067352294921875,
0.006183624267578125,
-0.0174560546875,
0.017425537109375,
-0.00141143798828125,
-0.017913818359375,
0.008636474609375,
0.0226593017578125,
0.007099151611328125,
-0.00023066997528076172,
0.0076751708984375,
0.0284271240234375,
0.005489349365234375,
0.0102996826171875,
0.00571441650390625,
0.0027637481689453125,
-0.0006432533264160156,
-0.046600341796875,
-0.06597900390625,
-0.006443023681640625,
0.0025272369384765625,
-0.006183624267578125,
-0.0213470458984375,
-0.01401519775390625,
-0.007781982421875,
-0.025390625,
0.0185089111328125,
0.019439697265625,
-0.03173828125,
0.018218994140625,
0.00762176513671875,
0.01284027099609375,
0.0011444091796875,
-0.00791168212890625,
0.01348114013671875,
0.0158538818359375,
0.01314544677734375,
-0.00989532470703125,
0.0218353271484375,
-0.01123809814453125,
0.01181793212890625,
-0.02154541015625,
0.0012617111206054688,
-0.01123809814453125,
0.006320953369140625,
0.006450653076171875,
-0.0272064208984375,
0.0231781005859375,
0.0287628173828125,
0.056488037109375,
-0.0028667449951171875,
-0.01197052001953125,
0.0028820037841796875,
-0.01267242431640625,
-0.029144287109375,
0.00304412841796875,
0.019012451171875,
-0.01003265380859375,
0.020782470703125,
0.0199737548828125,
0.0177764892578125,
-0.03057861328125,
0.05218505859375,
0.01678466796875,
-0.0305023193359375,
-0.0013647079467773438,
0.008270263671875,
0.01045989990234375,
0.002521514892578125,
0.0008778572082519531,
0.003940582275390625,
-0.0121612548828125,
0.00562286376953125,
-0.005634307861328125,
0.0130157470703125,
-0.0040283203125,
0.00777435302734375,
0.0280914306640625,
0.0217132568359375,
-0.006927490234375,
0.0006632804870605469,
0.0007390975952148438,
0.00018584728240966797,
-0.00827789306640625,
0.0099945068359375,
-0.010101318359375,
0.0220489501953125,
-0.0128173828125,
0.0035762786865234375,
-0.01143646240234375,
-0.018707275390625,
-0.01456451416015625,
0.00885009765625,
0.00859832763671875,
-0.0161590576171875,
-0.013427734375,
-0.01491546630859375,
-0.03619384765625,
-0.0301971435546875,
-0.00351715087890625,
0.00821685791015625,
0.00629425048828125,
-0.0060577392578125,
-0.0489501953125,
-0.0190582275390625,
0.003437042236328125,
-0.037994384765625,
-0.01544189453125,
0.0003490447998046875,
-0.0006437301635742188,
0.0282440185546875,
-0.035491943359375,
0.006999969482421875,
-0.0016832351684570312,
-0.00893402099609375,
0.020721435546875,
-0.001369476318359375,
-0.03045654296875,
-0.01026153564453125,
0.00960540771484375,
-0.0029449462890625,
-0.01580810546875,
0.0203704833984375,
0.02105712890625,
-0.01128387451171875,
0.00687408447265625,
0.019775390625,
0.03759765625,
0.019134521484375,
-0.0106353759765625,
0.01520538330078125,
-0.019744873046875,
0.00513458251953125,
-0.0011882781982421875,
0.016845703125,
-0.007259368896484375,
0.057525634765625,
-0.0247039794921875,
-0.006855010986328125,
0.0035114288330078125,
0.0013589859008789062,
0.00533294677734375,
0.0017185211181640625,
-0.0172882080078125,
-0.0179595947265625,
-0.055511474609375,
-0.0226898193359375,
-0.035369873046875,
-0.016693115234375,
-0.0003266334533691406,
0.03082275390625,
-0.01800537109375,
-0.007305145263671875,
-0.00004494190216064453,
0.03594970703125,
0.023590087890625,
-0.0103759765625,
-0.0192718505859375,
0.008392333984375,
0.0289306640625,
-0.0419921875,
0.0168304443359375,
0.006992340087890625,
-0.00040030479431152344,
0.01126861572265625,
0.00372314453125,
0.04010009765625,
0.02520751953125,
-0.00804901123046875,
-0.0110321044921875,
0.016448974609375,
-0.0009860992431640625,
-0.00665283203125,
-0.01549530029296875,
-0.0142974853515625,
0.033966064453125,
-0.033050537109375,
-0.0012798309326171875,
0.0203704833984375,
0.0139007568359375,
0.034210205078125,
-0.004787445068359375,
-0.056365966796875,
0.0194091796875,
0.032135009765625,
0.03424072265625,
0.06494140625,
0.01425933837890625,
0.0421142578125,
0.032867431640625,
-0.016082763671875,
0.003948211669921875,
-0.0091705322265625,
0.00732421875,
0.034332275390625,
-0.0165252685546875,
0.0114593505859375,
-0.034942626953125,
0.027252197265625,
0.0190582275390625,
-0.0139007568359375,
-0.0262451171875,
0.0077362060546875,
0.01067352294921875,
-0.019287109375,
-0.00836944580078125,
0.0172271728515625,
0.0246124267578125,
0.00826263427734375,
0.05157470703125,
-0.0229949951171875,
0.0369873046875,
-0.0033893585205078125,
-0.0100250244140625,
0.01399993896484375,
-0.00994110107421875,
-0.0228424072265625,
0.0186614990234375,
0.022918701171875,
-0.005550384521484375,
-0.00390625,
-0.01129150390625,
0.052154541015625,
-0.022247314453125,
0.01593017578125,
0.0009822845458984375,
-0.0416259765625,
0.040008544921875,
0.02081298828125,
0.008880615234375,
0.015838623046875,
-0.034576416015625,
0.0218048095703125,
-0.01166534423828125,
-0.0201568603515625,
0.00040650367736816406,
0.021728515625,
-0.03515625,
-0.02606201171875,
0.02294921875,
-0.017730712890625,
-0.00011628866195678711,
0.00659942626953125,
-0.004383087158203125,
-0.023101806640625,
0.01025390625,
-0.031982421875,
0.0135498046875,
-0.0284271240234375,
0.02569580078125,
0.01218414306640625,
0.0043487548828125,
-0.005184173583984375,
0.016082763671875,
-0.0127716064453125,
-0.043701171875,
0.01727294921875,
-0.031005859375,
-0.011871337890625,
-0.0038013458251953125,
0.0059814453125,
0.00930023193359375,
0.01110076904296875,
-0.0084228515625,
-0.0062103271484375,
0.00862884521484375,
0.017059326171875,
0.014923095703125,
-0.040008544921875,
-0.020751953125,
-0.00621795654296875,
0.0034351348876953125,
-0.00914764404296875,
0.0001996755599975586,
-0.007122039794921875,
-0.01494598388671875,
0.0203704833984375,
0.0268096923828125,
-0.0264739990234375,
-0.01189422607421875,
0.006877899169921875,
-0.0036773681640625,
-0.016937255859375,
0.0159912109375,
-0.007183074951171875,
-0.0181884765625,
0.00650787353515625,
0.006771087646484375,
-0.028961181640625,
0.00785064697265625,
0.0067901611328125,
0.025634765625,
-0.005939483642578125,
-0.035186767578125,
0.0240020751953125,
-0.0008716583251953125,
0.006954193115234375,
-0.002788543701171875,
-0.01549530029296875,
-0.0011749267578125,
-0.0298919677734375,
-0.0191650390625,
0.0208740234375,
-0.0243377685546875,
-0.017547607421875,
-0.0025615692138671875,
0.014251708984375,
-0.01361083984375,
0.021026611328125,
-0.003276824951171875,
-0.01551055908203125,
0.030548095703125,
-0.03802490234375,
0.006961822509765625,
0.01329803466796875,
-0.0275421142578125,
0.022857666015625,
0.00452423095703125,
0.039764404296875,
-0.00010484457015991211,
0.0023956298828125,
0.022918701171875,
-0.0107421875,
0.004215240478515625,
-0.0160064697265625,
0.0308990478515625,
-0.0117645263671875,
-0.0105133056640625,
0.0115509033203125,
0.00980377197265625,
-0.02142333984375,
-0.018310546875,
0.0060577392578125,
0.01468658447265625,
-0.001617431640625,
0.035003662109375,
0.0238189697265625,
0.017547607421875,
0.01727294921875,
-0.010284423828125,
0.033294677734375,
-0.02880859375,
0.01058197021484375,
0.01265716552734375,
0.00617218017578125,
-0.01666259765625,
-0.03302001953125,
-0.0208282470703125,
-0.0009469985961914062,
-0.03875732421875,
0.002216339111328125,
-0.0031280517578125,
0.019317626953125,
-0.0305328369140625,
-0.0140533447265625,
-0.01184844970703125,
-0.0001710653305053711,
-0.03680419921875,
0.02606201171875,
-0.0167999267578125,
-0.03863525390625,
0.0133056640625,
-0.01137542724609375,
0.018951416015625,
-0.0232086181640625,
0.0130615234375,
-0.019073486328125,
-0.0640869140625,
-0.01302337646484375,
0.0014390945434570312,
0.00983428955078125,
-0.0192108154296875,
-0.019989013671875,
-0.04205322265625,
0.027740478515625,
-0.04437255859375,
-0.01506805419921875,
-0.0165863037109375,
-0.019012451171875,
-0.00507354736328125,
0.021209716796875,
0.0286407470703125,
0.027435302734375,
0.0077056884765625,
0.01554107666015625,
0.001354217529296875,
0.005367279052734375,
-0.0224456787109375,
-0.005710601806640625,
0.01013946533203125,
0.043060302734375,
-0.031707763671875,
-0.0318603515625,
-0.0236053466796875,
0.0030059814453125,
-0.0034999847412109375,
0.026031494140625,
-0.005054473876953125,
-0.02593994140625,
-0.00036978721618652344,
-0.01367950439453125,
-0.005992889404296875,
-0.002277374267578125,
0.01100921630859375,
-0.0175628662109375,
0.008148193359375,
0.0003249645233154297,
-0.0206298828125,
0.00299072265625,
0.01007843017578125,
-0.0184326171875,
-0.0186004638671875,
0.021942138671875,
-0.050567626953125,
0.0141143798828125,
0.0261688232421875,
0.0159149169921875,
-0.0193634033203125,
-0.020904541015625,
-0.00998687744140625,
-0.01251220703125,
-0.0168304443359375,
-0.0260467529296875,
0.0345458984375,
0.019287109375,
-0.0012216567993164062,
0.009124755859375,
0.030364990234375,
-0.00533294677734375,
0.0307769775390625,
-0.015960693359375,
-0.024444580078125,
-0.004268646240234375,
0.0089874267578125,
0.0178680419921875,
0.02166748046875,
0.032958984375,
-0.04290771484375,
-0.029693603515625,
-0.0018949508666992188,
-0.02777099609375,
-0.025146484375,
-0.0018739700317382812,
0.011566162109375,
0.009796142578125,
0.03179931640625,
0.0017251968383789062,
-0.0063018798828125,
0.0181884765625,
0.002918243408203125,
0.0222015380859375,
-0.032196044921875,
-0.042694091796875,
0.01049041748046875,
0.01192474365234375,
-0.00004029273986816406,
-0.021240234375,
0.0006337165832519531,
-0.0021343231201171875,
0.0168609619140625,
0.0069580078125,
-0.012725830078125,
0.0013189315795898438,
-0.01422119140625,
0.023590087890625,
-0.00315093994140625,
-0.0299530029296875,
-0.0254364013671875,
-0.0020503997802734375,
-0.0014448165893554688,
-0.0037746429443359375,
0.0138397216796875,
0.016876220703125,
-0.0360107421875,
-0.03179931640625,
-0.00458526611328125,
0.0289764404296875,
0.034271240234375,
-0.021728515625,
-0.0253753662109375,
0.01457977294921875,
0.06268310546875,
-0.0308837890625,
0.020172119140625,
0.005695343017578125,
-0.01983642578125,
-0.05328369140625,
-0.009429931640625,
-0.0079803466796875,
-0.028411865234375,
-0.006595611572265625,
-0.0020847320556640625,
-0.01299285888671875,
0.022491455078125,
-0.00762939453125,
-0.0187225341796875,
0.00215911865234375,
-0.00005513429641723633,
-0.0233154296875,
-0.006343841552734375,
-0.01149749755859375,
0.0238037109375,
0.0128936767578125,
0.00666046142578125,
0.001800537109375,
-0.0032405853271484375,
0.01203155517578125,
0.03778076171875,
-0.01152801513671875,
0.055206298828125,
-0.0211029052734375,
0.00218963623046875,
0.043548583984375,
0.0345458984375,
-0.029937744140625,
-0.018035888671875,
-0.025238037109375,
-0.0167083740234375,
-0.0022716522216796875,
0.0146942138671875,
-0.005092620849609375,
0.0087738037109375,
0.034454345703125,
-0.0311431884765625,
0.030517578125,
-0.005584716796875,
-0.0014791488647460938,
0.0139617919921875,
-0.00948333740234375,
0.00887298583984375,
-0.0074462890625,
0.0013818740844726562,
0.0501708984375,
0.0484619140625,
-0.003875732421875,
0.02081298828125,
0.0017042160034179688,
-0.046478271484375,
0.007343292236328125,
-0.0096893310546875,
-0.0211181640625,
0.01305389404296875,
-0.0008664131164550781,
-0.039642333984375,
0.00644683837890625,
-0.00968170166015625,
0.0287322998046875,
0.0014286041259765625,
-0.00330352783203125,
0.002620697021484375,
-0.003131866455078125,
0.0089111328125,
0.0169677734375,
-0.02642822265625,
0.046295166015625,
0.02215576171875,
0.00907135009765625,
-0.009796142578125,
0.00582122802734375,
-0.0080413818359375,
-0.01502227783203125,
0.00345611572265625,
-0.0014562606811523438,
0.033905029296875,
-0.01192474365234375,
0.0272369384765625,
-0.02874755859375,
-0.017852783203125,
0.03802490234375,
-0.003551483154296875,
0.020355224609375,
-0.010223388671875,
-0.0064239501953125,
0.0142822265625,
0.0211944580078125,
0.004398345947265625,
-0.0150299072265625,
0.0222320556640625,
-0.03131103515625,
-0.025421142578125,
-0.006595611572265625,
0.036224365234375,
0.0238494873046875,
0.006160736083984375,
-0.0009474754333496094,
-0.01214599609375,
0.0204620361328125,
-0.025665283203125,
-0.0181732177734375,
-0.016021728515625,
-0.01116180419921875,
0.011199951171875,
-0.01377105712890625,
-0.015869140625,
0.017669677734375,
0.0013637542724609375,
-0.009368896484375,
0.0210113525390625,
-0.005252838134765625,
0.02777099609375,
-0.0014619827270507812,
-0.02294921875,
-0.0308074951171875,
-0.04718017578125,
0.01898193359375,
0.023345947265625,
0.0093231201171875,
-0.0063629150390625,
-0.0038738250732421875,
0.0081329345703125,
0.02593994140625,
0.0260772705078125,
0.0016231536865234375,
0.01702880859375,
0.002323150634765625,
-0.00954437255859375,
0.050689697265625,
-0.031463623046875,
-0.01209259033203125,
-0.004764556884765625,
-0.0211334228515625,
-0.01383209228515625,
-0.020538330078125,
0.0202178955078125,
0.0242767333984375,
-0.039703369140625,
-0.0214996337890625,
0.0303497314453125,
-0.021514892578125,
-0.0154876708984375,
0.0130157470703125,
-0.01364898681640625,
-0.019989013671875,
0.00292205810546875,
-0.0137786865234375,
-0.0162353515625,
-0.017547607421875,
0.01406097412109375,
0.01212310791015625,
-0.0262451171875,
-0.00678253173828125,
0.015472412109375,
-0.021728515625,
-0.0003662109375,
0.01068115234375,
-0.01073455810546875,
0.05157470703125,
-0.0185089111328125,
-0.0035686492919921875,
-0.0168914794921875,
-0.00823211669921875,
0.016693115234375,
0.0001361370086669922,
0.0261993408203125,
-0.006931304931640625,
-0.0172576904296875,
-0.01129913330078125,
-0.03570556640625,
0.0158843994140625,
0.01312255859375,
0.0107269287109375,
-0.006786346435546875,
-0.00403594970703125,
-0.0005841255187988281,
0.036163330078125,
-0.0154876708984375,
-0.011566162109375,
-0.0120391845703125,
-0.030517578125,
0.01548004150390625,
0.035919189453125,
0.0288238525390625,
-0.020111083984375,
0.0025768280029296875,
0.0302734375,
-0.0100555419921875,
-0.0278472900390625,
-0.03240966796875,
-0.02410888671875,
-0.0116424560546875,
0.01338958740234375,
0.03411865234375,
-0.033538818359375,
-0.02618408203125,
-0.0146331787109375,
0.005313873291015625,
0.01102447509765625,
-0.008941650390625,
-0.036865234375,
0.029510498046875,
0.0044097900390625,
0.0149078369140625,
0.020477294921875,
-0.0195770263671875,
0.0228424072265625,
-0.007595062255859375,
-0.01126861572265625,
-0.042572021484375,
-0.0250091552734375,
-0.03326416015625,
-0.0215606689453125,
0.032928466796875,
0.003093719482421875,
-0.0237884521484375,
0.0283660888671875,
-0.010498046875,
0.0218353271484375,
0.006374359130859375,
0.004161834716796875,
0.01044464111328125,
0.0020656585693359375,
0.011016845703125,
-0.0017757415771484375,
0.017578125,
0.0019931793212890625,
0.01456451416015625,
0.000896453857421875,
-0.03485107421875,
0.02679443359375,
-0.00861358642578125,
0.0252532958984375,
0.0011606216430664062,
0.01226043701171875,
0.0265350341796875,
0.0030307769775390625,
0.00016164779663085938,
-0.006500244140625,
-0.0059051513671875,
-0.03485107421875,
0.0181884765625,
0.0260009765625,
0.018157958984375,
0.01093292236328125,
-0.01898193359375,
-0.0125274658203125,
-0.01378631591796875,
-0.01366424560546875,
0.0240325927734375,
-0.048095703125,
0.01456451416015625,
0.0179595947265625,
-0.0021076202392578125,
0.0104827880859375,
-0.0176544189453125,
0.014190673828125,
-0.00662994384765625,
-0.01300048828125,
-0.02490234375,
-0.0009546279907226562,
-0.0097503662109375,
-0.0018825531005859375,
-0.016754150390625,
-0.0036449432373046875,
0.0208587646484375,
0.01904296875,
-0.006805419921875,
0.03704833984375,
-0.01186370849609375,
0.0012416839599609375,
0.0229644775390625,
-0.005779266357421875,
0.0225830078125,
-0.00672149658203125,
0.0189361572265625,
-0.0236663818359375,
-0.01306915283203125,
-0.004581451416015625,
-0.0021381378173828125,
0.0323486328125,
-0.04327392578125,
0.000713348388671875,
0.034515380859375,
0.0158233642578125,
-0.043975830078125,
0.038787841796875,
0.021881103515625,
0.004810333251953125,
0.013153076171875,
-0.0038585662841796875,
-0.0406494140625,
0.00986480712890625,
0.005374908447265625,
0.0254058837890625,
0.01355743408203125,
0.00812530517578125,
-0.01374053955078125,
0.0272064208984375,
0.0038166046142578125,
0.0179290771484375,
0.004840850830078125,
0.019866943359375,
-0.023406982421875,
-0.008026123046875,
0.005954742431640625,
-0.0255584716796875,
-0.018035888671875,
0.04254150390625,
0.0077362060546875,
0.00308990478515625,
0.006938934326171875,
-0.00733184814453125,
-0.0178985595703125,
-0.0032672882080078125,
0.03753662109375,
-0.0029621124267578125,
-0.004741668701171875,
0.008453369140625,
-0.022613525390625,
0.0134429931640625,
0.01197052001953125,
0.00292205810546875,
-0.004486083984375,
-0.0210723876953125,
0.00860595703125,
0.0323486328125,
0.006252288818359375,
-0.013763427734375,
0.02130126953125,
-0.00759124755859375,
-0.0189056396484375,
-0.0232696533203125,
-0.03924560546875,
-0.007495880126953125,
-0.0074005126953125,
-0.0034580230712890625,
0.031280517578125,
-0.017425537109375,
0.016845703125,
0.0307464599609375,
0.00812530517578125,
-0.0245513916015625,
-0.035888671875,
-0.00121307373046875,
0.01166534423828125,
0.01519012451171875,
0.007411956787109375,
-0.01526641845703125,
-0.018310546875,
0.00379180908203125,
0.0153350830078125,
0.006805419921875,
0.03192138671875,
0.0010585784912109375,
-0.01242828369140625,
0.004772186279296875,
-0.0030193328857421875,
-0.00571441650390625,
-0.00878143310546875,
0.00884246826171875,
-0.0306854248046875,
-0.006580352783203125,
-0.0229644775390625,
-0.00015175342559814453,
-0.00856781005859375,
-0.0160064697265625,
0.01168060302734375,
0.027130126953125,
0.028656005859375,
0.0185089111328125,
-0.00868988037109375,
-0.016021728515625,
0.00853729248046875,
0.00933074951171875,
-0.00753021240234375,
-0.020904541015625,
-0.023681640625,
-0.00384521484375,
-0.01983642578125,
-0.019866943359375,
-0.01280975341796875,
0.034576416015625,
-0.00682830810546875,
-0.01416778564453125,
0.022674560546875,
-0.013153076171875,
0.00785064697265625,
-0.0020847320556640625,
0.00299835205078125,
0.038482666015625,
-0.022186279296875,
0.04132080078125,
0.00356292724609375,
-0.026824951171875,
-0.0012264251708984375,
-0.0277252197265625,
0.0033855438232421875,
-0.0277099609375,
0.0271148681640625,
0.0063323974609375,
0.0126800537109375,
0.006282806396484375,
-0.02911376953125,
0.0243988037109375,
-0.01508331298828125,
-0.03131103515625,
-0.0025634765625,
0.00347900390625,
-0.0006699562072753906,
0.04168701171875,
0.012451171875,
0.0016794204711914062,
-0.0005846023559570312,
-0.02593994140625,
-0.009735107421875,
-0.0232696533203125,
0.006378173828125,
-0.006114959716796875,
0.0122833251953125,
-0.022186279296875,
-0.0181427001953125,
-0.0026569366455078125,
-0.005252838134765625,
0.0181884765625,
-0.0201416015625,
-0.0234832763671875,
0.017822265625,
-0.00986480712890625,
-0.0092926025390625,
0.01434326171875,
0.0129547119140625,
-0.0302276611328125,
0.0193634033203125,
0.00739288330078125,
0.007465362548828125,
-0.0079193115234375,
-0.0055999755859375,
-0.007472991943359375,
-0.00127410888671875,
0.0215606689453125,
-0.046051025390625,
0.020965576171875,
0.004009246826171875,
-0.01318359375,
0.01441192626953125,
0.035400390625,
-0.033935546875,
0.00803375244140625,
-0.019866943359375,
0.005451202392578125,
-0.0029850006103515625,
0.01036834716796875,
-0.0223388671875,
0.00946807861328125,
-0.0006742477416992188,
-0.00405120849609375,
-0.00954437255859375,
-0.0162811279296875,
0.006099700927734375,
0.0021495819091796875,
0.00045561790466308594,
0.0271453857421875,
-0.024932861328125,
0.002101898193359375,
-0.0291595458984375,
0.01480865478515625,
-0.0248870849609375,
-0.01119232177734375,
0.0162200927734375,
-0.01183319091796875,
0.0304107666015625,
0.0023555755615234375,
-0.004344940185546875,
0.0163726806640625,
-0.005367279052734375,
0.0204925537109375,
-0.01421356201171875,
-0.021148681640625,
0.01126861572265625,
0.005321502685546875,
-0.00901031494140625,
0.01244354248046875,
0.01302337646484375,
0.01438140869140625,
0.002017974853515625,
-0.0173187255859375,
-0.037139892578125,
0.037994384765625,
0.007152557373046875,
-0.0206451416015625,
-0.010101318359375,
-0.002353668212890625,
-0.01514434814453125,
0.0089111328125,
-0.01136016845703125,
-0.016510009765625,
0.01001739501953125,
-0.00620269775390625,
-0.0117340087890625,
-0.0310821533203125,
-0.0025920867919921875,
0.02703857421875,
0.01427459716796875,
-0.01412200927734375,
0.014190673828125,
0.03369140625,
-0.035308837890625,
0.0066070556640625,
0.0135955810546875,
-0.011688232421875,
-0.020721435546875,
0.0231475830078125,
-0.00215911865234375,
-0.00405120849609375,
-0.01190185546875,
-0.01910400390625,
0.005100250244140625,
-0.0701904296875,
-0.01226806640625,
-0.029144287109375,
0.03179931640625,
0.035064697265625,
-0.006046295166015625,
0.01511383056640625,
0.018951416015625,
0.00919342041015625,
0.0164337158203125,
0.040771484375,
0.041961669921875,
0.00374603271484375,
0.011199951171875,
0.002239227294921875,
0.007297515869140625,
-0.0096282958984375,
-0.039947509765625,
0.01143646240234375,
-0.0239715576171875,
-0.00775146484375,
0.015777587890625,
-0.016326904296875,
0.01490020751953125,
-0.030548095703125,
0.0017271041870117188,
-0.0184478759765625,
0.00039505958557128906,
0.00446319580078125,
-0.001811981201171875,
0.00644683837890625,
-0.00775909423828125,
0.031646728515625,
0.0025653839111328125,
0.0167236328125,
-0.0018177032470703125,
0.01397705078125,
0.0007338523864746094,
0.0157623291015625,
-0.00839996337890625,
-0.0288848876953125,
-0.0009622573852539062,
0.002162933349609375,
-0.006969451904296875,
0.0088958740234375,
-0.0020389556884765625,
-0.0265045166015625,
-0.0013141632080078125,
0.005207061767578125,
0.0155181884765625,
0.00470733642578125,
-0.060272216796875,
0.01885986328125,
0.00514984130859375,
0.01262664794921875,
0.01204681396484375,
-0.01910400390625,
0.0143280029296875,
0.0170440673828125,
-0.0180816650390625,
-0.00962066650390625,
-0.0021305084228515625,
0.0094146728515625,
0.00875091552734375,
-0.0174560546875,
0.006500244140625,
-0.01335906982421875,
-0.00681304931640625,
0.010101318359375,
0.0013494491577148438,
-0.022308349609375,
-0.00196075439453125,
-0.0239715576171875,
-0.006023406982421875,
-0.03131103515625,
0.01163482666015625,
-0.02691650390625,
-0.007843017578125,
-0.00347137451171875,
-0.0003743171691894531,
-0.0045318603515625,
0.0290679931640625,
0.033538818359375,
0.003246307373046875,
-0.033843994140625,
-0.0015344619750976562,
0.00970458984375,
-0.000438690185546875,
-0.00826263427734375,
-0.0271148681640625,
-0.006069183349609375,
0.0198822021484375,
-0.00420379638671875,
0.006885528564453125,
-0.005252838134765625,
-0.044097900390625,
0.004459381103515625,
0.00814056396484375,
0.0400390625,
-0.041259765625,
0.0254058837890625,
-0.01131439208984375,
-0.01419830322265625,
-0.01302337646484375,
-0.004573822021484375,
-0.00665283203125,
-0.01486968994140625,
0.01079559326171875,
-0.002986907958984375,
0.0034732818603515625,
-0.034149169921875,
0.0253753662109375,
-0.016632080078125,
-0.0015859603881835938,
-0.01122283935546875,
-0.006427764892578125,
0.006649017333984375,
-0.0040435791015625,
-0.009124755859375,
0.01221466064453125,
-0.008209228515625,
0.0311126708984375,
-0.02996826171875,
0.040679931640625,
-0.0055694580078125,
0.006038665771484375,
-0.035858154296875,
0.051971435546875,
0.0091400146484375,
0.005290985107421875,
-0.004268646240234375,
0.00838470458984375,
0.019073486328125,
0.03179931640625,
0.008544921875,
0.01666259765625,
0.0186309814453125,
0.02069091796875,
0.007549285888671875,
-0.00356292724609375,
0.024871826171875,
-0.0040283203125,
0.0206756591796875,
-0.01033782958984375,
0.027862548828125,
0.0206756591796875,
-0.0014476776123046875,
-0.0328369140625,
0.007694244384765625,
-0.0205535888671875,
-0.01983642578125,
0.0177764892578125,
-0.00788116455078125,
-0.0261383056640625,
0.006008148193359375,
-0.01367950439453125,
0.015777587890625,
-0.036529541015625,
-0.040557861328125,
0.034210205078125,
0.04144287109375,
0.0241851806640625,
-0.01593017578125,
-0.020172119140625,
0.00301361083984375,
0.0125274658203125,
-0.02630615234375,
0.00746917724609375,
-0.033935546875,
-0.030517578125,
0.0104217529296875,
-0.01441192626953125,
-0.0205535888671875,
-0.004734039306640625,
-0.004180908203125,
0.041595458984375,
-0.01422119140625,
0.01299285888671875,
0.0100860595703125,
0.0186004638671875,
-0.0036525726318359375,
0.004608154296875,
-0.049591064453125,
0.0111846923828125,
0.027923583984375,
0.03411865234375,
-0.03619384765625,
0.0010433197021484375,
-0.033660888671875,
-0.02880859375,
-0.029754638671875,
0.037811279296875,
0.0216522216796875,
-0.0270538330078125,
0.00965118408203125,
0.0007028579711914062,
-0.0228118896484375,
-0.00689697265625,
0.004886627197265625,
0.01287841796875,
-0.0158538818359375,
-0.003841400146484375,
-0.0083770751953125,
-0.008819580078125,
-0.0245208740234375,
0.02264404296875,
-0.0106048583984375,
0.01081085205078125,
-0.024993896484375,
0.027252197265625,
0.034942626953125,
-0.04107666015625,
0.0117950439453125,
0.032440185546875,
0.00756072998046875,
-0.0192718505859375,
-0.01457977294921875,
0.021270751953125,
0.0165557861328125,
-0.0136566162109375,
0.01995849609375,
0.01424407958984375,
-0.005985260009765625,
0.044708251953125,
0.034210205078125,
-0.052642822265625,
0.0234527587890625,
0.024169921875,
-0.0173187255859375,
0.00027179718017578125,
-0.01227569580078125,
-0.02349853515625,
0.006710052490234375,
0.01507568359375,
-0.01515960693359375,
0.0092315673828125,
-0.0123748779296875,
-0.01806640625,
0.00299072265625,
-0.005809783935546875,
0.0077667236328125,
0.020751953125,
-0.01275634765625,
0.0090179443359375,
0.0220184326171875,
-0.0130767822265625,
0.0045623779296875,
0.027374267578125,
-0.012054443359375,
-0.0010366439819335938,
0.0006804466247558594,
-0.0274810791015625,
-0.0019197463989257812,
0.01372528076171875,
-0.017486572265625,
0.004100799560546875,
-0.01314544677734375,
0.00939178466796875,
0.0196380615234375,
-0.020721435546875,
0.0009183883666992188,
-0.00870513916015625,
0.0249786376953125,
-0.00786590576171875,
0.015716552734375,
-0.0023403167724609375,
-0.00484466552734375,
0.00323486328125,
-0.0051727294921875,
0.00408935546875,
0.020111083984375,
0.0367431640625,
0.00927734375,
0.000652313232421875,
0.0416259765625,
0.005504608154296875,
0.0066070556640625,
0.01451873779296875,
-0.01299285888671875,
0.0243072509765625,
0.00568389892578125,
0.0282440185546875,
0.0357666015625,
-0.0187835693359375,
0.0007128715515136719,
-0.00321197509765625,
-0.005462646484375,
0.02557373046875,
0.0079345703125,
0.0090789794921875,
0.005634307861328125,
0.00885772705078125,
-0.024078369140625,
0.004852294921875,
0.0017528533935546875,
0.0206298828125,
0.003753662109375,
-0.020538330078125,
0.006198883056640625,
0.00849151611328125,
0.00644683837890625,
-0.00791168212890625,
-0.0367431640625,
0.013336181640625,
-0.0279083251953125,
-0.0106048583984375,
0.026092529296875,
-0.0163116455078125,
0.0097503662109375,
-0.00838470458984375,
0.01062774658203125,
0.007244110107421875,
0.017333984375,
0.052581787109375,
0.0491943359375,
0.0261077880859375,
0.0178680419921875,
0.025482177734375,
-0.0162353515625,
0.004673004150390625,
-0.01702880859375,
-0.003704071044921875,
0.021484375,
0.019927978515625,
0.033599853515625,
-0.004638671875,
0.021820068359375,
0.020965576171875,
0.0187835693359375,
-0.002410888671875,
-0.0040435791015625,
0.015716552734375,
-0.022918701171875,
-0.0150909423828125,
0.039642333984375,
-0.02008056640625,
-0.0092010498046875,
-0.001842498779296875,
-0.004161834716796875,
0.01424407958984375,
-0.04412841796875,
-0.0053863525390625,
-0.0244293212890625,
0.0198822021484375,
0.0273284912109375,
0.017547607421875,
0.024566650390625,
0.0155792236328125,
0.00609588623046875,
-0.0249786376953125,
-0.01253509521484375,
-0.01549530029296875,
0.0199432373046875,
-0.034088134765625,
-0.01258087158203125,
0.01287078857421875,
-0.0206756591796875,
-0.0037384033203125,
0.024658203125,
-0.03369140625,
0.01038360595703125,
-0.001926422119140625,
-0.0095977783203125,
-0.04156494140625,
0.009429931640625,
-0.04888916015625,
-0.004100799560546875,
-0.034454345703125,
0.0171661376953125,
0.011962890625,
-0.0131072998046875,
-0.029205322265625,
0.006725311279296875,
0.022064208984375,
-0.0124664306640625,
-0.00272369384765625,
-0.013763427734375,
0.0291290283203125,
-0.026641845703125,
-0.0026302337646484375,
0.01519012451171875,
0.00325775146484375,
-0.0246734619140625,
0.0216217041015625,
0.0249481201171875,
0.0285186767578125,
0.025909423828125,
-0.00307464599609375,
-0.021331787109375,
-0.006500244140625,
0.02630615234375,
-0.0182037353515625,
0.0025730133056640625,
0.01042938232421875,
0.01514434814453125,
-0.022003173828125,
0.0158233642578125,
-0.0011768341064453125,
0.0154266357421875,
0.008636474609375,
0.0014743804931640625,
0.01477813720703125,
0.057098388671875,
-0.001354217529296875,
-0.00798797607421875,
-0.038482666015625,
0.007740020751953125,
0.036041259765625,
0.00872039794921875,
-0.0292205810546875,
0.0020122528076171875,
0.01434326171875,
-0.01739501953125,
0.00870513916015625,
0.0038127899169921875,
0.018707275390625,
-0.0245513916015625,
-0.0173187255859375,
0.0531005859375,
0.012664794921875,
-0.0273895263671875,
0.045684814453125,
0.01441192626953125,
-0.01375579833984375,
-0.0068817138671875,
-0.0245819091796875,
0.00783538818359375,
0.012298583984375,
-0.005031585693359375,
0.003875732421875,
0.0218658447265625,
-0.0016002655029296875,
-0.0080108642578125,
0.01512908935546875,
-0.03045654296875,
-0.0192413330078125,
-0.02001953125,
0.01068878173828125,
-0.0034580230712890625,
-0.0004138946533203125,
0.005859375,
-0.0095977783203125,
0.0016393661499023438,
-0.0258636474609375,
0.01184844970703125,
0.0003261566162109375,
0.010009765625,
-0.0208892822265625,
-0.00885772705078125,
0.040557861328125,
-0.00959014892578125,
-0.00157928466796875,
-0.0277099609375,
-0.0013532638549804688,
0.01131439208984375,
-0.034423828125,
0.00400543212890625,
-0.00482940673828125,
-0.041778564453125,
-0.012359619140625,
-0.04718017578125,
-0.006244659423828125,
0.00453948974609375,
-0.01021575927734375,
0.0204010009765625,
-0.0174713134765625,
0.04412841796875,
0.025299072265625,
-0.0023174285888671875,
0.01171875,
-0.003658294677734375,
0.0179443359375,
0.00792694091796875,
-0.0028629302978515625,
0.02001953125,
0.003326416015625,
0.0125885009765625,
-0.0035343170166015625,
-0.00656890869140625,
0.031341552734375,
-0.0228271484375,
-0.006511688232421875,
0.0219879150390625,
-0.0259552001953125,
-0.0222015380859375,
-0.01168060302734375,
-0.017303466796875,
-0.031585693359375,
-0.0005626678466796875,
0.0172882080078125,
0.01470947265625,
0.0065155029296875,
0.0173492431640625,
-0.0135650634765625,
0.01114654541015625,
-0.03460693359375,
0.044097900390625,
0.0096282958984375,
0.0010728836059570312,
-0.034271240234375,
-0.015228271484375,
0.0254669189453125,
-0.01410675048828125,
-0.0330810546875,
0.006465911865234375,
-0.01519012451171875,
-0.0287628173828125,
-0.0166778564453125,
0.032806396484375,
0.026153564453125,
0.0134124755859375,
-0.033447265625,
0.0137786865234375,
-0.002552032470703125,
-0.0021953582763671875,
-0.032440185546875,
0.0215301513671875,
0.0167388916015625,
0.005245208740234375,
-0.0114288330078125,
-0.0252838134765625,
-0.0057830810546875,
-0.011962890625,
0.0491943359375,
-0.0249786376953125,
-0.04571533203125,
0.0169219970703125,
0.008819580078125,
0.0113372802734375,
-0.03240966796875,
-0.0130767822265625,
0.0650634765625,
-0.01247406005859375,
0.004192352294921875,
-0.037200927734375,
0.019622802734375,
-0.0104217529296875,
0.024505615234375,
-0.0232086181640625,
-0.039337158203125,
-0.019775390625,
-0.013458251953125,
-0.01800537109375,
-0.00908660888671875,
0.01849365234375,
0.00649261474609375,
0.0150604248046875,
0.006290435791015625,
-0.022186279296875,
-0.004245758056640625,
0.006343841552734375,
0.0191497802734375,
0.002407073974609375,
0.027740478515625,
0.032623291015625,
-0.023468017578125,
0.02105712890625,
-0.007099151611328125,
-0.0294189453125,
-0.00765228271484375,
-0.00482940673828125,
0.019683837890625,
-0.0211334228515625,
0.002658843994140625,
-0.009002685546875,
0.0036602020263671875,
-0.00821685791015625,
0.0206756591796875,
0.023529052734375,
0.039581298828125,
0.027252197265625,
0.0086517333984375,
0.002063751220703125,
0.006931304931640625,
-0.00664520263671875,
-0.0011148452758789062,
-0.00989532470703125,
0.026519775390625,
-0.0004296302795410156,
0.0139923095703125,
0.0107574462890625,
-0.001285552978515625,
0.0016231536865234375,
-0.0186767578125,
0.0160369873046875,
0.0062103271484375,
0.0101470947265625,
-0.0017480850219726562,
-0.014190673828125,
0.01197052001953125,
0.03662109375,
0.02099609375,
-0.006877899169921875,
-0.0062408447265625,
-0.016143798828125,
-0.00937652587890625,
-0.0029296875,
0.0155487060546875,
0.0109405517578125,
-0.0196075439453125,
0.00457000732421875,
0.00627899169921875,
-0.0059051513671875,
0.0187225341796875,
-0.0350341796875,
-0.006381988525390625,
0.004848480224609375,
-0.0017223358154296875,
0.0290679931640625,
0.01280975341796875,
-0.03912353515625,
-0.024688720703125,
0.00977325439453125,
-0.0262298583984375,
-0.003936767578125,
0.005374908447265625,
-0.0014162063598632812,
-0.013336181640625,
-0.0038318634033203125,
-0.01026153564453125,
0.00820159912109375,
0.032623291015625,
-0.007785797119140625,
0.014984130859375,
-0.00814056396484375,
-0.00463104248046875,
-0.01702880859375,
0.0225982666015625,
0.0020542144775390625,
0.0267181396484375,
-0.0149993896484375,
-0.014923095703125,
0.00798797607421875,
0.0235137939453125,
0.017608642578125,
0.027435302734375,
0.0064239501953125,
-0.038604736328125,
-0.01123809814453125,
-0.04150390625,
-0.0164642333984375,
-0.001865386962890625,
-0.007320404052734375,
0.0157318115234375,
-0.020233154296875,
0.0286407470703125,
0.0205230712890625,
0.0024204254150390625,
-0.02349853515625,
-0.004886627197265625,
-0.0010995864868164062,
0.042999267578125,
0.0273895263671875,
0.0225830078125,
0.028839111328125,
-0.016448974609375,
-0.02294921875,
0.006771087646484375,
-0.01189422607421875,
-0.026397705078125,
-0.007061004638671875,
0.0156402587890625,
-0.003208160400390625,
0.01525115966796875,
-0.0157928466796875,
-0.01513671875,
-0.031982421875,
-0.027130126953125,
0.016326904296875,
0.0093994140625,
0.0301971435546875,
0.0174560546875,
-0.04290771484375,
-0.00551605224609375,
0.0017299652099609375,
-0.0166778564453125,
-0.032867431640625,
0.04351806640625,
-0.0015649795532226562,
-0.023590087890625,
0.0191497802734375,
0.041900634765625,
-0.0107269287109375,
-0.0083160400390625,
0.045928955078125,
0.00812530517578125,
-0.011993408203125,
0.02960205078125,
0.00809478759765625,
0.00745391845703125,
-0.0207672119140625,
0.0121307373046875,
0.001316070556640625,
0.019073486328125,
0.0027027130126953125,
-0.0210113525390625,
-0.0079498291015625,
-0.023162841796875,
0.0072784423828125,
0.038299560546875,
-0.004291534423828125,
-0.042327880859375,
0.003116607666015625,
-0.003536224365234375,
-0.04132080078125,
-0.0019779205322265625,
-0.0141143798828125,
0.00691986083984375,
-0.0153656005859375,
0.0017023086547851562,
-0.0118865966796875,
-0.035797119140625,
-0.00936126708984375,
-0.01448822021484375,
0.005718231201171875,
-0.0215911865234375,
-0.0248260498046875,
-0.00353240966796875,
-0.00559234619140625,
0.0113677978515625,
-0.00457000732421875,
-0.020172119140625,
-0.018524169921875,
0.0268096923828125,
0.047027587890625,
0.019622802734375,
0.0169525146484375,
0.0212554931640625,
0.01410675048828125,
0.01461029052734375,
0.01218414306640625,
-0.01708984375,
0.00373077392578125,
-0.01514434814453125,
-0.0147552490234375,
-0.00984954833984375,
-0.0005512237548828125,
0.00989532470703125,
0.01470184326171875,
0.00101470947265625,
0.01204681396484375,
0.0004229545593261719,
-0.0022029876708984375,
0.0214080810546875,
0.004962921142578125,
-0.016845703125,
-0.01873779296875,
-0.025299072265625,
0.01441192626953125,
0.00861358642578125,
0.00502777099609375,
0.0031299591064453125,
0.0289306640625,
-0.0013275146484375,
-0.032745361328125,
0.0216217041015625,
0.006504058837890625,
0.0033416748046875,
-0.00286102294921875,
0.01432037353515625,
-0.00006073713302612305,
0.016143798828125,
0.01384735107421875,
-0.00731658935546875,
-0.004116058349609375,
-0.01123809814453125,
-0.01340484619140625,
0.0030574798583984375,
0.0164337158203125,
-0.0127716064453125,
0.0171356201171875,
0.016632080078125,
0.0057525634765625,
-0.00909423828125,
0.013397216796875,
0.0132598876953125,
0.0121917724609375,
-0.015838623046875,
0.006072998046875,
0.007568359375,
0.031280517578125,
0.01064300537109375,
-0.01067352294921875,
0.01898193359375,
-0.0160064697265625,
-0.01158905029296875,
-0.0009179115295410156,
-0.028778076171875,
0.029510498046875,
0.007843017578125,
-0.0406494140625,
0.009185791015625,
-0.00786590576171875,
0.0160980224609375,
-0.011138916015625,
-0.02362060546875,
-0.01727294921875,
0.0083465576171875,
0.00672149658203125,
-0.0169677734375,
-0.020751953125,
0.0120697021484375,
-0.001461029052734375,
0.000171661376953125,
0.01068878173828125,
-0.004543304443359375,
-0.0160064697265625,
-0.0224761962890625,
-0.0189056396484375,
0.007381439208984375,
0.019256591796875,
-0.0163726806640625,
0.01007080078125,
-0.007110595703125,
-0.039642333984375,
0.027679443359375,
-0.0180206298828125,
0.042694091796875,
-0.044921875,
0.0034942626953125,
0.01678466796875,
-0.0188751220703125,
0.0194091796875,
0.03179931640625,
0.01806640625,
0.0133056640625,
0.00003236532211303711,
0.0036525726318359375,
0.0258026123046875,
0.036346435546875,
-0.031951904296875,
0.01145172119140625,
0.007465362548828125,
0.05303955078125,
0.036376953125,
-0.0297698974609375,
-0.0196533203125,
0.00726318359375,
-0.01371002197265625,
0.00366973876953125,
-0.004444122314453125,
-0.00015056133270263672,
0.01311492919921875,
0.01509857177734375,
-0.006008148193359375,
0.0231170654296875,
-0.0194244384765625,
-0.006732940673828125,
0.0211029052734375,
0.0006008148193359375,
-0.017852783203125,
0.0200042724609375,
0.002105712890625,
-0.019500732421875,
-0.024169921875,
0.0128326416015625,
-0.025421142578125,
0.007080078125,
-0.00868988037109375,
-0.0100555419921875,
0.016937255859375,
0.00165557861328125,
-0.005565643310546875,
-0.0248260498046875,
0.00543975830078125,
0.01116943359375,
-0.0052947998046875,
0.01248931884765625,
0.0006709098815917969,
-0.01212310791015625,
-0.0078125,
0.0014972686767578125,
-0.007110595703125,
-0.005321502685546875,
0.0220947265625,
-0.019073486328125,
-0.0282440185546875,
-0.00005537271499633789,
0.018798828125,
-0.0079193115234375,
-0.0224456787109375,
0.02593994140625,
-0.004459381103515625,
-0.03460693359375,
0.03338623046875,
0.0638427734375,
-0.02020263671875,
0.000025212764739990234,
0.002552032470703125,
0.00030922889709472656,
0.010650634765625,
0.0196533203125,
0.0073089599609375,
0.0276031494140625,
-0.0019702911376953125,
-0.0136260986328125,
-0.02239990234375,
0.004566192626953125,
-0.00951385498046875,
0.01094818115234375,
-0.033447265625,
0.004657745361328125,
-0.0214996337890625,
-0.0040740966796875,
-0.004428863525390625,
0.0024051666259765625,
-0.003948211669921875,
-0.01322174072265625,
0.018218994140625,
-0.019744873046875,
0.0217437744140625,
-0.036865234375,
0.006656646728515625,
-0.0030651092529296875,
-0.017730712890625,
-0.001514434814453125,
-0.0185699462890625,
-0.0240936279296875,
-0.004276275634765625,
0.0173797607421875,
-0.00621795654296875,
-0.0275115966796875,
-0.015625,
0.00348663330078125,
-0.01324462890625,
-0.01332855224609375,
0.005161285400390625,
-0.01163482666015625,
0.0054779052734375,
0.017181396484375,
-0.0026950836181640625,
-0.014801025390625,
0.010345458984375,
-0.0254669189453125,
0.0168914794921875,
-0.048614501953125,
-0.00200653076171875,
-0.0123291015625,
-0.0195159912109375,
-0.01515960693359375,
0.0196075439453125,
0.00988006591796875,
-0.0207061767578125,
0.016448974609375,
-0.0380859375,
-0.01042938232421875,
-0.0221099853515625,
-0.00335693359375,
0.000965118408203125,
-0.025238037109375,
-0.007770538330078125,
-0.0030651092529296875,
0.01024627685546875,
0.0020923614501953125,
-0.0007081031799316406,
-0.0230560302734375,
0.006793975830078125,
-0.0207977294921875,
0.03314208984375,
0.0005388259887695312,
0.01195526123046875,
-0.0018472671508789062,
0.0228118896484375,
0.00616455078125,
-0.01214599609375,
-0.0166778564453125,
-0.0082244873046875,
-0.0037021636962890625,
0.00066375732421875,
-0.022216796875,
-0.004833221435546875,
0.003387451171875,
0.01108551025390625,
-0.022705078125,
-0.032440185546875,
-0.01422119140625,
0.00926971435546875,
0.0011281967163085938,
-0.004947662353515625,
-0.0171661376953125,
0.01495361328125,
0.042388916015625,
0.00043463706970214844,
-0.02093505859375,
0.007038116455078125,
0.01067352294921875,
0.01519012451171875,
-0.003208160400390625,
0.0114593505859375,
-0.003997802734375,
0.019561767578125,
0.0272369384765625,
0.003971099853515625,
0.0117645263671875,
0.0081939697265625,
-0.0002092123031616211,
-0.0097198486328125,
0.0241851806640625,
-0.010284423828125,
0.0318603515625,
-0.002620697021484375,
-0.0159454345703125,
-0.023223876953125,
0.01568603515625,
-0.01995849609375,
0.0273895263671875,
-0.023162841796875,
-0.01305389404296875,
-0.02032470703125,
0.0050506591796875,
0.02093505859375,
-0.0247344970703125,
-0.037078857421875,
0.0031070709228515625,
0.01276397705078125,
0.0025501251220703125,
0.004974365234375,
-0.0002529621124267578,
0.012481689453125,
-0.0165252685546875,
0.02001953125,
-0.015380859375,
-0.032501220703125,
-0.0202178955078125,
-0.0065460205078125,
0.005825042724609375,
0.0064239501953125,
0.0003871917724609375,
-0.0251922607421875,
-0.004634857177734375,
0.01131439208984375,
-0.04541015625,
-0.004730224609375,
-0.009429931640625,
-0.0015001296997070312,
-0.02197265625,
0.0097198486328125,
-0.045196533203125,
0.01053619384765625,
0.025634765625,
-0.005390167236328125,
-0.00508880615234375,
0.0062255859375,
-0.0230560302734375,
0.0189666748046875,
-0.0006070137023925781,
0.00543212890625,
-0.00797271728515625,
0.0006799697875976562,
-0.018310546875,
0.01446533203125,
-0.030303955078125,
0.0184326171875,
-0.01224517822265625,
-0.01385498046875,
-0.026397705078125,
-0.017486572265625,
0.00859832763671875,
0.0167083740234375,
-0.002124786376953125,
0.0306396484375,
-0.004802703857421875,
-0.0216064453125,
-0.01629638671875,
-0.0003974437713623047,
0.0247650146484375,
0.0158233642578125,
0.0027828216552734375,
0.0204010009765625,
0.0008044242858886719,
-0.0035877227783203125,
0.005184173583984375,
0.03741455078125,
-0.003559112548828125,
-0.01348114013671875,
0.00850677490234375,
-0.0034275054931640625,
0.0233612060546875,
0.02532958984375,
-0.050018310546875,
-0.00788116455078125,
0.029052734375,
0.0142059326171875,
-0.00830078125,
0.0126495361328125,
0.00688934326171875,
-0.003631591796875,
0.01230621337890625,
-0.014373779296875,
-0.02423095703125,
-0.0001653432846069336,
0.0277252197265625,
-0.0160675048828125,
-0.01641845703125,
-0.025909423828125,
-0.045989990234375,
0.034149169921875,
0.048065185546875,
-0.01922607421875,
-0.0231781005859375,
-0.0162200927734375,
0.0076751708984375,
0.006500244140625,
-0.015899658203125,
-0.00249481201171875,
0.049530029296875,
-0.032196044921875,
0.01812744140625,
0.016326904296875,
0.0015726089477539062,
0.0057525634765625,
0.00024116039276123047,
0.003345489501953125,
-0.01282501220703125,
-0.0124664306640625,
-0.0099945068359375,
-0.04400634765625,
0.00579071044921875,
-0.0126953125,
-0.00730133056640625,
0.002655029296875,
0.00040268898010253906,
-0.0012645721435546875,
-0.00638580322265625,
0.0258941650390625,
0.011138916015625,
-0.0141448974609375,
-0.032196044921875,
-0.002269744873046875,
0.046356201171875,
0.0033855438232421875,
-0.004673004150390625,
-0.0127716064453125,
0.0199737548828125,
0.00007641315460205078,
-0.0099639892578125,
0.006908416748046875,
-0.034332275390625,
-0.0019254684448242188,
0.0258026123046875,
-0.00577545166015625,
0.01197052001953125,
0.01149749755859375,
-0.0120086669921875,
-0.004116058349609375,
-0.00591278076171875,
0.025115966796875,
0.00362396240234375,
0.01128387451171875,
0.0018377304077148438,
0.023468017578125,
0.0110015869140625,
-0.03265380859375,
0.05224609375,
-0.0099334716796875,
-0.0177001953125,
0.019683837890625,
0.0002956390380859375,
0.00628662109375,
0.01282501220703125,
0.01136016845703125,
-0.0014324188232421875,
-0.0091400146484375,
-0.00787353515625,
0.0139007568359375,
0.0206298828125,
-0.0251007080078125,
0.00971221923828125,
0.01213836669921875,
-0.00917816162109375,
0.007419586181640625,
-0.013427734375,
0.01415252685546875,
0.00894927978515625,
0.009490966796875,
-0.016204833984375,
0.0292205810546875,
0.01453399658203125,
0.01120758056640625,
-0.010528564453125,
-0.0008831024169921875,
0.00958251953125,
-0.021240234375,
-0.004199981689453125,
0.005035400390625,
0.01230621337890625,
-0.0294647216796875,
0.01910400390625,
0.00579071044921875,
0.0019779205322265625,
0.036865234375,
0.012115478515625,
0.002689361572265625,
-0.00571441650390625,
-0.0143585205078125,
0.00325775146484375,
0.0172119140625,
-0.0029754638671875,
-0.0206298828125,
-0.01100921630859375,
-0.006702423095703125,
-0.002910614013671875,
-0.0228424072265625,
-0.0217742919921875,
-0.01447296142578125,
-0.007354736328125,
-0.014892578125,
0.01153564453125,
0.029144287109375,
-0.00225067138671875,
-0.017333984375,
0.002044677734375,
-0.00836181640625,
0.02728271484375,
0.01947021484375,
-0.017120361328125,
0.0313720703125,
-0.035919189453125,
-0.024078369140625,
-0.03228759765625,
-0.02490234375,
-0.02874755859375,
0.00814056396484375,
-0.00945281982421875,
0.0004420280456542969,
-0.0238494873046875,
0.011932373046875,
-0.0186614990234375,
0.022247314453125,
-0.021026611328125,
-0.00951385498046875,
-0.01348876953125,
-0.00399017333984375,
0.01407623291015625,
-0.024749755859375,
0.028045654296875,
0.0183563232421875,
-0.017822265625,
0.01934814453125,
0.02374267578125,
-0.0064849853515625,
-0.006763458251953125,
0.004787445068359375,
-0.0139923095703125,
0.0146484375,
0.043914794921875,
-0.0301666259765625,
0.0262603759765625,
0.0294342041015625,
-0.0004718303680419922,
0.021026611328125,
-0.00209808349609375,
0.0088043212890625,
0.0243377685546875,
-0.02850341796875,
0.0029773712158203125,
0.015045166015625
] |
ours_547
|
There are two possibilities: either the diagonals face a side (i.e., are parallel to some side), or the diagonals face a vertex. For each case, there are 5 possible directions (1 for each pair of vertices and sides). In the first case, there are 5 diagonals for each direction, giving \(\binom{5}{2} = 10\) pairs for each direction. In the second case, there are 4 diagonals for each direction, giving \(\binom{4}{2} = 6\) pairs for each direction. This gives \(5 \times 10 + 5 \times 6 = 80\) total pairs.
\(\boxed{80}\)
|
80
|
{
"competition": "us_comps",
"dataset": "Ours",
"posts": null,
"source": "OMOSoln2.md"
}
|
Each pair of vertices of a regular 10-sided polygon is connected by a line segment. How many unordered pairs of distinct parallel line segments can be chosen from these segments?
|
[
"/Mathematics/DiscreteMathematics/Combinatorics/BinomialCoefficients",
"/Mathematics/DiscreteMathematics/Combinatorics/Enumeration",
"/Mathematics/DiscreteMathematics/Combinatorics/GeneralCombinatorics",
"/Mathematics/Geometry/CombinatorialGeometry",
"/Mathematics/Geometry/PlaneGeometry/Polygons/ConvexPolygon",
"/Mathematics/Geometry/PlaneGeometry/Polygons/Decagon",
"/Mathematics/Geometry/PlaneGeometry/Polygons/EquiangularPolygon",
"/Mathematics/Geometry/PlaneGeometry/Polygons/EquilateralPolygon",
"/Mathematics/Geometry/PlaneGeometry/Polygons/RegularDecagon",
"/Mathematics/Geometry/PlaneGeometry/Polygons/RegularPolygon",
"/Mathematics/Geometry/PlaneGeometry/Polygons/SimplePolygon",
"/Mathematics/Geometry/Symmetry/RotationalSymmetry"
] |
Classify all segments by the five possible parallel directions (side‑parallel or vertex‑parallel) and count unordered pairs within each direction.
|
[
-0.0001424551010131836,
-0.03143310546875,
0.0202484130859375,
0.0151824951171875,
-0.0002257823944091797,
0.0169525146484375,
0.044769287109375,
-0.0226898193359375,
0.01557159423828125,
0.01084136962890625,
-0.004291534423828125,
-0.004383087158203125,
-0.00438690185546875,
-0.020477294921875,
-0.037078857421875,
-0.0036640167236328125,
-0.0033817291259765625,
0.0017557144165039062,
0.0012569427490234375,
-0.0059051513671875,
-0.0085601806640625,
0.006755828857421875,
-0.042388916015625,
0.0303955078125,
0.0024280548095703125,
-0.0250396728515625,
-0.02099609375,
0.0157623291015625,
0.0102691650390625,
0.0136566162109375,
0.0024700164794921875,
-0.028228759765625,
0.0235595703125,
-0.01190185546875,
0.0030040740966796875,
0.014739990234375,
-0.002117156982421875,
-0.00785064697265625,
-0.007152557373046875,
-0.0640869140625,
0.006710052490234375,
-0.0262298583984375,
0.0102691650390625,
0.0107421875,
-0.0096435546875,
0.0192413330078125,
0.0035247802734375,
0.02716064453125,
-0.01345062255859375,
-0.00197601318359375,
0.0008096694946289062,
0.01203155517578125,
-0.0254364013671875,
-0.0176849365234375,
0.004726409912109375,
-0.054229736328125,
-0.009124755859375,
-0.0007295608520507812,
-0.0223846435546875,
0.0038280487060546875,
0.0045318603515625,
-0.0157012939453125,
-0.005512237548828125,
-0.0235443115234375,
-0.007564544677734375,
-0.0101165771484375,
0.00896453857421875,
-0.0224609375,
0.00740814208984375,
-0.021270751953125,
-0.035888671875,
-0.022857666015625,
0.0058746337890625,
0.0008754730224609375,
0.01204681396484375,
-0.0279693603515625,
-0.0117340087890625,
0.0168609619140625,
0.00601959228515625,
0.00445556640625,
0.0028705596923828125,
0.0130767822265625,
0.01039886474609375,
0.00016641616821289062,
0.01267242431640625,
0.00998687744140625,
0.0259246826171875,
-0.004695892333984375,
0.0289764404296875,
-0.0077056884765625,
0.005092620849609375,
-0.00658416748046875,
0.0010328292846679688,
0.039306640625,
0.0007634162902832031,
-0.0081634521484375,
0.01007080078125,
-0.0162506103515625,
-0.016204833984375,
0.00959014892578125,
-0.007762908935546875,
-0.0079803466796875,
-0.004329681396484375,
-0.0169219970703125,
-0.0330810546875,
-0.0201568603515625,
-0.0172576904296875,
-0.0006566047668457031,
-0.005321502685546875,
-0.0012683868408203125,
0.008209228515625,
0.01267242431640625,
0.00926971435546875,
0.01029205322265625,
0.0153045654296875,
-0.01287841796875,
0.004703521728515625,
-0.0164031982421875,
-0.0117034912109375,
-0.0056610107421875,
-0.0006847381591796875,
0.0162506103515625,
-0.00035119056701660156,
0.00968170166015625,
0.01154327392578125,
-0.0396728515625,
-0.0124664306640625,
-0.030181884765625,
-0.0295867919921875,
0.019256591796875,
0.030670166015625,
0.0005888938903808594,
-0.0295257568359375,
-0.041656494140625,
0.016754150390625,
-0.0011606216430664062,
0.00011044740676879883,
0.003082275390625,
0.0171356201171875,
-0.003818511962890625,
0.0013866424560546875,
-0.00775909423828125,
0.0078277587890625,
-0.039337158203125,
-0.0106201171875,
-0.0240478515625,
-0.0069732666015625,
-0.043487548828125,
0.0198974609375,
0.005344390869140625,
0.0111236572265625,
-0.007656097412109375,
0.0129852294921875,
0.0233154296875,
-0.010345458984375,
0.006404876708984375,
-0.0017719268798828125,
0.0153656005859375,
0.0261688232421875,
0.0172576904296875,
-0.01291656494140625,
0.00586700439453125,
0.018707275390625,
0.0217437744140625,
0.0019483566284179688,
0.0096893310546875,
-0.0202789306640625,
-0.005222320556640625,
-0.01293182373046875,
0.02203369140625,
-0.0081024169921875,
0.00257110595703125,
0.01103973388671875,
-0.019561767578125,
-0.0178985595703125,
-0.00046753883361816406,
-0.004741668701171875,
0.017333984375,
-0.006622314453125,
-0.0243072509765625,
0.002086639404296875,
-0.033966064453125,
0.0211334228515625,
-0.0006656646728515625,
0.0231475830078125,
0.0074615478515625,
-0.0016889572143554688,
0.00787353515625,
0.01544952392578125,
0.01531982421875,
-0.004199981689453125,
-0.068603515625,
-0.004482269287109375,
0.0100250244140625,
-0.0024929046630859375,
-0.01483154296875,
-0.017578125,
0.011016845703125,
0.002246856689453125,
0.01384735107421875,
0.001293182373046875,
-0.01084136962890625,
0.0011730194091796875,
0.0043487548828125,
0.01222991943359375,
-0.0102081298828125,
0.00669097900390625,
-0.00958251953125,
0.0009164810180664062,
-0.00390625,
-0.00693511962890625,
-0.01250457763671875,
-0.0193634033203125,
-0.006160736083984375,
-0.00939178466796875,
-0.012786865234375,
-0.0196533203125,
-0.0085296630859375,
0.0264892578125,
-0.0206298828125,
0.01561737060546875,
0.00569915771484375,
-0.01549530029296875,
0.00980377197265625,
-0.020965576171875,
0.004993438720703125,
0.0020961761474609375,
-0.003108978271484375,
0.0271453857421875,
0.01023101806640625,
0.02911376953125,
0.006427764892578125,
-0.016204833984375,
-0.01233673095703125,
0.0016002655029296875,
0.002044677734375,
-0.02215576171875,
0.001079559326171875,
0.0017995834350585938,
0.0197601318359375,
0.02069091796875,
-0.0188140869140625,
0.00786590576171875,
-0.0026035308837890625,
-0.0010519027709960938,
-0.004528045654296875,
0.00537872314453125,
-0.019927978515625,
0.005931854248046875,
-0.0146484375,
-0.019500732421875,
0.0177764892578125,
-0.0013570785522460938,
-0.0024013519287109375,
-0.0091094970703125,
0.0010995864868164062,
-0.020599365234375,
-0.017822265625,
-0.0005016326904296875,
-0.0190887451171875,
-0.01294708251953125,
0.000029385089874267578,
0.0020999908447265625,
-0.01343536376953125,
0.0031375885009765625,
0.029388427734375,
0.0204925537109375,
-0.0098114013671875,
0.0214385986328125,
-0.0011301040649414062,
0.03375244140625,
-0.01323699951171875,
-0.033203125,
0.00868988037109375,
-0.004329681396484375,
-0.01111602783203125,
0.006061553955078125,
0.0185546875,
0.027252197265625,
0.0138092041015625,
-0.00311279296875,
0.00909423828125,
0.01238250732421875,
0.02410888671875,
0.0024871826171875,
-0.0017366409301757812,
-0.0013446807861328125,
-0.005527496337890625,
-0.00951385498046875,
0.0005393028259277344,
0.0019683837890625,
-0.005535125732421875,
-0.01490020751953125,
-0.0118865966796875,
0.013824462890625,
-0.01374053955078125,
0.0031528472900390625,
-0.00496673583984375,
0.003276824951171875,
0.0015344619750976562,
0.0193328857421875,
-0.031829833984375,
0.020263671875,
0.0281524658203125,
0.0020008087158203125,
0.0225372314453125,
0.01544189453125,
-0.0214385986328125,
-0.01702880859375,
0.004917144775390625,
0.01219940185546875,
0.01056671142578125,
0.0029201507568359375,
-0.007080078125,
0.0316162109375,
-0.0325927734375,
-0.007358551025390625,
0.018524169921875,
-0.0116424560546875,
-0.004421234130859375,
0.0185546875,
-0.01971435546875,
0.0268707275390625,
-0.0162353515625,
0.0625,
-0.003406524658203125,
0.01462554931640625,
0.0188140869140625,
-0.017791748046875,
0.0165863037109375,
-0.0180511474609375,
0.023651123046875,
-0.028533935546875,
-0.0203704833984375,
-0.032806396484375,
-0.004909515380859375,
0.005138397216796875,
0.037109375,
0.01172637939453125,
-0.0014791488647460938,
0.004688262939453125,
0.034210205078125,
0.009246826171875,
-0.0017957687377929688,
-0.007537841796875,
0.027191162109375,
-0.06304931640625,
-0.0135345458984375,
-0.04718017578125,
-0.00945281982421875,
-0.0173492431640625,
0.0198974609375,
0.00678253173828125,
-0.00016415119171142578,
-0.0296478271484375,
0.000980377197265625,
-0.0164794921875,
-0.004596710205078125,
0.009002685546875,
0.0279083251953125,
0.00516510009765625,
-0.01367950439453125,
-0.0116424560546875,
-0.005283355712890625,
-0.007320404052734375,
-0.045806884765625,
0.0013904571533203125,
0.0306854248046875,
-0.036163330078125,
-0.030792236328125,
0.007312774658203125,
-0.0147705078125,
-0.003910064697265625,
-0.0209197998046875,
0.0112762451171875,
0.016387939453125,
0.00710296630859375,
0.0139617919921875,
-0.007175445556640625,
-0.0135345458984375,
0.00753021240234375,
0.0163726806640625,
-0.01031494140625,
0.028076171875,
-0.006763458251953125,
0.0126800537109375,
0.015594482421875,
-0.0184173583984375,
-0.02496337890625,
0.02056884765625,
-0.003505706787109375,
0.00818634033203125,
-0.00829315185546875,
-0.0087127685546875,
0.02874755859375,
-0.00446319580078125,
0.0087432861328125,
0.0034732818603515625,
0.0614013671875,
0.0030956268310546875,
-0.0096435546875,
0.0009202957153320312,
-0.01403045654296875,
0.006557464599609375,
0.01262664794921875,
-0.007732391357421875,
0.0010509490966796875,
-0.0015239715576171875,
-0.00876617431640625,
-0.01194000244140625,
0.013641357421875,
0.037628173828125,
-0.003215789794921875,
-0.037384033203125,
0.0025043487548828125,
-0.0091094970703125,
0.01491546630859375,
0.02056884765625,
-0.047698974609375,
-0.01479339599609375,
-0.0020160675048828125,
-0.01552581787109375,
0.0020046234130859375,
-0.00887298583984375,
0.043701171875,
0.0113677978515625,
0.01153564453125,
0.04534912109375,
0.0244293212890625,
0.007965087890625,
0.031463623046875,
-0.014892578125,
0.0007152557373046875,
0.07177734375,
0.003841400146484375,
0.01348114013671875,
0.027435302734375,
0.0166015625,
0.005435943603515625,
-0.0038394927978515625,
0.0018835067749023438,
-0.03564453125,
0.01318359375,
-0.01216888427734375,
-0.015869140625,
0.022216796875,
0.0088043212890625,
0.031585693359375,
0.0025730133056640625,
0.032470703125,
-0.0124664306640625,
-0.04376220703125,
-0.0205535888671875,
-0.031982421875,
0.020263671875,
0.0270538330078125,
-0.0011930465698242188,
-0.0170440673828125,
-0.015655517578125,
-0.01438140869140625,
-0.0204925537109375,
0.003936767578125,
-0.0111236572265625,
-0.0006709098815917969,
-0.0125274658203125,
-0.01788330078125,
-0.020721435546875,
-0.0016613006591796875,
0.0628662109375,
-0.00362396240234375,
-0.01137542724609375,
-0.0220184326171875,
0.0003268718719482422,
0.002407073974609375,
-0.0355224609375,
-0.0022182464599609375,
0.00421905517578125,
0.01018524169921875,
0.004787445068359375,
-0.006824493408203125,
-0.028350830078125,
0.01302337646484375,
0.022369384765625,
0.025115966796875,
0.005832672119140625,
0.0204620361328125,
0.0266265869140625,
0.01430511474609375,
0.006549835205078125,
0.0010967254638671875,
0.005084991455078125,
0.01551055908203125,
-0.0293731689453125,
-0.03167724609375,
-0.023773193359375,
-0.028717041015625,
0.025482177734375,
-0.0195770263671875,
0.0279541015625,
0.0015726089477539062,
-0.006824493408203125,
0.0145721435546875,
-0.0232391357421875,
-0.01568603515625,
-0.01329803466796875,
-0.0205535888671875,
0.03326416015625,
-0.04052734375,
0.007740020751953125,
0.0210418701171875,
-0.00933074951171875,
0.0158538818359375,
0.0222625732421875,
-0.06561279296875,
0.01543426513671875,
-0.003368377685546875,
-0.007793426513671875,
-0.0220184326171875,
-0.01277923583984375,
0.0360107421875,
-0.019439697265625,
0.023468017578125,
-0.01361083984375,
-0.007587432861328125,
-0.0242156982421875,
0.038360595703125,
0.0341796875,
-0.024017333984375,
-0.018157958984375,
0.01267242431640625,
-0.0082550048828125,
-0.01143646240234375,
-0.043548583984375,
-0.01035308837890625,
-0.0050201416015625,
0.0013933181762695312,
-0.00949859619140625,
0.00525665283203125,
0.0272064208984375,
-0.0002684593200683594,
-0.014984130859375,
-0.0223236083984375,
0.0161285400390625,
-0.000885009765625,
0.007572174072265625,
-0.01325225830078125,
-0.00044608116149902344,
0.01473236083984375,
-0.005321502685546875,
-0.006000518798828125,
0.0207977294921875,
0.0191192626953125,
-0.0021266937255859375,
-0.00652313232421875,
-0.024383544921875,
0.0005817413330078125,
-0.037445068359375,
-0.03277587890625,
-0.002643585205078125,
0.00083160400390625,
-0.005771636962890625,
0.0258331298828125,
0.004425048828125,
0.0053863525390625,
0.0108642578125,
-0.0277862548828125,
-0.002307891845703125,
0.00559234619140625,
-0.036712646484375,
-0.041412353515625,
0.00641632080078125,
-0.004344940185546875,
0.009307861328125,
0.0078887939453125,
0.03436279296875,
0.00028133392333984375,
-0.00141143798828125,
0.007518768310546875,
0.0228118896484375,
-0.04241943359375,
0.032257080078125,
0.02587890625,
-0.0220184326171875,
-0.0222930908203125,
0.0450439453125,
0.0118865966796875,
-0.014068603515625,
-0.0007605552673339844,
0.037109375,
0.00661468505859375,
-0.006618499755859375,
0.026641845703125,
-0.0023517608642578125,
0.00495147705078125,
-0.0182037353515625,
-0.01025390625,
0.032135009765625,
0.0001920461654663086,
-0.0111541748046875,
0.0036182403564453125,
-0.002742767333984375,
-0.041961669921875,
0.0014858245849609375,
-0.0108642578125,
-0.0272979736328125,
-0.0213470458984375,
0.03125,
0.01593017578125,
0.0026149749755859375,
0.015838623046875,
-0.0129852294921875,
-0.00033855438232421875,
-0.00598907470703125,
0.0198516845703125,
0.030181884765625,
-0.017333984375,
-0.01210784912109375,
-0.01059722900390625,
-0.03436279296875,
0.041656494140625,
-0.0222320556640625,
-0.0157318115234375,
-0.00916290283203125,
0.01242828369140625,
0.01111602783203125,
-0.03875732421875,
-0.0048065185546875,
-0.047607421875,
-0.00585174560546875,
-0.033416748046875,
0.006610870361328125,
-0.03240966796875,
0.033355712890625,
-0.015655517578125,
0.0027370452880859375,
-0.040679931640625,
-0.0278167724609375,
0.0227203369140625,
0.0367431640625,
-0.0019550323486328125,
-0.0257720947265625,
0.043731689453125,
0.040924072265625,
-0.046966552734375,
0.02471923828125,
0.0106048583984375,
-0.0196990966796875,
0.0145721435546875,
0.0014715194702148438,
-0.002857208251953125,
-0.0249786376953125,
-0.0230255126953125,
-0.0022411346435546875,
0.003192901611328125,
0.00989532470703125,
-0.01152801513671875,
0.009246826171875,
-0.01233673095703125,
0.03228759765625,
0.0025272369384765625,
-0.0012531280517578125,
-0.0037078857421875,
-0.0015535354614257812,
0.01361083984375,
-0.0209197998046875,
-0.003940582275390625,
0.0017833709716796875,
0.00015306472778320312,
0.0210113525390625,
0.028778076171875,
0.006969451904296875,
0.0096282958984375,
-0.0159759521484375,
-0.0229339599609375,
0.037445068359375,
-0.0143890380859375,
-0.0023403167724609375,
0.00047969818115234375,
0.03314208984375,
0.0033435821533203125,
-0.00656890869140625,
0.036834716796875,
0.0233154296875,
-0.0148162841796875,
0.009063720703125,
0.03607177734375,
0.0221405029296875,
-0.001972198486328125,
0.023712158203125,
0.044647216796875,
0.0202484130859375,
-0.0165863037109375,
-0.006618499755859375,
-0.0018968582153320312,
0.01120758056640625,
0.0215911865234375,
0.01593017578125,
-0.03558349609375,
-0.04449462890625,
-0.01317596435546875,
0.0037136077880859375,
-0.0450439453125,
0.0244598388671875,
0.00540924072265625,
-0.00029850006103515625,
-0.01122283935546875,
0.006542205810546875,
0.013427734375,
-0.0053253173828125,
-0.0162506103515625,
-0.0225982666015625,
-0.0102691650390625,
-0.04193115234375,
-0.0018110275268554688,
-0.007293701171875,
-0.01395416259765625,
-0.022308349609375,
-0.01220703125,
-0.00200653076171875,
0.0029659271240234375,
0.01450347900390625,
-0.01087188720703125,
-0.033050537109375,
-0.021087646484375,
-0.00988006591796875,
0.004413604736328125,
0.0005288124084472656,
-0.025115966796875,
-0.06146240234375,
0.01788330078125,
0.01166534423828125,
-0.0272064208984375,
0.002834320068359375,
0.007396697998046875,
-0.04315185546875,
-0.0113983154296875,
0.00872039794921875,
-0.0246124267578125,
0.002353668212890625,
-0.0166168212890625,
0.0364990234375,
0.01499176025390625,
0.01215362548828125,
0.020233154296875,
-0.004886627197265625,
-0.0031871795654296875,
-0.00023293495178222656,
-0.0006585121154785156,
0.004116058349609375,
0.007045745849609375,
0.0286712646484375,
-0.0207977294921875,
0.038421630859375,
-0.00962066650390625,
-0.0269012451171875,
0.0301055908203125,
0.0214691162109375,
-0.01373291015625,
-0.031646728515625,
0.002201080322265625,
-0.05810546875,
-0.014190673828125,
0.0179443359375,
-0.00902557373046875,
-0.0157470703125,
-0.039764404296875,
-0.00013339519500732422,
0.01910400390625,
-0.039215087890625,
0.04376220703125,
-0.00876617431640625,
-0.00983428955078125,
0.0175933837890625,
0.00170135498046875,
-0.005809783935546875,
0.004657745361328125,
-0.04815673828125,
-0.01136016845703125,
0.019989013671875,
-0.031402587890625,
-0.0125274658203125,
-0.0237579345703125,
-0.0014476776123046875,
0.02093505859375,
-0.01953125,
-0.00029850006103515625,
-0.00696563720703125,
-0.0064849853515625,
0.0296783447265625,
-0.01403045654296875,
0.0187530517578125,
0.03204345703125,
-0.016754150390625,
0.0118408203125,
0.017578125,
0.0079193115234375,
-0.0020465850830078125,
-0.0103759765625,
-0.001529693603515625,
-0.0005660057067871094,
0.0107879638671875,
-0.0404052734375,
-0.0048065185546875,
0.004795074462890625,
0.0078887939453125,
-0.01108551025390625,
0.007122039794921875,
0.01334381103515625,
-0.0232086181640625,
0.005077362060546875,
-0.00800323486328125,
0.007343292236328125,
-0.007080078125,
-0.0031757354736328125,
0.0068359375,
-0.007080078125,
0.01361083984375,
0.02490234375,
0.014892578125,
0.017822265625,
-0.001728057861328125,
0.02532958984375,
-0.036834716796875,
-0.0031871795654296875,
-0.01029205322265625,
0.01238250732421875,
-0.0166473388671875,
-0.007537841796875,
0.0003848075866699219,
0.007289886474609375,
0.01107025146484375,
0.0193328857421875,
0.00556182861328125,
0.004734039306640625,
0.0154266357421875,
-0.01509857177734375,
0.0249786376953125,
-0.006561279296875,
-0.0166778564453125,
-0.01215362548828125,
0.0022640228271484375,
0.009429931640625,
0.0298309326171875,
-0.005039215087890625,
0.0282745361328125,
-0.00438690185546875,
-0.032867431640625,
0.004505157470703125,
0.0022735595703125,
0.030670166015625,
0.01561737060546875,
0.04205322265625,
-0.0129547119140625,
0.00769805908203125,
0.00445556640625,
0.0142669677734375,
0.01154327392578125,
-0.01290130615234375,
0.004669189453125,
-0.01270294189453125,
-0.002750396728515625,
-0.03302001953125,
0.020355224609375,
0.021575927734375,
0.01076507568359375,
-0.03643798828125,
-0.009124755859375,
-0.01454925537109375,
0.0203857421875,
-0.01126861572265625,
0.008697509765625,
0.017486572265625,
0.0201873779296875,
0.0069732666015625,
0.045013427734375,
0.02117919921875,
-0.03814697265625,
-0.0170440673828125,
0.036468505859375,
0.02410888671875,
0.0374755859375,
-0.0306396484375,
0.03839111328125,
0.0235443115234375,
-0.00949859619140625,
-0.0171661376953125,
0.0121307373046875,
0.025909423828125,
0.0312042236328125,
-0.0211334228515625,
0.0203094482421875,
-0.0033435821533203125,
-0.01389312744140625,
-0.023193359375,
0.0231170654296875,
-0.039337158203125,
-0.01096343994140625,
-0.0095977783203125,
0.01145172119140625,
-0.029449462890625,
0.005077362060546875,
0.01145172119140625,
0.007617950439453125,
0.0007691383361816406,
0.01641845703125,
-0.004337310791015625,
-0.006618499755859375,
0.01197052001953125,
-0.01056671142578125,
0.00322723388671875,
-0.020477294921875,
-0.01654052734375,
-0.007465362548828125,
-0.000640869140625,
-0.044342041015625,
-0.01067352294921875,
-0.01947021484375,
0.016387939453125,
-0.00899505615234375,
-0.00757598876953125,
0.03765869140625,
0.00972747802734375,
-0.00673675537109375,
0.00835418701171875,
0.015960693359375,
-0.03759765625,
-0.01367950439453125,
0.0051727294921875,
-0.02288818359375,
-0.006771087646484375,
-0.020477294921875,
0.0225830078125,
0.004547119140625,
-0.01555633544921875,
-0.031524658203125,
0.028228759765625,
-0.059112548828125,
-0.047821044921875,
0.033203125,
0.005321502685546875,
-0.0265655517578125,
0.0019445419311523438,
0.02777099609375,
0.041351318359375,
0.0161285400390625,
-0.014007568359375,
-0.00019681453704833984,
-0.0003266334533691406,
0.00531768798828125,
0.0053558349609375,
-0.030517578125,
0.004302978515625,
-0.0377197265625,
-0.0005092620849609375,
0.00998687744140625,
0.0009632110595703125,
-0.01084136962890625,
-0.0023021697998046875,
0.0022258758544921875,
-0.0135498046875,
-0.01483154296875,
-0.0017023086547851562,
-0.036102294921875,
0.024871826171875,
0.00930023193359375,
0.0194854736328125,
-0.00928497314453125,
0.0311279296875,
0.0195770263671875,
0.01476287841796875,
-0.01332855224609375,
-0.03338623046875,
-0.0027294158935546875,
-0.0157318115234375,
-0.0010585784912109375,
0.031005859375,
0.036224365234375,
0.00919342041015625,
0.043853759765625,
0.031707763671875,
-0.028350830078125,
0.02032470703125,
0.02349853515625,
0.00818634033203125,
-0.01788330078125,
-0.0312042236328125,
-0.018157958984375,
-0.00653839111328125,
-0.01219940185546875,
-0.01654052734375,
-0.021759033203125,
-0.005290985107421875,
0.02215576171875,
0.01461029052734375,
-0.01058197021484375,
-0.004364013671875,
0.0033550262451171875,
0.0029315948486328125,
0.032012939453125,
0.017822265625,
-0.0291595458984375,
0.0128021240234375,
0.0130767822265625,
-0.032623291015625,
0.0189056396484375,
-0.0222015380859375,
0.0214080810546875,
-0.0280303955078125,
-0.0012607574462890625,
-0.0235595703125,
-0.0013589859008789062,
0.00988006591796875,
-0.024383544921875,
0.0018129348754882812,
0.003459930419921875,
-0.008270263671875,
0.0083770751953125,
0.041107177734375,
-0.03167724609375,
0.035247802734375,
-0.0051422119140625,
-0.01224517822265625,
-0.00472259521484375,
-0.0275726318359375,
-0.01549530029296875,
-0.023162841796875,
-0.0212554931640625,
-0.0085906982421875,
-0.005992889404296875,
0.0211944580078125,
0.0207061767578125,
-0.001903533935546875,
-0.0027027130126953125,
0.030487060546875,
-0.0238800048828125,
-0.00560760498046875,
-0.00018227100372314453,
-0.005855560302734375,
-0.01416778564453125,
-0.008880615234375,
-0.00843048095703125,
-0.0161590576171875,
0.025115966796875,
-0.029693603515625,
-0.01386260986328125,
-0.002872467041015625,
0.0156402587890625,
0.00009161233901977539,
-0.026947021484375,
-0.006591796875,
0.02301025390625,
0.000629425048828125,
-0.01444244384765625,
-0.0281219482421875,
-0.0277099609375,
0.0233306884765625,
0.0005307197570800781,
0.0035381317138671875,
-0.01538848876953125,
0.0274200439453125,
0.0010042190551757812,
-0.01374053955078125,
0.0195159912109375,
-0.0274200439453125,
-0.003658294677734375,
0.004795074462890625,
-0.02642822265625,
-0.01141357421875,
-0.0009899139404296875,
0.0103302001953125,
-0.0185546875,
0.024383544921875,
0.037872314453125,
-0.01061248779296875,
0.020538330078125,
-0.0303802490234375,
0.005260467529296875,
-0.0083770751953125,
-0.005146026611328125,
-0.01505279541015625,
0.00144195556640625,
0.0035533905029296875,
-0.037567138671875,
-0.007843017578125,
0.00217437744140625,
-0.007171630859375,
0.02337646484375,
-0.0085601806640625,
0.01009368896484375,
-0.002086639404296875,
0.0166778564453125,
0.005863189697265625,
-0.0141448974609375,
0.01445770263671875,
0.0220794677734375,
0.01531219482421875,
0.0087127685546875,
0.01284027099609375,
-0.0025501251220703125,
-0.045745849609375,
0.00469970703125,
0.0231781005859375,
0.0002970695495605469,
0.008514404296875,
-0.0048370361328125,
-0.03680419921875,
-0.0298614501953125,
0.0245819091796875,
0.0084991455078125,
0.01007843017578125,
-0.049102783203125,
0.00705718994140625,
0.0035114288330078125,
0.0062255859375,
0.0097198486328125,
-0.007171630859375,
-0.0280914306640625,
-0.02276611328125,
-0.02301025390625,
-0.052215576171875,
-0.0019359588623046875,
0.0168304443359375,
0.00988006591796875,
0.044219970703125,
0.0206451416015625,
-0.01404571533203125,
0.020660400390625,
0.007686614990234375,
-0.0382080078125,
0.00818634033203125,
-0.0096588134765625,
0.017791748046875,
0.0089874267578125,
-0.026123046875,
0.01300811767578125,
0.0198974609375,
-0.016754150390625,
0.0182342529296875,
0.04193115234375,
-0.0233917236328125,
-0.00518798828125,
0.01708984375,
-0.0308074951171875,
0.0158233642578125,
-0.034423828125,
-0.0265655517578125,
0.007415771484375,
0.0005588531494140625,
0.0251007080078125,
0.002361297607421875,
-0.02532958984375,
0.017669677734375,
-0.005756378173828125,
0.019927978515625,
0.005268096923828125,
-0.01238250732421875,
-0.0080718994140625,
-0.0204315185546875,
-0.0318603515625,
-0.012481689453125,
0.0029239654541015625,
0.006134033203125,
0.02105712890625,
0.00746917724609375,
-0.0234375,
-0.003849029541015625,
-0.00377655029296875,
0.011138916015625,
0.007579803466796875,
0.023223876953125,
-0.0197296142578125,
-0.0316162109375,
0.0078582763671875,
0.0258331298828125,
0.029510498046875,
0.041412353515625,
0.01303863525390625,
0.038818359375,
-0.014617919921875,
-0.0141754150390625,
-0.0158233642578125,
0.004180908203125,
0.021331787109375,
0.0157318115234375,
-0.042022705078125,
-0.0025691986083984375,
-0.0089263916015625,
-0.0022563934326171875,
-0.008575439453125,
-0.03411865234375,
0.0120697021484375,
-0.0211944580078125,
0.0194091796875,
-0.04217529296875,
-0.01152801513671875,
-0.01302337646484375,
-0.0166168212890625,
-0.011962890625,
-0.004364013671875,
-0.0302734375,
0.0023326873779296875,
-0.0029888153076171875,
-0.0025691986083984375,
-0.00656890869140625,
-0.01300048828125,
-0.00934600830078125,
0.01113128662109375,
0.04486083984375,
-0.0233917236328125,
0.00859832763671875,
-0.0211944580078125,
-0.027252197265625,
-0.00026416778564453125,
0.005695343017578125,
0.0191802978515625,
0.0243988037109375,
0.037506103515625,
0.007228851318359375,
-0.0091094970703125,
-0.0023212432861328125,
0.0009303092956542969,
-0.005645751953125,
0.025787353515625,
-0.00995635986328125,
-0.0172119140625,
0.0050201416015625,
-0.02862548828125,
0.04736328125,
0.0214996337890625,
0.01253509521484375,
0.053192138671875,
0.0008549690246582031,
-0.0132293701171875,
0.005401611328125,
-0.047637939453125,
0.017578125,
-0.010345458984375,
0.0228271484375,
0.013214111328125,
0.007381439208984375,
-0.0082855224609375,
0.0270233154296875,
-0.0021610260009765625,
-0.000476837158203125,
0.04815673828125,
-0.008880615234375,
-0.011749267578125,
0.0253448486328125,
-0.011199951171875,
-0.003936767578125,
-0.013702392578125,
0.05230712890625,
-0.010101318359375,
-0.0005154609680175781,
-0.000240325927734375,
-0.025848388671875,
0.0018377304077148438,
-0.0311126708984375,
-0.0009908676147460938,
0.022705078125,
-0.004177093505859375,
-0.0180511474609375,
-0.003215789794921875,
-0.00617218017578125,
0.0018482208251953125,
-0.0000909566879272461,
-0.002681732177734375,
0.028350830078125,
-0.0020313262939453125,
-0.0252838134765625,
0.0034637451171875,
0.0185546875,
-0.00908660888671875,
0.0010318756103515625,
0.0210113525390625,
0.0037441253662109375,
0.0198516845703125,
-0.0277099609375,
-0.0019388198852539062,
0.00005882978439331055,
-0.020111083984375,
0.0302734375,
0.02099609375,
0.0291748046875,
-0.0251922607421875,
0.01215362548828125,
-0.03240966796875,
0.0038127899169921875,
-0.005222320556640625,
0.00684356689453125,
-0.01561737060546875,
0.0015401840209960938,
-0.0082855224609375,
0.0119171142578125,
0.00341033935546875,
-0.0006737709045410156,
0.00632476806640625,
-0.023406982421875,
-0.0019388198852539062,
-0.002155303955078125,
-0.0198822021484375,
0.007228851318359375,
0.003025054931640625,
0.00611114501953125,
0.01308441162109375,
-0.0242767333984375,
0.03924560546875,
0.014801025390625,
-0.01221466064453125,
-0.0016012191772460938,
-0.00035572052001953125,
-0.006198883056640625,
0.021484375,
-0.00623321533203125,
0.04193115234375,
-0.0170440673828125,
-0.03887939453125,
-0.0218505859375,
0.01038360595703125,
-0.0265960693359375,
0.01357269287109375,
-0.0012569427490234375,
-0.0016012191772460938,
0.0297088623046875,
-0.00934600830078125,
-0.0186767578125,
-0.026947021484375,
-0.0025272369384765625,
-0.00513458251953125,
-0.0169830322265625,
-0.0142974853515625,
0.0090179443359375,
-0.0003674030303955078,
-0.00014483928680419922,
-0.0021209716796875,
0.001522064208984375,
0.0253143310546875,
0.01392364501953125,
0.0247802734375,
-0.005863189697265625,
0.0018482208251953125,
-0.016845703125,
-0.0137939453125,
-0.0168914794921875,
0.0029354095458984375,
0.0067138671875,
-0.0615234375,
0.038665771484375,
0.004611968994140625,
-0.0411376953125,
0.0237579345703125,
0.019378662109375,
-0.0191192626953125,
0.0312042236328125,
-0.01367950439453125,
0.03436279296875,
0.01161956787109375,
0.00901031494140625,
0.01995849609375,
-0.010894775390625,
0.05316162109375,
-0.0199737548828125,
-0.00896453857421875,
-0.01398468017578125,
0.01824951171875,
0.0011806488037109375,
0.0038585662841796875,
-0.039093017578125,
0.0117645263671875,
-0.007579803466796875,
-0.01546478271484375,
0.01120758056640625,
0.008941650390625,
-0.015899658203125,
0.022705078125,
0.0035228729248046875,
-0.0005755424499511719,
0.0004642009735107422,
-0.0152587890625,
-0.01515960693359375,
-0.0174407958984375,
-0.00902557373046875,
-0.00580596923828125,
-0.0275726318359375,
0.0035991668701171875,
0.022857666015625,
-0.036834716796875,
0.00732421875,
0.0149383544921875,
0.01995849609375,
-0.0023746490478515625,
-0.037567138671875,
-0.0306854248046875,
0.036376953125,
0.002674102783203125,
-0.0276336669921875,
0.0027637481689453125,
-0.004058837890625,
-0.01371002197265625,
-0.02056884765625,
-0.0170440673828125,
-0.0172271728515625,
-0.0032863616943359375,
0.0276947021484375,
0.041473388671875,
0.006252288818359375,
-0.01409149169921875,
-0.0239715576171875,
0.006839752197265625,
-0.0299530029296875,
0.0107574462890625,
0.0002694129943847656,
0.0008196830749511719,
-0.0101165771484375,
-0.00921630859375,
-0.029022216796875,
0.01116943359375,
-0.0211944580078125,
0.007404327392578125,
-0.0328369140625,
0.034423828125,
0.00933074951171875,
-0.020660400390625,
0.022491455078125,
0.0233001708984375,
0.0119476318359375,
0.0141754150390625,
0.0175323486328125,
-0.0170135498046875,
0.0160369873046875,
0.0143585205078125,
-0.055023193359375,
-0.00487518310546875,
-0.002704620361328125,
0.0268096923828125,
0.001445770263671875,
0.034332275390625,
-0.004337310791015625,
0.026702880859375,
0.011810302734375,
-0.007503509521484375,
-0.003307342529296875,
0.018829345703125,
0.009185791015625,
-0.00086212158203125,
-0.021270751953125,
0.0307464599609375,
0.0288543701171875,
-0.0238800048828125,
-0.004444122314453125,
-0.0242156982421875,
-0.01206207275390625,
-0.00374603271484375,
0.0027561187744140625,
0.014678955078125,
0.006168365478515625,
-0.0039825439453125,
-0.019439697265625,
0.003910064697265625,
-0.00982666015625,
-0.005977630615234375,
0.01837158203125,
0.016815185546875,
0.03369140625,
0.042694091796875,
-0.0158233642578125,
-0.00982666015625,
0.00020611286163330078,
0.01052093505859375,
-0.01020050048828125,
-0.031524658203125,
-0.013671875,
0.0117034912109375,
0.0208282470703125,
-0.0197601318359375,
-0.015472412109375,
-0.01348114013671875,
-0.020721435546875,
0.0036907196044921875,
-0.01013946533203125,
-0.0294342041015625,
-0.01751708984375,
0.025848388671875,
-0.00069427490234375,
-0.037261962890625,
-0.012664794921875,
-0.01313018798828125,
0.0197906494140625,
-0.017181396484375,
0.00762939453125,
-0.002292633056640625,
-0.011138916015625,
-0.03466796875,
0.0037708282470703125,
0.0265655517578125,
-0.00020170211791992188,
-0.0012903213500976562,
-0.00829315185546875,
-0.022735595703125,
-0.0017709732055664062,
-0.0131683349609375,
0.0218963623046875,
-0.00891876220703125,
0.034332275390625,
-0.02825927734375,
-0.06304931640625,
-0.00696563720703125,
-0.0167083740234375,
0.03131103515625,
-0.019561767578125,
-0.0248565673828125,
-0.0018711090087890625,
0.007122039794921875,
-0.0219573974609375,
-0.027862548828125,
0.0124053955078125,
-0.0147552490234375,
-0.018707275390625,
-0.025390625,
0.029754638671875,
0.0127410888671875,
0.01078033447265625,
0.013641357421875,
0.005512237548828125,
-0.00290679931640625,
-0.01275634765625,
0.005615234375,
0.005458831787109375,
0.011810302734375,
0.016754150390625,
0.00553131103515625,
-0.02447509765625,
0.0177459716796875,
-0.018157958984375,
0.0175323486328125,
-0.03704833984375,
0.00617218017578125,
0.005138397216796875,
0.0255126953125,
-0.00022804737091064453,
-0.01430511474609375,
0.002349853515625,
-0.0188446044921875,
0.023468017578125,
-0.0128631591796875,
0.00728607177734375,
0.011962890625,
0.028045654296875,
0.007793426513671875,
-0.005031585693359375,
0.0179595947265625,
-0.0170135498046875,
-0.0281829833984375,
0.0009860992431640625,
-0.04083251953125,
0.050262451171875,
0.00855255126953125,
0.01329803466796875,
0.01178741455078125,
0.005886077880859375,
-0.01377105712890625,
0.029541015625,
-0.0013599395751953125,
0.03021240234375,
0.005748748779296875,
-0.01806640625,
-0.0222625732421875,
0.037353515625,
0.00858306884765625,
0.0014925003051757812,
0.0186309814453125,
-0.0031681060791015625,
0.00876617431640625,
-0.005859375,
0.021881103515625,
0.00826263427734375,
-0.004261016845703125,
-0.01470184326171875,
0.0361328125,
-0.00893402099609375,
0.044586181640625,
-0.04559326171875,
0.0109100341796875,
0.0131683349609375,
0.0175628662109375,
-0.0160675048828125,
-0.01297760009765625,
0.034210205078125,
-0.0123748779296875,
0.0074462890625,
-0.003173828125,
0.0030364990234375,
-0.024169921875,
-0.005458831787109375,
-0.009552001953125,
0.0014142990112304688,
-0.0026092529296875,
0.0083160400390625,
0.0164794921875,
0.00848388671875,
0.01345062255859375,
-0.04022216796875,
0.023529052734375,
0.047119140625,
0.006938934326171875,
-0.034515380859375,
0.020416259765625,
0.00341033935546875,
-0.0082244873046875,
0.016143798828125,
-0.0134429931640625,
-0.023529052734375,
0.018829345703125,
0.025726318359375,
0.0109710693359375,
0.01534271240234375,
0.005809783935546875,
0.037353515625,
-0.0169830322265625,
-0.003589630126953125,
0.0384521484375,
0.0168914794921875,
-0.0283355712890625,
-0.028411865234375,
0.00702667236328125,
0.02508544921875,
-0.003063201904296875,
-0.0038928985595703125,
-0.0006117820739746094,
-0.024932861328125,
-0.00916290283203125,
0.0190582275390625,
0.01081085205078125,
0.008026123046875,
-0.0227508544921875,
-0.0310211181640625,
-0.056304931640625,
0.0215606689453125,
-0.0046539306640625,
0.0186614990234375,
-0.0023174285888671875,
0.01349639892578125,
-0.004001617431640625,
-0.0282745361328125,
-0.004364013671875,
-0.0018224716186523438,
-0.021270751953125,
0.0238800048828125,
0.01555633544921875,
-0.03790283203125,
0.01549530029296875,
0.009429931640625,
0.0243072509765625,
-0.02142333984375,
-0.003665924072265625,
0.00939178466796875,
-0.033111572265625,
0.00042510032653808594,
0.033355712890625,
-0.004283905029296875,
-0.00569915771484375,
-0.006084442138671875,
0.022613525390625,
0.0127716064453125,
-0.0206756591796875,
0.004505157470703125,
-0.00533294677734375,
-0.019439697265625,
0.012298583984375,
-0.00754547119140625,
0.0014858245849609375,
-0.0239715576171875,
0.0150299072265625,
0.0113525390625,
0.002834320068359375,
-0.0283050537109375,
-0.00994110107421875,
0.01349639892578125,
0.0033721923828125,
-0.021026611328125,
0.033782958984375,
-0.01160430908203125,
-0.01421356201171875,
0.022979736328125,
-0.02423095703125,
-0.0032100677490234375,
0.03900146484375,
-0.002574920654296875,
0.01202392578125,
-0.0180816650390625,
-0.0016374588012695312,
0.026092529296875,
-0.0299224853515625,
0.0252838134765625,
0.02325439453125,
0.015594482421875,
0.01045989990234375,
0.0086669921875,
0.0005946159362792969,
0.0229644775390625,
-0.0207061767578125,
0.0107574462890625,
0.01824951171875,
-0.0218658447265625,
0.044464111328125,
0.005130767822265625,
-0.016571044921875,
-0.01393890380859375,
-0.0249176025390625,
-0.00946807861328125,
0.0172271728515625,
-0.02447509765625,
-0.021087646484375,
0.021697998046875,
0.0236053466796875,
0.006511688232421875,
-0.0063323974609375,
-0.0032806396484375,
0.01091766357421875,
-0.000751495361328125,
-0.0051422119140625,
-0.00295257568359375,
-0.003543853759765625,
0.01267242431640625,
0.0036907196044921875,
0.002285003662109375,
0.020416259765625,
-0.0186004638671875,
0.003559112548828125,
0.06427001953125,
0.01369476318359375,
-0.0036449432373046875,
0.00876617431640625,
-0.0445556640625,
0.025909423828125,
-0.0178680419921875,
0.019134521484375,
-0.0120086669921875,
-0.01678466796875,
0.00037217140197753906,
0.0019397735595703125,
0.017791748046875,
-0.0149993896484375,
0.036163330078125,
0.00884246826171875,
-0.0012311935424804688,
-0.01201629638671875,
0.01424407958984375,
-0.0018053054809570312,
0.006435394287109375,
0.0031585693359375,
-0.0165252685546875,
0.01812744140625,
-0.01232147216796875,
-0.0278778076171875,
0.036590576171875,
-0.0063629150390625,
0.005054473876953125,
-0.01513671875,
-0.0085906982421875,
0.029754638671875,
-0.0224456787109375,
-0.032318115234375,
-0.0161895751953125,
0.01178741455078125,
0.0160369873046875,
-0.040252685546875,
0.0202789306640625,
-0.0135345458984375,
-0.00727081298828125,
0.027618408203125,
0.01146697998046875,
0.033416748046875,
0.0248260498046875,
0.033782958984375,
0.01525115966796875,
0.0272979736328125,
0.022735595703125,
-0.00939178466796875,
-0.0007696151733398438,
-0.00251007080078125,
-0.004131317138671875,
0.022613525390625,
0.0153656005859375,
0.01043701171875,
-0.021820068359375,
0.0075225830078125,
-0.0049896240234375,
0.01317596435546875,
-0.03253173828125,
0.0058135986328125,
0.01428985595703125,
0.01222991943359375,
-0.003292083740234375,
0.002155303955078125,
0.01323699951171875,
-0.0034275054931640625,
0.0038166046142578125,
-0.0010023117065429688,
0.00591278076171875,
-0.01230621337890625,
0.00385284423828125,
-0.005184173583984375,
-0.00098419189453125,
0.04388427734375,
0.01151275634765625,
-0.01007843017578125,
0.00418853759765625,
0.0285186767578125,
-0.0121002197265625,
0.0263214111328125,
0.01374053955078125,
-0.0121002197265625,
-0.00649261474609375,
-0.0082855224609375,
-0.0318603515625,
0.0148162841796875,
0.00652313232421875,
-0.00374603271484375,
-0.01337432861328125,
-0.0098724365234375,
-0.0033416748046875,
0.003582000732421875,
0.007183074951171875,
-0.033660888671875,
0.003692626953125,
0.033966064453125,
-0.0286712646484375,
0.01251983642578125,
0.05029296875,
-0.0122833251953125,
0.00881195068359375,
-0.0285186767578125,
-0.0238189697265625,
0.0137786865234375,
-0.021728515625,
-0.03533935546875,
-0.018463134765625,
0.032440185546875,
0.00505828857421875,
0.0391845703125,
0.017364501953125,
-0.0200653076171875,
0.0223541259765625,
0.013427734375,
-0.0302886962890625,
0.0131988525390625,
-0.000995635986328125,
-0.03729248046875,
0.0227813720703125,
-0.00806427001953125,
-0.024505615234375,
0.00843048095703125,
-0.00833892822265625,
-0.017303466796875,
-0.0229644775390625,
0.004970550537109375,
-0.01184844970703125,
0.00037217140197753906,
0.0037670135498046875,
0.00017631053924560547,
-0.05462646484375,
0.0142669677734375,
-0.05474853515625,
-0.007411956787109375,
0.01004791259765625,
-0.00617218017578125,
0.0162200927734375,
0.013397216796875,
-0.007068634033203125,
-0.0303192138671875,
-0.0283966064453125,
-0.02899169921875,
-0.01262664794921875,
0.00975799560546875,
0.0159149169921875,
-0.00421142578125,
0.004863739013671875,
0.04571533203125,
0.0345458984375,
-0.017608642578125,
0.0242919921875,
0.028533935546875,
0.0203399658203125,
-0.00421905517578125,
0.00035500526428222656,
-0.01873779296875,
0.02117919921875,
-0.007396697998046875,
-0.0009326934814453125,
-0.038299560546875,
0.0028591156005859375,
-0.004489898681640625,
-0.0009918212890625,
0.051361083984375,
-0.0233001708984375,
-0.040863037109375,
-0.0165863037109375,
0.004852294921875,
0.0078277587890625,
-0.0034961700439453125,
-0.00856781005859375,
0.00858306884765625,
0.01007080078125,
-0.015777587890625,
0.0262603759765625,
-0.01416015625,
-0.03546142578125,
-0.01494598388671875,
-0.002437591552734375,
0.0180206298828125,
-0.006099700927734375,
0.0012311935424804688,
0.0026149749755859375,
-0.0186614990234375,
0.0007147789001464844,
0.0171661376953125,
0.03875732421875,
0.00962066650390625,
-0.00446319580078125,
-0.00765228271484375,
-0.0078582763671875,
0.01177978515625,
-0.0024433135986328125,
0.032684326171875,
-0.001861572265625,
-0.007305145263671875,
-0.002147674560546875,
-0.0014047622680664062,
-0.013671875,
-0.01068878173828125,
0.006534576416015625,
-0.0090484619140625,
-0.0191802978515625,
0.0082244873046875,
-0.0114593505859375,
-0.006359100341796875,
-0.0092315673828125,
0.0036029815673828125,
0.0119171142578125,
-0.0047760009765625,
0.010711669921875,
-0.01168060302734375,
0.0005993843078613281,
-0.002056121826171875,
-0.01428985595703125,
0.038665771484375,
0.0138397216796875,
-0.024627685546875,
0.0203399658203125,
-0.00908660888671875,
-0.047576904296875,
-0.0033245086669921875,
-0.0261383056640625,
-0.023834228515625,
0.0243072509765625,
0.000324249267578125,
-0.0242919921875,
-0.02337646484375,
0.022674560546875,
0.02386474609375,
-0.0103607177734375,
-0.026275634765625,
-0.023651123046875,
-0.0282135009765625,
0.0118408203125,
0.03662109375,
-0.021392822265625,
-0.017120361328125,
-0.0142669677734375,
0.00017631053924560547,
-0.007236480712890625,
0.032562255859375,
-0.0008068084716796875,
0.0138397216796875,
0.03375244140625,
0.0179901123046875,
0.0124664306640625,
0.0159759521484375,
-0.02398681640625,
0.01427459716796875,
0.00960540771484375,
-0.0360107421875,
-0.0015478134155273438,
0.0394287109375,
-0.032379150390625,
0.03204345703125,
-0.02203369140625,
-0.0347900390625,
0.0097503662109375,
-0.007549285888671875,
-0.0299072265625,
-0.032470703125,
0.0221710205078125,
0.0115966796875,
0.00470733642578125,
0.03338623046875,
0.012847900390625,
-0.00955963134765625,
-0.025970458984375,
-0.0265045166015625,
-0.00555419921875,
0.01873779296875,
0.030059814453125,
0.00301361083984375,
-0.00885009765625,
0.0253753662109375,
0.018585205078125,
-0.00463104248046875,
-0.054595947265625,
0.001132965087890625,
-0.0574951171875,
0.0098114013671875,
0.0285491943359375,
-0.023681640625,
-0.0209808349609375,
-0.033233642578125,
-0.0020771026611328125,
0.01445770263671875,
-0.004863739013671875,
-0.034698486328125,
-0.0153961181640625,
0.00304412841796875,
0.001003265380859375,
0.00811767578125,
-0.0272369384765625,
0.01629638671875,
0.0162811279296875,
-0.01030731201171875,
-0.0287933349609375,
0.041259765625,
-0.01317596435546875,
0.0221710205078125,
0.03863525390625,
-0.0011091232299804688,
-0.0159454345703125,
-0.0157928466796875,
-0.002506256103515625,
0.0112457275390625,
0.00653076171875,
-0.001483917236328125,
-0.0101318359375,
-0.024993896484375,
0.0189971923828125,
-0.012908935546875,
-0.00266265869140625,
0.024688720703125,
-0.0244598388671875,
-0.0104217529296875,
0.00511932373046875,
-0.0256500244140625,
-0.00007784366607666016,
0.0079803466796875,
-0.01035308837890625,
-0.030853271484375,
0.00508880615234375,
0.00899505615234375,
-0.0117950439453125,
-0.02178955078125,
0.0080413818359375,
0.0035724639892578125,
0.028411865234375,
0.0152740478515625,
-0.01070404052734375,
0.01439666748046875,
0.00873565673828125,
-0.023101806640625,
-0.0023860931396484375,
0.01548004150390625,
0.0133514404296875,
-0.00899505615234375,
0.03607177734375,
-0.011871337890625,
0.00701904296875,
0.01036834716796875,
0.0104522705078125,
-0.0240631103515625,
0.014495849609375,
-0.00130462646484375,
0.0020847320556640625,
-0.0250244140625,
0.00005823373794555664,
0.007781982421875,
0.0478515625,
-0.0131683349609375,
-0.040802001953125,
0.0092010498046875,
0.031646728515625,
0.0130615234375,
-0.042877197265625,
-0.0136566162109375,
0.0227813720703125,
0.00445556640625,
0.023773193359375,
0.003734588623046875,
0.0177459716796875,
-0.0214080810546875,
-0.00954437255859375,
0.04266357421875,
0.0057525634765625,
-0.0034847259521484375,
0.0022907257080078125,
-0.0037708282470703125,
-0.01995849609375,
-0.0236968994140625,
0.0159149169921875,
0.01837158203125,
-0.0341796875,
-0.013092041015625,
-0.01544952392578125,
-0.0350341796875,
0.007228851318359375,
0.0157623291015625,
0.017242431640625,
0.037750244140625,
0.027435302734375,
-0.01044464111328125,
-0.0310516357421875,
0.0174713134765625,
0.00992584228515625,
0.0007138252258300781,
-0.0021457672119140625,
-0.0255584716796875,
0.0071258544921875,
0.01153564453125,
0.0169677734375,
-0.00812530517578125,
-0.006938934326171875,
-0.0120697021484375,
-0.003147125244140625,
-0.003082275390625,
0.0029735565185546875,
-0.025787353515625,
-0.0032901763916015625,
-0.0262908935546875,
0.0131072998046875,
0.00850677490234375,
-0.0159759521484375,
-0.004192352294921875,
0.0287322998046875,
-0.01445770263671875,
0.00981903076171875,
0.036590576171875,
0.007015228271484375,
0.00046372413635253906,
-0.00295257568359375,
0.0308990478515625,
0.023162841796875,
0.01165008544921875,
-0.007038116455078125,
-0.00783538818359375,
0.0019350051879882812,
-0.001239776611328125,
-0.005176544189453125,
0.0298309326171875,
-0.0177764892578125,
0.0090179443359375,
0.0081939697265625,
-0.02789306640625,
0.017578125,
0.032684326171875,
-0.0218963623046875,
0.033050537109375,
0.0031585693359375,
0.003753662109375,
-0.0264739990234375,
-0.05096435546875,
0.00267791748046875,
0.0022068023681640625,
-0.006557464599609375,
0.0011472702026367188,
-0.0073089599609375,
-0.0218963623046875,
0.0121307373046875,
-0.0190887451171875,
-0.0298919677734375,
-0.0190582275390625,
0.01477813720703125,
-0.00357818603515625,
-0.00939178466796875,
-0.005718231201171875,
0.03265380859375,
-0.0099639892578125,
0.034454345703125,
0.0193328857421875,
0.0177764892578125,
-0.0247344970703125,
0.045196533203125,
0.00047397613525390625,
-0.0064544677734375,
0.006500244140625,
-0.0087890625,
0.05255126953125,
-0.011322021484375,
0.00012612342834472656,
0.004695892333984375,
0.032379150390625,
-0.005390167236328125,
-0.0032196044921875,
0.00807952880859375,
0.004367828369140625,
-0.0181121826171875,
-0.021270751953125,
0.0291900634765625,
-0.0418701171875,
0.020111083984375,
0.0291900634765625,
-0.032196044921875,
-0.0099029541015625,
-0.006237030029296875,
0.035614013671875,
-0.0022602081298828125,
-0.05108642578125,
-0.01039886474609375,
0.01366424560546875,
-0.006572723388671875,
0.023284912109375,
-0.0035190582275390625,
0.0159912109375,
0.0011091232299804688,
0.0204010009765625,
0.007419586181640625,
-0.00974273681640625,
-0.03460693359375,
0.0177154541015625,
0.01267242431640625,
0.03363037109375,
0.013763427734375,
0.00019347667694091797,
0.009002685546875,
-0.039520263671875,
0.005588531494140625,
0.006084442138671875,
-0.021575927734375,
-0.00846099853515625,
0.0117950439453125,
-0.02301025390625,
0.006011962890625,
-0.00731658935546875,
0.040130615234375,
-0.01629638671875,
0.00647735595703125,
-0.03643798828125,
0.0190887451171875,
0.011505126953125,
-0.014739990234375,
0.0245208740234375,
-0.0003070831298828125,
-0.01476287841796875,
0.01387786865234375,
-0.0203094482421875,
-0.01654052734375,
-0.01294708251953125,
-0.00048160552978515625,
-0.01323699951171875,
0.03131103515625,
0.003978729248046875,
-0.0110321044921875,
-0.0157012939453125,
-0.03326416015625,
0.0123748779296875,
0.047882080078125,
-0.00146484375,
0.0038356781005859375,
-0.00917816162109375,
0.02679443359375,
0.0073089599609375,
-0.0288238525390625,
-0.0257568359375,
-0.04388427734375,
0.0176544189453125,
-0.0129547119140625,
-0.01373291015625,
0.005771636962890625,
0.003978729248046875,
0.0194549560546875,
-0.0184173583984375,
0.0015764236450195312,
-0.00537109375,
0.0012226104736328125,
0.013519287109375,
0.0081939697265625,
0.00824737548828125,
0.0095062255859375,
0.0239715576171875,
-0.01177978515625,
-0.030792236328125,
0.01898193359375,
0.0109405517578125,
0.036041259765625,
0.0010633468627929688,
0.006977081298828125,
0.01548004150390625,
0.002532958984375,
-0.019378662109375,
-0.01611328125,
0.00511932373046875,
0.01247406005859375,
0.012176513671875,
0.0309295654296875,
0.012908935546875,
0.023681640625,
0.0343017578125,
-0.01439666748046875,
-0.0073089599609375,
-0.00629425048828125,
-0.028594970703125,
-0.0288238525390625,
0.0038356781005859375,
0.034332275390625,
-0.00238037109375,
-0.01641845703125,
0.033294677734375,
-0.023193359375,
-0.0347900390625,
0.01068878173828125,
-0.0231170654296875,
0.021148681640625,
0.0278778076171875,
-0.002643585205078125,
-0.0061187744140625,
-0.004390716552734375,
0.00022530555725097656,
-0.0062103271484375,
-0.0250244140625,
-0.0078887939453125,
-0.00788116455078125,
0.0023212432861328125,
0.0218353271484375,
-0.004604339599609375,
0.007747650146484375,
-0.0194549560546875,
-0.0015010833740234375,
-0.00640106201171875,
-0.010406494140625,
-0.00800323486328125,
-0.01407623291015625,
-0.00429534912109375,
-0.0119171142578125,
0.022491455078125,
-0.0070037841796875,
0.0207672119140625,
-0.0024471282958984375,
-0.0179443359375,
0.037567138671875,
-0.026824951171875,
-0.005146026611328125,
-0.01163482666015625,
0.0015077590942382812,
-0.0103302001953125,
0.0061187744140625,
-0.01262664794921875,
-0.0225982666015625,
-0.0032711029052734375,
-0.011932373046875,
-0.0178985595703125,
0.043731689453125,
-0.0278778076171875,
0.028106689453125,
0.01507568359375,
-0.00417327880859375,
0.0118560791015625,
0.0229034423828125,
0.0023250579833984375,
0.010528564453125,
-0.01247406005859375,
0.01206207275390625,
0.046875,
0.012451171875,
-0.007038116455078125,
-0.0130615234375,
0.0252227783203125,
-0.0029010772705078125,
0.00493621826171875,
0.001922607421875,
-0.0019359588623046875,
0.013671875,
-0.0174102783203125,
0.021087646484375,
0.031646728515625,
0.0032482147216796875,
0.016357421875,
0.00009369850158691406,
0.0101318359375,
0.0204010009765625,
-0.0246124267578125,
0.0092010498046875,
-0.0078277587890625,
0.00872802734375,
-0.01751708984375,
0.01541900634765625,
0.00823974609375,
0.01544952392578125,
0.0219573974609375,
-0.005283355712890625,
-0.01134490966796875,
-0.0242767333984375,
-0.00255584716796875,
-0.031463623046875,
-0.01177978515625,
0.0291748046875,
0.00066375732421875,
0.01493072509765625,
0.0081329345703125,
-0.017059326171875,
0.0227203369140625,
-0.0259552001953125,
0.04705810546875,
0.01001739501953125,
-0.0295867919921875,
-0.0018568038940429688,
0.006023406982421875,
-0.0350341796875,
0.0257415771484375,
0.00469970703125,
0.0146026611328125,
-0.006626129150390625,
-0.01236724853515625,
-0.006977081298828125,
0.028656005859375,
0.0020160675048828125,
0.01209259033203125,
0.005336761474609375,
0.0175933837890625,
-0.004268646240234375,
-0.0081024169921875,
-0.0281219482421875,
0.026397705078125,
-0.0129241943359375,
-0.0002460479736328125,
0.032470703125,
0.0238189697265625,
0.016876220703125,
-0.0149993896484375,
0.0230712890625,
0.012908935546875,
0.0164642333984375,
0.0024242401123046875,
-0.02703857421875,
0.0206756591796875,
0.017059326171875,
0.00028228759765625,
0.026885986328125,
0.0307769775390625,
0.0008945465087890625,
0.0277099609375,
-0.039031982421875,
-0.005512237548828125,
-0.00946044921875,
0.0184783935546875,
-0.0198822021484375,
0.0011892318725585938,
0.00591278076171875,
0.019134521484375,
0.007312774658203125,
-0.00047206878662109375,
0.040924072265625,
-0.0193023681640625,
0.004985809326171875,
-0.0268707275390625,
-0.0035915374755859375,
-0.01390838623046875,
-0.0003306865692138672,
0.009796142578125,
-0.0443115234375,
0.041107177734375,
-0.0182342529296875,
0.0236358642578125,
0.0068817138671875,
0.00110626220703125,
0.004924774169921875,
-0.01398468017578125,
0.017120361328125,
0.0168609619140625,
0.000026404857635498047,
-0.01129150390625,
0.027069091796875,
-0.0034580230712890625,
-0.018280029296875,
0.028961181640625,
-0.003253936767578125,
-0.00307464599609375,
0.0031642913818359375,
0.01265716552734375,
0.00534820556640625,
-0.050628662109375,
-0.0034008026123046875,
0.005786895751953125,
-0.0027065277099609375,
-0.0287628173828125,
-0.0031452178955078125,
0.0187225341796875,
0.0130157470703125,
-0.00147247314453125,
0.005344390869140625,
-0.0005030632019042969,
-0.017364501953125,
-0.0156097412109375,
-0.0035915374755859375,
0.0518798828125,
0.036224365234375,
-0.01041412353515625,
0.0234222412109375,
-0.00759124755859375,
-0.0034885406494140625,
-0.017822265625,
0.0101318359375,
-0.00907135009765625,
-0.01154327392578125,
0.001590728759765625,
0.03143310546875,
-0.0175323486328125,
0.0004508495330810547,
-0.027099609375,
-0.0184478759765625,
-0.0010137557983398438,
0.004535675048828125,
-0.0242156982421875,
0.003997802734375,
0.0282440185546875,
0.005916595458984375,
-0.01580810546875,
-0.006694793701171875,
-0.005893707275390625,
0.0024738311767578125,
-0.0028781890869140625,
0.0081329345703125,
-0.000522613525390625,
0.0205078125,
0.0017747879028320312,
-0.00688934326171875,
-0.020263671875,
-0.0305023193359375,
-0.0193328857421875,
0.00943756103515625,
-0.0170440673828125,
0.00958251953125,
-0.014312744140625,
-0.022674560546875,
-0.0113067626953125,
0.038848876953125,
-0.0135955810546875,
-0.00405120849609375,
-0.03472900390625,
0.010162353515625,
-0.00482940673828125,
-0.0031032562255859375,
-0.0274810791015625,
-0.006343841552734375,
-0.0042572021484375,
0.006351470947265625,
-0.004467010498046875,
-0.010009765625,
0.01090240478515625,
0.0291900634765625,
0.0029201507568359375,
-0.001972198486328125,
-0.00921630859375,
0.01049041748046875,
0.0306396484375
] |
ours_548
|
Let the largest of the three numbers be \(a\). We have the following equations:
\[
\begin{aligned}
a^2 + b^2 + c^2 &= 160, \\
a &= b + c, \\
b - c &= 4.
\end{aligned}
\]
Substituting \(a = b + c\) into the first equation gives:
\[
(b + c)^2 + b^2 + c^2 = 160.
\]
Expanding and simplifying, we have:
\[
b^2 + 2bc + c^2 + b^2 + c^2 = 160,
\]
which simplifies to:
\[
2b^2 + 2bc + 2c^2 = 160.
\]
Dividing the entire equation by 2, we get:
\[
b^2 + bc + c^2 = 80.
\]
Now, using the equation \(b - c = 4\), we multiply both sides by \(b^2 + bc + c^2\):
\[
(b^2 + bc + c^2)(b - c) = 80 \times 4.
\]
This simplifies to:
\[
b^3 - c^3 = 320.
\]
Thus, the positive difference between the cubes of the smaller two numbers is \(\boxed{320}\).
|
320
|
{
"competition": "us_comps",
"dataset": "Ours",
"posts": null,
"source": "OMOSoln2.md"
}
|
The sum of the squares of three positive numbers is \(160\). One of the numbers is equal to the sum of the other two. The difference between the smaller two numbers is \(4\). What is the positive difference between the cubes of the smaller two numbers?
|
[
"/Mathematics/Algebra/AlgebraicEquations/SimultaneousEquations",
"/Mathematics/Algebra/AlgebraicIdentities/AlgebraicIdentity",
"/Mathematics/Algebra/AlgebraicIdentities/PolynomialIdentity",
"/Mathematics/Algebra/Polynomials/Polynomial",
"/Mathematics/Algebra/Polynomials/PolynomialIdentity",
"/Mathematics/Algebra/Sums/PowerSum",
"/Mathematics/Algebra/Sums/Sum"
] |
Apply the factorization b³−c³ = (b−c)(b²+bc+c²) after using a = b+c to find b²+bc+c².
|
[
-0.0001747608184814453,
0.00345611572265625,
0.0191497802734375,
-0.0081329345703125,
-0.0005950927734375,
0.0183258056640625,
-0.01355743408203125,
-0.0280303955078125,
0.0084686279296875,
-0.0269775390625,
-0.019500732421875,
0.009857177734375,
-0.0014314651489257812,
0.01349639892578125,
0.0018711090087890625,
0.0239715576171875,
0.020538330078125,
0.004817962646484375,
0.0167694091796875,
-0.0029087066650390625,
-0.011932373046875,
0.005321502685546875,
-0.046966552734375,
0.006549835205078125,
-0.0058135986328125,
-0.0253143310546875,
-0.018218994140625,
-0.0023899078369140625,
-0.0064239501953125,
0.004119873046875,
-0.02850341796875,
-0.01154327392578125,
-0.000675201416015625,
0.007762908935546875,
-0.0007567405700683594,
0.016082763671875,
0.013153076171875,
0.0021457672119140625,
-0.037933349609375,
-0.038665771484375,
0.00872039794921875,
0.06011962890625,
-0.0216522216796875,
0.0196380615234375,
-0.0201873779296875,
-0.00319671630859375,
0.005924224853515625,
-0.0307769775390625,
0.00847625732421875,
0.0032024383544921875,
-0.004547119140625,
0.0160064697265625,
-0.0100860595703125,
-0.0006198883056640625,
-0.00021195411682128906,
-0.04168701171875,
0.0192108154296875,
-0.002971649169921875,
-0.027740478515625,
-0.01116943359375,
0.01050567626953125,
-0.0148162841796875,
0.01438140869140625,
-0.01461029052734375,
0.0018987655639648438,
-0.00365447998046875,
0.01364898681640625,
-0.0423583984375,
0.0024089813232421875,
0.00218963623046875,
0.034881591796875,
0.00789642333984375,
-0.00020051002502441406,
0.00933074951171875,
0.0134735107421875,
-0.003269195556640625,
-0.0030975341796875,
0.00045371055603027344,
-0.0077972412109375,
0.0042572021484375,
0.01480865478515625,
0.01190948486328125,
0.002460479736328125,
-0.0037975311279296875,
0.0019044876098632812,
0.04095458984375,
-0.02288818359375,
0.002811431884765625,
-0.0255584716796875,
-0.01715087890625,
-0.0009093284606933594,
0.0139923095703125,
-0.01160430908203125,
0.0235595703125,
-0.0052032470703125,
0.008056640625,
-0.0096282958984375,
0.01446533203125,
-0.0229644775390625,
0.004131317138671875,
-0.004665374755859375,
-0.0148468017578125,
-0.0006570816040039062,
-0.025177001953125,
0.003559112548828125,
-0.002017974853515625,
0.0083160400390625,
0.0023822784423828125,
0.0038623809814453125,
-0.0003273487091064453,
0.0158233642578125,
-0.003635406494140625,
0.038665771484375,
0.01004791259765625,
-0.003192901611328125,
0.01384735107421875,
0.0166015625,
0.023712158203125,
-0.01483154296875,
0.0252532958984375,
-0.01007843017578125,
0.0035037994384765625,
-0.003326416015625,
-0.01824951171875,
0.0194091796875,
0.007030487060546875,
-0.00548553466796875,
-0.00930023193359375,
0.0030918121337890625,
0.01297760009765625,
0.00731658935546875,
0.0012845993041992188,
-0.00762176513671875,
-0.0051116943359375,
-0.07159423828125,
-0.003231048583984375,
0.033660888671875,
0.0164947509765625,
-0.0181884765625,
0.002910614013671875,
0.0003478527069091797,
0.0015153884887695312,
-0.00247955322265625,
-0.014923095703125,
0.007785797119140625,
-0.0160064697265625,
0.00787353515625,
-0.03497314453125,
0.0007061958312988281,
-0.008087158203125,
-0.004146575927734375,
0.00202178955078125,
0.00949859619140625,
0.0180206298828125,
-0.02069091796875,
-0.0002522468566894531,
0.0114288330078125,
0.0114593505859375,
-0.008636474609375,
0.0132598876953125,
0.0033512115478515625,
-0.007293701171875,
-0.0219268798828125,
0.0014467239379882812,
0.004589080810546875,
-0.00011610984802246094,
0.005481719970703125,
0.004871368408203125,
-0.003406524658203125,
-0.0017499923706054688,
0.015838623046875,
0.0018215179443359375,
-0.004680633544921875,
-0.005565643310546875,
-0.0022563934326171875,
-0.00897216796875,
-0.0262298583984375,
0.006893157958984375,
-0.006404876708984375,
-0.0002675056457519531,
-0.0140380859375,
-0.033905029296875,
0.0270843505859375,
0.00788116455078125,
0.0150604248046875,
-0.005771636962890625,
0.007114410400390625,
-0.00809478759765625,
0.0272979736328125,
0.006061553955078125,
-0.01812744140625,
-0.0023345947265625,
-0.009857177734375,
0.0114288330078125,
-0.0080413818359375,
-0.0099639892578125,
-0.01495361328125,
0.007007598876953125,
0.034881591796875,
0.0020351409912109375,
-0.01248931884765625,
-0.002330780029296875,
0.018951416015625,
-0.0121917724609375,
0.0097198486328125,
0.0104827880859375,
0.0119171142578125,
0.006061553955078125,
0.0009021759033203125,
0.00982666015625,
0.005992889404296875,
0.04473876953125,
-0.00045752525329589844,
-0.0291900634765625,
-0.004558563232421875,
-0.01523590087890625,
-0.005863189697265625,
-0.0121612548828125,
-0.0025196075439453125,
0.01358795166015625,
0.00789642333984375,
0.00597381591796875,
0.01090240478515625,
-0.023040771484375,
-0.006359100341796875,
0.01399993896484375,
0.0106353759765625,
-0.0145111083984375,
-0.0063018798828125,
0.0130157470703125,
-0.005283355712890625,
-0.00853729248046875,
0.0105743408203125,
-0.01263427734375,
-0.0213165283203125,
-0.00508880615234375,
-0.037353515625,
-0.001911163330078125,
-0.0007987022399902344,
0.0203399658203125,
0.0377197265625,
-0.0255889892578125,
0.00597381591796875,
0.003345489501953125,
0.004009246826171875,
0.00476837158203125,
0.0010309219360351562,
-0.016937255859375,
-0.001743316650390625,
-0.00998687744140625,
0.01558685302734375,
0.005153656005859375,
0.000023186206817626953,
-0.01203155517578125,
-0.006778717041015625,
-0.005340576171875,
0.0269012451171875,
0.02935791015625,
0.00458526611328125,
0.00951385498046875,
-0.006893157958984375,
-0.0186309814453125,
-0.0195159912109375,
0.00347900390625,
0.0055999755859375,
0.004734039306640625,
0.0487060546875,
-0.009429931640625,
0.0275726318359375,
-0.0244598388671875,
0.000965118408203125,
0.0037441253662109375,
-0.00951385498046875,
0.0302886962890625,
0.0268707275390625,
0.012054443359375,
0.01242828369140625,
0.008270263671875,
0.0096588134765625,
-0.0202789306640625,
0.0097503662109375,
-0.00847625732421875,
-0.0035572052001953125,
0.00933074951171875,
0.00844573974609375,
0.00347900390625,
0.0462646484375,
0.00566864013671875,
-0.0135040283203125,
0.0273895263671875,
-0.003421783447265625,
-0.020477294921875,
-0.002933502197265625,
0.005893707275390625,
0.045166015625,
0.00257110595703125,
0.00019788742065429688,
0.004756927490234375,
0.01031494140625,
0.0177459716796875,
0.008636474609375,
-0.003513336181640625,
0.00600433349609375,
-0.0077667236328125,
0.0279541015625,
0.026519775390625,
-0.004795074462890625,
-0.0080718994140625,
0.01297760009765625,
-0.00870513916015625,
-0.01025390625,
0.017303466796875,
-0.01010894775390625,
-0.0025539398193359375,
-0.04058837890625,
-0.06170654296875,
0.0171051025390625,
0.01409149169921875,
-0.004245758056640625,
0.0299072265625,
0.0140838623046875,
0.0026378631591796875,
0.01319122314453125,
0.011474609375,
0.0228118896484375,
0.0028667449951171875,
0.014984130859375,
-0.002544403076171875,
-0.011383056640625,
0.019744873046875,
-0.007843017578125,
0.0184173583984375,
0.003154754638671875,
-0.005641937255859375,
-0.004978179931640625,
-0.004608154296875,
-0.005435943603515625,
-0.006855010986328125,
-0.009765625,
0.0002193450927734375,
0.0207977294921875,
-0.03466796875,
0.0016775131225585938,
-0.0095977783203125,
-0.040863037109375,
0.0093231201171875,
0.00042748451232910156,
-0.00238037109375,
0.0167388916015625,
-0.044189453125,
0.01461029052734375,
0.0004229545593261719,
0.041595458984375,
-0.0110321044921875,
-0.0272369384765625,
-0.01678466796875,
0.009979248046875,
0.01375579833984375,
0.00717926025390625,
-0.00191497802734375,
-0.005992889404296875,
-0.01233673095703125,
0.00722503662109375,
-0.0251007080078125,
0.01374053955078125,
-0.006439208984375,
-0.01383209228515625,
0.01861572265625,
-0.0080413818359375,
-0.004299163818359375,
-0.00650787353515625,
0.0181427001953125,
-0.0021572113037109375,
-0.0123748779296875,
0.0208587646484375,
0.0179901123046875,
-0.0072784423828125,
-0.0093231201171875,
0.028289794921875,
0.0165863037109375,
-0.004245758056640625,
0.007381439208984375,
-0.014678955078125,
-0.00501251220703125,
0.01422882080078125,
-0.0005397796630859375,
-0.0130157470703125,
-0.040191650390625,
0.003993988037109375,
0.005741119384765625,
0.0054931640625,
-0.0007567405700683594,
-0.0135040283203125,
0.0172576904296875,
0.021881103515625,
-0.070556640625,
0.0083160400390625,
0.01136016845703125,
0.0103759765625,
-0.005279541015625,
-0.0347900390625,
0.00383758544921875,
-0.0191650390625,
-0.0014066696166992188,
-0.009918212890625,
0.0003502368927001953,
-0.01102447509765625,
0.0254058837890625,
-0.002216339111328125,
0.0182037353515625,
0.041015625,
0.006504058837890625,
-0.0029773712158203125,
-0.00162506103515625,
-0.05059814453125,
-0.01154327392578125,
0.021759033203125,
-0.00409698486328125,
0.01187896728515625,
-0.0053253173828125,
-0.01322174072265625,
-0.0164642333984375,
-0.04595947265625,
0.0171966552734375,
0.035308837890625,
0.0012359619140625,
-0.0227813720703125,
0.034027099609375,
0.0166015625,
0.0004696846008300781,
0.0239105224609375,
-0.028533935546875,
0.004688262939453125,
0.0143280029296875,
0.018890380859375,
0.021942138671875,
-0.01580810546875,
0.002193450927734375,
0.03314208984375,
0.0238189697265625,
-0.027099609375,
0.02587890625,
0.0036830902099609375,
0.006206512451171875,
0.0297698974609375,
0.0082550048828125,
-0.01258087158203125,
0.00989532470703125,
-0.0245513916015625,
-0.0176239013671875,
-0.017974853515625,
-0.00217437744140625,
0.0283966064453125,
-0.0039215087890625,
-0.05316162109375,
0.013946533203125,
0.03302001953125,
-0.0262298583984375,
-0.024932861328125,
0.0034046173095703125,
-0.007457733154296875,
0.0201873779296875,
-0.0068511962890625,
0.01313018798828125,
-0.030059814453125,
0.0193939208984375,
-0.0161590576171875,
0.0034885406494140625,
0.021697998046875,
0.0107269287109375,
0.01380157470703125,
-0.00006216764450073242,
-0.0247650146484375,
-0.0203857421875,
-0.01702880859375,
0.0256805419921875,
-0.0214691162109375,
0.0175628662109375,
-0.0224609375,
0.01360321044921875,
0.0220947265625,
-0.0182647705078125,
-0.025299072265625,
-0.014617919921875,
-0.01087188720703125,
0.030029296875,
0.0194854736328125,
0.00710296630859375,
-0.019683837890625,
-0.0214996337890625,
0.0338134765625,
0.0245361328125,
-0.0220947265625,
-0.027923583984375,
-0.0022983551025390625,
-0.00615692138671875,
-0.005588531494140625,
0.0106048583984375,
-0.007091522216796875,
0.0030803680419921875,
0.028076171875,
-0.01385498046875,
0.0206451416015625,
-0.00321197509765625,
0.00872039794921875,
-0.044769287109375,
0.0267791748046875,
-0.0225067138671875,
0.036895751953125,
0.0029468536376953125,
-0.0021495819091796875,
0.019775390625,
0.017364501953125,
-0.0184173583984375,
0.025970458984375,
0.035614013671875,
0.0188140869140625,
0.00946807861328125,
-0.0007867813110351562,
-0.0016450881958007812,
-0.043426513671875,
-0.00652313232421875,
0.038055419921875,
0.0118408203125,
-0.0005350112915039062,
0.0247650146484375,
-0.01861572265625,
0.035491943359375,
-0.0009713172912597656,
-0.037994384765625,
-0.01149749755859375,
-0.022857666015625,
0.00848388671875,
0.013519287109375,
-0.0213623046875,
0.00893402099609375,
0.0253448486328125,
-0.020751953125,
0.03399658203125,
0.032073974609375,
0.01479339599609375,
-0.0299224853515625,
-0.0285186767578125,
-0.0113677978515625,
0.021270751953125,
0.013702392578125,
0.0019626617431640625,
0.036834716796875,
-0.011474609375,
0.0030689239501953125,
0.00807952880859375,
-0.005550384521484375,
-0.01557159423828125,
0.0226287841796875,
-0.0020236968994140625,
0.01052093505859375,
-0.006137847900390625,
-0.002410888671875,
-0.0237274169921875,
0.00627899169921875,
0.01535797119140625,
-0.053070068359375,
0.047943115234375,
0.0038089752197265625,
0.00899505615234375,
-0.0367431640625,
0.0011415481567382812,
-0.02099609375,
0.001399993896484375,
-0.01233673095703125,
0.0230712890625,
-0.0027866363525390625,
-0.01450347900390625,
0.014678955078125,
0.01971435546875,
-0.0035839080810546875,
-0.00717926025390625,
0.00481414794921875,
0.0294647216796875,
-0.02294921875,
0.007266998291015625,
0.00911712646484375,
-0.0016393661499023438,
-0.007488250732421875,
-0.032684326171875,
-0.0161895751953125,
-0.01172637939453125,
0.03570556640625,
-0.002490997314453125,
0.01096343994140625,
0.001094818115234375,
0.022918701171875,
0.00815582275390625,
-0.006397247314453125,
0.007663726806640625,
-0.009735107421875,
0.0123138427734375,
0.0029354095458984375,
0.015167236328125,
0.0008206367492675781,
0.047515869140625,
0.025177001953125,
-0.0158538818359375,
0.016204833984375,
-0.010040283203125,
-0.006534576416015625,
-0.01349639892578125,
0.005779266357421875,
0.0226287841796875,
-0.0146331787109375,
0.00860595703125,
0.0122222900390625,
-0.050384521484375,
0.02325439453125,
0.0255889892578125,
0.0418701171875,
-0.044097900390625,
0.005329132080078125,
0.0098724365234375,
0.006015777587890625,
-0.004901885986328125,
0.00341796875,
0.02569580078125,
-0.01308441162109375,
-0.0087738037109375,
-0.0008678436279296875,
0.00634002685546875,
-0.006481170654296875,
0.042724609375,
-0.01081085205078125,
0.00037384033203125,
0.0394287109375,
0.01346588134765625,
-0.0172271728515625,
0.0011472702026367188,
-0.0022220611572265625,
0.01529693603515625,
0.0379638671875,
-0.032928466796875,
-0.044281005859375,
0.018280029296875,
-0.010772705078125,
-0.01654052734375,
-0.0245208740234375,
-0.010223388671875,
0.0179290771484375,
-0.02886962890625,
0.0086822509765625,
-0.0245819091796875,
0.001373291015625,
-0.02301025390625,
0.03961181640625,
0.0194549560546875,
0.011749267578125,
-0.004749298095703125,
0.0191497802734375,
-0.0124664306640625,
-0.01318359375,
0.0139923095703125,
0.0015192031860351562,
0.00284576416015625,
0.0021228790283203125,
-0.00574493408203125,
0.00044608116149902344,
-0.00447845458984375,
-0.0033779144287109375,
0.00998687744140625,
0.0070343017578125,
0.031463623046875,
-0.01043701171875,
-0.0186004638671875,
0.01079559326171875,
-0.009613037109375,
-0.044677734375,
-0.01568603515625,
0.007335662841796875,
0.024566650390625,
-0.011444091796875,
0.00616455078125,
-0.0233612060546875,
-0.002750396728515625,
0.01849365234375,
0.0246429443359375,
0.0198516845703125,
0.019775390625,
0.0036106109619140625,
0.014068603515625,
0.015106201171875,
0.025848388671875,
0.029327392578125,
0.00330352783203125,
0.00992584228515625,
-0.00390625,
0.045562744140625,
0.0249786376953125,
-0.0163421630859375,
0.01541900634765625,
0.003055572509765625,
0.0118255615234375,
-0.01500701904296875,
-0.004413604736328125,
0.0279541015625,
0.01377105712890625,
0.006862640380859375,
-0.0032176971435546875,
-0.0242919921875,
-0.0016498565673828125,
0.007297515869140625,
-0.04730224609375,
0.028839111328125,
-0.00746917724609375,
-0.0285491943359375,
-0.0011014938354492188,
-0.01422882080078125,
-0.01418304443359375,
0.030609130859375,
0.0224761962890625,
-0.0278778076171875,
-0.0028629302978515625,
-0.015533447265625,
-0.006927490234375,
0.026947021484375,
-0.042755126953125,
-0.0032863616943359375,
0.032989501953125,
0.002475738525390625,
0.0282745361328125,
-0.03424072265625,
-0.00989532470703125,
0.00856781005859375,
-0.005420684814453125,
-0.0297088623046875,
-0.00299072265625,
0.0070648193359375,
0.0178985595703125,
-0.0284271240234375,
0.01050567626953125,
-0.036163330078125,
-0.017242431640625,
0.023651123046875,
0.0182037353515625,
-0.0146026611328125,
0.0213165283203125,
-0.013031005859375,
0.0107574462890625,
0.04315185546875,
-0.02581787109375,
-0.00894927978515625,
-0.0014324188232421875,
-0.01910400390625,
0.03863525390625,
-0.0004024505615234375,
0.0089111328125,
-0.041656494140625,
0.00823974609375,
-0.0318603515625,
0.0034160614013671875,
-0.006931304931640625,
0.0291900634765625,
0.01153564453125,
0.0195159912109375,
0.017547607421875,
-0.0095062255859375,
-0.01255035400390625,
0.01641845703125,
-0.0159912109375,
-0.024078369140625,
-0.018463134765625,
-0.0184173583984375,
0.023223876953125,
-0.0167083740234375,
0.010498046875,
-0.001293182373046875,
0.0136260986328125,
0.03082275390625,
-0.00408935546875,
-0.040435791015625,
0.04083251953125,
0.0145416259765625,
-0.0026760101318359375,
0.02044677734375,
0.0018062591552734375,
0.0175323486328125,
-0.0260162353515625,
-0.0170745849609375,
0.02294921875,
0.0028285980224609375,
0.0300445556640625,
0.006122589111328125,
-0.007808685302734375,
0.038421630859375,
0.0163726806640625,
-0.006168365478515625,
0.017852783203125,
-0.018890380859375,
-0.0111541748046875,
-0.0026798248291015625,
-0.0031566619873046875,
-0.0189361572265625,
-0.0106353759765625,
-0.0029754638671875,
-0.018585205078125,
0.00574493408203125,
0.02166748046875,
0.039886474609375,
-0.006298065185546875,
-0.0196990966796875,
-0.0125274658203125,
0.0173797607421875,
0.008544921875,
0.0250244140625,
0.0200042724609375,
-0.0010471343994140625,
-0.045257568359375,
0.00527191162109375,
0.0052947998046875,
0.02008056640625,
-0.01503753662109375,
-0.020355224609375,
0.0161895751953125,
-0.035247802734375,
0.007282257080078125,
0.0017070770263671875,
0.0117340087890625,
0.005462646484375,
-0.01480865478515625,
-0.04193115234375,
-0.0193023681640625,
0.0173492431640625,
0.026458740234375,
-0.0214385986328125,
0.01263427734375,
-0.0263671875,
0.012420654296875,
-0.036865234375,
0.0008225440979003906,
0.0256805419921875,
0.0037136077880859375,
-0.03021240234375,
0.0006327629089355469,
0.010284423828125,
-0.009307861328125,
-0.0036678314208984375,
-0.026214599609375,
-0.0198974609375,
0.006938934326171875,
-0.003192901611328125,
0.0190582275390625,
0.0086822509765625,
-0.0179901123046875,
0.026153564453125,
0.0292816162109375,
-0.018035888671875,
0.0236968994140625,
-0.01284027099609375,
-0.0195159912109375,
0.034698486328125,
-0.0191497802734375,
-0.005680084228515625,
0.01486968994140625,
-0.00099945068359375,
0.00743865966796875,
0.01413726806640625,
0.0098876953125,
-0.01309967041015625,
-0.0026264190673828125,
-0.005401611328125,
-0.006671905517578125,
0.01140594482421875,
-0.01096343994140625,
0.047393798828125,
0.0049591064453125,
-0.004486083984375,
-0.0061798095703125,
0.019287109375,
0.0086517333984375,
0.045684814453125,
0.00470733642578125,
-0.01197052001953125,
-0.0233917236328125,
0.0189056396484375,
-0.035980224609375,
-0.011322021484375,
-0.01018524169921875,
-0.0249176025390625,
0.0008831024169921875,
0.02899169921875,
0.0187530517578125,
-0.028778076171875,
-0.003391265869140625,
-0.01605224609375,
-0.0140380859375,
-0.004444122314453125,
-0.0062408447265625,
0.0217742919921875,
0.03753662109375,
-0.006587982177734375,
0.015380859375,
0.02197265625,
-0.0279998779296875,
-0.0181121826171875,
-0.01029205322265625,
-0.00628662109375,
-0.0022945404052734375,
-0.056243896484375,
-0.0247802734375,
-0.02935791015625,
-0.007808685302734375,
0.0017957687377929688,
0.0267791748046875,
-0.010284423828125,
-0.014556884765625,
0.01788330078125,
0.0165557861328125,
-0.0251617431640625,
-0.00603485107421875,
-0.004917144775390625,
-0.023834228515625,
-0.03167724609375,
-0.0240478515625,
-0.0202178955078125,
0.0157623291015625,
-0.035980224609375,
-0.021026611328125,
0.03338623046875,
-0.0191802978515625,
0.009490966796875,
0.03643798828125,
-0.00029397010803222656,
0.00962066650390625,
0.04278564453125,
0.0271759033203125,
-0.01242828369140625,
0.00823211669921875,
-0.004863739013671875,
-0.0266876220703125,
0.01453399658203125,
-0.016021728515625,
-0.0210723876953125,
0.002567291259765625,
-0.0183563232421875,
-0.01410675048828125,
0.005504608154296875,
-0.00726318359375,
-0.0009303092956542969,
0.0170135498046875,
0.00370025634765625,
0.011260986328125,
-0.004100799560546875,
-0.0094146728515625,
0.0176239013671875,
-0.005344390869140625,
-0.023162841796875,
0.00460052490234375,
0.00867462158203125,
-0.031036376953125,
0.0212554931640625,
0.00795745849609375,
0.006702423095703125,
-0.0038967132568359375,
0.0037593841552734375,
0.039093017578125,
-0.02215576171875,
-0.0012044906616210938,
0.006412506103515625,
-0.0027675628662109375,
-0.0089569091796875,
0.0217132568359375,
0.01519012451171875,
-0.020233154296875,
0.0026264190673828125,
0.017303466796875,
-0.01065826416015625,
-0.0250244140625,
0.01448822021484375,
0.02044677734375,
-0.003276824951171875,
-0.01800537109375,
0.00571441650390625,
-0.00623321533203125,
-0.02105712890625,
0.003734588623046875,
-0.04400634765625,
-0.0192413330078125,
-0.0196533203125,
-0.0024929046630859375,
0.01255035400390625,
-0.0026702880859375,
0.042205810546875,
0.014617919921875,
0.0052490234375,
0.034027099609375,
0.0103759765625,
0.0027179718017578125,
-0.0011529922485351562,
0.0216827392578125,
-0.0231781005859375,
0.0033931732177734375,
0.0067291259765625,
-0.0159454345703125,
-0.0160980224609375,
-0.01561737060546875,
-0.0249481201171875,
0.018798828125,
0.0222320556640625,
0.007617950439453125,
-0.00910186767578125,
0.005764007568359375,
0.02288818359375,
0.02960205078125,
-0.0234527587890625,
-0.0280914306640625,
0.0028533935546875,
0.02117919921875,
-0.0163726806640625,
0.0089874267578125,
0.00406646728515625,
-0.0053863525390625,
-0.00481414794921875,
0.046722412109375,
0.01338958740234375,
-0.0267791748046875,
-0.01641845703125,
-0.01214599609375,
0.0189361572265625,
-0.0207977294921875,
0.0017452239990234375,
0.017364501953125,
0.025299072265625,
0.0089263916015625,
-0.01107025146484375,
0.024200439453125,
-0.028228759765625,
-0.005367279052734375,
-0.01214599609375,
-0.0002608299255371094,
0.00543975830078125,
-0.0016603469848632812,
0.0049285888671875,
0.05535888671875,
-0.0134429931640625,
0.021514892578125,
0.022735595703125,
0.0166015625,
-0.0364990234375,
-0.05010986328125,
-0.0008273124694824219,
0.0113067626953125,
-0.02374267578125,
0.00836181640625,
0.004138946533203125,
0.006481170654296875,
-0.0340576171875,
0.0018749237060546875,
0.015411376953125,
0.040740966796875,
-0.0011014938354492188,
0.0179443359375,
0.0271453857421875,
0.028961181640625,
0.0243988037109375,
-0.014373779296875,
-0.0131378173828125,
-0.0181121826171875,
-0.0108489990234375,
0.01058197021484375,
-0.0223388671875,
-0.0008478164672851562,
0.00498199462890625,
0.0176544189453125,
-0.019012451171875,
-0.0121307373046875,
-0.002719879150390625,
0.01206207275390625,
0.0330810546875,
-0.01430511474609375,
0.023590087890625,
-0.0288543701171875,
0.0166015625,
-0.00714874267578125,
0.017822265625,
0.03253173828125,
-0.0229339599609375,
0.04766845703125,
0.0008487701416015625,
0.01708984375,
0.01739501953125,
0.01439666748046875,
0.00738525390625,
0.01552581787109375,
0.00623321533203125,
0.00428009033203125,
0.0008378028869628906,
-0.0122222900390625,
-0.005084991455078125,
-0.01032257080078125,
0.01148223876953125,
0.0201416015625,
0.0310821533203125,
0.007526397705078125,
-0.0239715576171875,
0.012115478515625,
0.015869140625,
-0.037811279296875,
-0.00843048095703125,
0.01084136962890625,
-0.01316070556640625,
0.005954742431640625,
-0.0298309326171875,
0.0178680419921875,
-0.003749847412109375,
0.038848876953125,
-0.0023651123046875,
0.0100250244140625,
-0.0013456344604492188,
0.000553131103515625,
-0.03167724609375,
0.0008578300476074219,
-0.0231781005859375,
0.0306396484375,
-0.02093505859375,
0.01654052734375,
0.0176544189453125,
0.0259552001953125,
0.0213165283203125,
0.006931304931640625,
0.0030765533447265625,
-0.02984619140625,
-0.006183624267578125,
-0.0226898193359375,
0.001956939697265625,
-0.01030731201171875,
-0.0005321502685546875,
-0.01555633544921875,
0.057952880859375,
-0.0142059326171875,
0.034454345703125,
-0.015411376953125,
0.00850677490234375,
-0.003528594970703125,
-0.0027313232421875,
0.03887939453125,
0.0244293212890625,
-0.0007257461547851562,
-0.005443572998046875,
-0.00922393798828125,
-0.04339599609375,
0.017669677734375,
0.007114410400390625,
0.01389312744140625,
-0.000751495361328125,
0.035614013671875,
-0.0131988525390625,
0.0006003379821777344,
0.042266845703125,
-0.0099639892578125,
-0.011627197265625,
-0.01399993896484375,
0.0360107421875,
0.0117645263671875,
-0.0012788772583007812,
-0.02044677734375,
-0.013671875,
0.01212310791015625,
-0.04205322265625,
0.0021915435791015625,
-0.0276031494140625,
0.024688720703125,
-0.0181732177734375,
-0.050048828125,
0.00481414794921875,
-0.02978515625,
0.02691650390625,
0.041046142578125,
-0.0013303756713867188,
0.0362548828125,
0.01068115234375,
0.0164642333984375,
-0.0034923553466796875,
0.007068634033203125,
-0.004367828369140625,
0.007198333740234375,
-0.0292816162109375,
-0.01049041748046875,
0.0304412841796875,
0.017303466796875,
0.006366729736328125,
-0.0302734375,
-0.0037326812744140625,
0.0161285400390625,
0.0006642341613769531,
0.0100250244140625,
-0.0467529296875,
0.01369476318359375,
0.0041351318359375,
0.0187835693359375,
-0.0122833251953125,
-0.00098419189453125,
-0.016693115234375,
-0.0123138427734375,
-0.035797119140625,
-0.000007927417755126953,
-0.015350341796875,
0.00963592529296875,
0.00899505615234375,
-0.0040130615234375,
0.028411865234375,
0.0017719268798828125,
0.00931549072265625,
0.0169830322265625,
0.0255889892578125,
0.01776123046875,
0.023895263671875,
-0.0240020751953125,
0.0153961181640625,
-0.004955291748046875,
0.017059326171875,
0.00969696044921875,
-0.005870819091796875,
0.0196075439453125,
-0.0306549072265625,
0.01751708984375,
-0.0212860107421875,
0.00469207763671875,
-0.0170135498046875,
-0.0019969940185546875,
-0.024139404296875,
0.0321044921875,
-0.00433349609375,
0.009063720703125,
-0.01477813720703125,
0.049957275390625,
-0.001300811767578125,
0.044708251953125,
0.0157470703125,
-0.004100799560546875,
-0.00839996337890625,
-0.0097808837890625,
-0.0043182373046875,
0.042236328125,
0.00852203369140625,
0.011627197265625,
-0.004974365234375,
-0.01027679443359375,
0.00951385498046875,
0.01244354248046875,
0.0291290283203125,
-0.00750732421875,
-0.017120361328125,
0.0057525634765625,
0.00626373291015625,
0.04364013671875,
0.0030612945556640625,
0.004253387451171875,
-0.004543304443359375,
-0.00872802734375,
-0.0007300376892089844,
-0.0213775634765625,
-0.0128326416015625,
-0.0289764404296875,
0.015411376953125,
-0.0015277862548828125,
-0.00908660888671875,
-0.0025386810302734375,
0.01386260986328125,
-0.03741455078125,
0.01515960693359375,
0.037750244140625,
0.0250396728515625,
0.02313232421875,
-0.0032711029052734375,
0.0163116455078125,
-0.0171661376953125,
0.025115966796875,
-0.0073394775390625,
-0.0003745555877685547,
-0.00836181640625,
-0.02032470703125,
-0.0196685791015625,
0.00959014892578125,
0.0123748779296875,
0.021087646484375,
0.007598876953125,
0.0252838134765625,
0.0152130126953125,
-0.0266265869140625,
0.0096588134765625,
-0.0156097412109375,
0.01678466796875,
0.008148193359375,
0.00402069091796875,
0.00724029541015625,
0.00638580322265625,
0.048736572265625,
-0.0033969879150390625,
-0.017578125,
-0.0164947509765625,
0.0014429092407226562,
0.01165008544921875,
0.0010614395141601562,
-0.007396697998046875,
0.00516510009765625,
-0.0098419189453125,
-0.019622802734375,
0.00743865966796875,
-0.044677734375,
0.01322174072265625,
-0.01332855224609375,
-0.006252288818359375,
-0.01288604736328125,
0.0245513916015625,
0.0010852813720703125,
0.030364990234375,
-0.01207733154296875,
0.0276947021484375,
0.006412506103515625,
0.03228759765625,
-0.00685882568359375,
-0.01276397705078125,
-0.0302276611328125,
-0.0079498291015625,
0.02618408203125,
0.0030803680419921875,
-0.00022721290588378906,
0.038818359375,
-0.0095062255859375,
-0.02056884765625,
-0.020050048828125,
0.0289459228515625,
0.046844482421875,
-0.00737762451171875,
-0.007762908935546875,
-0.03802490234375,
-0.0004317760467529297,
-0.004299163818359375,
0.017364501953125,
0.0009908676147460938,
0.0154266357421875,
-0.0020084381103515625,
0.01061248779296875,
0.0137176513671875,
0.0252227783203125,
-0.0240020751953125,
-0.00691986083984375,
-0.017730712890625,
0.0159759521484375,
-0.03924560546875,
0.0000635385513305664,
0.0092010498046875,
-0.03106689453125,
-0.0190277099609375,
-0.0007996559143066406,
0.0206451416015625,
-0.001708984375,
-0.03955078125,
-0.006191253662109375,
-0.004161834716796875,
0.000022411346435546875,
0.004947662353515625,
0.008453369140625,
0.0189666748046875,
-0.046051025390625,
0.005359649658203125,
0.005084991455078125,
0.0295562744140625,
0.0609130859375,
-0.018310546875,
0.01390838623046875,
0.026824951171875,
-0.0009851455688476562,
-0.01059722900390625,
0.00907135009765625,
0.01293182373046875,
0.0100555419921875,
0.0166473388671875,
-0.02056884765625,
-0.0177154541015625,
-0.01221466064453125,
0.0300750732421875,
0.01247406005859375,
-0.00811004638671875,
-0.021881103515625,
-0.0113677978515625,
-0.033111572265625,
-0.01245880126953125,
-0.0203704833984375,
-0.013824462890625,
0.0071563720703125,
-0.00681304931640625,
-0.010009765625,
0.0014772415161132812,
0.01103973388671875,
0.0008721351623535156,
0.01377105712890625,
-0.02130126953125,
-0.024444580078125,
0.0282440185546875,
0.00824737548828125,
-0.024200439453125,
0.01898193359375,
0.0232391357421875,
-0.005794525146484375,
-0.005977630615234375,
0.0225067138671875,
-0.0016498565673828125,
-0.040435791015625,
0.0181884765625,
-0.005229949951171875,
-0.0073699951171875,
-0.03936767578125,
0.0032444000244140625,
0.0230560302734375,
-0.01512908935546875,
-0.051055908203125,
0.0258941650390625,
-0.035125732421875,
0.017486572265625,
0.0357666015625,
-0.0025272369384765625,
-0.0172271728515625,
0.00457763671875,
-0.0152587890625,
-0.02703857421875,
0.03424072265625,
-0.0198211669921875,
-0.007297515869140625,
0.04217529296875,
-0.037933349609375,
0.0038509368896484375,
-0.01172637939453125,
0.0065155029296875,
-0.0282745361328125,
-0.00678253173828125,
0.00921630859375,
-0.0048675537109375,
0.00716400146484375,
-0.0048675537109375,
0.017333984375,
0.0391845703125,
0.04541015625,
0.010955810546875,
-0.0169830322265625,
0.0056610107421875,
0.024322509765625,
-0.0171051025390625,
0.015472412109375,
-0.00640869140625,
0.017486572265625,
-0.007785797119140625,
0.0158233642578125,
-0.03668212890625,
-0.0284576416015625,
0.0272064208984375,
0.0001608133316040039,
-0.0020751953125,
-0.02276611328125,
0.01033782958984375,
0.0260772705078125,
-0.00428009033203125,
-0.039093017578125,
-0.038116455078125,
0.007354736328125,
0.01107025146484375,
0.0193328857421875,
0.00533294677734375,
-0.016265869140625,
0.022491455078125,
0.040130615234375,
-0.01477813720703125,
0.00445556640625,
-0.0027942657470703125,
-0.0269775390625,
-0.01194000244140625,
-0.0035533905029296875,
0.021240234375,
0.03082275390625,
0.051025390625,
-0.00988006591796875,
0.01422119140625,
-0.0285797119140625,
-0.001514434814453125,
0.040313720703125,
0.0146484375,
0.0316162109375,
0.0036754608154296875,
-0.03997802734375,
0.0113983154296875,
0.0136566162109375,
0.0171966552734375,
0.01340484619140625,
-0.0262451171875,
0.004787445068359375,
0.02410888671875,
-0.004123687744140625,
0.00038242340087890625,
0.034820556640625,
0.008758544921875,
-0.04974365234375,
-0.020233154296875,
-0.0048980712890625,
0.004680633544921875,
-0.008209228515625,
0.0335693359375,
0.00440216064453125,
-0.00511932373046875,
-0.038909912109375,
-0.0023097991943359375,
-0.0010023117065429688,
0.01026153564453125,
-0.030853271484375,
0.0299224853515625,
-0.038238525390625,
0.0221405029296875,
0.0198822021484375,
-0.057098388671875,
-0.0121307373046875,
0.0036029815673828125,
0.020721435546875,
-0.027740478515625,
-0.024993896484375,
0.01496124267578125,
-0.0184173583984375,
-0.057861328125,
0.0178985595703125,
-0.0022563934326171875,
-0.01361846923828125,
-0.00665283203125,
-0.0333251953125,
-0.0010080337524414062,
0.01030731201171875,
-0.00009918212890625,
0.01407623291015625,
-0.0076751708984375,
-0.02783203125,
-0.0233612060546875,
-0.006961822509765625,
-0.0232696533203125,
0.012115478515625,
0.0023784637451171875,
-0.0086212158203125,
0.0197601318359375,
-0.007549285888671875,
0.04315185546875,
0.00551605224609375,
0.03961181640625,
0.01457977294921875,
-0.01049041748046875,
0.01085662841796875,
0.0102386474609375,
-0.00130462646484375,
0.0257568359375,
-0.027069091796875,
0.005916595458984375,
-0.00775909423828125,
-0.0260162353515625,
-0.029022216796875,
0.003421783447265625,
0.024383544921875,
0.0129852294921875,
-0.0242767333984375,
-0.0003616809844970703,
-0.0255584716796875,
0.00888824462890625,
0.0184783935546875,
0.013916015625,
0.00957489013671875,
-0.004329681396484375,
0.0237884521484375,
-0.041473388671875,
0.0087432861328125,
0.005596160888671875,
0.033203125,
-0.017913818359375,
-0.006649017333984375,
0.00782012939453125,
0.015960693359375,
0.01422882080078125,
0.03802490234375,
0.02886962890625,
-0.01166534423828125,
0.00335693359375,
-0.0037288665771484375,
-0.007213592529296875,
-0.0020542144775390625,
-0.0135040283203125,
0.025299072265625,
-0.0333251953125,
0.006046295166015625,
-0.003124237060546875,
-0.0220794677734375,
-0.0038585662841796875,
-0.00962066650390625,
-0.0169525146484375,
0.01520538330078125,
0.029449462890625,
-0.03472900390625,
0.01049041748046875,
-0.0399169921875,
0.002887725830078125,
0.0305023193359375,
-0.0293426513671875,
0.0135040283203125,
0.0015277862548828125,
0.020904541015625,
-0.0287017822265625,
-0.0222015380859375,
-0.01123809814453125,
0.00279998779296875,
0.007061004638671875,
0.01383209228515625,
0.007045745849609375,
0.05078125,
0.0013971328735351562,
-0.0033092498779296875,
-0.00433349609375,
0.0035419464111328125,
0.03192138671875,
0.0210418701171875,
0.04595947265625,
0.01515960693359375,
0.0204315185546875,
-0.0333251953125,
0.020660400390625,
0.0011186599731445312,
0.0281982421875,
-0.0134124755859375,
0.023773193359375,
0.02630615234375,
-0.0312042236328125,
-0.0187835693359375,
-0.025970458984375,
-0.00262451171875,
-0.0103912353515625,
0.00048732757568359375,
-0.01824951171875,
-0.00623321533203125,
-0.0078125,
0.0235443115234375,
-0.01200103759765625,
0.0263824462890625,
-0.0092926025390625,
-0.038543701171875,
-0.0052337646484375,
-0.050506591796875,
-0.0023822784423828125,
-0.007183074951171875,
-0.01358795166015625,
0.026611328125,
-0.0015783309936523438,
-0.01702880859375,
-0.0013866424560546875,
0.0184173583984375,
-0.0333251953125,
0.00437164306640625,
-0.0090484619140625,
0.02349853515625,
-0.0052642822265625,
-0.0173797607421875,
0.00860595703125,
-0.00489044189453125,
-0.0277099609375,
0.03631591796875,
-0.0220489501953125,
0.01263427734375,
-0.0170440673828125,
-0.00038433074951171875,
0.0206146240234375,
-0.003936767578125,
-0.016937255859375,
0.005893707275390625,
0.0028514862060546875,
-0.00905609130859375,
-0.00476837158203125,
-0.02313232421875,
-0.0016088485717773438,
-0.007427215576171875,
-0.0234375,
0.0247344970703125,
-0.00740814208984375,
-0.0137176513671875,
-0.007022857666015625,
-0.03485107421875,
-0.004337310791015625,
0.0175933837890625,
-0.0130615234375,
-0.01837158203125,
-0.0210723876953125,
0.035797119140625,
-0.008697509765625,
0.01934814453125,
0.0165252685546875,
0.006805419921875,
0.004238128662109375,
-0.0021076202392578125,
0.023406982421875,
0.0343017578125,
-0.005603790283203125,
-0.01378631591796875,
0.0005812644958496094,
0.004863739013671875,
0.00399017333984375,
0.00263214111328125,
0.00046539306640625,
-0.037811279296875,
0.0146331787109375,
0.005130767822265625,
-0.015716552734375,
-0.0251312255859375,
0.01216888427734375,
0.032806396484375,
-0.00447845458984375,
0.005435943603515625,
-0.01519012451171875,
0.018798828125,
0.00960540771484375,
0.042449951171875,
0.019866943359375,
-0.00435638427734375,
0.0139007568359375,
-0.006366729736328125,
0.016204833984375,
0.005367279052734375,
-0.0041961669921875,
-0.025115966796875,
0.0188751220703125,
-0.0024662017822265625,
-0.00191497802734375,
-0.0025043487548828125,
-0.0240478515625,
0.024261474609375,
0.03173828125,
0.0082855224609375,
-0.03240966796875,
0.0003859996795654297,
0.0019273757934570312,
-0.00817108154296875,
0.004894256591796875,
-0.0296478271484375,
-0.02960205078125,
-0.0301055908203125,
-0.0230255126953125,
-0.002559661865234375,
-0.0023593902587890625,
0.002384185791015625,
0.036376953125,
-0.0236968994140625,
0.0009946823120117188,
0.00788116455078125,
0.0021152496337890625,
-0.01131439208984375,
0.02264404296875,
0.0051116943359375,
0.01502227783203125,
-0.0296783447265625,
-0.0185089111328125,
0.016754150390625,
0.008270263671875,
-0.007221221923828125,
0.005001068115234375,
0.0114593505859375,
-0.01308441162109375,
-0.0230560302734375,
-0.020843505859375,
-0.0256500244140625,
-0.018035888671875,
-0.0196533203125,
0.0140228271484375,
-0.0015306472778320312,
-0.052001953125,
-0.009674072265625,
0.00705718994140625,
0.0341796875,
0.0024261474609375,
-0.01141357421875,
0.01053619384765625,
-0.0156402587890625,
0.019317626953125,
0.021270751953125,
-0.058807373046875,
0.032867431640625,
-0.015655517578125,
0.0296478271484375,
0.03387451171875,
-0.053436279296875,
-0.0186309814453125,
0.00878143310546875,
-0.006679534912109375,
-0.01434326171875,
0.019500732421875,
0.0198974609375,
-0.011993408203125,
0.012725830078125,
0.0033359527587890625,
-0.007114410400390625,
-0.005161285400390625,
-0.0218505859375,
-0.0322265625,
0.017425537109375,
0.0049285888671875,
0.036041259765625,
-0.00946807861328125,
0.027984619140625,
-0.011627197265625,
0.0242156982421875,
0.03314208984375,
0.00824737548828125,
-0.00931549072265625,
0.01453399658203125,
0.0024662017822265625,
-0.0023326873779296875,
0.00927734375,
0.0136260986328125,
-0.01218414306640625,
-0.0150299072265625,
-0.022552490234375,
-0.0051116943359375,
0.00873565673828125,
-0.01119232177734375,
-0.0309295654296875,
-0.0185089111328125,
-0.007110595703125,
-0.01081085205078125,
-0.033935546875,
-0.0224151611328125,
-0.01885986328125,
-0.0070953369140625,
0.0582275390625,
-0.0390625,
0.0008087158203125,
-0.02923583984375,
0.006755828857421875,
-0.033935546875,
-0.01081085205078125,
-0.0280303955078125,
-0.00879669189453125,
0.01971435546875,
-0.014373779296875,
-0.036590576171875,
-0.0240325927734375,
-0.01340484619140625,
0.0236968994140625,
0.00588226318359375,
0.01013946533203125,
-0.0046539306640625,
0.0034942626953125,
0.004302978515625,
0.00818634033203125,
0.0233306884765625,
0.0104522705078125,
-0.003803253173828125,
-0.00742340087890625,
-0.05029296875,
-0.0350341796875,
-0.005023956298828125,
-0.007297515869140625,
-0.0014820098876953125,
0.0154266357421875,
0.0006594657897949219,
0.0033206939697265625,
-0.0016622543334960938,
0.0294952392578125,
-0.03826904296875,
-0.01093292236328125,
0.0352783203125,
-0.01171875,
-0.0224456787109375,
-0.003040313720703125,
-0.02392578125,
0.00431060791015625,
0.00008296966552734375,
0.02728271484375,
0.0093841552734375,
0.007381439208984375,
-0.01439666748046875,
0.002864837646484375,
-0.005222320556640625,
0.006305694580078125,
-0.004146575927734375,
0.0188446044921875,
-0.0246429443359375,
-0.00662994384765625,
0.001407623291015625,
0.00982666015625,
-0.0225830078125,
0.00946044921875,
-0.01409149169921875,
0.02911376953125,
0.032135009765625,
-0.00251007080078125,
0.01416015625,
-0.021514892578125,
-0.005588531494140625,
0.0123443603515625,
-0.0008082389831542969,
0.0131378173828125,
-0.01885986328125,
-0.002277374267578125,
-0.02203369140625,
-0.026947021484375,
0.0159149169921875,
-0.009368896484375,
0.006610870361328125,
-0.0130767822265625,
-0.0007863044738769531,
-0.01079559326171875,
0.01128387451171875,
-0.010986328125,
-0.03338623046875,
-0.0022220611572265625,
0.0096588134765625,
-0.0229339599609375,
-0.0138702392578125,
-0.02423095703125,
0.00971221923828125,
-0.046173095703125,
0.014190673828125,
0.0223541259765625,
-0.00409698486328125,
-0.01354217529296875,
-0.01032257080078125,
0.0133056640625,
-0.0206451416015625,
0.01044464111328125,
0.009063720703125,
0.0006809234619140625,
0.016021728515625,
-0.004486083984375,
-0.0272216796875,
-0.002193450927734375,
-0.0251007080078125,
0.00884246826171875,
-0.0298614501953125,
-0.01039886474609375,
-0.031585693359375,
0.00769805908203125,
0.01068115234375,
0.0017843246459960938,
-0.01111602783203125,
0.039459228515625,
0.0110626220703125,
-0.0291900634765625,
-0.029052734375,
0.0249786376953125,
-0.00826263427734375,
0.037261962890625,
0.010589599609375,
0.0079498291015625,
-0.0201416015625,
0.013641357421875,
0.0049896240234375,
-0.0052337646484375,
0.01209259033203125,
0.0216064453125,
-0.038238525390625,
0.0044403076171875,
0.0236053466796875,
0.03485107421875,
0.01462554931640625,
0.0052490234375,
0.002307891845703125,
0.0004687309265136719,
-0.033203125,
0.005313873291015625,
-0.026397705078125,
-0.003276824951171875,
0.033599853515625,
-0.0043792724609375,
-0.0167999267578125,
0.01739501953125,
-0.025177001953125,
-0.055572509765625,
-0.0003490447998046875,
-0.0028018951416015625,
0.00005614757537841797,
0.040740966796875,
-0.0147247314453125,
-0.0078887939453125,
0.01337432861328125,
-0.0240478515625,
-0.00628662109375,
-0.028411865234375,
-0.0025730133056640625,
-0.059600830078125,
-0.0257415771484375,
0.02471923828125,
-0.0303802490234375,
0.023956298828125,
-0.01062774658203125,
0.004924774169921875,
0.0007386207580566406,
0.00498199462890625,
-0.0082855224609375,
-0.00864410400390625,
-0.004215240478515625,
0.025543212890625,
-0.01751708984375,
0.00893402099609375,
0.0281219482421875,
-0.0202484130859375,
-0.006618499755859375,
-0.003910064697265625,
0.044677734375,
-0.0036869049072265625,
0.01424407958984375,
-0.00945281982421875,
0.0014858245849609375,
-0.029815673828125,
0.004749298095703125,
0.00018966197967529297,
-0.01422882080078125,
-0.0037670135498046875,
-0.01416015625,
0.024322509765625,
-0.01454925537109375,
0.0027904510498046875,
-0.00286102294921875,
-0.00643157958984375,
0.016815185546875,
-0.02276611328125,
-0.003993988037109375,
-0.01122283935546875,
-0.00862884521484375,
-0.01103973388671875,
-0.01428985595703125,
-0.02374267578125,
0.019500732421875,
-0.0017147064208984375,
0.0184326171875,
0.027130126953125,
0.01267242431640625,
-0.00452423095703125,
0.00836944580078125,
0.0264434814453125,
0.0281829833984375,
-0.03631591796875,
-0.003692626953125,
-0.008392333984375,
-0.0029449462890625,
0.018157958984375,
-0.0011606216430664062,
0.0113983154296875,
0.0147857666015625,
-0.00004166364669799805,
-0.00603485107421875,
-0.0195159912109375,
-0.034088134765625,
-0.0074920654296875,
0.0235595703125,
-0.032623291015625,
-0.00977325439453125,
-0.018218994140625,
0.01617431640625,
0.0133514404296875,
0.02783203125,
0.0220184326171875,
-0.0131072998046875,
0.00893402099609375,
-0.026397705078125,
0.02484130859375,
0.01102447509765625,
-0.0244140625,
0.0077362060546875,
0.01381683349609375,
-0.0252227783203125,
0.01708984375,
-0.011962890625,
-0.05877685546875,
0.0304718017578125,
-0.01406097412109375,
-0.002460479736328125,
-0.0158538818359375,
0.007717132568359375,
0.0010471343994140625,
0.005916595458984375,
-0.001468658447265625,
-0.04107666015625,
-0.01050567626953125,
0.0195465087890625,
-0.0061798095703125,
0.0206451416015625,
-0.03582763671875,
-0.0236663818359375,
0.025177001953125,
-0.0005860328674316406,
0.0104217529296875,
-0.013885498046875,
-0.0235443115234375,
-0.00026607513427734375,
0.0086822509765625,
0.017547607421875,
-0.018280029296875,
0.00482940673828125,
0.0295867919921875,
-0.0212860107421875,
0.0257110595703125,
-0.04437255859375,
0.0083465576171875,
-0.0007748603820800781,
0.0106658935546875,
-0.0023174285888671875,
-0.01032257080078125,
0.0261077880859375,
0.01158905029296875,
0.0204010009765625,
0.01861572265625,
-0.0008292198181152344,
-0.01419830322265625,
-0.0186767578125,
0.0059967041015625,
-0.010009765625,
-0.006984710693359375,
-0.0181121826171875,
0.0192108154296875,
-0.01751708984375,
-0.01239013671875,
0.01219940185546875,
0.028106689453125,
-0.016815185546875,
0.0216522216796875,
0.00799560546875,
-0.005413055419921875,
0.0219573974609375,
0.0098419189453125,
-0.0290679931640625,
0.021636962890625,
0.01702880859375,
0.01265716552734375,
0.00919342041015625,
0.0184173583984375,
0.0071868896484375,
-0.01494598388671875,
0.0287017822265625,
0.0031909942626953125,
-0.0455322265625,
-0.0203399658203125,
-0.007793426513671875,
0.0264739990234375,
0.01611328125,
-0.024261474609375,
0.0111236572265625,
0.005725860595703125,
-0.0185546875,
0.0001068115234375,
0.028045654296875,
0.0035305023193359375,
0.022247314453125,
-0.015289306640625,
-0.00418853759765625,
-0.0007243156433105469,
-0.030609130859375,
-0.0130157470703125,
0.0006632804870605469,
-0.0228729248046875,
-0.009307861328125,
0.0036602020263671875,
0.00804901123046875,
-0.003803253173828125,
-0.02325439453125,
0.026763916015625,
-0.0017652511596679688,
0.01274871826171875,
-0.0024089813232421875,
0.014923095703125,
0.0050811767578125,
0.021026611328125,
-0.0267181396484375,
0.01168060302734375,
-0.017303466796875,
0.0121917724609375,
-0.0204010009765625,
0.028228759765625,
-0.0309600830078125,
-0.0001989603042602539,
-0.00830078125,
0.00004756450653076172,
0.0173797607421875,
-0.004238128662109375,
0.004390716552734375,
-0.0245819091796875,
-0.0100250244140625,
-0.00804901123046875,
0.00624847412109375,
-0.0281524658203125,
0.040924072265625,
0.01399993896484375,
0.0031299591064453125,
0.0103912353515625,
0.0155792236328125,
0.007476806640625,
0.0035247802734375,
0.02386474609375,
0.0156707763671875,
0.0103912353515625,
0.0300140380859375,
-0.0223846435546875,
-0.0201416015625,
-0.0015897750854492188,
0.0276336669921875,
-0.007175445556640625,
-0.0289154052734375,
0.00359344482421875,
-0.0179901123046875,
-0.032623291015625,
-0.0092620849609375,
0.004932403564453125,
-0.01125335693359375,
-0.0133819580078125,
-0.01213836669921875,
-0.0036754608154296875,
0.0178375244140625,
-0.016937255859375,
0.0367431640625,
-0.049407958984375,
-0.027069091796875,
-0.03900146484375,
0.0295562744140625,
0.0234375,
-0.0308074951171875,
0.01520538330078125,
0.0242919921875,
0.0084381103515625,
0.0182952880859375,
-0.0006699562072753906,
0.02325439453125,
-0.031402587890625,
0.0012311935424804688,
0.0030384063720703125,
-0.01934814453125,
0.0052032470703125,
0.0230255126953125,
-0.017547607421875,
-0.0020694732666015625,
0.0163116455078125,
-0.023651123046875,
-0.00014030933380126953,
0.043121337890625,
-0.011962890625,
-0.001689910888671875,
-0.0477294921875,
0.00785064697265625,
-0.0263519287109375,
0.0160369873046875,
-0.0222015380859375,
-0.0179443359375,
0.0176239013671875,
-0.042327880859375,
0.02618408203125,
-0.029388427734375,
-0.0175323486328125,
0.007732391357421875,
-0.0274810791015625,
-0.01422119140625,
-0.037109375,
0.0308380126953125,
0.01666259765625,
0.019012451171875,
0.005603790283203125,
0.006420135498046875,
-0.0526123046875,
0.01293182373046875,
0.04852294921875,
0.0115814208984375,
-0.00920867919921875,
0.0248260498046875,
0.01303863525390625,
0.0189208984375,
-0.01080322265625,
-0.0200653076171875,
0.020233154296875,
-0.0174560546875,
-0.034271240234375,
0.0182342529296875,
0.003978729248046875,
-0.003787994384765625,
0.0085601806640625,
-0.0082550048828125,
-0.02978515625,
0.01219940185546875,
-0.0049896240234375,
0.023040771484375,
0.0204010009765625,
0.00484466552734375,
-0.0091705322265625,
-0.032440185546875,
0.026123046875,
-0.0219268798828125,
-0.029510498046875,
-0.006862640380859375,
-0.020660400390625,
-0.032867431640625,
-0.01116180419921875,
0.0006418228149414062,
0.0018243789672851562,
0.0066070556640625,
0.0196533203125,
0.0279083251953125,
0.06488037109375,
0.033416748046875,
-0.0007233619689941406,
-0.0022182464599609375,
0.0163116455078125,
0.01079559326171875,
0.014434814453125,
-0.006412506103515625,
0.00658416748046875,
-0.008148193359375,
0.023406982421875,
-0.041961669921875,
-0.016265869140625,
0.021697998046875,
-0.003696441650390625,
-0.0270233154296875,
-0.01445770263671875,
0.0111236572265625,
-0.01531982421875,
-0.019256591796875,
-0.0183563232421875,
0.04443359375,
-0.00035834312438964844,
0.013885498046875,
-0.01007843017578125,
-0.042510986328125,
-0.0029087066650390625,
0.020050048828125,
0.0132293701171875,
-0.03216552734375,
-0.00572967529296875,
0.025665283203125,
0.053558349609375,
-0.0207977294921875,
0.0139923095703125,
-0.01442718505859375,
-0.0253753662109375,
-0.0035686492919921875,
-0.0159149169921875,
-0.00728607177734375,
0.007244110107421875,
0.01506805419921875,
0.0045318603515625,
0.00864410400390625,
-0.006671905517578125,
0.0105133056640625,
-0.01120758056640625,
0.00861358642578125,
-0.0061492919921875,
-0.004611968994140625,
0.0341796875,
0.0034847259521484375,
-0.01507568359375,
-0.00806427001953125,
-0.020050048828125,
-0.00799560546875,
0.01934814453125,
0.0290985107421875,
-0.017547607421875,
-0.004180908203125,
-0.0185394287109375,
0.00583648681640625,
-0.0009560585021972656,
-0.0157318115234375,
-0.0312347412109375,
0.0229034423828125,
0.0018568038940429688,
0.029449462890625,
-0.0123138427734375,
-0.0184478759765625,
-0.0009236335754394531,
-0.0117340087890625,
-0.000579833984375,
0.00803375244140625,
0.03277587890625,
0.003940582275390625,
-0.00753021240234375,
0.0160675048828125,
0.0283660888671875,
0.0279541015625,
0.023223876953125,
-0.01873779296875,
-0.0157318115234375,
0.016143798828125,
0.00887298583984375,
0.00923919677734375,
-0.021942138671875,
0.05072021484375,
0.006511688232421875,
0.022186279296875,
0.0085601806640625,
-0.014495849609375,
0.031646728515625,
-0.01076507568359375,
0.0114288330078125,
0.0191802978515625,
-0.0458984375,
-0.005458831787109375,
0.00891876220703125,
0.00348663330078125,
-0.0173797607421875,
-0.002483367919921875,
-0.028228759765625,
0.0130157470703125,
0.01276397705078125,
-0.0247955322265625,
-0.01422119140625,
0.0012807846069335938,
-0.0199432373046875,
0.0154571533203125,
-0.0082550048828125,
-0.0108795166015625,
0.0137481689453125,
0.00479888916015625,
-0.012176513671875,
0.0203399658203125,
-0.0172271728515625,
0.033050537109375,
-0.007503509521484375,
-0.00870513916015625,
0.0282440185546875,
0.000675201416015625,
-0.0195159912109375,
-0.0257720947265625,
0.038482666015625,
-0.02166748046875,
0.01105499267578125,
-0.0024013519287109375,
0.0102386474609375,
0.0018215179443359375,
0.00832366943359375,
0.007526397705078125,
-0.02728271484375,
-0.0201416015625,
-0.0233612060546875,
-0.0157012939453125,
0.060821533203125,
-0.0158538818359375,
-0.00553131103515625,
-0.00027823448181152344,
0.0211944580078125,
-0.023956298828125,
-0.0093536376953125,
0.0107269287109375,
0.0169525146484375,
-0.0111846923828125,
0.00554656982421875,
-0.007659912109375,
0.003894805908203125,
0.044769287109375,
-0.0091552734375,
0.020538330078125,
0.0194244384765625,
-0.01561737060546875,
-0.035491943359375,
-0.0218658447265625,
0.016937255859375,
-0.0038242340087890625,
0.002162933349609375,
-0.00843048095703125,
0.026123046875,
-0.0055999755859375,
-0.03216552734375,
0.0195465087890625,
-0.00988006591796875,
0.0001914501190185547,
0.033721923828125,
0.048309326171875,
-0.015350341796875,
-0.00936126708984375,
0.003643035888671875,
-0.0026721954345703125,
-0.00997161865234375,
-0.018463134765625,
0.0061492919921875,
0.0009469985961914062,
0.00858306884765625,
-0.014678955078125,
-0.029327392578125,
-0.016387939453125,
0.014007568359375,
-0.0005898475646972656,
-0.030975341796875,
0.003208160400390625,
0.01392364501953125,
0.020904541015625,
-0.004638671875,
0.0247039794921875,
-0.030792236328125,
0.020477294921875,
-0.04376220703125,
0.0171661376953125,
-0.017333984375,
-0.03912353515625,
0.0065460205078125,
-0.0243682861328125,
0.001323699951171875,
0.016021728515625,
0.01175689697265625,
-0.01049041748046875,
-0.01137542724609375,
0.01070404052734375,
0.0109405517578125,
0.007450103759765625,
-0.02764892578125,
-0.008819580078125,
-0.014678955078125,
-0.002826690673828125,
0.0283660888671875,
-0.0090484619140625,
-0.0097503662109375,
-0.027862548828125,
-0.0286407470703125,
-0.020233154296875,
0.02362060546875,
0.0152130126953125,
-0.007434844970703125,
-0.007434844970703125,
-0.0118865966796875,
-0.0166168212890625,
0.0200042724609375,
0.030059814453125,
0.007965087890625,
0.010894775390625,
-0.035552978515625,
0.00800323486328125,
-0.005222320556640625,
-0.00789642333984375,
-0.034576416015625,
-0.0207366943359375,
-0.0021991729736328125,
-0.01105499267578125,
-0.0022144317626953125,
-0.0005812644958496094,
0.0105438232421875,
0.042205810546875,
-0.00945281982421875,
0.015594482421875,
0.0152587890625,
0.01275634765625,
-0.0175323486328125,
-0.0207977294921875,
0.034332275390625,
0.0286712646484375,
0.0125732421875,
-0.0086822509765625,
0.02703857421875,
-0.01348876953125,
0.025177001953125,
0.0223541259765625,
-0.0025959014892578125,
-0.029449462890625,
0.04510498046875,
-0.01224517822265625,
-0.005741119384765625,
0.0054473876953125,
-0.0013933181762695312,
-0.02435302734375,
0.01186370849609375,
0.04461669921875,
-0.0157470703125,
0.009552001953125,
-0.0034732818603515625,
0.01898193359375
] |
ours_549
|
The answer is $55$. We can successively swap $1,3,5, \ldots, 19$ into their proper positions. This takes $10$ swaps for $1$, then $9$ swaps for $3$, and so on, giving $10+9+8+\cdots+1=55$ total swaps. To see that $55$ is the minimum, notice that initially the number of pairs of geese $(a, b)$ such that $a<b$ but geese $a$ is after geese $b$ is $55$, and the number of these bad pairs decreases by at most $1$ with each swap. Because when the geese are ordered, there are $0$ such bad pairs, we need at least $55$ swaps, so the answer is $55$.
Note: In general, for any permutation $\pi$ of a sequence of integers, the number of pairs $(a, b)$ such that $a<b$ and $a$ comes after $b$ is known as the number of inversions of the permutation.
\(\boxed{55}\)
|
55
|
{
"competition": "us_comps",
"dataset": "Ours",
"posts": null,
"source": "OMOSoln2.md"
}
|
There are $20$ geese numbered $1$ through $20$ standing in a line. The even numbered geese are standing at the front in the order $2,4, \ldots, 20$, where $2$ is at the front of the line. Then the odd numbered geese are standing behind them in the order, $1,3,5, \ldots, 19$, where $19$ is at the end of the line. The geese want to rearrange themselves in order, so that they are ordered $1,2, \ldots, 20$ ( $1$ is at the front), and they do this by successively swapping two adjacent geese. What is the minimum number of swaps required to achieve this formation?
|
[
"/Mathematics/DiscreteMathematics/Combinatorics/CombinatorialOptimization",
"/Mathematics/DiscreteMathematics/Combinatorics/Permutations",
"/Mathematics/DiscreteMathematics/GeneralDiscreteMathematics/ConcreteMath",
"/Mathematics/DiscreteMathematics/GeneralDiscreteMathematics/ConcreteMathematics",
"/Mathematics/DiscreteMathematics/GeneralDiscreteMathematics/DiscreteMath",
"/Mathematics/DiscreteMathematics/GeneralDiscreteMathematics/DiscreteMathematics"
] |
Use the inversion count of the permutation, since each adjacent swap reduces inversions by at most one.
|
[
0.00015425682067871094,
-0.0276947021484375,
0.012420654296875,
0.0287322998046875,
0.0006504058837890625,
0.0008463859558105469,
0.025360107421875,
-0.0205078125,
0.021697998046875,
0.0278472900390625,
0.009429931640625,
-0.01430511474609375,
-0.0014982223510742188,
-0.0148162841796875,
-0.057098388671875,
-0.01132965087890625,
0.041046142578125,
0.0283966064453125,
-0.0322265625,
-0.00637054443359375,
-0.0255584716796875,
-0.0025424957275390625,
-0.0157318115234375,
0.0068359375,
-0.01065826416015625,
-0.03692626953125,
-0.0232391357421875,
0.0028553009033203125,
-0.011016845703125,
-0.0009613037109375,
-0.035919189453125,
-0.0091552734375,
0.0095062255859375,
-0.014556884765625,
0.0057525634765625,
0.002536773681640625,
0.05133056640625,
-0.01102447509765625,
-0.040252685546875,
-0.0279998779296875,
-0.0213623046875,
-0.014556884765625,
0.005779266357421875,
0.0013723373413085938,
-0.02020263671875,
0.044769287109375,
0.0006794929504394531,
0.0182037353515625,
-0.0218658447265625,
-0.00814056396484375,
-0.00966644287109375,
0.0069580078125,
0.01556396484375,
-0.02154541015625,
-0.0298309326171875,
-0.08111572265625,
-0.0019216537475585938,
0.006744384765625,
-0.0038509368896484375,
0.002674102783203125,
-0.005283355712890625,
-0.0044403076171875,
-0.00714111328125,
-0.0113067626953125,
-0.00440216064453125,
-0.003429412841796875,
0.0105438232421875,
0.022369384765625,
0.0018301010131835938,
0.0130767822265625,
-0.004703521728515625,
0.0119781494140625,
-0.042510986328125,
0.0111083984375,
-0.0174407958984375,
-0.0236663818359375,
-0.0194549560546875,
-0.00875091552734375,
0.0250244140625,
0.0006246566772460938,
0.018341064453125,
0.014739990234375,
0.007587432861328125,
0.0159149169921875,
-0.0033626556396484375,
0.025726318359375,
0.0274505615234375,
-0.0240478515625,
0.035400390625,
-0.01190948486328125,
-0.00543212890625,
-0.021942138671875,
0.0142364501953125,
0.02520751953125,
0.00046062469482421875,
0.0237274169921875,
0.01369476318359375,
-0.0177154541015625,
-0.040191650390625,
0.00893402099609375,
-0.003314971923828125,
-0.0091552734375,
0.016357421875,
-0.0073394775390625,
-0.006504058837890625,
-0.012847900390625,
-0.0107879638671875,
0.024810791015625,
-0.0265960693359375,
-0.004383087158203125,
-0.0047149658203125,
0.0045013427734375,
0.058074951171875,
0.0023136138916015625,
-0.0189971923828125,
-0.0011730194091796875,
0.0006456375122070312,
-0.00025582313537597656,
-0.003124237060546875,
0.025634765625,
0.006862640380859375,
0.0243072509765625,
0.0083770751953125,
0.0237274169921875,
0.01409912109375,
-0.0091552734375,
0.004833221435546875,
0.004085540771484375,
0.007572174072265625,
0.01030731201171875,
-0.0241851806640625,
-0.0163421630859375,
-0.048370361328125,
-0.00887298583984375,
-0.0266571044921875,
-0.00933074951171875,
0.01812744140625,
-0.00487518310546875,
0.01220703125,
-0.0137176513671875,
-0.00002384185791015625,
0.01012420654296875,
-0.0007772445678710938,
-0.033843994140625,
0.0025634765625,
0.0293731689453125,
0.0013799667358398438,
-0.0308837890625,
0.019378662109375,
-0.015716552734375,
-0.0048370361328125,
0.004180908203125,
0.028106689453125,
-0.0062103271484375,
0.002349853515625,
0.0117950439453125,
0.0219573974609375,
0.004604339599609375,
-0.0004153251647949219,
-0.0007977485656738281,
0.00347900390625,
0.0008721351623535156,
0.02490234375,
0.028839111328125,
-0.013427734375,
0.01255035400390625,
-0.017486572265625,
0.0008578300476074219,
0.00817108154296875,
0.0166778564453125,
-0.0009322166442871094,
-0.0240631103515625,
0.0023403167724609375,
-0.0208892822265625,
-0.007778167724609375,
-0.00792694091796875,
-0.0037174224853515625,
0.0028533935546875,
0.0024776458740234375,
-0.0023288726806640625,
-0.0035800933837890625,
-0.0408935546875,
0.031768798828125,
0.0176544189453125,
0.021697998046875,
0.01263427734375,
0.0033550262451171875,
0.00029921531677246094,
0.0305023193359375,
0.01052093505859375,
0.0038890838623046875,
-0.00971221923828125,
-0.0014944076538085938,
-0.002292633056640625,
-0.004741668701171875,
-0.0010004043579101562,
-0.027130126953125,
0.0257110595703125,
-0.0006380081176757812,
0.01523590087890625,
0.0040130615234375,
0.002849578857421875,
-0.01255035400390625,
0.01065826416015625,
0.006988525390625,
-0.001811981201171875,
0.0108642578125,
-0.00251007080078125,
-0.01367950439453125,
0.00457000732421875,
-0.004070281982421875,
-0.0172576904296875,
-0.02789306640625,
0.0054473876953125,
-0.006748199462890625,
-0.0006899833679199219,
-0.00640869140625,
-0.0180511474609375,
0.0062408447265625,
-0.00861358642578125,
-0.002613067626953125,
0.00447845458984375,
-0.01529693603515625,
-0.01320648193359375,
-0.03289794921875,
0.00791168212890625,
0.011932373046875,
0.00428009033203125,
0.002101898193359375,
0.01560211181640625,
0.0265655517578125,
0.006557464599609375,
0.004756927490234375,
-0.017120361328125,
-0.0193328857421875,
-0.000006139278411865234,
0.0208587646484375,
-0.0067596435546875,
0.009307861328125,
0.01788330078125,
0.028472900390625,
-0.005435943603515625,
-0.0014352798461914062,
0.0018863677978515625,
-0.00598907470703125,
-0.01215362548828125,
-0.0010862350463867188,
0.0033245086669921875,
0.00920867919921875,
-0.006259918212890625,
-0.0268096923828125,
-0.004669189453125,
-0.00461578369140625,
0.00159454345703125,
0.0172271728515625,
0.0006885528564453125,
-0.003238677978515625,
0.000023424625396728516,
-0.007663726806640625,
-0.005619049072265625,
-0.022857666015625,
0.00045418739318847656,
-0.00757598876953125,
0.0016937255859375,
0.0014123916625976562,
-0.034637451171875,
0.005214691162109375,
0.006763458251953125,
0.0193939208984375,
0.0038509368896484375,
0.021148681640625,
-0.003559112548828125,
0.01030731201171875,
0.0011043548583984375,
0.025604248046875,
0.00319671630859375,
0.0006275177001953125,
0.004749298095703125,
-0.0070343017578125,
0.019866943359375,
0.004863739013671875,
-0.037200927734375,
-0.04071044921875,
-0.00516510009765625,
0.021453857421875,
0.001918792724609375,
0.0161590576171875,
-0.007762908935546875,
-0.01312255859375,
-0.00494384765625,
-0.007030487060546875,
-0.032745361328125,
0.0152740478515625,
0.0101470947265625,
0.020904541015625,
-0.034759521484375,
0.00218963623046875,
0.005817413330078125,
0.00002682209014892578,
-0.013153076171875,
-0.0027484893798828125,
-0.0230560302734375,
0.00615692138671875,
0.02215576171875,
-0.00811767578125,
0.0177154541015625,
-0.00957489013671875,
0.016754150390625,
-0.0071563720703125,
0.023223876953125,
-0.00435638427734375,
0.00646209716796875,
0.0149993896484375,
0.006927490234375,
0.023162841796875,
-0.0139923095703125,
-0.004032135009765625,
0.006256103515625,
-0.01453399658203125,
-0.0107574462890625,
0.01202392578125,
-0.004730224609375,
0.006343841552734375,
-0.0032215118408203125,
0.023590087890625,
0.022735595703125,
0.0024242401123046875,
0.0156707763671875,
-0.004024505615234375,
0.00811004638671875,
-0.01551055908203125,
0.01522064208984375,
-0.04815673828125,
0.001094818115234375,
-0.0165863037109375,
0.0152130126953125,
-0.0022640228271484375,
0.00823974609375,
0.00836944580078125,
0.0020427703857421875,
-0.01654052734375,
-0.01474761962890625,
0.0228271484375,
0.00540924072265625,
0.00989532470703125,
0.0087432861328125,
-0.012603759765625,
0.004566192626953125,
-0.006549835205078125,
-0.0077667236328125,
0.01319122314453125,
0.01509857177734375,
0.066162109375,
0.00531768798828125,
-0.023223876953125,
0.0098114013671875,
-0.007568359375,
0.00949859619140625,
0.0193328857421875,
0.028350830078125,
-0.001148223876953125,
0.0034160614013671875,
-0.0087127685546875,
-0.02484130859375,
0.02337646484375,
-0.02545166015625,
-0.003932952880859375,
0.002819061279296875,
-0.032196044921875,
0.005031585693359375,
0.0041046142578125,
-0.00013840198516845703,
-0.034759521484375,
-0.031402587890625,
-0.048095703125,
0.0101165771484375,
-0.01371002197265625,
0.021881103515625,
-0.0291748046875,
-0.01617431640625,
0.01739501953125,
0.0240020751953125,
-0.0094757080078125,
0.0372314453125,
-0.0207672119140625,
0.01313018798828125,
-0.0272674560546875,
0.02178955078125,
-0.029541015625,
0.002246856689453125,
0.00643157958984375,
-0.03570556640625,
0.0007910728454589844,
0.0248260498046875,
-0.00972747802734375,
0.0323486328125,
0.00945281982421875,
0.00909423828125,
0.050872802734375,
-0.0025424957275390625,
0.01654052734375,
-0.0051727294921875,
-0.01320648193359375,
0.03466796875,
0.02215576171875,
-0.00919342041015625,
-0.01861572265625,
-0.011444091796875,
0.002368927001953125,
-0.029510498046875,
0.027191162109375,
0.016326904296875,
0.00506591796875,
-0.00412750244140625,
-0.00335693359375,
-0.00572967529296875,
0.01253509521484375,
0.0267181396484375,
-0.005962371826171875,
-0.00690460205078125,
-0.0214080810546875,
-0.049896240234375,
-0.018463134765625,
-0.007110595703125,
0.03228759765625,
0.0163726806640625,
-0.006977081298828125,
0.03656005859375,
-0.00756072998046875,
0.033538818359375,
0.051483154296875,
-0.00948333740234375,
0.0294342041015625,
0.0281524658203125,
0.00008207559585571289,
0.0209808349609375,
0.008148193359375,
-0.016754150390625,
-0.001399993896484375,
-0.002658843994140625,
-0.0022449493408203125,
-0.00905609130859375,
0.017364501953125,
-0.01195526123046875,
-0.016265869140625,
0.003681182861328125,
0.0214691162109375,
0.006671905517578125,
-0.014312744140625,
0.003269195556640625,
-0.02764892578125,
-0.0086822509765625,
-0.0028553009033203125,
0.0200653076171875,
-0.00223541259765625,
0.031982421875,
-0.01151275634765625,
-0.0033397674560546875,
-0.0108642578125,
-0.00012421607971191406,
-0.0291900634765625,
-0.039276123046875,
-0.00186920166015625,
-0.01206207275390625,
-0.04193115234375,
0.009796142578125,
0.0098724365234375,
0.005496978759765625,
0.05511474609375,
0.003307342529296875,
-0.0263519287109375,
-0.02508544921875,
0.027496337890625,
0.0094146728515625,
-0.01239776611328125,
0.043060302734375,
-0.001110076904296875,
0.029815673828125,
0.034515380859375,
-0.0181732177734375,
-0.02490234375,
0.00531005859375,
0.0016651153564453125,
0.023590087890625,
-0.00962066650390625,
0.00555419921875,
0.038665771484375,
-0.01367950439453125,
0.01349639892578125,
-0.01806640625,
0.0164642333984375,
0.0128021240234375,
-0.004291534423828125,
-0.05389404296875,
-0.0220184326171875,
-0.031158447265625,
0.0027446746826171875,
-0.02374267578125,
0.0007300376892089844,
0.0180816650390625,
0.029693603515625,
0.040496826171875,
0.0100250244140625,
0.0241241455078125,
0.008575439453125,
-0.02593994140625,
0.041107177734375,
-0.01352691650390625,
-0.01763916015625,
-0.01175689697265625,
-0.0206756591796875,
0.0221099853515625,
0.01264190673828125,
-0.036285400390625,
0.021575927734375,
0.00543212890625,
0.0271148681640625,
-0.0006742477416992188,
-0.024871826171875,
-0.0012989044189453125,
-0.0151519775390625,
0.001476287841796875,
0.0136260986328125,
0.03607177734375,
-0.000385284423828125,
0.005382537841796875,
0.0258636474609375,
-0.0279693603515625,
-0.0084381103515625,
0.0087738037109375,
-0.01009368896484375,
-0.045166015625,
0.022308349609375,
-0.0162200927734375,
-0.03082275390625,
0.0174407958984375,
0.00766754150390625,
0.0249176025390625,
-0.02069091796875,
0.031524658203125,
-0.02032470703125,
-0.004039764404296875,
0.009124755859375,
0.00467681884765625,
-0.004119873046875,
-0.01593017578125,
0.032867431640625,
-0.0050506591796875,
-0.01995849609375,
-0.00002008676528930664,
0.006771087646484375,
-0.009185791015625,
-0.018707275390625,
-0.033905029296875,
0.02093505859375,
-0.006778717041015625,
0.01229095458984375,
-0.0006704330444335938,
0.012481689453125,
0.033447265625,
-0.003635406494140625,
0.0297698974609375,
-0.004032135009765625,
-0.01174163818359375,
0.00371551513671875,
-0.0007710456848144531,
-0.008941650390625,
0.0132598876953125,
-0.011199951171875,
-0.0080718994140625,
0.0008301734924316406,
-0.017303466796875,
-0.03076171875,
-0.0006051063537597656,
-0.0357666015625,
-0.0265350341796875,
-0.013824462890625,
0.00799560546875,
0.00881195068359375,
-0.0044403076171875,
0.028564453125,
0.01277923583984375,
0.00038695335388183594,
-0.003948211669921875,
0.00856781005859375,
0.029998779296875,
-0.00408935546875,
-0.0014591217041015625,
-0.01548004150390625,
-0.0038814544677734375,
-0.0216827392578125,
0.003978729248046875,
0.0061187744140625,
-0.0029296875,
-0.00836944580078125,
-0.0260009765625,
-0.00811767578125,
-0.03118896484375,
0.0244293212890625,
0.00244903564453125,
0.010894775390625,
-0.022064208984375,
-0.0296478271484375,
0.0211944580078125,
0.004245758056640625,
0.007434844970703125,
-0.0323486328125,
0.040863037109375,
-0.0300140380859375,
-0.0164794921875,
-0.0018711090087890625,
-0.005706787109375,
0.0088348388671875,
-0.003009796142578125,
0.0408935546875,
0.024200439453125,
-0.0026264190673828125,
0.004146575927734375,
0.0042724609375,
0.0018024444580078125,
-0.042755126953125,
-0.0234375,
-0.0214691162109375,
-0.0023365020751953125,
-0.01103973388671875,
-0.0269012451171875,
-0.0182342529296875,
-0.0197296142578125,
0.0267333984375,
0.014404296875,
-0.043304443359375,
-0.0548095703125,
0.0282135009765625,
-0.0196685791015625,
0.00537872314453125,
-0.02716064453125,
-0.012603759765625,
0.0029888153076171875,
0.0110321044921875,
-0.023956298828125,
-0.0303802490234375,
0.0017404556274414062,
0.0032939910888671875,
-0.03350830078125,
-0.001247406005859375,
-0.00347900390625,
-0.029693603515625,
-0.006519317626953125,
-0.0238189697265625,
0.00920867919921875,
-0.0026416778564453125,
-0.0206756591796875,
-0.0171051025390625,
-0.002002716064453125,
-0.00738525390625,
-0.00313568115234375,
-0.0013637542724609375,
-0.0229034423828125,
0.0205535888671875,
-0.01166534423828125,
0.0192718505859375,
0.0010309219360351562,
0.0007452964782714844,
-0.00894927978515625,
-0.00629425048828125,
-0.018890380859375,
0.0084991455078125,
0.02679443359375,
0.0452880859375,
0.0198516845703125,
-0.00273895263671875,
-0.019073486328125,
-0.026397705078125,
0.01352691650390625,
0.0298614501953125,
-0.01398468017578125,
0.0220184326171875,
-0.037384033203125,
-0.000492095947265625,
0.0153045654296875,
0.006229400634765625,
0.0145416259765625,
0.058502197265625,
-0.0269622802734375,
0.02056884765625,
-0.007503509521484375,
0.017425537109375,
-0.01284027099609375,
0.01226806640625,
0.02197265625,
-0.0168914794921875,
-0.050262451171875,
-0.016693115234375,
0.0240325927734375,
-0.041656494140625,
-0.010528564453125,
0.0236358642578125,
-0.0134429931640625,
-0.0220947265625,
0.00836944580078125,
-0.02044677734375,
0.0227508544921875,
0.023834228515625,
0.019622802734375,
0.034820556640625,
-0.0302276611328125,
0.004802703857421875,
0.0010118484497070312,
-0.022308349609375,
0.020294189453125,
-0.002185821533203125,
-0.016143798828125,
-0.042510986328125,
-0.00848388671875,
-0.005779266357421875,
0.01076507568359375,
0.007232666015625,
0.0017652511596679688,
0.038970947265625,
-0.0020999908447265625,
-0.0271148681640625,
-0.0230865478515625,
0.024078369140625,
-0.02911376953125,
0.048858642578125,
-0.0247039794921875,
-0.03289794921875,
-0.0178375244140625,
-0.0304107666015625,
0.0012378692626953125,
0.04766845703125,
0.0025634765625,
-0.0029964447021484375,
0.00850677490234375,
-0.029296875,
-0.04241943359375,
-0.0172271728515625,
-0.0187225341796875,
-0.0251312255859375,
-0.027496337890625,
0.0305938720703125,
0.0010194778442382812,
0.013153076171875,
0.0054779052734375,
-0.01282501220703125,
0.007602691650390625,
0.0207366943359375,
0.004878997802734375,
-0.0190582275390625,
-0.0190582275390625,
0.0168304443359375,
0.041290283203125,
0.01459503173828125,
-0.003437042236328125,
-0.01497650146484375,
0.01922607421875,
0.0230865478515625,
-0.007022857666015625,
-0.005016326904296875,
0.0276336669921875,
-0.033416748046875,
-0.0195159912109375,
-0.035797119140625,
-0.027191162109375,
0.01187896728515625,
0.00647735595703125,
-0.02325439453125,
0.0027675628662109375,
-0.010528564453125,
0.033599853515625,
-0.0204315185546875,
-0.0032367706298828125,
-0.019317626953125,
-0.0018787384033203125,
-0.02056884765625,
0.0163726806640625,
-0.016143798828125,
-0.00377655029296875,
-0.0229339599609375,
0.00021374225616455078,
-0.003353118896484375,
-0.034454345703125,
-0.038726806640625,
0.0024261474609375,
0.0291748046875,
0.01058197021484375,
-0.002887725830078125,
-0.0218963623046875,
-0.0108184814453125,
0.014739990234375,
0.0184173583984375,
0.042236328125,
-0.01544952392578125,
0.01788330078125,
-0.002223968505859375,
0.0155029296875,
0.00923919677734375,
-0.026763916015625,
-0.01035308837890625,
0.021240234375,
0.016693115234375,
-0.01433563232421875,
-0.030364990234375,
0.007152557373046875,
0.0096893310546875,
0.006622314453125,
-0.007598876953125,
-0.01885986328125,
-0.0032196044921875,
0.0255584716796875,
0.022216796875,
0.014617919921875,
0.0123138427734375,
-0.0190887451171875,
0.018341064453125,
-0.0113525390625,
-0.032958984375,
-0.0229644775390625,
0.0148468017578125,
0.00464630126953125,
-0.017547607421875,
0.03460693359375,
0.00199127197265625,
0.00371551513671875,
-0.00975799560546875,
-0.0119171142578125,
0.01493072509765625,
0.01453399658203125,
-0.0139007568359375,
-0.00197601318359375,
-0.0389404296875,
0.0291900634765625,
-0.012908935546875,
0.02117919921875,
-0.007617950439453125,
-0.0106658935546875,
-0.0023441314697265625,
0.0106353759765625,
-0.0112152099609375,
-0.0179595947265625,
0.032073974609375,
0.00788116455078125,
0.01296234130859375,
-0.00887298583984375,
0.00501251220703125,
-0.038238525390625,
-0.01300811767578125,
0.0272674560546875,
0.006694793701171875,
0.0006456375122070312,
-0.009368896484375,
0.056182861328125,
-0.0018444061279296875,
0.00630950927734375,
-0.0169830322265625,
0.0293426513671875,
0.032623291015625,
-0.0030651092529296875,
-0.006778717041015625,
0.00994873046875,
-0.001277923583984375,
-0.0197906494140625,
0.01441192626953125,
-0.02508544921875,
-0.002841949462890625,
-0.01134490966796875,
-0.0005102157592773438,
0.0078277587890625,
0.0338134765625,
-0.0018262863159179688,
-0.006389617919921875,
-0.0080108642578125,
0.029388427734375,
0.00832366943359375,
0.0167999267578125,
0.0267791748046875,
-0.01485443115234375,
0.0011081695556640625,
0.019805908203125,
-0.04083251953125,
0.007396697998046875,
-0.0158538818359375,
0.0220489501953125,
0.036407470703125,
0.0026569366455078125,
0.0002815723419189453,
0.00775146484375,
0.0179901123046875,
0.0181121826171875,
-0.007904052734375,
-0.022247314453125,
0.01837158203125,
0.00969696044921875,
0.0268096923828125,
-0.010162353515625,
-0.0268402099609375,
0.0114593505859375,
0.00494384765625,
0.04315185546875,
-0.03607177734375,
-0.0178985595703125,
-0.00536346435546875,
0.0226898193359375,
0.03363037109375,
0.00247955322265625,
-0.019561767578125,
-0.004108428955078125,
0.0147705078125,
0.02801513671875,
0.0088958740234375,
-0.00907135009765625,
-0.01494598388671875,
-0.0099639892578125,
0.01763916015625,
-0.04449462890625,
0.00942230224609375,
0.00464630126953125,
0.035675048828125,
0.0048065185546875,
0.0232086181640625,
0.0113067626953125,
0.01715087890625,
-0.020233154296875,
-0.01751708984375,
-0.0018377304077148438,
-0.0019378662109375,
0.009674072265625,
-0.0186614990234375,
-0.03826904296875,
0.0229034423828125,
-0.00971221923828125,
0.03546142578125,
-0.032867431640625,
0.004261016845703125,
-0.0035419464111328125,
0.0080718994140625,
-0.00724029541015625,
0.0119781494140625,
0.0009093284606933594,
0.01183319091796875,
0.002155303955078125,
-0.004100799560546875,
-0.0222625732421875,
-0.01177978515625,
0.031280517578125,
0.009796142578125,
0.0214996337890625,
-0.00437164306640625,
-0.05108642578125,
-0.018890380859375,
-0.00445556640625,
0.0064239501953125,
-0.01226043701171875,
0.0208892822265625,
0.011077880859375,
-0.035369873046875,
-0.00806427001953125,
-0.0037822723388671875,
0.00597381591796875,
-0.0260009765625,
-0.007740020751953125,
-0.01380157470703125,
-0.01470947265625,
0.00464630126953125,
-0.007244110107421875,
-0.0028209686279296875,
-0.032806396484375,
-0.034149169921875,
0.058349609375,
-0.032440185546875,
-0.01525115966796875,
0.005825042724609375,
0.0170135498046875,
-0.026824951171875,
-0.02459716796875,
0.0235443115234375,
-0.0092620849609375,
0.00136566162109375,
0.0155029296875,
-0.01023101806640625,
-0.043792724609375,
0.0007996559143066406,
-0.022705078125,
0.01256561279296875,
-0.014129638671875,
0.03350830078125,
-0.0012197494506835938,
-0.0059356689453125,
0.004749298095703125,
-0.0181884765625,
-0.0189056396484375,
0.02496337890625,
0.0311126708984375,
0.01015472412109375,
0.004581451416015625,
0.0038051605224609375,
-0.0208740234375,
-0.00638580322265625,
0.025421142578125,
-0.0136871337890625,
0.0039043426513671875,
-0.0006284713745117188,
0.01393890380859375,
0.002742767333984375,
0.018524169921875,
-0.037811279296875,
-0.027130126953125,
0.022979736328125,
0.00164031982421875,
0.0083160400390625,
-0.01233673095703125,
0.01351165771484375,
-0.029632568359375,
-0.0123443603515625,
-0.03424072265625,
-0.0286102294921875,
-0.0017538070678710938,
0.005031585693359375,
-0.0662841796875,
0.02362060546875,
-0.00540924072265625,
-0.0037441253662109375,
-0.042236328125,
-0.02294921875,
-0.026611328125,
0.004344940185546875,
-0.021820068359375,
0.013214111328125,
0.01187896728515625,
-0.01519775390625,
0.0091552734375,
-0.0191802978515625,
0.037567138671875,
0.0009775161743164062,
-0.03778076171875,
-0.0084381103515625,
0.01108551025390625,
-0.0269012451171875,
-0.0072021484375,
-0.007091522216796875,
0.002178192138671875,
-0.0012149810791015625,
0.035797119140625,
-0.0060272216796875,
-0.028564453125,
-0.014251708984375,
-0.0002655982971191406,
0.02984619140625,
-0.0255584716796875,
0.0079193115234375,
-0.001712799072265625,
0.007503509521484375,
0.0004730224609375,
-0.0211639404296875,
-0.01003265380859375,
0.020355224609375,
0.0235595703125,
0.004314422607421875,
-0.0213623046875,
0.041473388671875,
-0.006572723388671875,
0.0091094970703125,
0.005161285400390625,
-0.0002796649932861328,
0.0287017822265625,
0.004650115966796875,
-0.007579803466796875,
-0.00777435302734375,
-0.00595855712890625,
0.0189361572265625,
-0.0340576171875,
0.020782470703125,
0.01776123046875,
-0.0134735107421875,
0.02392578125,
-0.013275146484375,
-0.00511932373046875,
0.040618896484375,
-0.0104217529296875,
-0.03076171875,
-0.0350341796875,
0.005489349365234375,
-0.0462646484375,
-0.006641387939453125,
-0.0115509033203125,
-0.0067138671875,
-0.0013980865478515625,
-0.019439697265625,
-0.01062774658203125,
-0.01214599609375,
-0.0009417533874511719,
-0.005035400390625,
0.020294189453125,
-0.0031280517578125,
0.0172119140625,
-0.0189971923828125,
0.005401611328125,
-0.033294677734375,
0.0217742919921875,
-0.05340576171875,
-0.0031795501708984375,
0.01558685302734375,
0.0171051025390625,
-0.025909423828125,
0.0026378631591796875,
-0.0175933837890625,
-0.03509521484375,
0.020355224609375,
0.0009603500366210938,
-0.01044464111328125,
-0.0108184814453125,
-0.006961822509765625,
-0.00726318359375,
0.006313323974609375,
-0.0036792755126953125,
0.017242431640625,
-0.0050506591796875,
-0.053009033203125,
-0.01331329345703125,
-0.00656890869140625,
-0.007686614990234375,
0.017120361328125,
0.021820068359375,
0.030303955078125,
0.00917816162109375,
-0.0286102294921875,
0.0239410400390625,
-0.01812744140625,
0.003406524658203125,
0.015899658203125,
-0.008819580078125,
0.018768310546875,
-0.0014581680297851562,
0.00742340087890625,
0.00832366943359375,
0.0196533203125,
0.00868988037109375,
0.0240325927734375,
0.006717681884765625,
-0.02447509765625,
-0.0034942626953125,
0.0139617919921875,
-0.0181427001953125,
-0.015777587890625,
-0.0294036865234375,
-0.0176544189453125,
-0.00826263427734375,
-0.040283203125,
0.049774169921875,
0.010406494140625,
-0.04766845703125,
0.01593017578125,
-0.0279388427734375,
-0.005878448486328125,
-0.02374267578125,
-0.004810333251953125,
0.011474609375,
-0.00411224365234375,
0.04351806640625,
-0.02996826171875,
-0.0051116943359375,
-0.0007643699645996094,
0.043121337890625,
0.0083770751953125,
0.0047760009765625,
0.00424957275390625,
0.010986328125,
0.0218048095703125,
-0.0016546249389648438,
-0.0260162353515625,
-0.026763916015625,
-0.0006933212280273438,
-0.004383087158203125,
0.04705810546875,
-0.021636962890625,
-0.0219573974609375,
0.02105712890625,
-0.0071258544921875,
-0.031402587890625,
-0.003322601318359375,
-0.02838134765625,
0.022613525390625,
0.003082275390625,
0.01085662841796875,
-0.0232391357421875,
-0.0389404296875,
0.01085662841796875,
-0.0261383056640625,
-0.03515625,
-0.016845703125,
-0.00815582275390625,
-0.0455322265625,
0.0009746551513671875,
-0.02093505859375,
-0.0215606689453125,
-0.0040435791015625,
-0.01904296875,
0.00408935546875,
0.001705169677734375,
-0.01276397705078125,
-0.0202178955078125,
-0.0007772445678710938,
-0.019989013671875,
-0.005001068115234375,
-0.01097869873046875,
-0.00412750244140625,
0.017242431640625,
0.034149169921875,
-0.008514404296875,
0.0185089111328125,
-0.0133514404296875,
-0.0144195556640625,
-0.0088653564453125,
0.014007568359375,
0.0308380126953125,
0.056304931640625,
-0.0228118896484375,
-0.00934600830078125,
-0.004974365234375,
-0.00920867919921875,
0.008056640625,
-0.0165863037109375,
0.0059814453125,
-0.0122222900390625,
-0.006580352783203125,
0.01263427734375,
-0.03753662109375,
0.034759521484375,
0.004058837890625,
0.024444580078125,
0.0293121337890625,
0.00766754150390625,
-0.021881103515625,
0.005096435546875,
-0.02825927734375,
0.036834716796875,
0.0207977294921875,
0.0245208740234375,
0.015777587890625,
0.0209197998046875,
-0.0170440673828125,
0.0156707763671875,
0.0205841064453125,
0.004329681396484375,
0.029541015625,
0.0213775634765625,
-0.016876220703125,
-0.006008148193359375,
-0.01432037353515625,
0.03955078125,
0.00386810302734375,
0.005207061767578125,
0.0230255126953125,
0.0008502006530761719,
0.01369476318359375,
-0.035736083984375,
-0.0164337158203125,
0.005924224853515625,
0.01309967041015625,
-0.01192474365234375,
-0.01227569580078125,
0.02093505859375,
0.009979248046875,
0.0146484375,
-0.01464080810546875,
0.01541900634765625,
0.027679443359375,
0.01058197021484375,
0.022369384765625,
-0.01220703125,
0.004474639892578125,
0.01357269287109375,
0.007598876953125,
0.0364990234375,
0.0173187255859375,
-0.003002166748046875,
0.023468017578125,
-0.013580322265625,
0.00563812255859375,
-0.0244903564453125,
-0.00823211669921875,
0.0099029541015625,
-0.009765625,
0.0177001953125,
-0.033935546875,
-0.0234222412109375,
0.00027632713317871094,
0.023406982421875,
-0.01806640625,
-0.004085540771484375,
-0.026123046875,
0.017486572265625,
0.0195159912109375,
0.0219879150390625,
-0.0059661865234375,
-0.006229400634765625,
0.0202484130859375,
0.004913330078125,
0.0226287841796875,
0.0039520263671875,
-0.007480621337890625,
0.00982666015625,
-0.0086822509765625,
-0.0092315673828125,
0.01422119140625,
-0.032073974609375,
0.0185089111328125,
0.0333251953125,
-0.00823211669921875,
-0.042236328125,
-0.0040283203125,
0.006317138671875,
0.0265350341796875,
0.00319671630859375,
0.033416748046875,
-0.006717681884765625,
-0.018157958984375,
-0.02935791015625,
-0.01549530029296875,
0.0174407958984375,
-0.019012451171875,
0.00971221923828125,
-0.03021240234375,
0.0162200927734375,
0.05377197265625,
-0.0150299072265625,
0.01169586181640625,
0.0018472671508789062,
-0.0340576171875,
-0.019378662109375,
0.006633758544921875,
0.0130767822265625,
-0.0160369873046875,
0.0281524658203125,
-0.007537841796875,
0.012847900390625,
0.00995635986328125,
-0.0199127197265625,
0.0248260498046875,
-0.0125579833984375,
-0.0015497207641601562,
0.022705078125,
-0.0423583984375,
0.02435302734375,
0.00997161865234375,
-0.024169921875,
-0.031280517578125,
0.04681396484375,
0.0012979507446289062,
-0.022003173828125,
0.04132080078125,
0.00826263427734375,
0.0213775634765625,
0.0164031982421875,
-0.01058197021484375,
0.00772857666015625,
-0.005199432373046875,
0.0109100341796875,
0.0223846435546875,
-0.008575439453125,
0.0235137939453125,
-0.0260162353515625,
-0.01010894775390625,
-0.0162506103515625,
0.0233612060546875,
-0.0214996337890625,
-0.027374267578125,
-0.0157928466796875,
-0.019989013671875,
0.01026153564453125,
-0.036468505859375,
-0.0121002197265625,
0.01190948486328125,
0.023223876953125,
0.0021686553955078125,
-0.017822265625,
-0.0203857421875,
0.005741119384765625,
0.000023424625396728516,
-0.00395965576171875,
-0.0179901123046875,
-0.01557159423828125,
-0.020538330078125,
0.01155853271484375,
-0.0141754150390625,
0.03076171875,
-0.033203125,
0.0238800048828125,
-0.0010929107666015625,
0.01285552978515625,
-0.00823974609375,
0.0011844635009765625,
-0.0065155029296875,
0.0262908935546875,
0.0178375244140625,
-0.00603485107421875,
-0.01319122314453125,
-0.0078582763671875,
-0.006328582763671875,
-0.025238037109375,
0.03375244140625,
-0.0165252685546875,
-0.006683349609375,
0.018585205078125,
0.01263427734375,
-0.004669189453125,
0.00482177734375,
0.005954742431640625,
-0.01171875,
-0.0308837890625,
-0.0038547515869140625,
0.007717132568359375,
0.005428314208984375,
-0.033111572265625,
0.012176513671875,
-0.025482177734375,
0.03192138671875,
-0.00870513916015625,
0.00914764404296875,
0.0234527587890625,
0.0023708343505859375,
0.00766754150390625,
-0.0207977294921875,
0.00809478759765625,
-0.01287841796875,
-0.00539398193359375,
-0.01103973388671875,
0.01361083984375,
-0.01151275634765625,
0.004810333251953125,
-0.0197601318359375,
-0.0262298583984375,
0.006549835205078125,
-0.024932861328125,
-0.0293731689453125,
-0.003147125244140625,
-0.00496673583984375,
0.027801513671875,
0.06976318359375,
0.0124053955078125,
0.01467132568359375,
-0.0002779960632324219,
0.006954193115234375,
0.041412353515625,
0.005001068115234375,
-0.008819580078125,
0.0157470703125,
-0.0176544189453125,
-0.0038013458251953125,
-0.004184722900390625,
-0.0367431640625,
-0.0149688720703125,
0.01245880126953125,
0.026824951171875,
0.01337432861328125,
0.00284576416015625,
-0.00433349609375,
0.0241241455078125,
-0.022369384765625,
0.0220947265625,
-0.0008330345153808594,
0.017852783203125,
-0.0193939208984375,
-0.01226043701171875,
-0.0026721954345703125,
-0.0277099609375,
-0.01206207275390625,
0.0096588134765625,
-0.0034923553466796875,
-0.032135009765625,
-0.01397705078125,
-0.005626678466796875,
-0.00548553466796875,
0.0103607177734375,
-0.004150390625,
-0.0182037353515625,
0.01476287841796875,
-0.019378662109375,
-0.00121307373046875,
-0.024261474609375,
0.0032939910888671875,
-0.0035953521728515625,
-0.0276031494140625,
-0.00176239013671875,
-0.036529541015625,
-0.015625,
-0.0228118896484375,
0.040069580078125,
0.0083160400390625,
0.01412200927734375,
0.021453857421875,
-0.005077362060546875,
0.0058441162109375,
0.0180816650390625,
0.06121826171875,
0.006587982177734375,
-0.0202178955078125,
0.007476806640625,
-0.006664276123046875,
-0.00908660888671875,
-0.033477783203125,
0.03680419921875,
0.029876708984375,
-0.00972747802734375,
-0.0025386810302734375,
-0.01410675048828125,
0.0023174285888671875,
0.023773193359375,
-0.00457000732421875,
-0.006404876708984375,
0.00036072731018066406,
-0.01012420654296875,
-0.001415252685546875,
-0.00215911865234375,
-0.03509521484375,
0.0013875961303710938,
0.0396728515625,
-0.01837158203125,
-0.01373291015625,
-0.0109100341796875,
0.0173797607421875,
0.00637054443359375,
0.019012451171875,
0.0024566650390625,
-0.01497650146484375,
0.004138946533203125,
0.0296173095703125,
-0.006298065185546875,
0.003940582275390625,
0.0113983154296875,
-0.0162506103515625,
-0.0081634521484375,
0.0036487579345703125,
-0.0311126708984375,
0.01812744140625,
-0.05364990234375,
0.000091552734375,
0.0305633544921875,
0.0238189697265625,
-0.0003345012664794922,
-0.038421630859375,
0.003955841064453125,
-0.0168304443359375,
0.0209808349609375,
0.0008044242858886719,
-0.0169677734375,
0.0213165283203125,
-0.033172607421875,
-0.01529693603515625,
-0.01824951171875,
0.00439453125,
-0.0156707763671875,
-0.0029296875,
-0.0011081695556640625,
-0.00762939453125,
-0.005645751953125,
0.002498626708984375,
0.03424072265625,
-0.0159149169921875,
0.0228729248046875,
0.0128936767578125,
-0.00516510009765625,
-0.00698089599609375,
0.003444671630859375,
0.0186004638671875,
0.002635955810546875,
-0.0209503173828125,
0.016693115234375,
-0.00014543533325195312,
0.00620269775390625,
0.032257080078125,
0.0220947265625,
-0.0032291412353515625,
-0.01052093505859375,
0.01290130615234375,
-0.00045013427734375,
0.004558563232421875,
0.005008697509765625,
-0.0229949951171875,
0.0097808837890625,
0.0093994140625,
-0.04962158203125,
0.019378662109375,
0.0540771484375,
-0.002498626708984375,
0.0101318359375,
0.01274871826171875,
0.01421356201171875,
-0.00312042236328125,
0.004680633544921875,
0.01047515869140625,
0.019866943359375,
-0.0018873214721679688,
-0.0299224853515625,
0.00957489013671875,
-0.0157623291015625,
0.01204681396484375,
0.0068817138671875,
-0.00865936279296875,
0.047027587890625,
-0.03509521484375,
0.0013751983642578125,
-0.01488494873046875,
0.0155029296875,
0.016265869140625,
-0.0230865478515625,
0.023284912109375,
-0.02545166015625,
-0.022216796875,
-0.009979248046875,
-0.00295257568359375,
0.00688934326171875,
0.0175018310546875,
-0.0225067138671875,
-0.01064300537109375,
0.00699615478515625,
-0.0160675048828125,
0.0309295654296875,
-0.00450897216796875,
0.01242828369140625,
0.055816650390625,
0.0014562606811523438,
0.0066986083984375,
-0.01338958740234375,
0.0233917236328125,
0.0215911865234375,
-0.006343841552734375,
-0.021575927734375,
0.0244140625,
-0.0239715576171875,
0.01067352294921875,
0.0116119384765625,
-0.0243377685546875,
0.030364990234375,
-0.0149383544921875,
0.006378173828125,
-0.020843505859375,
0.01500701904296875,
-0.004459381103515625,
0.0215301513671875,
0.01934814453125,
0.005931854248046875,
0.010650634765625,
-0.07574462890625,
-0.00170135498046875,
-0.00011259317398071289,
-0.0210418701171875,
0.006969451904296875,
0.01189422607421875,
-0.032012939453125,
0.023468017578125,
0.0002601146697998047,
0.002475738525390625,
-0.01444244384765625,
-0.0255889892578125,
-0.0198974609375,
-0.0115814208984375,
-0.01113128662109375,
0.01026153564453125,
-0.026123046875,
0.00640106201171875,
-0.0021152496337890625,
0.04656982421875,
0.0147705078125,
-0.018310546875,
0.01512908935546875,
-0.014007568359375,
0.0187225341796875,
-0.0299224853515625,
-0.0097198486328125,
-0.04693603515625,
-0.0263519287109375,
-0.0157470703125,
0.00769805908203125,
-0.0029315948486328125,
-0.0136871337890625,
-0.0010166168212890625,
0.0217437744140625,
0.01959228515625,
-0.0153961181640625,
0.0030422210693359375,
-0.0082550048828125,
-0.016357421875,
0.01525115966796875,
-0.01088714599609375,
-0.006626129150390625,
-0.00653839111328125,
-0.00485992431640625,
0.0176239013671875,
-0.036712646484375,
0.0128021240234375,
-0.013397216796875,
0.0306854248046875,
0.00021278858184814453,
0.0227203369140625,
0.0031337738037109375,
0.055999755859375,
-0.01312255859375,
-0.0130615234375,
-0.01190948486328125,
-0.007106781005859375,
0.00907135009765625,
-0.01263427734375,
-0.0258941650390625,
0.01473236083984375,
-0.00995635986328125,
0.0012788772583007812,
0.016693115234375,
-0.01007080078125,
-0.00943756103515625,
0.0256195068359375,
-0.01090240478515625,
-0.015289306640625,
-0.00432586669921875,
0.005786895751953125,
0.0009660720825195312,
0.008087158203125,
0.00628662109375,
-0.0016622543334960938,
-0.01042938232421875,
0.0306243896484375,
0.0306243896484375,
0.0311737060546875,
-0.0165557861328125,
0.0222015380859375,
0.005718231201171875,
-0.0105743408203125,
0.02069091796875,
0.00567626953125,
0.0460205078125,
0.00848388671875,
-0.016815185546875,
-0.0033473968505859375,
-0.038726806640625,
0.01522064208984375,
-0.0060882568359375,
0.00217437744140625,
-0.010345458984375,
-0.038665771484375,
-0.013580322265625,
0.016510009765625,
0.016387939453125,
-0.0195770263671875,
-0.0239105224609375,
0.01293182373046875,
0.00943756103515625,
0.0099945068359375,
0.0185089111328125,
0.031646728515625,
0.036956787109375,
0.0017795562744140625,
0.009368896484375,
0.0275115966796875,
0.005279541015625,
-0.0306396484375,
-0.0067138671875,
0.00588226318359375,
-0.01093292236328125,
-0.04541015625,
0.02667236328125,
0.0341796875,
-0.00978851318359375,
-0.0297088623046875,
-0.0189361572265625,
0.007244110107421875,
-0.00879669189453125,
0.003040313720703125,
-0.016937255859375,
-0.01177215576171875,
0.00452423095703125,
0.0130462646484375,
0.0062713623046875,
0.03106689453125,
0.02789306640625,
-0.011383056640625,
0.0134429931640625,
0.021209716796875,
0.007236480712890625,
0.01287078857421875,
-0.008941650390625,
0.0064544677734375,
0.0025653839111328125,
0.0218505859375,
0.0039005279541015625,
0.01317596435546875,
-0.00909423828125,
0.0186004638671875,
0.0136260986328125,
-0.0173492431640625,
0.0022258758544921875,
0.001667022705078125,
0.008056640625,
-0.007785797119140625,
-0.0026493072509765625,
0.0005125999450683594,
0.02276611328125,
0.00339508056640625,
0.0126953125,
-0.035919189453125,
0.02667236328125,
0.00261688232421875,
0.00746917724609375,
0.0037212371826171875,
-0.01513671875,
0.0234527587890625,
-0.00730133056640625,
0.01251983642578125,
0.02227783203125,
0.0086669921875,
-0.0048828125,
0.025634765625,
0.030364990234375,
-0.019500732421875,
-0.0238189697265625,
-0.0146026611328125,
0.004974365234375,
0.01015472412109375,
0.0108795166015625,
-0.0297698974609375,
-0.018402099609375,
-0.005451202392578125,
0.0033969879150390625,
-0.003326416015625,
-0.01294708251953125,
0.004657745361328125,
-0.0166168212890625,
0.034423828125,
-0.03668212890625,
-0.004032135009765625,
0.022064208984375,
0.00505828857421875,
0.01015472412109375,
-0.0240936279296875,
-0.0095672607421875,
0.01416778564453125,
-0.0019254684448242188,
-0.0280609130859375,
-0.0176849365234375,
0.0137481689453125,
-0.010406494140625,
0.032928466796875,
0.033782958984375,
0.01169586181640625,
0.002323150634765625,
0.0142822265625,
-0.0272979736328125,
0.0226287841796875,
0.00479888916015625,
-0.029022216796875,
0.005916595458984375,
0.0006513595581054688,
-0.049560546875,
0.0273895263671875,
-0.00010454654693603516,
-0.0239410400390625,
-0.01690673828125,
0.0275421142578125,
0.0041656494140625,
-0.0038661956787109375,
-0.00754547119140625,
-0.003780364990234375,
-0.015411376953125,
0.0238800048828125,
0.028076171875,
0.0198211669921875,
0.0087127685546875,
0.0200958251953125,
-0.0062408447265625,
0.00971221923828125,
0.0015010833740234375,
-0.01885986328125,
-0.01071929931640625,
-0.01715087890625,
0.005645751953125,
0.00548553466796875,
0.0031585693359375,
-0.01222991943359375,
0.006038665771484375,
0.038787841796875,
0.0014190673828125,
-0.015106201171875,
0.0230255126953125,
0.0019474029541015625,
0.0254669189453125,
0.004093170166015625,
0.0142822265625,
-0.00354766845703125,
0.031707763671875,
-0.0140380859375,
-0.02716064453125,
-0.01100921630859375,
-0.017913818359375,
0.0132598876953125,
0.001079559326171875,
0.0150299072265625,
-0.0194091796875,
-0.01824951171875,
0.01538848876953125,
-0.009613037109375,
0.015655517578125,
0.0008158683776855469,
-0.0274200439453125,
-0.00998687744140625,
0.018646240234375,
0.019378662109375,
0.007617950439453125,
0.01128387451171875,
-0.008270263671875,
-0.03155517578125,
0.0071563720703125,
-0.0025787353515625,
-0.007625579833984375,
0.006893157958984375,
0.004299163818359375,
-0.0089569091796875,
0.0721435546875,
0.0226593017578125,
0.029022216796875,
0.0296783447265625,
-0.0011014938354492188,
-0.01183319091796875,
-0.0041656494140625,
0.006877899169921875,
0.010894775390625,
-0.0015554428100585938,
-0.0056304931640625,
0.021728515625,
0.00817108154296875,
-0.00698089599609375,
-0.0355224609375,
-0.0104827880859375,
0.0157470703125,
-0.0066375732421875,
-0.034271240234375,
0.020111083984375,
0.0032939910888671875,
-0.0027618408203125,
0.0017986297607421875,
0.0021114349365234375,
-0.007266998291015625,
0.00466156005859375,
-0.016754150390625,
0.0004591941833496094,
0.0036182403564453125,
-0.006290435791015625,
-0.00568389892578125,
-0.0116119384765625,
-0.0011959075927734375,
-0.0157928466796875,
-0.00159454345703125,
0.0043487548828125,
-0.01502227783203125,
-0.04095458984375,
-0.0243682861328125,
-0.0369873046875,
0.016815185546875,
0.0229949951171875,
-0.0187225341796875,
0.01406097412109375,
0.028411865234375,
-0.007495880126953125,
-0.0165252685546875,
-0.034698486328125,
-0.045867919921875,
-0.0010328292846679688,
0.002105712890625,
0.0007762908935546875,
-0.01146697998046875,
-0.00848388671875,
0.0170135498046875,
0.0232696533203125,
-0.0107269287109375,
0.037109375,
0.0404052734375,
0.032440185546875,
0.007732391357421875,
0.02392578125,
0.005218505859375,
0.01422882080078125,
0.0009713172912597656,
-0.0091094970703125,
-0.0307464599609375,
0.0134429931640625,
0.0297088623046875,
0.0166015625,
-0.03460693359375,
0.025604248046875,
-0.019500732421875,
-0.03216552734375,
-0.0020771026611328125,
0.0177001953125,
-0.031219482421875,
0.01064300537109375,
0.0015811920166015625,
0.00035309791564941406,
-0.004154205322265625,
0.010986328125,
0.0007586479187011719,
-0.0211944580078125,
-0.0263519287109375,
-0.01007843017578125,
0.010986328125,
0.0240325927734375,
0.0180206298828125,
-0.0215606689453125,
-0.004222869873046875,
0.0186767578125,
0.033538818359375,
-0.0004000663757324219,
-0.01519012451171875,
0.019866943359375,
-0.016326904296875,
0.0055694580078125,
0.0210418701171875,
-0.035247802734375,
0.0303802490234375,
0.003292083740234375,
-0.0179595947265625,
-0.006237030029296875,
0.0019626617431640625,
0.019287109375,
0.01015472412109375,
0.0095367431640625,
-0.0110931396484375,
-0.0015468597412109375,
-0.004360198974609375,
0.00572967529296875,
0.0208282470703125,
-0.03497314453125,
0.0222930908203125,
0.00958251953125,
0.005889892578125,
0.01299285888671875,
0.032257080078125,
0.001338958740234375,
-0.0347900390625,
-0.007274627685546875,
-0.0095062255859375,
-0.026519775390625,
0.01036834716796875,
-0.006267547607421875,
-0.00937652587890625,
0.0084381103515625,
0.0007891654968261719,
0.0141143798828125,
-0.0237884521484375,
0.00849151611328125,
0.01142120361328125,
0.019195556640625,
0.00452423095703125,
0.026763916015625,
0.0159149169921875,
0.0048980712890625,
-0.01136016845703125,
-0.024658203125,
-0.00014281272888183594,
-0.01468658447265625,
0.020294189453125,
-0.01470947265625,
0.0182342529296875,
-0.0031566619873046875,
0.00004965066909790039,
0.0210418701171875,
-0.01511383056640625,
0.00402069091796875,
0.0220184326171875,
-0.0318603515625,
-0.01027679443359375,
-0.0196685791015625,
0.01971435546875,
0.0027027130126953125,
0.0192718505859375,
-0.026580810546875,
-0.0063323974609375,
0.0113525390625,
0.0168914794921875,
-0.037872314453125,
0.0142974853515625,
0.0005502700805664062,
-0.025665283203125,
-0.0155029296875,
-0.00009143352508544922,
0.00653076171875,
0.004062652587890625,
-0.01035308837890625,
-0.01361846923828125,
-0.015655517578125,
0.0355224609375,
0.0112152099609375,
0.00623321533203125,
0.0210723876953125,
-0.01068878173828125,
-0.01129913330078125,
0.00807952880859375,
0.025909423828125,
0.0167236328125,
-0.0067291259765625,
0.01336669921875,
0.00870513916015625,
0.00519561767578125,
-0.009490966796875,
-0.01006317138671875,
-0.00846099853515625,
-0.02008056640625,
-0.0086212158203125,
0.02734375,
-0.00756072998046875,
-0.024993896484375,
0.023956298828125,
-0.007442474365234375,
0.0181427001953125,
-0.01247406005859375,
0.035919189453125,
0.005161285400390625,
0.0472412109375,
-0.004261016845703125,
0.0034885406494140625,
0.00273895263671875,
0.02734375,
-0.0023097991943359375,
-0.0179290771484375,
0.0124359130859375,
0.0027408599853515625,
-0.005725860595703125,
-0.0067138671875,
-0.0195159912109375,
0.0030040740966796875,
0.033294677734375,
0.0081787109375,
0.0004379749298095703,
-0.0177459716796875,
0.01293182373046875,
-0.017669677734375,
-0.0267181396484375,
0.0212249755859375,
-0.00856781005859375,
0.0252532958984375,
0.0028705596923828125,
-0.033905029296875,
-0.0025043487548828125,
-0.004604339599609375,
-0.0025577545166015625,
0.03302001953125,
0.0167999267578125,
-0.0016937255859375,
0.035736083984375,
0.0251922607421875,
0.021820068359375,
-0.0259246826171875,
-0.0247039794921875,
-0.006435394287109375,
-0.018463134765625,
-0.04962158203125,
-0.01314544677734375,
0.015655517578125,
0.00778961181640625,
0.0004096031188964844,
-0.0171661376953125,
-0.002597808837890625,
0.01250457763671875,
0.01222991943359375,
-0.035919189453125,
-0.0135650634765625,
0.00406646728515625,
0.0115966796875,
-0.00603485107421875,
-0.0152130126953125,
0.01788330078125,
-0.02471923828125,
-0.03375244140625,
0.00812530517578125,
-0.00405120849609375,
-0.02105712890625,
0.0009260177612304688,
-0.0130462646484375,
-0.0200653076171875,
-0.01407623291015625,
0.029693603515625,
-0.0304412841796875,
0.0154266357421875,
-0.015228271484375,
0.024200439453125,
-0.003841400146484375,
0.0321044921875,
0.0184783935546875,
0.037506103515625,
-0.0107574462890625,
0.0286865234375,
0.025726318359375,
-0.00180816650390625,
0.034912109375,
-0.0204925537109375,
0.043365478515625,
0.0139617919921875,
-0.0160675048828125,
0.01160430908203125,
0.0159912109375,
0.006683349609375,
0.01087188720703125,
0.01030731201171875,
0.01509857177734375,
0.02142333984375,
-0.05938720703125,
0.0283966064453125,
-0.030792236328125,
-0.0197296142578125,
-0.0098724365234375,
-0.0139923095703125,
-0.01476287841796875,
-0.0105438232421875,
-0.0318603515625,
-0.006511688232421875,
-0.0024700164794921875,
-0.00572967529296875,
-0.01541900634765625,
0.0009374618530273438,
0.03607177734375,
-0.0149688720703125,
0.04962158203125,
0.00611114501953125,
0.018829345703125,
-0.00254058837890625,
0.0070343017578125,
0.014251708984375,
0.0265045166015625,
-0.004146575927734375,
-0.0123443603515625,
-0.01812744140625,
-0.02117919921875,
-0.00899505615234375,
0.01177215576171875,
0.01317596435546875,
-0.0005121231079101562,
-0.019866943359375,
-0.009918212890625,
0.04461669921875,
-0.0224456787109375,
0.047698974609375,
-0.00033783912658691406,
-0.003925323486328125,
-0.00907135009765625,
0.0154876708984375,
0.002040863037109375,
-0.016693115234375,
-0.02734375,
-0.01505279541015625,
0.019500732421875,
0.004360198974609375,
0.0201416015625,
0.0216522216796875,
-0.008697509765625,
-0.037872314453125,
-0.022003173828125,
0.025146484375,
0.01477813720703125,
0.01197052001953125,
-0.0159454345703125,
-0.036285400390625,
0.0172576904296875,
-0.006099700927734375,
-0.00852203369140625,
0.024871826171875,
0.034423828125,
0.01023101806640625,
0.0242919921875,
0.02001953125,
0.0252227783203125,
-0.0225372314453125,
-0.0174407958984375,
-0.00974273681640625,
-0.00850677490234375,
-0.0020771026611328125,
0.0045623779296875,
-0.00262451171875,
0.02362060546875,
0.009735107421875,
0.0207977294921875,
-0.01074981689453125,
-0.01300048828125,
-0.006305694580078125,
0.0182037353515625,
-0.0296630859375,
-0.022064208984375,
-0.0179290771484375,
0.0104522705078125,
-0.0236968994140625,
-0.0167694091796875,
-0.0014295578002929688,
0.0002999305725097656,
-0.006099700927734375,
-0.037384033203125,
0.006488800048828125,
0.029022216796875,
0.01184844970703125,
-0.032470703125,
-0.0088043212890625,
0.028961181640625,
0.0243988037109375,
0.029388427734375,
0.042449951171875,
0.023529052734375,
-0.0146942138671875,
0.03204345703125,
-0.00662994384765625,
-0.0095062255859375,
0.0115966796875,
-0.03179931640625,
-0.031890869140625,
-0.03411865234375,
0.026885986328125,
-0.0082244873046875,
-0.00931549072265625,
-0.00508880615234375,
0.01273345947265625,
-0.041015625,
0.005706787109375,
-0.0025234222412109375,
0.03375244140625,
0.0072784423828125,
-0.012786865234375,
-0.01561737060546875,
0.01537322998046875,
0.011260986328125,
-0.0108795166015625,
-0.0192718505859375,
0.0207977294921875,
-0.00937652587890625,
-0.0259552001953125,
0.01091766357421875,
-0.0192108154296875,
0.0198822021484375,
0.0051116943359375,
0.019134521484375,
0.012969970703125,
-0.019927978515625,
-0.034942626953125,
-0.013336181640625,
0.00682830810546875,
-0.0521240234375,
0.0173187255859375,
0.005802154541015625,
-0.0201416015625,
0.00333404541015625,
0.005096435546875,
-0.00524139404296875,
0.007244110107421875,
-0.038299560546875,
0.0037631988525390625,
-0.00799560546875,
0.0170135498046875,
-0.0105133056640625,
0.0037403106689453125,
0.008148193359375,
0.0193939208984375,
0.0016613006591796875,
-0.00867462158203125,
-0.0130767822265625,
-0.0019855499267578125,
0.02691650390625,
-0.0130157470703125,
0.019989013671875,
-0.032989501953125,
0.05230712890625,
-0.004878997802734375,
0.0016031265258789062,
-0.0203094482421875,
0.0196075439453125,
0.00905609130859375,
0.00655364990234375,
-0.0088348388671875,
-0.0151519775390625,
0.0304412841796875,
-0.00225830078125,
0.0011930465698242188,
-0.012664794921875,
0.03594970703125,
0.00551605224609375,
-0.0177001953125,
0.0219879150390625,
-0.01268768310546875,
0.014495849609375,
0.002513885498046875,
-0.01107025146484375,
0.00909423828125,
-0.01071929931640625,
-0.008392333984375,
0.0223541259765625,
-0.01023101806640625,
-0.006786346435546875,
0.001354217529296875,
-0.006622314453125,
0.032562255859375,
0.00911712646484375,
0.041412353515625,
-0.005359649658203125,
0.003322601318359375,
0.01035308837890625,
-0.013031005859375,
0.0008306503295898438,
-0.0118408203125,
0.04388427734375,
-0.01039886474609375,
0.019287109375,
0.0221099853515625,
-0.0295867919921875,
0.0106353759765625,
0.031585693359375,
0.02130126953125,
0.00634002685546875,
-0.006290435791015625,
0.0011463165283203125,
0.0027065277099609375,
-0.027923583984375,
-0.00971221923828125,
-0.01032257080078125,
0.0169677734375,
-0.031768798828125,
-0.0245361328125,
-0.0246429443359375,
0.021270751953125,
-0.005039215087890625,
0.0215606689453125,
0.0002111196517944336,
0.009429931640625,
0.01495361328125,
-0.024871826171875,
-0.031768798828125,
-0.01200103759765625,
-0.040740966796875,
0.01329803466796875,
0.0266876220703125,
0.029296875,
0.0076751708984375,
-0.00550079345703125,
0.0055694580078125,
-0.024078369140625,
0.016937255859375,
0.01001739501953125,
-0.051300048828125,
-0.0178375244140625,
0.031829833984375,
-0.0114288330078125,
-0.020751953125,
0.02081298828125,
-0.0223388671875,
-0.0017423629760742188,
-0.008819580078125,
-0.002288818359375,
0.0246429443359375,
0.032806396484375,
-0.037261962890625,
-0.01172637939453125,
-0.004383087158203125,
0.03741455078125,
0.004489898681640625,
-0.0169219970703125,
-0.00298309326171875,
-0.002590179443359375,
-0.01568603515625,
-0.00897979736328125,
0.0203704833984375,
-0.01454925537109375,
0.01233673095703125,
0.015716552734375,
-0.020965576171875,
0.004192352294921875,
-0.01519012451171875,
0.032562255859375,
0.0014886856079101562,
0.006649017333984375,
0.02410888671875,
0.01444244384765625,
0.0195770263671875,
0.0224456787109375,
-0.0079803466796875,
-0.02044677734375,
0.018646240234375,
0.0118560791015625,
0.0190887451171875,
-0.01001739501953125,
-0.01161956787109375,
0.040130615234375,
0.01300048828125,
-0.033294677734375,
-0.006740570068359375,
-0.0159759521484375,
-0.05255126953125,
-0.010955810546875,
0.01190948486328125,
-0.01268768310546875,
0.007236480712890625,
-0.011383056640625,
-0.001346588134765625,
0.0015878677368164062,
0.01305389404296875,
-0.0032901763916015625,
-0.04010009765625,
-0.01067352294921875,
-0.0304718017578125,
0.05133056640625,
0.0115203857421875,
-0.021881103515625,
0.0250701904296875,
-0.0198211669921875,
0.0129547119140625,
-0.016265869140625,
-0.0015001296997070312,
-0.01178741455078125,
-0.0157623291015625,
-0.0157470703125,
0.0004367828369140625,
-0.024261474609375,
-0.0248565673828125,
0.01126861572265625,
0.0023937225341796875,
0.01029205322265625,
0.003971099853515625,
-0.0316162109375,
-0.006511688232421875,
0.04510498046875,
-0.032440185546875,
0.005077362060546875,
-0.0024089813232421875,
-0.0293731689453125,
0.01340484619140625,
-0.0187225341796875,
0.03680419921875,
0.0194091796875,
0.017120361328125,
-0.00875091552734375,
-0.022735595703125,
-0.0083465576171875,
-0.00988006591796875,
-0.0164337158203125,
0.01091766357421875,
0.011749267578125,
0.0260772705078125,
0.005420684814453125,
-0.01168060302734375,
-0.0295562744140625,
0.013580322265625,
-0.012420654296875,
-0.01161956787109375,
-0.0017690658569335938,
-0.006072998046875,
0.020660400390625,
0.03997802734375,
0.01776123046875,
0.0517578125,
0.003047943115234375,
0.0087738037109375,
-0.0140838623046875,
0.003055572509765625,
0.0002956390380859375,
0.051025390625,
0.0019054412841796875,
0.02069091796875,
-0.009368896484375,
-0.024444580078125,
-0.03594970703125
] |
ours_550
|
Let the rectangle be \( PQRC \), where \( P \) is on \( AC \), \( Q \) is on \( AB \), and \( R \) is on \( BC \). Let \( AP = a \), \( PQ = b \), \( QR = c \), and \( BR = d \). From similar triangles, we have \( ad = bc \). Also, from the given information, \( cd = 64 \) and \( ab = 1024 \). Multiplying these gives \( abcd = 1024 \cdot 64 \). Since \( ad = bc \), we have \( ad = bc = 32 \cdot 8 = 256 \).
Thus, the area of the rectangle is \(\boxed{256}\).
|
256
|
{
"competition": "us_comps",
"dataset": "Ours",
"posts": null,
"source": "OMOSoln2.md"
}
|
Let \( \triangle ABC \) be a right triangle with a right angle at \( C \). Two lines, one parallel to \( AC \) and the other parallel to \( BC \), intersect on the hypotenuse \( AB \). The lines cut the triangle into two triangles and a rectangle. The two triangles have areas \( 512 \) and \( 32 \). What is the area of the rectangle?
|
[
"/Mathematics/Geometry/Dissection/TriangleDissection",
"/Mathematics/Geometry/PlaneGeometry/GeometricSimilarity/Homothecy",
"/Mathematics/Geometry/PlaneGeometry/GeometricSimilarity/Homothetic",
"/Mathematics/Geometry/PlaneGeometry/GeometricSimilarity/HomotheticTriangles",
"/Mathematics/Geometry/PlaneGeometry/GeometricSimilarity/Similar",
"/Mathematics/Geometry/PlaneGeometry/GeometricSimilarity/Similarity",
"/Mathematics/Geometry/PlaneGeometry/Rectangles/Rectangle",
"/Mathematics/Geometry/PlaneGeometry/Triangles/TriangleProperties"
] |
Apply similarity of the small right triangles to get ad = bc, then use the given triangle areas (as products of leg lengths) to solve for the rectangle area.
|
[
-0.00003784894943237305,
-0.051361083984375,
0.053314208984375,
0.007213592529296875,
-0.00011843442916870117,
0.02056884765625,
0.01180267333984375,
-0.007549285888671875,
0.006725311279296875,
-0.02105712890625,
-0.03564453125,
0.0187835693359375,
-0.00458526611328125,
0.006015777587890625,
0.022796630859375,
0.01073455810546875,
-0.0217437744140625,
-0.01145172119140625,
0.041595458984375,
-0.0008096694946289062,
-0.01198577880859375,
-0.0018167495727539062,
-0.031280517578125,
0.01910400390625,
0.006195068359375,
0.005100250244140625,
-0.0171356201171875,
-0.01316070556640625,
0.005298614501953125,
-0.00676727294921875,
-0.021636962890625,
-0.02606201171875,
-0.002498626708984375,
-0.00482177734375,
-0.00003933906555175781,
0.012298583984375,
0.0243072509765625,
-0.0008168220520019531,
-0.031890869140625,
-0.0465087890625,
0.008758544921875,
0.0032901763916015625,
-0.00881195068359375,
0.0028076171875,
0.0124053955078125,
0.0212249755859375,
-0.00597381591796875,
0.018890380859375,
-0.0082244873046875,
0.01922607421875,
0.002872467041015625,
0.0156707763671875,
-0.0174713134765625,
-0.01409149169921875,
0.023101806640625,
-0.06640625,
-0.005504608154296875,
0.01275634765625,
-0.0034923553466796875,
0.008636474609375,
-0.006999969482421875,
-0.005641937255859375,
0.0254974365234375,
-0.0113372802734375,
-0.00566864013671875,
-0.00455474853515625,
-0.005344390869140625,
-0.017578125,
-0.0015850067138671875,
0.004055023193359375,
0.047332763671875,
-0.0045623779296875,
-0.004161834716796875,
-0.004886627197265625,
-0.00737762451171875,
-0.0095062255859375,
-0.0030040740966796875,
0.0102081298828125,
0.01629638671875,
0.007144927978515625,
-0.01123809814453125,
0.0045318603515625,
0.008941650390625,
0.005157470703125,
0.01010894775390625,
0.007190704345703125,
0.005828857421875,
0.00522613525390625,
0.01184844970703125,
-0.0087738037109375,
0.0005784034729003906,
-0.0015687942504882812,
-0.0229644775390625,
-0.0330810546875,
0.0124359130859375,
0.005077362060546875,
-0.0033321380615234375,
0.006221771240234375,
-0.0133209228515625,
0.013885498046875,
-0.01641845703125,
-0.023223876953125,
-0.005893707275390625,
-0.0257415771484375,
0.0182342529296875,
-0.02294921875,
-0.0004374980926513672,
0.0117950439453125,
0.0095977783203125,
-0.00383758544921875,
0.0159912109375,
0.0007290840148925781,
0.052032470703125,
0.032135009765625,
0.01837158203125,
-0.01169586181640625,
-0.01251220703125,
0.010894775390625,
-0.0222930908203125,
0.01611328125,
0.0078887939453125,
0.027740478515625,
0.01148223876953125,
0.005847930908203125,
0.02154541015625,
-0.0286865234375,
-0.004970550537109375,
-0.005931854248046875,
-0.00812530517578125,
0.0040740966796875,
-0.005603790283203125,
-0.0014963150024414062,
-0.0228271484375,
-0.0008540153503417969,
-0.00887298583984375,
0.025054931640625,
0.0255279541015625,
0.0012540817260742188,
0.006771087646484375,
-0.0149078369140625,
-0.0025882720947265625,
0.0016183853149414062,
-0.0011911392211914062,
-0.036590576171875,
-0.00897979736328125,
-0.020172119140625,
-0.005161285400390625,
0.00044918060302734375,
0.01910400390625,
0.01113128662109375,
0.0068359375,
-0.0112152099609375,
0.007080078125,
0.03167724609375,
0.0062103271484375,
0.004425048828125,
0.006740570068359375,
0.02313232421875,
-0.006130218505859375,
-0.00420379638671875,
-0.01165008544921875,
0.00536346435546875,
0.000621795654296875,
0.0165252685546875,
-0.006809234619140625,
-0.0221710205078125,
0.00841522216796875,
0.00778961181640625,
-0.0195465087890625,
0.00016880035400390625,
0.01287841796875,
-0.0255889892578125,
-0.0002090930938720703,
-0.0007719993591308594,
-0.00353240966796875,
0.0102386474609375,
-0.00862884521484375,
0.00640869140625,
-0.0026397705078125,
0.0149993896484375,
-0.0033092498779296875,
-0.01439666748046875,
0.060699462890625,
0.006500244140625,
0.0169677734375,
0.004512786865234375,
-0.000046312808990478516,
0.01465606689453125,
0.03271484375,
0.01378631591796875,
-0.007904052734375,
-0.0357666015625,
-0.0218963623046875,
-0.00299835205078125,
-0.003803253173828125,
-0.0017099380493164062,
-0.03106689453125,
-0.0099334716796875,
-0.004123687744140625,
0.0128326416015625,
0.005573272705078125,
-0.034942626953125,
0.0318603515625,
0.0033397674560546875,
-0.004009246826171875,
-0.0021495819091796875,
0.0176544189453125,
-0.005817413330078125,
0.004665374755859375,
0.0110321044921875,
0.0015554428100585938,
0.0167236328125,
-0.005878448486328125,
-0.042144775390625,
-0.027069091796875,
-0.0208587646484375,
-0.0151519775390625,
-0.01216888427734375,
0.005535125732421875,
0.0198211669921875,
-0.004032135009765625,
-0.004283905029296875,
-0.002582550048828125,
0.005645751953125,
-0.00579833984375,
0.00847625732421875,
0.030975341796875,
-0.0008234977722167969,
-0.013885498046875,
-0.01462554931640625,
-0.00902557373046875,
0.01210784912109375,
-0.01448822021484375,
0.0084991455078125,
-0.0177764892578125,
0.00725555419921875,
-0.0241241455078125,
0.01177978515625,
0.005680084228515625,
0.012115478515625,
0.031219482421875,
-0.0239715576171875,
0.0002956390380859375,
0.0099945068359375,
-0.01169586181640625,
0.010650634765625,
0.0185394287109375,
-0.01093292236328125,
-0.026092529296875,
-0.0260162353515625,
-0.014556884765625,
-0.00870513916015625,
-0.005184173583984375,
-0.0240478515625,
-0.00647735595703125,
0.0005745887756347656,
-0.0043792724609375,
0.03106689453125,
0.00585174560546875,
-0.0124359130859375,
-0.005474090576171875,
-0.0191802978515625,
-0.00795745849609375,
-0.0146636962890625,
-0.0004715919494628906,
0.019287109375,
0.005279541015625,
-0.0038928985595703125,
0.014556884765625,
-0.00402069091796875,
0.05682373046875,
-0.0089263916015625,
0.007049560546875,
0.0136260986328125,
0.008331298828125,
-0.017486572265625,
0.0123748779296875,
0.007366180419921875,
0.005794525146484375,
-0.0025424957275390625,
0.0132598876953125,
-0.0203399658203125,
-0.04180908203125,
0.0115203857421875,
-0.009552001953125,
-0.011444091796875,
0.047027587890625,
-0.0209503173828125,
0.0005955696105957031,
0.031951904296875,
0.0033855438232421875,
0.00958251953125,
-0.0155029296875,
-0.0195770263671875,
0.07061767578125,
0.0204315185546875,
-0.0097503662109375,
0.01558685302734375,
-0.01416015625,
-0.01212310791015625,
0.016387939453125,
-0.0166473388671875,
0.00225830078125,
0.0156707763671875,
0.043182373046875,
0.03436279296875,
0.0006265640258789062,
0.004116058349609375,
-0.01971435546875,
-0.033935546875,
-0.023223876953125,
-0.01226806640625,
-0.032073974609375,
0.0012350082397460938,
-0.0089263916015625,
-0.0426025390625,
0.007442474365234375,
0.004291534423828125,
-0.01425933837890625,
-0.004100799560546875,
-0.01061248779296875,
-0.0027141571044921875,
0.0107421875,
-0.008056640625,
0.026123046875,
-0.0246734619140625,
0.027008056640625,
0.00910186767578125,
0.0236968994140625,
0.00261688232421875,
0.01971435546875,
0.030975341796875,
-0.00724029541015625,
-0.0299835205078125,
-0.0009899139404296875,
0.0018033981323242188,
-0.00919342041015625,
0.0007691383361816406,
0.0156402587890625,
0.00945281982421875,
0.0006737709045410156,
0.00809478759765625,
0.0210418701171875,
-0.073974609375,
-0.0165252685546875,
0.0274200439453125,
0.004726409912109375,
-0.0073699951171875,
-0.01000213623046875,
-0.0135040283203125,
0.007110595703125,
-0.0086517333984375,
-0.00112152099609375,
0.01446533203125,
0.01299285888671875,
0.005023956298828125,
-0.0212860107421875,
0.00223541259765625,
0.012359619140625,
0.004146575927734375,
0.00513458251953125,
-0.00632476806640625,
-0.00789642333984375,
0.005588531494140625,
-0.03814697265625,
-0.03350830078125,
-0.003871917724609375,
0.0009026527404785156,
0.0122528076171875,
-0.0015420913696289062,
-0.0018215179443359375,
0.0191650390625,
-0.0084228515625,
-0.0006127357482910156,
0.0380859375,
0.03515625,
-0.0150299072265625,
0.0122833251953125,
-0.000762939453125,
0.0008420944213867188,
-0.0283660888671875,
-0.037750244140625,
-0.01898193359375,
0.035888671875,
-0.004390716552734375,
0.0096893310546875,
-0.005645751953125,
0.0218505859375,
-0.007457733154296875,
0.0040435791015625,
0.0141448974609375,
0.01355743408203125,
-0.019561767578125,
-0.00545501708984375,
-0.033294677734375,
0.01171112060546875,
0.00010389089584350586,
0.0095367431640625,
0.05389404296875,
-0.01491546630859375,
-0.07281494140625,
-0.0103912353515625,
-0.00733184814453125,
0.0225982666015625,
0.012237548828125,
0.00860595703125,
-0.02191162109375,
0.054168701171875,
0.0087890625,
-0.0157470703125,
0.01366424560546875,
0.0031108856201171875,
0.0006799697875976562,
0.0031566619873046875,
-0.0229949951171875,
0.0152435302734375,
0.0033969879150390625,
0.008056640625,
0.0066680908203125,
-0.009185791015625,
0.0036220550537109375,
0.00009143352508544922,
0.014251708984375,
-0.007442474365234375,
0.01366424560546875,
-0.006256103515625,
-0.008575439453125,
0.0225830078125,
-0.0247039794921875,
0.0015039443969726562,
0.01233673095703125,
-0.00403594970703125,
0.005397796630859375,
0.026824951171875,
-0.01065826416015625,
0.0032196044921875,
-0.004169464111328125,
0.0012273788452148438,
-0.0006589889526367188,
0.007801055908203125,
-0.065185546875,
-0.01419830322265625,
0.003936767578125,
-0.0009613037109375,
0.006923675537109375,
-0.0157928466796875,
-0.003955841064453125,
-0.00917816162109375,
-0.00109100341796875,
-0.0007491111755371094,
-0.04376220703125,
0.00672149658203125,
0.01666259765625,
-0.060272216796875,
0.017791748046875,
0.01053619384765625,
0.0002677440643310547,
-0.025787353515625,
-0.0184173583984375,
-0.011749267578125,
0.00568389892578125,
0.0283660888671875,
0.04315185546875,
-0.006610870361328125,
0.004638671875,
-0.0136260986328125,
-0.0157928466796875,
0.022552490234375,
0.0019969940185546875,
-0.00553131103515625,
-0.018341064453125,
-0.0236053466796875,
-0.003131866455078125,
-0.0185394287109375,
-0.0276641845703125,
0.0180511474609375,
-0.002353668212890625,
0.0232696533203125,
-0.041290283203125,
0.0179443359375,
-0.006519317626953125,
-0.018035888671875,
0.034454345703125,
-0.02313232421875,
0.003292083740234375,
0.0262603759765625,
-0.00037789344787597656,
-0.018524169921875,
0.019073486328125,
0.0037937164306640625,
0.002109527587890625,
0.04296875,
-0.018798828125,
-0.02374267578125,
-0.0222320556640625,
0.0001291036605834961,
-0.0129547119140625,
0.00748443603515625,
-0.016510009765625,
0.0115203857421875,
0.00600433349609375,
-0.0041351318359375,
-0.0059967041015625,
-0.00766754150390625,
0.01470184326171875,
-0.0330810546875,
0.0283355712890625,
-0.0222320556640625,
0.0162200927734375,
-0.013427734375,
-0.01140594482421875,
0.0030975341796875,
0.0096893310546875,
-0.028045654296875,
0.0482177734375,
0.00959014892578125,
0.0024890899658203125,
-0.0084228515625,
-0.0137786865234375,
0.0312042236328125,
0.00084686279296875,
0.016448974609375,
0.01885986328125,
-0.01549530029296875,
0.0016469955444335938,
0.0094757080078125,
0.017425537109375,
-0.01776123046875,
-0.0260162353515625,
-0.0273590087890625,
-0.01374053955078125,
0.00322723388671875,
-0.0148773193359375,
0.003765106201171875,
-0.00981903076171875,
-0.00685882568359375,
-0.0020427703857421875,
0.03155517578125,
0.0212860107421875,
0.0122222900390625,
-0.032012939453125,
-0.0287933349609375,
0.01438140869140625,
0.0034503936767578125,
-0.00778961181640625,
-0.0117340087890625,
0.00894927978515625,
0.00885772705078125,
-0.00579833984375,
0.01279449462890625,
0.010894775390625,
-0.0019664764404296875,
-0.0190887451171875,
0.00917816162109375,
-0.049774169921875,
-0.0118865966796875,
-0.05743408203125,
0.0008935928344726562,
-0.02008056640625,
0.01390838623046875,
0.01155853271484375,
0.0178070068359375,
-0.007595062255859375,
-0.0032596588134765625,
0.002559661865234375,
-0.012939453125,
0.0207672119140625,
-0.033355712890625,
-0.020477294921875,
-0.04193115234375,
-0.01467132568359375,
-0.033843994140625,
0.0019092559814453125,
0.014312744140625,
0.0083465576171875,
-0.0253143310546875,
-0.01415252685546875,
0.006504058837890625,
0.01141357421875,
-0.0084686279296875,
0.042938232421875,
0.01201629638671875,
-0.006542205810546875,
-0.02716064453125,
-0.0194091796875,
-0.0196380615234375,
-0.0234832763671875,
-0.0138397216796875,
0.040252685546875,
0.0234832763671875,
-0.03680419921875,
0.01311492919921875,
-0.00022673606872558594,
-0.029571533203125,
-0.004180908203125,
-0.008941650390625,
-0.018768310546875,
0.0089263916015625,
-0.0070343017578125,
0.0171051025390625,
-0.0180511474609375,
-0.0021495819091796875,
0.0037670135498046875,
-0.00440216064453125,
0.01560211181640625,
0.0189056396484375,
-0.0156402587890625,
0.0274505615234375,
0.0243988037109375,
-0.0207977294921875,
-0.027679443359375,
-0.01515960693359375,
-0.0298004150390625,
-0.0029277801513671875,
-0.0076751708984375,
0.00927734375,
-0.03369140625,
-0.019012451171875,
-0.035858154296875,
-0.01788330078125,
-0.0174560546875,
0.0287017822265625,
0.01995849609375,
0.0217437744140625,
0.007404327392578125,
-0.00945281982421875,
0.037109375,
-0.0169830322265625,
0.0070343017578125,
-0.03497314453125,
-0.0248565673828125,
-0.01358795166015625,
0.031951904296875,
0.0035915374755859375,
-0.026092529296875,
-0.0262908935546875,
0.01560211181640625,
0.00943756103515625,
-0.02032470703125,
-0.0168304443359375,
0.018798828125,
0.0190277099609375,
0.01824951171875,
-0.046722412109375,
-0.020416259765625,
-0.0163421630859375,
0.0016603469848632812,
-0.0217132568359375,
-0.0290374755859375,
0.0292205810546875,
-0.0209808349609375,
0.03656005859375,
0.00494384765625,
-0.004970550537109375,
-0.01525115966796875,
-0.003688812255859375,
-0.0020198822021484375,
0.01384735107421875,
0.055755615234375,
0.00894927978515625,
-0.0301513671875,
-0.0286102294921875,
0.01270294189453125,
0.036590576171875,
-0.029571533203125,
0.0085906982421875,
-0.0377197265625,
-0.01200103759765625,
0.04058837890625,
0.0386962890625,
-0.038421630859375,
0.03582763671875,
-0.0204925537109375,
-0.00846099853515625,
-0.002292633056640625,
0.00934600830078125,
-0.02276611328125,
-0.0032863616943359375,
0.01678466796875,
-0.013671875,
-0.01056671142578125,
0.0049591064453125,
0.049041748046875,
0.0045166015625,
0.00738525390625,
0.0155181884765625,
-0.02764892578125,
-0.010955810546875,
0.0162811279296875,
0.01117706298828125,
-0.0024547576904296875,
0.030059814453125,
-0.0098419189453125,
0.0230712890625,
-0.00812530517578125,
0.004505157470703125,
0.01367950439453125,
-0.01053619384765625,
0.0279083251953125,
-0.0213623046875,
0.0195159912109375,
-0.00882720947265625,
0.02960205078125,
-0.0147705078125,
-0.0226593017578125,
0.006805419921875,
0.0008745193481445312,
0.00264739990234375,
-0.0202484130859375,
0.01678466796875,
-0.041229248046875,
-0.036651611328125,
-0.010833740234375,
0.023834228515625,
-0.0268707275390625,
-0.01558685302734375,
-0.0160064697265625,
-0.00787353515625,
-0.029205322265625,
-0.02703857421875,
-0.0012121200561523438,
0.006072998046875,
-0.0266571044921875,
-0.01849365234375,
-0.01111602783203125,
0.053558349609375,
0.0161895751953125,
-0.0035037994384765625,
-0.04742431640625,
0.0009336471557617188,
-0.008880615234375,
-0.007843017578125,
-0.00455474853515625,
0.0198974609375,
-0.00786590576171875,
0.0167083740234375,
0.00439453125,
-0.01244354248046875,
-0.00009554624557495117,
0.020660400390625,
0.006877899169921875,
-0.01468658447265625,
0.006603240966796875,
-0.0082244873046875,
0.0103607177734375,
0.006755828857421875,
-0.01398468017578125,
0.0006022453308105469,
0.0058441162109375,
-0.0214996337890625,
0.03753662109375,
0.005207061767578125,
-0.015716552734375,
-0.0256805419921875,
-0.016510009765625,
0.0263824462890625,
0.015655517578125,
-0.01751708984375,
-0.014678955078125,
-0.00017726421356201172,
0.00659942626953125,
-0.005950927734375,
-0.02362060546875,
-0.0200653076171875,
-0.0160369873046875,
-0.02081298828125,
0.021759033203125,
-0.005878448486328125,
-0.0035381317138671875,
0.01922607421875,
0.0104217529296875,
-0.006351470947265625,
-0.023345947265625,
0.00986480712890625,
0.0283660888671875,
0.01227569580078125,
-0.04229736328125,
-0.004024505615234375,
0.042999267578125,
0.0056915283203125,
0.01250457763671875,
-0.0157012939453125,
0.00518035888671875,
-0.007701873779296875,
-0.0079193115234375,
0.0225372314453125,
0.000415802001953125,
-0.0095367431640625,
0.01367950439453125,
0.0201263427734375,
0.0345458984375,
0.00542449951171875,
0.005069732666015625,
-0.0169677734375,
0.00019359588623046875,
-0.01364898681640625,
-0.0031871795654296875,
-0.0119781494140625,
0.000030040740966796875,
0.0032253265380859375,
0.0172576904296875,
-0.01219940185546875,
-0.00463104248046875,
0.0273590087890625,
0.04241943359375,
0.0142364501953125,
-0.01727294921875,
0.0159912109375,
0.0017480850219726562,
0.01218414306640625,
-0.0023937225341796875,
0.016510009765625,
0.007289886474609375,
-0.03338623046875,
-0.0159149169921875,
-0.0014810562133789062,
0.0298614501953125,
-0.02001953125,
0.01479339599609375,
0.01727294921875,
-0.041656494140625,
0.016876220703125,
-0.029266357421875,
-0.0013751983642578125,
-0.0197906494140625,
0.01200103759765625,
0.0020771026611328125,
-0.017120361328125,
0.0264434814453125,
-0.01316070556640625,
0.03857421875,
-0.0224609375,
-0.025543212890625,
0.00888824462890625,
-0.005542755126953125,
0.0081939697265625,
0.01006317138671875,
-0.05126953125,
-0.025970458984375,
-0.047943115234375,
0.00572967529296875,
0.0102996826171875,
0.034576416015625,
0.0034027099609375,
0.01142120361328125,
-0.006771087646484375,
-0.00278472900390625,
0.0289764404296875,
0.035491943359375,
-0.0117645263671875,
0.026702880859375,
0.01763916015625,
-0.0240020751953125,
0.016632080078125,
0.01479339599609375,
-0.00833892822265625,
-0.01239776611328125,
0.0205535888671875,
0.014007568359375,
0.00823211669921875,
0.0211639404296875,
-0.0019369125366210938,
-0.0037593841552734375,
0.00299835205078125,
-0.017822265625,
-0.00563812255859375,
0.01398468017578125,
0.00885772705078125,
0.03948974609375,
-0.005702972412109375,
0.03570556640625,
-0.01210784912109375,
0.0266876220703125,
-0.01611328125,
0.03204345703125,
0.0345458984375,
0.001033782958984375,
0.035614013671875,
0.036651611328125,
0.0147705078125,
-0.00274658203125,
-0.044952392578125,
-0.01480865478515625,
-0.005329132080078125,
-0.0141143798828125,
-0.01325225830078125,
0.006984710693359375,
0.031158447265625,
0.022857666015625,
-0.00933074951171875,
-0.00855255126953125,
-0.005115509033203125,
-0.0191802978515625,
-0.005939483642578125,
0.034515380859375,
-0.0181732177734375,
-0.00004595518112182617,
-0.038055419921875,
0.015716552734375,
-0.00917816162109375,
-0.0018129348754882812,
0.0121002197265625,
0.018463134765625,
0.00848388671875,
-0.0003209114074707031,
-0.03106689453125,
-0.0203094482421875,
0.026519775390625,
0.00713348388671875,
0.02593994140625,
-0.0208740234375,
0.01226806640625,
0.011962890625,
0.040618896484375,
-0.008544921875,
-0.0264129638671875,
0.001979827880859375,
0.01318359375,
-0.0192413330078125,
0.0024738311767578125,
0.032745361328125,
0.039337158203125,
0.000278472900390625,
-0.04449462890625,
-0.0200958251953125,
-0.058013916015625,
0.01396942138671875,
0.022064208984375,
-0.054595947265625,
0.00238800048828125,
0.005611419677734375,
-0.01068878173828125,
-0.0022449493408203125,
-0.0153045654296875,
0.00438690185546875,
0.01113128662109375,
0.0165557861328125,
0.005153656005859375,
0.026397705078125,
0.00885009765625,
-0.00850677490234375,
-0.00003159046173095703,
0.0256805419921875,
0.0229644775390625,
-0.01349639892578125,
-0.0120086669921875,
0.0016765594482421875,
0.006134033203125,
-0.00858306884765625,
0.002532958984375,
0.0279541015625,
0.023040771484375,
0.0023441314697265625,
-0.005329132080078125,
-0.012786865234375,
-0.00814056396484375,
-0.002178192138671875,
0.019622802734375,
0.01546478271484375,
0.0128021240234375,
-0.00218963623046875,
0.0284271240234375,
-0.0223541259765625,
0.018798828125,
0.004215240478515625,
0.0155487060546875,
0.0243988037109375,
0.0214996337890625,
0.0063934326171875,
-0.01922607421875,
0.01013946533203125,
0.00946807861328125,
0.0014276504516601562,
-0.003765106201171875,
-0.010284423828125,
0.00959014892578125,
0.033294677734375,
0.0025615692138671875,
0.0211639404296875,
-0.005413055419921875,
-0.048919677734375,
-0.001972198486328125,
0.00980377197265625,
0.01142120361328125,
-0.0287322998046875,
-0.01422119140625,
0.018402099609375,
-0.031951904296875,
0.03033447265625,
-0.0250091552734375,
-0.02252197265625,
0.0290374755859375,
-0.00321197509765625,
0.017608642578125,
-0.0082855224609375,
0.0177001953125,
-0.01560211181640625,
-0.0206451416015625,
0.043365478515625,
-0.032257080078125,
-0.03167724609375,
0.0139923095703125,
0.01560211181640625,
-0.00044226646423339844,
0.039764404296875,
-0.0224609375,
-0.0220489501953125,
0.0254058837890625,
0.06134033203125,
0.0018100738525390625,
-0.0221099853515625,
0.0094757080078125,
0.0012359619140625,
0.00691986083984375,
-0.0215606689453125,
0.025238037109375,
-0.0090789794921875,
0.01361846923828125,
-0.0198516845703125,
0.0271148681640625,
-0.03375244140625,
-0.05126953125,
-0.0272216796875,
-0.008575439453125,
0.025238037109375,
-0.033905029296875,
0.003543853759765625,
0.0217742919921875,
-0.0006680488586425781,
0.0281982421875,
-0.0130615234375,
-0.01244354248046875,
0.00604248046875,
0.01116180419921875,
0.00530242919921875,
-0.036041259765625,
0.0009298324584960938,
-0.002017974853515625,
-0.004322052001953125,
0.0124359130859375,
0.007518768310546875,
0.01551055908203125,
0.0115509033203125,
-0.016143798828125,
-0.0208892822265625,
0.0126495361328125,
-0.03302001953125,
0.015594482421875,
-0.03277587890625,
0.0211334228515625,
0.01502227783203125,
0.0044097900390625,
0.0102691650390625,
0.0009579658508300781,
-0.0024089813232421875,
0.01212310791015625,
-0.022064208984375,
0.03424072265625,
0.025421142578125,
0.037750244140625,
0.004795074462890625,
-0.039306640625,
-0.0153350830078125,
-0.0206756591796875,
-0.0221710205078125,
0.0241851806640625,
-0.00479888916015625,
-0.0005517005920410156,
0.012969970703125,
0.00914764404296875,
-0.01274871826171875,
0.009490966796875,
0.035186767578125,
0.01303863525390625,
0.0020656585693359375,
-0.03875732421875,
0.01424407958984375,
-0.0045928955078125,
0.005832672119140625,
-0.02752685546875,
0.004047393798828125,
0.01617431640625,
-0.03924560546875,
0.036712646484375,
0.023895263671875,
0.031341552734375,
-0.03765869140625,
0.006561279296875,
0.03753662109375,
-0.005035400390625,
-0.01971435546875,
-0.0153656005859375,
-0.0182952880859375,
0.0037078857421875,
0.00957489013671875,
-0.0036468505859375,
0.005764007568359375,
0.002742767333984375,
0.01654052734375,
0.0216064453125,
-0.000576019287109375,
0.014556884765625,
0.035614013671875,
0.01110076904296875,
-0.00783538818359375,
-0.027008056640625,
0.00966644287109375,
0.0211334228515625,
-0.00893402099609375,
0.0194854736328125,
-0.0175323486328125,
0.0239715576171875,
0.033050537109375,
0.0038127899169921875,
0.00018548965454101562,
-0.00893402099609375,
-0.01297760009765625,
-0.022857666015625,
-0.0240020751953125,
0.01102447509765625,
0.01088714599609375,
-0.0015878677368164062,
0.006061553955078125,
0.0159912109375,
0.012420654296875,
0.0097503662109375,
0.042633056640625,
0.00911712646484375,
-0.01092529296875,
0.00787353515625,
0.028167724609375,
0.04443359375,
0.0090179443359375,
-0.020843505859375,
0.0039215087890625,
0.01047515869140625,
0.00557708740234375,
-0.0187225341796875,
0.0243072509765625,
-0.01702880859375,
-0.0180511474609375,
0.0270538330078125,
-0.038818359375,
-0.040557861328125,
0.0071563720703125,
-0.0192413330078125,
-0.0214080810546875,
-0.0069732666015625,
0.0242462158203125,
0.0109710693359375,
-0.01031494140625,
-0.0175018310546875,
-0.0130157470703125,
0.0095062255859375,
0.007415771484375,
0.029693603515625,
-0.00177764892578125,
-0.002288818359375,
0.0245513916015625,
-0.01042938232421875,
-0.01239776611328125,
-0.01412200927734375,
0.0240631103515625,
0.012298583984375,
0.0048370361328125,
-0.00882720947265625,
0.00954437255859375,
-0.006103515625,
-0.003856658935546875,
0.00801849365234375,
-0.0022144317626953125,
-0.0198516845703125,
0.035491943359375,
0.0158233642578125,
-0.0233154296875,
0.047271728515625,
0.00165557861328125,
0.0021533966064453125,
-0.0038051605224609375,
-0.011199951171875,
-0.005157470703125,
0.006500244140625,
0.00339508056640625,
-0.003147125244140625,
0.02618408203125,
0.0052642822265625,
0.00039386749267578125,
0.0012979507446289062,
-0.02313232421875,
-0.0223846435546875,
0.02813720703125,
-0.0176544189453125,
0.032196044921875,
0.004665374755859375,
0.01201629638671875,
0.0127105712890625,
-0.0206298828125,
0.007221221923828125,
-0.0234375,
-0.0174407958984375,
-0.01018524169921875,
-0.000995635986328125,
-0.0173797607421875,
0.01160430908203125,
0.0181884765625,
-0.01031494140625,
-0.001308441162109375,
0.0302734375,
-0.005237579345703125,
0.024444580078125,
0.031982421875,
-0.0002892017364501953,
0.030975341796875,
0.015380859375,
0.0195465087890625,
0.015625,
0.0044097900390625,
0.019134521484375,
-0.0159454345703125,
-0.0130157470703125,
0.0122528076171875,
-0.01276397705078125,
0.0230560302734375,
0.017852783203125,
-0.012451171875,
-0.00308990478515625,
-0.043304443359375,
0.02398681640625,
-0.0029277801513671875,
0.00574493408203125,
0.0235748291015625,
0.0245513916015625,
-0.004802703857421875,
0.0192413330078125,
-0.0217132568359375,
-0.0207366943359375,
-0.02099609375,
0.0010480880737304688,
-0.0187225341796875,
-0.00492095947265625,
-0.027740478515625,
0.033782958984375,
-0.004947662353515625,
-0.00146484375,
0.03680419921875,
0.004123687744140625,
-0.026580810546875,
0.0186309814453125,
-0.06561279296875,
0.01030731201171875,
0.0272674560546875,
0.012054443359375,
-0.017578125,
-0.0190887451171875,
-0.0007967948913574219,
0.0084381103515625,
0.05157470703125,
-0.01317596435546875,
0.003513336181640625,
-0.0111846923828125,
-0.005222320556640625,
-0.004367828369140625,
-0.01232147216796875,
-0.023345947265625,
0.0068817138671875,
0.01177215576171875,
-0.01427459716796875,
0.03375244140625,
-0.011932373046875,
-0.01435089111328125,
-0.00904083251953125,
0.0073699951171875,
0.01424407958984375,
0.024627685546875,
0.020233154296875,
-0.01009368896484375,
0.01020050048828125,
-0.004344940185546875,
-0.00923919677734375,
0.0269927978515625,
0.003818511962890625,
0.0051422119140625,
0.0272064208984375,
0.00568389892578125,
-0.01357269287109375,
-0.022430419921875,
-0.00794219970703125,
0.023681640625,
0.020111083984375,
0.01132965087890625,
0.0194854736328125,
0.0167694091796875,
-0.00798797607421875,
0.041229248046875,
-0.00959014892578125,
-0.00031566619873046875,
0.00962066650390625,
-0.00431060791015625,
0.02520751953125,
0.0005426406860351562,
0.0045928955078125,
0.01065826416015625,
-0.01593017578125,
0.0228271484375,
0.00141143798828125,
-0.03948974609375,
0.0257415771484375,
0.02386474609375,
0.0022792816162109375,
0.0010089874267578125,
0.024139404296875,
-0.0232086181640625,
0.0009126663208007812,
-0.0094451904296875,
0.036956787109375,
0.0154266357421875,
-0.0245208740234375,
0.007678985595703125,
-0.00823211669921875,
-0.01532745361328125,
-0.00469970703125,
-0.01517486572265625,
-0.017425537109375,
-0.014434814453125,
0.01262664794921875,
-0.0232086181640625,
-0.01004791259765625,
-0.0219268798828125,
0.00290679931640625,
-0.019866943359375,
0.0167236328125,
-0.0020465850830078125,
0.01480865478515625,
0.0073699951171875,
0.00157928466796875,
0.021759033203125,
0.019805908203125,
0.019805908203125,
-0.0144805908203125,
-0.00672149658203125,
0.01529693603515625,
0.02044677734375,
-0.00506591796875,
0.001987457275390625,
0.011444091796875,
-0.0011644363403320312,
-0.030426025390625,
0.00603485107421875,
0.00397491455078125,
-0.032562255859375,
0.0323486328125,
-0.00861358642578125,
0.0236663818359375,
0.014678955078125,
-0.034820556640625,
-0.019073486328125,
-0.0007028579711914062,
0.01824951171875,
0.00543212890625,
0.023193359375,
0.0158843994140625,
0.0119476318359375,
0.007717132568359375,
0.0238189697265625,
0.0251922607421875,
0.02197265625,
-0.00740814208984375,
-0.01409912109375,
0.00010472536087036133,
-0.01119232177734375,
-0.041748046875,
0.02880859375,
-0.00919342041015625,
-0.041961669921875,
0.040740966796875,
-0.0220184326171875,
-0.018951416015625,
-0.0197906494140625,
-0.0311279296875,
-0.013916015625,
0.007755279541015625,
-0.011016845703125,
-0.0140533447265625,
0.0025177001953125,
0.0107879638671875,
0.0220794677734375,
-0.045806884765625,
0.00768280029296875,
0.0128631591796875,
-0.00945281982421875,
0.01287841796875,
-0.0016307830810546875,
-0.01345062255859375,
0.044036865234375,
0.0225677490234375,
-0.0404052734375,
-0.01377105712890625,
0.008514404296875,
-0.035430908203125,
-0.005344390869140625,
0.00720977783203125,
0.002742767333984375,
0.01263427734375,
0.0028705596923828125,
-0.01318359375,
-0.0081939697265625,
0.0282745361328125,
-0.004238128662109375,
0.0193328857421875,
-0.042083740234375,
0.014801025390625,
0.00611114501953125,
0.004161834716796875,
-0.03363037109375,
-0.00972747802734375,
0.0016345977783203125,
0.0310821533203125,
-0.00876617431640625,
-0.01358795166015625,
0.004688262939453125,
0.028228759765625,
0.01235198974609375,
-0.0193023681640625,
0.01515960693359375,
0.0002624988555908203,
-0.000640869140625,
0.0194549560546875,
-0.0321044921875,
0.0170745849609375,
-0.00653076171875,
0.019805908203125,
0.0018510818481445312,
-0.00904083251953125,
0.02239990234375,
0.027557373046875,
0.00576019287109375,
0.0296173095703125,
0.00746917724609375,
0.01084136962890625,
0.00762939453125,
0.00881195068359375,
0.0207366943359375,
0.012481689453125,
0.0225677490234375,
0.005130767822265625,
-0.0196075439453125,
0.0078887939453125,
-0.009002685546875,
-0.0228424072265625,
-0.0222320556640625,
0.00008803606033325195,
-0.0097503662109375,
0.013885498046875,
-0.0083465576171875,
0.0186614990234375,
0.012969970703125,
-0.0036411285400390625,
0.042816162109375,
-0.0274200439453125,
0.0168304443359375,
-0.035064697265625,
0.00033402442932128906,
0.029052734375,
0.0270538330078125,
0.04241943359375,
0.01287841796875,
-0.027862548828125,
0.0120697021484375,
0.0200653076171875,
-0.029632568359375,
0.0296173095703125,
-0.0012197494506835938,
-0.005092620849609375,
0.037628173828125,
0.02423095703125,
-0.007648468017578125,
0.018341064453125,
0.024810791015625,
0.01080322265625,
-0.01751708984375,
-0.004119873046875,
0.01065826416015625,
0.0255279541015625,
-0.0009870529174804688,
-0.0008931159973144531,
-0.020599365234375,
0.022430419921875,
0.01284027099609375,
0.01280975341796875,
0.005096435546875,
-0.005168914794921875,
-0.007587432861328125,
-0.004161834716796875,
0.01287841796875,
0.017669677734375,
0.0029850006103515625,
-0.020599365234375,
-0.00930023193359375,
-0.0308380126953125,
0.00274658203125,
0.03802490234375,
-0.0057373046875,
0.043487548828125,
0.003742218017578125,
0.031585693359375,
-0.06146240234375,
-0.028411865234375,
-0.029327392578125,
0.03314208984375,
0.001361846923828125,
0.00476837158203125,
0.0059967041015625,
0.015533447265625,
0.01543426513671875,
-0.047271728515625,
0.033905029296875,
-0.00826263427734375,
0.0010023117065429688,
-0.0202789306640625,
0.01314544677734375,
0.046539306640625,
-0.003978729248046875,
-0.016021728515625,
0.02557373046875,
0.0225372314453125,
-0.01322174072265625,
0.0301971435546875,
-0.004199981689453125,
-0.0274810791015625,
0.01837158203125,
-0.014984130859375,
-0.0238189697265625,
0.038177490234375,
-0.01447296142578125,
-0.0121612548828125,
0.025360107421875,
-0.0156707763671875,
-0.0171356201171875,
0.0153045654296875,
-0.0060882568359375,
0.0185546875,
0.0144500732421875,
-0.0029163360595703125,
0.022552490234375,
0.0179901123046875,
0.0027179718017578125,
-0.0008592605590820312,
0.01294708251953125,
0.0245819091796875,
-0.0085906982421875,
-0.00217437744140625,
-0.0193634033203125,
0.0215606689453125,
-0.0240325927734375,
-0.00936126708984375,
-0.0123138427734375,
-0.01708984375,
0.0131988525390625,
-0.039459228515625,
-0.003482818603515625,
-0.0021343231201171875,
0.04974365234375,
-0.0460205078125,
0.003284454345703125,
-0.01338958740234375,
-0.0169525146484375,
0.029815673828125,
0.012359619140625,
-0.0248870849609375,
0.005146026611328125,
-0.01227569580078125,
0.00811004638671875,
-0.0078125,
0.0193023681640625,
0.0163421630859375,
0.0145721435546875,
-0.00867462158203125,
-0.004802703857421875,
0.00829315185546875,
0.0035762786865234375,
0.0032253265380859375,
-0.018798828125,
0.0287933349609375,
0.005825042724609375,
-0.007511138916015625,
-0.005828857421875,
-0.0643310546875,
0.0150909423828125,
0.007617950439453125,
-0.005527496337890625,
-0.005100250244140625,
0.0132293701171875,
0.01091766357421875,
0.006237030029296875,
-0.000965118408203125,
-0.0268096923828125,
-0.02642822265625,
0.00994873046875,
0.01102447509765625,
0.019561767578125,
0.01123809814453125,
-0.008575439453125,
-0.03289794921875,
0.0101470947265625,
-0.02435302734375,
-0.0217742919921875,
0.0249481201171875,
-0.015228271484375,
-0.0022068023681640625,
0.01097869873046875,
-0.006195068359375,
0.0272369384765625,
0.037750244140625,
-0.026031494140625,
-0.0035457611083984375,
0.01788330078125,
0.042327880859375,
0.045379638671875,
0.0171966552734375,
-0.003719329833984375,
0.005603790283203125,
0.00792694091796875,
0.014404296875,
0.0137481689453125,
0.00942230224609375,
-0.0062255859375,
0.017059326171875,
0.009490966796875,
-0.00787353515625,
-0.01187896728515625,
0.01424407958984375,
0.022705078125,
0.009979248046875,
0.0228729248046875,
-0.0263214111328125,
-0.041229248046875,
-0.018280029296875,
0.01971435546875,
-0.004955291748046875,
0.0160369873046875,
-0.0016326904296875,
0.0177154541015625,
-0.007511138916015625,
-0.0390625,
0.00144195556640625,
0.0299224853515625,
-0.043365478515625,
-0.0113983154296875,
0.01369476318359375,
-0.0157318115234375,
0.0296478271484375,
0.021240234375,
-0.0173187255859375,
0.0169219970703125,
0.0193328857421875,
0.00728607177734375,
-0.0010204315185546875,
-0.005096435546875,
0.009429931640625,
0.023284912109375,
-0.007480621337890625,
0.0243072509765625,
0.007656097412109375,
0.01430511474609375,
-0.0146331787109375,
0.010498046875,
0.0017366409301757812,
-0.019775390625,
-0.032958984375,
0.0236663818359375,
0.0204315185546875,
0.007434844970703125,
0.01259613037109375,
0.01018524169921875,
-0.0154571533203125,
-0.01666259765625,
-0.014923095703125,
0.0213165283203125,
-0.01192474365234375,
-0.015289306640625,
0.00376129150390625,
-0.0120391845703125,
0.01316070556640625,
0.0206298828125,
-0.0141448974609375,
-0.0249786376953125,
0.0101318359375,
0.01806640625,
0.0257110595703125,
0.01293182373046875,
0.0439453125,
0.01560211181640625,
-0.03948974609375,
-0.000865936279296875,
0.0187530517578125,
0.051910400390625,
-0.007724761962890625,
-0.018646240234375,
-0.0240936279296875,
-0.006107330322265625,
-0.01348876953125,
0.00791168212890625,
-0.00994873046875,
-0.016357421875,
0.00514984130859375,
0.0097198486328125,
-0.01064300537109375,
0.0027103424072265625,
-0.049560546875,
0.0276336669921875,
-0.0267333984375,
0.004543304443359375,
0.006679534912109375,
0.004974365234375,
0.04119873046875,
-0.0010166168212890625,
0.002101898193359375,
0.0187225341796875,
0.0224151611328125,
-0.036712646484375,
-0.0124053955078125,
0.00937652587890625,
-0.001964569091796875,
0.0093231201171875,
0.049041748046875,
-0.01224517822265625,
0.007472991943359375,
-0.0200958251953125,
0.01055145263671875,
0.02105712890625,
0.038421630859375,
0.0005125999450683594,
0.0202178955078125,
0.018951416015625,
-0.0045623779296875,
-0.027130126953125,
0.00818634033203125,
-0.040924072265625,
0.00487518310546875,
0.0347900390625,
-0.0175323486328125,
0.00478363037109375,
-0.0027408599853515625,
-0.0088348388671875,
-0.0081787109375,
-0.0092926025390625,
-0.0396728515625,
0.02288818359375,
0.0170745849609375,
0.017333984375,
0.011749267578125,
-0.00038123130798339844,
0.047607421875,
0.01348876953125,
-0.0034351348876953125,
0.040802001953125,
-0.020416259765625,
-0.0175933837890625,
0.01018524169921875,
-0.01255035400390625,
-0.002231597900390625,
-0.03973388671875,
-0.006130218505859375,
-0.0660400390625,
0.005496978759765625,
-0.0216064453125,
-0.020965576171875,
-0.00559234619140625,
0.01372528076171875,
0.03179931640625,
0.00623321533203125,
0.019073486328125,
0.01514434814453125,
0.003643035888671875,
0.0225372314453125,
0.00870513916015625,
0.01190185546875,
0.0108795166015625,
-0.0309295654296875,
-0.0029506683349609375,
-0.00777435302734375,
-0.0189666748046875,
-0.019287109375,
-0.01436614990234375,
-0.00335693359375,
-0.018280029296875,
0.00018870830535888672,
0.01390838623046875,
0.0148773193359375,
-0.00749969482421875,
0.00933074951171875,
-0.01023101806640625,
0.0168304443359375,
-0.0204925537109375,
0.01031494140625,
-0.006755828857421875,
0.0258941650390625,
0.0159149169921875,
0.006160736083984375,
0.01186370849609375,
-0.0227508544921875,
0.0240478515625,
-0.01010894775390625,
-0.035797119140625,
0.03790283203125,
-0.004489898681640625,
-0.03466796875,
-0.005260467529296875,
0.00499725341796875,
-0.0313720703125,
0.0011758804321289062,
-0.0223388671875,
-0.0018672943115234375,
-0.0014047622680664062,
-0.02825927734375,
0.004077911376953125,
-0.0149993896484375,
0.005260467529296875,
-0.050140380859375,
0.0301055908203125,
-0.007114410400390625,
-0.0015316009521484375,
-0.01488494873046875,
-0.0172576904296875,
0.00644683837890625,
-0.030609130859375,
0.0216217041015625,
-0.0280609130859375,
-0.00572967529296875,
0.004199981689453125,
0.0225067138671875,
0.0216064453125,
-0.0198516845703125,
-0.00223541259765625,
0.034210205078125,
0.0089111328125,
-0.0201568603515625,
-0.0222320556640625,
0.009307861328125,
-0.01526641845703125,
0.03460693359375,
0.016815185546875,
-0.0132598876953125,
0.0038890838623046875,
0.03448486328125,
-0.023895263671875,
0.024505615234375,
0.020538330078125,
-0.00501251220703125,
-0.00008493661880493164,
0.0159759521484375,
-0.0062103271484375,
-0.01090240478515625,
0.0003769397735595703,
-0.004894256591796875,
-0.008575439453125,
0.0126800537109375,
0.0168304443359375,
0.007450103759765625,
0.00003427267074584961,
0.0164794921875,
-0.01499176025390625,
0.01073455810546875,
0.022186279296875,
-0.011016845703125,
-0.008087158203125,
0.00925445556640625,
0.016845703125,
-0.01824951171875,
-0.0011568069458007812,
0.0276641845703125,
-0.00791168212890625,
-0.0164337158203125,
0.0157623291015625,
-0.024871826171875,
-0.0022182464599609375,
-0.0220947265625,
-0.005046844482421875,
0.048004150390625,
0.05029296875,
-0.0197601318359375,
0.0224456787109375,
-0.004131317138671875,
0.0338134765625,
-0.015289306640625,
-0.02362060546875,
-0.0008592605590820312,
0.0235748291015625,
-0.04290771484375,
-0.0086212158203125,
-0.004268646240234375,
-0.0009450912475585938,
-0.02972412109375,
-0.013092041015625,
0.0188446044921875,
-0.042327880859375,
-0.0318603515625,
-0.0003097057342529297,
-0.0003559589385986328,
0.0230712890625,
-0.0204925537109375,
0.0275115966796875,
-0.0056304931640625,
0.0009012222290039062,
0.0093994140625,
0.01141357421875,
-0.01128387451171875,
-0.0184478759765625,
-0.02508544921875,
0.01270294189453125,
-0.0235595703125,
-0.0245819091796875,
-0.01666259765625,
-0.025665283203125,
-0.013427734375,
0.0222320556640625,
0.00719451904296875,
0.0110626220703125,
-0.0040130615234375,
-0.0029430389404296875,
-0.0029125213623046875,
-0.0391845703125,
-0.0054931640625,
0.00232696533203125,
0.0033588409423828125,
0.0009298324584960938,
-0.0016050338745117188,
-0.00896453857421875,
0.015838623046875,
-0.001796722412109375,
0.0372314453125,
-0.002590179443359375,
-0.0305023193359375,
-0.0015707015991210938,
0.01154327392578125,
0.0111541748046875,
-0.0303802490234375,
-0.00505828857421875,
0.025421142578125,
-0.00380706787109375,
0.0032958984375,
-0.0029296875,
-0.0223388671875,
-0.03076171875,
0.01104736328125,
0.019378662109375,
0.006397247314453125,
-0.012908935546875,
-0.032867431640625,
0.0167999267578125,
-0.0276947021484375,
-0.030242919921875,
-0.0006546974182128906,
0.0140380859375,
0.0079803466796875,
-0.004871368408203125,
0.037994384765625,
0.0298309326171875,
0.0177154541015625,
0.01141357421875,
0.000446319580078125,
-0.01071929931640625,
-0.010162353515625,
-0.019775390625,
0.01067352294921875,
0.005062103271484375,
-0.0133819580078125,
-0.043060302734375,
-0.0229644775390625,
-0.02301025390625,
-0.00019741058349609375,
-0.019378662109375,
0.0121307373046875,
-0.00440216064453125,
0.0296630859375,
0.001220703125,
0.0017538070678710938,
0.020721435546875,
-0.02197265625,
-0.03814697265625,
-0.005924224853515625,
-0.004810333251953125,
-0.025390625,
-0.0111083984375,
0.0287017822265625,
-0.03839111328125,
0.0100860595703125,
0.006298065185546875,
0.0056610107421875,
0.01100921630859375,
0.0279541015625,
-0.00989532470703125,
-0.0008516311645507812,
-0.0024166107177734375,
0.0024871826171875,
-0.01163482666015625,
0.002864837646484375,
0.02099609375,
0.004482269287109375,
-0.023712158203125,
0.005462646484375,
0.03759765625,
0.005321502685546875,
0.0035114288330078125,
0.0263824462890625,
-0.011810302734375,
-0.01303863525390625,
-0.0195770263671875,
-0.0089569091796875,
-0.0147705078125,
0.033935546875,
-0.007511138916015625,
0.048553466796875,
0.01447296142578125,
-0.015899658203125,
0.0032978057861328125,
-0.0079345703125,
-0.009368896484375,
-0.00604248046875,
-0.004261016845703125,
-0.009429931640625,
-0.030792236328125,
-0.004016876220703125,
-0.033843994140625,
0.012786865234375,
-0.00763702392578125,
-0.00638580322265625,
0.0201568603515625,
0.0005002021789550781,
0.00617218017578125,
-0.0035228729248046875,
-0.0263214111328125,
0.054656982421875,
0.045013427734375,
-0.03277587890625,
-0.01812744140625,
-0.038726806640625,
0.035552978515625,
-0.01422882080078125,
-0.0253448486328125,
0.005496978759765625,
0.0037593841552734375,
-0.01157379150390625,
-0.005558013916015625,
0.003841400146484375,
0.006320953369140625,
0.01366424560546875,
0.00894927978515625,
0.00029158592224121094,
0.01215362548828125,
-0.0009350776672363281,
0.004741668701171875,
0.004558563232421875,
0.01273345947265625,
0.00774383544921875,
0.01020050048828125,
-0.0157623291015625,
-0.0182342529296875,
0.00139617919921875,
-0.0017805099487304688,
-0.0028820037841796875,
0.0144195556640625,
-0.0020198822021484375,
-0.0267333984375,
-0.00386810302734375,
0.0308074951171875,
-0.04205322265625,
-0.0010156631469726562,
-0.00672149658203125,
-0.0254364013671875,
0.0009775161743164062,
0.01555633544921875,
-0.00128936767578125,
-0.03387451171875,
0.0003705024719238281,
0.004474639892578125,
0.0206451416015625,
0.0068206787109375,
0.007251739501953125,
0.0033111572265625,
-0.006481170654296875,
0.03680419921875,
0.0220947265625,
0.04046630859375,
0.02783203125,
-0.0196075439453125,
-0.017578125,
0.015838623046875,
-0.0165863037109375,
0.0121002197265625,
-0.03515625,
0.0217742919921875,
0.008819580078125,
0.00252532958984375,
0.016082763671875,
0.01334381103515625,
0.0196075439453125,
0.0233306884765625,
0.017242431640625,
-0.01409149169921875,
0.0022220611572265625,
0.01654052734375,
0.023406982421875,
0.029449462890625,
-0.0029296875,
0.0193328857421875,
0.0227203369140625,
-0.0288543701171875,
-0.0037975311279296875,
0.03021240234375,
-0.0006866455078125,
0.010284423828125,
-0.00662994384765625,
0.01256561279296875,
0.026702880859375,
-0.01282501220703125,
0.0198516845703125,
-0.03961181640625,
-0.0184326171875,
0.0150909423828125,
0.004856109619140625,
0.0142059326171875,
0.0186004638671875,
-0.016845703125,
-0.022552490234375,
0.016571044921875,
0.0004723072052001953,
0.0205841064453125,
0.01337432861328125,
0.005062103271484375,
-0.01116180419921875,
0.01512908935546875,
-0.0043182373046875,
-0.015960693359375,
-0.031829833984375,
-0.036834716796875,
0.033355712890625,
-0.020782470703125,
-0.027374267578125,
0.0034618377685546875,
-0.004230499267578125,
0.005916595458984375,
0.0135650634765625,
0.004909515380859375,
-0.00041604042053222656,
0.042999267578125,
0.0236358642578125,
0.0235748291015625,
0.023712158203125,
-0.015655517578125,
-0.01140594482421875,
0.003215789794921875,
-0.01418304443359375,
-0.01995849609375,
0.00885772705078125,
-0.0224456787109375,
0.01180267333984375,
-0.04119873046875,
-0.02264404296875,
-0.01152801513671875,
-0.002124786376953125,
-0.0026950836181640625,
-0.01473236083984375,
-0.0047454833984375,
0.0202484130859375,
-0.025909423828125,
-0.024810791015625,
0.029571533203125,
0.0081787109375,
-0.0089569091796875,
0.0218353271484375,
-0.0024738311767578125,
-0.01044464111328125,
0.0009675025939941406,
0.024566650390625,
0.0086212158203125,
-0.01129150390625,
0.0100250244140625,
0.01418304443359375,
-0.032135009765625,
0.009735107421875,
0.02117919921875,
-0.006313323974609375,
0.0307769775390625,
0.01259613037109375,
0.007602691650390625,
-0.0113372802734375,
0.0169830322265625,
0.01538848876953125,
-0.0287322998046875,
-0.02294921875,
-0.00815582275390625,
-0.0009679794311523438,
-0.00630950927734375,
0.0159149169921875,
0.03375244140625,
0.0152435302734375,
0.0115203857421875,
-0.0200347900390625,
-0.0005540847778320312,
-0.009765625,
0.01690673828125,
-0.039520263671875,
-0.0207977294921875,
-0.002452850341796875,
-0.010589599609375,
0.0019397735595703125,
0.0114593505859375,
0.00388336181640625,
-0.0052032470703125,
-0.0066986083984375,
0.04150390625,
-0.0194244384765625,
0.0103302001953125,
-0.001766204833984375,
-0.026031494140625,
0.01232147216796875,
-0.0244598388671875,
0.007007598876953125,
-0.012664794921875,
-0.038909912109375,
-0.019012451171875,
-0.010894775390625,
-0.0032291412353515625,
0.00318145751953125,
0.01546478271484375,
-0.01041412353515625,
-0.00890350341796875,
-0.004741668701171875,
0.00589752197265625,
-0.0164794921875,
0.0136566162109375,
0.0285797119140625,
-0.0225372314453125,
0.0023860931396484375,
0.05322265625,
-0.01276397705078125,
0.01910400390625,
-0.0215606689453125,
0.01751708984375,
-0.01885986328125,
0.0290374755859375,
-0.040863037109375,
0.0015249252319335938,
-0.0191497802734375,
-0.009490966796875,
0.012359619140625,
-0.0188446044921875,
0.00080108642578125,
-0.003025054931640625,
-0.017364501953125,
0.0135498046875,
0.002147674560546875,
0.01160430908203125,
-0.00855255126953125,
-0.00833892822265625,
-0.0216827392578125,
0.006107330322265625,
-0.048828125,
0.0109710693359375,
-0.00255584716796875,
0.01445770263671875,
-0.0301666259765625,
0.013763427734375,
-0.03350830078125,
0.0214996337890625,
-0.029449462890625,
0.00910186767578125,
0.00460052490234375,
-0.0012302398681640625,
0.01166534423828125,
-0.00852203369140625,
-0.01296234130859375,
-0.00853729248046875,
0.00684356689453125,
0.022308349609375,
0.004024505615234375,
0.0031986236572265625,
-0.0031757354736328125,
-0.03179931640625,
0.01015472412109375,
0.0113372802734375,
-0.01161956787109375,
-0.0107574462890625,
0.043212890625,
-0.001277923583984375,
-0.010009765625,
-0.00331878662109375,
0.01548004150390625,
0.01203155517578125,
-0.020965576171875,
0.0126495361328125,
0.03863525390625,
0.00888824462890625,
-0.0222930908203125,
0.0234527587890625,
0.037445068359375,
0.01116180419921875,
0.01517486572265625,
-0.00037169456481933594,
0.0125732421875,
-0.004108428955078125,
0.046630859375,
0.016510009765625,
-0.0233612060546875,
-0.031768798828125,
0.0013055801391601562,
-0.0233154296875,
-0.01285552978515625,
0.053497314453125,
0.0189361572265625,
-0.00923919677734375,
0.011322021484375,
-0.0015239715576171875,
-0.0452880859375,
-0.0119781494140625,
-0.01508331298828125,
0.044921875,
0.040740966796875,
-0.017669677734375,
-0.005489349365234375,
-0.0084991455078125,
-0.01364898681640625,
0.005123138427734375,
0.0006108283996582031,
0.016357421875,
-0.013702392578125,
0.00044655799865722656,
0.0280609130859375,
0.0009274482727050781,
0.0004801750183105469,
-0.03875732421875,
-0.0162811279296875,
0.0004901885986328125,
-0.022735595703125,
0.026214599609375,
0.0135345458984375,
-0.008514404296875,
-0.01230621337890625,
0.014434814453125,
-0.01519012451171875,
-0.01110076904296875,
0.01013946533203125,
-0.0013885498046875,
-0.0057373046875,
-0.008392333984375,
0.01050567626953125,
0.005161285400390625,
-0.0001926422119140625,
-0.03778076171875,
-0.015228271484375,
0.0198211669921875,
-0.0085296630859375,
-0.01154327392578125,
-0.0038394927978515625,
-0.01122283935546875,
0.01117706298828125,
-0.016937255859375,
-0.0228424072265625,
-0.0009541511535644531,
-0.00455474853515625,
-0.0070343017578125,
0.006595611572265625,
-0.0182342529296875,
-0.0406494140625,
-0.01073455810546875,
-0.01256561279296875,
0.025482177734375,
0.0038242340087890625,
0.0220947265625,
0.01123046875,
0.01226043701171875,
-0.0006518363952636719,
0.0185699462890625,
-0.0160369873046875,
0.02337646484375,
-0.0021266937255859375,
-5.364418029785156e-7,
0.036468505859375,
0.0022106170654296875,
0.006771087646484375,
0.01171112060546875,
-0.050994873046875,
0.006244659423828125,
0.0026340484619140625,
0.00048804283142089844,
0.0176544189453125,
-0.026641845703125,
0.042144775390625,
0.023895263671875,
0.052276611328125,
0.019073486328125,
-0.0129547119140625,
0.0019664764404296875,
0.005718231201171875,
0.01386260986328125,
-0.03265380859375,
0.016510009765625,
0.0035152435302734375,
0.036163330078125,
0.041656494140625,
0.004741668701171875,
0.0006647109985351562,
0.00006908178329467773,
-0.043121337890625,
0.0037784576416015625,
-0.008453369140625,
-0.0004706382751464844,
-0.0033111572265625,
-0.026092529296875,
0.0361328125,
0.019744873046875,
-0.00893402099609375,
0.03607177734375,
-0.0316162109375,
-0.0052947998046875,
0.00531768798828125,
-0.00437164306640625,
-0.022125244140625,
0.022674560546875,
0.007465362548828125,
-0.00885772705078125,
0.0345458984375,
-0.0131988525390625,
-0.002197265625,
0.02069091796875,
-0.0159454345703125,
0.01123046875,
-0.01418304443359375,
-0.049896240234375,
0.017669677734375,
0.01471710205078125,
0.002254486083984375,
-0.0169525146484375,
0.006847381591796875,
0.00004094839096069336,
0.0223236083984375,
0.010528564453125,
-0.006534576416015625,
0.00018656253814697266,
-0.010467529296875,
-0.00864410400390625,
0.016632080078125,
0.0053863525390625,
-0.0163421630859375,
0.034820556640625,
-0.0114593505859375,
-0.01035308837890625,
0.018768310546875,
0.0146484375,
-0.032958984375,
-0.00827789306640625,
-0.0229644775390625,
0.01555633544921875,
0.015869140625,
-0.0058441162109375,
0.01328277587890625,
0.02081298828125,
-0.006977081298828125,
-0.0131988525390625,
-0.017608642578125,
0.013031005859375,
0.0333251953125,
-0.0322265625,
-0.018890380859375,
0.03631591796875,
-0.00909423828125,
0.011260986328125,
-0.002307891845703125,
-0.02197265625,
0.015350341796875,
-0.0144195556640625,
-0.03082275390625,
-0.001079559326171875,
-0.0079803466796875,
-0.044097900390625,
0.0008211135864257812,
-0.01181793212890625,
-0.004669189453125,
0.01328277587890625,
-0.01174163818359375,
-0.00562286376953125,
-0.00574493408203125,
-0.0143585205078125,
-0.0173492431640625,
-0.0139923095703125,
0.002643585205078125,
-0.0041351318359375,
0.0087127685546875,
-0.01763916015625,
-0.00623321533203125,
-0.0174102783203125,
0.0112762451171875,
-0.007602691650390625,
-0.0106658935546875,
-0.0132598876953125,
-0.0192413330078125,
-0.00002390146255493164,
-0.0094146728515625,
0.01103973388671875,
0.0184783935546875,
-0.038543701171875,
-0.02130126953125,
0.0037994384765625,
-0.0164794921875,
-0.006900787353515625,
-0.00737762451171875,
-0.045196533203125,
0.0219879150390625,
-0.019256591796875,
0.032470703125,
0.0118865966796875,
-0.00524139404296875,
-0.038543701171875,
0.01528167724609375,
0.01509857177734375,
0.04205322265625,
0.00078582763671875,
-0.047088623046875,
0.02069091796875,
-0.0440673828125,
-0.011810302734375,
0.03717041015625,
0.01137542724609375,
-0.01947021484375,
0.0010213851928710938,
-0.0038318634033203125,
0.0268402099609375,
0.01593017578125,
0.01483917236328125,
0.00534820556640625,
0.0039043426513671875,
0.0142364501953125,
-0.015716552734375,
0.016021728515625,
0.013916015625,
-0.01258087158203125,
-0.019500732421875,
0.0017881393432617188,
0.0005831718444824219,
0.0108184814453125,
0.011993408203125,
-0.0199127197265625,
-0.03173828125,
-0.02984619140625,
0.0176239013671875,
-0.002994537353515625,
-0.0269622802734375,
0.0215301513671875,
-0.000007212162017822266,
0.0195159912109375,
-0.0032806396484375,
0.0012044906616210938,
0.00823974609375,
-0.013427734375,
-0.0086212158203125,
-0.006626129150390625,
-0.005023956298828125,
0.01505279541015625,
0.0184783935546875
] |
ours_551
|
Notice that \(x=2011^{2011}\). Because \(2011\) is prime, \(x\) has \(2012\) positive integer factors.
\(\boxed{2012}\)
|
2012
|
{
"competition": "us_comps",
"dataset": "Ours",
"posts": null,
"source": "OMOSoln2.md"
}
|
If
$$
2011^{2011^{2012}}=x^{x}
$$
for some positive integer \(x\), how many positive integer factors does \(x\) have?
|
[
"/Mathematics/DiscreteMathematics/DivisionProblems",
"/Mathematics/DiscreteMathematics/GeneralDiscreteMathematics/DiscreteMath",
"/Mathematics/DiscreteMathematics/GeneralDiscreteMathematics/DiscreteMathematics",
"/Mathematics/NumberTheory/Divisors/Divides",
"/Mathematics/NumberTheory/Divisors/Divisible",
"/Mathematics/NumberTheory/Divisors/Divisor",
"/Mathematics/NumberTheory/GeneralNumberTheory/ElementaryNumberTheory",
"/Mathematics/NumberTheory/GeneralNumberTheory/HigherArithmetic",
"/Mathematics/NumberTheory/GeneralNumberTheory/NumberTheory",
"/Mathematics/NumberTheory/PrimeNumbers/MiscellaneousPrimes",
"/Mathematics/NumberTheory/PrimeNumbers/PrimeFactorization"
] |
Match the exponents by expressing x as a power of 2011, giving x = 2011^{2011}.
|
[
-0.00006443262100219727,
-0.0181121826171875,
0.0233917236328125,
0.0352783203125,
-0.0005693435668945312,
0.03546142578125,
0.019287109375,
-0.0010166168212890625,
-0.004180908203125,
-0.00917816162109375,
0.0262603759765625,
-0.079345703125,
-0.0017518997192382812,
0.0236053466796875,
-0.0207366943359375,
-0.039794921875,
0.043731689453125,
0.0129547119140625,
-0.00013971328735351562,
-0.0026073455810546875,
-0.0066375732421875,
-0.01316070556640625,
-0.0204315185546875,
0.051666259765625,
-0.041900634765625,
-0.01995849609375,
-0.018524169921875,
-0.0190582275390625,
0.01186370849609375,
-0.00296783447265625,
-0.01078033447265625,
-0.00730133056640625,
0.0251617431640625,
-0.0340576171875,
0.0014057159423828125,
-0.0166778564453125,
-0.0119476318359375,
-0.0016155242919921875,
-0.01296234130859375,
-0.032867431640625,
0.0018339157104492188,
0.031494140625,
0.005008697509765625,
0.006229400634765625,
0.0070648193359375,
-0.0029773712158203125,
-0.00449371337890625,
0.005680084228515625,
0.006481170654296875,
-0.00492095947265625,
0.0002237558364868164,
0.0001341104507446289,
0.0269317626953125,
-0.019317626953125,
-0.047393798828125,
-0.04296875,
0.00909423828125,
0.005298614501953125,
0.02276611328125,
0.00138092041015625,
0.00037550926208496094,
-0.0186614990234375,
0.0045166015625,
-0.00891876220703125,
-0.0008826255798339844,
-0.0159454345703125,
0.0216217041015625,
-0.0005512237548828125,
0.0034236907958984375,
0.0018320083618164062,
0.000034332275390625,
0.004108428955078125,
-0.01410675048828125,
0.00771331787109375,
0.023223876953125,
-0.0119476318359375,
-0.00728607177734375,
0.004528045654296875,
0.04364013671875,
0.01364898681640625,
-0.00740814208984375,
-0.0012292861938476562,
0.019866943359375,
0.00608062744140625,
0.00893402099609375,
0.031280517578125,
-0.00476837158203125,
0.00644683837890625,
-0.0021533966064453125,
-0.013153076171875,
0.0010833740234375,
0.07720947265625,
-0.0009741783142089844,
-0.03985595703125,
-0.003864288330078125,
0.007419586181640625,
0.01323699951171875,
-0.0162811279296875,
-0.024078369140625,
0.0123291015625,
-0.024444580078125,
-0.00970458984375,
-0.004291534423828125,
-0.00982666015625,
-0.07049560546875,
-0.009490966796875,
-0.0171356201171875,
0.012237548828125,
0.0164337158203125,
-0.0069732666015625,
-0.00701141357421875,
-0.0004520416259765625,
-0.0001093149185180664,
0.0163421630859375,
-0.02020263671875,
0.01517486572265625,
0.005977630615234375,
0.008056640625,
0.00829315185546875,
-0.007232666015625,
0.005504608154296875,
0.0341796875,
-0.0008063316345214844,
0.0206146240234375,
0.01263427734375,
-1.1920928955078125e-7,
0.00962066650390625,
0.0017642974853515625,
-0.004608154296875,
-0.0137481689453125,
0.022857666015625,
0.01041412353515625,
-0.039306640625,
-0.01995849609375,
-0.0408935546875,
0.00531005859375,
0.0023441314697265625,
-0.007160186767578125,
0.005123138427734375,
-0.019927978515625,
0.006839752197265625,
-0.0213775634765625,
-0.004215240478515625,
-0.0091094970703125,
0.01238250732421875,
0.004673004150390625,
0.0083465576171875,
-0.0487060546875,
0.00658416748046875,
-0.00677490234375,
0.01371002197265625,
0.003322601318359375,
0.0038013458251953125,
0.0240020751953125,
0.015716552734375,
0.01336669921875,
0.008941650390625,
0.005977630615234375,
0.007904052734375,
-0.0060272216796875,
0.01416778564453125,
0.007511138916015625,
-0.0249176025390625,
0.0035305023193359375,
-0.006351470947265625,
-0.01137542724609375,
0.004177093505859375,
-0.019775390625,
-0.007274627685546875,
-0.033905029296875,
0.01239013671875,
0.0095062255859375,
0.015899658203125,
-0.0155181884765625,
-0.0069122314453125,
0.0251617431640625,
-0.0179443359375,
0.003780364990234375,
0.007080078125,
-0.0171661376953125,
-0.005535125732421875,
-0.01422119140625,
0.01389312744140625,
-0.0082244873046875,
0.0117950439453125,
-0.0186767578125,
-0.00011461973190307617,
0.02081298828125,
0.0216827392578125,
0.0001741647720336914,
-0.01459503173828125,
-0.027557373046875,
-0.0016374588012695312,
-0.004375457763671875,
-0.01209259033203125,
0.0025959014892578125,
-0.005771636962890625,
0.001979827880859375,
0.01427459716796875,
0.011993408203125,
-0.007472991943359375,
0.016082763671875,
0.047576904296875,
0.02984619140625,
-0.0162506103515625,
0.00685882568359375,
0.0245513916015625,
-0.0157012939453125,
-0.007083892822265625,
0.0017461776733398438,
0.0082244873046875,
0.002529144287109375,
-0.0020542144775390625,
-0.06536865234375,
-0.020416259765625,
-0.00998687744140625,
-0.0189666748046875,
0.0137176513671875,
0.02532958984375,
-0.0286712646484375,
0.0025177001953125,
0.00768280029296875,
-0.0031890869140625,
0.002166748046875,
-0.0143890380859375,
-0.02105712890625,
0.006229400634765625,
0.0155181884765625,
-0.002696990966796875,
0.0038928985595703125,
0.02032470703125,
0.0118408203125,
-0.01508331298828125,
0.0076141357421875,
0.0100860595703125,
0.005756378173828125,
-0.027008056640625,
0.00620269775390625,
0.0004642009735107422,
0.001316070556640625,
0.00698089599609375,
-0.030853271484375,
-0.005016326904296875,
-0.0029888153076171875,
0.0038356781005859375,
0.0025634765625,
0.0012845993041992188,
-0.002788543701171875,
-0.01052093505859375,
-0.02166748046875,
-0.003498077392578125,
-0.0034656524658203125,
0.00356292724609375,
-0.0030803680419921875,
0.013641357421875,
-0.02142333984375,
0.01392364501953125,
-0.045074462890625,
0.0038890838623046875,
0.024200439453125,
-0.0020618438720703125,
-0.03192138671875,
-0.01910400390625,
-0.014373779296875,
-0.026092529296875,
0.006130218505859375,
-0.01209259033203125,
-0.01309967041015625,
0.0191192626953125,
0.0191802978515625,
0.0271759033203125,
-0.00789642333984375,
-0.018218994140625,
-0.007480621337890625,
-0.022064208984375,
-0.02362060546875,
0.0050201416015625,
0.002666473388671875,
0.016693115234375,
-0.00994110107421875,
0.027557373046875,
0.005611419677734375,
-0.0168914794921875,
0.012664794921875,
-0.0027446746826171875,
-0.00946807861328125,
0.0151519775390625,
-0.0308685302734375,
-0.0189361572265625,
0.01042938232421875,
0.008331298828125,
0.0055999755859375,
-0.0328369140625,
-0.0094451904296875,
0.043701171875,
-0.0029544830322265625,
-0.000316619873046875,
0.0157928466796875,
-0.01038360595703125,
-0.01245880126953125,
0.021392822265625,
0.01073455810546875,
-0.0037975311279296875,
0.0166778564453125,
0.005046844482421875,
0.004337310791015625,
-0.0006632804870605469,
0.01468658447265625,
-0.005657196044921875,
-0.0350341796875,
0.0024471282958984375,
-0.0007824897766113281,
-0.0038051605224609375,
0.031280517578125,
-0.015594482421875,
-0.044769287109375,
0.0023593902587890625,
0.0111236572265625,
-0.0008139610290527344,
-0.004425048828125,
-0.01280975341796875,
-0.0035037994384765625,
-0.0069580078125,
0.0033740997314453125,
-0.00859832763671875,
0.0130462646484375,
0.01502227783203125,
0.0168609619140625,
-0.0128631591796875,
0.0318603515625,
-0.051727294921875,
0.0248565673828125,
0.0168914794921875,
-0.00012242794036865234,
-0.0037403106689453125,
0.01654052734375,
0.0020275115966796875,
0.022796630859375,
-0.00563812255859375,
-0.005157470703125,
-0.00521087646484375,
-0.021697998046875,
0.031585693359375,
0.004764556884765625,
-0.016876220703125,
-0.00531005859375,
0.00968170166015625,
-0.017669677734375,
-0.01430511474609375,
-0.01317596435546875,
0.0199432373046875,
0.00485992431640625,
-0.0205078125,
-0.0004925727844238281,
-0.038116455078125,
0.01448822021484375,
0.0029144287109375,
0.004058837890625,
0.0286407470703125,
0.0031223297119140625,
0.01395416259765625,
-0.01611328125,
0.00809478759765625,
-0.0017261505126953125,
-0.0018739700317382812,
-0.013671875,
0.00299072265625,
0.00826263427734375,
-0.0243988037109375,
0.0038585662841796875,
-0.01485443115234375,
-0.0247039794921875,
-0.003879547119140625,
-0.0126953125,
-0.03741455078125,
0.0013532638549804688,
0.01580810546875,
-0.0017538070678710938,
0.0005550384521484375,
0.0269622802734375,
0.0168609619140625,
0.0011606216430664062,
-0.0189971923828125,
0.04095458984375,
-0.0075225830078125,
-0.025115966796875,
-0.00432586669921875,
-0.036773681640625,
-0.031280517578125,
0.01021575927734375,
-0.01220703125,
0.0070343017578125,
-0.003814697265625,
0.00860595703125,
-0.024322509765625,
-0.01515960693359375,
-0.0113677978515625,
-0.00420379638671875,
0.02716064453125,
-0.009521484375,
0.021392822265625,
0.00006496906280517578,
0.0009169578552246094,
0.036895751953125,
0.01041412353515625,
-0.01110076904296875,
-0.01568603515625,
-0.0038280487060546875,
-0.01047515869140625,
0.006317138671875,
0.0155181884765625,
-0.035919189453125,
0.0311279296875,
0.0058746337890625,
0.0106964111328125,
-0.0135650634765625,
0.04425048828125,
-0.012908935546875,
-0.0249786376953125,
0.0004355907440185547,
-0.0037479400634765625,
-0.0014944076538085938,
0.00817108154296875,
-0.0080718994140625,
0.0021190643310546875,
0.0157012939453125,
-0.047149658203125,
0.01763916015625,
0.0287322998046875,
-0.004207611083984375,
0.006725311279296875,
-0.012542724609375,
-0.00859832763671875,
0.0081024169921875,
-0.00751495361328125,
0.0176239013671875,
-0.0125885009765625,
0.0029926300048828125,
-0.0176849365234375,
0.0261383056640625,
-0.0177459716796875,
0.007022857666015625,
-0.0256195068359375,
0.002361297607421875,
-0.035186767578125,
0.002941131591796875,
-0.006671905517578125,
0.024810791015625,
-0.02093505859375,
-0.018951416015625,
-0.006053924560546875,
0.01033782958984375,
-0.00270843505859375,
-0.00241851806640625,
-0.00559234619140625,
0.006439208984375,
0.0305023193359375,
-0.009735107421875,
0.006031036376953125,
-0.03924560546875,
-0.01434326171875,
-0.027374267578125,
-0.035125732421875,
-0.00745391845703125,
-0.036773681640625,
-0.00630950927734375,
-0.024810791015625,
0.0125274658203125,
0.0111236572265625,
-0.0036334991455078125,
-0.00211334228515625,
-0.02960205078125,
0.049957275390625,
-0.0203399658203125,
-0.01371002197265625,
0.020965576171875,
0.01337432861328125,
0.042724609375,
-0.0085296630859375,
-0.00836181640625,
0.032562255859375,
-0.01511383056640625,
0.003215789794921875,
0.0159454345703125,
0.0082550048828125,
0.039520263671875,
0.04046630859375,
0.0017833709716796875,
-0.018524169921875,
0.0209808349609375,
0.036651611328125,
0.03662109375,
-0.0072479248046875,
-0.0151824951171875,
-0.0244598388671875,
-0.0289154052734375,
-0.0010690689086914062,
-0.0010690689086914062,
-0.0030956268310546875,
0.0180816650390625,
0.01318359375,
-0.0038127899169921875,
-0.0133819580078125,
0.020111083984375,
0.00922393798828125,
0.0027294158935546875,
0.0172119140625,
-0.000004589557647705078,
-0.00444793701171875,
-0.010711669921875,
-0.0002655982971191406,
0.00691986083984375,
0.0236968994140625,
0.00799560546875,
0.0180206298828125,
-0.0148773193359375,
0.008209228515625,
0.00632476806640625,
0.006847381591796875,
-0.0250396728515625,
-0.0020046234130859375,
0.007122039794921875,
0.034332275390625,
0.002197265625,
0.01433563232421875,
-0.00046563148498535156,
0.026458740234375,
-0.0167999267578125,
0.0096588134765625,
-0.00278472900390625,
-0.0277862548828125,
-0.0054168701171875,
-0.019683837890625,
0.03289794921875,
-0.00742340087890625,
0.00505828857421875,
0.0164947509765625,
-0.01995849609375,
-0.01291656494140625,
0.0142059326171875,
-0.0075531005859375,
0.00853729248046875,
-0.00988006591796875,
-0.00852203369140625,
0.0092926025390625,
-0.03900146484375,
-0.0156707763671875,
0.014129638671875,
-0.01242828369140625,
0.027008056640625,
0.00971221923828125,
0.0034694671630859375,
0.027984619140625,
0.00894927978515625,
0.002719879150390625,
0.0298919677734375,
-0.00933074951171875,
-0.0016431808471679688,
-0.0262908935546875,
0.023651123046875,
0.008026123046875,
0.00167083740234375,
0.00846099853515625,
0.00960540771484375,
0.0088348388671875,
-0.0020904541015625,
0.0012369155883789062,
-0.0250396728515625,
-0.01959228515625,
-0.0301513671875,
-0.01568603515625,
-0.0019397735595703125,
-0.012939453125,
0.007686614990234375,
0.0038623809814453125,
-0.00650787353515625,
-0.0261383056640625,
0.0217742919921875,
-0.015869140625,
-0.03863525390625,
0.018310546875,
0.007053375244140625,
-0.02520751953125,
-0.029266357421875,
0.039306640625,
-0.0234527587890625,
0.0247344970703125,
0.0097198486328125,
0.02264404296875,
0.016021728515625,
-0.009185791015625,
-0.0027923583984375,
-0.0108184814453125,
0.019317626953125,
0.01343536376953125,
-0.018951416015625,
0.0197296142578125,
-0.00995635986328125,
-0.025604248046875,
0.004207611083984375,
0.05474853515625,
0.0187835693359375,
0.00894927978515625,
-0.0079498291015625,
-0.005352020263671875,
-0.0210113525390625,
0.0006585121154785156,
0.050567626953125,
0.0005426406860351562,
-0.007694244384765625,
0.0249786376953125,
-0.01244354248046875,
0.027984619140625,
0.0227203369140625,
0.0146484375,
0.020843505859375,
0.00479888916015625,
-0.02935791015625,
0.0313720703125,
-0.02105712890625,
-0.032257080078125,
-0.007091522216796875,
0.02276611328125,
0.00785064697265625,
-0.0106353759765625,
-0.0238494873046875,
0.011474609375,
0.025238037109375,
-0.01953125,
-0.004703521728515625,
0.0207366943359375,
-0.024200439453125,
0.035919189453125,
0.01788330078125,
0.00984954833984375,
0.00882720947265625,
-0.0033435821533203125,
0.0001481771469116211,
-0.0262908935546875,
0.00127410888671875,
0.022186279296875,
0.0074462890625,
-0.0051116943359375,
-0.064453125,
0.01477813720703125,
-0.004192352294921875,
-0.0026149749755859375,
0.01263427734375,
-0.0078125,
0.0038661956787109375,
-0.00820159912109375,
-0.011444091796875,
-0.0167694091796875,
0.0181427001953125,
0.0121917724609375,
0.03985595703125,
-0.0016527175903320312,
-0.017669677734375,
-0.0081634521484375,
0.01422119140625,
-0.00244903564453125,
0.026702880859375,
0.0268402099609375,
-0.0157318115234375,
-0.035919189453125,
-0.0008563995361328125,
0.00009357929229736328,
-0.019744873046875,
0.026031494140625,
0.01641845703125,
0.031463623046875,
-0.020751953125,
0.008697509765625,
-0.0303192138671875,
0.011260986328125,
-0.035797119140625,
-0.018463134765625,
0.0005888938903808594,
0.031341552734375,
0.0196075439453125,
0.004375457763671875,
-0.0035610198974609375,
0.02978515625,
-0.015899658203125,
0.01715087890625,
0.004001617431640625,
0.0006089210510253906,
-0.0057525634765625,
0.0005207061767578125,
-0.003116607666015625,
0.003574371337890625,
-0.0006260871887207031,
0.0103912353515625,
0.028106689453125,
0.01006317138671875,
-0.023590087890625,
0.0164031982421875,
-0.02557373046875,
-0.02679443359375,
-0.0247802734375,
0.02685546875,
-0.0169219970703125,
0.01678466796875,
-0.01192474365234375,
-0.0045623779296875,
-0.030548095703125,
-0.00316619873046875,
0.017364501953125,
-0.0258331298828125,
0.01094818115234375,
-0.0251312255859375,
-0.0133514404296875,
-0.021148681640625,
-0.008209228515625,
-0.019073486328125,
0.055755615234375,
0.0198516845703125,
-0.01178741455078125,
-0.0091552734375,
-0.017303466796875,
-0.019500732421875,
0.009857177734375,
-0.01033782958984375,
0.0171966552734375,
0.0166778564453125,
-0.004459381103515625,
0.0137786865234375,
-0.02252197265625,
-0.0229034423828125,
0.01299285888671875,
0.00600433349609375,
-0.004192352294921875,
0.013671875,
-0.0011196136474609375,
-0.024078369140625,
-0.010986328125,
0.013702392578125,
-0.04473876953125,
0.0152740478515625,
0.00643157958984375,
0.0275726318359375,
-0.00846099853515625,
0.0283660888671875,
-0.01605224609375,
0.00650787353515625,
0.009613037109375,
-0.01081085205078125,
0.0013761520385742188,
0.02099609375,
0.0027523040771484375,
0.0244903564453125,
0.03240966796875,
0.010345458984375,
-0.0224761962890625,
-0.02117919921875,
-0.00298309326171875,
0.0294036865234375,
-0.01049041748046875,
0.010467529296875,
0.0247650146484375,
-0.03033447265625,
0.020416259765625,
0.0085906982421875,
-0.01543426513671875,
-0.00740814208984375,
-0.0017070770263671875,
-0.0130615234375,
0.0002162456512451172,
0.00823974609375,
0.046661376953125,
-0.02117919921875,
-0.0188140869140625,
0.01514434814453125,
0.0145721435546875,
0.03472900390625,
-0.01175689697265625,
-0.012786865234375,
-0.004848480224609375,
0.039764404296875,
-0.00476837158203125,
0.027496337890625,
-0.0352783203125,
0.0169830322265625,
-0.00907135009765625,
-0.0150604248046875,
0.0051727294921875,
0.00766754150390625,
-0.03704833984375,
0.0270843505859375,
-0.01012420654296875,
-0.00766754150390625,
0.0212249755859375,
0.0220947265625,
-0.0010204315185546875,
-0.0552978515625,
-0.01065826416015625,
-0.0236663818359375,
-0.00926971435546875,
-0.02764892578125,
0.00007033348083496094,
0.0123748779296875,
-0.026824951171875,
-0.037841796875,
0.01898193359375,
-0.006988525390625,
-0.005962371826171875,
0.0292510986328125,
-0.0014142990112304688,
-0.00475311279296875,
0.0301361083984375,
0.0288238525390625,
-0.037109375,
0.0125732421875,
0.005687713623046875,
0.017669677734375,
-0.0227203369140625,
0.0008254051208496094,
0.000036776065826416016,
0.0028057098388671875,
0.0161895751953125,
-0.0044097900390625,
-0.019439697265625,
0.018585205078125,
-0.01387786865234375,
-0.038421630859375,
0.007297515869140625,
-0.024658203125,
0.0303192138671875,
0.01141357421875,
0.0135345458984375,
-0.0216064453125,
-0.02703857421875,
0.032623291015625,
0.02325439453125,
0.01529693603515625,
0.028656005859375,
-0.005741119384765625,
-0.0254669189453125,
-0.006824493408203125,
-0.02423095703125,
0.0063629150390625,
-0.00710296630859375,
0.0165557861328125,
-0.031402587890625,
-0.0009937286376953125,
-0.013092041015625,
-0.0236663818359375,
-0.0262451171875,
-0.0087738037109375,
0.016632080078125,
0.0197296142578125,
0.01556396484375,
0.00887298583984375,
0.01593017578125,
0.00003987550735473633,
0.01430511474609375,
-0.0161285400390625,
0.01506805419921875,
0.0169677734375,
-0.0045318603515625,
-0.03326416015625,
-0.0248565673828125,
-0.01021575927734375,
0.00797271728515625,
-0.0035839080810546875,
-0.012939453125,
0.0380859375,
-0.0007147789001464844,
0.0051116943359375,
-0.023712158203125,
0.0090789794921875,
0.0221099853515625,
0.00879669189453125,
0.01910400390625,
0.021575927734375,
-0.01031494140625,
-0.00817108154296875,
0.0279998779296875,
0.0186309814453125,
0.0038051605224609375,
-0.0082244873046875,
-0.061065673828125,
-0.0007610321044921875,
-0.0030002593994140625,
0.0275726318359375,
0.019866943359375,
0.0283050537109375,
0.033416748046875,
-0.0016450881958007812,
-0.0160064697265625,
-0.0013408660888671875,
-0.0249786376953125,
-0.01085662841796875,
-0.00351715087890625,
-0.00847625732421875,
-0.0006070137023925781,
-0.00766754150390625,
0.003231048583984375,
-0.0176239013671875,
-0.055145263671875,
-0.0237579345703125,
-0.01313018798828125,
0.03607177734375,
0.0216217041015625,
-0.03350830078125,
-0.0257415771484375,
0.0018291473388671875,
0.0015859603881835938,
0.032318115234375,
0.0019292831420898438,
-0.0012845993041992188,
-0.0148773193359375,
-0.0032291412353515625,
0.0298614501953125,
-0.050140380859375,
-0.002071380615234375,
-0.0250244140625,
-0.009765625,
0.01122283935546875,
0.0194549560546875,
0.0197601318359375,
-0.0293121337890625,
-0.00789642333984375,
-0.00699615478515625,
0.001888275146484375,
-0.0010890960693359375,
-0.0189361572265625,
0.006275177001953125,
-0.01316070556640625,
0.029296875,
0.007110595703125,
0.0037384033203125,
-0.0150299072265625,
-0.00257110595703125,
0.0308990478515625,
0.0166015625,
0.006786346435546875,
0.0237579345703125,
0.0098876953125,
-0.01320648193359375,
-0.0012035369873046875,
-0.01152801513671875,
0.0011873245239257812,
0.052642822265625,
-0.0230255126953125,
-0.01708984375,
0.0282440185546875,
0.0071258544921875,
-0.0211029052734375,
0.028228759765625,
-0.005031585693359375,
-0.00893402099609375,
-0.0192718505859375,
0.033203125,
-0.0161895751953125,
0.00616455078125,
-0.01018524169921875,
-0.005794525146484375,
0.0262908935546875,
-0.0261077880859375,
-0.02679443359375,
0.0192413330078125,
-0.047393798828125,
0.0007476806640625,
0.0092926025390625,
0.00562286376953125,
0.017181396484375,
-0.0220794677734375,
0.01369476318359375,
0.0007729530334472656,
-0.00951385498046875,
-0.00646209716796875,
-0.0289306640625,
-0.0106353759765625,
0.0004322528839111328,
0.023040771484375,
-0.0062713623046875,
0.004901885986328125,
-0.005847930908203125,
0.0183868408203125,
-0.00994873046875,
0.000751495361328125,
0.0111541748046875,
-0.015289306640625,
-0.0037593841552734375,
0.0114593505859375,
0.02752685546875,
-0.01035308837890625,
0.0191497802734375,
0.033294677734375,
-0.036956787109375,
-0.0019521713256835938,
0.042388916015625,
-0.0100860595703125,
-0.0060577392578125,
0.007640838623046875,
-0.0384521484375,
0.0017299652099609375,
-0.01055908203125,
-0.00496673583984375,
-0.035614013671875,
0.01052093505859375,
0.0066375732421875,
-0.0221099853515625,
-0.002170562744140625,
-0.00965118408203125,
0.00043082237243652344,
-0.0244140625,
0.003559112548828125,
0.00310516357421875,
0.0185394287109375,
0.006412506103515625,
-0.0044708251953125,
0.010833740234375,
-0.015625,
-0.022918701171875,
0.0115966796875,
-0.02447509765625,
-0.019622802734375,
0.01210784912109375,
0.031494140625,
0.00269317626953125,
-0.00983428955078125,
-0.008819580078125,
-0.0067291259765625,
0.02728271484375,
-0.024688720703125,
0.00505828857421875,
0.030487060546875,
0.034210205078125,
-0.0272216796875,
-0.01467132568359375,
0.0206756591796875,
-0.021942138671875,
0.010406494140625,
-0.0149078369140625,
-0.007152557373046875,
-0.0254974365234375,
0.00580596923828125,
-0.006465911865234375,
-0.0109405517578125,
0.0015497207641601562,
0.041473388671875,
0.0201416015625,
0.00009143352508544922,
-0.0284576416015625,
0.005397796630859375,
-0.022308349609375,
-0.0128936767578125,
-0.00494384765625,
0.03363037109375,
0.027801513671875,
0.0017337799072265625,
-0.01171875,
0.0009160041809082031,
-0.00937652587890625,
0.0164337158203125,
-0.01287078857421875,
0.016021728515625,
0.0214691162109375,
0.0193328857421875,
0.0228729248046875,
0.019622802734375,
-0.05224609375,
-0.0007266998291015625,
-0.01558685302734375,
-0.021881103515625,
0.00004857778549194336,
0.001789093017578125,
0.0127716064453125,
-0.00634765625,
0.0088043212890625,
0.0031642913818359375,
-0.0273590087890625,
-0.003841400146484375,
-0.001293182373046875,
0.01513671875,
0.0002777576446533203,
0.013641357421875,
-0.0155792236328125,
0.01114654541015625,
-0.0037746429443359375,
-0.049072265625,
0.03851318359375,
0.006374359130859375,
0.024017333984375,
-0.0160369873046875,
-0.0027942657470703125,
-0.0018062591552734375,
-0.011505126953125,
0.028045654296875,
-0.01129913330078125,
-0.0163421630859375,
-0.01861572265625,
0.01186370849609375,
-0.0202178955078125,
-0.0041351318359375,
-0.02410888671875,
0.0338134765625,
-0.01373291015625,
0.028472900390625,
0.0256805419921875,
-0.013031005859375,
-0.0220489501953125,
-0.00783538818359375,
0.0144195556640625,
0.0016336441040039062,
0.0165252685546875,
-0.0237884521484375,
-0.010711669921875,
-0.016265869140625,
0.0115203857421875,
-0.005031585693359375,
0.0156402587890625,
-0.02001953125,
-0.0093994140625,
-0.039642333984375,
0.00656890869140625,
0.0216827392578125,
-0.006053924560546875,
0.0109100341796875,
0.028045654296875,
0.004955291748046875,
0.0217132568359375,
-0.00939178466796875,
0.019866943359375,
0.0149383544921875,
0.01250457763671875,
-0.0224761962890625,
0.005252838134765625,
-0.007965087890625,
-0.001918792724609375,
-0.00759124755859375,
-0.025604248046875,
-0.021453857421875,
-0.005664825439453125,
0.0045166015625,
0.0305328369140625,
0.00888824462890625,
-0.0245513916015625,
0.01204681396484375,
-0.01003265380859375,
-0.0290679931640625,
0.01543426513671875,
0.007724761962890625,
0.030914306640625,
-0.053497314453125,
-0.0179901123046875,
-0.0082244873046875,
0.0178375244140625,
0.006046295166015625,
0.00603485107421875,
-0.021270751953125,
-0.0345458984375,
-0.01105499267578125,
0.04730224609375,
-0.033538818359375,
0.00922393798828125,
0.017181396484375,
-0.015533447265625,
-0.00679779052734375,
-0.0201263427734375,
-0.0092010498046875,
0.022796630859375,
-0.034576416015625,
0.0179595947265625,
0.00948333740234375,
0.0233001708984375,
-0.034332275390625,
-0.0132293701171875,
-0.00997161865234375,
-0.021636962890625,
0.01491546630859375,
-0.0029468536376953125,
-0.0016326904296875,
0.000942230224609375,
0.00933074951171875,
0.001110076904296875,
-0.01206207275390625,
0.01056671142578125,
-0.0279998779296875,
0.035736083984375,
0.016876220703125,
-0.019195556640625,
-0.0019073486328125,
-0.0084228515625,
0.00586700439453125,
-0.01442718505859375,
-0.0003788471221923828,
0.01227569580078125,
0.01348876953125,
-0.010711669921875,
-0.004520416259765625,
-0.03973388671875,
0.033660888671875,
0.006931304931640625,
-0.013671875,
-0.03143310546875,
-0.0143890380859375,
0.006717681884765625,
-0.01739501953125,
0.0032253265380859375,
-0.01375579833984375,
-0.005931854248046875,
-0.01026153564453125,
-0.0267181396484375,
0.018035888671875,
0.0196685791015625,
0.010406494140625,
0.008544921875,
-0.01019287109375,
-0.023895263671875,
-0.0174713134765625,
0.011138916015625,
0.0195159912109375,
-0.0179290771484375,
0.048004150390625,
0.0089874267578125,
-0.049041748046875,
-0.004909515380859375,
-0.001377105712890625,
-0.0025844573974609375,
0.0006470680236816406,
0.01447296142578125,
0.004627227783203125,
-0.0171356201171875,
0.01140594482421875,
0.0293121337890625,
-0.021728515625,
0.020172119140625,
0.00238800048828125,
0.00653076171875,
0.005405426025390625,
0.0148162841796875,
-0.0413818359375,
-0.02813720703125,
0.02020263671875,
0.05084228515625,
0.004177093505859375,
0.01458740234375,
-0.038970947265625,
0.033660888671875,
-0.010955810546875,
0.0148468017578125,
0.0125732421875,
-0.0106353759765625,
-0.045867919921875,
0.0178985595703125,
-0.012115478515625,
-0.005401611328125,
0.0255584716796875,
0.01373291015625,
-0.002201080322265625,
0.00719451904296875,
-0.0118560791015625,
-0.0240631103515625,
0.01049041748046875,
0.02880859375,
0.017822265625,
0.016326904296875,
-0.060516357421875,
-0.0059814453125,
0.004070281982421875,
-0.00421905517578125,
0.050506591796875,
-0.0015211105346679688,
-0.00811767578125,
0.044219970703125,
-0.006305694580078125,
0.0261688232421875,
0.01279449462890625,
0.01215362548828125,
0.0006432533264160156,
0.020721435546875,
0.0151214599609375,
-0.01129150390625,
-0.00787353515625,
-0.01428985595703125,
-0.0084381103515625,
-0.0199127197265625,
-0.004283905029296875,
0.02362060546875,
0.0236968994140625,
0.00463104248046875,
-0.0231781005859375,
-0.007293701171875,
-0.0142822265625,
0.029937744140625,
-0.00179290771484375,
0.0171051025390625,
0.045745849609375,
-0.021514892578125,
-0.020843505859375,
0.0258026123046875,
0.01153564453125,
0.01629638671875,
0.0131072998046875,
0.035736083984375,
-0.01001739501953125,
-0.0030231475830078125,
-0.0015764236450195312,
-0.036041259765625,
-0.003009796142578125,
0.00829315185546875,
-0.0062408447265625,
-0.0087738037109375,
0.00946044921875,
0.0012464523315429688,
-0.052886962890625,
-0.0259857177734375,
0.01238250732421875,
0.01384735107421875,
0.0203399658203125,
0.01042938232421875,
0.003833770751953125,
-0.0016336441040039062,
-0.022308349609375,
-0.004398345947265625,
-0.0158233642578125,
-0.00766754150390625,
0.0187835693359375,
0.0081024169921875,
-0.0146331787109375,
0.0086822509765625,
-0.0040740966796875,
0.0053558349609375,
-0.01418304443359375,
-0.0148468017578125,
-0.0303802490234375,
-0.022430419921875,
-0.0110931396484375,
0.007366180419921875,
-0.011444091796875,
0.0194549560546875,
-0.01013946533203125,
0.0251617431640625,
-0.0029888153076171875,
0.032989501953125,
0.019744873046875,
-0.034393310546875,
-0.0244293212890625,
0.047119140625,
-0.0093536376953125,
0.0018510818481445312,
-0.024505615234375,
0.0065765380859375,
-0.0372314453125,
0.054931640625,
0.037261962890625,
-0.01328277587890625,
0.006679534912109375,
0.0186309814453125,
0.0267333984375,
-0.01395416259765625,
0.00044155120849609375,
-0.012603759765625,
-0.020233154296875,
-0.009735107421875,
0.019866943359375,
-0.0283966064453125,
0.0290985107421875,
-0.0190887451171875,
-0.00894927978515625,
-0.0152740478515625,
0.0159912109375,
0.025726318359375,
-0.03759765625,
0.015777587890625,
-0.019500732421875,
-0.006076812744140625,
0.01629638671875,
0.0010986328125,
-0.019256591796875,
0.00293731689453125,
0.01250457763671875,
-0.002841949462890625,
-0.01280975341796875,
-0.018341064453125,
-0.032623291015625,
0.01904296875,
-0.01073455810546875,
-0.0010175704956054688,
0.001636505126953125,
-0.019195556640625,
0.022125244140625,
0.0170745849609375,
-0.0182952880859375,
0.046966552734375,
0.0151824951171875,
-0.037994384765625,
0.003326416015625,
-0.0179901123046875,
-0.02783203125,
0.010406494140625,
0.0217742919921875,
-0.00794219970703125,
0.025421142578125,
-0.009124755859375,
0.002960205078125,
0.03179931640625,
0.0280609130859375,
-0.01235198974609375,
0.006496429443359375,
-0.0064239501953125,
0.01085662841796875,
-0.036285400390625,
0.03485107421875,
0.0108184814453125,
0.007366180419921875,
-0.017425537109375,
0.01274871826171875,
0.007068634033203125,
-0.00870513916015625,
-0.0000032782554626464844,
0.0135650634765625,
-0.0194854736328125,
0.005756378173828125,
-0.01189422607421875,
-0.0086212158203125,
0.0146331787109375,
0.031585693359375,
0.0072784423828125,
-0.01357269287109375,
0.0087127685546875,
0.01222991943359375,
-0.0247650146484375,
0.01352691650390625,
-0.00417327880859375,
0.00691986083984375,
-0.0079803466796875,
-0.014739990234375,
-0.029296875,
-0.014678955078125,
-0.0238494873046875,
0.005863189697265625,
-0.037689208984375,
0.02386474609375,
-0.00379180908203125,
0.027191162109375,
0.01000213623046875,
-0.0034999847412109375,
0.025909423828125,
0.019866943359375,
0.02008056640625,
-0.0389404296875,
-0.0170745849609375,
0.043243408203125,
0.01351165771484375,
-0.014251708984375,
-0.003459930419921875,
-0.0270233154296875,
-0.011627197265625,
0.015838623046875,
0.0036182403564453125,
0.0201873779296875,
0.00029468536376953125,
-0.039764404296875,
-0.0003864765167236328,
0.0025634765625,
0.00322723388671875,
-0.050384521484375,
0.0061492919921875,
0.0017185211181640625,
0.00690460205078125,
0.019866943359375,
-0.012359619140625,
-0.0245819091796875,
0.0065155029296875,
0.0169219970703125,
-0.00046133995056152344,
0.029296875,
-0.00942230224609375,
-0.01032257080078125,
-0.06610107421875,
0.0162811279296875,
-0.038055419921875,
0.003742218017578125,
-0.006946563720703125,
0.038604736328125,
-0.0423583984375,
0.0224761962890625,
-0.00861358642578125,
0.05322265625,
0.030731201171875,
-0.0235748291015625,
-0.0229339599609375,
0.01454925537109375,
-0.01318359375,
-0.01092529296875,
0.0041351318359375,
-0.01348114013671875,
-0.033111572265625,
-0.001575469970703125,
-0.0112762451171875,
0.045440673828125,
0.0028018951416015625,
-0.0208587646484375,
0.00928497314453125,
-0.00433349609375,
0.0000209808349609375,
0.053680419921875,
0.01216888427734375,
0.00885772705078125,
-0.00910186767578125,
0.019561767578125,
-0.00970458984375,
-0.017364501953125,
-0.0009927749633789062,
0.024749755859375,
0.00554656982421875,
-0.004985809326171875,
-0.048828125,
0.003940582275390625,
0.00428009033203125,
-0.03515625,
0.0124359130859375,
-0.015869140625,
0.003604888916015625,
0.0015745162963867188,
-0.0025730133056640625,
0.0183258056640625,
0.022735595703125,
-0.00337982177734375,
0.0254364013671875,
-0.0025844573974609375,
-0.01451873779296875,
-0.0018825531005859375,
-0.030059814453125,
-0.003543853759765625,
0.013031005859375,
-0.005313873291015625,
-0.00870513916015625,
0.0005130767822265625,
-0.00945281982421875,
0.006519317626953125,
-0.026275634765625,
0.0214996337890625,
-0.00897979736328125,
-0.01078033447265625,
-0.0015497207641601562,
0.0106658935546875,
-0.0149993896484375,
-0.0313720703125,
-0.01232147216796875,
-0.0023345947265625,
-0.0228424072265625,
-0.0194854736328125,
0.0406494140625,
0.0023784637451171875,
-0.024383544921875,
0.0236663818359375,
0.01019287109375,
-0.0167236328125,
-0.036163330078125,
-0.038177490234375,
-0.0022449493408203125,
-0.0242462158203125,
0.01438140869140625,
-0.00292205810546875,
-0.0034847259521484375,
-0.022979736328125,
0.007709503173828125,
0.00417327880859375,
0.0023136138916015625,
-0.014373779296875,
-0.016357421875,
0.009368896484375,
0.006763458251953125,
0.0032024383544921875,
-0.00830841064453125,
-0.019683837890625,
0.0172882080078125,
-0.040191650390625,
0.03448486328125,
0.02813720703125,
-0.0012216567993164062,
-0.0014600753784179688,
-0.0008578300476074219,
-0.0141448974609375,
0.020751953125,
-0.00572967529296875,
-0.034027099609375,
0.004505157470703125,
-0.00304412841796875,
-0.02423095703125,
-0.00389862060546875,
-0.05194091796875,
0.0294647216796875,
0.000682830810546875,
-0.006580352783203125,
0.0169830322265625,
-0.00940704345703125,
-0.042266845703125,
-0.01152801513671875,
0.01462554931640625,
-0.0078125,
0.03509521484375,
0.00787353515625,
0.024505615234375,
0.0245208740234375,
0.002460479736328125,
0.004344940185546875,
-0.0085296630859375,
-0.005474090576171875,
0.002685546875,
-0.0250091552734375,
0.0294036865234375,
0.018951416015625,
0.0234222412109375,
0.0226287841796875,
0.0020427703857421875,
0.01427459716796875,
-0.016754150390625,
0.0166778564453125,
-0.00626373291015625,
-0.0278778076171875,
0.016693115234375,
0.0068206787109375,
-0.00370025634765625,
0.0261077880859375,
0.01030731201171875,
-0.01398468017578125,
0.00930023193359375,
-0.0280914306640625,
0.033721923828125,
0.01508331298828125,
-0.0051422119140625,
-0.0100555419921875,
-0.0260467529296875,
-0.019134521484375,
0.0205230712890625,
-0.01041412353515625,
0.0008082389831542969,
-0.00705718994140625,
0.0005636215209960938,
-0.006214141845703125,
-0.0210418701171875,
0.0174560546875,
-0.00970458984375,
0.036376953125,
-0.0194854736328125,
0.0018768310546875,
0.0151214599609375,
-0.0306549072265625,
-0.039794921875,
0.0296173095703125,
-0.032623291015625,
0.0265045166015625,
-0.00211334228515625,
0.0038509368896484375,
0.004611968994140625,
0.03167724609375,
0.043853759765625,
-0.01021575927734375,
0.007678985595703125,
-0.0258026123046875,
0.0036029815673828125,
-0.00040268898010253906,
-0.0042572021484375,
0.00799560546875,
0.002410888671875,
-0.02032470703125,
0.0186309814453125,
-0.004436492919921875,
0.0067596435546875,
0.0188751220703125,
-0.01108551025390625,
0.003223419189453125,
-0.02655029296875,
0.00281524658203125,
-0.01062774658203125,
-0.0200347900390625,
-0.038726806640625,
0.025634765625,
-0.0021915435791015625,
0.0243682861328125,
-0.0202789306640625,
0.02105712890625,
-0.0101776123046875,
0.00955963134765625,
0.0099945068359375,
-0.01513671875,
-0.0225830078125,
-0.005199432373046875,
-0.047332763671875,
-0.0179595947265625,
0.025787353515625,
-0.01013946533203125,
0.005336761474609375,
0.01238250732421875,
0.05584716796875,
0.0226898193359375,
-0.0303802490234375,
0.0194854736328125,
0.0188751220703125,
0.0018367767333984375,
0.0137176513671875,
-0.042083740234375,
0.0136260986328125,
-0.025482177734375,
-0.0017175674438476562,
0.046478271484375,
0.021209716796875,
-0.03021240234375,
0.006328582763671875,
0.0235443115234375,
-0.01593017578125,
0.01438140869140625,
0.006458282470703125,
0.0201263427734375,
0.01244354248046875,
-0.008056640625,
0.0008921623229980469,
0.003810882568359375,
-0.00896453857421875,
-0.0241851806640625,
0.0202178955078125,
-0.005191802978515625,
0.016876220703125,
-0.0060577392578125,
0.0229034423828125,
-0.019378662109375,
0.00540924072265625,
-0.005126953125,
0.006931304931640625,
0.019744873046875,
0.02978515625,
-0.0213165283203125,
0.00193023681640625,
-0.0191650390625,
-0.016082763671875,
-0.0089569091796875,
0.01369476318359375,
-0.007221221923828125,
0.004871368408203125,
0.0005397796630859375,
0.004150390625,
-0.0239105224609375,
-0.0252838134765625,
-0.0289764404296875,
0.037506103515625,
0.021392822265625,
-0.00988006591796875,
-0.00836181640625,
0.026763916015625,
-0.0060882568359375,
-0.0006961822509765625,
0.0025615692138671875,
0.005908966064453125,
-0.01490020751953125,
-0.0017557144165039062,
-0.023895263671875,
0.00376129150390625,
0.0083465576171875,
-0.0103607177734375,
0.01849365234375,
-0.0224456787109375,
0.005950927734375,
0.00914764404296875,
0.020263671875,
-0.025970458984375,
-0.010955810546875,
0.0017194747924804688,
-0.01666259765625,
-0.025238037109375,
-0.01441192626953125,
0.0035266876220703125,
-0.04974365234375,
-0.011962890625,
-0.00457763671875,
0.02044677734375,
0.0290374755859375,
0.021759033203125,
-0.0166168212890625,
0.0103759765625,
-0.012054443359375,
0.0361328125,
0.001007080078125,
-0.01739501953125,
-0.01971435546875,
0.01158905029296875,
-0.01202392578125,
0.06787109375,
0.0033512115478515625,
0.036773681640625,
0.022186279296875,
-0.007781982421875,
0.00460052490234375,
0.013671875,
-0.01203155517578125,
-0.018585205078125,
0.00563812255859375,
-0.000579833984375,
0.020538330078125,
-0.00008594989776611328,
-0.0369873046875,
-0.007740020751953125,
0.00762176513671875,
0.018402099609375,
0.025726318359375,
-0.00021898746490478516,
-0.0168914794921875,
0.014129638671875,
0.00696563720703125,
0.02703857421875,
0.004680633544921875,
-0.0482177734375,
0.013671875,
0.01224517822265625,
-0.00846099853515625,
0.005847930908203125,
0.0030956268310546875,
-0.00548553466796875,
0.023773193359375,
-0.00399017333984375,
-0.023681640625,
0.025299072265625,
0.01202392578125,
-0.0193328857421875,
0.0043182373046875,
0.007587432861328125,
0.01253509521484375,
0.01983642578125,
-0.00399017333984375,
0.008544921875,
-0.01641845703125,
0.01494598388671875,
0.02032470703125,
-0.0292816162109375,
0.080810546875,
-0.0196075439453125,
0.032012939453125,
-0.0103759765625,
-0.0261688232421875,
0.006786346435546875,
-0.00045490264892578125,
-0.01678466796875,
-0.01812744140625,
-0.01141357421875,
0.0213623046875,
0.031158447265625,
0.01690673828125,
-0.00212860107421875,
-0.0167999267578125,
0.0010366439819335938,
-0.0506591796875,
-0.01143646240234375,
0.02996826171875,
-0.0007762908935546875,
0.007488250732421875,
0.046600341796875,
-0.007465362548828125,
0.0140838623046875,
0.017608642578125,
-0.0029850006103515625,
-0.0106658935546875,
0.0008301734924316406,
0.0017337799072265625,
-0.002597808837890625,
0.006378173828125,
0.020233154296875,
-0.042236328125,
0.005641937255859375,
0.00431060791015625,
-0.030303955078125,
0.017578125,
0.0013074874877929688,
-0.0010652542114257812,
-0.0102081298828125,
0.0083160400390625,
0.0182952880859375,
0.0072479248046875,
-0.005069732666015625,
0.001789093017578125,
0.003505706787109375,
-0.00479888916015625,
-0.007244110107421875,
0.00341033935546875,
-0.00144195556640625,
0.01143646240234375,
-0.0003933906555175781,
0.02520751953125,
0.0190887451171875,
0.01959228515625,
0.00806427001953125,
0.002574920654296875,
0.046905517578125,
0.037841796875,
-0.0238037109375,
-0.047698974609375,
-0.02197265625,
-0.03375244140625,
0.0202789306640625,
0.0127716064453125,
0.0291595458984375,
-0.01947021484375,
-0.0341796875,
0.01171875,
-0.012237548828125,
0.0316162109375,
-0.0263824462890625,
0.0216217041015625,
-0.021148681640625,
-0.010955810546875,
-0.0260467529296875,
-0.0004911422729492188,
-0.003246307373046875,
-0.016571044921875,
-0.013427734375,
-0.006805419921875,
-0.01172637939453125,
-0.041290283203125,
-0.00951385498046875,
-0.0150604248046875,
-0.0194549560546875,
0.042144775390625,
0.004108428955078125,
-0.003414154052734375,
-0.0038604736328125,
0.00807952880859375,
-0.02960205078125,
-0.03656005859375,
0.041229248046875,
-0.0038299560546875,
-0.03643798828125,
-0.0175628662109375,
-0.02044677734375,
-0.01474761962890625,
0.01561737060546875,
-0.01372528076171875,
0.03546142578125,
0.0091400146484375,
-0.01071929931640625,
-0.016632080078125,
0.00048470497131347656,
-0.0179901123046875,
0.0006737709045410156,
0.021942138671875,
0.01666259765625,
0.01322174072265625,
-0.0083465576171875,
-0.01421356201171875,
0.017120361328125,
-0.0242462158203125,
0.0000014901161193847656,
0.00043272972106933594,
0.00812530517578125,
0.00884246826171875,
0.00901031494140625,
-0.0141754150390625,
-0.0176239013671875,
-0.0159149169921875,
-0.037933349609375,
-0.01995849609375,
0.004802703857421875,
0.013031005859375,
0.0192413330078125,
0.0019407272338867188,
-0.0033817291259765625,
0.04803466796875,
-0.0197601318359375,
-0.024139404296875,
-0.004241943359375,
-0.0111846923828125,
-0.02947998046875,
-0.01361083984375,
0.0406494140625,
-0.0152435302734375,
-0.0435791015625,
0.0167999267578125,
-0.0026302337646484375,
0.0160675048828125,
-0.000637054443359375,
0.0186309814453125,
0.018646240234375,
-0.005584716796875,
0.00391387939453125,
0.0244598388671875,
0.01763916015625,
-0.0273284912109375,
-0.0413818359375,
-0.027679443359375,
-0.01032257080078125,
0.0037746429443359375,
0.004581451416015625,
-0.00665283203125,
0.0276031494140625,
-0.00644683837890625,
0.0035266876220703125,
0.0494384765625,
-0.005512237548828125,
-0.0279693603515625,
0.0158233642578125,
-0.0100250244140625,
0.016326904296875,
0.0068511962890625,
0.007457733154296875,
0.0264129638671875,
0.0013322830200195312,
-0.0112152099609375,
0.016876220703125,
0.0099945068359375,
-0.00893402099609375,
0.0251312255859375,
-0.0013713836669921875,
0.02685546875,
-0.00745391845703125,
0.0139617919921875,
0.0196380615234375,
-0.00533294677734375,
0.005649566650390625,
-0.0259552001953125,
-0.00843048095703125,
-0.029083251953125,
-0.041290283203125,
0.05718994140625,
-0.020477294921875,
0.00775146484375,
0.01074981689453125,
-0.004253387451171875,
-0.0233306884765625,
-0.035797119140625,
0.00992584228515625,
-0.005260467529296875,
0.023712158203125,
0.0304412841796875,
-0.0078887939453125,
0.009124755859375,
-0.01090240478515625,
0.01369476318359375,
0.0137786865234375,
-0.0204925537109375,
-0.01056671142578125,
0.037384033203125,
0.0222320556640625,
0.0007691383361816406,
-0.01500701904296875,
0.020355224609375,
-0.01131439208984375,
-0.0108184814453125,
-0.0267181396484375,
0.019073486328125,
-0.010772705078125,
0.0165863037109375,
0.0107574462890625,
-0.026611328125,
0.01038360595703125,
-0.00839996337890625,
-0.001251220703125,
0.0223388671875,
0.0134124755859375,
0.020721435546875,
0.0257110595703125,
0.003131866455078125,
0.0014171600341796875,
-0.01367950439453125,
-0.00901031494140625,
-0.007160186767578125,
0.002552032470703125,
0.0056915283203125,
-0.0005574226379394531,
0.034423828125,
0.0245513916015625,
-0.006134033203125,
-0.022308349609375,
0.0096435546875,
-0.033721923828125,
-0.035125732421875,
-0.00342559814453125,
-0.01800537109375,
0.00826263427734375,
-0.0057373046875,
-0.0189056396484375,
0.008331298828125,
0.0277252197265625,
-0.01082611083984375,
-0.00853729248046875,
0.031494140625,
0.01050567626953125,
0.015472412109375,
-0.007534027099609375,
0.054779052734375,
-0.0215606689453125,
0.0150604248046875,
0.006732940673828125,
-0.0105438232421875,
-0.0164337158203125,
-0.0029392242431640625,
0.01183319091796875,
-0.0026340484619140625,
-0.005924224853515625,
0.02716064453125,
-0.00347137451171875,
-0.0106048583984375,
0.0157928466796875,
-0.02264404296875,
-0.01139068603515625,
-0.035858154296875,
0.0076141357421875,
-0.02618408203125,
-0.022491455078125,
0.02166748046875,
0.036651611328125,
0.00339508056640625,
0.023040771484375,
0.0267791748046875,
0.0292816162109375,
-0.03155517578125,
-0.0156707763671875,
-0.0274200439453125,
0.0168304443359375,
0.008758544921875,
0.01751708984375,
0.0089874267578125,
0.028472900390625,
0.0255279541015625,
0.0185089111328125,
-0.0118560791015625,
0.02252197265625,
-0.00473785400390625,
-0.01230621337890625,
0.01258087158203125,
-0.038909912109375,
0.0012989044189453125,
-0.01380157470703125,
-0.013519287109375,
-0.034271240234375,
-0.00788116455078125,
0.0024051666259765625,
0.00702667236328125,
-0.01543426513671875,
-0.023712158203125,
0.00675201416015625,
-0.0074005126953125,
-0.02301025390625,
-0.0235137939453125,
-0.0020751953125,
-0.02764892578125,
-0.00766754150390625,
-0.0157318115234375,
0.004230499267578125,
0.0138092041015625,
-0.0015697479248046875,
-0.0161590576171875,
0.0081634521484375,
-0.0114898681640625,
-0.00958251953125,
-0.003559112548828125,
0.00374603271484375,
0.0189666748046875,
-0.002132415771484375,
0.0164642333984375,
-0.01499176025390625,
0.0106658935546875,
-0.0015392303466796875,
0.0187225341796875,
-0.018524169921875,
0.011444091796875,
0.006496429443359375,
-0.00759124755859375,
0.0088348388671875,
0.0164794921875,
-0.0330810546875,
0.028167724609375,
-0.003910064697265625,
-0.01038360595703125,
-0.0112762451171875,
0.005809783935546875,
-0.0056610107421875,
-0.0141448974609375,
-0.006565093994140625,
-0.0171661376953125,
-0.005096435546875,
0.012908935546875,
0.0016565322875976562,
0.01010894775390625,
0.0042572021484375,
0.04315185546875,
-0.01036834716796875,
0.0033283233642578125,
0.0027561187744140625,
-0.002475738525390625,
-0.0240936279296875,
0.00975799560546875,
0.048919677734375,
-0.00359344482421875,
-0.01284027099609375,
0.021942138671875,
0.027191162109375,
-0.0007410049438476562,
-0.0005965232849121094,
-0.0232086181640625,
0.02850341796875,
0.0146636962890625,
-0.0240478515625,
-0.0216827392578125,
0.0212860107421875,
0.007198333740234375,
-0.0377197265625,
-0.0006761550903320312,
0.0265960693359375,
0.0030956268310546875,
0.0011243820190429688,
-0.01161956787109375,
-0.0243682861328125,
-0.013946533203125,
-0.0229949951171875,
0.005886077880859375,
0.0272674560546875,
0.007167816162109375,
0.002742767333984375,
0.05462646484375,
-0.0109710693359375,
0.01396942138671875,
-0.020782470703125,
-0.0093536376953125,
-0.003597259521484375,
-0.006908416748046875,
0.00914764404296875,
-0.00539398193359375,
-0.033660888671875,
0.00676727294921875,
0.004581451416015625,
0.02734375,
-0.00888824462890625,
0.002765655517578125,
0.006317138671875,
0.0323486328125,
-0.003963470458984375,
-0.0023250579833984375,
0.02069091796875,
-0.0018482208251953125,
-0.0221710205078125,
-0.011077880859375,
0.009368896484375,
-0.0189666748046875,
-0.01190185546875,
0.01558685302734375,
-0.0216064453125,
-0.0108642578125,
-0.00435638427734375,
-0.020904541015625,
-0.0212860107421875,
-0.0218963623046875,
0.0145263671875,
-0.040740966796875,
0.00676727294921875,
0.0124359130859375,
0.0203704833984375,
0.03057861328125,
-0.02093505859375,
0.01078033447265625,
-0.02215576171875,
-0.007335662841796875,
-0.007114410400390625,
-0.0185394287109375,
0.0157470703125,
0.01904296875,
0.00977325439453125,
-0.02899169921875,
0.0221405029296875,
0.006420135498046875,
-0.0135498046875,
-0.029296875,
0.01093292236328125,
-0.0180511474609375,
0.0158233642578125,
0.01271820068359375,
0.0260772705078125,
-0.0041961669921875,
-0.01197052001953125,
-0.01198577880859375,
0.017578125,
0.000934600830078125,
0.0030536651611328125,
-0.0016088485717773438,
0.0136871337890625,
0.0135650634765625,
-0.030029296875,
0.029571533203125,
0.0254058837890625,
0.02801513671875,
0.018341064453125,
-0.01322174072265625,
0.02874755859375,
0.016693115234375,
-0.0115203857421875,
-0.0283660888671875,
0.0277557373046875,
0.0277252197265625,
-0.041046142578125,
-0.020477294921875,
-0.0031604766845703125,
0.051544189453125,
0.0015993118286132812,
-0.003177642822265625,
0.05401611328125,
-0.029083251953125,
-0.0189361572265625,
0.0015888214111328125,
0.04400634765625,
-0.006011962890625,
0.022369384765625,
0.007503509521484375,
-0.0093841552734375,
-0.00418853759765625,
-0.0219573974609375,
0.007190704345703125,
-0.002628326416015625,
0.031402587890625,
0.0207061767578125,
-0.011383056640625,
-0.014678955078125,
0.008056640625,
-0.044921875,
-0.018829345703125,
-0.0203704833984375,
0.037628173828125,
0.03607177734375,
0.013763427734375,
-0.02301025390625,
-0.017333984375,
-0.019378662109375,
0.046661376953125,
0.0014944076538085938,
0.026153564453125,
-0.0205078125,
-0.0236053466796875,
0.004974365234375,
-0.014892578125,
0.01226806640625,
-0.0033054351806640625,
-0.020416259765625,
0.026947021484375,
-0.0236968994140625,
0.0006594657897949219,
0.00638580322265625,
0.00164031982421875,
-0.0144500732421875,
0.046600341796875,
-0.035064697265625,
-0.0215301513671875,
-0.027801513671875,
-0.022216796875,
0.003330230712890625,
-0.0032787322998046875,
-0.00968170166015625,
-0.025604248046875,
-0.02337646484375,
-0.0108795166015625,
-0.0250396728515625,
0.01605224609375,
-0.0167694091796875,
-0.022979736328125,
-0.0114593505859375,
0.00814056396484375,
0.0165557861328125,
-0.0046844482421875,
0.0105438232421875,
-0.035552978515625,
0.002513885498046875,
0.00789642333984375,
0.051239013671875,
-0.0065460205078125,
-0.047698974609375,
0.0127716064453125,
-0.010528564453125,
0.0042572021484375,
0.01084136962890625,
-0.001506805419921875,
0.010772705078125,
0.0343017578125,
0.026336669921875,
-0.048309326171875,
-0.0216217041015625,
0.012176513671875,
-0.01226043701171875,
-0.0285491943359375,
0.03594970703125,
-0.0010194778442382812,
0.02899169921875,
0.061492919921875,
-0.029052734375,
0.01248931884765625,
-0.0038013458251953125,
0.0183258056640625,
0.0018892288208007812,
-0.0169677734375,
-0.01007843017578125,
-0.0007462501525878906,
0.032867431640625,
0.00917816162109375,
0.002162933349609375,
-0.0042877197265625,
0.029998779296875,
0.0169830322265625,
-0.01000213623046875,
0.01119232177734375,
-0.0300750732421875,
0.005695343017578125,
0.054229736328125,
-0.013885498046875,
0.0145416259765625,
-0.040069580078125,
-0.0186004638671875,
0.008392333984375,
0.01404571533203125,
0.0019159317016601562,
-0.008880615234375,
-0.00994873046875,
-0.004730224609375,
0.034210205078125,
-0.016204833984375,
0.03387451171875,
-0.0237884521484375,
-0.00350189208984375,
0.00829315185546875,
0.0300445556640625,
0.00390625,
-0.01287841796875,
-0.00027632713317871094,
-0.029449462890625,
0.0021915435791015625,
-0.00368499755859375,
-0.006664276123046875,
-0.0010013580322265625,
-0.0025844573974609375,
0.0021343231201171875,
0.0027523040771484375,
-0.006175994873046875,
-0.00484466552734375,
-0.00893402099609375,
0.0010366439819335938,
-0.01351165771484375,
0.00605010986328125,
-0.0235137939453125,
0.0079498291015625,
0.0043792724609375,
0.027191162109375,
0.02362060546875,
0.01415252685546875,
-0.02410888671875,
0.0230560302734375,
-0.007598876953125,
-0.01197052001953125,
0.0213470458984375,
0.0207061767578125,
-0.00365447998046875,
0.01557159423828125,
0.01261138916015625,
-0.00403594970703125,
-0.0010747909545898438,
-0.043426513671875,
0.0272369384765625,
0.0029144287109375,
-0.01837158203125,
-0.0128631591796875,
0.0161895751953125,
-0.00836181640625,
-0.0037250518798828125,
-0.0277099609375,
0.0064239501953125,
0.0271759033203125,
-0.005237579345703125,
-0.0206298828125,
-0.02386474609375,
-0.0184173583984375,
0.0023746490478515625,
-0.0281524658203125,
0.0098724365234375,
0.0158538818359375,
0.0070953369140625,
-0.0271759033203125,
0.01425933837890625,
-0.0335693359375,
0.002964019775390625,
0.0164947509765625,
-0.019561767578125,
-0.03350830078125,
-0.019775390625,
0.044830322265625,
0.0077056884765625,
-0.00012373924255371094,
-0.0183258056640625,
-0.01837158203125,
-0.022247314453125,
0.00852203369140625,
-0.0031108856201171875,
-0.017303466796875,
-0.024139404296875,
0.007152557373046875,
-0.0271148681640625,
0.0161895751953125,
0.036468505859375,
0.0008273124694824219,
-0.0088958740234375,
-0.018035888671875,
-0.0152587890625,
-0.0121307373046875,
-0.0013647079467773438,
-0.006359100341796875,
-0.03131103515625,
0.0171661376953125,
0.0093994140625,
-0.00289154052734375,
-0.018768310546875,
0.0030727386474609375,
0.005428314208984375,
-0.035308837890625,
0.0162200927734375,
-0.0196075439453125,
-0.0103912353515625,
-0.01537322998046875,
-0.00933837890625,
-0.00443267822265625,
0.01001739501953125,
0.028045654296875,
-0.0023059844970703125,
-0.037200927734375,
0.0384521484375,
-0.03424072265625,
-0.00446319580078125,
-0.004901885986328125,
0.0001951456069946289,
0.0034770965576171875,
-0.0135955810546875,
0.0183258056640625,
0.00237274169921875,
-0.01163482666015625,
0.01190948486328125,
0.01366424560546875,
-0.00684356689453125,
-0.021697998046875,
-0.000598907470703125,
-0.043548583984375,
0.00039649009704589844,
0.016754150390625,
0.0064544677734375,
-0.01751708984375,
-0.01122283935546875,
-0.006687164306640625,
0.024261474609375,
0.0263671875,
-0.0109100341796875,
-0.0263519287109375,
0.006008148193359375,
0.01146697998046875,
0.01348114013671875,
-0.00606536865234375,
-0.023101806640625,
-0.0007748603820800781,
-0.01268768310546875,
-0.0048675537109375,
-0.0396728515625,
0.00881195068359375,
-0.01033782958984375,
-0.0198974609375,
-0.03167724609375,
-0.00878143310546875,
-0.02423095703125
] |
ours_552
|
The number of trailing zeros when \( 2012! \) is written in base \( p \) is given by
\[
\left\lfloor\frac{2012}{p}\right\rfloor + \left\lfloor\frac{2012}{p^{2}}\right\rfloor + \cdots
\]
We require this sum to be at least \( p \):
\[
\left\lfloor\frac{2012}{p}\right\rfloor + \left\lfloor\frac{2012}{p^{2}}\right\rfloor + \cdots \geq p
\]
This implies:
\[
\frac{2012}{p-1} = \frac{2012}{p} + \frac{2012}{p^{2}} + \cdots > p
\]
From this inequality, we derive:
\[
p(p-1) < 2012
\]
Since \( p \) is a prime number, we find that \( p \leq 43 \). Checking \( p = 43 \), we see it satisfies the inequality, so the largest prime \( p \) is \( 43 \).
\(\boxed{43}\)
|
43
|
{
"competition": "us_comps",
"dataset": "Ours",
"posts": null,
"source": "OMOSoln2.md"
}
|
Find the largest prime number \( p \) such that when \( 2012! \) is written in base \( p \), it has at least \( p \) trailing zeroes.
|
[
"/Mathematics/NumberTheory/GeneralNumberTheory/ElementaryNumberTheory",
"/Mathematics/NumberTheory/GeneralNumberTheory/HigherArithmetic",
"/Mathematics/NumberTheory/GeneralNumberTheory/NumberTheory",
"/Mathematics/NumberTheory/PrimeNumbers/PrimeNumberProperties"
] |
Use Legendre’s formula for the exponent of p in 2012! and bound the sum by a geometric series to obtain p(p‑1) < 2012.
|
[
-0.000044286251068115234,
-0.015045166015625,
0.0231781005859375,
0.02471923828125,
-0.00016009807586669922,
0.0130157470703125,
0.01806640625,
0.019989013671875,
0.0029163360595703125,
0.016693115234375,
-0.01349639892578125,
-0.043243408203125,
-0.003292083740234375,
0.0246734619140625,
-0.0217742919921875,
-0.01273345947265625,
0.032501220703125,
0.0030078887939453125,
-0.01216888427734375,
-0.004608154296875,
-0.00396728515625,
-0.00765228271484375,
-0.0081024169921875,
0.02093505859375,
-0.0172882080078125,
-0.00386810302734375,
-0.0143280029296875,
0.0008268356323242188,
0.0256805419921875,
-0.025909423828125,
-0.03594970703125,
0.0039215087890625,
0.0208892822265625,
-0.020904541015625,
0.0019702911376953125,
-0.01238250732421875,
-0.03448486328125,
-0.0025577545166015625,
0.0245819091796875,
-0.0118408203125,
0.00592803955078125,
0.0379638671875,
0.00821685791015625,
0.01369476318359375,
-0.034332275390625,
0.039794921875,
-0.01013946533203125,
-0.0268402099609375,
-0.0016050338745117188,
-0.012939453125,
-0.0005464553833007812,
0.00872039794921875,
0.0089569091796875,
-0.007411956787109375,
-0.04583740234375,
-0.06695556640625,
0.0217742919921875,
0.005802154541015625,
0.0318603515625,
-0.016571044921875,
-0.00408935546875,
-0.033905029296875,
0.00860595703125,
0.0028839111328125,
0.006435394287109375,
-0.0236968994140625,
0.006069183349609375,
0.0084991455078125,
-0.0077972412109375,
-0.0099945068359375,
0.03204345703125,
-0.00537872314453125,
-0.0260772705078125,
0.0170440673828125,
0.0266571044921875,
-0.01366424560546875,
-0.0006151199340820312,
-0.0036144256591796875,
-0.0220489501953125,
0.00983428955078125,
-0.0098419189453125,
0.002887725830078125,
0.01233673095703125,
0.048614501953125,
0.01319122314453125,
-0.0033702850341796875,
0.017608642578125,
-0.0005779266357421875,
-0.01160430908203125,
-0.0032291412353515625,
0.00949859619140625,
0.03948974609375,
0.00527191162109375,
0.00797271728515625,
0.0018777847290039062,
-0.0006365776062011719,
-0.001033782958984375,
-0.00640106201171875,
-0.01239776611328125,
0.00858306884765625,
-0.01519012451171875,
-0.0008225440979003906,
0.0051422119140625,
-0.00873565673828125,
-0.061676025390625,
-0.006877899169921875,
-0.0211944580078125,
0.006763458251953125,
-0.01557159423828125,
-0.015869140625,
0.01251220703125,
0.0025501251220703125,
-0.0160369873046875,
-0.0217132568359375,
-0.0010356903076171875,
0.020263671875,
0.0101165771484375,
0.00760650634765625,
0.0083770751953125,
0.01047515869140625,
-0.00021135807037353516,
0.009765625,
-0.002376556396484375,
0.02703857421875,
-0.00860595703125,
-0.02960205078125,
0.00255584716796875,
-0.01285552978515625,
-0.0224456787109375,
0.005161285400390625,
0.035614013671875,
0.0285797119140625,
-0.041412353515625,
-0.0224456787109375,
-0.027618408203125,
-0.003726959228515625,
0.01959228515625,
-0.0159454345703125,
0.00821685791015625,
0.0061492919921875,
0.00620269775390625,
-0.005863189697265625,
-0.0078887939453125,
0.0030155181884765625,
0.006305694580078125,
0.0261688232421875,
0.008270263671875,
-0.02740478515625,
-0.0011749267578125,
-0.023193359375,
-0.0054779052734375,
-0.005367279052734375,
0.0168914794921875,
0.007183074951171875,
-0.002986907958984375,
0.021881103515625,
0.00911712646484375,
0.02264404296875,
-0.00498199462890625,
-0.0036525726318359375,
-0.01355743408203125,
0.0034427642822265625,
-0.01082611083984375,
-0.0023174285888671875,
-0.00933837890625,
-0.0160064697265625,
0.01503753662109375,
-0.03363037109375,
0.01143646240234375,
-0.029449462890625,
0.0041351318359375,
-0.0010461807250976562,
0.021392822265625,
-0.00921630859375,
-0.035858154296875,
0.000972747802734375,
-0.0111541748046875,
-0.01434326171875,
0.01369476318359375,
-0.00036072731018066406,
-0.00217437744140625,
-0.0202484130859375,
0.036102294921875,
-0.00510406494140625,
0.0008220672607421875,
-0.0173187255859375,
-0.0170135498046875,
0.00736236572265625,
0.017791748046875,
-0.0009765625,
-0.00034046173095703125,
0.004962921142578125,
0.0233154296875,
0.0149688720703125,
-0.0158538818359375,
-0.00826263427734375,
0.002040863037109375,
0.0005936622619628906,
0.020355224609375,
0.0113983154296875,
0.0033588409423828125,
0.0224456787109375,
0.02947998046875,
0.016845703125,
-0.00653839111328125,
0.01143646240234375,
0.0156707763671875,
-0.0023059844970703125,
-0.005344390869140625,
0.004253387451171875,
0.0249481201171875,
-0.0227813720703125,
-0.0021228790283203125,
-0.046966552734375,
-0.01085662841796875,
-0.0177459716796875,
-0.009552001953125,
0.00011134147644042969,
0.01485443115234375,
-0.05413818359375,
0.019378662109375,
0.00946044921875,
0.0124359130859375,
-0.01593017578125,
-0.004367828369140625,
-0.01058197021484375,
-0.01055908203125,
-0.0005593299865722656,
-0.0107421875,
0.0156097412109375,
-0.015716552734375,
0.016571044921875,
-0.00785064697265625,
0.0035572052001953125,
0.026763916015625,
-0.00858306884765625,
0.0128173828125,
-0.00225830078125,
0.01279449462890625,
-0.0131378173828125,
0.0161285400390625,
-0.0255584716796875,
-0.01313018798828125,
-0.0130462646484375,
-0.00872039794921875,
0.01318359375,
0.006092071533203125,
0.007598876953125,
-0.0074462890625,
-0.0272369384765625,
-0.007198333740234375,
-0.0017671585083007812,
0.0021190643310546875,
-0.0044097900390625,
0.01427459716796875,
-0.00858306884765625,
0.0002129077911376953,
-0.0252532958984375,
-0.01276397705078125,
0.025726318359375,
0.0033054351806640625,
-0.0196990966796875,
-0.014678955078125,
-0.01453399658203125,
0.01708984375,
-0.054107666015625,
-0.0261688232421875,
-0.028717041015625,
0.027496337890625,
0.01181793212890625,
0.01812744140625,
-0.0151214599609375,
-0.0011663436889648438,
0.0029850006103515625,
0.01141357421875,
-0.0125732421875,
0.011260986328125,
-0.005870819091796875,
-0.009796142578125,
0.007205963134765625,
0.00708770751953125,
0.0013971328735351562,
-0.0247039794921875,
0.0176239013671875,
0.0027980804443359375,
-0.007221221923828125,
-0.03472900390625,
-0.0219268798828125,
-0.00962066650390625,
0.009796142578125,
-0.006946563720703125,
0.0081939697265625,
-0.0063934326171875,
0.010284423828125,
0.0433349609375,
0.0180511474609375,
0.0020008087158203125,
0.039581298828125,
0.00443267822265625,
-0.0168914794921875,
0.012451171875,
0.0078277587890625,
-0.0185546875,
-0.00807952880859375,
-0.00011044740676879883,
-0.001857757568359375,
-0.0130157470703125,
0.004848480224609375,
-0.01215362548828125,
-0.013763427734375,
0.0037631988525390625,
0.0020904541015625,
0.0006785392761230469,
-0.0028400421142578125,
-0.00962066650390625,
-0.0250091552734375,
-0.0236968994140625,
0.017181396484375,
-0.0178985595703125,
0.0098876953125,
0.01119232177734375,
0.0199737548828125,
-0.03948974609375,
-0.0096282958984375,
-0.0170440673828125,
-0.0181732177734375,
0.0233154296875,
0.0013055801391601562,
-0.005519866943359375,
0.01593017578125,
-0.053924560546875,
0.0099945068359375,
0.0171966552734375,
-0.002277374267578125,
0.0009179115295410156,
-0.0032253265380859375,
-0.019622802734375,
0.036285400390625,
-0.006992340087890625,
-0.01363372802734375,
-0.0026721954345703125,
-0.0218505859375,
0.03167724609375,
0.00478363037109375,
0.0239715576171875,
0.01071929931640625,
0.0020923614501953125,
-0.0230255126953125,
-0.031463623046875,
-0.0302734375,
-0.005229949951171875,
0.004337310791015625,
-0.004344940185546875,
-0.0183258056640625,
0.0131988525390625,
-0.005603790283203125,
-0.0015954971313476562,
0.0289459228515625,
0.005153656005859375,
0.01215362548828125,
-0.0166473388671875,
-0.0005917549133300781,
-0.00794219970703125,
0.00241851806640625,
-0.0031795501708984375,
-0.006603240966796875,
-0.0126953125,
-0.004001617431640625,
-0.0252685546875,
-0.006336212158203125,
-0.00972747802734375,
-0.0152435302734375,
0.010040283203125,
-0.0062255859375,
-0.051116943359375,
-0.00005924701690673828,
-0.0032176971435546875,
0.004817962646484375,
-0.00852203369140625,
0.005054473876953125,
0.0076141357421875,
0.03125,
0.0010538101196289062,
0.039093017578125,
-0.015289306640625,
-0.00029015541076660156,
0.0019283294677734375,
-0.024688720703125,
-0.0255584716796875,
0.0284576416015625,
-0.0164794921875,
-0.0033473968505859375,
0.0165863037109375,
0.020599365234375,
0.0080413818359375,
-0.038970947265625,
-0.004993438720703125,
0.017974853515625,
0.006664276123046875,
0.00624847412109375,
0.0174407958984375,
-0.0016498565673828125,
-0.010223388671875,
0.025726318359375,
0.010955810546875,
-0.018463134765625,
-0.0223388671875,
-0.0087432861328125,
0.00446319580078125,
-0.003597259521484375,
0.0140533447265625,
-0.0137939453125,
-0.0007772445678710938,
-0.023468017578125,
0.022430419921875,
0.004436492919921875,
0.0255584716796875,
-0.00998687744140625,
-0.057159423828125,
0.01009368896484375,
0.0122833251953125,
-0.045318603515625,
0.0296783447265625,
-0.031463623046875,
0.01300811767578125,
0.0251312255859375,
-0.02587890625,
0.0263519287109375,
0.020416259765625,
0.0214996337890625,
0.013153076171875,
-0.02215576171875,
0.044403076171875,
0.0304107666015625,
-0.00817108154296875,
0.02398681640625,
0.01029205322265625,
0.0176849365234375,
-0.040435791015625,
0.0173187255859375,
0.017669677734375,
-0.01702880859375,
0.0019445419311523438,
0.007354736328125,
-0.006500244140625,
0.003753662109375,
0.0218048095703125,
0.018341064453125,
-0.0311737060546875,
-0.01837158203125,
-0.0233306884765625,
-0.01259613037109375,
0.025390625,
-0.029022216796875,
-0.01140594482421875,
0.00970458984375,
0.0213165283203125,
0.01285552978515625,
0.0015468597412109375,
-0.0298309326171875,
0.0016078948974609375,
-0.031829833984375,
-0.0174102783203125,
-0.00720977783203125,
-0.0127410888671875,
0.00011134147644042969,
-0.038360595703125,
0.0240631103515625,
0.0038738250732421875,
-0.00261688232421875,
-0.0282745361328125,
-0.054290771484375,
0.00040721893310546875,
-0.01506805419921875,
-0.043212890625,
0.035186767578125,
-0.00237274169921875,
0.037841796875,
-0.00180816650390625,
-0.016326904296875,
0.0203399658203125,
-0.0171051025390625,
-0.026336669921875,
0.039581298828125,
-0.0277099609375,
0.01392364501953125,
0.026580810546875,
-0.0165557861328125,
-0.0203857421875,
0.050445556640625,
0.01528167724609375,
0.03204345703125,
-0.01548004150390625,
-0.0189208984375,
-0.01971435546875,
0.0012254714965820312,
-0.01007843017578125,
0.01273345947265625,
0.0035152435302734375,
0.003269195556640625,
-0.007335662841796875,
-0.0204925537109375,
-0.0218658447265625,
0.0345458984375,
0.016265869140625,
-0.0018749237060546875,
0.032958984375,
0.017913818359375,
0.01242828369140625,
-0.021636962890625,
-0.0131072998046875,
-0.00429534912109375,
0.01107025146484375,
-0.033111572265625,
0.0019178390502929688,
-0.05340576171875,
0.0144805908203125,
0.003726959228515625,
-0.013519287109375,
-0.004695892333984375,
-0.02056884765625,
0.019256591796875,
0.0252685546875,
0.0057373046875,
0.016387939453125,
0.01181793212890625,
0.0240631103515625,
-0.0159759521484375,
0.0255584716796875,
-0.004886627197265625,
-0.01419830322265625,
-0.0119476318359375,
0.00421905517578125,
0.0005664825439453125,
-0.0180511474609375,
0.018829345703125,
0.0105743408203125,
-0.018768310546875,
0.00420379638671875,
0.007709503173828125,
0.011688232421875,
0.0012693405151367188,
0.047637939453125,
-0.017059326171875,
-0.0183868408203125,
0.0189666748046875,
-0.02215576171875,
-0.022216796875,
-0.01369476318359375,
-0.00788116455078125,
-0.007350921630859375,
0.0068511962890625,
0.0181121826171875,
-0.0022373199462890625,
-0.014801025390625,
0.02508544921875,
0.005725860595703125,
-0.01558685302734375,
-0.0247650146484375,
-0.0092620849609375,
0.03558349609375,
-0.007404327392578125,
-0.005279541015625,
0.005489349365234375,
-0.0060272216796875,
-0.02459716796875,
0.0257720947265625,
0.0136566162109375,
-0.0235595703125,
-0.03509521484375,
-0.037872314453125,
0.01131439208984375,
-0.0111236572265625,
-0.0189971923828125,
-0.0082244873046875,
-0.009735107421875,
-0.017364501953125,
0.00540924072265625,
0.0014734268188476562,
-0.024078369140625,
0.0174560546875,
-0.00647735595703125,
-0.0211944580078125,
-0.01148223876953125,
0.0282135009765625,
0.00722503662109375,
0.013580322265625,
0.006999969482421875,
-0.0058746337890625,
0.0013265609741210938,
-0.00909423828125,
-0.0008258819580078125,
0.0178680419921875,
0.01458740234375,
0.00594329833984375,
0.0025234222412109375,
0.00074005126953125,
-0.01502227783203125,
0.007049560546875,
-0.01556396484375,
0.02886962890625,
-0.01317596435546875,
-0.00811767578125,
0.004131317138671875,
0.018402099609375,
-0.01023101806640625,
-0.0158233642578125,
0.03875732421875,
-0.00940704345703125,
-0.0286712646484375,
0.0235748291015625,
-0.01349639892578125,
0.02801513671875,
0.0145263671875,
0.008758544921875,
-0.0012121200561523438,
-0.01181793212890625,
-0.01508331298828125,
0.029205322265625,
-0.058624267578125,
0.003139495849609375,
-0.048004150390625,
-0.0262603759765625,
-0.0009665489196777344,
-0.004970550537109375,
-0.0074920654296875,
0.024322509765625,
-0.003917694091796875,
0.0020351409912109375,
-0.0264434814453125,
-0.04058837890625,
-0.0217742919921875,
0.0198211669921875,
-0.0027446746826171875,
0.0386962890625,
0.01137542724609375,
0.017181396484375,
-0.0018148422241210938,
0.0007939338684082031,
-0.0156402587890625,
-0.00009971857070922852,
0.0126495361328125,
0.01323699951171875,
-0.0421142578125,
-0.005161285400390625,
0.00772857666015625,
-0.03082275390625,
0.00730133056640625,
0.036651611328125,
0.017486572265625,
-0.0048828125,
-0.008514404296875,
-0.030029296875,
0.0263824462890625,
-0.00630950927734375,
0.036773681640625,
0.0155181884765625,
-0.04620361328125,
-0.00508880615234375,
0.0226898193359375,
-0.0104827880859375,
0.01336669921875,
0.043975830078125,
-0.0022792816162109375,
-0.0262451171875,
-0.020751953125,
-0.01107025146484375,
-0.0165252685546875,
0.026641845703125,
-0.0006742477416992188,
0.0232086181640625,
-0.049957275390625,
0.042724609375,
-0.00740814208984375,
0.0179443359375,
-0.034210205078125,
-0.0241851806640625,
-0.0078277587890625,
0.0253448486328125,
0.007770538330078125,
0.017578125,
-0.00977325439453125,
0.01245880126953125,
-0.008697509765625,
-0.0007386207580566406,
0.035491943359375,
-0.007167816162109375,
-0.00795745849609375,
-0.0117340087890625,
0.0290374755859375,
0.0038547515869140625,
0.0219268798828125,
-0.0011816024780273438,
0.00551605224609375,
0.00806427001953125,
-0.045257568359375,
0.032196044921875,
-0.0188751220703125,
-0.007747650146484375,
0.02703857421875,
0.027069091796875,
-0.0010042190551757812,
0.00565338134765625,
-0.00870513916015625,
-0.003345489501953125,
-0.029998779296875,
0.0254364013671875,
0.0081329345703125,
-0.0289459228515625,
0.0037860870361328125,
0.0103302001953125,
-0.0484619140625,
-0.036834716796875,
-0.00557708740234375,
-0.005184173583984375,
0.02197265625,
0.0123443603515625,
-0.007389068603515625,
0.010894775390625,
0.00007468461990356445,
-0.0176849365234375,
0.0104522705078125,
-0.019134521484375,
0.0224456787109375,
0.021728515625,
0.0299530029296875,
-0.019287109375,
-0.0133514404296875,
-0.039764404296875,
-0.0066375732421875,
0.004184722900390625,
0.0275726318359375,
-0.0225372314453125,
0.005832672119140625,
-0.03924560546875,
0.0022487640380859375,
-0.001483917236328125,
-0.025726318359375,
0.00415802001953125,
-0.017913818359375,
0.04925537109375,
0.0187835693359375,
0.01200103759765625,
0.011627197265625,
-0.00991058349609375,
0.035064697265625,
0.026153564453125,
-0.04010009765625,
-0.0036678314208984375,
-0.016326904296875,
0.02459716796875,
0.06640625,
0.005931854248046875,
-0.0283660888671875,
0.006587982177734375,
0.014617919921875,
0.0126190185546875,
-0.028167724609375,
-0.0018205642700195312,
-0.0174407958984375,
-0.028228759765625,
-0.0169830322265625,
-0.007129669189453125,
0.0205841064453125,
-0.0262603759765625,
-0.0005507469177246094,
-0.03594970703125,
-0.027099609375,
-0.01520538330078125,
0.0177459716796875,
-0.0208892822265625,
-0.008056640625,
0.03607177734375,
-0.018096923828125,
0.027069091796875,
-0.006099700927734375,
-0.00235748291015625,
0.01319122314453125,
0.0177764892578125,
-0.01073455810546875,
0.01047515869140625,
-0.009307861328125,
-0.01470947265625,
0.005279541015625,
-0.0003190040588378906,
-0.0243682861328125,
-0.0191497802734375,
-0.05096435546875,
0.040496826171875,
-0.033782958984375,
0.034912109375,
0.0200347900390625,
0.013397216796875,
-0.0131683349609375,
-0.0159912109375,
0.028289794921875,
0.0013580322265625,
-0.00974273681640625,
-0.036651611328125,
0.0310211181640625,
0.0112152099609375,
-0.007129669189453125,
-0.0218353271484375,
0.024505615234375,
0.035736083984375,
-0.017547607421875,
0.0122528076171875,
0.0299530029296875,
-0.0199127197265625,
0.03460693359375,
0.027130126953125,
-0.0164794921875,
0.01221466064453125,
0.005886077880859375,
0.051422119140625,
-0.0069122314453125,
0.009246826171875,
-0.0011548995971679688,
0.007251739501953125,
0.01387786865234375,
0.0018100738525390625,
0.00940704345703125,
0.00936126708984375,
-0.021484375,
-0.029052734375,
0.010406494140625,
0.0144805908203125,
0.0199127197265625,
-0.0000025033950805664062,
-0.013946533203125,
0.01549530029296875,
-0.0219268798828125,
0.017852783203125,
0.00232696533203125,
0.01387786865234375,
0.006320953369140625,
0.00550079345703125,
-0.01473236083984375,
-0.019317626953125,
-0.004329681396484375,
-0.0220794677734375,
0.004573822021484375,
0.0222930908203125,
-0.00733184814453125,
0.0124359130859375,
-0.0235595703125,
0.00679779052734375,
-0.0018854141235351562,
-0.011138916015625,
-0.023651123046875,
0.043670654296875,
0.017669677734375,
-0.005809783935546875,
0.033233642578125,
-0.01824951171875,
0.04205322265625,
-0.0052490234375,
0.0013933181762695312,
-0.0025920867919921875,
-0.0186004638671875,
-0.0243377685546875,
-0.051239013671875,
0.00756072998046875,
-0.0428466796875,
-0.008697509765625,
-0.021820068359375,
-0.004268646240234375,
0.001499176025390625,
-0.016204833984375,
-0.005405426025390625,
-0.008026123046875,
0.0013685226440429688,
0.00862884521484375,
0.0208282470703125,
0.0018110275268554688,
0.0030059814453125,
-0.01232147216796875,
0.0295562744140625,
0.0308990478515625,
0.005130767822265625,
-0.0032863616943359375,
-0.0016574859619140625,
0.013580322265625,
0.0267181396484375,
0.0306243896484375,
0.0203094482421875,
0.0179595947265625,
-0.005054473876953125,
0.02459716796875,
0.0065460205078125,
-0.0117034912109375,
-0.005825042724609375,
0.006069183349609375,
-0.0050811767578125,
0.01296234130859375,
-0.004772186279296875,
-0.006755828857421875,
-0.0110015869140625,
-0.0092010498046875,
-0.01470947265625,
0.0268402099609375,
0.01538848876953125,
0.028594970703125,
0.006862640380859375,
0.0194091796875,
-0.036407470703125,
-0.0231781005859375,
-0.00687408447265625,
0.0020923614501953125,
0.00762176513671875,
-0.01383209228515625,
0.0007519721984863281,
0.04205322265625,
0.00421905517578125,
-0.03033447265625,
-0.01824951171875,
0.008636474609375,
0.021148681640625,
0.016632080078125,
0.0264739990234375,
0.018951416015625,
-0.0157928466796875,
0.0084686279296875,
-0.0292816162109375,
-0.0226593017578125,
-0.002178192138671875,
0.0264434814453125,
0.01212310791015625,
-0.0124969482421875,
0.02606201171875,
-0.008087158203125,
0.0092010498046875,
-0.04034423828125,
0.0051116943359375,
-0.00890350341796875,
0.021759033203125,
0.021728515625,
0.01885986328125,
0.0206298828125,
-0.0181121826171875,
-0.0038394927978515625,
-0.01113128662109375,
0.0013761520385742188,
0.0233917236328125,
0.032470703125,
0.0171051025390625,
-0.008544921875,
0.0186767578125,
-0.03204345703125,
0.0280914306640625,
-0.01175689697265625,
0.00664520263671875,
-0.01212310791015625,
-0.00079345703125,
0.00032448768615722656,
0.03533935546875,
-0.0222320556640625,
-0.0006318092346191406,
0.00616455078125,
-0.019744873046875,
-0.036956787109375,
-0.0166168212890625,
-0.072998046875,
0.00592041015625,
-0.000247955322265625,
0.034515380859375,
0.0245513916015625,
0.026153564453125,
0.03521728515625,
-0.012542724609375,
-0.0270843505859375,
0.0031642913818359375,
0.00246429443359375,
-0.019989013671875,
0.0008678436279296875,
0.01499176025390625,
-0.004497528076171875,
0.02093505859375,
0.0301361083984375,
-0.00196075439453125,
0.006488800048828125,
-0.00955963134765625,
0.02069091796875,
-0.030029296875,
0.02374267578125,
0.0014905929565429688,
0.034698486328125,
-0.036865234375,
-0.0278472900390625,
-0.00405120849609375,
-0.00533294677734375,
0.019500732421875,
0.0027370452880859375,
-0.0242156982421875,
-0.005702972412109375,
-0.0010385513305664062,
0.012359619140625,
0.01593017578125,
0.0084991455078125,
-0.0223236083984375,
-0.0159759521484375,
0.03057861328125,
0.011688232421875,
-0.006786346435546875,
0.01212310791015625,
-0.00826263427734375,
0.02825927734375,
-0.023895263671875,
-0.01303863525390625,
0.018341064453125,
0.00897216796875,
-0.0153045654296875,
0.01580810546875,
0.004669189453125,
-0.02459716796875,
-0.0067901611328125,
0.03680419921875,
0.0011768341064453125,
-0.018646240234375,
0.0110015869140625,
-0.0206298828125,
0.005596160888671875,
-0.016326904296875,
-0.00490570068359375,
-0.01045989990234375,
0.00818634033203125,
-0.0015239715576171875,
0.0080413818359375,
0.02618408203125,
0.009979248046875,
0.004711151123046875,
-0.038238525390625,
0.0265350341796875,
-0.0223541259765625,
0.016510009765625,
-0.01451873779296875,
0.0137176513671875,
-0.0210113525390625,
-0.01763916015625,
-0.0023784637451171875,
-0.01358795166015625,
-0.00807952880859375,
0.0095367431640625,
0.0145263671875,
-0.01158905029296875,
-0.014739990234375,
0.0009160041809082031,
0.010986328125,
0.0188751220703125,
-0.0211029052734375,
0.01543426513671875,
0.0328369140625,
-0.0043182373046875,
-0.0304412841796875,
0.0018825531005859375,
-0.00732421875,
0.021820068359375,
-0.01285552978515625,
-0.0290985107421875,
0.0181427001953125,
0.0147705078125,
0.0175323486328125,
0.0135040283203125,
0.0018453598022460938,
-0.01788330078125,
-0.01540374755859375,
-0.0162506103515625,
0.025360107421875,
-0.01306915283203125,
-0.007472991943359375,
-0.005023956298828125,
-0.01812744140625,
0.01390838623046875,
-0.020111083984375,
0.0236053466796875,
-0.007343292236328125,
0.01204681396484375,
-0.0084686279296875,
0.01432037353515625,
0.009979248046875,
0.0038700103759765625,
-0.0310821533203125,
-0.035247802734375,
0.026092529296875,
0.042083740234375,
0.0169525146484375,
-0.00896453857421875,
-0.023681640625,
-0.00047588348388671875,
-0.0357666015625,
-0.02093505859375,
-0.0009069442749023438,
0.0033855438232421875,
-0.031951904296875,
0.01300811767578125,
-0.0094451904296875,
-0.0245361328125,
0.00734710693359375,
-0.00460052490234375,
-0.024505615234375,
0.0192108154296875,
0.0170135498046875,
-0.01375579833984375,
-0.004451751708984375,
-0.0166168212890625,
-0.024322509765625,
-0.00582122802734375,
-0.0014925003051757812,
-0.005035400390625,
-0.004215240478515625,
0.00855255126953125,
-0.0029354095458984375,
0.0030727386474609375,
-0.0101470947265625,
-0.0236053466796875,
-0.0047760009765625,
-0.0447998046875,
-0.0263671875,
-0.019775390625,
-0.004940032958984375,
-0.0022220611572265625,
0.021392822265625,
0.0049285888671875,
-0.0032596588134765625,
-0.010223388671875,
-0.012481689453125,
-0.0134124755859375,
-0.01267242431640625,
0.007747650146484375,
-0.0091705322265625,
-0.0029621124267578125,
-0.014923095703125,
0.0147705078125,
-0.023345947265625,
-0.0050811767578125,
-0.00940704345703125,
-0.02325439453125,
0.0189971923828125,
0.03802490234375,
-0.01129150390625,
-0.0138092041015625,
-0.0247039794921875,
-0.0261993408203125,
-0.0259552001953125,
-0.0004246234893798828,
0.01861572265625,
-0.005584716796875,
-0.004444122314453125,
0.0193023681640625,
0.00943756103515625,
-0.004184722900390625,
0.028778076171875,
-0.0234527587890625,
-0.026611328125,
-0.01788330078125,
0.037322998046875,
-0.01053619384765625,
-0.0241546630859375,
0.004520416259765625,
0.0071563720703125,
-0.003971099853515625,
0.00031948089599609375,
-0.0001443624496459961,
0.033355712890625,
-0.011474609375,
0.01849365234375,
0.0131683349609375,
-0.000247955322265625,
-0.00273895263671875,
0.0089569091796875,
-0.04052734375,
-0.0305023193359375,
0.0207061767578125,
0.01445770263671875,
-0.0260467529296875,
0.00036907196044921875,
-0.007190704345703125,
0.0164337158203125,
0.0077362060546875,
-0.005954742431640625,
-0.0140533447265625,
0.0007195472717285156,
0.026214599609375,
0.00286865234375,
-0.0123291015625,
-0.0202789306640625,
-0.004558563232421875,
0.0262908935546875,
-0.0253448486328125,
0.0223541259765625,
-0.0041351318359375,
-0.0035266876220703125,
-0.01134490966796875,
-0.0018014907836914062,
0.0026607513427734375,
-0.0011548995971679688,
-0.0206298828125,
-0.0236968994140625,
-0.00772857666015625,
-0.0270843505859375,
0.00006580352783203125,
0.00852203369140625,
-0.01468658447265625,
-0.0418701171875,
0.0231781005859375,
0.023040771484375,
0.01934814453125,
0.0302581787109375,
0.0127105712890625,
0.00490570068359375,
-0.022705078125,
0.0106048583984375,
-0.0156707763671875,
-0.005565643310546875,
0.0170135498046875,
-0.0065155029296875,
0.0318603515625,
0.0244598388671875,
-0.01517486572265625,
-0.0191192626953125,
-0.007427215576171875,
-0.0167388916015625,
0.025299072265625,
-0.022674560546875,
-0.0186767578125,
-0.02642822265625,
0.00559234619140625,
0.051788330078125,
-0.00969696044921875,
-0.00923919677734375,
0.023101806640625,
-0.00644683837890625,
0.0245513916015625,
-0.000010907649993896484,
-0.01025390625,
-0.0147552490234375,
0.0115966796875,
0.03900146484375,
-0.00005561113357543945,
0.0101318359375,
-0.0222015380859375,
0.01482391357421875,
0.01654052734375,
-0.01392364501953125,
0.022552490234375,
-0.0047454833984375,
-0.0292510986328125,
0.000743865966796875,
-0.0209503173828125,
-0.00688934326171875,
-0.0011148452758789062,
0.0032444000244140625,
-0.0165252685546875,
-0.0009112358093261719,
-0.0047149658203125,
-0.042572021484375,
0.0174407958984375,
-0.0025634765625,
0.01142120361328125,
0.017059326171875,
-0.00431060791015625,
0.014373779296875,
-0.01531982421875,
-0.00888824462890625,
0.00013554096221923828,
0.00955963134765625,
-0.0134429931640625,
0.0285491943359375,
-0.00948333740234375,
0.0229034423828125,
0.0202178955078125,
-0.006114959716796875,
0.01248931884765625,
0.02252197265625,
-0.027130126953125,
-0.04302978515625,
0.00939178466796875,
0.03045654296875,
-0.0002086162567138672,
-0.0372314453125,
-0.0206756591796875,
0.0302276611328125,
0.03448486328125,
0.009124755859375,
-0.022003173828125,
-0.0265350341796875,
0.002628326416015625,
0.018707275390625,
-0.019683837890625,
0.0096588134765625,
0.023345947265625,
-0.0172119140625,
-0.01837158203125,
-0.007625579833984375,
-0.027587890625,
0.0221099853515625,
0.0013217926025390625,
0.00829315185546875,
0.0004317760467529297,
-0.002109527587890625,
0.00333404541015625,
-0.057708740234375,
0.005229949951171875,
0.00811004638671875,
-0.0106964111328125,
-0.0160675048828125,
-0.0023326873779296875,
-0.0009260177612304688,
-0.0256195068359375,
-0.0174560546875,
0.013580322265625,
0.0057373046875,
-0.0007276535034179688,
0.01059722900390625,
-0.00841522216796875,
0.0021209716796875,
-0.038848876953125,
-0.00209808349609375,
-0.00962066650390625,
0.01082611083984375,
0.00604248046875,
-0.005157470703125,
-0.0258331298828125,
-0.00621795654296875,
-0.01299285888671875,
0.0323486328125,
0.0053558349609375,
-0.0038509368896484375,
-0.0224151611328125,
-0.003894805908203125,
0.0012454986572265625,
-0.004230499267578125,
-0.032745361328125,
0.011199951171875,
-0.0157928466796875,
0.0307769775390625,
0.02081298828125,
0.032012939453125,
0.005496978759765625,
-0.0300140380859375,
-0.02984619140625,
0.05511474609375,
-0.006793975830078125,
0.00835418701171875,
-0.00394439697265625,
0.005680084228515625,
-0.0243072509765625,
0.020172119140625,
0.03887939453125,
-0.0184326171875,
0.0419921875,
0.03216552734375,
0.029388427734375,
0.00359344482421875,
0.0162811279296875,
-0.01336669921875,
0.0230560302734375,
0.0107269287109375,
0.01169586181640625,
0.0002949237823486328,
0.00653076171875,
-0.0166778564453125,
-0.035308837890625,
0.004482269287109375,
-0.01220703125,
0.01529693603515625,
0.0001443624496459961,
0.00960540771484375,
-0.0180511474609375,
-0.048675537109375,
-0.030731201171875,
0.01403045654296875,
-0.015777587890625,
0.0112762451171875,
0.01139068603515625,
-0.0274200439453125,
0.0257415771484375,
0.0129547119140625,
-0.035858154296875,
-0.0126800537109375,
0.023651123046875,
0.00670623779296875,
-0.0107574462890625,
-0.0029735565185546875,
0.00235748291015625,
-0.002918243408203125,
0.000579833984375,
0.01013946533203125,
-0.00257110595703125,
-0.0290069580078125,
-0.0028362274169921875,
0.029144287109375,
-0.005584716796875,
0.03466796875,
0.0286865234375,
-0.025177001953125,
0.048858642578125,
-0.002124786376953125,
0.0016651153564453125,
0.04730224609375,
0.0255584716796875,
0.0016126632690429688,
0.0006976127624511719,
0.0070953369140625,
-0.0158843994140625,
-0.050933837890625,
0.0357666015625,
-0.0008130073547363281,
0.04791259765625,
-0.02484130859375,
-0.016815185546875,
-0.01873779296875,
0.01071929931640625,
-0.0087890625,
-0.01611328125,
-0.01322174072265625,
0.0249176025390625,
-0.002655029296875,
0.01776123046875,
0.0379638671875,
0.01441192626953125,
0.00646209716796875,
-0.00685882568359375,
0.01352691650390625,
0.00717926025390625,
-0.0116424560546875,
-0.030364990234375,
0.01218414306640625,
-0.00806427001953125,
0.00952911376953125,
-0.0159149169921875,
0.00542449951171875,
-0.01308441162109375,
-0.0252532958984375,
0.029052734375,
-0.013580322265625,
0.0239105224609375,
0.01690673828125,
0.0185546875,
0.01922607421875,
-0.01410675048828125,
0.00359344482421875,
0.00627899169921875,
0.0018682479858398438,
-0.0059661865234375,
-0.0025920867919921875,
0.01326751708984375,
0.001209259033203125,
0.02532958984375,
-0.0156402587890625,
-0.022247314453125,
-0.0199127197265625,
0.00836944580078125,
0.0038280487060546875,
0.0264129638671875,
0.004528045654296875,
0.01190948486328125,
0.019287109375,
0.00852203369140625,
-0.00820159912109375,
-0.040863037109375,
-0.007160186767578125,
-0.0179595947265625,
0.00818634033203125,
0.0487060546875,
-0.01261138916015625,
-0.03424072265625,
0.003086090087890625,
0.03369140625,
-0.01221466064453125,
0.00859832763671875,
-0.030731201171875,
-0.008331298828125,
-0.02801513671875,
-0.002285003662109375,
-0.0037670135498046875,
0.0148468017578125,
-0.04681396484375,
0.007167816162109375,
-0.0282440185546875,
0.030303955078125,
-0.023101806640625,
0.01788330078125,
0.006221771240234375,
-0.01313018798828125,
-0.0343017578125,
0.0060272216796875,
0.0007677078247070312,
-0.0004093647003173828,
-0.032501220703125,
-0.021636962890625,
-0.030181884765625,
0.02484130859375,
-0.018035888671875,
0.0035839080810546875,
0.0013723373413085938,
-0.0283203125,
-0.00640106201171875,
0.0089111328125,
-0.006565093994140625,
0.01432037353515625,
0.0026721954345703125,
-0.0028018951416015625,
-0.0106201171875,
0.01375579833984375,
-0.00334930419921875,
0.0179901123046875,
-0.011688232421875,
0.00003170967102050781,
-0.005340576171875,
-0.0265960693359375,
0.0007996559143066406,
-0.0163726806640625,
-0.0037288665771484375,
-0.03802490234375,
-0.00937652587890625,
-0.0004563331604003906,
-0.0201873779296875,
-0.017333984375,
0.032440185546875,
0.017913818359375,
0.017425537109375,
0.01032257080078125,
-0.00027441978454589844,
0.0301361083984375,
0.0006613731384277344,
-0.025146484375,
-0.0181121826171875,
0.0054931640625,
0.00798797607421875,
0.01959228515625,
-0.0004582405090332031,
-0.008758544921875,
-0.01216888427734375,
0.017364501953125,
-0.006103515625,
0.047454833984375,
0.00894927978515625,
-0.00998687744140625,
-0.0178375244140625,
0.0321044921875,
0.0411376953125,
-0.0166168212890625,
-0.003498077392578125,
0.01399993896484375,
0.010162353515625,
0.020233154296875,
0.0183258056640625,
-0.00952911376953125,
-0.0008192062377929688,
0.026458740234375,
0.0100860595703125,
0.028900146484375,
0.006870269775390625,
-0.03021240234375,
-0.02203369140625,
0.01154327392578125,
0.03228759765625,
0.0036907196044921875,
-0.0271453857421875,
-0.0252838134765625,
0.01314544677734375,
-0.0218353271484375,
-0.0084228515625,
0.011505126953125,
0.0240936279296875,
-0.00959014892578125,
-0.00684356689453125,
0.0007853507995605469,
0.004367828369140625,
0.0034656524658203125,
0.0186614990234375,
-0.013671875,
0.0050201416015625,
0.0193634033203125,
-0.0033512115478515625,
-0.004116058349609375,
-0.0068206787109375,
-0.03424072265625,
0.020294189453125,
-0.018341064453125,
-0.0016880035400390625,
0.01233673095703125,
0.0032787322998046875,
-0.0200042724609375,
-0.0151214599609375,
-0.02764892578125,
0.02264404296875,
0.008636474609375,
-0.0014314651489257812,
0.00800323486328125,
0.01593017578125,
-0.0187530517578125,
0.0067291259765625,
-0.00875091552734375,
-0.004581451416015625,
0.038909912109375,
0.0310516357421875,
0.035980224609375,
0.014404296875,
-0.00394439697265625,
0.01267242431640625,
-0.013824462890625,
0.00876617431640625,
-0.01143646240234375,
-0.024658203125,
0.03564453125,
0.02923583984375,
0.01480865478515625,
0.05218505859375,
0.01715087890625,
0.0158538818359375,
0.00759124755859375,
0.00739288330078125,
0.00679779052734375,
-0.0180206298828125,
0.003387451171875,
0.0372314453125,
-0.009521484375,
0.04150390625,
-0.0169525146484375,
0.002895355224609375,
0.02398681640625,
-0.02471923828125,
0.037506103515625,
0.011688232421875,
-0.017242431640625,
0.0019016265869140625,
-0.01085662841796875,
0.00228118896484375,
0.018951416015625,
-0.0021495819091796875,
-0.01995849609375,
-0.02850341796875,
0.004726409912109375,
-0.005889892578125,
-0.015655517578125,
0.0121307373046875,
-0.033172607421875,
0.0228271484375,
-0.01015472412109375,
-0.010406494140625,
0.036346435546875,
-0.0296173095703125,
-0.021240234375,
0.033203125,
-0.01517486572265625,
-0.0035552978515625,
0.01195526123046875,
0.0008172988891601562,
0.01316070556640625,
0.02557373046875,
0.027008056640625,
0.00888824462890625,
0.0005965232849121094,
-0.0168609619140625,
0.004825592041015625,
-0.026641845703125,
-0.001232147216796875,
-0.004344940185546875,
0.01517486572265625,
-0.0118255615234375,
0.0223846435546875,
-0.0223236083984375,
-0.00038051605224609375,
0.0183563232421875,
-0.0285797119140625,
-0.007480621337890625,
0.00811004638671875,
-0.01169586181640625,
-0.0138397216796875,
0.00450897216796875,
0.005107879638671875,
-0.0063629150390625,
0.008880615234375,
0.01486968994140625,
-0.031097412109375,
0.0018358230590820312,
0.00872039794921875,
0.021759033203125,
-0.02001953125,
-0.003368377685546875,
-0.0014219284057617188,
0.00594329833984375,
0.00267791748046875,
0.033935546875,
0.004856109619140625,
-0.00539398193359375,
-0.01047515869140625,
0.020660400390625,
0.0298309326171875,
0.00464630126953125,
-0.004726409912109375,
0.004299163818359375,
0.01166534423828125,
-0.0291290283203125,
-0.0012140274047851562,
-0.0263519287109375,
0.0092315673828125,
0.0135498046875,
0.0066070556640625,
0.022247314453125,
-0.0070953369140625,
-0.0193328857421875,
0.011810302734375,
-0.029998779296875,
-0.0017709732055664062,
0.017120361328125,
-0.03302001953125,
-0.00859832763671875,
0.0108489990234375,
0.0007376670837402344,
0.00960540771484375,
0.01287841796875,
0.007007598876953125,
0.0079345703125,
0.0289306640625,
0.0185089111328125,
-0.0044708251953125,
-0.0222320556640625,
0.009033203125,
-0.01117706298828125,
-0.001750946044921875,
-0.004764556884765625,
-0.018463134765625,
0.0191497802734375,
0.048431396484375,
-0.00090789794921875,
0.012542724609375,
0.00864410400390625,
-0.01531982421875,
-0.006317138671875,
0.0196075439453125,
0.0345458984375,
0.002773284912109375,
-0.01328277587890625,
0.00864410400390625,
-0.0262298583984375,
0.005626678466796875,
0.025360107421875,
0.01331329345703125,
-0.004024505615234375,
-0.024749755859375,
-0.01522064208984375,
0.00913238525390625,
-0.00774383544921875,
0.0010499954223632812,
0.006664276123046875,
0.03192138671875,
0.023223876953125,
0.018280029296875,
-0.01537322998046875,
0.015899658203125,
-0.0279541015625,
-0.0186614990234375,
0.006633758544921875,
-0.00479888916015625,
-0.0015392303466796875,
0.00274658203125,
0.0014753341674804688,
0.00786590576171875,
-0.0408935546875,
0.0038242340087890625,
-0.0015344619750976562,
-0.005611419677734375,
0.0229339599609375,
0.01003265380859375,
-0.01554107666015625,
-0.003856658935546875,
-0.018798828125,
0.021514892578125,
0.01617431640625,
0.022430419921875,
-0.00447845458984375,
0.00753021240234375,
0.0029888153076171875,
0.0189971923828125,
0.01294708251953125,
-0.01558685302734375,
-0.00691986083984375,
-0.01410675048828125,
-0.0038242340087890625,
0.058685302734375,
0.00930023193359375,
0.0224151611328125,
0.00794219970703125,
0.0033779144287109375,
0.015869140625,
-0.031280517578125,
-0.019683837890625,
-0.019317626953125,
0.004146575927734375,
-0.0020503997802734375,
-0.01253509521484375,
0.006500244140625,
-0.002532958984375,
0.024169921875,
0.0307159423828125,
0.00007915496826171875,
0.0203857421875,
-0.017242431640625,
0.014373779296875,
-0.037628173828125,
-0.03460693359375,
0.0230865478515625,
-0.0236053466796875,
0.01331329345703125,
0.011932373046875,
0.0072174072265625,
0.01056671142578125,
-0.001804351806640625,
0.011199951171875,
0.0014743804931640625,
-0.00421142578125,
-0.0207977294921875,
-0.020843505859375,
0.021514892578125,
-0.01320648193359375,
-0.0119781494140625,
-0.0214385986328125,
0.0020008087158203125,
0.037384033203125,
-0.00887298583984375,
0.01021575927734375,
0.0227203369140625,
-0.004016876220703125,
0.01103973388671875,
0.033294677734375,
-0.0031871795654296875,
0.06658935546875,
0.00287628173828125,
0.04168701171875,
0.00930023193359375,
-0.03424072265625,
0.01409912109375,
-0.01090240478515625,
-0.0086669921875,
-0.024871826171875,
0.00539398193359375,
0.0045623779296875,
0.0209503173828125,
0.01058197021484375,
-0.0318603515625,
0.00959014892578125,
-0.0234832763671875,
-0.0017805099487304688,
-0.0251617431640625,
0.005428314208984375,
-0.0116119384765625,
0.0113983154296875,
0.010101318359375,
0.0043182373046875,
0.003963470458984375,
0.01488494873046875,
-0.039031982421875,
0.035919189453125,
-0.004512786865234375,
0.0101776123046875,
0.0312042236328125,
0.016357421875,
-0.01441192626953125,
-0.03814697265625,
0.02130126953125,
0.00493621826171875,
-0.01021575927734375,
0.005687713623046875,
0.0016946792602539062,
0.05224609375,
0.00722503662109375,
-0.01904296875,
0.01511383056640625,
-0.0246429443359375,
-0.03070068359375,
0.00579071044921875,
-0.00769805908203125,
-0.006504058837890625,
-0.01544952392578125,
-0.0217132568359375,
0.0180816650390625,
-0.0023136138916015625,
0.0268707275390625,
0.01531219482421875,
0.016632080078125,
0.017333984375,
-0.00530242919921875,
-0.025146484375,
0.03192138671875,
0.061798095703125,
-0.01247406005859375,
-0.00933074951171875,
-0.02191162109375,
-0.01399993896484375,
0.01690673828125,
-0.006687164306640625,
-0.008636474609375,
0.019073486328125,
0.005260467529296875,
0.00220489501953125,
-0.00487518310546875,
0.04345703125,
0.004718780517578125,
0.00868988037109375,
0.0007271766662597656,
0.014495849609375,
-0.028411865234375,
0.001804351806640625,
0.0216217041015625,
-0.005229949951171875,
-0.0193634033203125,
-0.0102081298828125,
0.004238128662109375,
-0.01381683349609375,
0.00020241737365722656,
-0.0168304443359375,
-0.0433349609375,
0.037811279296875,
0.0124359130859375,
0.04022216796875,
0.01313018798828125,
0.0230560302734375,
-0.0034732818603515625,
0.0005249977111816406,
0.062225341796875,
-0.00536346435546875,
-0.0025806427001953125,
0.0024623870849609375,
0.003002166748046875,
-0.0131072998046875,
0.016387939453125,
-0.036407470703125,
0.00943756103515625,
-0.01218414306640625,
-0.00006181001663208008,
0.002033233642578125,
-0.0200347900390625,
0.031402587890625,
0.0061187744140625,
0.0026836395263671875,
0.0297393798828125,
0.003997802734375,
0.00762176513671875,
-0.01387786865234375,
0.0288543701171875,
-0.033447265625,
-0.0203857421875,
0.00284576416015625,
0.0259552001953125,
0.01163482666015625,
0.000050067901611328125,
0.01397705078125,
0.0035877227783203125,
-0.01300048828125,
-0.044342041015625,
0.004917144775390625,
0.0003750324249267578,
-0.01287841796875,
0.02557373046875,
0.0156097412109375,
-0.01390838623046875,
0.01058197021484375,
-0.013916015625,
-0.029632568359375,
-0.00946807861328125,
-0.0287322998046875,
-0.001522064208984375,
-0.0267333984375,
0.0075531005859375,
-0.0150909423828125,
-0.015228271484375,
-0.0026302337646484375,
-0.0299224853515625,
-0.01226806640625,
-0.002330780029296875,
0.0270538330078125,
-0.0006194114685058594,
-0.0002899169921875,
-0.026580810546875,
0.0298004150390625,
0.001781463623046875,
-0.0156097412109375,
0.00557708740234375,
-0.06689453125,
0.0125274658203125,
0.019775390625,
0.040435791015625,
-0.0225830078125,
0.0058135986328125,
-0.057586669921875,
-0.005947113037109375,
0.0226898193359375,
0.007190704345703125,
0.002674102783203125,
0.043731689453125,
-0.018341064453125,
0.013580322265625,
0.021881103515625,
0.006931304931640625,
0.00799560546875,
-0.0297088623046875,
0.005451202392578125,
0.019439697265625,
0.0011348724365234375,
0.018890380859375,
-0.034149169921875,
0.010894775390625,
0.0064239501953125,
-0.0191497802734375,
0.0211944580078125,
-0.01322174072265625,
0.0011043548583984375,
-0.00603485107421875,
-0.03448486328125,
-0.01702880859375,
-0.007080078125,
-0.02850341796875,
0.049530029296875,
-0.0160369873046875,
0.0026397705078125,
0.00896453857421875,
-0.005779266357421875,
-0.012115478515625,
-0.0200347900390625,
-0.02984619140625,
0.01044464111328125,
-0.003078460693359375,
0.0491943359375,
-0.019439697265625,
0.0214385986328125,
-0.02252197265625,
0.026641845703125,
-0.00962066650390625,
0.01024627685546875,
0.0083770751953125,
0.007228851318359375,
0.0116424560546875,
-0.0094146728515625,
-0.03033447265625,
0.028045654296875,
-0.0132293701171875,
-0.0068511962890625,
-0.03265380859375,
0.0029506683349609375,
0.0016613006591796875,
0.00894927978515625,
0.005611419677734375,
0.006969451904296875,
0.020721435546875,
-0.05010986328125,
0.0011806488037109375,
0.00577545166015625,
0.0333251953125,
0.0176239013671875,
0.032958984375,
0.003643035888671875,
0.004302978515625,
0.006580352783203125,
0.030029296875,
0.0028896331787109375,
-0.0482177734375,
0.007305145263671875,
-0.02252197265625,
0.01555633544921875,
0.000499725341796875,
0.0029964447021484375,
-0.0172271728515625,
0.018768310546875,
-0.04278564453125,
0.007801055908203125,
0.00016129016876220703,
0.00788116455078125,
-0.01519775390625,
-0.0159759521484375,
0.01751708984375,
0.009552001953125,
0.049041748046875,
-0.023162841796875,
-0.01152801513671875,
0.03070068359375,
-0.0026607513427734375,
0.0038585662841796875,
0.0012149810791015625,
0.005161285400390625,
-0.01015472412109375,
-0.00612640380859375,
0.0032825469970703125,
-0.029876708984375,
0.00963592529296875,
-0.010955810546875,
0.029144287109375,
0.004039764404296875,
-0.004169464111328125,
0.004917144775390625,
0.00432586669921875,
0.004108428955078125,
0.00637054443359375,
0.00876617431640625,
-0.0135040283203125,
-0.006633758544921875,
0.041717529296875,
-0.0265960693359375,
-0.00040721893310546875,
-0.0010042190551757812,
0.031585693359375,
0.00370025634765625,
-0.001491546630859375,
0.022247314453125,
0.003490447998046875,
-0.00724029541015625,
0.000026881694793701172,
-0.0242919921875,
-0.0005793571472167969,
0.034088134765625,
-0.01031494140625,
0.01233673095703125,
0.0192413330078125,
0.033172607421875,
0.041412353515625,
0.03173828125,
0.019561767578125,
-0.0286712646484375,
0.004058837890625,
0.004489898681640625,
-0.0306396484375,
-0.00727081298828125,
-0.0303955078125,
-0.00417327880859375,
-0.00514984130859375,
0.0152587890625,
0.002178192138671875,
0.035430908203125,
-0.0110626220703125,
-0.00966644287109375,
-0.0228424072265625,
0.012664794921875,
0.0015802383422851562,
-0.0267333984375,
0.00848388671875,
-0.0228271484375,
0.00193023681640625,
-0.007724761962890625,
-0.0173187255859375,
-0.0216522216796875,
-0.012054443359375,
-0.0270843505859375,
0.01486968994140625,
0.0118408203125,
-0.0122833251953125,
-0.006214141845703125,
0.0162200927734375,
-0.022796630859375,
0.0290069580078125,
0.0015039443969726562,
-0.02008056640625,
-0.01383209228515625,
0.036712646484375,
-0.0010328292846679688,
0.01165008544921875,
0.00807952880859375,
0.0025691986083984375,
0.01271820068359375,
0.016845703125,
-0.0345458984375,
-0.020111083984375,
0.00034308433532714844,
0.01398468017578125,
-0.012237548828125,
0.005153656005859375,
0.006587982177734375,
-0.0216827392578125,
0.01751708984375,
0.00908660888671875,
-0.00464630126953125,
0.002696990966796875,
0.03277587890625,
-0.008575439453125,
0.0055694580078125,
-0.01195526123046875,
0.02032470703125,
-0.007122039794921875,
-0.027862548828125,
0.020172119140625,
0.0166168212890625,
-0.00594329833984375,
-0.018707275390625,
0.033905029296875,
0.0093231201171875,
-0.000020802021026611328,
0.04302978515625,
-0.00749969482421875,
0.0095672607421875,
-0.0216064453125,
-0.0307464599609375,
0.017852783203125,
-0.0004572868347167969,
0.0216217041015625,
-0.004421234130859375,
0.007755279541015625,
-0.00514984130859375,
-0.012237548828125,
-0.0207061767578125,
0.0157623291015625,
0.011016845703125,
-0.005107879638671875,
0.0291595458984375,
-0.00260162353515625,
-0.0120697021484375,
0.0108642578125,
0.00833892822265625,
0.07275390625,
-0.04229736328125,
-0.0033855438232421875,
0.046905517578125,
-0.0300140380859375,
0.0222930908203125,
-0.036895751953125,
-0.0129241943359375,
-0.01554107666015625,
-0.0105438232421875,
-0.01219940185546875,
0.01125335693359375,
-0.00672149658203125,
-0.0247039794921875,
0.0234527587890625,
0.01093292236328125,
0.006221771240234375,
0.01160430908203125,
-0.0009822845458984375,
-0.0015134811401367188,
-0.0030384063720703125,
-0.0216522216796875,
0.0216064453125,
-0.006549835205078125,
0.01485443115234375,
-0.00652313232421875,
-0.005451202392578125,
0.0028896331787109375,
0.00006377696990966797,
0.02685546875,
-0.025421142578125,
-0.0025959014892578125,
-0.01824951171875,
0.016143798828125,
-0.0011301040649414062,
0.0013303756713867188,
-0.0076904296875,
-0.0204620361328125,
0.01727294921875,
-0.030609130859375,
0.0216217041015625,
0.0213775634765625,
-0.006023406982421875,
0.040802001953125,
-0.0115203857421875,
0.0292205810546875,
0.0458984375,
-0.0010128021240234375,
0.025146484375,
0.01102447509765625,
-0.0203094482421875,
-0.016754150390625,
-0.01302337646484375,
-0.0002658367156982422,
-0.008819580078125,
-0.026275634765625,
-0.0211334228515625,
-0.0020198822021484375,
0.0126953125,
0.0001283884048461914,
0.0184478759765625,
-0.03265380859375,
-0.0090484619140625,
-0.0287322998046875,
0.03424072265625,
-0.0162353515625,
0.03631591796875,
-0.0137786865234375,
-0.0035247802734375,
-0.008514404296875,
-0.01434326171875,
0.0238800048828125,
0.0281219482421875,
-0.0021915435791015625,
0.004364013671875,
-0.0263824462890625,
-0.0185089111328125,
0.0121612548828125,
-0.002109527587890625,
-0.01219940185546875,
0.03399658203125,
-0.01537322998046875,
-0.0244903564453125,
-0.036529541015625,
0.01385498046875,
0.0296478271484375,
0.0132598876953125,
-0.004795074462890625,
0.055145263671875,
-0.015045166015625,
0.0011377334594726562,
0.028411865234375,
0.0251007080078125,
0.01389312744140625,
0.019622802734375,
0.0107269287109375,
-0.0235443115234375,
-0.0031337738037109375,
-0.035614013671875,
0.01148223876953125,
0.0183563232421875,
0.01038360595703125,
0.0224151611328125,
-0.0287322998046875,
-0.004428863525390625,
0.004566192626953125,
-0.0178680419921875,
-0.007465362548828125,
0.0131072998046875,
0.0687255859375,
0.0172271728515625,
0.0291748046875,
0.01371002197265625,
0.01055145263671875,
-0.038177490234375,
-0.006031036376953125,
0.011871337890625,
0.0372314453125,
-0.008453369140625,
-0.01119232177734375,
0.040557861328125,
0.017120361328125,
-0.00994873046875,
-0.00394439697265625,
-0.0177459716796875,
0.007572174072265625,
0.0021419525146484375,
0.031951904296875,
0.0100555419921875,
0.0158843994140625,
0.005603790283203125,
0.0272216796875,
-0.028167724609375,
-0.0186004638671875,
0.00008827447891235352,
-0.0226287841796875,
-0.00978851318359375,
0.0177459716796875,
-0.020050048828125,
-0.039520263671875,
-0.00018477439880371094,
0.015960693359375,
0.007965087890625,
-0.005802154541015625,
-0.0038433074951171875,
0.0169677734375,
-0.01445770263671875,
0.00878143310546875,
0.00887298583984375,
0.013916015625,
0.01904296875,
0.009796142578125,
0.002376556396484375,
0.0138397216796875,
0.0251007080078125,
-0.035980224609375,
-0.0184173583984375,
-0.007755279541015625,
-0.0204010009765625,
-0.01401519775390625,
0.0219573974609375,
-0.0090484619140625,
0.0250701904296875,
-0.000637054443359375,
0.004222869873046875,
-0.042144775390625,
-0.0237579345703125,
0.0173797607421875,
0.004573822021484375,
-0.03082275390625,
0.05340576171875,
0.003475189208984375,
0.037200927734375,
0.0010051727294921875,
-0.050445556640625,
-0.01494598388671875,
0.00830078125,
0.007259368896484375,
-0.0005421638488769531,
-0.0249176025390625,
0.0025424957275390625,
-0.01337432861328125,
-0.0128173828125,
0.025238037109375,
0.03204345703125,
-0.0173797607421875,
0.0293121337890625,
0.004337310791015625,
0.00304412841796875,
0.020355224609375,
-0.02374267578125,
-0.00041222572326660156,
0.0312042236328125,
0.01073455810546875,
-0.004917144775390625,
-0.004791259765625,
-0.00789642333984375,
0.0182342529296875,
0.019317626953125,
0.0264129638671875,
0.0207977294921875,
0.002834320068359375,
-0.0100860595703125,
0.018218994140625,
-0.0003230571746826172,
0.028717041015625,
-0.01229095458984375,
0.00949859619140625,
-0.0108795166015625,
-0.01314544677734375,
-0.006725311279296875,
-0.0201416015625,
-0.004596710205078125,
-0.0252227783203125,
0.0009570121765136719,
-0.00588226318359375,
0.04058837890625,
-0.0255584716796875,
0.0198822021484375,
0.0203094482421875,
0.0234375,
-0.01316070556640625,
0.0288238525390625,
0.01337432861328125,
0.0274200439453125,
-0.042724609375,
0.01337432861328125,
-0.0015211105346679688,
0.02130126953125,
-0.0169525146484375,
-0.003246307373046875,
0.02490234375,
-0.01129150390625,
-0.007793426513671875,
0.0303955078125,
0.017364501953125,
0.0223388671875,
-0.0006670951843261719,
0.008544921875,
-0.018890380859375,
0.0157928466796875,
0.01107025146484375,
-0.0022792816162109375,
0.004779815673828125,
-0.037200927734375,
0.021881103515625,
0.00949859619140625,
-0.0206756591796875,
-0.0156707763671875,
0.011444091796875,
0.0006031990051269531,
-0.0169525146484375,
-0.0223846435546875,
-0.01314544677734375,
0.037353515625,
-0.030059814453125,
-0.0245819091796875,
-0.006439208984375,
-0.034393310546875,
0.0178985595703125,
-0.005573272705078125,
-0.0064697265625,
0.029449462890625,
0.0171661376953125,
-0.0187530517578125,
0.0165863037109375,
-0.06390380859375,
0.0211181640625,
0.01393890380859375,
0.01190948486328125,
0.005207061767578125,
-0.01369476318359375,
0.005523681640625,
-0.0264892578125,
0.032562255859375,
-0.0129241943359375,
0.004878997802734375,
-0.005245208740234375,
0.00345611572265625,
0.00409698486328125,
0.0091552734375,
-0.020294189453125,
-0.0274505615234375,
-0.02532958984375,
0.033477783203125,
0.013031005859375,
0.0128631591796875,
0.00762176513671875,
-0.0201873779296875,
-0.00830841064453125,
-0.0105438232421875,
0.0167236328125,
0.011016845703125,
-0.039459228515625,
0.01947021484375,
0.007724761962890625,
-0.00949859619140625,
-0.02850341796875,
-0.0034122467041015625,
0.0095062255859375,
-0.040191650390625,
-0.01224517822265625,
-0.038360595703125,
-0.005397796630859375,
0.00852203369140625,
-0.034149169921875,
-0.00885009765625,
0.0166778564453125,
0.0106658935546875,
-0.019317626953125,
-0.02166748046875,
0.0362548828125,
-0.0243072509765625,
-0.022705078125,
0.00556182861328125,
0.025543212890625,
0.0257720947265625,
-0.0224456787109375,
0.0238037109375,
-0.010009765625,
0.01335906982421875,
-0.0244293212890625,
0.0298614501953125,
-0.0283203125,
-0.0031414031982421875,
0.00429534912109375,
-0.0196990966796875,
0.0227203369140625,
0.015289306640625,
0.0292816162109375,
0.0042724609375,
-0.0233917236328125,
-0.002933502197265625,
-0.00589752197265625,
-0.01263427734375,
0.0169677734375,
-0.00013315677642822266,
-0.001953125,
0.0177001953125,
0.0122528076171875,
0.02032470703125,
0.0018768310546875,
-0.0066070556640625,
-0.00714874267578125,
-0.0204925537109375,
-0.006992340087890625,
-0.00897216796875,
-0.025543212890625,
-0.0222625732421875,
0.006160736083984375,
-0.00658416748046875,
-0.04803466796875
] |
ours_553
|
Let \( O \) be the center of the two triangles. Let the hexagon be \( PQRSTU \) with \( P, Q \) on side \( AB \). Notice that \( O \) is equidistant from every side of the hexagon, so the areas of triangles \( OPQ, OQR, ORS, \ldots \) are all equal. In particular, they are all equal to \(\frac{1}{6} \cdot \frac{4}{5} = \frac{2}{15}\) of the area of \( ABC \). Let \( s \) be the length of side \( PQ \), and let \( h \) be the height of \( ABC \). Because the height of \( OPQ \) is \(\frac{h}{3}\), we have
\[
\frac{[OPQ]}{[ABC]} = \frac{s \cdot \frac{h}{3}}{1 \cdot h} = \frac{2}{15}
\]
so it follows that \( s = \frac{2}{5} \) and the answer is \( 2 + 5 = 7 \).
Note: Here \([XYZ]\) denotes the area of triangle \( XYZ \).
\(\boxed{7}\)
|
7
|
{
"competition": "us_comps",
"dataset": "Ours",
"posts": null,
"source": "OMOSoln2.md"
}
|
Let \( ABC \) be an equilateral triangle with side length \( 1 \). This triangle is rotated by some angle about its center to form triangle \( DEF \). The intersection of \( ABC \) and \( DEF \) is an equilateral hexagon with an area that is \(\frac{4}{5}\) the area of \( ABC \). The side length of this hexagon can be expressed in the form \(\frac{m}{n}\) where \( m \) and \( n \) are relatively prime positive integers. What is \( m+n \)?
|
[
"/Mathematics/Geometry/GeneralGeometry/Center",
"/Mathematics/Geometry/GeneralGeometry/EuclideanGeometry",
"/Mathematics/Geometry/GeneralGeometry/Geometry",
"/Mathematics/Geometry/PlaneGeometry/Hexagons",
"/Mathematics/Geometry/PlaneGeometry/Triangles/SpecialTriangles",
"/Mathematics/Geometry/PlaneGeometry/Triangles/TriangleProperties",
"/Mathematics/Geometry/Symmetry/RotationalSymmetry",
"/Mathematics/Geometry/Symmetry/Symmetric"
] |
Use the rotational symmetry to split the hexagon into six congruent triangles sharing the common center, then equate each triangle's area to the known fraction of the original triangle.
|
[
0.00013589859008789062,
-0.01195526123046875,
0.0098114013671875,
0.0100555419921875,
0.0009469985961914062,
0.010040283203125,
0.016876220703125,
-0.0018405914306640625,
0.0017557144165039062,
-0.000042557716369628906,
-0.03375244140625,
0.00734710693359375,
-0.00525665283203125,
0.04693603515625,
-0.0195465087890625,
0.0067291259765625,
-0.01071929931640625,
0.01456451416015625,
0.030426025390625,
0.0009202957153320312,
-0.00968170166015625,
-0.0125274658203125,
-0.05364990234375,
0.0176239013671875,
-0.001300811767578125,
-0.0211639404296875,
-0.020782470703125,
0.048126220703125,
-0.016357421875,
0.0243988037109375,
-0.0289154052734375,
-0.0132293701171875,
0.0037364959716796875,
0.0122833251953125,
-0.00010657310485839844,
0.004306793212890625,
0.0269622802734375,
0.004230499267578125,
-0.0255126953125,
-0.033935546875,
-0.0124359130859375,
-0.0158843994140625,
-0.0032062530517578125,
0.021636962890625,
-0.0118865966796875,
0.045745849609375,
-0.0024871826171875,
0.007190704345703125,
-0.011322021484375,
-0.004810333251953125,
0.0025119781494140625,
0.01007843017578125,
0.003192901611328125,
-0.0113067626953125,
-0.0292510986328125,
-0.0302734375,
-0.0266876220703125,
-0.001312255859375,
-0.0074310302734375,
-0.03179931640625,
-0.00225830078125,
0.023681640625,
-0.036407470703125,
-0.00543212890625,
0.0003178119659423828,
0.00405120849609375,
-0.01050567626953125,
-0.021087646484375,
-0.01338958740234375,
0.022247314453125,
0.02459716796875,
-0.040252685546875,
0.0025634765625,
0.0026760101318359375,
0.007244110107421875,
-0.00583648681640625,
0.0024394989013671875,
-0.004901885986328125,
0.0145721435546875,
-0.0015954971313476562,
-0.009002685546875,
0.0066070556640625,
0.0232696533203125,
-0.012451171875,
0.003993988037109375,
0.0142059326171875,
-0.0181732177734375,
0.00595855712890625,
0.05084228515625,
-0.0011873245239257812,
0.017913818359375,
0.01560211181640625,
-0.003570556640625,
-0.005535125732421875,
0.0113677978515625,
0.015350341796875,
0.00994110107421875,
-0.0094146728515625,
-0.0221710205078125,
0.0013780593872070312,
-0.02099609375,
-0.01506805419921875,
-0.0097198486328125,
-0.022796630859375,
0.00235748291015625,
-0.023284912109375,
-0.007320404052734375,
0.01175689697265625,
0.0115814208984375,
-0.0037021636962890625,
0.00640869140625,
-0.0022106170654296875,
0.0382080078125,
0.0202789306640625,
0.0040283203125,
-0.01373291015625,
0.033599853515625,
-0.01523590087890625,
-0.01280975341796875,
0.0264434814453125,
0.01404571533203125,
0.010711669921875,
-0.0011501312255859375,
0.0248870849609375,
0.0185546875,
-0.032806396484375,
-0.0010232925415039062,
-0.02557373046875,
-0.0283966064453125,
0.0021514892578125,
-0.001953125,
0.0177459716796875,
-0.031341552734375,
-0.022491455078125,
-0.00366973876953125,
-0.00232696533203125,
0.01393890380859375,
0.0107879638671875,
0.006633758544921875,
0.000041484832763671875,
-0.005207061767578125,
-0.018768310546875,
0.0157623291015625,
-0.07952880859375,
0.00815582275390625,
0.01007080078125,
0.0009088516235351562,
-0.01393890380859375,
0.01251220703125,
0.016815185546875,
-0.0127105712890625,
-0.0206146240234375,
0.0191192626953125,
0.0282135009765625,
-0.004390716552734375,
0.01026153564453125,
-0.004795074462890625,
0.003383636474609375,
-0.00107574462890625,
0.01617431640625,
-0.0026988983154296875,
-0.007099151611328125,
0.001800537109375,
0.02716064453125,
-0.00644683837890625,
-0.02850341796875,
0.01006317138671875,
0.00836944580078125,
-0.024627685546875,
0.0259857177734375,
-0.0033321380615234375,
-0.0171051025390625,
-0.00030541419982910156,
-0.006046295166015625,
0.0249176025390625,
-0.006839752197265625,
-0.00997161865234375,
-0.0167694091796875,
-0.0107421875,
0.0180816650390625,
0.017608642578125,
-0.009674072265625,
0.017364501953125,
-0.0173187255859375,
0.0253448486328125,
-0.005619049072265625,
0.0031986236572265625,
-0.00418853759765625,
0.002780914306640625,
-0.00403594970703125,
-0.01493072509765625,
-0.043914794921875,
-0.0125885009765625,
-0.00634765625,
0.017578125,
0.00582122802734375,
-0.0027027130126953125,
0.034942626953125,
0.0307769775390625,
0.0006098747253417969,
-0.00980377197265625,
0.0129241943359375,
0.048858642578125,
0.003688812255859375,
-0.015380859375,
-0.0084075927734375,
-0.00598907470703125,
0.006702423095703125,
-0.00925445556640625,
0.00475311279296875,
0.004970550537109375,
0.02685546875,
0.010955810546875,
-0.01404571533203125,
0.0021209716796875,
-0.00860595703125,
-0.01285552978515625,
0.00734710693359375,
0.01097869873046875,
0.01020050048828125,
0.031585693359375,
-0.011016845703125,
-0.0011091232299804688,
-0.01373291015625,
-0.01288604736328125,
0.0131378173828125,
0.021942138671875,
-0.009429931640625,
-0.002964019775390625,
-0.01458740234375,
0.0228271484375,
0.0289306640625,
0.0061798095703125,
0.006687164306640625,
-0.01058197021484375,
-0.006317138671875,
-0.02459716796875,
-0.0009407997131347656,
0.0178070068359375,
0.0130157470703125,
0.0312042236328125,
0.0019016265869140625,
-0.01396942138671875,
-0.007030487060546875,
-0.0082244873046875,
-0.00432586669921875,
0.018768310546875,
0.00943756103515625,
-0.00012099742889404297,
-0.0117340087890625,
-0.038421630859375,
0.006378173828125,
-0.001651763916015625,
-0.0208740234375,
-0.004489898681640625,
0.017791748046875,
0.005168914794921875,
-0.0142364501953125,
-0.0145721435546875,
0.007167816162109375,
-0.0146026611328125,
0.01509857177734375,
-0.015533447265625,
-0.0117340087890625,
-0.006931304931640625,
-0.01377105712890625,
-0.0245819091796875,
-0.006763458251953125,
-0.0006127357482910156,
-0.005001068115234375,
0.0408935546875,
-0.0007266998291015625,
-0.028656005859375,
0.002166748046875,
-0.03228759765625,
-0.0125274658203125,
0.0044403076171875,
0.00870513916015625,
0.0246429443359375,
0.00046825408935546875,
0.0216217041015625,
-0.0163116455078125,
-0.031585693359375,
0.01447296142578125,
0.01009368896484375,
-0.0140228271484375,
0.03533935546875,
-0.0135345458984375,
-0.0177459716796875,
0.032470703125,
0.004528045654296875,
0.0214996337890625,
-0.005054473876953125,
-0.00862884521484375,
0.050933837890625,
-0.017364501953125,
-0.0031070709228515625,
-0.0015058517456054688,
0.00875091552734375,
0.005954742431640625,
0.00255584716796875,
-0.011077880859375,
-0.0018262863159179688,
0.0391845703125,
0.0187225341796875,
0.026092529296875,
-0.0023975372314453125,
-0.0009918212890625,
-0.0251312255859375,
-0.00732421875,
0.0028533935546875,
0.0015621185302734375,
0.0025920867919921875,
-0.00519561767578125,
-0.01525115966796875,
-0.037841796875,
-0.00800323486328125,
0.003627777099609375,
-0.0137481689453125,
-0.01983642578125,
-0.0107574462890625,
-0.0135650634765625,
0.0006766319274902344,
0.005626678466796875,
0.038116455078125,
-0.003864288330078125,
0.0213623046875,
-0.017791748046875,
0.032073974609375,
0.00897216796875,
-0.0004925727844238281,
-0.00193023681640625,
0.0023403167724609375,
-0.031005859375,
0.0027008056640625,
-0.0047149658203125,
-0.0128021240234375,
0.01239776611328125,
-0.01093292236328125,
0.00848388671875,
0.0025005340576171875,
0.01155853271484375,
0.04608154296875,
-0.075439453125,
-0.040374755859375,
0.00966644287109375,
-0.0226287841796875,
0.00806427001953125,
-0.00246429443359375,
-0.001251220703125,
-0.0222015380859375,
-0.018280029296875,
0.00685882568359375,
0.044464111328125,
-0.0391845703125,
0.00765228271484375,
0.01548004150390625,
0.0025501251220703125,
-0.003742218017578125,
0.0228118896484375,
0.01824951171875,
-0.01462554931640625,
-0.0150299072265625,
0.0112457275390625,
-0.012542724609375,
-0.01110076904296875,
-0.005462646484375,
-0.01568603515625,
-0.0188446044921875,
-0.01210784912109375,
0.0020809173583984375,
-0.01340484619140625,
0.0004191398620605469,
-0.0168914794921875,
0.01397705078125,
0.0070343017578125,
0.01300048828125,
0.0170745849609375,
0.0164642333984375,
0.006683349609375,
-0.004878997802734375,
0.0009918212890625,
0.0093231201171875,
-0.0032749176025390625,
0.0164337158203125,
0.0170745849609375,
0.0200958251953125,
-0.00839996337890625,
-0.0218658447265625,
0.0034694671630859375,
0.01529693603515625,
0.004718780517578125,
0.01373291015625,
-0.006439208984375,
-0.0188446044921875,
0.00091552734375,
-0.00475311279296875,
0.00824737548828125,
0.042327880859375,
-0.0117645263671875,
-0.03173828125,
-0.00823974609375,
-0.01641845703125,
-0.0005593299865722656,
0.002750396728515625,
0.011444091796875,
-0.005092620849609375,
0.037872314453125,
-0.027557373046875,
0.00440216064453125,
-0.01274871826171875,
0.0219573974609375,
0.015869140625,
-0.01039886474609375,
-0.0135345458984375,
0.0002810955047607422,
-0.006092071533203125,
0.007534027099609375,
-0.0004410743713378906,
0.0056304931640625,
-0.00849151611328125,
0.004116058349609375,
0.011962890625,
-0.00411224365234375,
0.0268402099609375,
0.0249786376953125,
-0.01438140869140625,
0.0423583984375,
-0.01120758056640625,
-0.025970458984375,
0.011993408203125,
-0.0096588134765625,
0.00022125244140625,
0.05340576171875,
-0.01605224609375,
0.004344940185546875,
0.03955078125,
-0.029144287109375,
0.0016508102416992188,
0.0223236083984375,
-0.005153656005859375,
-0.01323699951171875,
-0.02301025390625,
-0.0135498046875,
0.00986480712890625,
-0.0009150505065917969,
0.0230865478515625,
0.034454345703125,
-0.043487548828125,
0.02496337890625,
0.00821685791015625,
0.01476287841796875,
-0.025970458984375,
0.006053924560546875,
0.027313232421875,
-0.0223388671875,
0.0283050537109375,
-0.006481170654296875,
-0.006244659423828125,
0.05389404296875,
0.00901031494140625,
0.006061553955078125,
-0.039031982421875,
0.036895751953125,
-0.01169586181640625,
0.01351165771484375,
-0.031402587890625,
0.004245758056640625,
-0.004169464111328125,
0.0025787353515625,
-0.01332855224609375,
-0.01299285888671875,
-0.01229095458984375,
-0.006244659423828125,
-0.01560211181640625,
0.01293182373046875,
0.0311431884765625,
0.0016603469848632812,
0.00048613548278808594,
-0.01256561279296875,
-0.0175628662109375,
0.01457977294921875,
-0.0021495819091796875,
0.047698974609375,
-0.004657745361328125,
0.0001589059829711914,
-0.01013946533203125,
0.0034656524658203125,
0.01258087158203125,
-0.021697998046875,
-0.01253509521484375,
0.060821533203125,
0.00044846534729003906,
-0.0143890380859375,
-0.032806396484375,
-0.01220703125,
0.0128326416015625,
0.00974273681640625,
-0.007686614990234375,
0.003200531005859375,
-0.0187530517578125,
-0.01212310791015625,
-0.028778076171875,
0.031463623046875,
0.00927734375,
-0.03857421875,
0.04974365234375,
-0.0143890380859375,
0.049835205078125,
0.013763427734375,
-0.00001621246337890625,
0.022705078125,
0.0172271728515625,
-0.00908660888671875,
0.044219970703125,
0.02813720703125,
0.004871368408203125,
0.005947113037109375,
0.004604339599609375,
0.01338958740234375,
-0.018463134765625,
0.026611328125,
0.0123291015625,
0.019317626953125,
0.006938934326171875,
0.021453857421875,
-0.004352569580078125,
0.0068206787109375,
-0.0030765533447265625,
-0.043182373046875,
0.016571044921875,
0.000008046627044677734,
-0.04254150390625,
0.006992340087890625,
-0.0174560546875,
0.0267486572265625,
-0.007663726806640625,
0.00720977783203125,
0.0014352798461914062,
0.003299713134765625,
0.0031223297119140625,
-0.036529541015625,
0.0272064208984375,
-0.0245513916015625,
0.0181884765625,
-0.005870819091796875,
-0.0165557861328125,
0.0335693359375,
-0.006450653076171875,
0.01326751708984375,
0.02044677734375,
0.00421905517578125,
-0.033294677734375,
0.01055908203125,
-0.01393890380859375,
0.0036754608154296875,
-0.0247650146484375,
0.002452850341796875,
-0.006969451904296875,
0.0139923095703125,
-0.00899505615234375,
0.0104522705078125,
-0.0190277099609375,
-0.026947021484375,
-0.0228424072265625,
-0.023895263671875,
0.01531219482421875,
-0.00521087646484375,
0.0015478134155273438,
-0.00904083251953125,
-0.00951385498046875,
-0.0045166015625,
-0.0038547515869140625,
0.01248931884765625,
0.023345947265625,
-0.047454833984375,
0.0015878677368164062,
-0.00899505615234375,
0.0100555419921875,
-0.03497314453125,
0.0196990966796875,
0.02655029296875,
-0.00879669189453125,
-0.0316162109375,
0.0137786865234375,
0.02197265625,
-0.0014171600341796875,
0.0159912109375,
0.003177642822265625,
0.001209259033203125,
-0.01275634765625,
0.026397705078125,
0.0304412841796875,
-0.01140594482421875,
-0.012176513671875,
-0.042022705078125,
0.0148162841796875,
0.024688720703125,
-0.00946807861328125,
0.01352691650390625,
0.01346588134765625,
-0.0355224609375,
-0.00379180908203125,
0.0005393028259277344,
-0.006786346435546875,
0.00605010986328125,
0.01605224609375,
0.01393890380859375,
0.0265960693359375,
0.0254364013671875,
-0.0005736351013183594,
-0.0210113525390625,
-0.025787353515625,
-0.00841522216796875,
0.033416748046875,
-0.0401611328125,
0.007904052734375,
0.005191802978515625,
-0.0167083740234375,
0.0039043426513671875,
-0.01328277587890625,
0.01515960693359375,
-0.00927734375,
0.0197906494140625,
0.0011091232299804688,
0.0010385513305664062,
-0.07122802734375,
-0.033721923828125,
-0.014495849609375,
-0.0092315673828125,
-0.01129150390625,
0.0333251953125,
0.0190277099609375,
-0.0200958251953125,
-0.0161590576171875,
0.00856781005859375,
-0.01355743408203125,
0.0080718994140625,
-0.00821685791015625,
-0.0213470458984375,
0.0494384765625,
-0.024322509765625,
0.0144805908203125,
-0.032867431640625,
-0.007640838623046875,
-0.00157928466796875,
0.0005030632019042969,
0.00801849365234375,
-0.0006189346313476562,
0.0213165283203125,
0.00824737548828125,
0.034149169921875,
0.00850677490234375,
0.037017822265625,
-0.00022912025451660156,
0.0158233642578125,
-0.037139892578125,
-0.005298614501953125,
0.031341552734375,
0.0216827392578125,
0.0105438232421875,
0.0034027099609375,
0.0177764892578125,
-0.0297698974609375,
0.003631591796875,
-0.02191162109375,
-0.025604248046875,
-0.022918701171875,
0.00884246826171875,
0.0297088623046875,
0.019561767578125,
-0.00676727294921875,
-0.0218048095703125,
-0.01227569580078125,
0.0032806396484375,
0.0340576171875,
-0.01134490966796875,
0.00551605224609375,
-0.00592041015625,
-0.01849365234375,
-0.0004019737243652344,
0.01409149169921875,
0.03790283203125,
0.0179595947265625,
-0.0341796875,
0.0269622802734375,
0.0043487548828125,
0.014739990234375,
0.01092529296875,
-0.0229339599609375,
0.032928466796875,
0.0272674560546875,
-0.00937652587890625,
-0.01454925537109375,
-0.011260986328125,
-0.01488494873046875,
-0.03277587890625,
-0.008209228515625,
-0.01513671875,
-0.005767822265625,
-0.022308349609375,
-0.03936767578125,
0.0296630859375,
-0.0209197998046875,
0.00691986083984375,
-0.020904541015625,
0.0174713134765625,
0.0005517005920410156,
-0.00765228271484375,
0.034393310546875,
-0.0270843505859375,
-0.0218048095703125,
-0.0023860931396484375,
-0.0200347900390625,
-0.0214691162109375,
-0.01678466796875,
-0.01727294921875,
-0.02215576171875,
-0.00021207332611083984,
-0.01047515869140625,
0.013092041015625,
0.037872314453125,
-0.021820068359375,
0.015869140625,
0.038360595703125,
-0.01287841796875,
0.007411956787109375,
-0.043548583984375,
-0.00798797607421875,
-0.01000213623046875,
0.006534576416015625,
-0.0325927734375,
0.00826263427734375,
0.0421142578125,
-0.0166778564453125,
0.01287078857421875,
-0.03204345703125,
-0.031646728515625,
-0.01438140869140625,
0.004413604736328125,
0.038055419921875,
-0.008575439453125,
0.034454345703125,
-0.0216217041015625,
0.00885009765625,
-0.006744384765625,
0.00937652587890625,
0.025665283203125,
0.009613037109375,
0.021209716796875,
0.001972198486328125,
-0.002895355224609375,
-0.01271820068359375,
-0.0293426513671875,
-0.028076171875,
0.01219940185546875,
0.0018529891967773438,
-0.00795745849609375,
-0.01056671142578125,
-0.00780487060546875,
-0.0168609619140625,
-0.00467681884765625,
0.01445770263671875,
0.007663726806640625,
-0.00005805492401123047,
0.00020825862884521484,
-0.01306915283203125,
-0.0041961669921875,
0.0164031982421875,
-0.01160430908203125,
0.0184326171875,
0.0004911422729492188,
0.018310546875,
0.03106689453125,
0.0236968994140625,
-0.003986358642578125,
-0.057525634765625,
-0.0310211181640625,
0.030548095703125,
-0.04083251953125,
0.017333984375,
-0.006267547607421875,
-0.008209228515625,
0.025665283203125,
-0.015350341796875,
0.007396697998046875,
0.0019588470458984375,
-0.00762176513671875,
0.005950927734375,
-0.01277923583984375,
-0.0099334716796875,
0.025299072265625,
-0.0022411346435546875,
-0.012786865234375,
0.0161285400390625,
-0.01331329345703125,
0.0020351409912109375,
-0.004169464111328125,
0.04180908203125,
0.0027675628662109375,
-0.004253387451171875,
-0.037445068359375,
-0.02447509765625,
-0.0101470947265625,
0.019683837890625,
-0.035491943359375,
0.01218414306640625,
-0.01241302490234375,
0.01151275634765625,
0.02337646484375,
0.01904296875,
-0.0103607177734375,
0.00983428955078125,
-0.0104217529296875,
0.02105712890625,
0.024566650390625,
-0.007549285888671875,
-0.0239105224609375,
0.00576019287109375,
0.0177001953125,
-0.026458740234375,
0.026611328125,
-0.032012939453125,
-0.0028209686279296875,
-0.0088348388671875,
0.0118865966796875,
0.009613037109375,
0.019775390625,
0.0111846923828125,
0.03289794921875,
0.0633544921875,
-0.0158233642578125,
-0.01506805419921875,
-0.0009455680847167969,
-0.051177978515625,
0.0106201171875,
-0.009002685546875,
0.01326751708984375,
-0.0134124755859375,
-0.0137786865234375,
0.01094818115234375,
-0.013885498046875,
-0.00571441650390625,
0.03326416015625,
0.03570556640625,
-0.0211944580078125,
-0.00649261474609375,
0.0242462158203125,
0.039093017578125,
0.0008950233459472656,
0.00264739990234375,
0.005870819091796875,
-0.0226898193359375,
0.0168914794921875,
0.00336456298828125,
-0.0004987716674804688,
0.0186004638671875,
0.0290374755859375,
0.01024627685546875,
-0.01500701904296875,
0.02783203125,
-0.021484375,
0.032684326171875,
-0.0184173583984375,
-0.003147125244140625,
0.0170135498046875,
-0.019561767578125,
0.02734375,
0.0296783447265625,
0.01016998291015625,
0.01377105712890625,
-0.006954193115234375,
-0.0010662078857421875,
0.01702880859375,
0.002105712890625,
-0.0097503662109375,
-0.006679534912109375,
-0.006732940673828125,
0.06671142578125,
-0.001232147216796875,
-0.024169921875,
-0.0548095703125,
-0.0049591064453125,
0.00258636474609375,
-0.025909423828125,
-0.0155487060546875,
0.0265655517578125,
-0.004688262939453125,
0.013641357421875,
-0.0031909942626953125,
-0.019439697265625,
-0.01340484619140625,
-0.019439697265625,
-0.0296630859375,
0.022003173828125,
-0.01357269287109375,
0.022613525390625,
0.004535675048828125,
-0.007541656494140625,
-0.032989501953125,
-0.02410888671875,
0.04779052734375,
0.02484130859375,
-0.01268768310546875,
0.01036834716796875,
-0.008819580078125,
-0.0064697265625,
0.016326904296875,
0.0287933349609375,
0.01453399658203125,
-0.0265655517578125,
-0.004306793212890625,
0.0267486572265625,
0.034881591796875,
0.00920867919921875,
-0.0026836395263671875,
0.015350341796875,
0.01416015625,
-0.0055389404296875,
-0.0178680419921875,
-0.0116729736328125,
0.034698486328125,
-0.00458526611328125,
-0.0030765533447265625,
-0.00010222196578979492,
-0.0216064453125,
-0.0260162353515625,
0.000024497509002685547,
-0.0291748046875,
0.0263824462890625,
-0.018768310546875,
0.005970001220703125,
0.01392364501953125,
-0.006946563720703125,
-0.0061187744140625,
-0.007671356201171875,
0.01654052734375,
-0.033660888671875,
0.02960205078125,
-0.022369384765625,
-0.022125244140625,
0.01165771484375,
0.043975830078125,
-0.0146484375,
0.0242156982421875,
0.00551605224609375,
-0.0176239013671875,
0.01116943359375,
0.020263671875,
0.016082763671875,
-0.0010280609130859375,
0.0228118896484375,
0.01678466796875,
0.031707763671875,
-0.033203125,
-0.007740020751953125,
0.007549285888671875,
0.004421234130859375,
0.0176849365234375,
0.0017423629760742188,
0.029327392578125,
0.04144287109375,
-0.0084991455078125,
-0.019012451171875,
0.0321044921875,
0.0030498504638671875,
0.0028972625732421875,
0.029327392578125,
-0.017059326171875,
0.00457763671875,
0.007843017578125,
-0.00734710693359375,
-0.0301666259765625,
-0.0190887451171875,
0.01364898681640625,
0.0166015625,
0.023773193359375,
0.0007767677307128906,
0.016754150390625,
0.007747650146484375,
-0.02435302734375,
0.0162506103515625,
0.0186309814453125,
-0.00508880615234375,
0.010589599609375,
-0.029388427734375,
-0.013336181640625,
-0.0019025802612304688,
0.01580810546875,
-0.0345458984375,
-0.0029659271240234375,
0.0290374755859375,
0.0146331787109375,
0.004245758056640625,
0.01309967041015625,
0.0168304443359375,
-0.020172119140625,
-0.0290374755859375,
0.032562255859375,
-0.0246734619140625,
-0.0007658004760742188,
0.0313720703125,
0.006343841552734375,
-0.016693115234375,
-0.00009357929229736328,
-0.0289154052734375,
-0.01959228515625,
0.0272674560546875,
0.0178375244140625,
0.00939178466796875,
-0.022857666015625,
0.0073089599609375,
0.0190277099609375,
0.004314422607421875,
-0.031951904296875,
0.04132080078125,
-0.028076171875,
0.03302001953125,
-0.01654052734375,
0.003444671630859375,
0.0103302001953125,
-0.0166015625,
-0.0313720703125,
-0.031280517578125,
-0.0007100105285644531,
-0.04425048828125,
-0.0185699462890625,
0.02001953125,
-0.0040130615234375,
0.0277099609375,
0.0023899078369140625,
-0.0020904541015625,
0.01464080810546875,
0.0079193115234375,
-0.00724029541015625,
-0.0167236328125,
0.0037593841552734375,
0.0038433074951171875,
-0.00621795654296875,
-0.003116607666015625,
-0.0095062255859375,
-0.00867462158203125,
0.037322998046875,
-0.035400390625,
-0.01995849609375,
-0.00016677379608154297,
-0.009124755859375,
0.0258636474609375,
-0.004886627197265625,
0.017852783203125,
0.0242767333984375,
0.019805908203125,
-0.0169525146484375,
0.01236724853515625,
0.0301513671875,
0.0168914794921875,
-0.0295867919921875,
-0.009613037109375,
-0.0163116455078125,
-0.00545501708984375,
0.0028285980224609375,
-0.052520751953125,
-0.0031757354736328125,
-0.019775390625,
0.0091705322265625,
0.0026912689208984375,
-0.005016326904296875,
-0.01038360595703125,
0.00656890869140625,
-0.012786865234375,
-0.0291900634765625,
0.03399658203125,
0.017120361328125,
0.004299163818359375,
0.026885986328125,
-0.0255889892578125,
0.0002510547637939453,
-0.0282745361328125,
-0.039093017578125,
0.010009765625,
-0.01410675048828125,
0.02838134765625,
-0.045013427734375,
0.00858306884765625,
-0.0090789794921875,
-0.005741119384765625,
-0.033538818359375,
0.016937255859375,
-0.00788116455078125,
0.0050811767578125,
0.0063629150390625,
0.003879547119140625,
-0.0182037353515625,
0.0074005126953125,
-0.00859832763671875,
0.0057830810546875,
0.012847900390625,
0.0028839111328125,
0.01320648193359375,
-0.0236968994140625,
0.0118255615234375,
0.013885498046875,
0.0257415771484375,
0.014251708984375,
-0.00335693359375,
-0.02178955078125,
-0.017822265625,
0.029541015625,
-0.021759033203125,
0.01280975341796875,
-0.0022430419921875,
-0.0055084228515625,
0.0212249755859375,
-0.0006451606750488281,
-0.0229644775390625,
-0.00995635986328125,
0.002429962158203125,
0.01483154296875,
0.045318603515625,
-0.0170440673828125,
-0.037200927734375,
0.0163116455078125,
0.01690673828125,
0.0131683349609375,
-0.0142974853515625,
-0.013702392578125,
0.0035991668701171875,
0.0258636474609375,
-0.015716552734375,
0.003997802734375,
-0.01265716552734375,
0.040679931640625,
0.006549835205078125,
-0.02130126953125,
-0.0231170654296875,
0.051513671875,
0.0036411285400390625,
-0.01128387451171875,
-0.0118255615234375,
0.01198577880859375,
-0.01198577880859375,
0.03955078125,
-0.00789642333984375,
-0.007259368896484375,
-0.01519775390625,
-0.042327880859375,
-0.00878143310546875,
0.0154571533203125,
-0.025726318359375,
0.0159149169921875,
-0.0025634765625,
-0.0207977294921875,
0.0197601318359375,
0.01143646240234375,
-0.00984954833984375,
-0.007320404052734375,
-0.019561767578125,
-0.0026226043701171875,
0.001300811767578125,
0.00476837158203125,
0.00335693359375,
0.005023956298828125,
-0.00018346309661865234,
0.002834320068359375,
0.0086822509765625,
-0.04425048828125,
-0.0179901123046875,
0.01238250732421875,
-0.00942230224609375,
-0.005352020263671875,
-0.0179443359375,
-0.0240478515625,
-0.003021240234375,
-0.034088134765625,
-0.01641845703125,
0.0362548828125,
-0.0189208984375,
-0.01021575927734375,
0.009368896484375,
0.012542724609375,
-0.01050567626953125,
0.03253173828125,
0.0124969482421875,
-0.0154266357421875,
0.0242156982421875,
-0.0196380615234375,
0.004547119140625,
0.0019044876098632812,
-0.018310546875,
-0.0008678436279296875,
0.02667236328125,
0.01081085205078125,
-0.0049591064453125,
-0.016876220703125,
0.0014047622680664062,
0.007476806640625,
-0.032196044921875,
0.012542724609375,
-0.0161285400390625,
-0.014434814453125,
0.0240325927734375,
-0.005664825439453125,
-0.01558685302734375,
0.01184844970703125,
0.0221099853515625,
0.004802703857421875,
0.01490020751953125,
0.057373046875,
-0.01363372802734375,
-0.0021953582763671875,
0.003261566162109375,
-0.036834716796875,
0.006542205810546875,
-0.016998291015625,
0.0318603515625,
0.01081085205078125,
-0.025970458984375,
-0.024993896484375,
-0.0152130126953125,
0.0004076957702636719,
0.01476287841796875,
0.041290283203125,
0.03277587890625,
-0.045074462890625,
-0.01206207275390625,
-0.0271453857421875,
-0.00206756591796875,
0.0165252685546875,
-0.033294677734375,
0.0253143310546875,
0.01334381103515625,
0.013092041015625,
0.0028285980224609375,
-0.01523590087890625,
-0.0399169921875,
-0.0308990478515625,
-0.0016126632690429688,
0.009033203125,
-0.010833740234375,
-0.01389312744140625,
-0.0034961700439453125,
0.0144805908203125,
0.00023114681243896484,
-0.0211334228515625,
0.000008821487426757812,
-0.00508880615234375,
-0.03955078125,
0.03704833984375,
-0.03094482421875,
0.035675048828125,
0.0050811767578125,
0.00260162353515625,
-0.0262908935546875,
-0.01033782958984375,
0.0120697021484375,
0.0058441162109375,
-0.003662109375,
0.019775390625,
0.01236724853515625,
-0.02764892578125,
-0.039093017578125,
-0.01515960693359375,
-0.0102996826171875,
-0.0205535888671875,
-0.01213836669921875,
-0.006435394287109375,
-0.020263671875,
0.04095458984375,
0.01067352294921875,
0.004852294921875,
0.0009555816650390625,
0.0097808837890625,
-0.00098419189453125,
0.027923583984375,
0.006862640380859375,
0.0184478759765625,
0.0228424072265625,
0.01006317138671875,
-0.0005078315734863281,
0.0271759033203125,
-0.044921875,
0.00540924072265625,
0.0390625,
-0.0106353759765625,
-0.0091400146484375,
0.0032520294189453125,
0.01551055908203125,
0.04656982421875,
0.007144927978515625,
-0.0009531974792480469,
-0.0026531219482421875,
0.0021419525146484375,
0.02850341796875,
0.0232391357421875,
-0.008636474609375,
-0.01291656494140625,
0.026214599609375,
-0.011383056640625,
-0.017364501953125,
-0.0180511474609375,
-0.0142669677734375,
-0.019775390625,
-0.0054473876953125,
0.00830841064453125,
-0.0289154052734375,
-0.0009279251098632812,
0.02154541015625,
0.0267181396484375,
-0.00782012939453125,
-0.0048675537109375,
0.0194854736328125,
0.0077972412109375,
0.053192138671875,
0.0006079673767089844,
-0.013397216796875,
0.006320953369140625,
-0.017120361328125,
-0.0169677734375,
-0.0377197265625,
0.0214691162109375,
0.0172119140625,
-0.020355224609375,
-0.0209197998046875,
0.00247955322265625,
-0.01526641845703125,
-0.0040740966796875,
-0.0123748779296875,
-0.001430511474609375,
-0.00400543212890625,
-0.006561279296875,
-0.023773193359375,
0.004039764404296875,
-0.019287109375,
0.00457763671875,
0.016571044921875,
0.004383087158203125,
0.00966644287109375,
0.0098724365234375,
-0.0029697418212890625,
-0.048858642578125,
0.0143890380859375,
0.004817962646484375,
-0.00507354736328125,
-0.04248046875,
-0.0221099853515625,
0.0036487579345703125,
-0.01324462890625,
-0.021209716796875,
0.01605224609375,
-0.033203125,
-0.0012826919555664062,
-0.017974853515625,
-0.01025390625,
0.04241943359375,
-0.049896240234375,
0.04034423828125,
0.01922607421875,
0.0257568359375,
0.016632080078125,
0.002788543701171875,
0.0322265625,
0.01120758056640625,
0.021026611328125,
-0.01318359375,
0.017059326171875,
-0.0031719207763671875,
-0.00804901123046875,
-0.00579071044921875,
-0.031402587890625,
-0.00015091896057128906,
-0.01059722900390625,
0.0216827392578125,
-0.0101470947265625,
-0.0286712646484375,
0.00876617431640625,
0.00612640380859375,
-0.0162200927734375,
-0.00215911865234375,
0.0275421142578125,
0.0192413330078125,
-0.0126953125,
-0.0022182464599609375,
0.0208892822265625,
-0.01433563232421875,
0.0176849365234375,
-0.009674072265625,
-0.005306243896484375,
0.0289306640625,
0.002002716064453125,
-0.0144195556640625,
0.0123748779296875,
-0.004207611083984375,
-0.029754638671875,
0.041107177734375,
-0.004032135009765625,
-0.0259552001953125,
-0.0050201416015625,
-0.0156402587890625,
-0.0118560791015625,
-0.0010128021240234375,
0.015472412109375,
-0.005939483642578125,
-0.0108642578125,
0.037872314453125,
0.036956787109375,
0.0035610198974609375,
-0.017608642578125,
0.001220703125,
0.006618499755859375,
0.017669677734375,
-0.0157012939453125,
-0.01230621337890625,
0.0212249755859375,
-0.00983428955078125,
0.01355743408203125,
-0.032470703125,
-0.03533935546875,
-0.006633758544921875,
0.0025882720947265625,
-0.04058837890625,
0.01291656494140625,
0.024810791015625,
-0.005870819091796875,
0.026214599609375,
0.038970947265625,
-0.0235748291015625,
0.0277099609375,
-0.01201629638671875,
0.0084075927734375,
-0.0054931640625,
-0.003597259521484375,
0.0223541259765625,
0.0318603515625,
0.0104217529296875,
-0.00064849853515625,
-0.0011587142944335938,
0.055206298828125,
-0.0302276611328125,
-0.0028743743896484375,
0.0247650146484375,
0.0154876708984375,
-0.02813720703125,
0.01214599609375,
0.0012063980102539062,
0.0028514862060546875,
0.003322601318359375,
0.0080413818359375,
0.01163482666015625,
-0.007755279541015625,
-0.0143280029296875,
-0.022064208984375,
-0.034942626953125,
-0.0148773193359375,
0.0215301513671875,
-0.0013637542724609375,
0.0210418701171875,
-0.0218048095703125,
0.00933837890625,
-0.007598876953125,
-0.0139617919921875,
0.0150909423828125,
0.0187530517578125,
0.01427459716796875,
0.00970458984375,
0.0008549690246582031,
0.0131072998046875,
-0.0296173095703125,
0.0236358642578125,
0.005626678466796875,
-0.020233154296875,
-0.00750732421875,
-0.0084228515625,
0.0099639892578125,
0.0175933837890625,
-0.0082244873046875,
-0.012054443359375,
0.01397705078125,
0.01617431640625,
0.003406524658203125,
-0.0185394287109375,
0.0047607421875,
0.01200103759765625,
-0.00798797607421875,
-0.0019083023071289062,
-0.007061004638671875,
-0.027435302734375,
-0.01064300537109375,
0.036651611328125,
-0.038818359375,
0.0011749267578125,
0.0001533031463623047,
-0.00872802734375,
-0.00955963134765625,
-0.0233306884765625,
0.02508544921875,
-0.01242828369140625,
-0.020721435546875,
-0.0014934539794921875,
-0.0159912109375,
-0.01026153564453125,
0.0458984375,
-0.004669189453125,
0.019744873046875,
0.023895263671875,
0.0089874267578125,
-0.018035888671875,
-0.0036754608154296875,
-0.020751953125,
0.0079498291015625,
-0.01045989990234375,
-0.002399444580078125,
-0.013458251953125,
0.00013887882232666016,
0.01666259765625,
-0.03131103515625,
0.0017452239990234375,
-0.0211334228515625,
-0.0036182403564453125,
0.01340484619140625,
0.01467132568359375,
0.042327880859375,
0.0032405853271484375,
-0.0015659332275390625,
0.042236328125,
0.026763916015625,
-0.016448974609375,
0.0177764892578125,
-0.00989532470703125,
0.005802154541015625,
0.0263671875,
-0.0165252685546875,
-0.020904541015625,
0.007518768310546875,
-0.0056304931640625,
-0.029205322265625,
-0.0065155029296875,
0.0123138427734375,
-0.0015869140625,
-0.01364898681640625,
-0.0433349609375,
0.00922393798828125,
-0.034515380859375,
-0.01166534423828125,
0.03594970703125,
0.01287078857421875,
-0.0120697021484375,
0.006744384765625,
0.01239776611328125,
-0.004070281982421875,
-0.01380157470703125,
-0.0010738372802734375,
-0.0254058837890625,
0.000022351741790771484,
0.0022068023681640625,
-0.0303802490234375,
0.000457763671875,
0.0177764892578125,
0.0239105224609375,
-0.0103759765625,
-0.0002830028533935547,
-0.01500701904296875,
0.0297698974609375,
-0.0285186767578125,
-0.01331329345703125,
-0.0172271728515625,
-0.0248870849609375,
0.007244110107421875,
0.011627197265625,
0.006931304931640625,
0.033294677734375,
0.0078277587890625,
0.01519775390625,
-0.0098876953125,
0.0024623870849609375,
0.03155517578125,
0.02642822265625,
-0.0181427001953125,
0.0145263671875,
-0.00319671630859375,
-0.0015726089477539062,
0.020294189453125,
0.002208709716796875,
0.0166015625,
-0.0240936279296875,
0.0316162109375,
0.053192138671875,
-0.0174102783203125,
0.00577545166015625,
-0.007080078125,
0.0111846923828125,
0.033538818359375,
-0.00408935546875,
-0.0097198486328125,
-0.01525115966796875,
-0.004673004150390625,
-0.01401519775390625,
0.01245880126953125,
0.032623291015625,
0.0015478134155273438,
-0.0233306884765625,
0.005130767822265625,
-0.004367828369140625,
-0.00643157958984375,
0.01285552978515625,
-0.007007598876953125,
-0.0026607513427734375,
0.033843994140625,
-0.0147705078125,
-0.0401611328125,
0.02166748046875,
-0.0002665519714355469,
-0.0200653076171875,
0.0161590576171875,
0.017730712890625,
0.0189666748046875,
0.0044708251953125,
-0.0036640167236328125,
0.02667236328125,
0.01629638671875,
0.0008716583251953125,
0.005359649658203125,
-0.006099700927734375,
0.001544952392578125,
0.0028438568115234375,
-0.019805908203125,
0.0227203369140625,
0.006511688232421875,
-0.0090179443359375,
-0.0261077880859375,
0.005115509033203125,
0.0006041526794433594,
0.011444091796875,
0.01342010498046875,
0.01039886474609375,
-0.0126495361328125,
-0.01303863525390625,
-0.028289794921875,
0.0025386810302734375,
0.0026416778564453125,
0.036865234375,
-0.0230255126953125,
-0.0019893646240234375,
0.012542724609375,
-0.031341552734375,
0.00009971857070922852,
0.003204345703125,
-0.0032501220703125,
0.00699615478515625,
-0.0125579833984375,
-0.0166473388671875,
0.01788330078125,
0.02215576171875,
0.005260467529296875,
0.024810791015625,
0.0018720626831054688,
0.0017366409301757812,
-0.0198974609375,
-0.00971221923828125,
0.0154571533203125,
0.029632568359375,
0.00713348388671875,
-0.00867462158203125,
0.009521484375,
0.0244140625,
-0.0228271484375,
0.0011081695556640625,
-0.0213623046875,
-0.0251312255859375,
-0.02227783203125,
0.00011056661605834961,
0.0198516845703125,
-0.02532958984375,
-0.005580902099609375,
0.004215240478515625,
0.0005350112915039062,
-0.00525665283203125,
-0.0023822784423828125,
-0.00850677490234375,
0.02093505859375,
0.0091552734375,
-0.0016317367553710938,
0.0012311935424804688,
-0.013397216796875,
0.02325439453125,
0.0164947509765625,
0.0080413818359375,
0.04296875,
0.00949859619140625,
0.006744384765625,
0.0201568603515625,
0.0128936767578125,
0.02886962890625,
-0.04266357421875,
0.0171661376953125,
0.0092010498046875,
0.00969696044921875,
0.003795623779296875,
-0.000667572021484375,
0.0100860595703125,
-0.01296234130859375,
0.002105712890625,
0.017120361328125,
-0.0037822723388671875,
-0.02191162109375,
0.01198577880859375,
0.0230712890625,
0.005062103271484375,
0.005359649658203125,
-0.02581787109375,
0.005397796630859375,
0.0078582763671875,
-0.0273590087890625,
-0.02532958984375,
-0.004467010498046875,
-0.00788116455078125,
0.0020198822021484375,
0.0130615234375,
-0.0012960433959960938,
0.0037899017333984375,
-0.02142333984375,
0.0137176513671875,
0.005344390869140625,
-0.0182342529296875,
0.016510009765625,
0.01386260986328125,
-0.02227783203125,
0.0191497802734375,
-0.0242767333984375,
0.002216339111328125,
0.0374755859375,
-0.0098876953125,
-0.0004863739013671875,
-0.037750244140625,
-0.005817413330078125,
0.040130615234375,
-0.0038204193115234375,
0.05035400390625,
-0.00504302978515625,
-0.0184326171875,
-0.007610321044921875,
0.010498046875,
0.00308990478515625,
-0.0132293701171875,
-0.0295562744140625,
0.005218505859375,
0.0135955810546875,
0.00939178466796875,
0.0167083740234375,
0.0182647705078125,
-0.0103607177734375,
0.007049560546875,
0.003734588623046875,
0.0014705657958984375,
-0.0081634521484375,
-0.01544189453125,
0.01153564453125,
-0.024200439453125,
0.0009388923645019531,
-0.032958984375,
0.034515380859375,
0.0016336441040039062,
-0.0088043212890625,
-0.01129913330078125,
-0.0284881591796875,
-0.0178680419921875,
-0.004924774169921875,
-0.0228118896484375,
0.030731201171875,
-0.012481689453125,
0.0277099609375,
-0.01177978515625,
0.01751708984375,
0.020904541015625,
-0.0284271240234375,
-0.006229400634765625,
-0.0126953125,
0.040374755859375,
-0.015777587890625,
-0.017852783203125,
0.0132293701171875,
-0.036376953125,
-0.004268646240234375,
-0.010772705078125,
0.0029544830322265625,
0.0311431884765625,
0.0341796875,
-0.00943756103515625,
0.0099639892578125,
-0.01329803466796875,
0.0162200927734375,
0.01422119140625,
0.0028820037841796875,
-0.0087890625,
-0.010986328125,
0.03375244140625,
-0.03094482421875,
-0.0251007080078125,
-0.00402069091796875,
-0.01192474365234375,
0.01024627685546875,
-0.00386810302734375,
0.011016845703125,
-0.0036067962646484375,
-0.036956787109375,
0.030181884765625,
0.0260772705078125,
-0.043609619140625,
-0.0192108154296875,
0.0240631103515625,
0.0025272369384765625,
0.0021343231201171875,
-0.0008754730224609375,
0.000762939453125,
0.00441741943359375,
-0.005191802978515625,
-0.00390625,
-0.0193634033203125,
0.0006551742553710938,
-0.0159912109375,
0.0047454833984375,
0.00891876220703125,
0.009246826171875,
-0.0169525146484375,
-0.045867919921875,
-0.00894927978515625,
-0.0249176025390625,
-0.0406494140625,
-0.0297698974609375,
-0.026458740234375,
0.00730133056640625,
0.01422119140625,
0.007343292236328125,
-0.0030002593994140625,
0.0026149749755859375,
0.040863037109375,
0.0097198486328125,
-0.006011962890625,
0.00951385498046875,
0.0194091796875,
-0.0222320556640625,
-0.004611968994140625,
0.0114593505859375,
-0.003398895263671875,
-0.006801605224609375,
0.0362548828125,
-0.0014543533325195312,
0.01143646240234375,
0.01387786865234375,
0.0026111602783203125,
0.0175933837890625,
0.0057830810546875,
-0.013763427734375,
-0.007640838623046875,
0.01116943359375,
-0.0308837890625,
0.0005970001220703125,
0.0196533203125,
0.02587890625,
-0.007137298583984375,
-0.01477813720703125,
0.03607177734375,
-0.0272064208984375,
-0.00673675537109375,
-0.0231781005859375,
0.029388427734375,
0.03643798828125,
-0.006221771240234375,
-0.0276641845703125,
-0.055084228515625,
-0.01047515869140625,
-0.0085601806640625,
0.0216827392578125,
0.012481689453125,
-0.01306915283203125,
0.005023956298828125,
0.00466156005859375,
0.01175689697265625,
0.00403594970703125,
0.00841522216796875,
0.038543701171875,
0.013214111328125,
-0.004985809326171875,
-0.01184844970703125,
0.01366424560546875,
0.0135040283203125,
-0.046112060546875,
0.0005707740783691406,
0.025421142578125,
-0.014495849609375,
-0.005329132080078125,
-0.028839111328125,
0.017364501953125,
0.01143646240234375,
0.0142364501953125,
0.01934814453125,
-0.00946044921875,
0.0017633438110351562,
-0.033538818359375,
-0.0131988525390625,
0.00186920166015625,
-0.023529052734375,
-0.005176544189453125,
0.00518798828125,
0.035186767578125,
-0.01007080078125,
0.034637451171875,
-0.018524169921875,
-0.01445770263671875,
-0.02618408203125,
-0.02484130859375,
-0.0026264190673828125,
-0.00121307373046875,
0.0014772415161132812,
-0.019866943359375,
-0.0325927734375,
-0.0066680908203125,
-0.0044097900390625,
0.003452301025390625,
-0.01258087158203125,
0.01029205322265625,
-0.001430511474609375,
-0.002216339111328125,
-0.0069122314453125,
0.0195465087890625,
-0.01218414306640625,
-0.037261962890625,
-0.001811981201171875,
0.0176849365234375,
-0.01090240478515625,
-0.019927978515625,
0.0239105224609375,
0.00203704833984375,
0.0136260986328125,
-0.0091552734375,
0.0142364501953125,
0.01690673828125,
-0.002765655517578125,
-0.0165557861328125,
0.018402099609375,
0.006320953369140625,
0.007259368896484375,
0.02197265625,
-0.03338623046875,
-0.02154541015625,
0.0221710205078125,
-0.0201416015625,
0.02313232421875,
-0.01346588134765625,
0.0059814453125,
0.005435943603515625,
0.031829833984375,
-0.019012451171875,
-0.005153656005859375,
-0.029296875,
0.01287841796875,
0.0251312255859375,
0.027587890625,
0.010650634765625,
0.0229339599609375,
0.06201171875,
0.025360107421875,
-0.01061248779296875,
-0.043243408203125,
-0.022186279296875,
-0.01090240478515625,
-0.0100250244140625,
-0.005519866943359375,
-0.050140380859375,
0.001354217529296875,
-0.0372314453125,
-0.003337860107421875,
-0.004360198974609375,
0.026458740234375,
0.0330810546875,
-0.003997802734375,
-0.0179443359375,
0.0099334716796875,
0.0206756591796875,
0.018341064453125,
-0.0126190185546875,
0.0172882080078125,
0.0029468536376953125,
-0.03289794921875,
-0.0108489990234375,
0.00949859619140625,
-0.04241943359375,
-0.0032806396484375,
-0.0064544677734375,
-0.0067596435546875,
0.010955810546875,
0.0379638671875,
-0.0141448974609375,
-0.0037097930908203125,
0.00455474853515625,
0.004558563232421875,
0.0206451416015625,
0.001796722412109375,
0.03533935546875,
-0.01160430908203125,
-0.002849578857421875,
-0.0081024169921875,
0.0037975311279296875,
0.01522064208984375,
-0.0205841064453125,
0.00650787353515625,
0.01158905029296875,
-0.0255126953125,
0.008148193359375,
-0.00799560546875,
-0.0215301513671875,
0.0308074951171875,
0.004547119140625,
0.0307159423828125,
0.000006377696990966797,
-0.020843505859375,
0.017822265625,
-0.03851318359375,
-0.00777435302734375,
-0.01154327392578125,
-0.00817108154296875,
0.0191497802734375,
-0.03509521484375,
-0.01532745361328125,
-0.0004773139953613281,
0.02667236328125,
0.00665283203125,
-0.032257080078125,
0.0207672119140625,
0.006519317626953125,
-0.000213623046875,
0.039581298828125,
-0.0255889892578125,
0.0064697265625,
0.005992889404296875,
0.010040283203125,
-0.00653839111328125,
0.0147857666015625,
0.020111083984375,
-0.001110076904296875,
-0.004730224609375,
0.00855255126953125,
0.01363372802734375,
0.01209259033203125,
0.021881103515625,
0.0270233154296875,
0.00691986083984375,
0.025909423828125,
0.007354736328125,
0.005603790283203125,
-0.004734039306640625,
-0.0007214546203613281,
-0.016815185546875,
-0.007534027099609375,
-0.001499176025390625,
-0.019378662109375,
0.0203399658203125,
-0.0006318092346191406,
-0.023223876953125,
-0.01131439208984375,
-0.029144287109375,
-0.029327392578125,
-0.006061553955078125,
0.01145172119140625,
0.00594329833984375,
-0.0029315948486328125,
-0.0177001953125,
-0.0191192626953125,
-0.007236480712890625,
-0.00276947021484375,
-0.023101806640625,
0.0086669921875,
0.00807952880859375,
-0.0225067138671875,
-0.03192138671875,
0.0265045166015625,
0.030364990234375,
0.0194091796875,
0.001987457275390625,
0.0089569091796875,
0.024505615234375,
-0.03887939453125,
-0.0117034912109375,
0.0170440673828125,
0.052490234375,
-0.0041961669921875,
-0.042510986328125,
0.01134490966796875,
-0.0030117034912109375,
-0.036376953125,
-0.035003662109375,
-0.059722900390625,
0.0110015869140625,
-0.0195159912109375,
0.01155853271484375,
0.022613525390625,
-0.004100799560546875,
0.003330230712890625,
-0.0070343017578125,
-0.006328582763671875,
-0.005580902099609375,
0.01611328125,
0.026763916015625,
0.0091094970703125,
-0.0171356201171875,
0.0210723876953125,
-0.004932403564453125,
0.028778076171875,
0.006683349609375,
-0.0313720703125,
0.02398681640625,
-0.01100921630859375,
0.0161285400390625,
0.00628662109375,
0.0113525390625,
0.027923583984375,
0.001667022705078125,
0.007427215576171875,
-0.03277587890625,
0.0031890869140625,
0.0114593505859375,
0.0161285400390625,
0.00438690185546875,
0.0081787109375,
0.00981903076171875,
-0.0289459228515625,
0.02001953125,
0.0007171630859375,
-0.029693603515625,
0.0094451904296875,
0.0262603759765625,
-0.0175018310546875,
0.037261962890625,
0.01995849609375,
-0.013641357421875,
-0.0032939910888671875,
0.0149078369140625,
0.021942138671875,
-0.003864288330078125,
0.0018978118896484375,
-0.00200653076171875,
-0.005954742431640625,
0.0457763671875,
-0.009033203125,
0.01139068603515625,
0.01263427734375,
0.0011119842529296875,
0.02069091796875,
0.015594482421875,
0.0239715576171875,
-0.006023406982421875,
0.01171875,
-0.00443267822265625,
-0.03387451171875,
-0.0011463165283203125,
0.027435302734375,
-0.03143310546875,
0.0184478759765625,
-0.007572174072265625,
-0.0029239654541015625,
0.0011310577392578125,
0.0199127197265625,
0.002838134765625,
-0.036102294921875,
-0.0020294189453125,
-0.003742218017578125,
-0.0279541015625,
-0.0061798095703125,
-0.03253173828125,
0.016937255859375,
0.00524139404296875,
-0.0225067138671875,
0.0225067138671875,
-0.0163116455078125,
0.00908660888671875,
0.0104522705078125,
-0.01395416259765625,
0.0063323974609375,
0.0122833251953125,
0.0001323223114013672,
-0.03759765625,
-0.0008559226989746094,
-0.0023651123046875,
-0.0272369384765625,
0.034698486328125,
0.014862060546875,
0.0160369873046875,
-0.0067901611328125,
0.03265380859375,
0.0185089111328125,
0.0148162841796875,
-0.01499176025390625,
-0.00792694091796875,
0.020477294921875,
-0.00860595703125,
-0.02325439453125,
0.042633056640625,
0.0132904052734375,
-0.02349853515625,
-0.0016183853149414062,
0.01959228515625,
-0.0012254714965820312,
-0.006290435791015625,
-0.018585205078125,
0.00907135009765625,
-0.006603240966796875,
-0.027313232421875,
0.0100555419921875,
-0.0208740234375,
-0.01175689697265625,
-0.0038623809814453125,
0.0013284683227539062,
0.0187225341796875,
-0.00705718994140625,
0.03466796875,
0.020477294921875,
-0.0386962890625,
0.00794219970703125,
-0.0037555694580078125,
0.031982421875,
-0.00878143310546875,
-0.015869140625,
-0.00383758544921875,
0.0288238525390625,
-0.02874755859375,
-0.020538330078125,
-0.0205230712890625,
0.03558349609375,
0.01384735107421875,
0.0170745849609375,
0.017120361328125,
0.00019407272338867188,
0.01239013671875,
0.0360107421875,
-0.0035724639892578125,
0.035400390625,
0.03948974609375,
-0.0023937225341796875,
0.0164794921875,
-0.023284912109375,
0.0184783935546875,
0.0034389495849609375,
0.0098419189453125,
-0.0350341796875,
0.0295257568359375,
-0.006237030029296875,
0.0186920166015625,
-0.003627777099609375,
0.00926971435546875,
0.0098876953125,
-0.0011272430419921875,
-0.0091094970703125,
0.0032405853271484375,
-0.005283355712890625,
-0.0022258758544921875,
-0.0272216796875,
-0.0205841064453125,
-0.037872314453125,
-0.0112762451171875,
0.029510498046875,
0.0193939208984375,
-0.01532745361328125,
0.0413818359375,
-0.00414276123046875,
0.005702972412109375,
-0.0312042236328125,
0.0307769775390625,
0.01050567626953125,
0.0027141571044921875,
-0.002899169921875,
-0.0047760009765625,
0.0181121826171875,
0.037139892578125,
0.005397796630859375,
-0.021881103515625,
0.00756072998046875,
0.018157958984375,
-0.0110931396484375,
0.04315185546875,
-0.01224517822265625,
0.0239105224609375,
-0.00220489501953125,
0.031005859375,
-0.004421234130859375,
-0.0017747879028320312,
0.03778076171875,
0.006549835205078125,
-0.0257110595703125,
0.020416259765625,
0.0097808837890625,
-0.0034275054931640625,
-0.017608642578125,
0.00908660888671875,
0.0230865478515625,
0.01465606689453125,
-0.00846099853515625,
0.01280975341796875,
0.0144195556640625,
0.005828857421875,
0.0128631591796875,
0.01540374755859375,
-0.00551605224609375,
0.01529693603515625,
0.0268707275390625,
-0.00838470458984375,
-0.005523681640625,
-0.0225372314453125,
-0.0246734619140625,
-0.050201416015625,
-0.0340576171875,
-0.01197052001953125,
-0.0019369125366210938,
-0.0228118896484375,
0.00937652587890625,
-0.02362060546875,
-0.01459503173828125,
-0.0221099853515625,
-0.006061553955078125,
0.0164337158203125,
-0.01300811767578125,
0.0087890625,
-0.0041046142578125,
-0.0006999969482421875,
0.0263519287109375,
0.0164947509765625,
-0.03924560546875,
-0.01947021484375,
0.003170013427734375,
0.0140228271484375,
0.047271728515625,
-0.028717041015625,
0.0100250244140625,
-0.03271484375,
0.00562286376953125,
0.031463623046875,
-0.037933349609375,
-0.00286865234375,
-0.00989532470703125,
0.005279541015625,
-0.0036983489990234375,
0.01904296875,
-0.0089111328125,
0.0024280548095703125,
0.0004057884216308594,
-0.0031948089599609375,
-0.0215301513671875,
0.0023670196533203125,
0.003971099853515625,
0.009857177734375,
-0.0191497802734375,
-0.0005335807800292969,
-0.03643798828125,
-0.02838134765625,
-0.055633544921875,
-0.0031642913818359375,
-0.0108489990234375,
-0.0273590087890625,
0.006412506103515625,
-0.01296234130859375,
-0.0171966552734375,
-0.00153350830078125,
-0.0018281936645507812,
0.012969970703125,
-0.01470947265625,
-0.000202178955078125,
-0.001506805419921875,
-0.01334381103515625,
-0.020751953125,
0.0340576171875,
0.037689208984375,
0.025665283203125,
0.0139923095703125,
0.0173492431640625,
-0.00617218017578125,
0.0382080078125,
0.0208282470703125,
0.0157928466796875,
0.018280029296875,
-0.016021728515625,
-0.00396728515625,
0.0158233642578125,
0.00942230224609375,
0.0229339599609375,
-0.035675048828125,
-0.02398681640625,
-0.00388336181640625,
0.0151824951171875,
-0.00537109375,
-0.019012451171875,
-0.02032470703125,
0.0291900634765625,
-0.01152801513671875,
0.044219970703125,
0.033905029296875,
-0.00592041015625,
0.00665283203125,
-0.00823211669921875,
-0.01509857177734375,
-0.01325225830078125,
-0.00018393993377685547,
0.0268096923828125,
0.02630615234375,
-0.0057373046875,
0.001361846923828125,
-0.00962066650390625,
-0.0135498046875,
0.021270751953125,
-0.03173828125,
0.031585693359375,
0.02752685546875,
-0.0445556640625,
0.029083251953125,
-0.00966644287109375,
-0.0130615234375,
0.017547607421875,
0.022369384765625,
-0.00994110107421875,
0.01708984375,
0.007068634033203125,
-0.0292205810546875,
-0.0178070068359375,
0.0258636474609375,
-0.00009828805923461914,
0.00519561767578125,
0.01030731201171875,
-0.004322052001953125,
0.00891876220703125,
0.00812530517578125,
0.018035888671875,
0.0105438232421875,
-0.035675048828125,
0.023590087890625,
0.005702972412109375,
0.03045654296875,
-0.00775909423828125,
0.0123748779296875,
0.007114410400390625,
-0.00738525390625,
0.04803466796875,
-0.0005292892456054688,
0.027191162109375,
0.0045928955078125,
-0.0169525146484375,
-0.0035724639892578125,
0.00007623434066772461,
-0.00247955322265625,
0.047698974609375,
-0.0298919677734375,
0.017059326171875,
0.0004906654357910156,
-0.0015592575073242188,
-0.030670166015625,
0.0278167724609375,
-0.005199432373046875,
-0.00228118896484375,
0.00867462158203125,
0.01039886474609375,
0.0132598876953125,
-0.01554107666015625,
-0.0152435302734375,
0.000812530517578125,
0.0067596435546875,
0.01544952392578125,
0.016204833984375,
-0.0008668899536132812,
-0.03363037109375,
0.0048980712890625,
0.00305938720703125,
0.044464111328125,
0.0283660888671875,
0.006908416748046875,
0.004291534423828125,
-0.01342010498046875,
-0.02362060546875,
-0.032623291015625,
-0.0189666748046875,
-0.004322052001953125,
0.0135345458984375,
-0.01447296142578125,
-0.01265716552734375,
0.0216064453125,
0.008575439453125,
-0.0038585662841796875,
0.007305145263671875,
-0.019439697265625,
0.006237030029296875,
-0.014434814453125,
-0.035797119140625,
-0.00458526611328125,
-0.00963592529296875,
-0.0269012451171875,
0.00696563720703125,
-0.00455474853515625,
-0.0196990966796875,
0.016693115234375,
-0.007472991943359375,
0.0017061233520507812,
-0.05596923828125,
-0.005939483642578125,
-0.0019550323486328125,
0.0478515625,
0.010009765625,
-0.03570556640625,
-0.01438140869140625,
-0.0269775390625,
-0.005558013916015625,
0.00914764404296875,
-0.021026611328125,
-0.00836181640625,
0.0307159423828125,
-0.0034732818603515625,
0.0163726806640625,
0.0053253173828125,
-0.0132293701171875,
-0.0143280029296875,
-0.03594970703125,
-0.005794525146484375,
0.03570556640625,
0.00792694091796875,
-0.0021266937255859375,
0.0184783935546875,
-0.05401611328125,
0.00954437255859375,
0.0177154541015625,
-0.009979248046875,
-0.026580810546875,
0.006229400634765625,
-0.0277862548828125,
-0.0007576942443847656,
0.0173492431640625,
0.008331298828125,
-0.0271148681640625,
0.0238037109375,
-0.023406982421875,
-0.0007977485656738281,
0.0242156982421875,
0.01447296142578125,
0.00502777099609375,
-0.030242919921875,
0.024658203125,
0.044891357421875,
-0.01007080078125,
0.032196044921875,
0.005283355712890625,
-0.0455322265625,
-0.027984619140625,
-0.005207061767578125,
0.03955078125,
0.006168365478515625,
0.050506591796875,
0.0303955078125,
-0.004787445068359375,
0.006702423095703125,
-0.01446533203125,
-0.01482391357421875,
0.0242767333984375,
0.02398681640625,
0.0002455711364746094,
0.00665283203125,
0.0016765594482421875,
0.0143890380859375
] |
ours_554
|
Notice that \(\frac{ab+1}{a+b}+1=\frac{ab+a+b+1}{a+b}=\frac{(a+1)(b+1)}{a+b}\) must be an integer. This implies \(a+b \mid a+1\) or \(a+b \mid b+1\), so either \(a=1\) or \(b=1\). It follows that we need \(a+1\) or \(b+1\) to be a prime. Since there are 26 primes less than or equal to 101 (the maximum possible value of \(a+1\)), we obtain \(26 \times 2 = 52\) pairs \((a, b)\). However, we overcount the \(a=b=1\) case, so the answer is 51.
\(\boxed{51}\)
|
51
|
{
"competition": "us_comps",
"dataset": "Ours",
"posts": null,
"source": "OMOSoln2.md"
}
|
Find the number of ordered pairs of positive integers \((a, b)\) with \(a+b\) prime, \(1 \leq a, b \leq 100\), and \(\frac{ab+1}{a+b}\) is an integer.
|
[
"/Mathematics/DiscreteMathematics/Combinatorics/Enumeration",
"/Mathematics/DiscreteMathematics/Combinatorics/GeneralCombinatorics",
"/Mathematics/DiscreteMathematics/DivisionProblems/SubsetSumProblem",
"/Mathematics/NumberTheory/Divisors/Divides",
"/Mathematics/NumberTheory/Divisors/Divisible",
"/Mathematics/NumberTheory/Divisors/Divisor",
"/Mathematics/NumberTheory/GeneralNumberTheory/ElementaryMethods",
"/Mathematics/NumberTheory/GeneralNumberTheory/ElementaryNumberTheory",
"/Mathematics/NumberTheory/GeneralNumberTheory/NumberTheory",
"/Mathematics/NumberTheory/Integers/Integer",
"/Mathematics/NumberTheory/Integers/N",
"/Mathematics/NumberTheory/Integers/PositiveInteger",
"/Mathematics/NumberTheory/Integers/Z-Plus",
"/Mathematics/NumberTheory/PrimeNumbers/PrimeSumsandProducts"
] |
Rewrite (ab+1)/(a+b)+1 as (a+1)(b+1)/(a+b) to force a+b to divide one of a+1 or b+1, forcing one variable to be 1.
|
[
-0.00025343894958496094,
-0.033721923828125,
0.01190185546875,
-0.004398345947265625,
-0.0011968612670898438,
0.0006761550903320312,
-0.01605224609375,
0.044677734375,
-0.007213592529296875,
-0.015716552734375,
0.0102081298828125,
-0.032928466796875,
-0.00469970703125,
-0.0301666259765625,
-0.03411865234375,
0.016265869140625,
0.048431396484375,
-0.0185699462890625,
0.01556396484375,
-0.0037212371826171875,
-0.0032749176025390625,
-0.01111602783203125,
-0.056427001953125,
0.00934600830078125,
0.01007080078125,
0.0173187255859375,
-0.0123443603515625,
-0.01351165771484375,
0.02386474609375,
0.0257568359375,
-0.0196075439453125,
0.00659942626953125,
-0.0144805908203125,
-0.0306396484375,
-0.0009288787841796875,
0.0038776397705078125,
0.00555419921875,
-0.007354736328125,
-0.013031005859375,
-0.0382080078125,
-0.004764556884765625,
0.008026123046875,
0.00893402099609375,
0.010284423828125,
0.006931304931640625,
0.01175689697265625,
-0.00002199411392211914,
0.01409149169921875,
-0.00684356689453125,
-0.008148193359375,
-0.007213592529296875,
0.0024776458740234375,
-0.0416259765625,
-0.005245208740234375,
-0.03076171875,
-0.037078857421875,
-0.003692626953125,
0.0013380050659179688,
-0.045166015625,
-0.036651611328125,
-0.0023040771484375,
0.0038585662841796875,
0.004299163818359375,
-0.032470703125,
-0.0021953582763671875,
-0.00579071044921875,
-0.0249786376953125,
-0.042022705078125,
0.0018587112426757812,
-0.00908660888671875,
0.06298828125,
-0.019012451171875,
0.0239410400390625,
-0.018463134765625,
-0.005054473876953125,
-0.0028324127197265625,
-0.01776123046875,
0.00318145751953125,
0.0184173583984375,
0.007354736328125,
0.008697509765625,
-0.00115966796875,
0.007488250732421875,
0.0195465087890625,
0.01131439208984375,
0.01409149169921875,
-0.028045654296875,
0.005176544189453125,
-0.0178985595703125,
-0.01142120361328125,
-0.001338958740234375,
0.01451873779296875,
0.0011358261108398438,
0.00725555419921875,
-0.0006575584411621094,
-0.0177764892578125,
0.01540374755859375,
-0.00890350341796875,
-0.0062255859375,
0.0116729736328125,
-0.00525665283203125,
-0.01093292236328125,
0.01812744140625,
-0.019073486328125,
-0.05804443359375,
-0.0057373046875,
-0.0231781005859375,
-0.013946533203125,
-0.0150604248046875,
-0.0088348388671875,
0.01020050048828125,
0.00974273681640625,
0.0133514404296875,
0.0167236328125,
0.03399658203125,
0.003841400146484375,
0.043243408203125,
0.00894927978515625,
-0.0032596588134765625,
-0.023193359375,
-0.0036945343017578125,
0.0190887451171875,
-0.0066375732421875,
0.0006632804870605469,
0.005767822265625,
0.003391265869140625,
-0.000713348388671875,
-0.030670166015625,
0.0036163330078125,
-0.01715087890625,
0.0174713134765625,
0.0086212158203125,
-0.063232421875,
-0.00888824462890625,
-0.050384521484375,
0.01399993896484375,
-0.01149749755859375,
0.010772705078125,
-0.0022792816162109375,
-0.0230255126953125,
-0.00307464599609375,
-0.0226898193359375,
-0.001216888427734375,
-0.00208282470703125,
0.015655517578125,
-0.0310821533203125,
-0.01456451416015625,
-0.040985107421875,
-0.0062103271484375,
0.006511688232421875,
-0.004913330078125,
-0.0129852294921875,
-0.00214385986328125,
-0.004886627197265625,
-0.005702972412109375,
0.0098876953125,
0.004711151123046875,
0.0106048583984375,
-0.00505828857421875,
0.01184844970703125,
0.003963470458984375,
-0.0011892318725585938,
-0.0032215118408203125,
0.00719451904296875,
-0.00504302978515625,
0.009033203125,
0.01396942138671875,
-0.00348663330078125,
-0.0162506103515625,
0.00455474853515625,
0.01361846923828125,
0.01410675048828125,
-0.0008206367492675781,
-0.019927978515625,
-0.0006613731384277344,
0.026824951171875,
0.00022971630096435547,
0.0263519287109375,
-0.017425537109375,
0.015838623046875,
0.01239776611328125,
-0.03485107421875,
-0.002262115478515625,
0.004764556884765625,
0.010040283203125,
-0.01526641845703125,
0.0005612373352050781,
0.025238037109375,
0.0227203369140625,
0.0074005126953125,
-0.007373809814453125,
-0.01194000244140625,
-0.006893157958984375,
0.001338958740234375,
-0.0038394927978515625,
-0.004352569580078125,
-0.0251007080078125,
-0.0176849365234375,
0.023223876953125,
0.0227203369140625,
-0.01464080810546875,
0.0003917217254638672,
-0.00789642333984375,
-0.0030059814453125,
0.016082763671875,
0.0146942138671875,
0.0018339157104492188,
-0.01038360595703125,
-0.0016775131225585938,
-0.00020241737365722656,
0.011322021484375,
0.0016727447509765625,
-0.006778717041015625,
-0.0379638671875,
-0.0292816162109375,
0.01055908203125,
-0.01873779296875,
-0.0018205642700195312,
0.00812530517578125,
-0.032257080078125,
-0.0067291259765625,
0.01629638671875,
-0.01387786865234375,
-0.01555633544921875,
-0.0179290771484375,
-0.0020351409912109375,
0.01351165771484375,
0.00531768798828125,
0.005970001220703125,
0.0007038116455078125,
0.04681396484375,
0.0206146240234375,
0.00395965576171875,
0.002925872802734375,
0.01068878173828125,
-0.01392364501953125,
-0.045379638671875,
-0.01419830322265625,
-0.010498046875,
-0.0023708343505859375,
0.00791168212890625,
-0.000827789306640625,
0.007358551025390625,
0.0123291015625,
-0.01922607421875,
0.0015153884887695312,
0.0075225830078125,
-0.0021495819091796875,
-0.002780914306640625,
0.001064300537109375,
-0.01291656494140625,
-0.004924774169921875,
-0.0235137939453125,
-0.020294189453125,
0.027099609375,
-0.0024967193603515625,
-0.0032062530517578125,
0.01381683349609375,
-0.007152557373046875,
0.00009888410568237305,
-0.011566162109375,
-0.04522705078125,
-0.004840850830078125,
-0.005706787109375,
0.00733184814453125,
0.002685546875,
0.0261688232421875,
0.0238494873046875,
-0.01702880859375,
-0.0085906982421875,
0.05169677734375,
-0.03192138671875,
-0.01776123046875,
-0.0146331787109375,
-0.0009183883666992188,
0.0004208087921142578,
-0.0120849609375,
0.0162200927734375,
0.0236358642578125,
-0.01340484619140625,
0.00785064697265625,
-0.0279693603515625,
-0.017730712890625,
-0.0056610107421875,
-0.0193023681640625,
-0.004215240478515625,
0.0023937225341796875,
-0.0191192626953125,
-0.006565093994140625,
-0.017181396484375,
-0.0010595321655273438,
-0.037109375,
0.006015777587890625,
0.004344940185546875,
0.0213775634765625,
0.0018491744995117188,
0.007556915283203125,
-0.01381683349609375,
0.0167999267578125,
0.0023097991943359375,
0.03753662109375,
-0.0200958251953125,
-0.004734039306640625,
0.0069732666015625,
-0.002315521240234375,
0.036590576171875,
0.01418304443359375,
0.009490966796875,
0.0159454345703125,
-0.00849151611328125,
0.01337432861328125,
0.004302978515625,
-0.00424957275390625,
-0.00844573974609375,
0.0017061233520507812,
-0.0338134765625,
-0.0084075927734375,
0.003307342529296875,
-0.01384735107421875,
0.0201263427734375,
0.027618408203125,
-0.01268768310546875,
-0.00946044921875,
-0.0011911392211914062,
-0.000031888484954833984,
-0.0020618438720703125,
-0.0006551742553710938,
0.007488250732421875,
-0.02227783203125,
0.04541015625,
-0.00821685791015625,
-0.0022602081298828125,
-0.0006771087646484375,
-0.019317626953125,
0.0018205642700195312,
0.00823974609375,
-0.024169921875,
0.0225372314453125,
0.01322174072265625,
0.0020275115966796875,
-0.015228271484375,
-0.0335693359375,
-0.0025882720947265625,
-0.0006542205810546875,
-0.01395416259765625,
0.029144287109375,
0.0007753372192382812,
-0.0277557373046875,
0.00638580322265625,
-0.0226898193359375,
0.00666046142578125,
0.0284271240234375,
0.012359619140625,
-0.018707275390625,
-0.041717529296875,
-0.00507354736328125,
-0.0007581710815429688,
-0.007537841796875,
-0.0333251953125,
0.03887939453125,
0.005138397216796875,
-0.0001913309097290039,
0.004489898681640625,
0.0067291259765625,
0.0274200439453125,
-0.024871826171875,
-0.023193359375,
0.0014057159423828125,
-0.01763916015625,
-0.0128631591796875,
-0.00995635986328125,
-0.005950927734375,
0.0133209228515625,
-0.0019626617431640625,
-0.035736083984375,
0.0204925537109375,
0.0225830078125,
0.013641357421875,
0.0160675048828125,
0.0008797645568847656,
-0.011688232421875,
0.00736236572265625,
0.00814056396484375,
0.0267333984375,
-0.0118408203125,
-0.0186767578125,
-0.0194549560546875,
-0.043792724609375,
-0.03314208984375,
0.0025844573974609375,
0.0026988983154296875,
0.0177764892578125,
0.0010976791381835938,
0.0233917236328125,
-0.01149749755859375,
-0.0031890869140625,
-0.0016384124755859375,
-0.004360198974609375,
0.04364013671875,
-0.005901336669921875,
-0.005977630615234375,
-0.0128021240234375,
-0.0279998779296875,
0.0191192626953125,
0.014862060546875,
0.00452423095703125,
0.0113677978515625,
-0.0063629150390625,
-0.012847900390625,
-0.0033779144287109375,
0.026123046875,
0.003353118896484375,
-0.01508331298828125,
-0.043670654296875,
-0.0017557144165039062,
0.01410675048828125,
0.0173187255859375,
0.00782012939453125,
-0.046630859375,
-0.032928466796875,
0.0020427703857421875,
-0.004238128662109375,
-0.0197601318359375,
0.0014829635620117188,
0.01277923583984375,
0.0225067138671875,
-0.007762908935546875,
0.00930023193359375,
-0.0084228515625,
0.0021381378173828125,
-0.0182952880859375,
-0.020416259765625,
0.0126953125,
0.040252685546875,
0.0179290771484375,
-0.0002956390380859375,
0.014373779296875,
0.0084991455078125,
0.007389068603515625,
0.03338623046875,
-0.037261962890625,
-0.0226593017578125,
-0.0242767333984375,
0.002979278564453125,
0.01222991943359375,
0.00951385498046875,
-0.0010538101196289062,
0.0174713134765625,
-0.05755615234375,
0.016448974609375,
-0.0120086669921875,
-0.002246856689453125,
0.0034809112548828125,
-0.0264434814453125,
-0.026611328125,
0.01605224609375,
0.028472900390625,
-0.00095367431640625,
-0.02496337890625,
-0.01369476318359375,
-0.0131378173828125,
0.0191497802734375,
-0.0226287841796875,
0.0159912109375,
-0.0325927734375,
-0.0042266845703125,
0.02288818359375,
0.0080718994140625,
0.0058441162109375,
-0.001338958740234375,
0.014556884765625,
0.005092620849609375,
0.0190582275390625,
-0.0201873779296875,
-0.042938232421875,
0.007328033447265625,
0.0019311904907226562,
-0.005992889404296875,
-0.005657196044921875,
0.0089263916015625,
0.038818359375,
-0.009521484375,
0.00855255126953125,
-0.0147247314453125,
0.020721435546875,
0.0303955078125,
0.036224365234375,
-0.0064697265625,
-0.004169464111328125,
-0.0210113525390625,
0.00977325439453125,
0.051788330078125,
-0.040008544921875,
-0.0183258056640625,
-0.025299072265625,
-0.01219940185546875,
0.0142669677734375,
-0.01739501953125,
-0.00762176513671875,
-0.01427459716796875,
0.01427459716796875,
-0.040374755859375,
0.00997161865234375,
0.006916046142578125,
-0.0027065277099609375,
-0.029449462890625,
0.04046630859375,
-0.0115509033203125,
0.0076904296875,
-0.031768798828125,
0.009918212890625,
-0.0224456787109375,
0.00624847412109375,
-0.02947998046875,
-0.0167083740234375,
-0.02716064453125,
-0.01169586181640625,
-0.02325439453125,
0.0123443603515625,
0.01439666748046875,
-0.039459228515625,
-0.005153656005859375,
0.024566650390625,
-0.001865386962890625,
0.0278778076171875,
-0.03173828125,
-0.02056884765625,
-0.0643310546875,
0.04315185546875,
-0.0010080337524414062,
0.00922393798828125,
-0.01071929931640625,
-0.033203125,
0.001209259033203125,
-0.0166168212890625,
0.004405975341796875,
-0.0015268325805664062,
-0.0039043426513671875,
0.04217529296875,
0.025482177734375,
0.00955963134765625,
-0.01386260986328125,
0.0063934326171875,
-0.0061187744140625,
-0.0167083740234375,
-0.00782012939453125,
0.00704193115234375,
0.01079559326171875,
-0.01149749755859375,
0.0440673828125,
0.03173828125,
0.0126190185546875,
-0.00585174560546875,
-0.00122833251953125,
-0.0125579833984375,
-0.006580352783203125,
-0.0116729736328125,
0.013702392578125,
-0.0140533447265625,
0.013397216796875,
0.0305023193359375,
0.0091094970703125,
-0.0074462890625,
-0.0240478515625,
0.01383209228515625,
-0.0193023681640625,
-0.01329803466796875,
-0.0213470458984375,
-0.01477813720703125,
-0.02191162109375,
-0.00963592529296875,
-0.032989501953125,
-0.01308441162109375,
0.02716064453125,
-0.01360321044921875,
0.0295562744140625,
-0.005619049072265625,
0.0205230712890625,
0.014862060546875,
-0.01169586181640625,
0.033050537109375,
-0.0006928443908691406,
0.020599365234375,
-0.013214111328125,
0.016571044921875,
0.0017681121826171875,
-0.00780487060546875,
0.01277923583984375,
0.0226593017578125,
0.021453857421875,
-0.0008821487426757812,
-0.00894927978515625,
0.01406097412109375,
0.00449371337890625,
-0.03155517578125,
0.016021728515625,
0.02276611328125,
0.0038852691650390625,
0.01030731201171875,
0.0004036426544189453,
0.00896453857421875,
0.00012576580047607422,
-0.04534912109375,
-0.0009918212890625,
-0.041778564453125,
-0.007381439208984375,
0.024658203125,
0.034149169921875,
0.01450347900390625,
-0.0121307373046875,
0.0130615234375,
-0.007297515869140625,
0.005832672119140625,
0.002330780029296875,
0.0125732421875,
0.039581298828125,
0.003108978271484375,
0.002216339111328125,
-0.043670654296875,
-0.01561737060546875,
0.005886077880859375,
-0.0021209716796875,
-0.0281982421875,
0.028289794921875,
-0.0094757080078125,
0.00971221923828125,
0.033721923828125,
-0.03338623046875,
0.00820159912109375,
0.0160675048828125,
-0.019256591796875,
-0.00984954833984375,
-0.004909515380859375,
-0.0186920166015625,
-0.01097869873046875,
-0.01523590087890625,
-0.03729248046875,
0.019287109375,
0.025238037109375,
-0.0202789306640625,
-0.0033168792724609375,
0.0035648345947265625,
0.0277862548828125,
-0.055267333984375,
0.00595855712890625,
0.0034465789794921875,
-0.00995635986328125,
-0.01549530029296875,
-0.01425933837890625,
-0.015350341796875,
-0.0180206298828125,
-0.023773193359375,
0.0165252685546875,
0.0169677734375,
0.00862884521484375,
0.026123046875,
0.0198822021484375,
-0.007091522216796875,
0.036376953125,
-0.0237884521484375,
0.0303802490234375,
0.0005674362182617188,
-0.007175445556640625,
0.004932403564453125,
-0.061798095703125,
-0.00955963134765625,
0.046356201171875,
-0.0308380126953125,
-0.0165252685546875,
-0.0310211181640625,
0.00859832763671875,
-0.03033447265625,
0.0152435302734375,
-0.00362396240234375,
0.0031375885009765625,
0.0244140625,
-0.00859832763671875,
-0.0037212371826171875,
0.04302978515625,
0.036895751953125,
0.018463134765625,
0.021209716796875,
0.00861358642578125,
-0.02313232421875,
0.005950927734375,
-0.0030536651611328125,
0.0009431838989257812,
0.0162506103515625,
-0.004207611083984375,
0.0209197998046875,
-0.0059967041015625,
-0.007534027099609375,
-0.04345703125,
0.0011186599731445312,
0.0175018310546875,
-0.033294677734375,
0.037384033203125,
-0.0268096923828125,
-0.016571044921875,
-0.03472900390625,
0.013275146484375,
-0.035430908203125,
-0.00223541259765625,
0.0100860595703125,
-0.020599365234375,
-0.01422119140625,
-0.038787841796875,
-0.00270843505859375,
-0.00881195068359375,
0.0043487548828125,
-0.013336181640625,
-0.006000518798828125,
0.004180908203125,
-0.0200958251953125,
-0.00780487060546875,
0.0196990966796875,
0.023468017578125,
-0.01030731201171875,
-0.004917144775390625,
-0.026458740234375,
-0.007747650146484375,
0.00960540771484375,
-0.0166473388671875,
-0.01377105712890625,
0.0382080078125,
0.00925445556640625,
0.0283966064453125,
-0.046600341796875,
0.0035419464111328125,
0.004486083984375,
-0.04736328125,
0.0032405853271484375,
0.0137176513671875,
-0.0263824462890625,
-0.022308349609375,
0.01222991943359375,
0.01678466796875,
-0.04315185546875,
-0.013153076171875,
0.0097503662109375,
0.0194244384765625,
-0.00007802248001098633,
0.003612518310546875,
0.00661468505859375,
-0.016998291015625,
-0.019775390625,
0.021240234375,
-0.0167694091796875,
0.02752685546875,
0.0012159347534179688,
0.0156402587890625,
-0.025390625,
-0.0396728515625,
-0.046844482421875,
-0.0247802734375,
0.0167388916015625,
0.003940582275390625,
-0.0440673828125,
-0.01556396484375,
-0.0102081298828125,
-0.052886962890625,
0.027191162109375,
-0.01343536376953125,
0.02789306640625,
0.03338623046875,
-0.04248046875,
-0.04315185546875,
-0.02496337890625,
-0.0201263427734375,
0.032684326171875,
-0.04010009765625,
-0.015899658203125,
0.006755828857421875,
-0.0170440673828125,
-0.022247314453125,
0.0426025390625,
-0.0210113525390625,
-0.01050567626953125,
0.06304931640625,
-0.0108795166015625,
-0.00615692138671875,
0.0234527587890625,
0.00225067138671875,
0.0006937980651855469,
-0.03070068359375,
-0.0092010498046875,
-0.0173187255859375,
0.0094146728515625,
0.014373779296875,
0.01480865478515625,
0.013153076171875,
0.0124969482421875,
-0.0046234130859375,
0.006366729736328125,
0.0007796287536621094,
-0.0244598388671875,
-0.034515380859375,
0.004119873046875,
-0.058929443359375,
-0.0025005340576171875,
-0.0187835693359375,
-0.0213470458984375,
-0.011138916015625,
0.0131683349609375,
-0.006687164306640625,
-0.036468505859375,
0.0090484619140625,
-0.00612640380859375,
0.0098724365234375,
0.035003662109375,
0.00183868408203125,
-0.00528717041015625,
-0.037017822265625,
-0.0196685791015625,
0.019866943359375,
0.01244354248046875,
0.019073486328125,
0.0214385986328125,
-0.004711151123046875,
0.0335693359375,
-0.0157928466796875,
0.049163818359375,
0.01617431640625,
-0.0019254684448242188,
-0.02752685546875,
0.00917816162109375,
-0.008880615234375,
-0.00445556640625,
0.01494598388671875,
0.003475189208984375,
0.01103973388671875,
-0.0029964447021484375,
-0.0037899017333984375,
0.01343536376953125,
0.00606536865234375,
-0.0115203857421875,
0.0181427001953125,
0.033355712890625,
-0.038818359375,
0.006561279296875,
0.02972412109375,
0.00218963623046875,
0.024261474609375,
-0.0218505859375,
0.0045318603515625,
0.00872039794921875,
-0.019439697265625,
0.0205535888671875,
0.00463104248046875,
-0.006366729736328125,
0.02093505859375,
0.0111083984375,
0.002300262451171875,
0.01259613037109375,
0.00836944580078125,
0.0175018310546875,
0.01334381103515625,
-0.0093841552734375,
-0.01560211181640625,
-0.0078582763671875,
-0.0225677490234375,
-0.02142333984375,
0.01454925537109375,
0.007232666015625,
-0.01160430908203125,
-0.000054776668548583984,
0.007633209228515625,
-0.01009368896484375,
-0.005817413330078125,
-0.02020263671875,
0.01617431640625,
0.015869140625,
0.01468658447265625,
-0.001461029052734375,
0.0343017578125,
0.019195556640625,
-0.0009927749633789062,
0.035797119140625,
0.0293426513671875,
0.0016984939575195312,
0.0245819091796875,
-0.0299072265625,
-0.0229644775390625,
-0.00327301025390625,
0.0236358642578125,
-0.00669097900390625,
0.017852783203125,
0.05328369140625,
-0.0312347412109375,
-0.0195770263671875,
-0.028411865234375,
0.00777435302734375,
0.0039215087890625,
-0.06573486328125,
0.022674560546875,
-0.0146636962890625,
-0.0028553009033203125,
-0.00022411346435546875,
0.0092926025390625,
-0.035736083984375,
-0.01515960693359375,
0.005321502685546875,
0.04107666015625,
-0.004802703857421875,
-0.0062408447265625,
-0.00909423828125,
-0.0128326416015625,
-0.00537109375,
-0.007068634033203125,
0.0136260986328125,
-0.00960540771484375,
-0.0043792724609375,
0.03125,
0.0036792755126953125,
-0.0012216567993164062,
-0.033294677734375,
-0.0204925537109375,
-0.0261383056640625,
-0.00370025634765625,
0.010498046875,
0.038726806640625,
0.00202178955078125,
-0.00543975830078125,
0.005401611328125,
-0.027862548828125,
-0.000141143798828125,
-0.00656890869140625,
-0.0010900497436523438,
-0.026031494140625,
-0.0296173095703125,
0.01873779296875,
0.022674560546875,
-0.0207061767578125,
-0.0183868408203125,
-0.0072021484375,
0.0177001953125,
-0.0219879150390625,
-0.039886474609375,
0.017608642578125,
0.0018215179443359375,
-0.00493621826171875,
0.01261138916015625,
0.036651611328125,
0.04815673828125,
0.01837158203125,
0.0130157470703125,
0.006801605224609375,
0.0157012939453125,
0.01271820068359375,
-0.0214080810546875,
-0.0008635520935058594,
0.0113983154296875,
0.004894256591796875,
-0.01139068603515625,
-0.007320404052734375,
0.036285400390625,
0.041290283203125,
0.0016069412231445312,
-0.0019893646240234375,
-0.011474609375,
-0.040618896484375,
0.0211639404296875,
-0.044952392578125,
0.0016050338745117188,
-0.0214080810546875,
0.012542724609375,
0.018646240234375,
0.0034084320068359375,
0.0296783447265625,
0.0112762451171875,
0.0074462890625,
-0.036712646484375,
-0.00980377197265625,
-0.0496826171875,
0.00972747802734375,
0.00725555419921875,
-0.036102294921875,
0.04229736328125,
0.006526947021484375,
0.018463134765625,
-0.0364990234375,
0.0059051513671875,
-0.00830078125,
0.004734039306640625,
-0.0167236328125,
0.0230255126953125,
0.01332855224609375,
-0.00861358642578125,
-0.0065155029296875,
-0.041107177734375,
-0.0214996337890625,
0.002063751220703125,
-0.01288604736328125,
0.0227813720703125,
-0.0024261474609375,
0.00807952880859375,
-0.0362548828125,
0.01540374755859375,
0.005626678466796875,
0.046295166015625,
-0.03753662109375,
-0.01348114013671875,
-0.01053619384765625,
0.03045654296875,
0.010528564453125,
-0.00616455078125,
0.04730224609375,
-0.00408172607421875,
-0.0308837890625,
0.015960693359375,
0.0160064697265625,
0.0216827392578125,
-0.01192474365234375,
0.007083892822265625,
-0.0192413330078125,
0.00525665283203125,
0.0039005279541015625,
0.023712158203125,
-0.0167236328125,
0.019012451171875,
-0.02740478515625,
-0.00540924072265625,
-0.01511383056640625,
-0.019866943359375,
-0.00205230712890625,
-0.0122222900390625,
-0.0117950439453125,
-0.0214385986328125,
0.011444091796875,
0.0152130126953125,
0.00833892822265625,
-0.01422119140625,
0.01187896728515625,
-0.0006666183471679688,
-0.018310546875,
-0.016632080078125,
-0.00960540771484375,
-0.0255584716796875,
0.00794219970703125,
0.0143280029296875,
0.0201568603515625,
0.006580352783203125,
0.035491943359375,
0.01123809814453125,
0.03057861328125,
0.01068115234375,
0.01496124267578125,
0.01204681396484375,
-0.0389404296875,
0.00885009765625,
0.0031280517578125,
-0.03192138671875,
-0.022491455078125,
0.024322509765625,
-0.0034389495849609375,
0.010711669921875,
0.0081329345703125,
-0.040374755859375,
0.0203399658203125,
0.02093505859375,
-0.0186004638671875,
-0.009918212890625,
-0.01081085205078125,
0.00885772705078125,
-0.0003814697265625,
0.0089263916015625,
-0.0239105224609375,
-0.020233154296875,
-0.00510406494140625,
0.0155792236328125,
-0.0291595458984375,
0.00002181529998779297,
0.00974273681640625,
0.0012960433959960938,
0.0160675048828125,
0.01428985595703125,
0.0003917217254638672,
-0.01168060302734375,
-0.0113067626953125,
-0.0143890380859375,
-0.0067901611328125,
0.0003998279571533203,
-0.05059814453125,
0.0243682861328125,
-0.0018672943115234375,
0.035888671875,
-0.0208587646484375,
0.00616455078125,
0.01094818115234375,
-0.0193634033203125,
0.021331787109375,
-0.038482666015625,
-0.0147552490234375,
-0.003429412841796875,
-0.002582550048828125,
0.0278472900390625,
0.06854248046875,
0.0142974853515625,
0.018829345703125,
-0.01541900634765625,
-0.01016998291015625,
0.0224456787109375,
-0.007659912109375,
0.00276947021484375,
0.0184478759765625,
0.0272369384765625,
0.023468017578125,
-0.0411376953125,
-0.00974273681640625,
0.0121917724609375,
-0.0182647705078125,
0.002582550048828125,
0.0299072265625,
0.0308990478515625,
-0.0037479400634765625,
-0.0061798095703125,
-0.048370361328125,
-0.0243682861328125,
-0.023284912109375,
-0.029754638671875,
-0.00539398193359375,
0.014984130859375,
0.00536346435546875,
0.004337310791015625,
0.003448486328125,
-0.0054779052734375,
0.01172637939453125,
-0.019683837890625,
-0.01291656494140625,
-0.001773834228515625,
0.0557861328125,
0.01116180419921875,
-0.01285552978515625,
-0.0216217041015625,
0.0037364959716796875,
0.00945281982421875,
0.0293426513671875,
-0.00925445556640625,
-0.00458526611328125,
-0.05084228515625,
-0.00896453857421875,
0.0288238525390625,
-0.0006551742553710938,
0.0274658203125,
-0.00997161865234375,
0.0091094970703125,
0.0236358642578125,
-0.03179931640625,
0.031219482421875,
-0.008270263671875,
-0.0172119140625,
-0.00852203369140625,
-0.02081298828125,
-0.007442474365234375,
-0.00891876220703125,
0.003368377685546875,
-0.0057373046875,
-0.037872314453125,
0.0160064697265625,
0.0123138427734375,
-0.0157623291015625,
-0.018951416015625,
0.0084075927734375,
0.016143798828125,
-0.0190582275390625,
-0.024139404296875,
-0.00946807861328125,
0.031402587890625,
-0.0386962890625,
0.0182342529296875,
-0.0017328262329101562,
-0.0308685302734375,
0.020782470703125,
-0.0009860992431640625,
-0.0350341796875,
0.0221710205078125,
0.0211029052734375,
-0.004825592041015625,
-0.009613037109375,
-0.02008056640625,
-0.01215362548828125,
-0.01177978515625,
0.0052032470703125,
0.0117645263671875,
-0.006015777587890625,
-0.0037174224853515625,
-0.006191253662109375,
-0.016571044921875,
0.0176239013671875,
-0.0225372314453125,
-0.02496337890625,
-0.00644683837890625,
-0.017578125,
-0.0288848876953125,
-0.0218658447265625,
0.0014247894287109375,
0.0012350082397460938,
-0.020721435546875,
-0.004604339599609375,
0.0157623291015625,
-0.0045928955078125,
0.001499176025390625,
-0.037139892578125,
-0.016326904296875,
-0.01090240478515625,
0.0178070068359375,
0.0172576904296875,
-0.004241943359375,
0.0000069141387939453125,
0.01064300537109375,
-0.0136871337890625,
-0.03973388671875,
0.006092071533203125,
-0.0127105712890625,
-0.007724761962890625,
0.0148468017578125,
0.017120361328125,
-0.0205078125,
0.0168304443359375,
-0.03271484375,
0.0230560302734375,
-0.032196044921875,
-0.00429534912109375,
-0.031280517578125,
-0.0165557861328125,
-0.01279449462890625,
-0.027374267578125,
0.028411865234375,
0.02685546875,
0.011505126953125,
0.0018644332885742188,
0.0013856887817382812,
0.005474090576171875,
0.048919677734375,
-0.01458740234375,
-0.01036834716796875,
-0.01267242431640625,
0.01439666748046875,
-0.00856781005859375,
0.03570556640625,
-0.001323699951171875,
0.0140838623046875,
0.01535797119140625,
-0.00695037841796875,
-0.0011119842529296875,
0.00890350341796875,
-0.0382080078125,
0.007450103759765625,
-0.0161895751953125,
0.0012273788452148438,
0.0008344650268554688,
0.002841949462890625,
-0.006458282470703125,
-0.0033473968505859375,
-0.004291534423828125,
0.007259368896484375,
0.0228424072265625,
-0.00936126708984375,
-0.0179595947265625,
0.0040130615234375,
-0.003948211669921875,
-0.0124664306640625,
-0.004528045654296875,
-0.027862548828125,
-0.0032806396484375,
-0.00022745132446289062,
-0.0145111083984375,
0.0187530517578125,
-0.006488800048828125,
0.0122833251953125,
0.004669189453125,
-0.00847625732421875,
-0.006397247314453125,
0.04144287109375,
-0.01335906982421875,
-0.00152587890625,
0.0008234977722167969,
-0.0181884765625,
0.0225067138671875,
-0.0080413818359375,
-0.0355224609375,
0.0213623046875,
0.01528167724609375,
-0.00457763671875,
-0.0116424560546875,
0.009063720703125,
0.006649017333984375,
-0.003993988037109375,
-0.00707244873046875,
-0.01041412353515625,
-0.0095977783203125,
0.01273345947265625,
0.00489044189453125,
0.0222015380859375,
-0.012420654296875,
0.0450439453125,
-0.037384033203125,
0.0028018951416015625,
0.03424072265625,
-0.02423095703125,
0.0014972686767578125,
-0.0174713134765625,
0.0101776123046875,
0.00395965576171875,
-0.0266265869140625,
0.0174713134765625,
0.040618896484375,
-0.01085662841796875,
0.00852203369140625,
0.0002779960632324219,
0.01922607421875,
0.02862548828125,
0.0469970703125,
-0.003849029541015625,
0.0220947265625,
0.0034942626953125,
-0.006206512451171875,
-0.04052734375,
-0.04132080078125,
-0.0301361083984375,
-0.02447509765625,
0.0024623870849609375,
0.0008683204650878906,
0.0017795562744140625,
0.017181396484375,
-0.002407073974609375,
0.0043182373046875,
-0.01947021484375,
0.007503509521484375,
-0.00701904296875,
-0.0031890869140625,
0.0205841064453125,
-0.0262451171875,
-0.004405975341796875,
-0.01514434814453125,
0.052032470703125,
-0.003246307373046875,
0.02142333984375,
0.00469970703125,
-0.0254669189453125,
-0.01142120361328125,
0.058746337890625,
-0.002490997314453125,
0.008514404296875,
-0.015716552734375,
0.033966064453125,
-0.04071044921875,
0.0299530029296875,
-0.01508331298828125,
-0.039306640625,
0.0163421630859375,
0.018157958984375,
-0.0404052734375,
0.037078857421875,
-0.00984954833984375,
0.006011962890625,
0.005916595458984375,
-0.00818634033203125,
-0.00815582275390625,
0.0019779205322265625,
0.043121337890625,
0.0001691579818725586,
-0.0015573501586914062,
-0.02655029296875,
0.0135498046875,
0.0204315185546875,
-0.01190185546875,
0.0031681060791015625,
-0.0256805419921875,
-0.0026760101318359375,
0.0146331787109375,
0.02069091796875,
-0.014556884765625,
0.00559234619140625,
0.0225982666015625,
-0.004119873046875,
-0.00884246826171875,
0.001369476318359375,
0.016510009765625,
-0.0002028942108154297,
0.004573822021484375,
-0.0165252685546875,
-0.016265869140625,
-0.03131103515625,
0.0246124267578125,
0.00026154518127441406,
-0.01529693603515625,
0.0016155242919921875,
0.01129150390625,
-0.0120849609375,
0.01105499267578125,
-0.01090240478515625,
-0.005245208740234375,
0.016937255859375,
-0.00971221923828125,
-0.01548004150390625,
0.0038928985595703125,
-0.00766754150390625,
-0.01371002197265625,
0.00037741661071777344,
-0.005405426025390625,
0.0070343017578125,
0.024169921875,
0.01363372802734375,
0.0189361572265625,
-0.020538330078125,
-0.00043201446533203125,
0.02142333984375,
-0.0036602020263671875,
0.0181121826171875,
0.0263824462890625,
0.0229034423828125,
-0.037139892578125,
-0.0229339599609375,
0.00333404541015625,
-0.03900146484375,
-0.0189208984375,
-0.00794219970703125,
0.0229339599609375,
-0.005794525146484375,
0.0239715576171875,
-0.00787353515625,
-0.03411865234375,
0.006114959716796875,
0.0130157470703125,
0.01418304443359375,
-0.01204681396484375,
-0.0114898681640625,
-0.03631591796875,
-0.022491455078125,
0.003246307373046875,
-0.01027679443359375,
-0.010284423828125,
0.006282806396484375,
-0.0035800933837890625,
0.01505279541015625,
0.01221466064453125,
0.01453399658203125,
0.0223236083984375,
0.016326904296875,
-0.0283660888671875,
0.0161285400390625,
0.0355224609375,
0.005031585693359375,
-0.00467681884765625,
-0.002292633056640625,
0.0240631103515625,
0.035491943359375,
-0.01238250732421875,
0.01177978515625,
-0.0127716064453125,
-0.027313232421875,
-0.00724029541015625,
0.0128173828125,
0.05316162109375,
0.007232666015625,
-0.036529541015625,
0.0087738037109375,
-0.0129241943359375,
-0.005756378173828125,
-0.035797119140625,
-0.0372314453125,
0.0166778564453125,
0.026580810546875,
0.043060302734375,
-0.0021915435791015625,
-0.0199432373046875,
0.0181884765625,
0.0133056640625,
-0.028717041015625,
0.0011844635009765625,
-0.037322998046875,
-0.00927734375,
-0.0123443603515625,
-0.032958984375,
-0.0088348388671875,
0.00940704345703125,
-0.0296173095703125,
-0.0034027099609375,
0.005718231201171875,
-0.0276336669921875,
-0.0018873214721679688,
0.032928466796875,
-0.00843048095703125,
-0.00848388671875,
-0.041656494140625,
-0.004398345947265625,
0.0148468017578125,
-0.0212860107421875,
0.01316070556640625,
0.0005097389221191406,
-0.0290374755859375,
0.00783538818359375,
-0.0053558349609375,
0.01168060302734375,
0.00774383544921875,
-0.0008902549743652344,
-0.0173492431640625,
0.01483154296875,
0.001873016357421875,
0.00753021240234375,
0.017303466796875,
0.03900146484375,
-0.0233001708984375,
-0.017120361328125,
-0.0242462158203125,
0.00463104248046875,
0.0167236328125,
-0.00974273681640625,
-0.01271820068359375,
0.0008287429809570312,
-0.0177001953125,
-0.0199127197265625,
-0.006099700927734375,
-0.040740966796875,
0.01177215576171875,
0.0102081298828125,
0.0019588470458984375,
-0.0215606689453125,
0.0187530517578125,
-0.006450653076171875,
-0.0006465911865234375,
0.011138916015625,
0.01276397705078125,
0.004634857177734375,
-0.0253143310546875,
-0.00882720947265625,
0.0246124267578125,
-0.0029811859130859375,
0.0211944580078125,
-0.019744873046875,
-0.0283966064453125,
-0.002323150634765625,
0.0263824462890625,
0.0313720703125,
0.0064697265625,
-0.01418304443359375,
0.0165252685546875,
0.01459503173828125,
-0.0110626220703125,
0.003047943115234375,
-0.00627899169921875,
-0.0005936622619628906,
0.0160369873046875,
-0.001781463623046875,
0.0255279541015625,
-0.006000518798828125,
0.0202484130859375,
0.0088958740234375,
0.01532745361328125,
0.0184173583984375,
-0.0142364501953125,
-0.01543426513671875,
-0.0103912353515625,
-0.00904083251953125,
0.0107574462890625,
0.006679534912109375,
-0.0069732666015625,
0.0141754150390625,
0.0022411346435546875,
0.0005259513854980469,
0.018157958984375,
0.01033782958984375,
0.0023632049560546875,
-0.00606536865234375,
0.043212890625,
0.01422882080078125,
0.0139923095703125,
0.037750244140625,
-0.0037689208984375,
0.0099639892578125,
0.007671356201171875,
-0.0087738037109375,
0.00469970703125,
0.019744873046875,
0.01087188720703125,
-0.007465362548828125,
-0.0189208984375,
0.0008029937744140625,
0.0020122528076171875,
0.004428863525390625,
-0.02484130859375,
-0.016632080078125,
-0.0272979736328125,
-0.01171112060546875,
-0.00495147705078125,
-0.019073486328125,
0.057403564453125,
-0.0060882568359375,
-0.00994110107421875,
0.01776123046875,
0.0025806427001953125,
0.031982421875,
-0.0019474029541015625,
-0.0234222412109375,
0.0074920654296875,
-0.003864288330078125,
-0.029052734375,
0.0198974609375,
-0.009552001953125,
0.003238677978515625,
0.02655029296875,
0.001964569091796875,
0.014984130859375,
0.00927734375,
-0.0163421630859375,
0.0089111328125,
0.025482177734375,
0.003513336181640625,
0.0146484375,
-0.0552978515625,
-0.018341064453125,
0.012969970703125,
-0.037445068359375,
0.0004248619079589844,
0.0253753662109375,
0.0224609375,
0.0164947509765625,
0.006092071533203125,
-0.0074615478515625,
0.04632568359375,
-0.006504058837890625,
0.02734375,
-0.0171966552734375,
0.00611114501953125,
0.0067901611328125,
-0.011138916015625,
0.003871917724609375,
-0.007801055908203125,
0.005985260009765625,
0.0264739990234375,
-0.003269195556640625,
0.000537872314453125,
0.0131988525390625,
0.030731201171875,
-0.006072998046875,
0.0250091552734375,
-0.0177459716796875,
-0.01387786865234375,
0.00144195556640625,
-0.019927978515625,
-0.0120391845703125,
0.0124969482421875,
-0.023193359375,
-0.0216827392578125,
0.0256805419921875,
-0.02435302734375,
-0.0058135986328125,
0.020050048828125,
-0.0244598388671875,
-0.0100250244140625,
0.0291748046875,
0.009796142578125,
-0.02081298828125,
0.031890869140625,
-0.001605987548828125,
-0.00811004638671875,
0.00461578369140625,
-0.01160430908203125,
-0.0199737548828125,
-0.00499725341796875,
-0.005405426025390625,
0.0006651878356933594,
-0.00487518310546875,
-0.0238494873046875,
-0.01080322265625,
-0.006237030029296875,
0.0037746429443359375,
0.021636962890625,
0.016265869140625,
-0.01142120361328125,
-0.04241943359375,
0.01418304443359375,
0.01320648193359375,
0.0174407958984375,
0.029327392578125,
0.0179901123046875,
0.0178680419921875,
-0.01361083984375,
-0.0225677490234375,
0.02545166015625,
-0.026824951171875,
-0.0214385986328125,
0.0211334228515625,
-0.005863189697265625,
-0.004978179931640625,
-0.039947509765625,
0.003162384033203125,
0.04193115234375,
0.014312744140625,
0.050445556640625,
0.02197265625,
-0.020416259765625,
-0.007724761962890625,
0.0369873046875,
0.0016956329345703125,
0.0233612060546875,
0.01490020751953125,
0.00267791748046875,
0.0125579833984375,
-0.055938720703125,
-0.01042938232421875,
0.014892578125,
-0.0198516845703125,
0.037811279296875,
0.004375457763671875,
-0.026947021484375,
-0.01483154296875,
-0.0147857666015625,
0.004978179931640625,
0.0167236328125,
-0.04119873046875,
-0.03173828125,
-0.0193328857421875,
-0.00490570068359375,
-0.01715087890625,
-0.004634857177734375,
-0.00295257568359375,
0.02410888671875,
-0.0137786865234375,
-0.0244140625,
0.002666473388671875,
0.0018396377563476562,
0.0018644332885742188,
0.006145477294921875,
0.004711151123046875,
0.0238189697265625,
-0.018585205078125,
0.02044677734375,
0.03668212890625,
-0.036041259765625,
0.04791259765625,
0.0013103485107421875,
-0.01001739501953125,
-0.01070404052734375,
-0.0239105224609375,
0.0156402587890625,
-0.0181427001953125,
-0.04669189453125,
-0.0020160675048828125,
0.003383636474609375,
0.035003662109375,
0.005859375,
-0.0126953125,
-0.0012369155883789062,
0.01239013671875,
-0.01384735107421875,
-0.0179443359375,
0.024871826171875,
0.044708251953125,
0.0086669921875,
-0.02734375,
-0.005695343017578125,
0.0164031982421875,
-0.029388427734375,
0.006591796875,
-0.03759765625,
-0.004451751708984375,
0.0056304931640625,
0.00901031494140625,
0.0128326416015625,
-0.0011682510375976562,
-0.0001405477523803711,
-0.02227783203125,
-0.0021266937255859375,
0.01202392578125,
-0.0016679763793945312,
-0.00738525390625,
0.0009236335754394531,
0.0089263916015625,
-0.03607177734375,
0.00989532470703125,
-0.019378662109375,
0.00682830810546875,
-0.0016241073608398438,
-0.0112457275390625,
0.0306549072265625,
0.01097869873046875,
-0.0101776123046875,
0.0011882781982421875,
0.00930023193359375,
0.03204345703125,
0.0281524658203125,
-0.0028057098388671875,
-0.00673675537109375,
-0.01171875,
0.005580902099609375,
0.012603759765625,
0.00977325439453125,
-0.00977325439453125,
0.0168304443359375,
-0.0016107559204101562,
-0.00708770751953125,
-0.0246734619140625,
0.0018253326416015625,
0.004199981689453125,
-0.04547119140625,
-0.038970947265625,
-0.0240478515625,
0.038970947265625,
-0.01678466796875,
0.036865234375,
0.003932952880859375,
-0.0190887451171875,
0.0269012451171875,
-0.005031585693359375,
-0.0272064208984375,
-0.0025234222412109375,
0.04345703125,
-0.046783447265625,
-0.0201568603515625,
0.0046234130859375,
0.008697509765625,
0.00508880615234375,
0.0147705078125,
-0.03985595703125,
0.0218963623046875,
0.0027713775634765625,
-0.0184326171875,
-0.002124786376953125,
-0.03277587890625,
-0.004169464111328125,
-0.005046844482421875,
-0.0677490234375,
0.0206451416015625,
0.028564453125,
0.00955963134765625,
-0.03387451171875,
0.01910400390625,
0.017486572265625,
0.0011911392211914062,
0.03076171875,
-0.021484375,
-0.018463134765625,
0.0303955078125,
-0.0029354095458984375,
-0.043121337890625,
0.0178985595703125,
-0.01213836669921875,
0.0001798868179321289,
0.00251007080078125,
-0.0095672607421875,
-0.006374359130859375,
0.01103973388671875,
0.007171630859375,
-0.0003848075866699219,
0.0164794921875,
0.00246429443359375,
0.0132598876953125,
0.0024566650390625,
-0.00466156005859375,
-0.0174560546875,
0.00437164306640625,
-0.0020656585693359375,
-0.021453857421875,
-0.031402587890625,
-0.00922393798828125,
0.030487060546875,
0.0012950897216796875,
-0.017181396484375,
-0.005573272705078125,
-0.03302001953125,
0.00351715087890625,
-0.0046539306640625,
0.00981903076171875,
-0.0037994384765625,
0.003826141357421875,
-0.00989532470703125,
0.0226593017578125,
-0.032135009765625,
0.006786346435546875,
-0.032562255859375,
-0.0411376953125,
0.006866455078125,
0.040069580078125,
-0.0015211105346679688,
-0.0163726806640625,
0.0186004638671875,
0.026885986328125,
-0.0066375732421875,
-0.006420135498046875,
0.034942626953125,
0.0438232421875,
-0.034698486328125,
-0.01479339599609375,
0.02008056640625,
-0.0166015625,
0.0189208984375,
0.009185791015625,
0.01290130615234375,
-0.0223236083984375,
-0.0021572113037109375,
0.004703521728515625,
-0.0020275115966796875,
0.0306396484375,
-0.004413604736328125,
-0.01123809814453125,
-0.01010894775390625,
-0.0007543563842773438,
-0.01019287109375,
-0.03497314453125,
0.0212860107421875,
0.0010900497436523438,
-0.01381683349609375,
-0.0015687942504882812,
0.0077056884765625,
-0.01195526123046875,
0.002162933349609375,
0.007373809814453125,
-0.004909515380859375,
0.0193328857421875,
0.0015392303466796875,
-0.01326751708984375,
-0.007251739501953125,
-0.01849365234375,
0.021636962890625,
-0.01212310791015625,
0.023712158203125,
0.002185821533203125,
0.0014142990112304688,
0.00931549072265625,
-0.019073486328125,
0.01146697998046875,
-0.03216552734375,
0.01085662841796875,
-0.01393890380859375,
-0.006778717041015625,
0.0018358230590820312,
-0.037139892578125,
-0.0235137939453125,
0.0197601318359375,
-0.002292633056640625,
-0.01032257080078125,
0.02508544921875,
0.005558013916015625,
0.027008056640625,
0.0014886856079101562,
0.006015777587890625,
-0.00588226318359375,
-0.0081939697265625,
0.000514984130859375,
0.027130126953125,
0.0166015625,
0.01493072509765625,
-0.0085601806640625,
-0.00865936279296875,
0.016448974609375,
0.0005145072937011719,
-0.0087890625,
-0.0100860595703125,
-0.02392578125,
-0.006855010986328125,
0.017852783203125,
-0.01788330078125,
0.00856781005859375,
-0.0179901123046875,
0.0014104843139648438,
0.0181427001953125,
0.0025920867919921875,
-0.01012420654296875,
-0.00341796875,
-0.019927978515625,
-0.041839599609375,
-0.045623779296875,
-0.014129638671875,
-0.0176544189453125,
0.0223388671875,
0.011810302734375,
-0.0265960693359375,
-0.00959014892578125,
0.00885772705078125,
-0.00479888916015625,
0.002155303955078125,
0.004611968994140625,
0.024505615234375,
-0.0261993408203125,
0.0298614501953125,
0.0235137939453125,
-0.03668212890625,
-0.020538330078125,
-0.012725830078125,
0.00634765625,
-0.01297760009765625,
-0.022247314453125,
0.041229248046875,
0.0002715587615966797,
-0.007843017578125,
-0.00717926025390625,
0.0211639404296875,
-0.0042572021484375,
0.01155853271484375,
-0.0462646484375,
0.0018033981323242188,
0.0198211669921875,
0.00934600830078125,
0.020751953125,
0.0309295654296875,
0.01241302490234375,
-0.004108428955078125,
-0.0014696121215820312,
0.016998291015625,
0.001827239990234375,
0.01227569580078125,
0.008880615234375,
-0.002811431884765625,
-0.00945281982421875,
-0.003047943115234375,
0.0255889892578125,
-0.021453857421875,
-0.03509521484375,
-0.00853729248046875,
-0.00356292724609375,
0.0020465850830078125,
0.004390716552734375,
-0.0254974365234375,
-0.002750396728515625,
-0.0008983612060546875,
-0.0227508544921875,
-0.0066680908203125,
-0.028076171875,
-0.009735107421875,
-0.0240478515625,
0.0032405853271484375,
-0.003841400146484375,
-0.0189971923828125,
0.037811279296875,
-0.0009889602661132812,
-0.0078277587890625,
0.0003497600555419922,
0.00829315185546875,
0.0230865478515625,
-0.008575439453125,
0.014556884765625,
0.0005154609680175781,
0.01010894775390625,
0.00537109375,
-0.007785797119140625,
0.0088348388671875,
-0.0192413330078125,
0.004131317138671875,
-0.01136016845703125,
-0.0322265625,
-0.0037631988525390625,
0.0244140625,
0.0095062255859375,
-0.0257568359375,
0.015045166015625,
0.026519775390625,
0.01116943359375,
0.0024585723876953125,
-0.0093994140625,
-0.03985595703125,
0.0308685302734375,
-0.0098876953125,
-0.0199432373046875,
0.010955810546875,
0.00865936279296875,
-0.016845703125,
-0.00225067138671875,
0.0148773193359375,
-0.0119171142578125,
-0.00492095947265625,
0.0290069580078125,
-0.0147705078125,
0.0055389404296875,
0.033721923828125,
-0.031463623046875,
-0.00017499923706054688,
-0.020416259765625,
0.0005965232849121094,
-0.030670166015625,
0.019989013671875,
-0.0228424072265625,
-0.0017805099487304688,
0.01898193359375,
-0.0003418922424316406,
-0.01258087158203125,
0.035552978515625,
-0.03594970703125,
0.01226043701171875,
-0.0132598876953125,
0.047210693359375,
-0.014434814453125,
-0.0221405029296875,
0.0049896240234375,
-0.017578125,
-0.0160980224609375,
0.003292083740234375,
0.029937744140625,
0.02362060546875,
-0.01277923583984375,
-0.01222991943359375,
0.00847625732421875,
-0.0039520263671875,
0.0238494873046875,
-0.018524169921875,
-0.01038360595703125,
-0.0194091796875,
0.045501708984375,
-0.0238189697265625,
-0.0033817291259765625,
0.011932373046875,
0.01461029052734375,
0.0158843994140625,
-0.01319122314453125,
0.01617431640625,
-0.00726318359375,
-0.00323486328125,
-0.01158905029296875,
-0.0167999267578125,
-0.01273345947265625,
0.0226287841796875,
0.0273895263671875,
-0.04669189453125,
0.0281524658203125,
0.0197601318359375,
0.01934814453125,
0.0069122314453125,
-0.015960693359375,
-0.0271759033203125,
-0.0062103271484375,
0.017730712890625,
-0.025848388671875,
0.007808685302734375,
0.0090179443359375,
-0.012176513671875,
0.0105133056640625,
0.0382080078125,
0.0147857666015625,
0.01171112060546875,
-0.00620269775390625,
0.00099945068359375,
0.0090789794921875,
0.0049285888671875,
0.003902435302734375,
0.0182342529296875,
-0.00641632080078125,
-0.0037021636962890625,
0.0126953125,
-0.0277862548828125,
-0.01215362548828125,
-0.00240325927734375,
-0.005733489990234375,
-0.005413055419921875,
0.018341064453125,
0.00778961181640625,
-0.016693115234375,
0.0086212158203125,
0.02655029296875,
-0.023040771484375,
-0.0139923095703125,
0.01458740234375,
-0.022369384765625,
-0.0177764892578125,
0.0145111083984375,
-0.0118865966796875,
0.0240478515625,
-0.012298583984375,
-0.007190704345703125,
0.035491943359375,
0.005828857421875,
0.00096893310546875,
-0.0110626220703125,
-0.02374267578125,
-0.004634857177734375,
0.0281982421875,
-0.01418304443359375,
-0.004772186279296875,
0.0068206787109375,
0.0003638267517089844,
-0.038543701171875,
0.0182037353515625,
-0.00475311279296875,
0.008697509765625,
0.0005373954772949219,
-0.00803375244140625,
-0.00806427001953125,
0.0133056640625,
0.0268402099609375,
-0.005558013916015625,
0.00011241436004638672,
0.02978515625,
-0.02471923828125,
-0.01568603515625,
0.010009765625,
0.0030384063720703125,
-0.0164337158203125,
0.007518768310546875,
0.0289764404296875,
-0.00323486328125,
0.005191802978515625,
-0.005077362060546875,
0.00925445556640625,
0.0117034912109375,
-0.0214691162109375,
0.0023784637451171875,
0.006343841552734375,
-0.0246429443359375,
0.01513671875,
-0.0199737548828125,
0.01432037353515625,
0.01544952392578125,
0.01070404052734375,
0.0115814208984375,
-0.022369384765625,
-0.004001617431640625,
-0.041412353515625,
-0.026458740234375,
-0.01120758056640625,
0.0017690658569335938,
-0.00237274169921875,
0.0279083251953125,
-0.01044464111328125,
0.01253509521484375,
0.01221466064453125,
-0.0516357421875,
0.0210113525390625,
0.004974365234375,
0.034454345703125,
-0.00579071044921875,
-0.0186920166015625,
0.01561737060546875,
0.032470703125,
-0.0135650634765625,
0.046478271484375,
-0.00122833251953125,
-0.00011640787124633789,
0.00592041015625,
0.0172119140625,
0.0145111083984375,
0.0240325927734375,
0.037872314453125,
0.045928955078125,
-0.0214691162109375,
-0.00460052490234375,
-0.001850128173828125,
-0.0162200927734375,
0.003063201904296875,
0.0105743408203125,
0.03826904296875,
-0.018798828125,
0.017364501953125,
-0.00759124755859375,
-0.0050811767578125,
0.00908660888671875,
-0.035064697265625,
-0.0012035369873046875,
0.00994873046875,
0.023895263671875,
0.0022983551025390625,
-0.0160369873046875,
0.01690673828125,
-0.01155853271484375,
0.02001953125,
-0.0040283203125,
-0.00902557373046875,
0.0012941360473632812,
0.0226593017578125,
-0.0179443359375,
-0.0156097412109375,
0.0253448486328125,
0.028900146484375,
0.0194549560546875,
-0.032470703125,
-0.012542724609375,
-0.003810882568359375,
-0.0006051063537597656,
-0.01088714599609375,
-0.031402587890625,
-0.00423431396484375,
-0.001483917236328125,
-0.01160430908203125,
0.007678985595703125,
0.023406982421875,
-0.022216796875,
0.00313568115234375,
0.00830841064453125,
0.00972747802734375,
-0.002105712890625,
0.02154541015625,
-0.020904541015625,
-0.01302337646484375,
0.0017366409301757812,
-0.026641845703125,
0.0218505859375,
-0.01953125,
-0.022247314453125,
0.03411865234375,
0.03375244140625,
-0.0198516845703125,
-0.0171051025390625,
0.0012311935424804688,
-0.03961181640625,
0.0015316009521484375,
0.010498046875,
0.00490570068359375,
0.028778076171875,
0.0237274169921875,
-0.0165863037109375,
0.0013170242309570312,
0.0269317626953125,
-0.0088958740234375,
0.0075225830078125,
-0.01012420654296875,
-0.01837158203125,
-0.00409698486328125,
0.006378173828125,
0.0113067626953125,
-0.005279541015625,
0.01080322265625,
0.0292510986328125,
-0.0012865066528320312,
0.015289306640625,
-0.0103607177734375,
-0.0189208984375,
-0.00841522216796875,
0.02734375,
0.017242431640625,
-0.0014781951904296875,
0.0256805419921875,
-0.023712158203125,
-0.0003616809844970703,
-0.0024738311767578125,
0.005504608154296875,
-0.0406494140625,
-0.003170013427734375,
-0.0174102783203125,
0.027252197265625,
0.03131103515625,
-0.01287078857421875,
0.0012311935424804688,
0.025299072265625,
0.0210418701171875,
0.0008258819580078125,
-0.0226898193359375,
0.0014514923095703125,
0.01105499267578125,
-0.02520751953125,
-0.00809478759765625,
0.0018177032470703125,
-0.0282745361328125,
-0.01140594482421875,
-0.013702392578125,
-0.0289459228515625,
-0.00424957275390625,
0.00443267822265625,
0.0139312744140625,
-0.0246124267578125,
0.0137176513671875,
-0.014373779296875,
-0.00472259521484375,
0.01136016845703125,
-0.00757598876953125,
-0.05145263671875,
-0.00566864013671875,
-0.0098724365234375,
0.00482940673828125,
-0.00815582275390625,
-0.00432586669921875,
0.0159454345703125,
-0.005100250244140625,
-0.0014581680297851562,
0.0217742919921875,
-0.00716400146484375,
-0.03326416015625,
-0.01141357421875,
0.0136260986328125,
0.0130157470703125,
0.01861572265625,
-0.0013990402221679688,
0.0021991729736328125,
0.0157470703125,
-0.0034313201904296875,
-0.02435302734375,
-0.01116943359375,
0.00730133056640625,
0.017333984375,
-0.00186920166015625,
0.03204345703125,
0.00580596923828125,
-0.00211334228515625,
0.01430511474609375,
-0.0276947021484375,
0.0238037109375,
0.01540374755859375,
0.0209197998046875,
0.0013856887817382812,
-0.026153564453125,
0.040863037109375,
-0.031219482421875,
-0.0124969482421875,
0.0036525726318359375,
0.0330810546875,
0.035491943359375,
0.0171051025390625,
0.0197906494140625,
-0.0169830322265625,
0.003650665283203125,
-0.000004112720489501953,
0.007236480712890625,
0.0305633544921875,
0.0054473876953125,
0.00740814208984375,
-0.00643157958984375,
-0.01311492919921875,
0.00429534912109375,
-0.002445220947265625,
0.023040771484375,
-0.013427734375,
-0.01239013671875,
-0.00119781494140625,
0.0163421630859375,
-0.03643798828125,
0.0078277587890625,
0.006160736083984375,
0.0171661376953125,
0.005680084228515625,
-0.001049041748046875,
-0.01535797119140625,
0.022796630859375,
0.029541015625,
-0.01476287841796875,
0.0185089111328125,
0.01678466796875,
0.0214691162109375,
-0.0127105712890625,
0.013458251953125,
0.01142120361328125,
-0.0196533203125,
0.00689697265625,
0.0302276611328125,
-0.03302001953125,
0.0254364013671875,
0.0031642913818359375,
-0.0352783203125,
0.007106781005859375,
0.0045623779296875,
0.02130126953125,
-0.021209716796875,
-0.006549835205078125,
-0.0183868408203125,
-0.013763427734375,
0.01947021484375,
0.0262451171875,
0.00949859619140625,
0.02374267578125,
-0.03375244140625,
-0.004486083984375,
0.0216064453125,
-0.00534820556640625,
0.0193328857421875,
-0.011993408203125,
-0.0265045166015625,
0.00836181640625,
0.023956298828125,
-0.0032329559326171875,
0.00910186767578125,
0.01282501220703125,
-0.0010042190551757812,
-0.0133209228515625,
-0.007213592529296875,
-0.01006317138671875,
0.0443115234375,
-0.03131103515625,
-0.036102294921875,
-0.04620361328125,
-0.0185394287109375,
0.037994384765625,
-0.0467529296875,
-0.015350341796875,
-0.0038776397705078125,
0.016937255859375,
0.0186614990234375,
-0.002956390380859375,
-0.032684326171875,
-0.01251220703125,
0.033935546875,
0.0106353759765625,
-0.042144775390625,
-0.01043701171875,
0.0178680419921875,
-0.0253448486328125,
0.0014858245849609375,
0.0166778564453125,
-0.0179595947265625,
-0.01178741455078125,
-0.0018129348754882812,
0.0185546875,
-0.0208740234375,
-0.0518798828125,
-0.01053619384765625,
-0.034942626953125,
-0.0002397298812866211,
0.0233612060546875,
0.0269927978515625,
-0.00634002685546875,
-0.028228759765625,
-0.0068359375,
0.0129241943359375,
-0.0017414093017578125,
-0.00945281982421875,
0.0088348388671875,
-0.004302978515625,
0.00829315185546875,
0.03057861328125,
-0.0281524658203125,
-0.023529052734375,
-0.0019197463989257812,
-0.00519561767578125,
0.0030155181884765625,
0.004116058349609375,
-0.01552581787109375,
-0.004123687744140625,
-0.0287933349609375,
-0.019439697265625,
0.0224151611328125,
0.0173492431640625,
-0.003025054931640625,
0.0205230712890625,
0.025482177734375,
-0.0180511474609375,
0.0007443428039550781,
-0.0167694091796875,
-0.0211029052734375,
0.00954437255859375,
-0.039459228515625,
0.01220703125,
0.0242156982421875,
0.040008544921875,
-0.03143310546875,
-0.00225067138671875,
-0.0270538330078125,
-0.02825927734375,
0.00017762184143066406,
0.020355224609375,
0.01129913330078125,
0.031280517578125,
-0.0211029052734375,
-0.009857177734375,
-0.0034637451171875,
0.00748443603515625,
0.00646209716796875,
0.00598907470703125,
-0.0004608631134033203,
-0.00339508056640625,
-0.0163726806640625,
-0.00983428955078125,
-0.0191650390625,
-0.0233154296875,
-0.011138916015625,
0.01297760009765625,
-0.0018873214721679688,
0.019622802734375,
-0.013824462890625,
-0.00736236572265625,
-0.0028400421142578125,
0.021087646484375,
0.01097869873046875,
-0.004638671875,
-0.00466156005859375
] |
ours_555
|
Notice that \(a+b+c=-3\) by Vieta's formulas. Let \(Q(x)\) be a polynomial such that \(Q(x)=P(x)+x+3\). Notice that \(Q(x)\) has \(a, b, c\) as roots by the first three conditions, so \(Q(x)=c(x^{3}+3x^{2}+5x+7)\) for some constant \(c\). By the last condition, we find \(c(-27+27-15+7)=-16\), so \(c=2\), and \(Q(x)=2x^{3}+6x^{2}+10x+14\). Now we have \(14=Q(0)=P(0)+0+3\), so \(P(0)=11\).
\(\boxed{11}\)
|
11
|
{
"competition": "us_comps",
"dataset": "Ours",
"posts": null,
"source": "OMOSoln2.md"
}
|
Let \(a, b, c\) be the roots of the cubic \(x^{3}+3x^{2}+5x+7\). Given that \(P\) is a cubic polynomial such that \(P(a)=b+c\), \(P(b)=c+a\), \(P(c)=a+b\), and \(P(a+b+c)=-16\), find \(P(0)\).
|
[
"/Mathematics/Algebra/AlgebraicEquations/AlgebraicEquation",
"/Mathematics/Algebra/AlgebraicEquations/CubicEquation",
"/Mathematics/Algebra/GeneralAlgebra/Algebra",
"/Mathematics/Algebra/Polynomials/CubicEquation",
"/Mathematics/Algebra/Polynomials/CubicPolynomial",
"/Mathematics/Algebra/Polynomials/MonicPolynomial",
"/Mathematics/Algebra/Polynomials/Polynomial",
"/Mathematics/Algebra/Polynomials/PolynomialRoots",
"/Mathematics/Algebra/Polynomials/VietasFormulas"
] |
Shift P by x+3 to create a polynomial that vanishes at a,b,c, forcing it to be a constant multiple of the known cubic.
|
[
-0.0000908970832824707,
0.001422882080078125,
-0.006671905517578125,
0.0204620361328125,
-0.0008707046508789062,
-0.00800323486328125,
0.0175323486328125,
0.00896453857421875,
0.009857177734375,
-0.042572021484375,
-0.002918243408203125,
-0.0234527587890625,
-0.0018291473388671875,
0.009735107421875,
-0.0127410888671875,
0.0077362060546875,
-0.0016069412231445312,
-0.02313232421875,
0.019561767578125,
-0.0035724639892578125,
-0.006984710693359375,
-0.030853271484375,
-0.04705810546875,
0.0202178955078125,
-0.0272369384765625,
0.037353515625,
-0.01812744140625,
-0.0220489501953125,
0.006988525390625,
-0.05755615234375,
-0.007171630859375,
-0.02783203125,
-0.012054443359375,
-0.033599853515625,
-0.0012531280517578125,
-0.01020050048828125,
-0.004974365234375,
-0.01145172119140625,
-0.007297515869140625,
-0.037872314453125,
-0.005146026611328125,
0.0218658447265625,
0.001247406005859375,
0.0439453125,
-0.01824951171875,
-0.004169464111328125,
0.00481414794921875,
0.01910400390625,
-0.0163726806640625,
0.006137847900390625,
0.0013055801391601562,
0.00623321533203125,
-0.0208282470703125,
-0.0037517547607421875,
-0.016754150390625,
-0.050689697265625,
-0.01556396484375,
-0.0033416748046875,
-0.041717529296875,
-0.045440673828125,
0.006587982177734375,
0.004886627197265625,
-0.004024505615234375,
-0.0259246826171875,
0.00730133056640625,
0.0016880035400390625,
0.033294677734375,
-0.045654296875,
0.00048613548278808594,
-0.00809478759765625,
0.040863037109375,
-0.0200347900390625,
-0.00437164306640625,
0.05694580078125,
0.0202789306640625,
-0.01308441162109375,
-0.0025997161865234375,
0.0137939453125,
0.01708984375,
0.0150604248046875,
-0.0285491943359375,
0.0139923095703125,
-0.001026153564453125,
-0.0255126953125,
0.01568603515625,
0.0219268798828125,
-0.036285400390625,
0.00792694091796875,
0.00971221923828125,
0.0004744529724121094,
0.0055999755859375,
-0.013824462890625,
0.0150909423828125,
0.01251220703125,
0.0004642009735107422,
-0.00923919677734375,
-0.0014905929565429688,
-0.00313568115234375,
-0.028167724609375,
0.01468658447265625,
-0.0119476318359375,
-0.0081787109375,
-0.005840301513671875,
-0.006801605224609375,
-0.056915283203125,
-0.00384521484375,
-0.00664520263671875,
0.0100250244140625,
0.00021004676818847656,
-0.001888275146484375,
0.0006947517395019531,
-0.01027679443359375,
0.025543212890625,
0.01141357421875,
0.0016851425170898438,
0.01102447509765625,
0.014129638671875,
0.0198822021484375,
-0.01177215576171875,
-0.03619384765625,
-0.0098876953125,
0.0157470703125,
0.008056640625,
-0.002948760986328125,
0.01226806640625,
0.0253448486328125,
-0.0004150867462158203,
-0.0054473876953125,
-0.01465606689453125,
-0.003612518310546875,
0.00998687744140625,
-0.0118408203125,
-0.01108551025390625,
-0.0273284912109375,
-0.0406494140625,
0.00763702392578125,
0.0070648193359375,
-0.006900787353515625,
-0.0184326171875,
0.0013055801391601562,
0.0015106201171875,
0.01300048828125,
0.01447296142578125,
-0.025482177734375,
0.0167999267578125,
-0.0007100105285644531,
0.00283050537109375,
-0.0263214111328125,
-0.01221466064453125,
-0.015716552734375,
0.00806427001953125,
-0.0116119384765625,
0.01378631591796875,
0.0083770751953125,
-0.0010118484497070312,
-0.0020923614501953125,
-0.002895355224609375,
0.0128631591796875,
-0.0098876953125,
0.0086822509765625,
-0.0215606689453125,
0.00017201900482177734,
0.00913238525390625,
0.002025604248046875,
0.00013172626495361328,
-0.015899658203125,
0.006267547607421875,
0.01076507568359375,
-0.004726409912109375,
-0.0009965896606445312,
0.01369476318359375,
-0.00832366943359375,
-0.009124755859375,
-0.01348114013671875,
-0.0157012939453125,
0.0055694580078125,
-0.0275115966796875,
0.0125274658203125,
-0.0019216537475585938,
0.0251922607421875,
-0.00934600830078125,
-0.031982421875,
-0.00849151611328125,
-0.0015172958374023438,
-0.00472259521484375,
-0.005863189697265625,
0.010772705078125,
0.0249481201171875,
0.018768310546875,
0.012908935546875,
-0.0384521484375,
0.0220184326171875,
-0.004589080810546875,
0.0156707763671875,
-0.02081298828125,
-0.004062652587890625,
-0.0273590087890625,
0.0005612373352050781,
-0.0009703636169433594,
0.017730712890625,
0.01444244384765625,
0.0246429443359375,
0.012237548828125,
0.01519775390625,
0.0099334716796875,
-0.00824737548828125,
0.0110931396484375,
-0.0096435546875,
-0.0178375244140625,
-0.005001068115234375,
0.00334930419921875,
0.0004115104675292969,
-0.01433563232421875,
-0.004901885986328125,
-0.01007080078125,
-0.01357269287109375,
-0.0186614990234375,
-0.00884246826171875,
-0.006183624267578125,
0.006839752197265625,
0.0174407958984375,
0.002742767333984375,
-0.01136016845703125,
-0.026275634765625,
-0.0003571510314941406,
0.01360321044921875,
-0.0116729736328125,
0.006801605224609375,
-0.01055145263671875,
0.00785064697265625,
-0.004840850830078125,
0.004367828369140625,
0.00850677490234375,
0.00627899169921875,
-0.005893707275390625,
0.0012454986572265625,
-0.0333251953125,
-0.0006532669067382812,
0.01145172119140625,
-0.0305023193359375,
0.005588531494140625,
-0.0224609375,
0.0310821533203125,
0.0188446044921875,
0.0024013519287109375,
-0.00701904296875,
0.0044097900390625,
-0.006008148193359375,
0.0036830902099609375,
-0.02105712890625,
-0.01088714599609375,
0.01629638671875,
-0.00875091552734375,
-0.01525115966796875,
-0.01251220703125,
-0.0102386474609375,
0.01715087890625,
-0.01155853271484375,
-0.0163726806640625,
0.0261993408203125,
-0.001743316650390625,
0.0013179779052734375,
-0.01007080078125,
-0.00868988037109375,
-0.01038360595703125,
0.0204315185546875,
0.014556884765625,
0.0021266937255859375,
0.024017333984375,
-0.0258331298828125,
0.0207977294921875,
-0.025299072265625,
-0.0104522705078125,
-0.00473785400390625,
0.02032470703125,
-0.0102081298828125,
-0.018280029296875,
0.0205230712890625,
0.01329803466796875,
-0.01058197021484375,
-0.004016876220703125,
0.023834228515625,
-0.0186309814453125,
0.0114898681640625,
-0.01032257080078125,
0.0083770751953125,
0.0153045654296875,
-0.0117340087890625,
-0.00787353515625,
0.0128173828125,
0.00811767578125,
-0.0220184326171875,
0.00400543212890625,
-0.01537322998046875,
0.0340576171875,
-0.0023708343505859375,
-0.01451873779296875,
0.0195770263671875,
-0.0059967041015625,
0.0004448890686035156,
0.0209808349609375,
-0.01258087158203125,
0.0013685226440429688,
-0.024932861328125,
0.004375457763671875,
0.004726409912109375,
0.0008826255798339844,
-0.01488494873046875,
-0.022308349609375,
0.0012950897216796875,
0.02740478515625,
-0.006542205810546875,
-0.00942230224609375,
0.0019779205322265625,
-0.05804443359375,
-0.035614013671875,
-0.0020313262939453125,
0.00807952880859375,
-0.023193359375,
-0.015777587890625,
0.01198577880859375,
-0.016143798828125,
0.0195465087890625,
-0.0028209686279296875,
0.0025386810302734375,
-0.0116729736328125,
0.00400543212890625,
-0.0185089111328125,
0.0020999908447265625,
0.01065826416015625,
-0.015228271484375,
-0.00691986083984375,
0.0233154296875,
-0.0273590087890625,
-0.002696990966796875,
0.01309967041015625,
-0.0009522438049316406,
0.01526641845703125,
0.0033435821533203125,
-0.0153656005859375,
0.00916290283203125,
0.00847625732421875,
0.0232391357421875,
0.0019025802612304688,
-0.01519775390625,
-0.0038623809814453125,
0.0005283355712890625,
0.007320404052734375,
-0.0017948150634765625,
-0.00830841064453125,
0.02374267578125,
0.00836944580078125,
-0.0141143798828125,
-0.0234222412109375,
-0.01407623291015625,
-0.0030422210693359375,
-0.01058197021484375,
0.002758026123046875,
-0.009124755859375,
0.00504302978515625,
-0.007801055908203125,
-0.0033740997314453125,
-0.003894805908203125,
0.01119232177734375,
0.00168609619140625,
0.025665283203125,
-0.03631591796875,
0.00876617431640625,
-0.03253173828125,
-0.0085906982421875,
-0.024322509765625,
0.005176544189453125,
0.019989013671875,
0.003444671630859375,
0.01959228515625,
0.0015897750854492188,
0.011138916015625,
0.01910400390625,
-0.0013751983642578125,
0.0196380615234375,
-0.0299835205078125,
0.04400634765625,
-0.02001953125,
0.0252532958984375,
-0.0063323974609375,
0.0016345977783203125,
-0.0126953125,
-0.026397705078125,
-0.0198822021484375,
0.006404876708984375,
-0.007335662841796875,
0.006305694580078125,
-0.00016105175018310547,
-0.016143798828125,
-0.0228271484375,
-0.062744140625,
0.0040740966796875,
0.0285186767578125,
0.02508544921875,
-0.026458740234375,
0.0202178955078125,
-0.03460693359375,
-0.0137176513671875,
-0.038482666015625,
-0.00024187564849853516,
0.00021922588348388672,
-0.00798797607421875,
-0.0043182373046875,
-0.02008056640625,
-0.0216064453125,
0.041351318359375,
0.030364990234375,
-0.01561737060546875,
-0.000934600830078125,
-0.006214141845703125,
-0.01151275634765625,
0.0097503662109375,
0.01375579833984375,
0.01470184326171875,
-0.0010251998901367188,
-0.006420135498046875,
-0.0299835205078125,
0.0111846923828125,
-0.0044097900390625,
0.0106964111328125,
0.03125,
-0.039703369140625,
0.004161834716796875,
-0.023590087890625,
-0.044464111328125,
0.030548095703125,
-0.00965118408203125,
0.0049285888671875,
0.04107666015625,
0.0106201171875,
0.025909423828125,
0.0177764892578125,
0.005390167236328125,
0.0047149658203125,
0.01520538330078125,
0.019195556640625,
0.01309967041015625,
-0.019378662109375,
-0.0172882080078125,
-0.01384735107421875,
0.00867462158203125,
-0.00547027587890625,
0.032562255859375,
-0.0038738250732421875,
-0.01267242431640625,
-0.0099945068359375,
-0.02490234375,
0.0194549560546875,
-0.0014200210571289062,
-0.0156707763671875,
0.005352020263671875,
0.0204315185546875,
-0.026885986328125,
0.00140380859375,
-0.020599365234375,
-0.0212249755859375,
0.003940582275390625,
-0.01174163818359375,
0.037078857421875,
-0.00478363037109375,
-0.00849151611328125,
-0.0140533447265625,
0.02362060546875,
0.026580810546875,
0.007293701171875,
0.010284423828125,
-0.030303955078125,
-0.046600341796875,
-0.0333251953125,
-0.03729248046875,
0.00981903076171875,
0.006381988525390625,
0.003841400146484375,
-0.017578125,
0.030059814453125,
0.0245361328125,
-0.01259613037109375,
-0.031585693359375,
-0.0013866424560546875,
-0.0056915283203125,
0.004947662353515625,
0.022247314453125,
0.01532745361328125,
-0.0335693359375,
0.0036373138427734375,
0.0120849609375,
0.057586669921875,
-0.030517578125,
-0.016021728515625,
-0.0234222412109375,
0.0032138824462890625,
0.0011262893676757812,
0.010498046875,
0.005100250244140625,
0.01081085205078125,
-0.0116119384765625,
-0.043304443359375,
0.052978515625,
-0.013763427734375,
0.01611328125,
-0.054931640625,
0.01067352294921875,
-0.007106781005859375,
0.0194244384765625,
0.0113372802734375,
0.026824951171875,
0.0125885009765625,
0.004638671875,
-0.042388916015625,
0.0297698974609375,
0.035491943359375,
0.01629638671875,
-0.0153656005859375,
-0.0002932548522949219,
0.0169677734375,
-0.022796630859375,
0.00787353515625,
0.0270843505859375,
-0.01317596435546875,
-0.00858306884765625,
0.006351470947265625,
0.0017452239990234375,
0.005908966064453125,
0.01093292236328125,
-0.00826263427734375,
0.03363037109375,
-0.01027679443359375,
-0.0259552001953125,
0.0000641942024230957,
-0.024261474609375,
-0.0011777877807617188,
0.0005240440368652344,
-0.0117645263671875,
0.058868408203125,
0.00850677490234375,
-0.0083465576171875,
-0.038177490234375,
-0.002368927001953125,
-0.031707763671875,
-0.00992584228515625,
0.0253448486328125,
-0.0300140380859375,
0.0283966064453125,
-0.029022216796875,
0.01488494873046875,
0.00885009765625,
0.007488250732421875,
0.027435302734375,
0.01395416259765625,
-0.0177001953125,
0.006290435791015625,
0.019866943359375,
0.0185089111328125,
-0.0026531219482421875,
-0.01210784912109375,
0.0269317626953125,
-0.0599365234375,
0.035064697265625,
0.005100250244140625,
-0.0137786865234375,
-0.017791748046875,
0.004642486572265625,
0.0157623291015625,
-0.00746917724609375,
-0.03070068359375,
-0.004764556884765625,
0.0309906005859375,
-0.0552978515625,
0.0213470458984375,
0.004451751708984375,
-0.0118865966796875,
-0.00542449951171875,
0.0022144317626953125,
0.01322174072265625,
-0.02386474609375,
0.022705078125,
0.01178741455078125,
0.004665374755859375,
0.0034236907958984375,
0.006195068359375,
-0.0079345703125,
0.0047149658203125,
0.01007080078125,
0.00543975830078125,
0.0015201568603515625,
0.01328277587890625,
0.004070281982421875,
0.007366180419921875,
0.006694793701171875,
0.0000050067901611328125,
-0.02410888671875,
0.017578125,
0.0068206787109375,
-0.0128326416015625,
0.010009765625,
0.035247802734375,
0.0180511474609375,
-0.045562744140625,
0.031646728515625,
-0.003055572509765625,
-0.0206146240234375,
-0.01512908935546875,
-0.00030159950256347656,
-0.01226043701171875,
0.0212554931640625,
-0.020599365234375,
-0.00875091552734375,
0.01406097412109375,
0.00525665283203125,
0.0238037109375,
0.001861572265625,
-0.020111083984375,
0.0064544677734375,
-0.00818634033203125,
0.0115966796875,
0.013153076171875,
0.0272216796875,
-0.0261993408203125,
0.0006113052368164062,
0.0005125999450683594,
0.004001617431640625,
-0.0104827880859375,
-0.01263427734375,
0.032012939453125,
-0.034912109375,
-0.016082763671875,
0.0164337158203125,
0.002140045166015625,
0.004131317138671875,
-0.006801605224609375,
0.0024929046630859375,
-0.0027637481689453125,
0.0058135986328125,
-0.02288818359375,
-0.0399169921875,
0.004909515380859375,
0.0266265869140625,
0.007030487060546875,
-0.042449951171875,
-0.0280609130859375,
-0.005275726318359375,
0.01506805419921875,
0.01387786865234375,
0.01194000244140625,
0.0170440673828125,
-0.01186370849609375,
0.01488494873046875,
0.0013742446899414062,
0.02630615234375,
-0.006168365478515625,
-0.01213836669921875,
-0.01207733154296875,
-0.004573822021484375,
0.006885528564453125,
0.013671875,
0.003360748291015625,
-0.01363372802734375,
-0.0008945465087890625,
0.0186920166015625,
-0.0037593841552734375,
-0.006526947021484375,
-0.004436492919921875,
-0.042755126953125,
0.047149658203125,
-0.02032470703125,
0.03466796875,
-0.0213470458984375,
0.0167999267578125,
-0.01214599609375,
0.0174102783203125,
-0.013214111328125,
-0.0084686279296875,
0.036163330078125,
0.00997161865234375,
-0.0028228759765625,
0.0130615234375,
0.0085296630859375,
0.008392333984375,
-0.0164947509765625,
-0.0036716461181640625,
0.006572723388671875,
0.01168060302734375,
-0.013763427734375,
0.017608642578125,
-0.01070404052734375,
0.014434814453125,
-0.0035610198974609375,
0.00597381591796875,
0.0224151611328125,
-0.0120697021484375,
-0.00809478759765625,
-0.006500244140625,
0.013946533203125,
0.0178070068359375,
-0.0225677490234375,
0.03216552734375,
-0.00251007080078125,
0.0271453857421875,
0.01065826416015625,
0.0007872581481933594,
-0.014312744140625,
0.001678466796875,
0.0287322998046875,
0.0020275115966796875,
-0.0169219970703125,
-0.035003662109375,
-0.0096282958984375,
0.00264739990234375,
-0.018768310546875,
-0.00926971435546875,
0.027435302734375,
0.0201263427734375,
-0.021209716796875,
-0.0025501251220703125,
-0.01302337646484375,
0.01490020751953125,
0.0196533203125,
-0.0408935546875,
0.010284423828125,
0.0160675048828125,
0.01403045654296875,
-0.004512786865234375,
-0.035430908203125,
0.006870269775390625,
0.0084381103515625,
-0.01462554931640625,
-0.01410675048828125,
-0.01392364501953125,
0.00858306884765625,
0.0289154052734375,
-0.0119781494140625,
-0.008636474609375,
-0.055816650390625,
-0.024993896484375,
-0.01702880859375,
0.039398193359375,
-0.025634765625,
0.0214996337890625,
0.0036830902099609375,
-0.0133819580078125,
0.00839996337890625,
0.0137481689453125,
-0.0130615234375,
0.003879547119140625,
0.0028476715087890625,
-0.006542205810546875,
0.034698486328125,
-0.0010156631469726562,
-0.0190887451171875,
-0.018280029296875,
-0.0188446044921875,
-0.004604339599609375,
-0.0111236572265625,
0.0287322998046875,
0.0160064697265625,
-0.032501220703125,
0.005596160888671875,
0.0118560791015625,
-0.0328369140625,
0.0196990966796875,
0.0209197998046875,
0.01275634765625,
-0.0158538818359375,
-0.035888671875,
0.036468505859375,
0.003971099853515625,
-0.004901885986328125,
-0.0210113525390625,
0.002796173095703125,
-0.00028824806213378906,
-0.004833221435546875,
-0.04638671875,
0.019195556640625,
0.0167694091796875,
-0.01184844970703125,
0.0023193359375,
0.0187835693359375,
0.0014181137084960938,
-0.006710052490234375,
0.0057220458984375,
-0.0010728836059570312,
-0.0274810791015625,
0.005535125732421875,
0.0183868408203125,
-0.030181884765625,
0.017425537109375,
0.004535675048828125,
0.01678466796875,
0.002483367919921875,
0.0007123947143554688,
0.00832366943359375,
0.0125274658203125,
-0.04681396484375,
-0.04681396484375,
-0.00489044189453125,
0.02685546875,
-0.01238250732421875,
0.00290679931640625,
0.048828125,
0.0018186569213867188,
0.00899505615234375,
-0.001605987548828125,
0.00975799560546875,
-0.0036487579345703125,
0.024658203125,
-0.00859832763671875,
0.0086212158203125,
-0.00688934326171875,
-0.0185699462890625,
0.005390167236328125,
0.0017347335815429688,
-0.0322265625,
0.0221405029296875,
0.0029582977294921875,
0.0121612548828125,
-0.0096435546875,
0.01340484619140625,
0.018035888671875,
-0.0086669921875,
-0.0201873779296875,
-0.01218414306640625,
0.0311279296875,
-0.00739288330078125,
0.0206146240234375,
0.007801055908203125,
-0.0307769775390625,
-0.01464080810546875,
0.00225067138671875,
-0.0211334228515625,
-0.039459228515625,
-0.0185394287109375,
-0.0022907257080078125,
0.01132965087890625,
-0.00934600830078125,
-0.0046539306640625,
0.0191802978515625,
0.034759521484375,
0.03179931640625,
-0.0229034423828125,
0.01306915283203125,
-0.0142974853515625,
-0.0247344970703125,
0.0565185546875,
-0.0029964447021484375,
0.0023479461669921875,
-0.0308990478515625,
0.022186279296875,
-0.004425048828125,
0.02459716796875,
0.01331329345703125,
-0.00644683837890625,
0.0210113525390625,
0.0251312255859375,
0.011962890625,
-0.002056121826171875,
0.004833221435546875,
-0.0164947509765625,
-0.0013685226440429688,
0.0161895751953125,
0.007904052734375,
-0.0116119384765625,
-0.00013303756713867188,
-0.0123138427734375,
0.0135498046875,
-0.03851318359375,
0.0238494873046875,
0.0020809173583984375,
-0.026153564453125,
-0.024993896484375,
-0.030059814453125,
0.0244293212890625,
0.0092926025390625,
0.0046844482421875,
0.021087646484375,
0.0028705596923828125,
0.02349853515625,
-0.0211944580078125,
0.004241943359375,
-0.0074615478515625,
-0.01824951171875,
0.0159454345703125,
0.01047515869140625,
-0.0212249755859375,
-0.0389404296875,
-0.0019989013671875,
-0.019378662109375,
0.01177978515625,
0.0007390975952148438,
-0.01715087890625,
0.0237884521484375,
-0.002056121826171875,
0.0224761962890625,
0.005603790283203125,
0.025970458984375,
-0.03466796875,
0.01873779296875,
-0.016510009765625,
0.00037384033203125,
-0.015899658203125,
-0.043243408203125,
-0.022125244140625,
-0.0154876708984375,
-0.0191497802734375,
-0.0008687973022460938,
0.00968170166015625,
-0.00870513916015625,
0.015625,
0.01528167724609375,
0.00787353515625,
-0.01934814453125,
0.00899505615234375,
-0.0246124267578125,
-0.0209503173828125,
-0.0216217041015625,
-0.004238128662109375,
0.010162353515625,
0.006771087646484375,
-0.03326416015625,
0.006221771240234375,
0.016021728515625,
-0.024078369140625,
-0.007904052734375,
-0.007625579833984375,
-0.03631591796875,
0.031646728515625,
0.00876617431640625,
0.041595458984375,
-0.016387939453125,
-0.0058135986328125,
-0.0273895263671875,
-0.005706787109375,
0.021728515625,
-0.027618408203125,
-0.0289764404296875,
0.01334381103515625,
-0.0270843505859375,
-0.0086517333984375,
-0.00817108154296875,
0.0149993896484375,
0.034271240234375,
-0.0166015625,
-0.00740814208984375,
0.048309326171875,
-0.007472991943359375,
-0.010711669921875,
-0.00940704345703125,
0.007965087890625,
-0.01122283935546875,
0.0203094482421875,
-0.008758544921875,
-0.038482666015625,
-0.0017156600952148438,
-0.02264404296875,
0.004741668701171875,
-0.00524139404296875,
0.0179901123046875,
-0.0080413818359375,
-0.0050048828125,
0.0445556640625,
-0.01442718505859375,
0.0016574859619140625,
0.00836944580078125,
0.03399658203125,
0.0110321044921875,
-0.01551055908203125,
-0.01055908203125,
-0.006763458251953125,
-0.029876708984375,
-0.006809234619140625,
0.0160369873046875,
-0.016510009765625,
0.0031871795654296875,
0.018524169921875,
0.03125,
0.016845703125,
-0.02593994140625,
0.0154266357421875,
-0.00846099853515625,
-0.0010128021240234375,
-0.0183258056640625,
0.0270538330078125,
0.0109710693359375,
0.004650115966796875,
0.0093841552734375,
-0.0271148681640625,
0.0187835693359375,
0.02716064453125,
-0.0364990234375,
-0.005336761474609375,
-0.03125,
0.030364990234375,
0.017120361328125,
-0.0171966552734375,
0.0096435546875,
-0.00778961181640625,
-0.00029969215393066406,
0.00778961181640625,
0.002780914306640625,
0.02197265625,
0.010589599609375,
-0.0087127685546875,
-0.00891876220703125,
-0.01309967041015625,
0.035736083984375,
0.028900146484375,
-0.00914764404296875,
-0.0135040283203125,
0.0213165283203125,
0.03271484375,
-0.0265350341796875,
0.0301971435546875,
0.0064544677734375,
0.0263214111328125,
-0.03973388671875,
0.003330230712890625,
0.03997802734375,
0.0028438568115234375,
-0.0142822265625,
-0.044219970703125,
0.006435394287109375,
0.007965087890625,
-0.0226287841796875,
0.0279388427734375,
0.0173492431640625,
-0.00482177734375,
0.006298065185546875,
-0.001399993896484375,
-0.01367950439453125,
-0.013702392578125,
0.011505126953125,
-0.0244293212890625,
-0.0017805099487304688,
-0.01497650146484375,
0.046661376953125,
0.031982421875,
0.0079803466796875,
0.01198577880859375,
-0.00960540771484375,
-0.0310516357421875,
-0.0253448486328125,
-0.028533935546875,
0.006443023681640625,
0.002925872802734375,
-0.034515380859375,
-0.00823211669921875,
-0.0133819580078125,
0.017608642578125,
-0.006427764892578125,
-0.0024967193603515625,
0.01255035400390625,
0.02587890625,
0.019287109375,
-0.01220703125,
0.02020263671875,
-0.0032253265380859375,
0.0149993896484375,
-0.04864501953125,
-0.01204681396484375,
-0.033599853515625,
0.0202789306640625,
-0.0128021240234375,
-0.013824462890625,
0.003276824951171875,
-0.017730712890625,
0.03509521484375,
-0.049224853515625,
-0.025604248046875,
-0.0015687942504882812,
-0.048431396484375,
0.043701171875,
0.0048828125,
-0.0202789306640625,
-0.04425048828125,
0.011932373046875,
-0.008941650390625,
0.018463134765625,
0.01236724853515625,
-0.0239715576171875,
0.038787841796875,
0.0248260498046875,
0.006427764892578125,
-0.0024127960205078125,
-0.013458251953125,
0.01971435546875,
-0.01355743408203125,
0.00861358642578125,
0.0110015869140625,
-0.006412506103515625,
0.01323699951171875,
0.038970947265625,
0.00017023086547851562,
-0.0004684925079345703,
0.021148681640625,
0.01309967041015625,
-0.0345458984375,
-0.015472412109375,
0.0228118896484375,
0.004856109619140625,
-0.0181732177734375,
0.004241943359375,
-0.036346435546875,
-0.0186309814453125,
0.0467529296875,
-0.021392822265625,
-0.002292633056640625,
-0.02838134765625,
0.030792236328125,
0.01763916015625,
0.0411376953125,
-0.0243988037109375,
-0.0343017578125,
-0.03631591796875,
-0.0032253265380859375,
-0.0237274169921875,
-0.006977081298828125,
-0.0012912750244140625,
0.01110076904296875,
0.005893707275390625,
-0.0012712478637695312,
0.014068603515625,
0.0002841949462890625,
-0.01464080810546875,
-0.0220947265625,
-0.0171966552734375,
-0.01015472412109375,
0.021453857421875,
-0.0040740966796875,
-0.0237579345703125,
-0.0106964111328125,
0.0262908935546875,
-0.0202178955078125,
-0.022613525390625,
-0.0095977783203125,
-0.003139495849609375,
0.0202484130859375,
0.015716552734375,
0.01045989990234375,
0.00606536865234375,
-0.0169219970703125,
-0.020965576171875,
-0.009674072265625,
-0.01015472412109375,
0.021636962890625,
-0.0026798248291015625,
-0.0005002021789550781,
0.0286712646484375,
0.0177764892578125,
0.00855255126953125,
0.00907135009765625,
0.01861572265625,
-0.0244293212890625,
-0.0174713134765625,
-0.0033626556396484375,
-0.0147705078125,
-0.003818511962890625,
-0.0081634521484375,
-0.021331787109375,
0.03717041015625,
0.0005712509155273438,
-0.01137542724609375,
0.016082763671875,
-0.0120086669921875,
0.05389404296875,
-0.06536865234375,
0.01477813720703125,
-0.01708984375,
-0.0168609619140625,
0.0360107421875,
-0.0034694671630859375,
0.01369476318359375,
-0.01139068603515625,
-0.008880615234375,
-0.029876708984375,
-0.0322265625,
-0.022216796875,
-0.039215087890625,
-0.004840850830078125,
0.006893157958984375,
-0.021942138671875,
-0.0184478759765625,
0.01270294189453125,
-0.000006854534149169922,
0.0225372314453125,
-0.01268768310546875,
0.00945281982421875,
0.01018524169921875,
0.040924072265625,
-0.039154052734375,
-0.0179290771484375,
-0.0029754638671875,
0.0093536376953125,
-0.0299224853515625,
0.009735107421875,
-0.01309967041015625,
-0.005207061767578125,
-0.0009541511535644531,
-0.0423583984375,
-0.02581787109375,
-0.0254974365234375,
0.0298919677734375,
0.004634857177734375,
-0.0016384124755859375,
0.00382232666015625,
-0.0161590576171875,
0.0233154296875,
0.00717926025390625,
-0.006320953369140625,
0.0009036064147949219,
-0.0259552001953125,
0.00818634033203125,
0.0020198822021484375,
0.034210205078125,
-0.006824493408203125,
-0.011016845703125,
0.0030670166015625,
-0.03155517578125,
0.0004355907440185547,
-0.0228271484375,
0.00591278076171875,
-0.01812744140625,
0.0001671314239501953,
-0.003017425537109375,
0.0295867919921875,
0.033935546875,
0.0087738037109375,
0.005496978759765625,
0.044403076171875,
-0.0149383544921875,
0.0238037109375,
-0.002948760986328125,
0.02130126953125,
-0.0171661376953125,
0.004146575927734375,
0.00832366943359375,
0.07989501953125,
0.0214691162109375,
-0.003337860107421875,
0.004940032958984375,
-0.01275634765625,
0.012359619140625,
-0.017791748046875,
-0.01078033447265625,
-0.0028858184814453125,
-0.005748748779296875,
0.003696441650390625,
-0.0128936767578125,
0.0163421630859375,
0.00792694091796875,
-0.0244140625,
-0.02362060546875,
0.0022678375244140625,
-0.0078277587890625,
-0.0157012939453125,
0.01178741455078125,
0.002902984619140625,
0.007228851318359375,
-0.005725860595703125,
-0.0307769775390625,
-0.0021724700927734375,
0.0069122314453125,
-0.03558349609375,
0.01062774658203125,
0.0193634033203125,
0.0269622802734375,
0.021575927734375,
0.0147552490234375,
0.0265655517578125,
0.001953125,
0.024871826171875,
-0.0264129638671875,
-0.01065826416015625,
-0.043487548828125,
-0.023529052734375,
0.01678466796875,
0.0108642578125,
0.00008678436279296875,
0.0182342529296875,
0.043914794921875,
0.0186920166015625,
-0.0016164779663085938,
-0.01447296142578125,
-0.01448822021484375,
0.01163482666015625,
-0.01177978515625,
-0.009765625,
0.004550933837890625,
-0.0018062591552734375,
-0.02264404296875,
0.045318603515625,
-0.0005359649658203125,
0.0161895751953125,
-0.01363372802734375,
0.0272674560546875,
-0.00550079345703125,
0.0145111083984375,
0.012115478515625,
-0.0220184326171875,
-0.0063934326171875,
-0.0004527568817138672,
-0.0009870529174804688,
-0.01568603515625,
0.006038665771484375,
-0.007015228271484375,
-0.02362060546875,
-0.0195770263671875,
0.0215606689453125,
0.00913238525390625,
0.0261077880859375,
0.02520751953125,
0.0202484130859375,
-0.0077972412109375,
-0.01512908935546875,
-0.021484375,
-0.0125885009765625,
-0.012969970703125,
0.0139312744140625,
0.0167694091796875,
-0.01076507568359375,
-0.0197906494140625,
-0.0068359375,
0.01415252685546875,
-0.01702880859375,
-0.0137481689453125,
0.0193023681640625,
0.02227783203125,
0.0071868896484375,
0.002063751220703125,
-0.07550048828125,
-0.001010894775390625,
0.0020656585693359375,
0.0073394775390625,
0.001953125,
0.0025463104248046875,
-0.00885009765625,
-0.04119873046875,
0.006744384765625,
0.0217437744140625,
-0.0171356201171875,
0.0052642822265625,
0.0056304931640625,
-0.0217742919921875,
-0.034820556640625,
0.0094451904296875,
0.0083465576171875,
-0.019439697265625,
-0.00630950927734375,
-0.009124755859375,
0.0172576904296875,
0.053680419921875,
0.01242828369140625,
-0.005428314208984375,
0.0162811279296875,
0.0021762847900390625,
-0.0078887939453125,
0.0311737060546875,
-0.003971099853515625,
-0.03912353515625,
-0.042633056640625,
0.005626678466796875,
0.0298614501953125,
0.019775390625,
-0.002269744873046875,
0.0172119140625,
0.023773193359375,
-0.00315093994140625,
-0.0266265869140625,
0.029632568359375,
0.00989532470703125,
-0.01251220703125,
0.0092010498046875,
-0.0219879150390625,
-0.026092529296875,
0.0142822265625,
0.01142120361328125,
-0.004573822021484375,
-0.0087432861328125,
0.00585174560546875,
-0.0211181640625,
-0.023223876953125,
0.0072174072265625,
0.007595062255859375,
0.011566162109375,
-0.0112152099609375,
0.0189666748046875,
0.0061492919921875,
0.0227203369140625,
0.00774383544921875,
-0.003662109375,
0.02655029296875,
0.0035953521728515625,
-0.0101470947265625,
0.0185394287109375,
0.00360107421875,
-0.0258331298828125,
0.0017499923706054688,
0.00403594970703125,
0.01235198974609375,
-0.0063018798828125,
0.010040283203125,
-0.0038623809814453125,
-0.023406982421875,
-0.006084442138671875,
0.0167999267578125,
-0.01335906982421875,
-0.003498077392578125,
0.0026092529296875,
0.022979736328125,
-0.0048675537109375,
-0.016357421875,
0.01415252685546875,
-0.006175994873046875,
-0.0156402587890625,
-0.0218963623046875,
-0.0097808837890625,
-0.01036834716796875,
0.021942138671875,
0.0217132568359375,
-0.040313720703125,
0.011322021484375,
-0.0235443115234375,
-0.0149383544921875,
0.02313232421875,
0.00021266937255859375,
0.00921630859375,
-0.0384521484375,
0.01580810546875,
-0.018829345703125,
-0.0102081298828125,
-0.0189056396484375,
0.02825927734375,
0.0148162841796875,
0.0304412841796875,
0.03509521484375,
0.0163421630859375,
0.0207977294921875,
-0.0184783935546875,
-0.01285552978515625,
0.014404296875,
-0.0184326171875,
-0.0211639404296875,
-0.01041412353515625,
0.039764404296875,
0.035247802734375,
-0.002838134765625,
-0.034027099609375,
-0.0151824951171875,
-0.0165252685546875,
0.01012420654296875,
-0.0186767578125,
0.0182952880859375,
-0.0016946792602539062,
-0.00963592529296875,
-0.009613037109375,
-0.0089569091796875,
-0.0230712890625,
0.00550079345703125,
0.027587890625,
-0.005527496337890625,
0.045074462890625,
-0.0035305023193359375,
-0.01107025146484375,
-0.0193939208984375,
0.0465087890625,
0.0164642333984375,
0.010955810546875,
-0.0259857177734375,
-0.0235595703125,
0.011199951171875,
0.0143890380859375,
-0.00818634033203125,
-0.006473541259765625,
0.0487060546875,
-0.01477813720703125,
0.017578125,
-0.0219879150390625,
-0.0012331008911132812,
0.011810302734375,
0.017913818359375,
0.003292083740234375,
-0.024627685546875,
-0.0170745849609375,
-0.0271759033203125,
0.00783538818359375,
0.006526947021484375,
-0.00737762451171875,
-0.0140533447265625,
-0.022918701171875,
0.02410888671875,
0.01248931884765625,
0.027313232421875,
0.0034732818603515625,
0.0206451416015625,
-0.0263214111328125,
-0.004993438720703125,
-0.0014057159423828125,
0.0290069580078125,
-0.01360321044921875,
0.037872314453125,
-0.01702880859375,
-0.01201629638671875,
-0.061737060546875,
0.003040313720703125,
-0.0009059906005859375,
-0.005413055419921875,
-0.007770538330078125,
0.0058135986328125,
-0.02471923828125,
0.0093231201171875,
0.026275634765625,
-0.051055908203125,
-0.0225982666015625,
0.0240325927734375,
-0.0116729736328125,
-0.0244903564453125,
-0.0030498504638671875,
-0.007232666015625,
-0.028594970703125,
0.007099151611328125,
0.0096588134765625,
0.037689208984375,
-0.0269927978515625,
-0.0027828216552734375,
-0.0046234130859375,
-0.00736236572265625,
0.00811004638671875,
-0.0059051513671875,
-0.0175323486328125,
-0.00313568115234375,
0.0232086181640625,
0.0148773193359375,
0.019622802734375,
0.0019378662109375,
0.000843048095703125,
-0.00275421142578125,
-0.0014514923095703125,
0.0080413818359375,
-0.0258636474609375,
0.03125,
0.0306243896484375,
0.01274871826171875,
0.0303497314453125,
0.017913818359375,
0.029693603515625,
0.018341064453125,
0.012420654296875,
-0.008575439453125,
-0.0010938644409179688,
0.01079559326171875,
0.007801055908203125,
-0.00765228271484375,
-0.0404052734375,
0.021270751953125,
0.028228759765625,
0.006381988525390625,
-0.038543701171875,
-0.00617218017578125,
-0.00043773651123046875,
-0.019561767578125,
-0.03216552734375,
0.01007843017578125,
0.01239776611328125,
0.016998291015625,
0.03912353515625,
-0.0277252197265625,
-0.0168914794921875,
-0.0034999847412109375,
0.0009822845458984375,
0.005054473876953125,
0.006168365478515625,
0.0172576904296875,
0.00670623779296875,
0.0211944580078125,
0.009124755859375,
0.026458740234375,
-0.0062713623046875,
0.00833892822265625,
-0.0113372802734375,
-0.0195465087890625,
0.00275421142578125,
0.0276947021484375,
0.0164642333984375,
-0.0081939697265625,
0.01285552978515625,
0.0022144317626953125,
0.0038318634033203125,
0.0008282661437988281,
0.0068817138671875,
-0.007411956787109375,
-0.00928497314453125,
0.022430419921875,
-0.01947021484375,
0.0193634033203125,
0.0121307373046875,
0.0469970703125,
0.0163421630859375,
-0.023956298828125,
0.029571533203125,
0.01311492919921875,
0.019866943359375,
-0.02081298828125,
0.01236724853515625,
0.0158233642578125,
-0.00720977783203125,
0.00098419189453125,
0.01177978515625,
0.00836944580078125,
0.0064239501953125,
-0.009918212890625,
0.0041351318359375,
0.003570556640625,
0.00164794921875,
0.024566650390625,
0.0137786865234375,
-0.0011234283447265625,
-0.00823974609375,
0.036773681640625,
0.0347900390625,
0.00616455078125,
-0.0264129638671875,
0.02783203125,
0.0172882080078125,
-0.033172607421875,
0.0135955810546875,
0.00037789344787597656,
-0.0116119384765625,
0.0296783447265625,
-0.0024356842041015625,
-0.014984130859375,
0.009857177734375,
-0.0302886962890625,
-0.00983428955078125,
0.0452880859375,
0.013641357421875,
-0.000972747802734375,
0.0093994140625,
0.031524658203125,
-0.0443115234375,
0.0173797607421875,
-0.00968170166015625,
-0.019256591796875,
0.016754150390625,
0.0096435546875,
-0.004718780517578125,
-0.01528167724609375,
-0.0117340087890625,
0.0029659271240234375,
0.0109100341796875,
0.038299560546875,
-0.002666473388671875,
0.0119171142578125,
0.00821685791015625,
-0.005489349365234375,
0.01413726806640625,
0.0240478515625,
0.01079559326171875,
-0.038055419921875,
0.032440185546875,
0.0003209114074707031,
-0.02008056640625,
-0.0208587646484375,
0.01837158203125,
-0.004741668701171875,
-0.001110076904296875,
-0.01145172119140625,
0.0027446746826171875,
0.0008039474487304688,
0.02716064453125,
0.0198822021484375,
0.029754638671875,
-0.0081939697265625,
-0.007801055908203125,
-0.0120697021484375,
-0.012603759765625,
-0.0030994415283203125,
-0.0214996337890625,
0.0019378662109375,
-0.053131103515625,
-0.018646240234375,
0.028564453125,
0.003170013427734375,
0.0178375244140625,
-0.00443267822265625,
0.01506805419921875,
0.0047149658203125,
0.024566650390625,
0.026885986328125,
0.00649261474609375,
-0.006622314453125,
0.03106689453125,
0.0243377685546875,
0.01013946533203125,
-0.0018854141235351562,
-0.0050506591796875,
0.0008301734924316406,
0.02691650390625,
0.0032196044921875,
-0.035736083984375,
0.01006317138671875,
-0.017059326171875,
-0.0116119384765625,
0.038330078125,
-0.0450439453125,
-0.015899658203125,
-0.0185546875,
0.017486572265625,
0.0308685302734375,
-0.029022216796875,
-0.033416748046875,
0.01519012451171875,
-0.007480621337890625,
0.03076171875,
0.0191802978515625,
-0.038726806640625,
0.023773193359375,
-0.003902435302734375,
-0.0213775634765625,
-0.01351165771484375,
-0.0137786865234375,
-0.0164337158203125,
0.00728607177734375,
-0.0157928466796875,
0.0101470947265625,
-0.0184478759765625,
0.01415252685546875,
0.0184326171875,
-0.009613037109375,
0.000514984130859375,
-0.03143310546875,
-0.00801849365234375,
-0.00556182861328125,
-0.012939453125,
-0.02349853515625,
-0.0268707275390625,
-0.0396728515625,
0.012969970703125,
0.00791168212890625,
-0.0287017822265625,
-0.033599853515625,
0.003520965576171875,
-0.0064239501953125,
-0.0290069580078125,
-0.0209197998046875,
-0.0016794204711914062,
-0.0019140243530273438,
-0.00682830810546875,
0.0125579833984375,
-0.04168701171875,
-0.0083160400390625,
-0.0148773193359375,
-0.0040740966796875,
-0.003421783447265625,
-0.00846099853515625,
-0.00917816162109375,
-0.0005970001220703125,
-0.0244293212890625,
0.0169677734375,
-0.041900634765625,
-0.0312042236328125,
-0.01415252685546875,
0.0080413818359375,
-0.001651763916015625,
0.01149749755859375,
-0.01396942138671875,
-0.0252685546875,
0.0019159317016601562,
-0.01248931884765625,
0.0440673828125,
0.00830078125,
0.0035648345947265625,
0.032196044921875,
-0.02734375,
0.0174407958984375,
-0.0137786865234375,
-0.041168212890625,
0.0123748779296875,
-0.0158538818359375,
0.01593017578125,
-0.0017910003662109375,
-0.0083465576171875,
0.0122833251953125,
0.00254058837890625,
0.006397247314453125,
-0.010162353515625,
-0.01256561279296875,
0.0116424560546875,
0.00342559814453125,
-0.027557373046875,
-0.01273345947265625,
-0.020751953125,
-0.0211181640625,
-0.00182342529296875,
-0.0262908935546875,
0.047271728515625,
0.02593994140625,
0.0233306884765625,
-0.03265380859375,
0.0072174072265625,
-0.02606201171875,
0.0036640167236328125,
0.039642333984375,
-0.01253509521484375,
-0.0031223297119140625,
0.01024627685546875,
0.0222930908203125,
0.008636474609375,
0.0149993896484375,
0.0119476318359375,
0.012359619140625,
0.0056915283203125,
-0.016998291015625,
-0.0240631103515625,
0.0047607421875,
0.01236724853515625,
-0.0262603759765625,
0.01146697998046875,
-0.0006618499755859375,
-0.01007843017578125,
-0.0154571533203125,
0.00054931640625,
-0.006771087646484375,
0.00803375244140625,
0.0175323486328125,
-0.0200958251953125,
0.0198516845703125,
0.0122528076171875,
-0.011444091796875,
-0.007419586181640625,
-0.037994384765625,
-0.005458831787109375,
0.02716064453125,
-0.0133056640625,
-0.005428314208984375,
-0.00547027587890625,
-0.0287322998046875,
-0.0088958740234375,
-0.010406494140625,
0.024871826171875,
-0.032989501953125,
0.04034423828125,
-0.023895263671875,
-0.007549285888671875,
0.0014638900756835938,
0.0014314651489257812,
0.01055145263671875,
0.018524169921875,
0.0016984939575195312,
-0.0168304443359375,
-0.0152740478515625,
0.0148468017578125,
-0.0284881591796875,
0.0142822265625,
-0.002422332763671875,
-0.0017375946044921875,
-0.0155487060546875,
0.019927978515625,
-0.0025386810302734375,
-0.0231475830078125,
-0.00843048095703125,
0.0168914794921875,
0.022125244140625,
-0.037384033203125,
0.022491455078125,
-0.0012493133544921875,
0.022125244140625,
-0.0011739730834960938,
0.011138916015625,
-0.0235595703125,
-0.0006623268127441406,
-0.01513671875,
0.0075225830078125,
0.0196533203125,
-0.003986358642578125,
-0.006923675537109375,
0.0226593017578125,
-0.020294189453125,
-0.020172119140625,
0.01149749755859375,
-0.00396728515625,
0.0218963623046875,
-0.017486572265625,
-0.00213623046875,
0.00539398193359375,
0.0546875,
0.01690673828125,
0.02679443359375,
0.007503509521484375,
0.006927490234375,
0.02490234375,
-0.0214385986328125,
-0.0009918212890625,
-0.0295562744140625,
-0.00125885009765625,
0.01416778564453125,
-0.01605224609375,
0.01511383056640625,
-0.01934814453125,
0.0090789794921875,
-0.0029239654541015625,
-0.0090789794921875,
-0.004425048828125,
0.0290985107421875,
-0.0204315185546875,
-0.0193634033203125,
-0.0094146728515625,
-0.00341796875,
0.02349853515625,
0.01016998291015625,
-0.01198577880859375,
-0.002635955810546875,
-0.01349639892578125,
0.0115203857421875,
0.007282257080078125,
0.032135009765625,
-0.01800537109375,
-0.00533294677734375,
-0.009033203125,
-0.01345062255859375,
0.05560302734375,
-0.011322021484375,
-0.0037822723388671875,
-0.0011310577392578125,
0.004917144775390625,
-0.00359344482421875,
-0.006671905517578125,
0.0007872581481933594,
-0.017974853515625,
0.0174407958984375,
0.0193634033203125,
-0.009552001953125,
0.00516510009765625,
-0.01593017578125,
0.0095672607421875,
0.017669677734375,
0.01253509521484375,
0.02105712890625,
-0.0171356201171875,
-0.01404571533203125,
-0.0189666748046875,
0.005153656005859375,
-0.007099151611328125,
0.00240325927734375,
0.01155853271484375,
-0.006694793701171875,
-0.002223968505859375,
-0.0014429092407226562,
0.04144287109375,
0.0120391845703125,
0.01224517822265625,
-0.027801513671875,
0.0124053955078125,
0.00838470458984375,
-0.006366729736328125,
0.016326904296875,
0.0174102783203125,
-0.00879669189453125,
0.0149383544921875,
-0.039794921875,
-0.04986572265625,
-0.026092529296875,
-0.020355224609375,
0.0008916854858398438,
0.003814697265625,
-0.033416748046875,
0.0120849609375,
-0.0166168212890625,
-0.0267791748046875,
0.03436279296875,
-0.00994873046875,
-0.003284454345703125,
0.010223388671875,
-0.01806640625,
-0.0018167495727539062,
0.0202484130859375,
-0.0014972686767578125,
-0.0123748779296875,
-0.0033206939697265625,
-0.0136566162109375,
-0.0020618438720703125,
-0.0298309326171875,
0.0246734619140625,
-0.050323486328125,
0.0007958412170410156,
0.0017251968383789062,
-0.020172119140625,
0.00881195068359375,
0.0237579345703125,
-0.01508331298828125,
-0.0031261444091796875,
0.0140228271484375,
-0.0032863616943359375,
-0.0031070709228515625,
0.02197265625,
0.032623291015625,
0.005855560302734375,
0.00021183490753173828,
-0.020416259765625,
0.0325927734375,
0.036773681640625,
-0.0008029937744140625,
0.01264190673828125,
-0.004718780517578125,
-0.0191192626953125,
0.0272674560546875,
0.006015777587890625,
0.01224517822265625,
0.00574493408203125,
-0.0214385986328125,
0.0210723876953125,
-0.004970550537109375,
-0.0032672882080078125,
0.024749755859375,
-0.037994384765625,
-0.01605224609375,
0.01922607421875,
0.0025634765625,
-0.0127410888671875,
-0.033477783203125,
-0.0221710205078125,
-0.020660400390625,
-0.034332275390625,
-0.000972747802734375,
0.0225372314453125,
0.02947998046875,
0.01042938232421875,
-0.0119476318359375,
0.013885498046875,
0.014251708984375,
0.0362548828125,
-0.00644683837890625,
0.0200042724609375,
0.01934814453125,
0.01264190673828125,
-0.00232696533203125,
0.02935791015625,
0.0079803466796875,
-0.0164337158203125,
-0.0115203857421875,
0.006336212158203125,
0.0322265625,
-0.0169830322265625,
0.00649261474609375,
0.032501220703125,
-0.0022373199462890625,
-0.039581298828125,
0.006378173828125,
-0.0009236335754394531,
0.034912109375,
-0.0136566162109375,
0.02001953125,
0.00530242919921875,
0.007328033447265625,
0.01385498046875,
-0.005035400390625,
-0.00637054443359375,
-0.0004405975341796875,
0.016326904296875,
0.01178741455078125,
0.01383209228515625,
-0.01250457763671875,
0.0198822021484375,
0.0335693359375,
-0.03546142578125,
-0.0036220550537109375,
0.016143798828125,
0.01312255859375,
0.0093231201171875,
-0.039581298828125,
-0.0106048583984375,
-0.01560211181640625,
0.0121307373046875,
-0.01229095458984375,
0.00310516357421875,
0.022705078125,
-0.0264434814453125,
0.042510986328125,
-0.0198516845703125,
0.0120086669921875,
0.020355224609375,
-0.0045623779296875,
0.00518798828125,
-0.047943115234375,
-0.01033782958984375,
-0.00589752197265625,
0.01412200927734375,
-0.01276397705078125,
-0.00035834312438964844,
-0.0006818771362304688,
0.007602691650390625,
-0.032958984375,
-0.0022754669189453125,
-0.0014324188232421875,
0.03289794921875,
-0.0217132568359375,
0.0316162109375,
-0.033355712890625,
0.03704833984375,
-0.0017528533935546875,
-0.0151214599609375,
0.00997161865234375,
-0.009765625,
-0.0199432373046875,
0.00521087646484375,
-0.02008056640625,
-0.01183319091796875,
0.0233917236328125,
-0.01172637939453125,
0.0006451606750488281,
0.022705078125,
-0.023162841796875,
0.044219970703125,
0.01180267333984375,
0.03076171875,
-0.0396728515625,
0.00646209716796875,
0.005802154541015625,
0.01690673828125,
0.020050048828125,
-0.007648468017578125,
-0.0003180503845214844,
-0.018890380859375,
0.04351806640625,
0.018035888671875,
0.01245880126953125,
0.0268402099609375,
-0.0273284912109375,
0.01336669921875,
0.020111083984375,
-0.04034423828125,
-0.0274810791015625,
-0.021209716796875,
-0.0208740234375,
0.0357666015625,
-0.0024242401123046875,
0.01068878173828125,
0.0259246826171875,
0.024444580078125,
-0.0258941650390625,
0.00853729248046875,
0.007358551025390625,
0.0036602020263671875,
0.0186309814453125,
0.004558563232421875,
-0.00933837890625,
0.0200958251953125,
-0.03387451171875,
-0.02630615234375,
0.0235137939453125,
-0.00785064697265625,
0.01181793212890625,
0.0377197265625,
-0.0250244140625,
0.00791168212890625,
-0.034759521484375,
0.01462554931640625,
-0.007686614990234375,
0.0263671875,
-0.02197265625,
-0.0022411346435546875,
-0.03643798828125,
0.0034275054931640625,
-0.031097412109375,
0.00676727294921875,
-0.0204315185546875,
0.028289794921875,
-0.003993988037109375,
-0.004955291748046875,
-0.0069122314453125,
-0.0005936622619628906,
-0.006481170654296875,
-0.03216552734375,
-0.00803375244140625,
-0.0256500244140625,
-0.004428863525390625,
0.018585205078125,
-0.014862060546875,
0.0216217041015625,
0.0035552978515625,
-0.059051513671875,
0.01074981689453125,
0.0141754150390625,
-0.0038051605224609375,
-0.0084686279296875,
0.0191192626953125,
0.01519012451171875,
0.0450439453125,
0.0193328857421875,
0.004062652587890625,
0.03106689453125,
0.01511383056640625,
-0.01457977294921875,
0.0033969879150390625,
-0.0200347900390625,
0.031707763671875,
-0.006359100341796875,
-0.0279083251953125,
0.016082763671875,
-0.00481414794921875,
-0.045318603515625,
-0.022735595703125,
-0.00807952880859375,
-0.0279083251953125,
0.0139617919921875,
-0.023651123046875,
-0.034576416015625,
0.007701873779296875,
-0.02728271484375,
0.0242462158203125,
-0.03863525390625,
-0.00555419921875,
-0.00537109375,
0.004894256591796875,
0.00804901123046875,
0.01529693603515625,
-0.00724029541015625,
0.0288543701171875,
-0.01183319091796875,
0.00627899169921875,
0.0217742919921875,
0.020904541015625,
0.00936126708984375,
-0.019287109375,
0.0208892822265625,
0.00031828880310058594,
0.01308441162109375,
0.0211944580078125,
0.01502227783203125,
0.00824737548828125,
0.03436279296875,
0.005077362060546875,
-0.0408935546875,
0.0285797119140625,
-0.027435302734375,
0.01995849609375,
-0.045501708984375,
-0.005908966064453125,
-0.0104217529296875,
0.01477813720703125,
-0.0156402587890625,
0.029815673828125,
0.031219482421875,
-0.006740570068359375,
0.007801055908203125,
-0.01413726806640625,
0.032928466796875,
-0.0167694091796875,
-0.027984619140625,
0.0243377685546875,
-0.02130126953125,
0.0211181640625,
0.0478515625,
0.0242462158203125,
-0.0175628662109375,
0.0216064453125,
-0.01454925537109375,
-0.021575927734375,
-0.0231170654296875,
0.0159149169921875,
0.0182952880859375,
0.053680419921875,
-0.019866943359375,
0.018218994140625,
-0.011077880859375,
-0.0277252197265625,
-0.00186920166015625,
0.00122833251953125,
0.0186309814453125,
-0.00046515464782714844,
0.01027679443359375,
-0.0003516674041748047,
0.03045654296875,
-0.010467529296875,
-0.0175323486328125,
0.0210113525390625,
-0.015350341796875,
0.00872039794921875,
0.0017910003662109375,
0.01328277587890625,
-0.0220794677734375,
-0.0305328369140625,
0.007068634033203125,
0.007633209228515625,
-0.01338958740234375,
0.023284912109375,
0.0032291412353515625,
-0.027008056640625,
0.00969696044921875,
-0.017730712890625,
0.0035247802734375,
0.036376953125,
0.0168304443359375,
-0.004535675048828125,
0.04461669921875,
0.0007686614990234375,
0.015869140625,
-0.022430419921875,
0.02508544921875,
0.0203704833984375,
0.026885986328125,
-0.01409149169921875,
0.0284271240234375,
0.00934600830078125,
0.003452301025390625,
-0.005825042724609375,
-0.0008068084716796875,
-0.002532958984375,
0.00957489013671875,
-0.006412506103515625,
0.02862548828125,
0.0147247314453125,
0.0087738037109375,
0.0279541015625,
-0.040863037109375,
0.034210205078125,
0.0233306884765625,
-0.0304107666015625,
-0.0286865234375,
-0.0139617919921875,
0.04168701171875,
0.00991058349609375,
-0.02081298828125,
0.0008320808410644531,
-0.006343841552734375,
0.0265045166015625,
0.02972412109375,
0.0109405517578125,
0.015869140625,
-0.055908203125,
-0.01059722900390625,
-0.0193023681640625,
0.0205841064453125,
0.005889892578125,
-0.00959014892578125,
-0.01197052001953125,
-0.0201263427734375,
-0.029449462890625,
-0.017730712890625,
0.0176239013671875,
0.0050811767578125,
-0.0019207000732421875,
-0.011077880859375,
0.0020923614501953125,
-0.0187835693359375,
-0.0176544189453125,
0.017181396484375,
0.0140838623046875,
-0.0338134765625,
-0.00820159912109375,
0.02484130859375,
0.0267333984375,
-0.039276123046875,
-0.00308990478515625,
-0.0223541259765625,
-0.0150146484375,
0.01153564453125,
-0.028564453125,
-0.00690460205078125,
-0.0189971923828125,
0.0177459716796875,
-0.0105743408203125,
-0.021270751953125,
0.0167694091796875,
0.0289459228515625,
-0.0291900634765625,
0.028411865234375,
-0.00186920166015625,
0.0377197265625,
0.019500732421875,
0.01788330078125,
-0.00199127197265625,
-0.01125335693359375,
0.0196685791015625,
0.03082275390625,
-0.0164337158203125,
0.01236724853515625,
0.0256805419921875,
0.03985595703125,
0.022613525390625,
-0.0037975311279296875,
0.001590728759765625,
0.0209197998046875,
0.0232086181640625,
0.023040771484375,
-0.0386962890625,
0.01617431640625,
0.017608642578125,
0.01165771484375,
0.01177978515625,
-0.024688720703125,
-0.003143310546875,
-0.0014696121215820312,
-0.01161956787109375,
-0.0012159347534179688,
0.01409912109375,
0.0178680419921875,
0.01715087890625,
0.04290771484375,
0.007266998291015625,
-0.00725555419921875,
-0.0166473388671875,
0.0204315185546875,
0.0350341796875,
-0.01280975341796875,
0.0135345458984375,
0.0009813308715820312,
-0.01451873779296875,
0.0283355712890625,
-0.00110626220703125,
-0.0289306640625,
0.00557708740234375,
0.004055023193359375,
0.00826263427734375,
0.019134521484375,
-0.0008788108825683594,
-0.007511138916015625,
-0.024566650390625,
0.04510498046875,
-0.02301025390625,
-0.002254486083984375,
-0.0014581680297851562,
0.020599365234375,
-0.01038360595703125,
0.00830841064453125,
0.057952880859375,
0.0047149658203125,
-0.0207366943359375,
0.00848388671875,
0.0023174285888671875,
0.033843994140625,
-0.01103973388671875,
-0.044525146484375,
0.01534271240234375,
0.012481689453125,
-0.0109405517578125,
-0.012115478515625,
-0.01213836669921875,
0.00943756103515625,
-0.005901336669921875,
0.01416015625,
-0.00852203369140625,
0.0197906494140625,
0.01192474365234375,
-0.018341064453125,
0.01470947265625,
0.0012645721435546875,
0.0016946792602539062,
-0.01389312744140625,
-0.002025604248046875,
-0.0031490325927734375,
0.0261077880859375,
0.032501220703125,
-0.01983642578125,
0.01253509521484375,
-0.01812744140625,
0.0206451416015625,
0.0136260986328125,
0.012847900390625,
0.017486572265625,
0.005458831787109375,
0.02276611328125,
-0.006771087646484375,
-0.0313720703125,
0.0011720657348632812,
0.00423431396484375,
-0.0141448974609375,
-0.0200347900390625,
0.0099334716796875,
-0.01629638671875,
0.002964019775390625,
-0.0081329345703125,
-0.0360107421875,
-0.0010833740234375,
0.035125732421875,
-0.024688720703125,
-0.004360198974609375,
0.0288543701171875,
0.0010576248168945312,
-0.01360321044921875,
-0.0129547119140625,
0.0235595703125,
-0.00495147705078125,
-0.005207061767578125,
-0.0270538330078125,
-0.005443572998046875,
0.019500732421875,
-0.044403076171875,
-0.03057861328125,
-0.03741455078125,
0.003566741943359375,
0.0007023811340332031,
0.0150909423828125,
-0.019622802734375,
-0.01409149169921875,
0.021209716796875,
0.02532958984375,
0.005340576171875,
-0.0033416748046875,
0.01425933837890625,
-0.036834716796875,
-0.0404052734375,
0.026397705078125,
-0.01483154296875,
-0.00896453857421875,
0.00475311279296875,
-0.037689208984375,
-0.007648468017578125,
-0.006969451904296875,
0.0167083740234375,
-0.0187835693359375,
0.006145477294921875,
0.01137542724609375,
-0.006717681884765625,
0.034942626953125,
-0.01378631591796875,
0.0138397216796875,
-0.0147857666015625,
-0.0029087066650390625,
0.0298004150390625,
-0.03802490234375,
-0.0106353759765625,
-0.0020294189453125,
0.01190185546875,
0.00791168212890625,
-0.033111572265625,
0.01910400390625,
-0.0049285888671875,
0.0281219482421875,
0.005474090576171875,
-0.04248046875,
-0.0196533203125,
0.013641357421875,
0.005115509033203125,
0.011627197265625,
-0.010406494140625,
-0.01092529296875,
-0.0010051727294921875,
-0.016082763671875,
0.01387786865234375,
0.01001739501953125,
0.000942230224609375,
-0.014617919921875,
0.00383758544921875,
0.00951385498046875,
-0.0145263671875,
0.027191162109375,
-0.00860595703125,
-0.01029205322265625,
0.008270263671875,
-0.006305694580078125,
0.00640106201171875,
0.0289459228515625,
0.01503753662109375,
-0.040740966796875,
0.0010290145874023438,
-0.0011911392211914062,
-0.00553131103515625
] |
ours_556
|
The answer is \(1006\).
When every permutation with \(n\) subsequences is written backwards, the number of subsequences in the new permutation is \(2012-n\). Thus, every pair averages to our answer, \(1006\).
\(\boxed{1006}\)
|
1006
|
{
"competition": "us_comps",
"dataset": "Ours",
"posts": null,
"source": "OMOSoln2.md"
}
|
Xavier takes a permutation of the numbers \(1\) through \(2011\) at random, where each permutation has an equal probability of being selected. He then cuts the permutation into increasing contiguous subsequences, such that each subsequence is as long as possible. Compute the expected number of such subsequences.
## Clarifications:
- An increasing contiguous subsequence is an increasing subsequence all of whose terms are adjacent in the original sequence. For example, \(1,3,4,5,2\) has two maximal increasing contiguous subsequences: \((1,3,4,5)\) and \((2)\).
|
[
"/Mathematics/DiscreteMathematics/Combinatorics/Enumeration",
"/Mathematics/DiscreteMathematics/Combinatorics/GeneralCombinatorics",
"/Mathematics/DiscreteMathematics/Combinatorics/Permutations",
"/Mathematics/DiscreteMathematics/GeneralDiscreteMathematics/DiscreteMath",
"/Mathematics/DiscreteMathematics/GeneralDiscreteMathematics/DiscreteMathematics",
"/Mathematics/ProbabilityandStatistics/Probability/ProbabilityAxioms",
"/Mathematics/ProbabilityandStatistics/Probability/ProbabilityMeasure",
"/Mathematics/ProbabilityandStatistics/Probability/ProbabilitySpace",
"/Mathematics/ProbabilityandStatistics/Probability/SampleSpace",
"/Mathematics/ProbabilityandStatistics/Runs/Run"
] |
Pair each permutation with its reverse, noting that the number of runs adds up to 2012, so the average is half of that.
|
[
-0.000004231929779052734,
-0.005817413330078125,
0.0298919677734375,
0.0300445556640625,
-0.00008559226989746094,
0.0207061767578125,
0.0126953125,
0.010406494140625,
-0.004558563232421875,
-0.0133209228515625,
0.03900146484375,
-0.042755126953125,
-0.004390716552734375,
-0.04638671875,
-0.010467529296875,
-0.047393798828125,
0.037322998046875,
0.025543212890625,
-0.016693115234375,
-0.002246856689453125,
0.0016641616821289062,
-0.03204345703125,
-0.029937744140625,
0.040863037109375,
-0.04388427734375,
-0.046539306640625,
-0.002956390380859375,
0.01031494140625,
0.0089569091796875,
-0.002971649169921875,
-0.033111572265625,
-0.00922393798828125,
0.040496826171875,
-0.01454925537109375,
-0.002681732177734375,
0.0125885009765625,
-0.00614166259765625,
-0.00250244140625,
-0.005092620849609375,
0.00910186767578125,
-0.0309295654296875,
0.0164947509765625,
0.01381683349609375,
0.01285552978515625,
-0.0005068778991699219,
0.01428985595703125,
0.00628662109375,
0.0105743408203125,
-0.009033203125,
0.020233154296875,
0.0018358230590820312,
0.0011110305786132812,
-0.00016999244689941406,
-0.01430511474609375,
-0.0263519287109375,
-0.06768798828125,
-0.0279693603515625,
-0.001102447509765625,
-0.0264434814453125,
-0.042724609375,
-0.0026378631591796875,
-0.0005192756652832031,
0.0091552734375,
0.0190582275390625,
0.0017728805541992188,
-0.0080413818359375,
-0.01267242431640625,
0.045928955078125,
0.007965087890625,
-0.01172637939453125,
-0.0027980804443359375,
-0.0234375,
-0.0267181396484375,
0.01291656494140625,
0.011474609375,
-0.004810333251953125,
-0.004718780517578125,
-0.004947662353515625,
0.030670166015625,
-0.006313323974609375,
-0.00988006591796875,
0.0041046142578125,
0.00494384765625,
0.009857177734375,
-0.00847625732421875,
0.04840087890625,
-0.007488250732421875,
-0.017486572265625,
0.03485107421875,
-0.01198577880859375,
0.01148223876953125,
0.00015163421630859375,
0.0182647705078125,
-0.0017232894897460938,
-0.0233306884765625,
0.003963470458984375,
0.02593994140625,
-0.0086822509765625,
-0.0168304443359375,
0.006374359130859375,
-0.01235198974609375,
0.00107574462890625,
0.0271759033203125,
0.005229949951171875,
-0.037841796875,
-0.0008788108825683594,
-0.0179290771484375,
-0.00949859619140625,
-0.0088043212890625,
0.0024318695068359375,
0.00244140625,
-0.003082275390625,
0.038299560546875,
0.019287109375,
0.00812530517578125,
0.01117706298828125,
0.0184478759765625,
-0.0169677734375,
0.01386260986328125,
0.0136260986328125,
0.003772735595703125,
0.0266265869140625,
0.00620269775390625,
0.01393890380859375,
0.00732421875,
-0.000579833984375,
-0.01401519775390625,
0.0200958251953125,
0.035919189453125,
-0.008758544921875,
-0.0261383056640625,
0.001094818115234375,
-0.07489013671875,
-0.004913330078125,
-0.050323486328125,
-0.0017261505126953125,
0.01824951171875,
-0.01910400390625,
0.0170745849609375,
-0.020050048828125,
0.01534271240234375,
-0.0006227493286132812,
0.00998687744140625,
0.01605224609375,
0.00757598876953125,
-0.00180816650390625,
0.01490020751953125,
-0.0509033203125,
0.0038471221923828125,
-0.0043792724609375,
0.0082550048828125,
0.00772857666015625,
-0.007965087890625,
-0.0196533203125,
0.02081298828125,
0.00865936279296875,
0.01454925537109375,
0.00959014892578125,
-0.0016069412231445312,
-0.01222991943359375,
-0.032928466796875,
-0.01074981689453125,
-0.0202484130859375,
0.006526947021484375,
-0.0169219970703125,
0.0067291259765625,
-0.0111083984375,
-0.0029735565185546875,
0.00521087646484375,
0.004772186279296875,
-0.007747650146484375,
0.0192413330078125,
0.0171356201171875,
-0.00902557373046875,
-0.0135345458984375,
0.01111602783203125,
-0.0155487060546875,
-0.0001271963119506836,
-0.00214385986328125,
-0.0017986297607421875,
-0.0116729736328125,
-0.002197265625,
-0.0030040740966796875,
-0.0019388198852539062,
0.03887939453125,
0.01300811767578125,
-0.0007658004760742188,
-0.01137542724609375,
0.0270233154296875,
0.006244659423828125,
0.007419586181640625,
0.0372314453125,
0.00749969482421875,
-0.015167236328125,
-0.006015777587890625,
-0.005542755126953125,
-0.020294189453125,
0.038665771484375,
0.01776123046875,
0.01971435546875,
0.01523590087890625,
0.0019016265869140625,
-0.016998291015625,
0.0106964111328125,
0.0076751708984375,
0.00135040283203125,
0.004810333251953125,
0.000331878662109375,
-0.00714874267578125,
-0.004268646240234375,
0.006259918212890625,
-0.0048370361328125,
-0.004528045654296875,
-0.01505279541015625,
-0.003170013427734375,
0.005001068115234375,
-0.00617218017578125,
0.0016946792602539062,
-0.0037021636962890625,
-0.030303955078125,
-0.0002925395965576172,
0.0088043212890625,
-0.01557159423828125,
-0.01541900634765625,
-0.0164031982421875,
0.0026607513427734375,
-0.005260467529296875,
0.0047760009765625,
-0.0016002655029296875,
0.007717132568359375,
-0.01236724853515625,
0.00954437255859375,
-0.0146636962890625,
-0.0128631591796875,
-0.0059814453125,
0.016143798828125,
0.0005135536193847656,
0.0088653564453125,
-0.0258636474609375,
0.01160430908203125,
0.01345062255859375,
-0.00910186767578125,
0.009185791015625,
-0.00519561767578125,
0.00788116455078125,
-0.01007080078125,
0.0090789794921875,
-0.00656890869140625,
0.0103302001953125,
-0.005168914794921875,
-0.0272979736328125,
-0.0196533203125,
-0.028472900390625,
0.0230560302734375,
0.029754638671875,
0.0167083740234375,
0.0172119140625,
-0.049163818359375,
-0.012054443359375,
-0.021209716796875,
-0.01480865478515625,
-0.01141357421875,
-0.004268646240234375,
0.007122039794921875,
-0.0083465576171875,
-0.010589599609375,
-0.0235748291015625,
-0.007167816162109375,
0.0049285888671875,
0.00788116455078125,
0.01540374755859375,
-0.0230560302734375,
-0.01171875,
0.0026607513427734375,
0.0104827880859375,
-0.01444244384765625,
-0.0062408447265625,
0.01499176025390625,
-0.0241241455078125,
0.00951385498046875,
0.01137542724609375,
-0.024078369140625,
0.02081298828125,
0.01454925537109375,
0.032501220703125,
-0.01531982421875,
-0.0147857666015625,
-0.0262908935546875,
-0.0056304931640625,
-0.0127105712890625,
-0.0028839111328125,
0.005950927734375,
-0.02630615234375,
0.0028133392333984375,
0.00482177734375,
-0.0489501953125,
0.017181396484375,
0.0026302337646484375,
0.017608642578125,
-0.0009555816650390625,
0.002727508544921875,
-0.0062103271484375,
0.0028705596923828125,
0.02197265625,
0.0176239013671875,
0.01477813720703125,
0.00389862060546875,
-0.006343841552734375,
-0.0237884521484375,
-0.0125885009765625,
-0.00014030933380126953,
-0.0009036064147949219,
0.0196533203125,
-0.00431060791015625,
0.0194854736328125,
-0.0447998046875,
-0.0023975372314453125,
0.005306243896484375,
-0.0023651123046875,
-0.01358795166015625,
0.0142364501953125,
-0.0011930465698242188,
-0.0215606689453125,
0.018463134765625,
-0.0018625259399414062,
-0.00018918514251708984,
0.01000213623046875,
0.0267181396484375,
-0.023345947265625,
0.0307159423828125,
-0.00995635986328125,
0.0289306640625,
-0.0087738037109375,
0.006916046142578125,
-0.00566864013671875,
0.0117950439453125,
-0.00977325439453125,
0.01319122314453125,
0.01407623291015625,
-0.004138946533203125,
-0.0255889892578125,
0.0025310516357421875,
-0.0037994384765625,
-0.0012407302856445312,
0.0135650634765625,
-0.0001875162124633789,
0.01169586181640625,
-0.0297393798828125,
-0.053741455078125,
0.0274810791015625,
-0.0270538330078125,
0.00439453125,
0.00879669189453125,
0.0091705322265625,
-0.027099609375,
0.0186004638671875,
-0.0274810791015625,
0.00406646728515625,
0.023681640625,
0.034698486328125,
0.01441192626953125,
-0.0236053466796875,
-0.0031032562255859375,
0.001613616943359375,
0.0110931396484375,
-0.00965118408203125,
-0.00827789306640625,
-0.00589752197265625,
-0.0181884765625,
0.01137542724609375,
-0.0029850006103515625,
-0.0222015380859375,
0.0080108642578125,
-0.043243408203125,
-0.0220794677734375,
0.0145416259765625,
-0.004360198974609375,
0.005687713623046875,
-0.014007568359375,
-0.002902984619140625,
0.0045166015625,
0.03192138671875,
0.0107879638671875,
0.02215576171875,
-0.03289794921875,
-0.005157470703125,
-0.01116180419921875,
0.006786346435546875,
-0.00507354736328125,
0.004398345947265625,
-0.0082244873046875,
-0.03253173828125,
-0.007274627685546875,
0.0052032470703125,
-0.01314544677734375,
0.0182037353515625,
-0.0009870529174804688,
0.0055694580078125,
0.0167388916015625,
-0.0238494873046875,
0.00970458984375,
-0.0048065185546875,
-0.005901336669921875,
0.059814453125,
0.0243377685546875,
0.002521514892578125,
-0.0161285400390625,
0.00455474853515625,
-0.0004172325134277344,
-0.00725555419921875,
-0.0051422119140625,
0.006160736083984375,
0.02740478515625,
0.01522064208984375,
-0.006160736083984375,
-0.00867462158203125,
0.00391387939453125,
0.040740966796875,
-0.031890869140625,
-0.0008368492126464844,
-0.00885772705078125,
-0.023162841796875,
-0.01058197021484375,
-0.0296783447265625,
0.04144287109375,
0.00848388671875,
0.023406982421875,
0.01335906982421875,
-0.01476287841796875,
0.029632568359375,
0.0186767578125,
-0.0046234130859375,
0.0011377334594726562,
0.010162353515625,
-0.0011081695556640625,
0.0068206787109375,
0.0140228271484375,
-0.0068206787109375,
-0.01806640625,
-0.014434814453125,
-0.01125335693359375,
0.0017690658569335938,
-0.01611328125,
-0.0224151611328125,
-0.0570068359375,
0.016387939453125,
0.01450347900390625,
0.022064208984375,
-0.0153961181640625,
0.03125,
-0.0207366943359375,
-0.0147552490234375,
-0.00757598876953125,
-0.01416778564453125,
-0.01360321044921875,
0.032318115234375,
0.01070404052734375,
-0.0648193359375,
0.021240234375,
-0.0189971923828125,
0.024627685546875,
-0.0214996337890625,
0.00048089027404785156,
-0.0278472900390625,
0.0018396377563476562,
-0.0075225830078125,
-0.0250701904296875,
0.0122528076171875,
0.020843505859375,
-0.0209808349609375,
-0.00041174888610839844,
-0.0178985595703125,
0.0261077880859375,
-0.007640838623046875,
-0.0262908935546875,
0.0210723876953125,
0.01540374755859375,
0.035675048828125,
-0.0178680419921875,
-0.0276336669921875,
-0.01264190673828125,
-0.010009765625,
0.0313720703125,
0.0572509765625,
0.0004296302795410156,
0.032501220703125,
0.03314208984375,
0.0008320808410644531,
-0.012725830078125,
-0.0162506103515625,
0.00908660888671875,
0.02301025390625,
-0.0042572021484375,
-0.00341033935546875,
-0.025360107421875,
-0.027557373046875,
-0.005260467529296875,
-0.006534576416015625,
-0.015106201171875,
0.01190185546875,
-0.0160369873046875,
0.008026123046875,
-0.020355224609375,
0.0219573974609375,
-0.020172119140625,
0.0137176513671875,
0.036041259765625,
0.016448974609375,
-0.0016813278198242188,
0.01446533203125,
-0.0098114013671875,
-0.003955841064453125,
0.0263824462890625,
-0.0382080078125,
0.006664276123046875,
-0.01200103759765625,
0.019775390625,
-0.005931854248046875,
-0.0246429443359375,
0.00879669189453125,
-0.0035076141357421875,
0.025177001953125,
0.0083160400390625,
-0.0257415771484375,
-0.0391845703125,
-0.021484375,
0.036407470703125,
-0.0031795501708984375,
-0.0177154541015625,
0.01204681396484375,
-0.020599365234375,
-0.0269012451171875,
0.007720947265625,
-0.01959228515625,
0.01352691650390625,
0.0151824951171875,
0.0204315185546875,
-0.00897979736328125,
-0.01171875,
0.00033593177795410156,
-0.0177001953125,
-0.0008907318115234375,
-0.01534271240234375,
0.00858306884765625,
-0.01453399658203125,
-0.025909423828125,
0.01525115966796875,
0.013671875,
-0.0018262863159179688,
-0.047821044921875,
0.0012121200561523438,
0.004734039306640625,
0.0238037109375,
-0.0029888153076171875,
-0.006511688232421875,
0.016082763671875,
-0.001201629638671875,
0.0157012939453125,
0.007373809814453125,
0.003566741943359375,
-0.025115966796875,
0.0362548828125,
-0.024688720703125,
0.01013946533203125,
-0.0164337158203125,
0.0160064697265625,
-0.0019664764404296875,
0.011138916015625,
0.00441741943359375,
-0.048553466796875,
0.00998687744140625,
-0.018096923828125,
-0.0087127685546875,
0.0214691162109375,
-0.01094818115234375,
-0.015716552734375,
0.0004916191101074219,
0.00003993511199951172,
-0.0208740234375,
-0.038909912109375,
-0.0009398460388183594,
0.043212890625,
-0.0131072998046875,
-0.01251983642578125,
0.02655029296875,
0.01331329345703125,
0.008544921875,
0.00775146484375,
0.0084991455078125,
0.0255279541015625,
-0.0134124755859375,
0.01873779296875,
-0.0124359130859375,
-0.00536346435546875,
0.003696441650390625,
-0.0264739990234375,
-0.0191802978515625,
-0.022064208984375,
0.0122222900390625,
-0.01557159423828125,
-0.0204620361328125,
-0.0114288330078125,
-0.033538818359375,
0.01025390625,
-0.0018758773803710938,
-0.00555419921875,
-0.00667572021484375,
0.01971435546875,
-0.02337646484375,
-0.01424407958984375,
0.0228424072265625,
0.0213470458984375,
-0.0027446746826171875,
0.01019287109375,
0.0380859375,
-0.0216522216796875,
-0.042510986328125,
-0.03076171875,
-0.0177764892578125,
-0.0106201171875,
-0.043060302734375,
0.005359649658203125,
0.0111541748046875,
0.0152740478515625,
-0.0092315673828125,
0.0305023193359375,
-0.027069091796875,
0.01148223876953125,
-0.0018901824951171875,
-0.0027217864990234375,
-0.004032135009765625,
-0.05169677734375,
0.008758544921875,
0.00731658935546875,
-0.01486968994140625,
-0.030426025390625,
-0.0221099853515625,
0.00911712646484375,
-0.006374359130859375,
-0.0024738311767578125,
0.007457733154296875,
0.02032470703125,
-0.00852203369140625,
-0.0526123046875,
-0.00994110107421875,
0.0175018310546875,
0.01380157470703125,
-0.004978179931640625,
0.0070953369140625,
0.0095367431640625,
-0.0136566162109375,
-0.025054931640625,
-0.0152587890625,
0.02911376953125,
-0.007381439208984375,
-0.01129913330078125,
-0.006145477294921875,
-0.01059722900390625,
0.040771484375,
-0.0041961669921875,
0.0094757080078125,
0.02337646484375,
0.02581787109375,
0.0110015869140625,
0.006977081298828125,
0.0187530517578125,
0.000400543212890625,
-0.01995849609375,
0.0125579833984375,
-0.00923919677734375,
-0.0196533203125,
0.01519775390625,
-0.0028781890869140625,
-0.0169677734375,
0.0268402099609375,
-0.013031005859375,
0.0057220458984375,
-0.0034618377685546875,
0.03131103515625,
0.049560546875,
0.020050048828125,
0.02789306640625,
0.030029296875,
-0.00563812255859375,
0.044952392578125,
-0.0303192138671875,
0.01447296142578125,
-0.00228118896484375,
-0.0188446044921875,
-0.0016717910766601562,
-0.01274871826171875,
-0.004589080810546875,
-0.0169830322265625,
0.00927734375,
0.0035247802734375,
-0.0146026611328125,
0.006534576416015625,
0.0167388916015625,
-0.006107330322265625,
0.01421356201171875,
-0.007198333740234375,
-0.0281829833984375,
0.021636962890625,
-0.0101165771484375,
0.053314208984375,
-0.034210205078125,
-0.021484375,
-0.002216339111328125,
-0.035308837890625,
-0.01105499267578125,
-0.0129852294921875,
0.01142120361328125,
-0.01503753662109375,
0.0264892578125,
-0.024932861328125,
0.022247314453125,
0.04010009765625,
-0.005550384521484375,
-0.0236053466796875,
0.01187896728515625,
-0.04193115234375,
-0.0005755424499511719,
-0.0261383056640625,
-0.034027099609375,
0.033599853515625,
-0.0208892822265625,
-0.0124969482421875,
-0.0127105712890625,
-0.0679931640625,
-0.0296783447265625,
0.00800323486328125,
-0.03216552734375,
0.00235748291015625,
-0.01448822021484375,
-0.00801849365234375,
0.0096588134765625,
-0.00827789306640625,
0.00890350341796875,
0.0302886962890625,
-0.01282501220703125,
0.013916015625,
-0.0200347900390625,
0.02557373046875,
-0.00641632080078125,
0.0213623046875,
-0.0075531005859375,
0.0119171142578125,
-0.0004246234893798828,
-0.007518768310546875,
-0.01148223876953125,
0.0088348388671875,
0.00154876708984375,
0.00745391845703125,
-0.022735595703125,
0.004451751708984375,
0.009674072265625,
0.0087890625,
0.01407623291015625,
-0.0494384765625,
0.015380859375,
-0.0291748046875,
0.01473236083984375,
-0.01360321044921875,
0.0082855224609375,
-0.013397216796875,
-0.008087158203125,
0.0051422119140625,
-0.004302978515625,
0.01549530029296875,
0.006053924560546875,
0.01383209228515625,
0.01360321044921875,
0.0198974609375,
-0.0171966552734375,
0.0109710693359375,
-0.00450897216796875,
-0.0215606689453125,
-0.0242919921875,
-0.039306640625,
-0.034820556640625,
-0.0283660888671875,
-0.019134521484375,
-0.0244903564453125,
0.01386260986328125,
-0.0009617805480957031,
0.00928497314453125,
-0.01154327392578125,
-0.03302001953125,
0.00940704345703125,
0.0220794677734375,
0.015777587890625,
0.007740020751953125,
-0.0162506103515625,
-0.00501251220703125,
0.008087158203125,
-0.007633209228515625,
0.00013709068298339844,
-0.0015478134155273438,
0.01047515869140625,
0.00005644559860229492,
0.048065185546875,
-0.01556396484375,
-0.02203369140625,
0.01531982421875,
0.0181427001953125,
0.01479339599609375,
0.045684814453125,
-0.0201263427734375,
-0.0283355712890625,
-0.00724029541015625,
0.01285552978515625,
-0.009124755859375,
0.037445068359375,
-0.003093719482421875,
-0.01154327392578125,
-0.0180206298828125,
0.024383544921875,
-0.036529541015625,
0.0304718017578125,
-0.01390838623046875,
-0.017608642578125,
0.0121307373046875,
-0.00782012939453125,
0.01456451416015625,
-0.0125579833984375,
0.00611114501953125,
0.01318359375,
0.0035800933837890625,
0.01507568359375,
-0.0020694732666015625,
-0.010528564453125,
0.00437164306640625,
0.026397705078125,
0.003326416015625,
0.00215911865234375,
0.005138397216796875,
-0.02386474609375,
0.04119873046875,
-0.00965118408203125,
-0.0166778564453125,
0.016693115234375,
0.025421142578125,
0.0012598037719726562,
0.00948333740234375,
-0.0001308917999267578,
-0.028350830078125,
-0.0004153251647949219,
0.007415771484375,
0.0160064697265625,
-0.0006122589111328125,
0.0142822265625,
0.0075225830078125,
-0.0003504753112792969,
0.0005106925964355469,
0.0185394287109375,
0.0186920166015625,
0.032196044921875,
0.00354766845703125,
-0.014801025390625,
-0.0225830078125,
-0.01305389404296875,
-0.03778076171875,
0.0175323486328125,
0.002391815185546875,
0.01300811767578125,
-0.03399658203125,
-0.0159454345703125,
0.0030422210693359375,
0.0243682861328125,
-0.030181884765625,
-0.01445770263671875,
-0.0345458984375,
0.030853271484375,
0.0016546249389648438,
-0.03216552734375,
-0.01537322998046875,
0.0220947265625,
0.032135009765625,
0.007843017578125,
-0.00778961181640625,
0.027252197265625,
-0.0203857421875,
0.0024089813232421875,
-0.00004851818084716797,
-0.0009622573852539062,
-0.0447998046875,
0.01546478271484375,
0.01528167724609375,
0.0135345458984375,
-0.018402099609375,
0.018463134765625,
-0.01568603515625,
0.0014963150024414062,
-0.0010805130004882812,
0.027191162109375,
-0.00034689903259277344,
0.0186309814453125,
0.0253753662109375,
0.015289306640625,
-0.043548583984375,
0.01824951171875,
-0.0223846435546875,
0.02020263671875,
-0.014892578125,
0.00943756103515625,
-0.01085662841796875,
0.01233673095703125,
-0.0145111083984375,
0.0155029296875,
0.017730712890625,
-0.003326416015625,
0.0379638671875,
0.017791748046875,
0.037384033203125,
-0.03717041015625,
0.0010709762573242188,
-0.01250457763671875,
0.034271240234375,
0.02398681640625,
0.06256103515625,
0.025604248046875,
0.010711669921875,
-0.0127105712890625,
-0.00458526611328125,
-0.0006346702575683594,
-0.008087158203125,
-0.0025043487548828125,
0.006908416748046875,
-0.04302978515625,
-0.00644683837890625,
-0.0169677734375,
0.0211639404296875,
-0.0190277099609375,
0.01910400390625,
0.002166748046875,
0.0112762451171875,
-0.0013408660888671875,
-0.01104736328125,
0.0169677734375,
-0.0078125,
0.0284423828125,
0.028045654296875,
-0.0251312255859375,
-0.02691650390625,
0.0008654594421386719,
-0.0085296630859375,
0.00018906593322753906,
-0.0076446533203125,
-0.05450439453125,
0.0121612548828125,
-0.0038318634033203125,
0.004619598388671875,
-0.0206756591796875,
0.0107421875,
0.01319122314453125,
0.017822265625,
-0.022613525390625,
0.01247406005859375,
-0.0030269622802734375,
-0.033905029296875,
0.0092010498046875,
-0.0221405029296875,
-0.053558349609375,
-0.0184173583984375,
0.041778564453125,
0.046295166015625,
-0.0035533905029296875,
-0.0013208389282226562,
0.00292205810546875,
0.04095458984375,
-0.032928466796875,
-0.0028591156005859375,
0.021514892578125,
-0.00783538818359375,
-0.0189971923828125,
-0.0232086181640625,
-0.016204833984375,
-0.01934814453125,
0.0007963180541992188,
-0.0198516845703125,
-0.0273284912109375,
-0.021209716796875,
0.0077362060546875,
0.0076141357421875,
0.0004336833953857422,
-0.0028705596923828125,
-0.0037403106689453125,
-0.0216217041015625,
-0.00514984130859375,
-0.01509857177734375,
0.00682830810546875,
-0.0185699462890625,
-0.0215606689453125,
0.0215911865234375,
0.0053863525390625,
-0.0219879150390625,
-0.0016384124755859375,
0.0014982223510742188,
0.0155487060546875,
-0.0094757080078125,
0.00891876220703125,
0.0312347412109375,
0.0031414031982421875,
-0.0170745849609375,
0.0325927734375,
-0.01535797119140625,
0.031219482421875,
0.005222320556640625,
0.024383544921875,
0.0161285400390625,
0.0088348388671875,
0.03509521484375,
0.0014295578002929688,
-0.01328277587890625,
-0.03607177734375,
-0.0091552734375,
0.008575439453125,
0.00595855712890625,
-0.041107177734375,
-0.0010747909545898438,
-0.0103759765625,
0.00637054443359375,
-0.0125885009765625,
-0.016265869140625,
-0.0164031982421875,
0.00954437255859375,
0.0018100738525390625,
0.0235443115234375,
-0.0008568763732910156,
0.01372528076171875,
0.0174713134765625,
-0.022247314453125,
0.005207061767578125,
-0.0015468597412109375,
0.00507354736328125,
-0.0007781982421875,
-0.00583648681640625,
-0.0019445419311523438,
-0.005626678466796875,
-0.00836944580078125,
-0.0180206298828125,
-0.0037384033203125,
0.0033740997314453125,
-0.0046844482421875,
-0.005626678466796875,
-0.0170745849609375,
0.005733489990234375,
-0.01187896728515625,
-0.0038318634033203125,
-0.009368896484375,
-0.0140838623046875,
0.01018524169921875,
-0.03106689453125,
-0.0170440673828125,
0.006900787353515625,
0.0100860595703125,
0.01045989990234375,
0.01708984375,
-0.00627899169921875,
0.0298614501953125,
-0.010528564453125,
-0.02069091796875,
0.0167083740234375,
-0.048492431640625,
0.021697998046875,
-0.003139495849609375,
-0.034088134765625,
-0.01009368896484375,
0.0615234375,
0.0242767333984375,
-0.0179901123046875,
-0.00027298927307128906,
0.005023956298828125,
-0.03350830078125,
0.032012939453125,
-0.01233673095703125,
0.0169830322265625,
0.01500701904296875,
-0.005706787109375,
0.0300140380859375,
-0.00765228271484375,
-0.024322509765625,
-0.052490234375,
0.0088348388671875,
0.0206146240234375,
-0.01303863525390625,
-0.0278472900390625,
0.01239013671875,
-0.019073486328125,
-0.007320404052734375,
-0.006793975830078125,
0.01224517822265625,
0.035247802734375,
0.01316070556640625,
-0.004657745361328125,
0.0064849853515625,
-0.0184326171875,
0.01513671875,
0.016510009765625,
-0.00852203369140625,
0.0219573974609375,
0.00836181640625,
0.01506805419921875,
-0.0027713775634765625,
-0.001697540283203125,
-0.0179290771484375,
-0.011383056640625,
0.0316162109375,
0.0009751319885253906,
-0.0089263916015625,
-0.017242431640625,
0.0229644775390625,
0.01343536376953125,
-0.0114898681640625,
-0.02459716796875,
0.0042724609375,
-0.024261474609375,
-0.006580352783203125,
-0.0238189697265625,
-0.0150909423828125,
0.00589752197265625,
0.042205810546875,
0.0347900390625,
-0.0107574462890625,
-0.00881195068359375,
-0.00222015380859375,
-0.0269317626953125,
-0.0168304443359375,
-0.0028820037841796875,
0.02447509765625,
-0.013885498046875,
0.0252838134765625,
-0.0073699951171875,
0.01593017578125,
-0.0262451171875,
0.00887298583984375,
0.0062255859375,
0.03912353515625,
0.024627685546875,
-0.004116058349609375,
-0.0058746337890625,
0.0037059783935546875,
-0.051116943359375,
-0.021331787109375,
-0.0107269287109375,
0.0006313323974609375,
-0.0115966796875,
-0.0003719329833984375,
0.044891357421875,
-0.00557708740234375,
-0.031402587890625,
0.015411376953125,
-0.0158233642578125,
-0.0194244384765625,
-0.006229400634765625,
0.03326416015625,
-0.0150299072265625,
-0.0127410888671875,
0.025787353515625,
0.0208892822265625,
0.0217132568359375,
0.0074615478515625,
0.0227813720703125,
0.00917816162109375,
-0.00949859619140625,
0.0021953582763671875,
0.001922607421875,
0.0114288330078125,
-0.040863037109375,
0.038421630859375,
-0.0107574462890625,
-0.01195526123046875,
-0.01824951171875,
0.0233001708984375,
0.0115203857421875,
-0.004596710205078125,
0.0208282470703125,
0.0178375244140625,
-0.0274658203125,
0.02606201171875,
-0.0175628662109375,
0.055572509765625,
-0.0168609619140625,
0.0183563232421875,
-0.0019311904907226562,
-0.0245513916015625,
0.0209808349609375,
-0.0161895751953125,
-0.01535797119140625,
0.0102996826171875,
0.00748443603515625,
-0.01953125,
0.0033969879150390625,
0.010986328125,
-0.006439208984375,
-0.004802703857421875,
-0.0236358642578125,
-0.0242156982421875,
0.01001739501953125,
0.0234832763671875,
0.007171630859375,
-0.016510009765625,
-0.003704071044921875,
0.0192108154296875,
0.0003197193145751953,
-0.0107879638671875,
-0.00144195556640625,
0.037506103515625,
-0.0024776458740234375,
0.004058837890625,
-0.0221710205078125,
-0.00811004638671875,
0.029510498046875,
0.002750396728515625,
-0.0167999267578125,
0.01824951171875,
-0.00937652587890625,
0.0081329345703125,
-0.01053619384765625,
-0.0170745849609375,
0.0290679931640625,
-0.01247406005859375,
-0.0194854736328125,
0.025665283203125,
-0.001171112060546875,
-0.0147857666015625,
-0.030303955078125,
0.01154327392578125,
0.00687408447265625,
0.03558349609375,
0.0152130126953125,
-0.00228118896484375,
0.0302734375,
0.03204345703125,
-0.0230865478515625,
0.005054473876953125,
0.04083251953125,
0.03759765625,
-0.001743316650390625,
0.010009765625,
-0.024017333984375,
0.02532958984375,
-0.0013628005981445312,
-0.003055572509765625,
0.03558349609375,
-0.00461578369140625,
-0.0384521484375,
0.0226593017578125,
-0.0117034912109375,
0.0172271728515625,
-0.0236358642578125,
-0.0014104843139648438,
-0.020416259765625,
-0.013519287109375,
-0.0118560791015625,
-0.016571044921875,
0.0300750732421875,
0.0116729736328125,
-0.0159454345703125,
-0.01461029052734375,
-0.0181732177734375,
-0.0026302337646484375,
0.0003848075866699219,
0.0014467239379882812,
0.0147857666015625,
0.0129852294921875,
-0.0197296142578125,
0.0260162353515625,
0.01369476318359375,
0.00965118408203125,
0.030548095703125,
0.00707244873046875,
0.0004227161407470703,
-0.0127410888671875,
0.01085662841796875,
-0.011199951171875,
0.00154876708984375,
-0.031646728515625,
-0.0258941650390625,
-0.0037708282470703125,
-0.0474853515625,
0.0261077880859375,
0.014556884765625,
-0.0292205810546875,
-0.0190887451171875,
0.01297760009765625,
-0.030242919921875,
0.004848480224609375,
0.00609588623046875,
-0.0026340484619140625,
0.0115966796875,
0.0006194114685058594,
-0.0005140304565429688,
0.01380157470703125,
-0.0110015869140625,
0.008514404296875,
0.006267547607421875,
-0.0006284713745117188,
0.0150146484375,
-0.00531768798828125,
-0.0157012939453125,
-0.0213470458984375,
0.0077362060546875,
0.007633209228515625,
-0.002124786376953125,
-0.0057830810546875,
0.032562255859375,
-0.0004811286926269531,
-0.0205841064453125,
-0.0174102783203125,
-0.027679443359375,
0.0247955322265625,
0.0144500732421875,
-0.0153961181640625,
0.000682830810546875,
-0.034942626953125,
-0.00803375244140625,
-0.034088134765625,
-0.005062103271484375,
0.0225830078125,
-0.0169830322265625,
-0.0008463859558105469,
-0.027191162109375,
0.01629638671875,
0.012054443359375,
0.0106964111328125,
0.0006489753723144531,
0.01467132568359375,
-0.00940704345703125,
-0.0309295654296875,
0.00873565673828125,
0.0206298828125,
0.00027060508728027344,
-0.005401611328125,
0.006237030029296875,
0.0260009765625,
0.002452850341796875,
0.00891876220703125,
-0.0036602020263671875,
-0.0234222412109375,
-0.01319122314453125,
0.0255279541015625,
-0.03082275390625,
0.0043487548828125,
0.01204681396484375,
0.01116180419921875,
-0.060211181640625,
0.039031982421875,
0.04266357421875,
-0.03668212890625,
0.01763916015625,
0.02685546875,
0.0140228271484375,
0.04486083984375,
-0.00453948974609375,
-0.0193939208984375,
-0.02044677734375,
-0.0010957717895507812,
0.0121917724609375,
0.0138397216796875,
0.050048828125,
-0.00888824462890625,
-0.01641845703125,
-0.018310546875,
0.0177001953125,
0.0031528472900390625,
-0.00440216064453125,
-0.007659912109375,
-0.0170135498046875,
-0.0176544189453125,
-0.0181884765625,
-0.011383056640625,
0.0015926361083984375,
0.0126190185546875,
-0.01271820068359375,
-0.03082275390625,
-0.00626373291015625,
0.001094818115234375,
-0.029510498046875,
0.0097503662109375,
-0.0372314453125,
0.028472900390625,
-0.00757598876953125,
-0.0261077880859375,
-0.004375457763671875,
0.0538330078125,
0.00653076171875,
0.014007568359375,
0.00024020671844482422,
0.025604248046875,
0.0035190582275390625,
-0.00034165382385253906,
-0.0194091796875,
-0.00981903076171875,
-0.0200958251953125,
-0.01763916015625,
-0.0003249645233154297,
-0.0054168701171875,
-0.0015649795532226562,
0.00806427001953125,
0.018280029296875,
-0.0113983154296875,
-0.00740814208984375,
-0.01357269287109375,
0.008453369140625,
-0.03179931640625,
-0.0016326904296875,
0.01044464111328125,
0.02117919921875,
-0.0105743408203125,
0.01053619384765625,
-0.00675201416015625,
-0.02313232421875,
-0.039764404296875,
0.01093292236328125,
-0.033050537109375,
0.00041103363037109375,
-0.0180206298828125,
-0.021820068359375,
0.04156494140625,
-0.00861358642578125,
-0.010955810546875,
-0.01166534423828125,
0.0179901123046875,
0.03546142578125,
-0.0115203857421875,
0.01436614990234375,
-0.01157379150390625,
-0.0212860107421875,
-0.0019197463989257812,
-0.026580810546875,
-0.005832672119140625,
0.01385498046875,
-0.0252685546875,
0.0243682861328125,
-0.0089111328125,
-0.0265655517578125,
0.004917144775390625,
0.01322174072265625,
0.00795745849609375,
-0.01552581787109375,
0.009307861328125,
0.013671875,
0.0173797607421875,
-0.01169586181640625,
-0.01103973388671875,
-0.0083160400390625,
-0.031402587890625,
-0.0355224609375,
0.00543975830078125,
-0.016693115234375,
0.00531005859375,
0.0242462158203125,
-0.000797271728515625,
0.00875091552734375,
-0.00047898292541503906,
0.00006151199340820312,
-0.0025577545166015625,
-0.0011081695556640625,
-0.0013332366943359375,
-0.0106658935546875,
-0.020843505859375,
-0.004329681396484375,
0.022247314453125,
-0.0033283233642578125,
0.0007181167602539062,
-0.0127105712890625,
0.0180206298828125,
-0.005706787109375,
-0.0228424072265625,
-0.0237579345703125,
0.0234527587890625,
0.0033092498779296875,
-0.00955963134765625,
-0.037445068359375,
0.007480621337890625,
-0.00839996337890625,
-0.0107574462890625,
0.037353515625,
-0.0587158203125,
-0.019805908203125,
-0.0220489501953125,
0.0099334716796875,
0.0104217529296875,
-0.0024871826171875,
0.0164794921875,
-0.01258087158203125,
0.03253173828125,
0.00811767578125,
-0.015289306640625,
0.0007677078247070312,
0.01250457763671875,
0.00279998779296875,
0.0189208984375,
0.026123046875,
-0.03662109375,
-0.042449951171875,
-0.0152740478515625,
-0.0482177734375,
-0.01352691650390625,
-0.01454925537109375,
0.01508331298828125,
0.033538818359375,
-0.01316070556640625,
0.033203125,
-0.01485443115234375,
-0.01151275634765625,
0.02386474609375,
0.0006060600280761719,
-0.035308837890625,
-0.0158538818359375,
-0.019134521484375,
-0.0211029052734375,
0.0060272216796875,
-0.0274810791015625,
0.004779815673828125,
0.0166168212890625,
0.00531005859375,
-0.0251312255859375,
-0.0078277587890625,
0.0273895263671875,
0.007595062255859375,
0.01232147216796875,
0.0270538330078125,
0.006504058837890625,
-0.031463623046875,
0.01039886474609375,
-0.0028533935546875,
-0.0034503936767578125,
-0.0246429443359375,
0.00011968612670898438,
-0.03009033203125,
0.0201263427734375,
-0.0205230712890625,
-0.004344940185546875,
-0.0189056396484375,
0.006103515625,
-0.0190887451171875,
0.01806640625,
-0.0051727294921875,
-0.0074462890625,
-0.0035190582275390625,
0.0024776458740234375,
-0.006999969482421875,
0.0018587112426757812,
-0.0199737548828125,
-0.0245361328125,
-0.01247406005859375,
0.0034351348876953125,
-0.0052947998046875,
0.0036602020263671875,
-0.0009975433349609375,
0.0028514862060546875,
-0.005008697509765625,
-0.0096588134765625,
0.0101318359375,
0.005008697509765625,
0.0171661376953125,
-0.0036067962646484375,
0.00942230224609375,
0.01454925537109375,
0.029937744140625,
-0.0112762451171875,
0.01435089111328125,
0.0018224716186523438,
0.022613525390625,
0.00970458984375,
0.0137481689453125,
0.00899505615234375,
-0.018035888671875,
0.0025787353515625,
0.031036376953125,
-0.03302001953125,
0.004955291748046875,
0.028656005859375,
-0.023345947265625,
-0.01715087890625,
-0.0095672607421875,
0.036590576171875,
0.0122833251953125,
-0.0034961700439453125,
0.00032973289489746094,
-0.0016965866088867188,
0.06256103515625,
0.00916290283203125,
0.005786895751953125,
-0.005313873291015625,
0.05340576171875,
-0.0226898193359375,
-0.0131683349609375,
0.00711822509765625,
-0.01251983642578125,
0.002254486083984375,
-0.0218963623046875,
-0.003826141357421875,
-0.00006264448165893555,
0.021636962890625,
0.010833740234375,
0.0260162353515625,
0.00019216537475585938,
-0.0071868896484375,
0.003658294677734375,
-0.0271148681640625,
-0.003643035888671875,
-0.0310821533203125,
-0.004169464111328125,
0.04541015625,
-0.0088653564453125,
0.0132904052734375,
-0.0028018951416015625,
0.0216217041015625,
0.014984130859375,
0.03472900390625,
-0.0026950836181640625,
0.004543304443359375,
-0.0157012939453125,
0.0311279296875,
0.037322998046875,
-0.0224761962890625,
0.045745849609375,
-0.0128326416015625,
-0.0240020751953125,
-0.003719329833984375,
-0.025909423828125,
0.0303955078125,
0.026641845703125,
0.019805908203125,
-0.0240325927734375,
-0.022735595703125,
-0.04254150390625,
0.032440185546875,
-0.006351470947265625,
0.015655517578125,
0.0203857421875,
-0.00954437255859375,
-0.0255889892578125,
-0.031829833984375,
-0.0037517547607421875,
0.01300048828125,
0.0239105224609375,
0.047515869140625,
-0.00023281574249267578,
0.00518798828125,
-0.061126708984375,
-0.02252197265625,
0.0233612060546875,
-0.006580352783203125,
0.0194091796875,
0.00817108154296875,
-0.0122222900390625,
0.0042877197265625,
-0.0193023681640625,
0.023895263671875,
0.0129852294921875,
-0.0105438232421875,
-0.0201416015625,
-0.030670166015625,
-0.0006256103515625,
-0.0113677978515625,
-0.005039215087890625,
0.03875732421875,
-0.00778961181640625,
0.00414276123046875,
-0.022216796875,
0.0046844482421875,
-0.0094451904296875,
-0.00341796875,
0.0167388916015625,
-0.003238677978515625,
0.01458740234375,
-0.01273345947265625,
-0.00933074951171875,
-0.003154754638671875,
0.00894927978515625,
0.014007568359375,
0.00882720947265625,
-0.0215911865234375,
0.048919677734375,
0.0115509033203125,
0.008453369140625,
0.00989532470703125,
0.0030956268310546875,
-0.00852203369140625,
0.0063934326171875,
-0.00571441650390625,
0.00669097900390625,
0.02447509765625,
-0.028839111328125,
0.0372314453125,
0.0030803680419921875,
0.06317138671875,
0.0162353515625,
-0.0106048583984375,
0.0017442703247070312,
0.027130126953125,
-0.01531982421875,
0.0419921875,
-0.026123046875,
-0.01488494873046875,
-0.021484375,
0.01485443115234375,
0.035797119140625,
-0.0308837890625,
-0.0176239013671875,
0.01456451416015625,
-0.01195526123046875,
0.00420379638671875,
0.00296783447265625,
-0.0252532958984375,
0.01605224609375,
0.0133819580078125,
-0.01702880859375,
-0.0007824897766113281,
0.0002627372741699219,
0.0038852691650390625,
-0.02294921875,
0.00699615478515625,
-0.0010128021240234375,
-0.00922393798828125,
-0.0259857177734375,
0.0291748046875,
0.0213623046875,
0.00466156005859375,
0.0019245147705078125,
0.00795745849609375,
-0.01363372802734375,
-0.000003159046173095703,
0.001293182373046875,
-0.0011568069458007812,
-0.00193023681640625,
-0.0178375244140625,
0.0101776123046875,
0.0012731552124023438,
-0.022125244140625,
0.019073486328125,
-0.0113983154296875,
0.0433349609375,
-0.037872314453125,
-0.0246124267578125,
0.010894775390625,
-0.0015735626220703125,
-0.0009551048278808594,
-0.006847381591796875,
-0.0117340087890625,
0.0128326416015625,
0.0183258056640625,
-0.022979736328125,
0.034088134765625,
0.039642333984375,
-0.0235748291015625,
0.031829833984375,
0.0202484130859375,
-0.003269195556640625,
0.0270843505859375,
-0.0054779052734375,
-0.007904052734375,
-0.0208282470703125,
0.0006394386291503906,
-0.0003833770751953125,
0.01284027099609375,
-0.004161834716796875,
0.0271759033203125,
0.0201873779296875,
-0.03924560546875,
0.01611328125,
0.0148773193359375,
-0.0020809173583984375,
-0.033966064453125,
-0.02569580078125,
-0.0285186767578125,
0.01959228515625,
-0.0167999267578125,
0.01708984375,
-0.005542755126953125,
-0.0012540817260742188,
-0.01345062255859375,
0.0219573974609375,
0.018402099609375,
-0.0061187744140625,
0.01123046875,
-0.00934600830078125,
0.008758544921875,
0.0108642578125,
0.029327392578125,
0.01605224609375,
-0.0110626220703125,
-0.0169677734375,
-0.019927978515625,
-0.017791748046875,
-0.044586181640625,
-0.00792694091796875,
-0.031951904296875,
0.0024967193603515625,
-0.0019159317016601562,
-0.0019969940185546875,
-0.0024280548095703125,
0.0150909423828125,
0.01219940185546875,
-0.0007748603820800781,
0.028350830078125,
-0.00882720947265625,
0.0289764404296875,
0.0205841064453125,
0.0130462646484375,
0.020904541015625,
-0.0198822021484375,
-0.005542755126953125,
0.00812530517578125,
-0.0000851750373840332,
-0.00279998779296875,
0.00846099853515625,
0.0201263427734375,
-0.0019216537475585938,
0.005466461181640625,
-0.0195770263671875,
-0.021331787109375,
0.0267181396484375,
0.0231475830078125,
0.0152130126953125,
0.0137786865234375,
-0.00010466575622558594,
0.0127716064453125,
-0.0100250244140625,
-0.0191497802734375,
0.013824462890625,
0.01715087890625,
0.0341796875,
-0.004241943359375,
-0.007137298583984375,
0.04547119140625,
0.00830841064453125,
0.050323486328125,
0.0007061958312988281,
0.005268096923828125,
0.007572174072265625,
0.0045318603515625,
-0.01947021484375,
-0.0322265625,
-0.024658203125,
0.01837158203125,
0.0160064697265625,
-0.007015228271484375,
-0.01641845703125,
-0.01441192626953125,
-0.004718780517578125,
-0.004474639892578125,
0.009063720703125,
0.004638671875,
0.0038127899169921875,
0.01154327392578125,
0.0284271240234375,
-0.019775390625,
0.0183563232421875,
0.013763427734375,
-0.0276031494140625,
0.0034198760986328125,
0.0084991455078125,
0.01239013671875,
0.0231781005859375,
0.01506805419921875,
-0.028045654296875,
-0.031036376953125,
-0.006519317626953125,
0.01165008544921875,
-0.007076263427734375,
-0.001979827880859375,
0.02392578125,
-0.01499176025390625,
0.0011873245239257812,
0.02911376953125,
0.0032958984375,
0.0285186767578125,
-0.005184173583984375,
-0.004001617431640625,
0.02142333984375,
0.0021228790283203125,
-0.0102996826171875,
0.00634002685546875,
0.0201873779296875,
0.006938934326171875,
0.0033245086669921875,
0.006496429443359375,
0.03338623046875,
-0.0103759765625,
-0.0085296630859375,
0.0197296142578125,
0.0008072853088378906,
0.0284576416015625,
0.0182037353515625,
-0.03033447265625,
-0.007171630859375,
-0.003818511962890625,
0.00616455078125,
-0.01380157470703125,
0.0046539306640625,
0.0011081695556640625,
0.01041412353515625,
-0.036041259765625,
-0.0104217529296875,
0.0307769775390625,
-0.01666259765625,
0.033050537109375,
0.006862640380859375,
0.01181793212890625,
-0.0201873779296875,
-0.00925445556640625,
-0.0090484619140625,
0.0055084228515625,
0.01219940185546875,
-0.00435638427734375,
0.005828857421875,
0.00847625732421875,
0.006519317626953125,
-0.0008673667907714844,
-0.04962158203125,
0.0282440185546875,
0.0153045654296875,
0.02227783203125,
-0.0267181396484375,
0.0105743408203125,
0.0321044921875,
-0.015899658203125,
0.040496826171875,
-0.023101806640625,
0.01499176025390625,
-0.0222625732421875,
-0.0004088878631591797,
-0.0007090568542480469,
-0.00921630859375,
-0.0115509033203125,
-0.0254058837890625,
0.0200347900390625,
0.00719451904296875,
-0.0204315185546875,
-0.0027828216552734375,
-0.00896453857421875,
-0.033447265625,
0.03839111328125,
-0.023681640625,
-0.0166778564453125,
0.0044708251953125,
-0.0207366943359375,
0.01105499267578125,
0.01483917236328125,
-0.008544921875,
-0.0281219482421875,
-0.017242431640625,
-0.0263824462890625,
0.03155517578125,
0.0040740966796875,
-0.003421783447265625,
-0.04693603515625,
-0.045745849609375,
-0.013214111328125,
-0.02093505859375,
0.035003662109375,
0.01499176025390625,
-0.0001971721649169922,
0.0148468017578125,
0.01348114013671875,
-0.0108795166015625,
0.006961822509765625,
-0.0065155029296875,
-0.0167083740234375,
-0.006137847900390625,
0.0034427642822265625,
0.04119873046875,
-0.0012187957763671875,
-0.0159912109375,
-0.01561737060546875,
0.0292816162109375,
0.0192718505859375,
0.0021572113037109375,
0.02923583984375,
0.0309295654296875,
-0.01544952392578125,
0.0038356781005859375,
0.00992584228515625,
0.0177459716796875,
-0.02630615234375,
0.01319122314453125,
-0.041412353515625,
-0.00556182861328125,
-0.0037593841552734375,
0.040435791015625,
-0.02862548828125,
-0.0011539459228515625,
-0.0152130126953125,
-0.000823974609375,
-0.00007009506225585938,
-0.01078033447265625,
-0.0128021240234375,
-0.0025348663330078125,
-0.017608642578125,
0.03802490234375,
-0.0178680419921875,
0.0185699462890625,
-0.0151214599609375,
0.0207366943359375,
-0.0050811767578125,
-0.023956298828125,
-0.021026611328125,
0.0185546875,
0.01117706298828125,
-0.0010786056518554688,
0.02459716796875,
0.02667236328125,
-0.00405120849609375,
-0.015350341796875,
-0.0086212158203125,
0.0015382766723632812,
-0.0265045166015625,
-0.0068511962890625,
0.006069183349609375,
-0.01287078857421875,
0.0181884765625,
0.0017309188842773438,
-0.0285186767578125,
0.004245758056640625,
0.0079345703125,
-0.0236968994140625,
0.01165008544921875,
0.0030460357666015625,
-0.006984710693359375,
0.012542724609375,
-0.0146942138671875,
0.01531982421875,
0.0152740478515625,
-0.046875,
0.01316070556640625,
0.0244598388671875,
-0.00992584228515625,
0.012664794921875,
0.01947021484375,
-0.0215301513671875,
0.0009937286376953125,
-0.0172882080078125,
-0.00495147705078125,
-0.036376953125,
0.0195770263671875,
-0.031494140625,
-0.0144500732421875,
0.006534576416015625,
-0.00592041015625,
0.0160369873046875,
-0.0296173095703125,
0.0124359130859375,
0.01151275634765625,
-0.006744384765625,
0.014251708984375,
-0.007678985595703125,
0.00557708740234375,
-0.0276947021484375,
-0.0269927978515625,
0.028411865234375,
0.0024051666259765625,
-0.004608154296875,
0.0100250244140625,
-0.00740814208984375,
0.055145263671875,
-0.012969970703125,
-0.01079559326171875,
0.0059814453125,
0.0171966552734375,
-0.003131866455078125,
0.055816650390625,
-0.018310546875,
-0.0341796875,
-0.040435791015625,
-0.003276824951171875,
-0.0038433074951171875,
0.005985260009765625,
-0.031158447265625,
0.043609619140625,
0.0298309326171875,
0.014923095703125,
-0.0447998046875,
0.00487518310546875,
0.00933074951171875,
-0.023681640625,
-0.0270843505859375,
0.0217437744140625,
0.039215087890625,
0.0229644775390625,
-0.035003662109375,
-0.007396697998046875,
0.01058197021484375,
0.0123291015625,
0.00885772705078125,
-0.0018415451049804688,
-0.0225982666015625,
-0.0105438232421875,
-0.0279388427734375,
-0.0101165771484375,
0.0338134765625,
-0.02587890625,
-0.0164642333984375,
0.0022029876708984375,
0.034515380859375,
0.004695892333984375,
-0.00426483154296875,
-0.0059814453125,
-0.00937652587890625,
-0.0276336669921875,
-0.0047760009765625,
0.015869140625,
-0.0157318115234375,
-0.0216522216796875,
-0.004352569580078125,
-0.0165863037109375,
-0.0086822509765625,
0.006099700927734375,
0.0044708251953125,
0.005001068115234375,
0.0281524658203125,
-0.0100860595703125,
0.042022705078125,
-0.0247802734375,
0.000040471553802490234,
-0.0294189453125,
-0.002483367919921875,
0.01172637939453125,
0.0025272369384765625,
0.01025390625,
-0.05059814453125,
-0.0114593505859375,
0.0006103515625,
0.0128021240234375,
-0.006847381591796875,
0.014495849609375,
-0.03851318359375,
-0.021484375,
-0.0015125274658203125,
-0.0189208984375,
0.0138702392578125,
0.0095977783203125,
0.0212249755859375,
-0.0274658203125,
-0.0201873779296875,
-0.02569580078125,
-0.01080322265625,
-0.0099639892578125,
-0.0015687942504882812,
0.02392578125,
-0.00426483154296875,
0.00292205810546875,
0.01090240478515625,
0.0201873779296875,
0.004634857177734375,
-0.0193939208984375,
0.007965087890625,
-0.0230255126953125,
-0.02471923828125,
-0.020477294921875,
0.01715087890625,
0.0171661376953125,
-0.0111236572265625,
-0.0016202926635742188,
-0.0041961669921875,
-0.003490447998046875,
0.0126800537109375,
-0.02325439453125,
-0.0159454345703125,
0.004184722900390625,
-0.0020160675048828125,
-0.02728271484375,
-0.034759521484375,
-0.0144500732421875,
-0.007110595703125,
-0.046478271484375,
-0.0172576904296875,
-0.01006317138671875,
-0.0306243896484375,
-0.013580322265625,
0.00304412841796875,
-0.007503509521484375,
-0.0201873779296875,
0.05029296875,
-0.0159454345703125,
0.00009083747863769531,
-0.0109405517578125,
0.0250244140625,
-0.01904296875,
-0.0017499923706054688,
0.04559326171875,
0.0169219970703125,
0.0123748779296875,
0.0460205078125,
0.0182647705078125,
0.001033782958984375,
0.01537322998046875,
-0.024322509765625,
0.0181427001953125,
-0.01503753662109375,
0.008819580078125,
0.00382232666015625,
0.005039215087890625,
-0.00992584228515625,
0.026641845703125,
-0.01160430908203125,
0.06884765625,
0.0178070068359375,
-0.00516510009765625,
0.0116119384765625,
0.0190277099609375,
0.0038547515869140625,
-0.002758026123046875,
0.0085296630859375,
0.036468505859375,
-0.035430908203125,
0.0153961181640625,
0.01509857177734375,
-0.014251708984375,
-0.0018749237060546875,
0.0207977294921875,
0.006267547607421875,
0.035247802734375,
0.00738525390625,
0.04425048828125,
0.00799560546875,
0.003814697265625,
-0.00778961181640625,
-0.0037860870361328125,
0.003856658935546875,
0.00856781005859375,
0.0015716552734375,
-0.005641937255859375,
-0.00240325927734375,
0.0130462646484375,
0.03167724609375,
0.0006461143493652344,
0.031463623046875,
0.0083770751953125,
-0.00981903076171875,
0.0160064697265625,
0.006195068359375,
0.01690673828125,
0.007144927978515625,
-0.01483154296875,
0.005321502685546875,
-0.00800323486328125,
-0.0016794204711914062,
-0.00989532470703125,
-0.0259857177734375,
0.00921630859375,
-0.024688720703125,
0.00787353515625,
0.03143310546875,
0.019012451171875,
0.0134735107421875,
0.0043792724609375,
-0.01419830322265625,
-0.0211029052734375,
-0.007568359375,
0.0196990966796875,
-0.0148162841796875,
0.0181884765625,
-0.00290679931640625,
0.007904052734375,
0.00928497314453125,
0.016448974609375,
-0.0038909912109375,
0.0005903244018554688,
0.00965118408203125,
-0.00862884521484375,
0.005588531494140625,
0.026214599609375,
-0.0181884765625,
-0.002880096435546875,
0.00046181678771972656,
0.01157379150390625,
0.0104522705078125,
0.0183563232421875,
-0.0097503662109375,
0.01727294921875,
-0.0242767333984375,
0.02227783203125,
0.0151824951171875,
0.00943756103515625,
0.0111846923828125,
0.00838470458984375,
-0.014984130859375,
-0.03887939453125,
0.0035610198974609375,
0.0051422119140625,
-0.0152130126953125,
-0.0239105224609375,
-0.016448974609375,
0.0279083251953125,
0.035888671875,
-0.044708251953125,
0.00502777099609375,
0.007137298583984375,
0.032989501953125,
-0.032440185546875,
0.0237884521484375,
0.00016617774963378906,
0.0270538330078125,
0.035675048828125,
-0.03131103515625,
0.0133514404296875,
-0.00804901123046875,
0.02618408203125,
-0.017547607421875,
-0.01214599609375,
0.003025054931640625,
-0.02044677734375,
0.00926971435546875,
-0.0047454833984375,
-0.01178741455078125,
-0.0038166046142578125,
0.00701141357421875,
0.0007877349853515625,
-0.0013036727905273438,
-0.01169586181640625,
-0.0310821533203125,
0.0287017822265625,
0.0209808349609375,
0.034210205078125,
-0.0029582977294921875,
0.0006670951843261719,
-0.001861572265625,
-0.0030364990234375,
0.0240478515625,
-0.0017538070678710938,
0.03955078125,
-0.0009694099426269531,
-0.01611328125,
0.015594482421875,
0.00592803955078125,
-0.0098876953125,
-0.0294342041015625,
0.009033203125,
0.0221099853515625,
-0.02301025390625,
-0.0133514404296875,
0.0007481575012207031,
-0.0272979736328125,
-0.01416778564453125,
0.046417236328125,
-0.0136566162109375,
0.0099945068359375,
0.005401611328125,
-0.0222625732421875,
-0.021240234375,
0.0082855224609375,
-0.0010900497436523438,
-0.032928466796875,
0.0235748291015625,
0.0017328262329101562,
-0.01541900634765625,
0.00489044189453125,
-0.026397705078125,
-0.0082244873046875,
0.01226806640625,
0.04254150390625,
0.0219573974609375,
-0.00392913818359375,
0.005443572998046875,
-0.00687408447265625,
0.0011949539184570312,
0.005340576171875,
0.037872314453125,
-0.026824951171875,
-0.0156707763671875,
0.0007605552673339844,
0.0155029296875,
0.00611114501953125,
0.03271484375,
0.032257080078125,
0.0333251953125,
0.0095977783203125,
-0.0210723876953125,
-0.006359100341796875,
-0.02166748046875,
0.011444091796875,
-0.0147705078125,
-0.0247039794921875,
0.007389068603515625,
0.0275115966796875,
0.0102691650390625,
0.0244293212890625,
-0.04046630859375,
0.006458282470703125,
0.012786865234375,
-0.0102691650390625,
0.0229949951171875,
-0.0160369873046875,
0.0256500244140625,
-0.00450897216796875,
0.027252197265625,
-0.011566162109375,
-0.00769805908203125,
0.0233306884765625,
0.0087127685546875,
0.02886962890625,
-0.0298614501953125,
0.037811279296875,
-0.007801055908203125,
0.0063018798828125,
0.046142578125,
-0.0152587890625,
0.045562744140625,
-0.033050537109375,
-0.00030040740966796875,
0.0003898143768310547,
0.00926971435546875,
0.04876708984375,
0.007404327392578125,
0.0193939208984375,
-0.031768798828125,
0.0196990966796875,
-0.038299560546875,
0.006397247314453125,
-0.0002627372741699219,
0.01123809814453125,
-0.04888916015625,
0.003124237060546875,
-0.004299163818359375,
0.00714874267578125,
0.0181121826171875,
0.01177978515625,
-0.01275634765625,
0.0109710693359375,
0.0177459716796875,
-0.01715087890625,
0.043212890625,
0.01213836669921875,
-0.00592041015625,
-0.002101898193359375,
-0.0185394287109375,
0.003978729248046875,
0.0249481201171875,
-0.00785064697265625,
0.0195159912109375,
-0.003814697265625,
0.016754150390625,
-0.01425933837890625,
-0.01212310791015625,
0.007476806640625,
-0.0068206787109375,
-0.01386260986328125,
-0.0033016204833984375,
-0.0024471282958984375,
-0.0018224716186523438,
-0.00372314453125,
0.0005154609680175781,
0.021820068359375,
-0.01001739501953125,
0.0240020751953125,
-0.020233154296875,
-0.006824493408203125,
-0.01641845703125,
0.00811004638671875,
-0.0270843505859375,
-0.035888671875,
-0.0021610260009765625,
0.024627685546875,
-0.0364990234375,
0.00565338134765625,
0.03497314453125,
0.002719879150390625,
0.03729248046875,
0.03656005859375,
-0.0028972625732421875,
-0.009796142578125,
-0.0061187744140625,
0.0197296142578125,
-0.0297393798828125,
-0.01259613037109375,
0.00836181640625,
0.01056671142578125,
-0.01496124267578125,
-0.003192901611328125,
-0.0110321044921875,
-0.0206451416015625,
0.035308837890625,
0.01464080810546875,
0.0106201171875,
0.0109405517578125,
0.036346435546875,
0.03326416015625,
0.01910400390625,
-0.019805908203125,
0.0215606689453125,
-0.0086212158203125,
-0.009185791015625,
-0.0132293701171875,
-0.0018482208251953125,
-0.052154541015625,
0.0229034423828125,
0.004100799560546875,
-0.0027637481689453125,
-0.01323699951171875,
0.03680419921875,
-0.005695343017578125,
-0.07159423828125,
-0.0158233642578125,
0.02874755859375,
0.01065826416015625,
0.0100250244140625,
-0.0240631103515625,
0.01418304443359375,
0.0034160614013671875,
-0.006740570068359375,
-0.0102691650390625,
-0.003231048583984375,
-0.01456451416015625,
-0.00312042236328125,
0.0088348388671875,
-0.005603790283203125,
-0.01099395751953125,
-0.0166778564453125,
-0.01389312744140625,
-0.005855560302734375,
-0.006160736083984375,
-0.0121917724609375,
-0.01513671875,
-0.00562286376953125,
0.001575469970703125,
-0.032989501953125,
-0.020050048828125,
0.004638671875,
-0.024932861328125,
-0.00036263465881347656,
0.0080413818359375,
0.01270294189453125,
-0.0008111000061035156,
0.0030498504638671875,
0.0230255126953125,
0.01314544677734375,
-0.00882720947265625,
-0.0117034912109375,
0.03515625,
-0.0268096923828125,
0.029510498046875,
0.0352783203125,
-0.006103515625,
-0.028167724609375,
-0.0205841064453125,
-0.01727294921875,
0.03387451171875,
0.016204833984375,
0.005588531494140625,
0.01171875,
-0.001171112060546875,
0.005863189697265625,
-0.033782958984375,
0.03497314453125,
-0.0220947265625,
-0.0177154541015625,
-0.007503509521484375,
0.004314422607421875,
0.01556396484375,
0.0087432861328125,
-0.0202484130859375,
-0.02459716796875,
-0.02545166015625,
0.0009908676147460938,
-0.0239715576171875
] |
ours_557
|
Dividing the two equations, we obtain \(a^{2}-ab+b^{2}=20\). Subtracting this from \(a^{2}+ab+b^{2}=45\), we obtain \(2ab=25\).
Thus, the value of \(2ab\) is \(\boxed{25}\).
|
25
|
{
"competition": "us_comps",
"dataset": "Ours",
"posts": null,
"source": "OMOSoln2.md"
}
|
Let \(a\) and \(b\) be real numbers that satisfy
\[
\begin{aligned}
a^{4}+a^{2} b^{2}+b^{4} & =900 \\
a^{2}+a b+b^{2} & =45
\end{aligned}
\]
Find the value of \(2ab\).
|
[
"/Mathematics/Algebra/AlgebraicEquations/AlgebraicEquation",
"/Mathematics/Algebra/AlgebraicEquations/SimultaneousEquations",
"/Mathematics/Algebra/AlgebraicIdentities/AlgebraicIdentity",
"/Mathematics/Algebra/AlgebraicIdentities/PolynomialIdentity",
"/Mathematics/Algebra/Polynomials/Polynomial",
"/Mathematics/Algebra/Polynomials/PolynomialEquation",
"/Mathematics/Algebra/Polynomials/QuadraticPolynomial",
"/Mathematics/Algebra/Polynomials/RealPolynomial",
"/Mathematics/Algebra/Polynomials/RealVariable",
"/Mathematics/Algebra/Polynomials/Variable"
] |
Recognize that a^4 + a^2 b^2 + b^4 = (a^2+ab+b^2)(a^2−ab+b^2) and use this factorization.
|
[
0.000021696090698242188,
-0.01326751708984375,
0.0291290283203125,
-0.0125274658203125,
0.00031256675720214844,
0.00888824462890625,
-0.00423431396484375,
0.0288238525390625,
0.01055145263671875,
-0.0084075927734375,
0.004070281982421875,
-0.01154327392578125,
-0.001811981201171875,
0.00955963134765625,
0.0214385986328125,
0.022247314453125,
-0.0003006458282470703,
0.0092315673828125,
0.04376220703125,
-0.004924774169921875,
-0.01078033447265625,
0.0120697021484375,
-0.0634765625,
0.005329132080078125,
-0.022247314453125,
-0.0113983154296875,
-0.01506805419921875,
-0.01389312744140625,
0.005641937255859375,
0.025238037109375,
0.015777587890625,
-0.01824951171875,
0.0253143310546875,
-0.0089874267578125,
-0.001667022705078125,
0.013153076171875,
0.035888671875,
-0.007274627685546875,
-0.03216552734375,
-0.01021575927734375,
-0.0002319812774658203,
0.0146026611328125,
-0.0178070068359375,
0.01102447509765625,
0.01128387451171875,
0.01213836669921875,
0.00037741661071777344,
0.0018072128295898438,
-0.024505615234375,
-0.017333984375,
0.0007448196411132812,
0.0165557861328125,
-0.02520751953125,
-0.0084075927734375,
-0.00885772705078125,
-0.0308837890625,
-0.0291748046875,
0.003475189208984375,
-0.0230712890625,
-0.022186279296875,
-0.00081634521484375,
0.0012159347534179688,
-0.033111572265625,
-0.037353515625,
-0.004657745361328125,
-0.00945281982421875,
-0.013214111328125,
-0.0218963623046875,
0.00630950927734375,
0.0030422210693359375,
0.028076171875,
-0.0095062255859375,
-0.0017528533935546875,
0.0210723876953125,
0.0189971923828125,
-0.00446319580078125,
-0.0092620849609375,
0.009765625,
-0.00434112548828125,
0.006519317626953125,
-0.0014944076538085938,
0.0216522216796875,
0.0185394287109375,
-0.04705810546875,
-0.0047607421875,
0.0015974044799804688,
-0.053375244140625,
0.0022106170654296875,
0.015655517578125,
-0.0153350830078125,
0.0031681060791015625,
0.006946563720703125,
-0.015838623046875,
0.0234832763671875,
-0.005828857421875,
0.016876220703125,
-0.004222869873046875,
0.0041961669921875,
-0.0148773193359375,
0.0108489990234375,
-0.0105133056640625,
-0.0242919921875,
0.003978729248046875,
-0.02301025390625,
-0.01082611083984375,
-0.01117706298828125,
-0.01372528076171875,
0.008880615234375,
-0.0196685791015625,
0.0038394927978515625,
0.01213836669921875,
-0.00551605224609375,
0.054840087890625,
0.02728271484375,
0.01727294921875,
-0.00988006591796875,
0.036163330078125,
0.01470947265625,
0.011199951171875,
0.0061187744140625,
-0.014129638671875,
0.01442718505859375,
-0.00876617431640625,
0.0105438232421875,
0.0050811767578125,
0.008697509765625,
-0.00946807861328125,
-0.02410888671875,
-0.0180511474609375,
0.0149078369140625,
0.0008101463317871094,
-0.0140533447265625,
-0.0230865478515625,
-0.02813720703125,
-0.0609130859375,
0.0281219482421875,
-0.0251007080078125,
0.0022487640380859375,
0.002132415771484375,
0.00004011392593383789,
-0.004619598388671875,
-0.0119476318359375,
0.0037593841552734375,
-0.0202484130859375,
-0.0081787109375,
-0.00470733642578125,
-0.00356292724609375,
0.00933837890625,
0.0177001953125,
-0.00848388671875,
0.004787445068359375,
-0.022552490234375,
0.0098876953125,
0.0192413330078125,
0.0058746337890625,
0.00537872314453125,
0.00817108154296875,
0.007266998291015625,
0.00009483098983764648,
0.0182037353515625,
-0.00038909912109375,
-0.0124969482421875,
-0.009124755859375,
0.0237579345703125,
0.0008172988891601562,
-0.002349853515625,
0.0172576904296875,
0.042816162109375,
-0.0419921875,
-0.00577545166015625,
0.017120361328125,
0.00264739990234375,
0.00666046142578125,
-0.01491546630859375,
-0.0038471221923828125,
0.00830841064453125,
-0.013519287109375,
0.031219482421875,
-0.014556884765625,
-0.002216339111328125,
-0.007171630859375,
-0.05224609375,
-0.0163421630859375,
0.0166778564453125,
0.018096923828125,
-0.027008056640625,
0.0079498291015625,
0.0123291015625,
0.0220489501953125,
0.0088958740234375,
-0.0041351318359375,
-0.0229034423828125,
-0.010040283203125,
-0.0052947998046875,
-0.00704193115234375,
-0.0032482147216796875,
-0.015899658203125,
-0.0013399124145507812,
0.0225830078125,
0.0093841552734375,
-0.0178680419921875,
0.01238250732421875,
0.024322509765625,
-0.00522613525390625,
0.025177001953125,
-0.0003254413604736328,
0.0045013427734375,
-0.015167236328125,
-0.002269744873046875,
-0.006866455078125,
0.01480865478515625,
0.017242431640625,
-0.00592041015625,
-0.00852203369140625,
-0.002971649169921875,
-0.01806640625,
-0.0172576904296875,
-0.00951385498046875,
-0.003246307373046875,
0.0201416015625,
-0.0030841827392578125,
0.005947113037109375,
-0.0196533203125,
-0.01206207275390625,
-0.027069091796875,
-0.004974365234375,
-0.0205841064453125,
-0.00568389892578125,
0.0014123916625976562,
-0.006591796875,
0.01502227783203125,
0.00469970703125,
-0.0012111663818359375,
0.01358795166015625,
-0.00449371337890625,
0.01971435546875,
-0.030242919921875,
-0.0022525787353515625,
0.00267791748046875,
-0.0025787353515625,
-0.0070648193359375,
-0.0156402587890625,
0.00421905517578125,
-0.0041961669921875,
0.00547027587890625,
-0.004833221435546875,
0.00505828857421875,
-0.0107879638671875,
0.0195770263671875,
-0.004642486572265625,
-0.01544952392578125,
0.0196075439453125,
-0.006866455078125,
-0.02032470703125,
-0.0236053466796875,
0.0011701583862304688,
0.01456451416015625,
0.0286407470703125,
-0.00522613525390625,
0.0307159423828125,
-0.01102447509765625,
-0.026611328125,
-0.0076751708984375,
0.00191497802734375,
-0.0098114013671875,
0.0379638671875,
0.016448974609375,
0.007762908935546875,
0.018890380859375,
-0.01166534423828125,
0.0187530517578125,
-0.01611328125,
-0.0170135498046875,
0.0024318695068359375,
-0.0006275177001953125,
0.01088714599609375,
-0.007904052734375,
-0.006542205810546875,
0.0309906005859375,
-0.0128631591796875,
-0.00487518310546875,
-0.002849578857421875,
-0.0265350341796875,
-0.00347137451171875,
0.0052337646484375,
0.01123809814453125,
0.036773681640625,
-0.0011692047119140625,
-0.0208892822265625,
0.01372528076171875,
0.0010442733764648438,
-0.0275421142578125,
-0.0063018798828125,
-0.00452423095703125,
0.0645751953125,
0.0276336669921875,
0.02569580078125,
-0.00876617431640625,
0.0021991729736328125,
0.0019054412841796875,
0.032745361328125,
-0.0028514862060546875,
-0.0010118484497070312,
-0.016326904296875,
0.016998291015625,
0.052642822265625,
0.0215911865234375,
0.0013246536254882812,
-0.00656890869140625,
-0.0057373046875,
0.0135345458984375,
-0.0025386810302734375,
-0.0089569091796875,
-0.0221099853515625,
-0.0318603515625,
-0.045196533203125,
-0.0006256103515625,
0.02783203125,
-0.004497528076171875,
0.00110626220703125,
0.0306854248046875,
0.0100860595703125,
0.01055145263671875,
0.0009374618530273438,
0.0124664306640625,
-0.027252197265625,
0.004543304443359375,
-0.004413604736328125,
0.0001558065414428711,
0.034515380859375,
-0.0166015625,
-0.000675201416015625,
0.01038360595703125,
-0.0224151611328125,
0.007778167724609375,
-0.006877899169921875,
0.000179290771484375,
0.015350341796875,
-0.01090240478515625,
-0.00506591796875,
0.0249481201171875,
-0.01113128662109375,
0.01543426513671875,
-0.0295867919921875,
-0.022186279296875,
0.0288238525390625,
0.002704620361328125,
-0.01432037353515625,
0.0016012191772460938,
-0.0294189453125,
0.0186614990234375,
0.004047393798828125,
0.004825592041015625,
0.00838470458984375,
-0.02734375,
-0.00972747802734375,
-0.0121612548828125,
-0.000972747802734375,
0.0169677734375,
0.02337646484375,
0.0019741058349609375,
0.0198822021484375,
0.0080413818359375,
0.007778167724609375,
-0.009307861328125,
0.0034542083740234375,
-0.038787841796875,
0.007144927978515625,
-0.0246124267578125,
0.01410675048828125,
-0.01352691650390625,
-0.0213775634765625,
0.01142120361328125,
-0.00024628639221191406,
0.003971099853515625,
-0.0042266845703125,
-0.02081298828125,
-0.0133819580078125,
-0.0032806396484375,
-0.0003540515899658203,
-0.0035686492919921875,
0.01439666748046875,
-0.01456451416015625,
0.01273345947265625,
0.00614166259765625,
-0.01421356201171875,
-0.023773193359375,
-0.04437255859375,
-0.01433563232421875,
0.0192108154296875,
0.0029659271240234375,
-0.017822265625,
0.00323486328125,
0.000621795654296875,
-0.00893402099609375,
-0.0318603515625,
0.0009937286376953125,
-0.00494384765625,
0.0036144256591796875,
-0.0224151611328125,
-0.051849365234375,
-0.002063751220703125,
-0.032196044921875,
-0.04071044921875,
0.0029926300048828125,
-0.00893402099609375,
0.01148223876953125,
-0.041595458984375,
-0.035430908203125,
-0.0096588134765625,
0.027008056640625,
0.003353118896484375,
0.00995635986328125,
-0.0209503173828125,
-0.024139404296875,
0.002117156982421875,
-0.0023632049560546875,
0.022613525390625,
0.0082550048828125,
-0.015869140625,
0.00977325439453125,
0.0032978057861328125,
0.006275177001953125,
0.031341552734375,
0.0284576416015625,
0.0214385986328125,
-0.035980224609375,
0.03564453125,
-0.0075531005859375,
-0.020538330078125,
0.00998687744140625,
-0.02069091796875,
-0.01125335693359375,
0.022705078125,
0.0141143798828125,
0.040191650390625,
0.026947021484375,
-0.01195526123046875,
0.0037059783935546875,
0.0279541015625,
-0.0145111083984375,
0.0157623291015625,
0.0036602020263671875,
-0.01404571533203125,
0.0325927734375,
-0.014404296875,
0.005573272705078125,
0.01462554931640625,
-0.025848388671875,
0.0205535888671875,
-0.024017333984375,
0.0244293212890625,
-0.0019159317016601562,
-0.0191802978515625,
-0.0110321044921875,
0.0243988037109375,
0.044403076171875,
0.00304412841796875,
-0.026885986328125,
0.01303863525390625,
-0.0004892349243164062,
0.0140838623046875,
-0.00959014892578125,
0.0280609130859375,
-0.033905029296875,
0.00008660554885864258,
-0.0000020265579223632812,
0.032379150390625,
0.0222625732421875,
-0.0107574462890625,
0.0028705596923828125,
-0.022979736328125,
-0.0146484375,
0.01033782958984375,
-0.038665771484375,
0.0297698974609375,
0.0123138427734375,
0.01074981689453125,
-0.01953125,
0.033447265625,
0.009613037109375,
-0.00811767578125,
-0.002162933349609375,
-0.0487060546875,
-0.00524139404296875,
0.0196380615234375,
0.0303955078125,
-0.0022563934326171875,
-0.0169830322265625,
-0.0116424560546875,
0.007640838623046875,
0.039276123046875,
-0.035736083984375,
-0.0272064208984375,
-0.03497314453125,
-0.0030879974365234375,
0.0153961181640625,
0.006168365478515625,
-0.0167999267578125,
-0.01336669921875,
0.009552001953125,
-0.0499267578125,
0.0042572021484375,
0.01708984375,
0.0037212371826171875,
-0.033172607421875,
0.01491546630859375,
0.0018148422241210938,
-0.000008463859558105469,
0.01190948486328125,
0.0295867919921875,
0.00543975830078125,
0.033599853515625,
-0.0252227783203125,
0.01360321044921875,
0.0141448974609375,
0.0121307373046875,
-0.025787353515625,
0.00499725341796875,
0.0150909423828125,
-0.0247650146484375,
-0.00046539306640625,
0.0009760856628417969,
-0.0206146240234375,
0.0205535888671875,
0.01148223876953125,
-0.0137939453125,
-0.0115203857421875,
0.0269927978515625,
0.0018157958984375,
-0.01361083984375,
-0.0411376953125,
-0.006500244140625,
0.033721923828125,
-0.01200103759765625,
-0.0081024169921875,
-0.00998687744140625,
0.0016183853149414062,
0.024261474609375,
0.01465606689453125,
-0.0176849365234375,
0.0079803466796875,
-0.0165252685546875,
-0.035614013671875,
0.0022068023681640625,
0.0034999847412109375,
-0.00750732421875,
0.0109100341796875,
-0.025634765625,
0.01103973388671875,
0.026336669921875,
0.0017452239990234375,
-0.0205535888671875,
-0.0060272216796875,
-0.034912109375,
-0.01165008544921875,
0.0181427001953125,
-0.0022830963134765625,
-0.0230712890625,
-0.0003445148468017578,
0.018341064453125,
-0.00876617431640625,
0.0457763671875,
-0.02142333984375,
0.0037670135498046875,
-0.0391845703125,
0.005664825439453125,
-0.00432586669921875,
0.021026611328125,
-0.003902435302734375,
-0.0213165283203125,
-0.022735595703125,
-0.035003662109375,
0.0085601806640625,
0.010009765625,
-0.01335906982421875,
-0.0064697265625,
-0.005645751953125,
0.0144805908203125,
-0.0460205078125,
0.045684814453125,
0.0200042724609375,
0.0020275115966796875,
0.001377105712890625,
-0.015533447265625,
-0.008575439453125,
-0.006221771240234375,
0.0095367431640625,
0.0018072128295898438,
-0.00859832763671875,
0.002532958984375,
0.033203125,
-0.00540924072265625,
0.0147705078125,
0.0226593017578125,
-0.00496673583984375,
0.00896453857421875,
-0.01305389404296875,
0.020355224609375,
0.00904083251953125,
0.04803466796875,
0.00788116455078125,
-0.02642822265625,
0.0249786376953125,
-0.0404052734375,
0.0030231475830078125,
-0.027740478515625,
0.0050201416015625,
-0.00656890869140625,
0.01448822021484375,
-0.0007262229919433594,
0.00972747802734375,
-0.0191650390625,
0.024078369140625,
0.0283966064453125,
0.0200347900390625,
-0.005680084228515625,
0.004444122314453125,
0.0167694091796875,
-0.0116729736328125,
-0.0036067962646484375,
-0.0293731689453125,
-0.0083770751953125,
-0.00653076171875,
-0.00577545166015625,
-0.0039215087890625,
-0.0018835067749023438,
-0.037078857421875,
0.0261383056640625,
-0.006465911865234375,
-0.0124053955078125,
0.0174102783203125,
-0.01081085205078125,
-0.033355712890625,
-0.00879669189453125,
0.0174713134765625,
-0.010589599609375,
0.041229248046875,
0.0033416748046875,
-0.010223388671875,
0.0185546875,
0.004306793212890625,
-0.00424957275390625,
-0.041229248046875,
-0.0031147003173828125,
0.0055389404296875,
-0.0104217529296875,
-0.031097412109375,
-0.0499267578125,
0.0008692741394042969,
-0.0031795501708984375,
0.00373077392578125,
-0.0248565673828125,
0.0178680419921875,
-0.0042724609375,
0.0016813278198242188,
-0.0024261474609375,
0.00412750244140625,
0.0190887451171875,
0.0250396728515625,
0.0181732177734375,
-0.0556640625,
-0.009033203125,
-0.00008785724639892578,
-0.061920166015625,
-0.017181396484375,
-0.00339508056640625,
-0.016845703125,
0.0533447265625,
0.0101318359375,
0.0205841064453125,
-0.044158935546875,
-0.0024433135986328125,
-0.01221466064453125,
-0.0204925537109375,
0.04254150390625,
0.0179595947265625,
-0.01076507568359375,
-0.0017414093017578125,
-0.0204010009765625,
-0.0023784637451171875,
0.036224365234375,
0.017730712890625,
0.0259857177734375,
0.0259552001953125,
0.0384521484375,
0.0006375312805175781,
0.00458526611328125,
0.018402099609375,
0.01708984375,
-0.0037174224853515625,
0.00948333740234375,
-0.0085906982421875,
-0.0185089111328125,
0.01031494140625,
0.00289154052734375,
0.005420684814453125,
0.013702392578125,
-0.0228118896484375,
-0.0213470458984375,
-0.01513671875,
-0.0206756591796875,
0.042877197265625,
-0.01947021484375,
-0.02117919921875,
-0.031463623046875,
-0.024383544921875,
-0.0281829833984375,
-0.020782470703125,
0.0106353759765625,
-0.0421142578125,
-0.00879669189453125,
-0.0265350341796875,
-0.02838134765625,
-0.0321044921875,
-0.00312042236328125,
0.0254364013671875,
-0.01256561279296875,
0.023468017578125,
-0.024200439453125,
0.0028209686279296875,
0.004673004150390625,
-0.01788330078125,
-0.002193450927734375,
0.06719970703125,
0.0216064453125,
-0.01262664794921875,
-0.042999267578125,
0.0181427001953125,
0.0243988037109375,
-0.01447296142578125,
-0.0025157928466796875,
-0.007694244384765625,
0.0234222412109375,
-0.00732421875,
0.0038204193115234375,
-0.0204010009765625,
-0.0428466796875,
-0.02587890625,
0.0239105224609375,
0.0081329345703125,
-0.0161285400390625,
-0.0030918121337890625,
-0.0183258056640625,
-0.00395965576171875,
-0.021026611328125,
0.013580322265625,
0.0041656494140625,
-0.01280975341796875,
-0.0114593505859375,
0.0159759521484375,
-0.03515625,
-0.01092529296875,
-0.03948974609375,
-0.0110015869140625,
-0.00887298583984375,
0.01094818115234375,
-0.0465087890625,
0.02008056640625,
0.035552978515625,
-0.019744873046875,
-0.0019893646240234375,
-0.0246734619140625,
0.003719329833984375,
0.0255889892578125,
-0.0345458984375,
-0.035125732421875,
-0.0169219970703125,
-0.04150390625,
0.03363037109375,
-0.0081787109375,
-0.028717041015625,
-0.0184326171875,
-0.01027679443359375,
-0.002658843994140625,
0.01873779296875,
-0.04852294921875,
0.028228759765625,
0.06414794921875,
0.00830078125,
-0.007587432861328125,
0.0109710693359375,
-0.035614013671875,
0.00208282470703125,
-0.044677734375,
-0.0055999755859375,
0.0016374588012695312,
-0.004131317138671875,
0.017791748046875,
0.006092071533203125,
0.0103912353515625,
-0.00884246826171875,
-0.001148223876953125,
-0.01177215576171875,
0.01212310791015625,
-0.0167083740234375,
-0.03106689453125,
-0.04815673828125,
-0.03143310546875,
0.01079559326171875,
0.01654052734375,
-0.03076171875,
-0.0246124267578125,
0.0205230712890625,
0.0180816650390625,
-0.00955963134765625,
0.014984130859375,
-0.0023593902587890625,
-0.010498046875,
0.0281219482421875,
-0.007106781005859375,
-0.00214385986328125,
-0.0345458984375,
-0.017364501953125,
0.027496337890625,
-0.0240020751953125,
0.0181121826171875,
0.0125732421875,
0.005710601806640625,
0.032684326171875,
-0.00501251220703125,
0.0275726318359375,
0.01485443115234375,
0.03240966796875,
-0.019012451171875,
-0.0167083740234375,
0.004581451416015625,
0.00835418701171875,
0.005950927734375,
0.007297515869140625,
0.0027446746826171875,
-0.003326416015625,
-0.0006918907165527344,
-0.01277923583984375,
-0.035980224609375,
-0.006244659423828125,
0.007068634033203125,
0.01043701171875,
-0.00959014892578125,
-0.0006885528564453125,
0.01177215576171875,
0.01148223876953125,
0.03302001953125,
-0.0197601318359375,
-0.0067291259765625,
0.00537872314453125,
-0.027679443359375,
0.0379638671875,
0.03277587890625,
0.01273345947265625,
0.0132293701171875,
0.004169464111328125,
-0.0309295654296875,
0.00997161865234375,
-0.01303863525390625,
-0.006061553955078125,
0.03057861328125,
0.03387451171875,
-0.0138397216796875,
-0.00743865966796875,
-0.0237579345703125,
0.017852783203125,
0.00612640380859375,
0.00807952880859375,
-0.016265869140625,
-0.0186614990234375,
0.041046142578125,
-0.03485107421875,
0.005252838134765625,
-0.019683837890625,
0.0268096923828125,
0.01215362548828125,
0.0362548828125,
0.0008325576782226562,
0.04071044921875,
0.03271484375,
0.0018672943115234375,
-0.0157928466796875,
0.03961181640625,
0.007450103759765625,
0.0193023681640625,
-0.0206756591796875,
0.00699615478515625,
0.0025615692138671875,
0.0028820037841796875,
-0.0011930465698242188,
-0.0014858245849609375,
-0.0022373199462890625,
-0.01140594482421875,
0.00013637542724609375,
-0.00414276123046875,
-0.000026166439056396484,
-0.033935546875,
-0.0298614501953125,
0.00933837890625,
-0.00030422210693359375,
-0.0179901123046875,
-0.02801513671875,
0.0234832763671875,
-0.01343536376953125,
-0.0284423828125,
0.03680419921875,
0.01047515869140625,
0.0382080078125,
-0.0017175674438476562,
-0.00887298583984375,
0.0025920867919921875,
-0.011383056640625,
-0.0105438232421875,
0.046783447265625,
-0.0258331298828125,
-0.00601959228515625,
0.00897216796875,
-0.024993896484375,
0.0039043426513671875,
-0.02984619140625,
-0.005664825439453125,
-0.012786865234375,
-0.042755126953125,
-0.0196990966796875,
0.0174560546875,
-0.00848388671875,
-0.0139617919921875,
0.00623321533203125,
-0.005184173583984375,
-0.01214599609375,
-0.006847381591796875,
0.0022792816162109375,
-0.037750244140625,
-0.005573272705078125,
0.039306640625,
0.018646240234375,
-0.002658843994140625,
0.00917816162109375,
-0.0186767578125,
0.005985260009765625,
0.0126800537109375,
-0.056732177734375,
0.0161590576171875,
0.0166015625,
0.00786590576171875,
0.003154754638671875,
0.037445068359375,
0.01364898681640625,
0.007389068603515625,
-0.0092926025390625,
0.0005068778991699219,
0.001049041748046875,
0.01177215576171875,
-0.0014438629150390625,
0.0081634521484375,
0.003757476806640625,
0.0193939208984375,
0.025299072265625,
-0.0179443359375,
-0.01239776611328125,
0.033721923828125,
-0.003948211669921875,
0.0208587646484375,
-0.00347900390625,
-0.010650634765625,
0.034576416015625,
-0.0255279541015625,
0.00955963134765625,
-0.0220947265625,
-0.004909515380859375,
-0.006809234619140625,
-0.0115814208984375,
0.00324249267578125,
0.021087646484375,
0.016876220703125,
-0.043212890625,
-0.04058837890625,
-0.025177001953125,
0.01019287109375,
0.04010009765625,
-0.0025501251220703125,
0.0177154541015625,
0.0027523040771484375,
0.035980224609375,
-0.045745849609375,
-0.01105499267578125,
-0.011962890625,
0.00391387939453125,
-0.0182952880859375,
-0.0191192626953125,
0.007472991943359375,
-0.00341033935546875,
0.024322509765625,
-0.02545166015625,
-0.0009036064147949219,
0.033935546875,
-0.021820068359375,
0.007633209228515625,
0.004032135009765625,
0.023529052734375,
-0.0102691650390625,
-0.01495361328125,
0.0029506683349609375,
0.00771331787109375,
-0.009521484375,
-0.01922607421875,
0.00811767578125,
0.01044464111328125,
0.0010318756103515625,
-0.018646240234375,
0.016937255859375,
0.01012420654296875,
-0.008056640625,
0.02435302734375,
-0.0002989768981933594,
-0.024078369140625,
-0.01430511474609375,
0.0280914306640625,
-0.00728607177734375,
0.024627685546875,
0.009521484375,
0.0086822509765625,
-0.05499267578125,
0.027374267578125,
-0.020599365234375,
-0.00827789306640625,
0.0025234222412109375,
-0.0484619140625,
-0.013519287109375,
-0.037841796875,
-0.0220489501953125,
0.00751495361328125,
0.00652313232421875,
0.0341796875,
-0.0208587646484375,
0.0164947509765625,
-0.0164642333984375,
0.0007848739624023438,
-0.026092529296875,
-0.0107421875,
-0.007411956787109375,
-0.0171966552734375,
0.0237884521484375,
0.035003662109375,
-0.00662994384765625,
-0.0012750625610351562,
0.0163421630859375,
-0.0002579689025878906,
-0.0081634521484375,
-0.0136871337890625,
0.007236480712890625,
0.0285186767578125,
-0.017852783203125,
0.0211944580078125,
0.0147857666015625,
0.00833892822265625,
-0.012237548828125,
0.0221405029296875,
0.0168914794921875,
0.0083160400390625,
-0.0080108642578125,
-0.0229949951171875,
0.023895263671875,
0.00998687744140625,
0.0184478759765625,
-0.0430908203125,
0.0005359649658203125,
-0.00894927978515625,
0.0074462890625,
0.005702972412109375,
-0.0028476715087890625,
-0.00988006591796875,
0.00911712646484375,
0.0290374755859375,
-0.036163330078125,
-0.047760009765625,
-0.00859832763671875,
0.0033779144287109375,
0.02838134765625,
-0.01654052734375,
-0.009521484375,
-0.0103912353515625,
0.004009246826171875,
-0.0023403167724609375,
-0.0272979736328125,
0.0205078125,
-0.0298919677734375,
0.0156707763671875,
0.023101806640625,
-0.0024127960205078125,
-0.03643798828125,
0.03607177734375,
0.038360595703125,
-0.01145172119140625,
-0.009063720703125,
-0.0121612548828125,
-0.015045166015625,
0.024993896484375,
0.0221405029296875,
0.0167236328125,
0.035614013671875,
0.02410888671875,
0.034820556640625,
-0.0111083984375,
-0.0011758804321289062,
0.025482177734375,
-0.00824737548828125,
-0.0104522705078125,
0.007740020751953125,
0.0029087066650390625,
0.0048370361328125,
-0.0210418701171875,
-0.0182342529296875,
-0.0097503662109375,
-0.008056640625,
0.0198974609375,
0.0223236083984375,
0.047698974609375,
-0.005260467529296875,
-0.025146484375,
-0.0202789306640625,
-0.032257080078125,
-0.01268768310546875,
-0.0230865478515625,
0.004009246826171875,
0.020263671875,
-0.006244659423828125,
0.019561767578125,
0.007122039794921875,
-0.00981903076171875,
0.0193634033203125,
-0.01158905029296875,
0.0096893310546875,
0.01100921630859375,
0.0163421630859375,
0.022674560546875,
0.01013946533203125,
-0.0238037109375,
0.021209716796875,
0.017608642578125,
0.006977081298828125,
-0.0253448486328125,
0.0033855438232421875,
0.0006899833679199219,
0.01132965087890625,
0.004703521728515625,
-0.007343292236328125,
0.01000213623046875,
-0.0189971923828125,
-0.0142669677734375,
-0.01393890380859375,
0.0008459091186523438,
0.0160369873046875,
0.006244659423828125,
0.0006246566772460938,
0.019500732421875,
-0.01824951171875,
0.0132293701171875,
0.0197296142578125,
0.004886627197265625,
-0.0178680419921875,
0.01007843017578125,
0.01461029052734375,
-0.03350830078125,
-0.0199737548828125,
-0.020294189453125,
-0.0057830810546875,
0.00154876708984375,
-0.0247802734375,
-0.01311492919921875,
-0.003368377685546875,
0.0249786376953125,
-0.034332275390625,
0.010650634765625,
0.01462554931640625,
-0.02508544921875,
0.027374267578125,
0.006237030029296875,
-0.01413726806640625,
0.040435791015625,
0.00902557373046875,
-0.01523590087890625,
-0.0007143020629882812,
0.003986358642578125,
-0.0233001708984375,
-0.011322021484375,
0.0007715225219726562,
-0.0301666259765625,
-0.00696563720703125,
0.01371002197265625,
-0.00308990478515625,
-0.0205841064453125,
-0.01366424560546875,
0.00295257568359375,
-0.01309967041015625,
0.002788543701171875,
-0.03717041015625,
-0.0009312629699707031,
0.000025391578674316406,
-0.0003597736358642578,
0.0086669921875,
0.0024509429931640625,
-0.0295867919921875,
-0.01160430908203125,
-0.0137481689453125,
0.004642486572265625,
-0.035614013671875,
-0.0216064453125,
0.01568603515625,
0.01800537109375,
0.0003859996795654297,
0.0360107421875,
0.0092620849609375,
-0.00670623779296875,
0.01751708984375,
-0.032928466796875,
0.00839996337890625,
-0.0293121337890625,
0.002887725830078125,
-0.00678253173828125,
0.03662109375,
0.02923583984375,
-0.01316070556640625,
-0.0254669189453125,
0.0085906982421875,
-0.004764556884765625,
0.0080413818359375,
-0.026031494140625,
-0.01354217529296875,
0.014251708984375,
0.0009675025939941406,
0.0499267578125,
0.01428985595703125,
-0.0009655952453613281,
-0.0024051666259765625,
0.020599365234375,
-0.0037021636962890625,
0.0269622802734375,
-0.00931549072265625,
-0.01305389404296875,
-0.00620269775390625,
0.021728515625,
0.007568359375,
0.026458740234375,
-0.01081085205078125,
-0.00737762451171875,
-0.01849365234375,
-0.0169525146484375,
0.01611328125,
-0.014312744140625,
-0.03497314453125,
0.008331298828125,
-0.044342041015625,
0.01279449462890625,
0.00811767578125,
0.0029239654541015625,
-0.0001856088638305664,
-0.01067352294921875,
0.049468994140625,
0.006984710693359375,
-0.00905609130859375,
-0.00445556640625,
-0.00977325439453125,
-0.002597808837890625,
-0.0022716522216796875,
-0.020172119140625,
-0.01200103759765625,
-0.0262298583984375,
0.00672149658203125,
0.00013625621795654297,
-0.01385498046875,
0.0301971435546875,
-0.0023784637451171875,
0.020477294921875,
0.00954437255859375,
0.0200653076171875,
0.00952911376953125,
0.0426025390625,
-0.0052032470703125,
-0.001132965087890625,
-0.009246826171875,
-0.053985595703125,
0.0005936622619628906,
0.00940704345703125,
-0.004314422607421875,
0.0137786865234375,
0.0200653076171875,
0.0220947265625,
-0.00933837890625,
-0.0147247314453125,
-0.0259552001953125,
-0.006824493408203125,
-0.0015287399291992188,
-0.0085296630859375,
0.00838470458984375,
-0.0010862350463867188,
-0.00936126708984375,
0.03607177734375,
0.008453369140625,
0.0233001708984375,
-0.00846099853515625,
-0.01064300537109375,
0.025665283203125,
-0.0181884765625,
-0.01264190673828125,
-0.018768310546875,
0.0189361572265625,
-0.01123046875,
-0.0126495361328125,
0.01396942138671875,
0.01403045654296875,
0.005786895751953125,
-0.01403045654296875,
0.01055145263671875,
0.017913818359375,
0.019927978515625,
0.0069580078125,
-0.0022945404052734375,
0.0419921875,
0.011383056640625,
0.015167236328125,
-0.00722503662109375,
-0.003917694091796875,
-0.00939178466796875,
0.022186279296875,
0.0252227783203125,
-0.0099639892578125,
-0.006008148193359375,
-0.0014276504516601562,
-0.01319122314453125,
-0.035614013671875,
-0.008880615234375,
-0.0037689208984375,
0.00013387203216552734,
-0.019775390625,
-0.00585174560546875,
-0.0128326416015625,
0.0057830810546875,
-0.0189971923828125,
0.02069091796875,
0.01255035400390625,
-0.0039215087890625,
-0.031341552734375,
-0.031585693359375,
0.0001518726348876953,
0.039031982421875,
-0.01403045654296875,
-0.01459503173828125,
-0.0019283294677734375,
-0.0037670135498046875,
-0.031982421875,
0.0270843505859375,
-0.0084991455078125,
-0.0269622802734375,
0.0024280548095703125,
0.003246307373046875,
-0.0221099853515625,
-0.001033782958984375,
-0.0297088623046875,
-0.0028362274169921875,
-0.0021877288818359375,
-0.00724029541015625,
0.0201416015625,
0.020233154296875,
-0.00621795654296875,
-0.0195770263671875,
0.005901336669921875,
0.0018014907836914062,
0.035308837890625,
0.03619384765625,
-0.038604736328125,
-0.015228271484375,
-0.013427734375,
-0.006435394287109375,
-0.01544952392578125,
0.00904083251953125,
0.0117034912109375,
-0.0107574462890625,
0.0014095306396484375,
0.0205078125,
-0.037139892578125,
-0.011962890625,
0.01129913330078125,
0.01422882080078125,
-0.006893157958984375,
-0.020172119140625,
-0.0010118484497070312,
-0.035888671875,
0.025115966796875,
-0.00606536865234375,
0.0151214599609375,
0.00577545166015625,
0.01454925537109375,
0.0012617111206054688,
0.0076904296875,
-0.01068115234375,
-0.037261962890625,
0.01239013671875,
-0.01007843017578125,
-0.0143890380859375,
-0.016845703125,
0.0023670196533203125,
-0.0185546875,
-0.004596710205078125,
0.01035308837890625,
0.0364990234375,
0.0005016326904296875,
0.04241943359375,
0.007694244384765625,
-0.01824951171875,
-0.0102691650390625,
-0.0159149169921875,
-0.02008056640625,
0.0030765533447265625,
0.002490997314453125,
0.01641845703125,
-0.00914764404296875,
-0.0251617431640625,
0.01364898681640625,
-0.02459716796875,
-0.006694793701171875,
0.0098876953125,
0.006610870361328125,
0.032257080078125,
0.0166015625,
0.0175933837890625,
-0.0267181396484375,
-0.00481414794921875,
-0.03656005859375,
-0.0007853507995605469,
0.0173797607421875,
-0.025421142578125,
-0.00707244873046875,
0.01153564453125,
0.01421356201171875,
-0.01035308837890625,
0.007965087890625,
-0.012237548828125,
-0.0031452178955078125,
0.0089111328125,
0.00197601318359375,
0.0140228271484375,
0.031280517578125,
0.0127105712890625,
-0.00528717041015625,
-0.004901885986328125,
0.034576416015625,
-0.004802703857421875,
-0.00936126708984375,
0.0167999267578125,
0.01409149169921875,
0.0416259765625,
-0.00453948974609375,
-0.004852294921875,
-0.02301025390625,
-0.03955078125,
0.01139068603515625,
-0.0159149169921875,
0.0214385986328125,
0.00627899169921875,
-0.0036411285400390625,
0.0460205078125,
0.0106201171875,
-0.00959014892578125,
0.014892578125,
0.0029468536376953125,
-0.0035305023193359375,
0.0303955078125,
0.03076171875,
0.005405426025390625,
0.0167388916015625,
0.0233917236328125,
0.01702880859375,
-0.0135650634765625,
-0.03155517578125,
-0.025604248046875,
-0.0187835693359375,
-0.013519287109375,
0.0117340087890625,
0.0105743408203125,
0.0153045654296875,
-0.04400634765625,
0.02142333984375,
-0.01226806640625,
-0.0111083984375,
0.0025539398193359375,
0.0038700103759765625,
0.0190582275390625,
-0.0252532958984375,
-0.0202484130859375,
0.0116119384765625,
0.0240325927734375,
-0.00562286376953125,
-0.021697998046875,
-0.0258026123046875,
-0.01357269287109375,
-0.0193328857421875,
0.0193939208984375,
0.039642333984375,
0.00484466552734375,
0.00005543231964111328,
-0.0146942138671875,
-0.00325775146484375,
-0.01436614990234375,
0.024444580078125,
0.046966552734375,
0.038177490234375,
0.0186767578125,
0.0061798095703125,
-0.029083251953125,
-0.0251312255859375,
0.020355224609375,
0.0045623779296875,
-0.00927734375,
0.0273590087890625,
-0.0174560546875,
-0.002338409423828125,
-0.00435638427734375,
-0.051910400390625,
0.00807952880859375,
-0.01256561279296875,
-0.01454925537109375,
-0.0310516357421875,
-0.01493072509765625,
0.01457977294921875,
-0.048309326171875,
0.002513885498046875,
0.0252532958984375,
0.026336669921875,
-0.04266357421875,
0.01561737060546875,
-0.00495147705078125,
-0.03900146484375,
0.010223388671875,
-0.0185546875,
-0.00984954833984375,
0.00665283203125,
0.035552978515625,
-0.0021648406982421875,
-0.0262603759765625,
-0.01410675048828125,
0.006946563720703125,
0.01139068603515625,
0.01511383056640625,
0.0021648406982421875,
-0.027191162109375,
-0.0050201416015625,
0.00827789306640625,
-0.01213836669921875,
0.00977325439453125,
0.007232666015625,
0.022247314453125,
0.055877685546875,
-0.0034046173095703125,
0.03558349609375,
-0.007755279541015625,
0.0050201416015625,
-0.017303466796875,
-0.016082763671875,
0.00759124755859375,
0.0161895751953125,
0.02972412109375,
0.0105743408203125,
-0.0308074951171875,
0.0230255126953125,
-0.01470184326171875,
0.0012941360473632812,
-0.0019130706787109375,
-0.0147857666015625,
0.0125579833984375,
0.0159149169921875,
0.021728515625,
-0.0079193115234375,
-0.0146636962890625,
0.00841522216796875,
0.0258026123046875,
-0.032562255859375,
-0.011199951171875,
-0.007640838623046875,
0.003421783447265625,
-0.0218658447265625,
-0.00910186767578125,
0.0266876220703125,
-0.012420654296875,
-0.0246429443359375,
-0.0105438232421875,
-0.013092041015625,
-0.020965576171875,
0.0244140625,
0.003787994384765625,
-0.01116180419921875,
0.035369873046875,
0.0087432861328125,
0.0149688720703125,
0.004489898681640625,
0.0050506591796875,
-0.005413055419921875,
0.00501251220703125,
0.003299713134765625,
-0.0233306884765625,
0.0152587890625,
-0.03680419921875,
0.067138671875,
0.007625579833984375,
-0.02655029296875,
0.034271240234375,
0.0011262893676757812,
0.0491943359375,
0.01410675048828125,
-0.0127105712890625,
-0.010223388671875,
0.007808685302734375,
0.0013513565063476562,
0.004650115966796875,
-0.01506805419921875,
-0.00722503662109375,
-0.00008928775787353516,
-0.0134124755859375,
0.0246734619140625,
0.02410888671875,
0.02178955078125,
0.01131439208984375,
0.0202484130859375,
-0.03192138671875,
0.040435791015625,
0.005908966064453125,
-0.010284423828125,
0.01262664794921875,
0.036529541015625,
0.0173187255859375,
0.02032470703125,
0.001232147216796875,
-0.0325927734375,
-0.01236724853515625,
-0.002582550048828125,
0.0269622802734375,
0.0005698204040527344,
0.0219268798828125,
-0.006389617919921875,
-0.01163482666015625,
-0.0083770751953125,
-0.012237548828125,
-0.0214385986328125,
0.01424407958984375,
-0.0271148681640625,
-0.03594970703125,
0.01259613037109375,
-0.0498046875,
-0.023956298828125,
0.0037250518798828125,
-0.0286407470703125,
0.0293731689453125,
0.02935791015625,
-0.00714874267578125,
-0.0162506103515625,
0.0235443115234375,
0.025146484375,
0.018585205078125,
-0.0005960464477539062,
0.00812530517578125,
0.00138092041015625,
-0.025177001953125,
0.01641845703125,
-0.0224456787109375,
-0.01409912109375,
0.0145416259765625,
0.0012598037719726562,
0.033111572265625,
-0.01102447509765625,
-0.01110076904296875,
-0.0121002197265625,
0.00738525390625,
-0.00787353515625,
0.01389312744140625,
-0.00574493408203125,
-0.0256195068359375,
0.0259857177734375,
0.0022220611572265625,
-0.03253173828125,
0.0007476806640625,
0.0075531005859375,
-0.0126800537109375,
-0.01678466796875,
-0.0241851806640625,
0.002201080322265625,
-0.0777587890625,
-0.01445770263671875,
0.01336669921875,
0.01099395751953125,
-0.012237548828125,
-0.00858306884765625,
0.0227508544921875,
0.013885498046875,
0.01263427734375,
-0.004451751708984375,
-0.0291900634765625,
-0.0298004150390625,
0.00119781494140625,
-0.00017750263214111328,
0.0212554931640625,
0.016204833984375,
-0.0077972412109375,
0.0032711029052734375,
0.042999267578125,
-0.039398193359375,
-0.0190277099609375,
0.0167236328125,
-0.026397705078125,
0.00968170166015625,
0.02728271484375,
0.00258636474609375,
0.0191192626953125,
-0.01519012451171875,
0.0301971435546875,
0.02581787109375,
-0.0297088623046875,
-0.0081634521484375,
0.006900787353515625,
-0.0286712646484375,
0.0191650390625,
0.01873779296875,
-0.0011577606201171875,
-0.01102447509765625,
-0.003604888916015625,
-0.0061798095703125,
0.006206512451171875,
-0.0006623268127441406,
0.0128021240234375,
0.007587432861328125,
-0.00839996337890625,
0.013519287109375,
-0.005413055419921875,
-0.0009393692016601562,
-0.0017452239990234375,
0.0156707763671875,
0.0241851806640625,
-0.005428314208984375,
-0.0004105567932128906,
0.00550079345703125,
-0.0093231201171875,
0.0097198486328125,
-0.00713348388671875,
0.002597808837890625,
-0.03076171875,
-0.00824737548828125,
0.0169677734375,
0.011810302734375,
-0.01641845703125,
-0.0231781005859375,
-0.041015625,
-0.039764404296875,
-0.0014886856079101562,
0.0178985595703125,
-0.00167083740234375,
-0.005252838134765625,
-0.0406494140625,
0.040008544921875,
0.01087188720703125,
-0.01885986328125,
0.0231475830078125,
-0.018707275390625,
-0.00004214048385620117,
0.003753662109375,
0.006404876708984375,
0.007537841796875,
-0.0288238525390625,
0.005893707275390625,
-0.0302886962890625,
-0.004810333251953125,
0.009552001953125,
-0.022796630859375,
-0.00910186767578125,
0.00627899169921875,
-0.0230712890625,
-0.0163421630859375,
0.0252227783203125,
0.0038242340087890625,
0.01285552978515625,
0.0194091796875,
-0.00635528564453125,
0.020355224609375,
0.008514404296875,
-0.039886474609375,
0.0038318634033203125,
0.00164031982421875,
0.016845703125,
0.0200042724609375,
-0.0033512115478515625,
-0.0219268798828125,
-0.02728271484375,
0.0206298828125,
-0.01129913330078125,
-0.0254669189453125,
0.0164794921875,
-0.0306854248046875,
0.003406524658203125,
-0.0018262863159179688,
-0.0014448165893554688,
-0.00923919677734375,
0.014068603515625,
-0.020660400390625,
0.0343017578125,
0.0003268718719482422,
0.0008034706115722656,
-0.005878448486328125,
0.0171051025390625,
0.0011768341064453125,
-0.00640106201171875,
0.0094146728515625,
-0.03643798828125,
-0.01036834716796875,
0.0220794677734375,
0.013397216796875,
-0.0277862548828125,
-0.01380157470703125,
0.00341796875,
-0.0170745849609375,
0.0016527175903320312,
-0.0276031494140625,
-0.0177459716796875,
0.002544403076171875,
-0.0008082389831542969,
0.0150299072265625,
-0.008544921875,
-0.020599365234375,
0.011993408203125,
-0.035003662109375,
-0.04974365234375,
-0.022857666015625,
0.016021728515625,
0.018463134765625,
-0.01383209228515625,
-0.006763458251953125,
0.0262603759765625,
0.0227203369140625,
-0.02301025390625,
-0.0121002197265625,
-0.0028324127197265625,
0.0086822509765625,
0.0181732177734375,
-0.0023517608642578125,
-0.018646240234375,
-0.007579803466796875,
0.00827789306640625,
-0.0018987655639648438,
0.0237579345703125,
0.0022640228271484375,
0.0212554931640625,
0.004367828369140625,
-0.0197601318359375,
0.0009665489196777344,
-0.0035400390625,
0.020721435546875,
-0.009613037109375,
0.00954437255859375,
-0.034423828125,
-0.0238037109375,
-0.01099395751953125,
-0.004459381103515625,
0.00080108642578125,
-0.00780487060546875,
0.01422119140625,
0.00893402099609375,
-0.0173492431640625,
0.01605224609375,
-0.0253143310546875,
-0.0267486572265625,
-0.0012683868408203125,
-0.0007257461547851562,
-0.01165771484375,
-0.0268402099609375,
-0.04046630859375,
0.01053619384765625,
-0.0115509033203125,
0.04779052734375,
-0.00920867919921875,
-0.0135955810546875,
-0.0110015869140625,
0.003082275390625,
0.00921630859375,
-0.030029296875,
-0.0036563873291015625,
0.02947998046875,
-0.007549285888671875,
-0.03387451171875,
0.0214080810546875,
0.0292205810546875,
-0.021240234375,
-0.009552001953125,
-0.01336669921875,
-0.0053558349609375,
0.0445556640625,
-0.00186920166015625,
0.0062713623046875,
0.004680633544921875,
0.0086822509765625,
0.0325927734375,
0.009307861328125,
0.0186920166015625,
0.0060577392578125,
-0.0178985595703125,
-0.03125,
-0.032135009765625,
-0.0166168212890625,
-0.0254058837890625,
0.00814056396484375,
-0.001842498779296875,
0.03363037109375,
-0.0333251953125,
0.0194091796875,
-0.0025081634521484375,
0.00872802734375,
-0.011627197265625,
-0.0034923553466796875,
-0.02020263671875,
-0.0256805419921875,
-0.006092071533203125,
-0.030792236328125,
-0.01251220703125,
0.0011425018310546875,
0.00858306884765625,
0.0235748291015625,
-0.01334381103515625,
-0.0150299072265625,
-0.01502227783203125,
0.005237579345703125,
-0.01097869873046875,
-0.01369476318359375,
-0.0174407958984375,
0.00820159912109375,
-0.020111083984375,
-0.037078857421875,
-0.012725830078125,
0.007518768310546875,
0.021484375,
-0.0280303955078125,
-0.004451751708984375,
-0.0121307373046875,
0.004474639892578125,
-0.003673553466796875,
-0.003269195556640625,
-0.0012836456298828125,
0.00991058349609375,
0.00811004638671875,
-0.0003826618194580078,
0.005908966064453125,
0.00824737548828125,
0.0223388671875,
-0.018829345703125,
-0.007415771484375,
0.00921630859375,
-0.029144287109375,
-0.00901031494140625,
-0.0117950439453125,
-0.00431060791015625,
-0.01517486572265625,
0.0185699462890625,
-0.0009303092956542969,
-0.00933837890625,
0.006870269775390625,
0.0084686279296875,
-0.0015306472778320312,
0.0084228515625,
-0.0303192138671875,
-0.0031452178955078125,
-0.0078887939453125,
-0.0012674331665039062,
-0.043243408203125,
-0.0063934326171875,
-0.005886077880859375,
-0.0035152435302734375,
-0.040618896484375,
-0.007732391357421875,
-0.005039215087890625,
-0.0147857666015625,
0.03314208984375,
-0.01273345947265625,
-0.036407470703125,
0.0231781005859375,
-0.021026611328125,
0.00641632080078125,
0.0283660888671875,
-0.01070404052734375,
-0.001708984375,
-0.003536224365234375,
0.04180908203125,
-0.0277862548828125,
-0.01374053955078125,
0.015899658203125,
-0.000598907470703125,
0.0218353271484375,
-0.012664794921875,
0.0036067962646484375,
0.0025539398193359375,
0.002796173095703125,
-0.0191497802734375,
-0.01264190673828125,
0.0289306640625,
0.01947021484375,
-0.01116943359375,
0.015289306640625,
0.0291748046875,
-0.006916046142578125,
-0.0143890380859375,
0.004001617431640625,
0.032867431640625,
0.0177459716796875,
0.0131072998046875,
0.004486083984375,
-0.006160736083984375,
-0.017913818359375,
0.0086822509765625,
0.00017392635345458984,
-0.0281982421875,
0.01285552978515625,
0.00551605224609375,
0.021270751953125,
-0.0273284912109375,
-0.03857421875,
0.0193939208984375,
-0.04925537109375,
-0.012542724609375,
-0.02203369140625,
-0.002773284912109375,
-0.0269622802734375,
-0.00634765625,
-0.01123046875,
-0.0157318115234375,
-0.02313232421875,
0.0207672119140625,
-0.00547027587890625,
0.0006413459777832031,
0.0148773193359375,
0.0054473876953125,
0.0028476715087890625,
-0.02667236328125,
0.033935546875,
0.01030731201171875,
0.0219573974609375,
0.01544952392578125,
0.004108428955078125,
0.0172271728515625,
0.0018682479858398438,
0.0021572113037109375,
-0.0184478759765625,
-0.0276031494140625,
0.0164947509765625,
0.03240966796875,
-0.00670623779296875,
-0.01226806640625,
0.02734375,
0.00726318359375,
-0.030487060546875,
-0.0211334228515625,
0.01336669921875,
-0.0285491943359375,
0.0143280029296875,
0.0268707275390625,
-0.04266357421875,
-0.019805908203125,
0.0286712646484375,
-0.0016050338745117188,
0.00785064697265625,
-0.005046844482421875,
0.0167388916015625,
0.0167999267578125,
0.03424072265625,
-0.0219573974609375,
0.0016460418701171875,
0.0219268798828125,
-0.027618408203125,
0.01220703125,
0.006443023681640625,
-0.0294036865234375,
0.0036067962646484375,
-0.0170440673828125,
-0.04315185546875,
0.00292205810546875,
0.0035495758056640625,
0.004245758056640625,
0.01430511474609375,
0.01076507568359375,
-0.00870513916015625,
0.015350341796875,
-0.03900146484375,
0.0255126953125,
0.0338134765625,
-0.00440216064453125,
0.01561737060546875,
-0.03326416015625,
-0.00786590576171875,
-0.003856658935546875,
0.0024623870849609375,
-0.01319122314453125,
-0.0154266357421875,
0.01169586181640625,
0.048095703125,
0.02362060546875,
0.0102081298828125,
-0.002223968505859375,
0.0084991455078125,
-0.0024280548095703125,
0.019012451171875,
-0.033355712890625,
0.0178375244140625,
0.015289306640625,
-0.0191192626953125,
-0.025054931640625,
-0.0179901123046875,
0.03228759765625,
-0.0171966552734375,
-0.019744873046875,
-0.0036449432373046875,
0.040435791015625,
-0.00982666015625,
0.014739990234375,
0.0153656005859375,
-0.031158447265625,
0.02288818359375,
0.040313720703125,
-0.010833740234375,
-0.026611328125,
0.036376953125,
-0.0025482177734375,
-0.00836944580078125,
0.02508544921875,
-0.00927734375,
0.01258087158203125,
-0.002925872802734375,
0.0416259765625,
0.0190277099609375,
0.00457763671875,
0.0145263671875,
-0.0178070068359375,
-0.0025386810302734375,
0.02508544921875,
0.01319122314453125,
-0.01373291015625,
-0.0181732177734375,
-0.032257080078125,
0.001972198486328125,
0.00768280029296875,
-0.014129638671875,
0.0058135986328125,
0.01540374755859375,
-0.003368377685546875,
0.02789306640625,
0.01050567626953125,
0.00799560546875,
0.007350921630859375,
0.031402587890625,
-0.016510009765625,
0.03961181640625,
-0.0234375,
-0.028228759765625,
0.0246124267578125,
-0.00583648681640625,
-0.0216217041015625,
0.0163726806640625,
-0.01000213623046875,
-0.004329681396484375,
-0.0186767578125,
0.0220489501953125,
0.026458740234375,
0.01971435546875,
-0.0159454345703125,
-0.001979827880859375,
-0.01091766357421875,
-0.0278472900390625,
-0.01275634765625,
-0.0083770751953125,
0.001171112060546875,
0.03460693359375,
0.0032215118408203125,
-0.0006909370422363281,
0.004436492919921875,
0.039642333984375,
-0.006160736083984375,
0.0030422210693359375,
0.005710601806640625,
-0.012115478515625,
0.034149169921875,
0.006072998046875,
-0.0204010009765625,
-0.0226593017578125,
0.0179901123046875,
-0.00540924072265625,
0.0516357421875,
-0.027435302734375,
0.01393890380859375,
-0.0054931640625,
0.003520965576171875,
0.00695037841796875,
-0.01016998291015625,
-0.00926971435546875,
0.004863739013671875,
0.01971435546875,
0.012542724609375,
-0.017303466796875,
0.01258087158203125,
-0.004695892333984375,
0.0305938720703125,
-0.00843048095703125,
-0.000659942626953125,
-0.0229339599609375,
0.0014743804931640625,
0.00980377197265625,
-0.0062408447265625,
-0.03131103515625,
-0.027130126953125,
-0.005870819091796875,
-0.021759033203125,
-0.00524139404296875,
0.007266998291015625,
-0.0308837890625,
0.01849365234375,
-0.0279541015625,
0.007740020751953125,
-0.0167388916015625,
-0.004062652587890625,
0.007778167724609375,
-0.01393890380859375,
0.0123748779296875,
-0.0025730133056640625,
-0.01061248779296875,
0.0028781890869140625,
0.040313720703125,
0.01165771484375,
-0.005290985107421875,
-0.0079345703125,
0.0367431640625,
-0.0211944580078125,
0.022308349609375,
0.006229400634765625,
-0.00690460205078125,
0.03021240234375,
0.002960205078125,
-0.0159149169921875,
-0.00804901123046875,
0.015869140625,
-0.024200439453125,
0.004486083984375,
-0.00795745849609375,
0.0421142578125,
-0.01511383056640625,
-0.0033359527587890625,
-0.015899658203125,
0.023162841796875,
0.0012369155883789062,
-0.0252838134765625,
0.0004608631134033203,
-0.03900146484375,
-0.0034084320068359375,
-0.0300750732421875,
-0.04217529296875,
-0.0024890899658203125,
-0.0194244384765625,
0.0211029052734375,
0.0202178955078125,
0.0076904296875,
-0.0118408203125,
0.0195770263671875,
-0.0003745555877685547,
-0.007602691650390625,
0.0198211669921875,
-0.003772735595703125,
-0.00839996337890625,
-0.001125335693359375,
0.0125579833984375,
0.01441192626953125,
-0.0201873779296875,
-0.0391845703125,
-0.004512786865234375,
-0.017059326171875,
-0.01224517822265625,
0.033905029296875,
-0.0169830322265625,
-0.0070343017578125,
0.0214996337890625,
-0.0024776458740234375,
-0.0219573974609375,
0.0094451904296875,
0.0128936767578125,
0.01427459716796875,
-0.0085296630859375,
0.0225677490234375,
-0.00884246826171875,
-0.00835418701171875,
0.0390625,
-0.0130615234375,
-0.02203369140625,
0.01457977294921875,
0.023773193359375,
0.01091766357421875,
0.0153961181640625,
-0.0095672607421875,
-0.003452301025390625,
0.0048065185546875,
0.02490234375,
0.024749755859375,
0.046630859375,
0.032958984375,
0.011932373046875,
-0.0035419464111328125,
0.028594970703125,
0.01142120361328125,
-0.01230621337890625,
-0.0007619857788085938,
0.01305389404296875,
0.0134735107421875,
0.008636474609375,
-0.0034313201904296875,
-0.010772705078125,
-0.00910186767578125,
-0.0029315948486328125,
-0.007537841796875,
0.00919342041015625,
-0.00711822509765625,
-0.0276336669921875,
-0.0153961181640625,
-0.0012302398681640625,
0.0269012451171875,
0.0179901123046875,
-0.0017938613891601562,
-0.0163421630859375,
-0.0313720703125,
-0.01611328125,
0.02325439453125,
-0.0227203369140625,
-0.01526641845703125,
0.005039215087890625,
0.034515380859375,
0.051025390625,
-0.031005859375,
0.01093292236328125,
-0.0006113052368164062,
0.034698486328125,
0.004852294921875,
-0.0229949951171875,
0.0015087127685546875,
0.032928466796875,
0.0181427001953125,
0.040863037109375,
0.01654052734375,
-0.0075225830078125,
0.01122283935546875,
-0.00421905517578125,
0.0037670135498046875,
-0.01070404052734375,
0.00472259521484375,
0.0275421142578125,
0.018218994140625,
0.017730712890625,
-0.0192413330078125,
-0.01450347900390625,
-0.02117919921875,
0.00746917724609375,
-0.013336181640625,
-0.02008056640625,
-0.0099029541015625,
-0.01392364501953125,
-0.0006527900695800781,
0.018707275390625,
-0.05364990234375,
-0.005809783935546875,
0.0018062591552734375,
0.02044677734375,
0.033843994140625,
0.0043792724609375,
-0.01494598388671875,
0.014801025390625,
-0.0079193115234375,
0.021148681640625,
-0.0161895751953125,
-0.00522613525390625,
0.0009889602661132812,
-0.0172882080078125,
0.001621246337890625,
-0.0172119140625,
0.01395416259765625,
0.045135498046875,
-0.0095062255859375,
-0.006153106689453125,
0.0129241943359375,
0.00650787353515625,
0.0247802734375,
-0.0386962890625,
0.00931549072265625,
0.015380859375,
0.021453857421875,
-0.00513458251953125,
-0.058380126953125,
0.01068878173828125,
0.00244903564453125,
0.0134735107421875,
0.035369873046875,
-0.00722503662109375,
0.010833740234375,
0.00811004638671875,
0.0005221366882324219,
0.00128173828125,
-0.0220184326171875,
-0.00559234619140625,
0.0216064453125,
0.0078887939453125,
0.004184722900390625,
-0.011688232421875,
-0.034423828125,
-0.0216064453125,
0.0228424072265625,
-0.0206451416015625,
0.00885009765625,
-0.00849151611328125,
-0.0007534027099609375,
0.014923095703125,
-0.01380157470703125,
-0.038787841796875,
-0.02203369140625,
0.0133514404296875,
0.0194854736328125,
0.04486083984375,
-0.0129241943359375,
-0.0218658447265625,
-0.01059722900390625,
0.033477783203125,
-0.0209808349609375,
0.034088134765625,
-0.0184478759765625,
-0.0033054351806640625,
-0.0199432373046875,
0.043060302734375,
-0.0036678314208984375,
-0.0281524658203125,
-0.0101776123046875,
-0.005931854248046875,
-0.00931549072265625,
0.0419921875,
-0.0037689208984375,
-0.01393890380859375,
-0.009124755859375,
-0.0161285400390625,
0.0269775390625,
-0.039520263671875,
0.0231781005859375,
-0.006931304931640625,
-0.01953125,
0.004261016845703125,
0.020416259765625,
0.012969970703125,
0.041290283203125,
-0.017303466796875,
0.013946533203125,
0.0101470947265625,
-0.0013208389282226562,
-0.036529541015625,
-0.0025768280029296875,
-0.0228118896484375,
-0.002178192138671875,
0.027740478515625,
-0.02490234375,
0.0218963623046875,
-0.04180908203125,
-0.0255126953125,
0.00555419921875,
-0.00852203369140625,
0.0163421630859375,
0.044921875,
0.0025787353515625,
-0.024658203125,
-0.0216064453125,
-0.0033092498779296875,
0.006389617919921875,
0.0015974044799804688,
-0.032073974609375,
0.01284027099609375,
-0.00821685791015625,
-0.00260162353515625,
-0.011474609375,
-0.0177459716796875,
-0.006359100341796875,
0.0200042724609375,
-0.0024127960205078125,
-0.0093231201171875,
0.0323486328125,
-0.0094451904296875,
-0.006237030029296875,
0.009185791015625,
0.019775390625,
0.004611968994140625,
0.01483917236328125,
-0.04827880859375,
0.00901031494140625,
0.021392822265625,
-0.0545654296875,
0.0038471221923828125,
-0.025482177734375,
0.0081634521484375,
0.01221466064453125,
-0.0104217529296875,
0.00482177734375,
-0.01328277587890625,
-0.0123748779296875,
0.0274810791015625,
0.0121612548828125,
-0.01422119140625,
-0.01849365234375,
-0.031646728515625,
-0.041900634765625,
0.0224609375,
0.0078887939453125,
0.0006208419799804688,
-0.040863037109375,
-0.0150909423828125,
-0.003170013427734375,
0.0103759765625,
-0.01325225830078125,
-0.00580596923828125,
-0.004398345947265625,
-0.02099609375,
-0.01296234130859375,
-0.003147125244140625,
-0.00170135498046875,
0.01239013671875,
0.0030975341796875,
-0.05224609375,
0.00205230712890625,
-0.0198974609375,
0.0262603759765625,
-0.00858306884765625,
-0.034820556640625,
-0.031951904296875,
0.0000020265579223632812,
0.031494140625,
0.01201629638671875,
0.0218505859375,
0.009063720703125,
-0.0548095703125,
-0.018341064453125,
-0.01113128662109375,
0.002166748046875,
0.024139404296875,
-0.0188446044921875,
0.02587890625,
0.02435302734375,
0.00226593017578125,
0.0243988037109375,
-0.0061798095703125,
-0.033111572265625,
-0.01291656494140625,
-0.0171966552734375,
-0.0031871795654296875,
-0.01097869873046875,
-0.007129669189453125,
-0.004863739013671875,
0.02105712890625,
-0.006526947021484375,
-0.0266265869140625,
-0.0143280029296875,
0.034912109375,
0.0134124755859375,
0.0026378631591796875,
-0.0027484893798828125,
-0.024566650390625,
-0.01300048828125
] |
ours_558
|
The answer is \(25\).
Suppose that \(r<\frac{50}{2}=25\). If the fly is on a vertex of the octahedron, then in the time it would take for the fly to crawl directly to one of the four adjacent vertices, each spider could possibly reach at most one vertex, thus stopping the fly from getting there. A spider can also block the fly by being on an edge adjacent to the fly's vertex, but again the spider blocks only one edge. Because there are only three spiders, the fly can always run to another vertex. This situation repeats indefinitely, so the fly is never caught.
If \(r>25\), then two spiders at the midpoints of opposite outer edges can contain the fly, each blocking two vertices. The third spider can catch the fly by making its way to the central vertex, cornering the fly on one of the four central edges. If \(r=25\), then the fly cannot definitely escape, though it's not guaranteed it gets caught, either. Regardless, our answer is \(c=25\).
\(\boxed{25}\)
|
25
|
{
"competition": "us_comps",
"dataset": "Ours",
"posts": null,
"source": "OMOSoln2.md"
}
|
A fly is being chased by three spiders on the edges of a regular octahedron. The fly has a speed of \(50\) meters per second, while each of the spiders has a speed of \(r\) meters per second. The spiders choose the (distinct) starting positions of all the bugs, with the requirement that the fly must begin at a vertex. Each bug knows the position of each other bug at all times, and the goal of the spiders is for at least one of them to catch the fly. What is the maximum \(c\) so that for any \(r<c\), the fly can always avoid being caught?
|
[
"/Mathematics/Geometry/GeneralGeometry/EuclideanGeometry",
"/Mathematics/Geometry/GeneralGeometry/Geometry",
"/Mathematics/Geometry/MultidimensionalGeometry/Polytopes/CrossPolytope",
"/Mathematics/Geometry/MultidimensionalGeometry/Polytopes/Hyperoctahedron",
"/Mathematics/Geometry/MultidimensionalGeometry/Polytopes/Polytope",
"/Mathematics/Geometry/SolidGeometry/Polyhedra/Octahedra",
"/Mathematics/Geometry/SolidGeometry/Polyhedra/PlatonicSolids",
"/Mathematics/RecreationalMathematics/Games/GameTheory/Game",
"/Mathematics/RecreationalMathematics/Puzzles/SpiderandFlyProblem"
] |
If a spider’s speed is less than half the fly’s, each spider can block only one of the four possible escape edges, so three spiders cannot seal all exits.
|
[
0.000025331974029541016,
0.0083770751953125,
0.0098724365234375,
-0.0462646484375,
-0.0000013113021850585938,
0.038330078125,
0.04803466796875,
-0.04351806640625,
0.01513671875,
0.0160675048828125,
0.01123809814453125,
-0.002048492431640625,
-0.0030193328857421875,
0.00019061565399169922,
-0.0037250518798828125,
0.00791168212890625,
-0.002605438232421875,
0.010162353515625,
-0.021240234375,
0.00038814544677734375,
-0.0206146240234375,
-0.031890869140625,
-0.07568359375,
-0.007114410400390625,
0.019775390625,
0.00669097900390625,
-0.0288543701171875,
0.0190277099609375,
-0.043304443359375,
0.01322174072265625,
-0.01371002197265625,
-0.00910186767578125,
-0.00653076171875,
0.003692626953125,
-0.0004680156707763672,
-0.01535797119140625,
0.01071929931640625,
0.00679779052734375,
0.0185546875,
-0.053436279296875,
-0.0012712478637695312,
-0.043609619140625,
0.0052490234375,
0.01471710205078125,
-0.055419921875,
0.035369873046875,
0.002353668212890625,
-0.0135345458984375,
0.006565093994140625,
-0.0111083984375,
-0.01187896728515625,
0.00542449951171875,
0.06988525390625,
-0.0127716064453125,
-0.01123046875,
-0.04840087890625,
0.002506256103515625,
-0.003326416015625,
0.003086090087890625,
0.0092010498046875,
0.00435638427734375,
0.00274658203125,
0.0200958251953125,
-0.01104736328125,
-0.00795745849609375,
-0.0070037841796875,
0.00469970703125,
-0.056060791015625,
0.007274627685546875,
-0.0151214599609375,
-0.01194000244140625,
0.034149169921875,
0.005603790283203125,
0.0099945068359375,
0.0321044921875,
-0.011993408203125,
-0.00736236572265625,
0.01236724853515625,
-0.002346038818359375,
0.0146484375,
0.0218353271484375,
0.00464630126953125,
0.0191650390625,
0.01152801513671875,
0.00640869140625,
-0.03570556640625,
0.0283355712890625,
-0.016876220703125,
0.0205230712890625,
-0.016265869140625,
0.000751495361328125,
0.0130157470703125,
0.011077880859375,
-0.0038127899169921875,
0.00310516357421875,
0.020721435546875,
0.019134521484375,
-0.00308990478515625,
-0.0076141357421875,
0.00289154052734375,
-0.005008697509765625,
-0.015838623046875,
0.0301971435546875,
-0.00225067138671875,
-0.0081024169921875,
-0.0081024169921875,
-0.00960540771484375,
0.01483917236328125,
-0.028472900390625,
0.0028591156005859375,
0.01529693603515625,
-0.00970458984375,
-0.0292205810546875,
0.016326904296875,
-0.017242431640625,
0.0099029541015625,
-0.034576416015625,
0.00435638427734375,
-0.010406494140625,
0.01259613037109375,
0.006927490234375,
-0.007610321044921875,
-0.00514984130859375,
0.01194000244140625,
-0.018463134765625,
-0.0421142578125,
-0.00675201416015625,
-0.024444580078125,
-0.0294952392578125,
0.00984954833984375,
-0.01116943359375,
0.019500732421875,
-0.01690673828125,
-0.0208587646484375,
-0.01360321044921875,
-0.006496429443359375,
0.0045623779296875,
0.005107879638671875,
0.008819580078125,
0.0002789497375488281,
0.0136260986328125,
-0.0031566619873046875,
0.0008602142333984375,
-0.00250244140625,
-0.019439697265625,
-0.0177764892578125,
0.0105743408203125,
-0.033294677734375,
0.0296630859375,
-0.00551605224609375,
-0.005401611328125,
-0.004817962646484375,
0.01708984375,
-0.006282806396484375,
-0.017425537109375,
0.0270843505859375,
-0.00962066650390625,
-0.012054443359375,
0.00240325927734375,
-0.0026531219482421875,
0.0056304931640625,
-0.0089263916015625,
0.0413818359375,
0.029815673828125,
0.007503509521484375,
0.0037593841552734375,
-0.0312042236328125,
0.00290679931640625,
-0.0101165771484375,
0.034454345703125,
0.009490966796875,
0.0016222000122070312,
0.003864288330078125,
-0.007320404052734375,
-0.0106048583984375,
0.003139495849609375,
-0.012969970703125,
0.0037212371826171875,
0.004505157470703125,
-0.010345458984375,
0.0123291015625,
-0.007781982421875,
0.05474853515625,
0.001712799072265625,
0.016693115234375,
-0.0019130706787109375,
0.00664520263671875,
-0.0026760101318359375,
0.017669677734375,
0.01103973388671875,
0.01145172119140625,
-0.015777587890625,
0.00693511962890625,
-0.01012420654296875,
-0.0003523826599121094,
0.0031452178955078125,
-0.01169586181640625,
-0.01739501953125,
0.0215301513671875,
0.0030612945556640625,
-0.01334381103515625,
-0.0051727294921875,
0.01459503173828125,
0.01119232177734375,
0.0207061767578125,
0.003582000732421875,
-0.01523590087890625,
-0.0016241073608398438,
0.009674072265625,
0.0019044876098632812,
0.023040771484375,
0.0024623870849609375,
-0.0023899078369140625,
0.0171966552734375,
-0.0004382133483886719,
-0.00986480712890625,
-0.00563812255859375,
-0.005146026611328125,
0.0081024169921875,
-0.026611328125,
0.0212554931640625,
-0.006969451904296875,
0.014129638671875,
0.00969696044921875,
-0.0156402587890625,
-0.0013322830200195312,
0.0134735107421875,
0.00748443603515625,
-0.00038886070251464844,
-0.00838470458984375,
0.01270294189453125,
-0.0012388229370117188,
-0.005954742431640625,
-0.02764892578125,
0.003498077392578125,
0.01009368896484375,
-0.0219573974609375,
-0.012115478515625,
-0.005878448486328125,
0.00487518310546875,
0.05902099609375,
-0.01345062255859375,
-0.0259552001953125,
-0.0063934326171875,
0.006633758544921875,
0.0020427703857421875,
-0.003353118896484375,
-0.004093170166015625,
-0.0156707763671875,
-0.021209716796875,
0.007762908935546875,
-0.006866455078125,
0.0196533203125,
-0.031494140625,
-0.0149993896484375,
0.0014171600341796875,
-0.01433563232421875,
0.0222625732421875,
-0.0101318359375,
0.036163330078125,
0.0061187744140625,
0.017730712890625,
0.0001285076141357422,
0.0095367431640625,
0.0178070068359375,
-0.036956787109375,
0.01280975341796875,
0.023406982421875,
0.01131439208984375,
-0.004055023193359375,
-0.0227508544921875,
0.004650115966796875,
-0.03375244140625,
0.0226593017578125,
0.0150909423828125,
-0.0012836456298828125,
0.01416778564453125,
0.009124755859375,
0.0144805908203125,
0.01552581787109375,
-0.0017070770263671875,
-0.0257720947265625,
0.003391265869140625,
-0.005123138427734375,
0.010833740234375,
-0.0145111083984375,
-0.0704345703125,
0.0036106109619140625,
-0.0006766319274902344,
0.00922393798828125,
0.00034356117248535156,
0.01422119140625,
0.0171966552734375,
-0.005695343017578125,
0.031890869140625,
0.0009555816650390625,
-0.01428985595703125,
0.0027675628662109375,
0.0021190643310546875,
-0.0030193328857421875,
0.007305145263671875,
-0.029205322265625,
0.021942138671875,
0.004520416259765625,
-0.005466461181640625,
0.03106689453125,
0.0097198486328125,
-0.00319671630859375,
-0.0251922607421875,
0.006801605224609375,
-0.0205230712890625,
-0.0015001296997070312,
0.01485443115234375,
-0.0111083984375,
-0.0208282470703125,
-0.05303955078125,
-0.002895355224609375,
0.004322052001953125,
-0.006595611572265625,
-0.02880859375,
0.0181884765625,
-0.0157928466796875,
0.01885986328125,
-0.0006270408630371094,
0.029144287109375,
0.008026123046875,
0.01064300537109375,
-0.00362396240234375,
-0.0031585693359375,
-0.0002689361572265625,
-0.00789642333984375,
0.006893157958984375,
-0.005939483642578125,
-0.021270751953125,
0.0017871856689453125,
0.0016193389892578125,
-0.0167694091796875,
0.03948974609375,
0.0198516845703125,
0.016265869140625,
-0.00818634033203125,
-0.0034885406494140625,
-0.0140838623046875,
-0.032257080078125,
0.004360198974609375,
0.005702972412109375,
-0.032958984375,
0.01264190673828125,
0.00679779052734375,
-0.01922607421875,
-0.0025634765625,
0.0023021697998046875,
0.0154266357421875,
0.0008754730224609375,
-0.03228759765625,
-0.01514434814453125,
0.020172119140625,
0.00899505615234375,
0.035247802734375,
0.0135955810546875,
0.0009946823120117188,
-0.0252685546875,
-0.0168304443359375,
-0.00104522705078125,
-0.001361846923828125,
0.0006346702575683594,
-0.00997161865234375,
-0.0005207061767578125,
-0.0413818359375,
-0.0169219970703125,
-0.00879669189453125,
0.01367950439453125,
0.0057830810546875,
0.0218048095703125,
0.00632476806640625,
0.007080078125,
0.0212860107421875,
-0.01496124267578125,
0.006671905517578125,
0.00463104248046875,
-0.021575927734375,
0.00749969482421875,
-0.03564453125,
0.01419830322265625,
0.0225372314453125,
-0.006076812744140625,
-0.00344085693359375,
-0.0322265625,
-0.0523681640625,
-0.0122222900390625,
-0.0045013427734375,
-0.0214080810546875,
-0.0110015869140625,
-0.0391845703125,
-0.00754547119140625,
0.0008540153503417969,
0.0027713775634765625,
0.03851318359375,
0.0185089111328125,
-0.005283355712890625,
-0.019317626953125,
0.00797271728515625,
-0.01515960693359375,
0.01277923583984375,
0.0209197998046875,
-0.00540924072265625,
-0.0014448165893554688,
0.056182861328125,
-0.00983428955078125,
0.0302734375,
-0.031463623046875,
-0.046844482421875,
0.0161285400390625,
-0.007598876953125,
-0.03643798828125,
0.0208587646484375,
0.0406494140625,
0.006641387939453125,
-0.049407958984375,
0.0080718994140625,
0.007801055908203125,
-0.0126953125,
-0.0275421142578125,
-0.0068817138671875,
0.03704833984375,
0.0260467529296875,
-0.054168701171875,
0.0267486572265625,
-0.018829345703125,
-0.0015010833740234375,
0.01074981689453125,
0.007099151611328125,
-0.01495361328125,
0.0418701171875,
-0.01898193359375,
-0.0017995834350585938,
0.022064208984375,
-0.0164642333984375,
-0.038330078125,
0.01568603515625,
-0.005191802978515625,
-0.0091705322265625,
0.00220489501953125,
-0.003665924072265625,
0.009429931640625,
-0.003650665283203125,
0.0218658447265625,
0.0019121170043945312,
0.0201263427734375,
-0.0347900390625,
0.029998779296875,
-0.06585693359375,
0.0352783203125,
-0.04248046875,
0.00478363037109375,
0.005184173583984375,
0.00809478759765625,
-0.0037937164306640625,
-0.03265380859375,
-0.05902099609375,
0.0015497207641601562,
-0.0218048095703125,
-0.040557861328125,
0.03961181640625,
0.0195159912109375,
-0.00637054443359375,
-0.0254364013671875,
0.0274505615234375,
0.044708251953125,
0.046661376953125,
0.007259368896484375,
-0.0250701904296875,
0.0049896240234375,
0.01171875,
-0.0277252197265625,
0.0301513671875,
0.00885009765625,
0.041412353515625,
0.01082611083984375,
-0.03302001953125,
-0.025115966796875,
0.0173492431640625,
0.04608154296875,
0.053680419921875,
0.015472412109375,
0.0012388229370117188,
0.0251312255859375,
0.018890380859375,
-0.01091766357421875,
-0.02362060546875,
0.0408935546875,
0.0036106109619140625,
0.0205230712890625,
-0.0228424072265625,
-0.01192474365234375,
0.0161590576171875,
0.0299224853515625,
0.0235748291015625,
0.01290130615234375,
-0.0213165283203125,
0.039825439453125,
-0.004787445068359375,
-0.003887176513671875,
0.00403594970703125,
-0.0170745849609375,
-0.0219573974609375,
0.0238189697265625,
-0.03955078125,
0.03314208984375,
0.0009446144104003906,
0.024444580078125,
0.0234832763671875,
0.0137481689453125,
-0.031951904296875,
0.0263519287109375,
-0.009429931640625,
0.00876617431640625,
-0.00872802734375,
0.01068115234375,
-0.0078582763671875,
-0.0170440673828125,
0.01450347900390625,
0.031036376953125,
0.002117156982421875,
-0.02386474609375,
0.028045654296875,
0.01250457763671875,
0.0469970703125,
0.01094818115234375,
-0.0095367431640625,
0.0162353515625,
-0.002803802490234375,
-0.015655517578125,
0.0012798309326171875,
-0.002899169921875,
-0.020660400390625,
0.0252227783203125,
-0.0195770263671875,
0.00809478759765625,
0.0159759521484375,
0.00264739990234375,
-0.0119476318359375,
0.0286712646484375,
-0.022125244140625,
0.00527191162109375,
-0.017730712890625,
0.0027923583984375,
0.0028591156005859375,
0.016845703125,
0.0122222900390625,
0.004711151123046875,
0.01358795166015625,
-0.02239990234375,
0.0001163482666015625,
0.0254974365234375,
-0.00035572052001953125,
-0.0021343231201171875,
-0.029083251953125,
0.0026493072509765625,
0.015533447265625,
0.01097869873046875,
0.01000213623046875,
0.0207672119140625,
0.025543212890625,
0.01531982421875,
-0.05828857421875,
-0.0026760101318359375,
-0.0124359130859375,
-0.0030117034912109375,
-0.0404052734375,
0.0179595947265625,
-0.00975799560546875,
0.0194854736328125,
0.02178955078125,
0.0006017684936523438,
0.0180511474609375,
-0.0085601806640625,
-0.016876220703125,
-0.014068603515625,
-0.012969970703125,
0.00983428955078125,
0.0037708282470703125,
0.00344085693359375,
-0.01666259765625,
0.0288848876953125,
-0.0234832763671875,
-0.004154205322265625,
0.007602691650390625,
0.00815582275390625,
-0.0050201416015625,
0.005023956298828125,
0.046417236328125,
0.020965576171875,
0.00824737548828125,
0.010223388671875,
-0.01213836669921875,
-0.01081085205078125,
0.027191162109375,
0.0202789306640625,
0.0160369873046875,
0.021270751953125,
-0.0254669189453125,
0.0002770423889160156,
-0.00402069091796875,
0.00913238525390625,
-0.0033702850341796875,
0.002758026123046875,
0.0025806427001953125,
-0.0006170272827148438,
-0.0017194747924804688,
-0.006458282470703125,
-0.001636505126953125,
-0.034820556640625,
0.045318603515625,
0.0167999267578125,
0.00661468505859375,
0.0022602081298828125,
-0.0126953125,
0.01152801513671875,
-0.0025539398193359375,
-0.013519287109375,
-0.00760650634765625,
0.0170135498046875,
0.055633544921875,
0.0204925537109375,
-0.035675048828125,
-0.0166473388671875,
-0.0309600830078125,
-0.008544921875,
-0.004497528076171875,
0.019317626953125,
0.0131683349609375,
-0.01343536376953125,
-0.002162933349609375,
-0.0143585205078125,
-0.0231781005859375,
-0.01959228515625,
-0.0241546630859375,
-0.00925445556640625,
0.034881591796875,
0.0157470703125,
-0.01239013671875,
0.02685546875,
-0.05023193359375,
-0.0289306640625,
0.01132965087890625,
-0.048004150390625,
-0.0037174224853515625,
-0.01291656494140625,
0.0008363723754882812,
-0.02264404296875,
-0.004627227783203125,
-0.0101165771484375,
-0.0034580230712890625,
0.0025920867919921875,
0.018951416015625,
0.0026187896728515625,
-0.035125732421875,
0.0033359527587890625,
0.005157470703125,
0.01451873779296875,
-0.01068878173828125,
-0.00572967529296875,
0.0215301513671875,
0.013671875,
-0.005702972412109375,
-0.01230621337890625,
-0.0213623046875,
-0.0035552978515625,
0.006153106689453125,
0.016815185546875,
-0.027923583984375,
0.0083465576171875,
-0.01528167724609375,
-0.0069122314453125,
0.034149169921875,
0.0157012939453125,
0.01338958740234375,
0.032928466796875,
0.003658294677734375,
-0.0188751220703125,
0.006816864013671875,
0.0191650390625,
-0.0109100341796875,
-0.0086212158203125,
0.050323486328125,
0.01480865478515625,
0.047607421875,
0.0063934326171875,
0.025726318359375,
0.00543212890625,
0.0071868896484375,
-0.011505126953125,
0.0263824462890625,
-0.01145172119140625,
0.00988006591796875,
-0.006824493408203125,
0.0325927734375,
-0.01214599609375,
-0.015716552734375,
0.0278778076171875,
0.00794219970703125,
0.0169677734375,
0.006839752197265625,
-0.02490234375,
-0.01407623291015625,
-0.01392364501953125,
-0.0152435302734375,
-0.03326416015625,
0.0169677734375,
-0.00850677490234375,
-0.0149688720703125,
-0.0293426513671875,
0.037384033203125,
0.0033397674560546875,
-0.0081024169921875,
-0.055999755859375,
-0.016937255859375,
0.0268707275390625,
0.004932403564453125,
-0.0288238525390625,
0.0014810562133789062,
0.0024852752685546875,
0.01023101806640625,
0.0003445148468017578,
0.0172119140625,
-0.031890869140625,
-0.0017728805541992188,
-0.050506591796875,
0.01019287109375,
0.007778167724609375,
-0.00431060791015625,
-0.0215301513671875,
-0.0024433135986328125,
-0.0105133056640625,
-0.026092529296875,
0.011749267578125,
-0.00811767578125,
-0.0024871826171875,
0.0198974609375,
0.02606201171875,
0.01151275634765625,
0.020538330078125,
-0.00046324729919433594,
-0.04669189453125,
0.00733184814453125,
-0.01171875,
0.01300811767578125,
0.01007080078125,
0.0146636962890625,
0.025970458984375,
-0.0012941360473632812,
0.0279083251953125,
-0.036102294921875,
-0.038665771484375,
0.0005517005920410156,
-0.00792694091796875,
-0.0070037841796875,
-0.01117706298828125,
-0.006755828857421875,
-0.01300048828125,
-0.0175628662109375,
0.0194854736328125,
-0.021636962890625,
0.03741455078125,
0.0017004013061523438,
-0.01006317138671875,
0.02593994140625,
0.0159149169921875,
-0.021820068359375,
-0.00901031494140625,
-0.0187530517578125,
-0.001522064208984375,
0.039398193359375,
0.0172882080078125,
-0.01403045654296875,
-0.03070068359375,
-0.01361083984375,
0.0131378173828125,
0.0004367828369140625,
0.0017042160034179688,
-0.0036067962646484375,
-0.034454345703125,
-0.0125732421875,
-0.0300140380859375,
-0.0252685546875,
-0.00879669189453125,
-0.0219879150390625,
0.03173828125,
-0.0190277099609375,
0.0081329345703125,
-0.02056884765625,
0.00176239013671875,
-0.0159759521484375,
0.0178985595703125,
-0.03662109375,
0.01837158203125,
-0.027130126953125,
0.0209197998046875,
-0.01306915283203125,
-0.039581298828125,
-0.0079193115234375,
0.00475311279296875,
0.0267791748046875,
0.0164337158203125,
0.00766754150390625,
-0.003509521484375,
0.023101806640625,
-0.023773193359375,
0.0263824462890625,
0.0038471221923828125,
-0.022796630859375,
-0.018096923828125,
0.004608154296875,
-0.005535125732421875,
0.0216064453125,
0.0136260986328125,
0.00882720947265625,
0.002567291259765625,
0.02593994140625,
0.0291595458984375,
0.0262603759765625,
-0.0119781494140625,
-0.01398468017578125,
0.01377105712890625,
0.01529693603515625,
-0.01251220703125,
-0.042816162109375,
-0.00981903076171875,
0.02117919921875,
0.023223876953125,
-0.0031070709228515625,
-0.016326904296875,
0.020233154296875,
-0.0258331298828125,
-0.003940582275390625,
0.040283203125,
-0.04559326171875,
-0.025360107421875,
0.00937652587890625,
0.0181884765625,
-0.0017900466918945312,
0.0249176025390625,
0.03814697265625,
0.037384033203125,
-0.0121612548828125,
0.0156707763671875,
-0.01486968994140625,
0.0091094970703125,
-0.004528045654296875,
0.00501251220703125,
0.04998779296875,
-0.04351806640625,
0.00601959228515625,
0.012054443359375,
0.03070068359375,
0.01190948486328125,
0.006107330322265625,
-0.010345458984375,
-0.030059814453125,
0.0090484619140625,
-0.02337646484375,
0.0226898193359375,
-0.05303955078125,
-0.005096435546875,
-0.02734375,
-0.0005779266357421875,
0.01186370849609375,
-0.03253173828125,
0.031707763671875,
0.0027637481689453125,
0.0036640167236328125,
0.0113983154296875,
0.03533935546875,
0.010345458984375,
0.03436279296875,
0.0013637542724609375,
0.012786865234375,
0.045013427734375,
-0.0286712646484375,
0.0146026611328125,
-0.014617919921875,
0.001804351806640625,
0.02484130859375,
-0.01396942138671875,
0.0088958740234375,
0.02471923828125,
-0.0144195556640625,
0.0047760009765625,
-0.0155487060546875,
0.01061248779296875,
0.02972412109375,
-0.007747650146484375,
-0.040283203125,
0.029693603515625,
-0.000621795654296875,
-0.0210723876953125,
-0.023345947265625,
-0.0129547119140625,
-0.00814056396484375,
-0.042327880859375,
0.02197265625,
0.0014057159423828125,
0.021636962890625,
-0.0025310516357421875,
-0.0233306884765625,
0.0032176971435546875,
0.0261383056640625,
0.015228271484375,
0.0211029052734375,
-0.01145172119140625,
0.0009717941284179688,
0.002956390380859375,
0.006145477294921875,
-0.009307861328125,
0.01540374755859375,
-0.019012451171875,
0.0140838623046875,
-0.0218353271484375,
0.0110626220703125,
-0.0017194747924804688,
-0.0080413818359375,
0.0118408203125,
0.00264739990234375,
0.06591796875,
-0.0200958251953125,
0.033233642578125,
0.007740020751953125,
0.006160736083984375,
0.005184173583984375,
-0.0094757080078125,
0.01493072509765625,
0.01812744140625,
-0.0213470458984375,
0.0113677978515625,
0.0165252685546875,
-0.006992340087890625,
-0.0008764266967773438,
0.015869140625,
-0.0289459228515625,
-0.004924774169921875,
0.0269622802734375,
0.011138916015625,
0.045806884765625,
-0.0050048828125,
-0.006832122802734375,
-0.01617431640625,
-0.0305328369140625,
-0.0046844482421875,
-0.01377105712890625,
0.003665924072265625,
0.00888824462890625,
-0.038330078125,
-0.0295257568359375,
-0.0157012939453125,
0.02142333984375,
0.0031299591064453125,
-0.006549835205078125,
-0.004398345947265625,
-0.0038013458251953125,
-0.00742340087890625,
0.0225830078125,
-0.00832366943359375,
0.01264190673828125,
-0.00556182861328125,
-0.0172119140625,
0.024932861328125,
-0.001293182373046875,
0.028472900390625,
0.0046539306640625,
0.019866943359375,
-0.001888275146484375,
0.00809478759765625,
-0.018341064453125,
-0.02001953125,
0.0085296630859375,
-0.01113128662109375,
0.018798828125,
0.04412841796875,
0.01214599609375,
-0.0111541748046875,
0.0260162353515625,
0.01493072509765625,
0.005451202392578125,
-0.018280029296875,
-0.017303466796875,
0.01210784912109375,
-0.0391845703125,
-0.0025997161865234375,
-0.0115814208984375,
0.007343292236328125,
0.019805908203125,
-0.005950927734375,
0.019073486328125,
-0.0006046295166015625,
0.0050811767578125,
-0.0369873046875,
0.0222930908203125,
0.03802490234375,
-0.0196685791015625,
-0.0050201416015625,
0.01220703125,
0.0202789306640625,
0.0008311271667480469,
0.0174102783203125,
-0.00591278076171875,
0.017852783203125,
-0.01425933837890625,
0.036285400390625,
0.00307464599609375,
0.0167694091796875,
0.0020008087158203125,
0.006015777587890625,
-0.0234222412109375,
-0.01128387451171875,
-0.0046844482421875,
-0.0203399658203125,
-0.01325225830078125,
-0.017425537109375,
-0.00899505615234375,
-0.00421142578125,
0.01526641845703125,
-0.021514892578125,
0.01328277587890625,
-0.0194091796875,
-0.0252685546875,
0.0182952880859375,
0.0214385986328125,
-0.01458740234375,
-0.03277587890625,
0.0195465087890625,
-0.0321044921875,
0.0097198486328125,
0.0029754638671875,
-0.0186309814453125,
-0.01226806640625,
0.004222869873046875,
0.0129241943359375,
-0.01457977294921875,
-0.018951416015625,
-0.0116424560546875,
0.0289459228515625,
0.00847625732421875,
-0.0031299591064453125,
0.004802703857421875,
-0.002838134765625,
0.0005335807800292969,
0.03509521484375,
-0.0260162353515625,
0.0007758140563964844,
0.0170745849609375,
0.005126953125,
-0.003498077392578125,
-0.0234222412109375,
0.0220947265625,
-0.006015777587890625,
-0.010589599609375,
0.0030612945556640625,
-0.029327392578125,
-0.0025844573974609375,
-0.01922607421875,
-0.000995635986328125,
-0.023773193359375,
0.004848480224609375,
0.0264739990234375,
0.01020050048828125,
-0.03350830078125,
-0.01041412353515625,
-0.00876617431640625,
0.03155517578125,
-0.01555633544921875,
0.027984619140625,
-0.0012311935424804688,
0.00853729248046875,
0.0061492919921875,
-0.0157928466796875,
0.00859832763671875,
-0.019134521484375,
-0.0038204193115234375,
0.005359649658203125,
-0.0210113525390625,
0.008209228515625,
-0.06463623046875,
0.0154266357421875,
0.020416259765625,
0.015869140625,
-0.0050201416015625,
-0.017059326171875,
-0.0270538330078125,
0.01357269287109375,
-0.01061248779296875,
0.0174102783203125,
-0.00209808349609375,
0.0293121337890625,
0.00499725341796875,
-0.021820068359375,
0.00798797607421875,
0.00626373291015625,
-0.01016998291015625,
-0.005458831787109375,
0.0282135009765625,
0.004680633544921875,
-0.0111846923828125,
-0.0018186569213867188,
0.01544952392578125,
-0.0026760101318359375,
-0.0010166168212890625,
0.01224517822265625,
-0.003665924072265625,
-0.006572723388671875,
0.02508544921875,
0.024810791015625,
-0.011383056640625,
-0.04443359375,
0.003612518310546875,
-0.0133209228515625,
-0.005367279052734375,
-0.025299072265625,
-0.0059051513671875,
0.0008993148803710938,
-0.0169830322265625,
0.0007305145263671875,
-0.0230560302734375,
0.00897216796875,
0.01416015625,
-0.04803466796875,
0.006561279296875,
-0.0239105224609375,
-0.004665374755859375,
0.00904083251953125,
-0.021026611328125,
0.019012451171875,
0.00910186767578125,
-0.0391845703125,
0.031402587890625,
-0.004314422607421875,
-0.029388427734375,
-0.00457000732421875,
0.01055908203125,
0.004138946533203125,
-0.00725555419921875,
0.02587890625,
-0.0008296966552734375,
-0.01904296875,
-0.007793426513671875,
0.01177215576171875,
-0.02972412109375,
0.032806396484375,
0.03240966796875,
0.0211029052734375,
-0.015899658203125,
0.0040130615234375,
0.00707244873046875,
-0.0009927749633789062,
-0.0341796875,
-0.0040283203125,
-0.01050567626953125,
-0.011749267578125,
0.0017652511596679688,
0.0231475830078125,
-0.0033893585205078125,
-0.0029926300048828125,
-0.00299835205078125,
-0.0168914794921875,
-0.04876708984375,
0.0026111602783203125,
-0.0006256103515625,
0.0018138885498046875,
-0.0278778076171875,
0.003932952880859375,
0.004589080810546875,
0.001255035400390625,
0.0161590576171875,
-0.026580810546875,
-0.0185546875,
0.0022869110107421875,
-0.0220794677734375,
0.0501708984375,
-0.01465606689453125,
-0.01959228515625,
0.0011043548583984375,
0.00556182861328125,
0.02655029296875,
0.045196533203125,
0.022186279296875,
0.0029010772705078125,
-0.0265350341796875,
-0.00281524658203125,
-0.04864501953125,
0.0222320556640625,
-0.0268707275390625,
-0.017303466796875,
0.00824737548828125,
-0.039398193359375,
-0.038421630859375,
-0.03741455078125,
-0.0231475830078125,
0.0010366439819335938,
-0.022674560546875,
0.002277374267578125,
0.015594482421875,
-0.006175994873046875,
-0.0034885406494140625,
0.004673004150390625,
0.005413055419921875,
0.041717529296875,
-0.01531219482421875,
0.004451751708984375,
-0.00949859619140625,
0.0469970703125,
0.0189361572265625,
0.0265655517578125,
0.003162384033203125,
0.0227813720703125,
0.00951385498046875,
-0.0018024444580078125,
0.0248565673828125,
0.0103607177734375,
0.0204315185546875,
-0.00295257568359375,
0.04412841796875,
-0.0166015625,
0.0183563232421875,
0.004871368408203125,
-0.01424407958984375,
0.00339508056640625,
-0.0161590576171875,
0.00333404541015625,
-0.01090240478515625,
-0.0230255126953125,
0.002361297607421875,
-0.00439453125,
-0.033721923828125,
-0.0222625732421875,
-0.0275421142578125,
0.00429534912109375,
-0.00955963134765625,
-0.0296630859375,
-0.00907135009765625,
0.00043654441833496094,
0.00981903076171875,
-0.0199432373046875,
0.0160675048828125,
0.0016565322875976562,
0.0036296844482421875,
0.006252288818359375,
-0.01465606689453125,
-0.0032215118408203125,
-0.0205230712890625,
0.023223876953125,
0.0208587646484375,
0.0487060546875,
-0.014556884765625,
-0.0165252685546875,
0.00909423828125,
-0.006824493408203125,
-0.0223388671875,
0.0209197998046875,
-0.031890869140625,
-0.0118560791015625,
-0.00592041015625,
0.02490234375,
-0.01198577880859375,
-0.012451171875,
0.0162353515625,
-0.0034236907958984375,
0.0301971435546875,
-0.002689361572265625,
-0.005344390869140625,
0.0005645751953125,
0.0255584716796875,
-0.005779266357421875,
-0.00760650634765625,
0.045654296875,
0.01412200927734375,
0.0189056396484375,
0.001750946044921875,
-0.01291656494140625,
-0.005329132080078125,
0.0073089599609375,
-0.045928955078125,
0.0162353515625,
-0.0180816650390625,
0.00963592529296875,
-0.013946533203125,
-0.024810791015625,
0.019866943359375,
0.012420654296875,
-0.0252227783203125,
-0.006927490234375,
0.034576416015625,
-0.0229339599609375,
-0.00872039794921875,
-0.00843048095703125,
0.01520538330078125,
0.0209503173828125,
0.0052032470703125,
-0.00710296630859375,
-0.01690673828125,
0.020843505859375,
-0.0183258056640625,
0.00418853759765625,
-0.010101318359375,
-0.01568603515625,
-0.020111083984375,
-0.0008969306945800781,
0.0003693103790283203,
-0.005428314208984375,
-0.014068603515625,
0.007076263427734375,
0.0020465850830078125,
-0.014617919921875,
0.028350830078125,
-0.0189056396484375,
0.0100860595703125,
-0.032073974609375,
0.003719329833984375,
-0.0158843994140625,
-0.005840301513671875,
-0.001026153564453125,
-0.01059722900390625,
0.019195556640625,
-0.024627685546875,
0.0017480850219726562,
0.034637451171875,
-0.03546142578125,
-0.028961181640625,
-0.00583648681640625,
-0.0013456344604492188,
0.0269317626953125,
-0.0017824172973632812,
-0.01611328125,
-0.021087646484375,
-0.0051422119140625,
-0.01096343994140625,
-0.002239227294921875,
-0.001850128173828125,
0.00888824462890625,
0.01519012451171875,
-0.00836944580078125,
-0.0291595458984375,
0.00870513916015625,
-0.05059814453125,
-0.0203399658203125,
0.0203857421875,
0.03314208984375,
-0.022674560546875,
-0.0091094970703125,
-0.005863189697265625,
0.00397491455078125,
0.0338134765625,
0.003387451171875,
0.0157012939453125,
0.01200103759765625,
-0.0024089813232421875,
0.0297088623046875,
0.01535797119140625,
0.0299224853515625,
0.04705810546875,
0.003368377685546875,
0.028778076171875,
-0.020233154296875,
-0.0003504753112792969,
-0.01331329345703125,
0.01885986328125,
-0.0034885406494140625,
0.03778076171875,
0.0018320083618164062,
-0.005706787109375,
0.0007715225219726562,
-0.01435089111328125,
0.00847625732421875,
0.0101318359375,
-0.0225677490234375,
0.0133514404296875,
0.01082611083984375,
0.013671875,
-0.01015472412109375,
-0.02191162109375,
-0.0208740234375,
-0.0025310516357421875,
-0.00995635986328125,
0.01528167724609375,
-0.0035114288330078125,
0.00885772705078125,
0.0179901123046875,
-0.01538848876953125,
-0.003631591796875,
0.005542755126953125,
0.0016508102416992188,
-0.01123046875,
-0.0186309814453125,
0.004795074462890625,
-0.0003039836883544922,
0.0056610107421875,
-0.028045654296875,
0.006214141845703125,
0.033203125,
-0.0155487060546875,
0.032989501953125,
0.0257110595703125,
0.0011272430419921875,
-0.0020084381103515625,
0.01800537109375,
0.0237884521484375,
0.0192108154296875,
-0.0447998046875,
0.00934600830078125,
0.00170135498046875,
-0.005809783935546875,
-0.0101165771484375,
-0.0079803466796875,
0.0178680419921875,
-0.0357666015625,
0.01806640625,
-0.0277862548828125,
-0.0151519775390625,
-0.00516510009765625,
0.0254669189453125,
0.0182037353515625,
0.005779266357421875,
-0.000377655029296875,
0.005767822265625,
-0.01244354248046875,
-0.02435302734375,
-0.01052093505859375,
0.0002551078796386719,
0.037506103515625,
-0.0072021484375,
-0.01003265380859375,
0.0187530517578125,
-0.01160430908203125,
0.009368896484375,
-0.0217742919921875,
-0.02349853515625,
0.004047393798828125,
0.051177978515625,
0.0267181396484375,
0.02032470703125,
0.0146942138671875,
-0.005428314208984375,
-0.015167236328125,
0.0010089874267578125,
0.0163726806640625,
-0.02166748046875,
0.0012121200561523438,
0.01560211181640625,
-0.00994873046875,
0.01415252685546875,
0.0018367767333984375,
-0.0298614501953125,
0.01030731201171875,
0.00597381591796875,
-0.005313873291015625,
0.0237884521484375,
0.003299713134765625,
-0.003971099853515625,
-0.0205230712890625,
0.01019287109375,
0.007419586181640625,
-0.061004638671875,
0.017120361328125,
-0.0009527206420898438,
0.0279388427734375,
0.004852294921875,
-0.005023956298828125,
-0.027923583984375,
-0.0014019012451171875,
-0.001232147216796875,
-0.0212249755859375,
0.01111602783203125,
0.004291534423828125,
0.0167083740234375,
0.0034503936767578125,
0.00414276123046875,
-0.0182037353515625,
0.01000213623046875,
-0.01727294921875,
-0.0214691162109375,
0.0083160400390625,
0.00484466552734375,
-0.0191802978515625,
0.01052093505859375,
0.0283660888671875,
0.004795074462890625,
-0.00778961181640625,
0.0183258056640625,
0.02337646484375,
-0.016204833984375,
-0.0281982421875,
-0.0036830902099609375,
-0.00960540771484375,
0.0224151611328125,
-0.0054473876953125,
0.022216796875,
0.00893402099609375,
0.0014524459838867188,
-0.0198516845703125,
-0.0012569427490234375,
-0.00860595703125,
0.0199432373046875,
0.0030040740966796875,
-0.0010089874267578125,
0.005619049072265625,
0.0224456787109375,
-0.02947998046875,
0.0279388427734375,
-0.017974853515625,
0.01715087890625,
-0.021484375,
-0.01178741455078125,
-0.009521484375,
0.036895751953125,
0.0089569091796875,
-0.048553466796875,
0.00577545166015625,
-0.01158905029296875,
-0.01788330078125,
0.016754150390625,
-0.0185089111328125,
0.0155487060546875,
0.01218414306640625,
-0.00640106201171875,
-0.0013570785522460938,
0.01953125,
0.002841949462890625,
0.036407470703125,
0.0158843994140625,
-0.0069732666015625,
-0.01430511474609375,
0.009735107421875,
-0.01336669921875,
0.0193634033203125,
0.01552581787109375,
-0.00565338134765625,
-0.035675048828125,
-0.007640838623046875,
0.0018634796142578125,
0.0226287841796875,
-0.00008809566497802734,
0.01386260986328125,
-0.0130157470703125,
-0.0101470947265625,
0.0100555419921875,
0.0242767333984375,
-0.0045166015625,
0.0171356201171875,
0.0177459716796875,
0.004398345947265625,
-0.02777099609375,
0.0127105712890625,
-0.0200042724609375,
-0.001178741455078125,
0.014434814453125,
-0.009552001953125,
0.0167236328125,
0.0175018310546875,
0.0218963623046875,
-0.03326416015625,
0.011322021484375,
-0.028778076171875,
0.018707275390625,
-0.01256561279296875,
0.0228271484375,
0.042205810546875,
-0.012298583984375,
-0.03387451171875,
-0.006717681884765625,
-0.034942626953125,
-0.008270263671875,
0.0029754638671875,
0.01145172119140625,
0.017333984375,
-0.0274810791015625,
-0.010406494140625,
0.012481689453125,
0.002079010009765625,
-0.00850677490234375,
0.0037899017333984375,
0.01531982421875,
0.0045318603515625,
0.0125885009765625,
0.01517486572265625,
0.004283905029296875,
0.049224853515625,
0.0206146240234375,
0.0160980224609375,
0.0009160041809082031,
0.007568359375,
-0.01009368896484375,
-0.031829833984375,
-0.0032444000244140625,
-0.01264190673828125,
0.00531768798828125,
0.023956298828125,
-0.0171051025390625,
0.0236358642578125,
0.030029296875,
-0.022003173828125,
-0.0273895263671875,
0.002513885498046875,
-0.016204833984375,
-0.0240020751953125,
0.029022216796875,
-0.0261993408203125,
-0.0162200927734375,
-0.0026874542236328125,
0.006679534912109375,
-0.0017290115356445312,
0.01505279541015625,
-0.01776123046875,
0.01081085205078125,
0.00676727294921875,
-0.0005979537963867188,
-0.019744873046875,
0.04217529296875,
0.008575439453125,
0.038177490234375,
-0.0230255126953125,
0.02056884765625,
0.055389404296875,
0.0193939208984375,
-0.0011510848999023438,
-0.0294952392578125,
0.043243408203125,
0.0206298828125,
0.025482177734375,
0.01837158203125,
-0.0075225830078125,
-0.006748199462890625,
0.0133056640625,
0.01078033447265625,
0.0005850791931152344,
-0.0014333724975585938,
0.00763702392578125,
-0.032257080078125,
-0.006988525390625,
0.03851318359375,
-0.006443023681640625,
0.007747650146484375,
0.0053558349609375,
0.004070281982421875,
0.02252197265625,
-0.00395965576171875,
-0.0185089111328125,
-0.01788330078125,
0.0017805099487304688,
0.0206146240234375,
-0.0262908935546875,
0.011505126953125,
0.0008678436279296875,
-0.0030040740966796875,
0.024932861328125,
0.01303863525390625,
0.0203857421875,
-0.010833740234375,
0.0015573501586914062,
0.02349853515625,
0.01471710205078125,
-0.021392822265625,
0.008453369140625,
0.022491455078125,
0.04241943359375,
-0.00579833984375,
0.005168914794921875,
-0.001079559326171875,
-0.01416778564453125,
0.0006399154663085938,
-0.006168365478515625,
-0.016326904296875,
0.03826904296875,
-0.0154876708984375,
0.0033702850341796875,
-0.0296478271484375,
-0.0267333984375,
-0.003376007080078125,
-0.0281829833984375,
0.00937652587890625,
0.0160980224609375,
-0.0154876708984375,
0.024383544921875,
-0.006378173828125,
0.00803375244140625,
-0.01010894775390625,
-0.0025081634521484375,
-0.0219573974609375,
0.016326904296875,
0.01458740234375,
0.012481689453125,
0.0031490325927734375,
-0.0279388427734375,
0.01251983642578125,
-0.007076263427734375,
0.0089569091796875,
-0.039459228515625,
0.0001277923583984375,
-0.01535797119140625,
0.01157379150390625,
-0.0014028549194335938,
-0.007488250732421875,
0.0295257568359375,
0.03125,
0.017547607421875,
-0.0220489501953125,
0.0204315185546875,
0.0244140625,
0.016571044921875,
0.0153045654296875,
-0.032073974609375,
0.01517486572265625,
-0.0008215904235839844,
-0.0165863037109375,
0.0028018951416015625,
0.0082244873046875,
0.006771087646484375,
0.00754547119140625,
-0.0132904052734375,
-0.003948211669921875,
-0.005451202392578125,
-0.01424407958984375,
-0.0167388916015625,
0.006404876708984375,
-0.00859832763671875,
0.0070037841796875,
0.0204620361328125,
-0.01953125,
0.0287628173828125,
0.0228118896484375,
0.014801025390625,
0.040618896484375,
0.002086639404296875,
0.023040771484375,
-0.01265716552734375,
-0.02239990234375,
0.00689697265625,
0.001499176025390625,
0.0697021484375,
-0.0164642333984375,
-0.0184783935546875,
-0.014129638671875,
0.019805908203125,
-0.0227203369140625,
-0.002552032470703125,
0.01082611083984375,
0.00980377197265625,
-0.022216796875,
-0.012420654296875,
0.0113525390625,
0.0121612548828125,
0.0384521484375,
-0.0087127685546875,
0.00658416748046875,
0.02984619140625,
0.00746917724609375,
-0.004207611083984375,
-0.035400390625,
-0.0034122467041015625,
-0.0009751319885253906,
-0.0120697021484375,
-0.006877899169921875,
0.0188140869140625,
-0.03607177734375,
-0.01165008544921875,
0.0012998580932617188,
-0.006923675537109375,
-0.0057220458984375,
-0.03143310546875,
0.00978851318359375,
-0.010833740234375,
0.0031280517578125,
0.010009765625,
0.00885009765625,
0.0303802490234375,
-0.0142669677734375,
-0.0185546875,
0.00788116455078125,
0.00008255243301391602,
0.00478363037109375,
-0.022369384765625,
-0.00572967529296875,
-0.0270233154296875,
0.0106201171875,
-0.0114288330078125,
-0.036773681640625,
-0.01226806640625,
0.006076812744140625,
0.00696563720703125,
-0.004039764404296875,
-0.031982421875,
0.0017032623291015625,
-0.0106201171875,
-0.0173797607421875,
-0.017913818359375,
0.00787353515625,
-0.02301025390625,
-0.013427734375,
-0.023773193359375,
0.0070037841796875,
-0.01336669921875,
0.01525115966796875,
-0.033111572265625,
-0.0036792755126953125,
-0.004180908203125,
-0.0237274169921875,
0.049835205078125,
-0.007259368896484375,
0.01013946533203125,
0.00408172607421875,
0.0011224746704101562,
-0.02691650390625,
-0.0008745193481445312,
0.032318115234375,
0.00682830810546875,
-0.02294921875,
-0.0117950439453125,
-0.03759765625,
0.0294952392578125,
-0.007488250732421875,
-0.0189666748046875,
-0.002628326416015625,
-0.01629638671875,
0.01119232177734375,
-0.004016876220703125,
-0.00595855712890625,
0.0237884521484375,
-0.00214385986328125,
0.0125274658203125,
-0.015594482421875,
-0.033355712890625,
0.045867919921875,
0.01363372802734375,
-0.0074615478515625,
0.0024776458740234375,
-0.01995849609375,
-0.005615234375,
0.028961181640625,
0.0259857177734375,
-0.033843994140625,
0.01953125,
-0.0311737060546875,
0.004535675048828125,
0.036651611328125,
-0.0244903564453125,
0.03521728515625,
-0.00746917724609375,
-0.0097503662109375,
0.0136566162109375,
0.0018863677978515625,
-0.0074920654296875,
0.02362060546875,
-0.001697540283203125,
-0.01097869873046875,
-0.02783203125,
0.0113372802734375,
-0.03411865234375,
-0.01383209228515625,
0.01641845703125,
0.006603240966796875,
-0.004726409912109375,
0.00885009765625,
0.0165863037109375,
-0.0140838623046875,
0.01221466064453125,
0.014556884765625,
-0.0013704299926757812,
-0.027191162109375,
0.009246826171875,
-0.018402099609375,
0.006519317626953125,
-0.0148162841796875,
0.0008521080017089844,
0.0100860595703125,
-0.0307159423828125,
0.014434814453125,
0.014190673828125,
-0.00008571147918701172,
-0.002044677734375,
0.0200347900390625,
0.0093536376953125,
-0.005756378173828125,
0.0181884765625,
-0.01519012451171875,
-0.00742340087890625,
-0.006237030029296875,
0.00913238525390625,
0.029052734375,
0.0174560546875,
0.04412841796875,
0.0302581787109375,
-0.01555633544921875,
-0.01441192626953125,
-0.0274200439453125,
0.032806396484375,
0.024810791015625,
0.01617431640625,
0.024169921875,
0.0031795501708984375,
-0.0023555755615234375,
0.00745391845703125,
0.0028858184814453125,
0.0007710456848144531,
-0.02783203125,
0.0036220550537109375,
0.010223388671875,
-0.0078125,
0.0159454345703125,
-0.020233154296875,
-0.034271240234375,
-0.060943603515625,
0.00905609130859375,
-0.02783203125,
0.00403594970703125,
-0.0264434814453125,
0.03643798828125,
-0.003368377685546875,
0.01666259765625,
0.01114654541015625,
0.04876708984375,
-0.00521087646484375,
-0.01514434814453125,
0.00864410400390625,
0.005603790283203125,
-0.0074005126953125,
0.006923675537109375,
0.0032196044921875,
-0.028167724609375,
-0.016204833984375,
-0.042022705078125,
0.0092926025390625,
-0.02032470703125,
0.0047760009765625,
-0.0132904052734375,
0.01119232177734375,
0.0005946159362792969,
-0.020721435546875,
0.01605224609375,
-0.01045989990234375,
-0.006130218505859375,
0.0106658935546875,
0.007129669189453125,
0.0003247261047363281,
-0.0003223419189453125,
-0.0173492431640625,
0.0228271484375,
-0.0023708343505859375,
-0.033447265625,
0.028564453125,
0.004169464111328125,
0.007640838623046875,
0.03173828125,
0.00833892822265625,
-0.0421142578125,
-0.0258026123046875,
-0.057037353515625,
-0.0145263671875,
0.0108489990234375,
-0.0037784576416015625,
0.0014657974243164062,
-0.0032787322998046875,
0.0191192626953125,
0.0235137939453125,
0.000606536865234375,
-0.0156097412109375,
-0.02752685546875,
0.00859832763671875,
-0.0222930908203125,
0.0157012939453125,
-0.035064697265625,
0.0082550048828125,
-0.0081634521484375,
-0.019012451171875,
0.03778076171875,
-0.00927734375,
0.045928955078125,
0.0124359130859375,
0.0034999847412109375,
-0.00859832763671875,
0.027984619140625,
0.0015993118286132812,
-0.03387451171875,
0.0136566162109375,
0.0242919921875,
-0.00984954833984375,
0.0069580078125,
0.02532958984375,
-0.013214111328125,
0.01464080810546875,
-0.024810791015625,
-0.040069580078125,
0.01505279541015625,
0.020263671875,
-0.019134521484375,
-0.00768280029296875,
-0.020782470703125,
0.020294189453125,
-0.001331329345703125,
0.01287078857421875,
0.025390625,
0.0028553009033203125,
-0.0211944580078125,
-0.0341796875,
0.0122222900390625,
0.04248046875,
0.0521240234375,
0.0110931396484375,
0.0022258758544921875,
-0.006282806396484375,
-0.006229400634765625,
-0.005725860595703125,
-0.005260467529296875,
0.003997802734375,
-0.04095458984375,
0.023651123046875,
-0.006317138671875,
-0.0214996337890625,
0.0362548828125,
-0.0059814453125,
0.00926971435546875,
0.01194000244140625,
0.0005106925964355469,
-0.00848388671875,
-0.008209228515625,
-0.005939483642578125,
-0.03326416015625,
-0.0225677490234375,
-0.0207977294921875,
0.00597381591796875,
-0.018798828125,
0.03558349609375,
0.02178955078125,
0.0290374755859375,
-0.00677490234375,
0.0279388427734375,
0.0240020751953125,
0.00624847412109375,
-0.00843048095703125,
-0.003353118896484375,
-0.037689208984375,
-0.0172271728515625,
-0.0158843994140625,
0.006710052490234375,
0.01409149169921875,
-0.0265655517578125,
0.007251739501953125,
-0.02008056640625,
-0.0245208740234375,
0.016143798828125,
0.041900634765625,
-0.01425933837890625,
0.01425933837890625,
-0.00696563720703125,
0.0123291015625,
-0.00815582275390625,
0.01727294921875,
-0.02862548828125,
0.025787353515625,
-0.002475738525390625,
0.00817108154296875,
-0.00043392181396484375,
0.01336669921875,
-0.01003265380859375,
0.01239776611328125,
-0.00595855712890625,
0.00392913818359375,
0.0111846923828125,
0.0400390625,
-0.0112762451171875,
-0.0185089111328125,
0.01024627685546875,
-0.007198333740234375,
-0.017486572265625,
0.005809783935546875,
-0.041412353515625,
0.007434844970703125,
0.007770538330078125,
0.003448486328125,
-0.0276031494140625,
0.02154541015625,
0.0021839141845703125,
0.020843505859375,
0.0008921623229980469,
0.0042877197265625,
0.01016998291015625,
0.0277252197265625,
0.0186767578125,
0.004978179931640625,
0.019775390625,
-0.01806640625,
-0.01372528076171875,
-0.020050048828125,
-0.023590087890625,
-0.0011072158813476562,
-0.014678955078125,
-0.0160675048828125,
0.0073699951171875,
-0.02239990234375,
0.0008397102355957031,
0.006412506103515625,
0.0126495361328125,
0.01169586181640625,
0.00432586669921875,
0.0232086181640625,
-0.00913238525390625,
-0.0221099853515625,
-0.0257415771484375,
0.0357666015625,
0.0108795166015625,
-0.01284027099609375,
0.00342559814453125,
-0.0066680908203125,
-0.00968170166015625,
-0.0243072509765625,
-0.023193359375,
0.006954193115234375,
-0.00376129150390625,
0.0012617111206054688,
0.0172882080078125,
-0.01200103759765625,
0.00795745849609375,
-0.007663726806640625,
0.0296478271484375,
-0.0163116455078125,
0.005184173583984375,
0.01190185546875,
-0.0134429931640625,
0.0119476318359375,
-0.0235137939453125,
-0.01432037353515625,
0.0052490234375,
0.00806427001953125,
-0.002231597900390625,
-0.011505126953125,
-0.003559112548828125,
-0.01715087890625,
0.0240325927734375,
0.0259857177734375,
0.00905609130859375,
0.005035400390625,
0.0006623268127441406,
0.016845703125,
-0.005252838134765625,
0.00400543212890625,
0.0204620361328125,
0.022247314453125,
0.005313873291015625,
0.0162811279296875,
0.0138092041015625,
0.0073394775390625,
-0.0024242401123046875,
-0.026519775390625,
0.0302276611328125,
0.00699615478515625,
0.00934600830078125,
-0.0034770965576171875,
0.0112457275390625,
-0.0169525146484375,
0.0037288665771484375,
-0.0316162109375,
-0.017059326171875,
-0.0197906494140625,
0.037689208984375,
-0.032562255859375,
0.00579833984375,
-0.01395416259765625,
0.02532958984375,
-0.01153564453125,
-0.0306243896484375,
-0.033050537109375,
0.01099395751953125,
-0.003108978271484375,
0.00653076171875,
-0.020263671875,
-0.0301513671875,
-0.017669677734375,
0.003231048583984375,
0.0062255859375,
0.025482177734375,
0.048492431640625,
-0.036956787109375,
0.0145416259765625,
-0.0032024383544921875,
0.015838623046875,
-0.0283660888671875,
0.032562255859375,
0.014923095703125,
-0.035888671875,
-0.01352691650390625,
0.0440673828125,
0.01265716552734375,
0.0053863525390625,
0.006725311279296875,
-0.01285552978515625,
-0.0139007568359375,
-0.0077667236328125,
-0.01139068603515625,
0.040618896484375,
0.055877685546875,
0.00342559814453125,
0.0006704330444335938,
-0.01488494873046875,
0.0015707015991210938,
-0.00913238525390625,
-0.0297698974609375,
0.01407623291015625,
-0.002536773681640625,
-0.0233001708984375,
-0.0224456787109375,
0.00008410215377807617,
0.0131683349609375,
-0.0174713134765625,
0.023590087890625,
-0.0129852294921875,
-0.0389404296875,
0.030487060546875,
-0.005550384521484375,
-0.001865386962890625,
-0.0019989013671875,
-0.033111572265625,
-0.0267181396484375,
0.04937744140625,
-0.01099395751953125,
-0.0003483295440673828,
0.0233306884765625,
-0.01092529296875,
0.00971221923828125,
0.01325225830078125,
0.0007109642028808594,
-0.0217132568359375,
0.032623291015625,
0.007244110107421875,
-0.0174713134765625,
-0.012847900390625,
0.01541900634765625,
-0.01122283935546875,
-0.0008678436279296875,
-0.0138092041015625,
0.00690460205078125,
0.0115509033203125,
0.00586700439453125,
0.025787353515625,
-0.005481719970703125,
-0.022613525390625,
-0.0218048095703125,
-0.0087890625,
0.0007171630859375,
0.007183074951171875,
0.0096282958984375,
0.01129913330078125,
0.0010881423950195312,
-0.01751708984375,
-0.034576416015625,
-0.0087738037109375,
-0.0023670196533203125,
0.005817413330078125,
0.00215911865234375,
0.00408172607421875,
-0.0252838134765625,
0.00603485107421875,
-0.025299072265625,
-0.004756927490234375,
-0.033294677734375,
-0.0109100341796875,
0.021270751953125,
0.0278778076171875,
-0.0284271240234375,
0.0089111328125,
0.0185089111328125,
-0.0018100738525390625,
-0.033599853515625,
0.0035152435302734375,
-0.0008945465087890625,
0.01107025146484375,
-0.03094482421875,
0.00901031494140625,
-0.01403045654296875,
0.0305938720703125,
-0.0257568359375,
-0.0255126953125,
0.0261383056640625,
0.0099334716796875,
0.003627777099609375,
-0.02154541015625,
-0.006397247314453125,
-0.004291534423828125,
-0.00786590576171875,
0.004550933837890625,
-0.02166748046875,
-0.006439208984375,
0.0171966552734375,
0.00884246826171875,
-0.0244293212890625,
-0.03277587890625,
-0.01168060302734375,
-0.01093292236328125,
0.00595855712890625,
-0.01416778564453125,
0.01708984375,
0.028656005859375,
-0.0239105224609375,
-0.01458740234375,
0.0308074951171875,
-0.033233642578125,
0.019256591796875,
0.00402069091796875,
-0.039306640625,
-0.039520263671875,
-0.001682281494140625,
-0.03509521484375,
0.0101776123046875,
0.034515380859375,
0.0014963150024414062,
-0.0084686279296875,
-0.021392822265625,
0.0262603759765625,
-0.038726806640625,
-0.00788116455078125,
-0.018768310546875,
0.0032176971435546875,
0.0099029541015625,
-0.0015850067138671875,
-0.006893157958984375,
0.020263671875,
-0.01331329345703125,
-0.0213165283203125,
0.0027599334716796875,
-0.02435302734375,
0.00687408447265625,
0.004909515380859375,
-0.007282257080078125,
0.004222869873046875,
-0.0183868408203125,
0.0006823539733886719,
-0.00027179718017578125,
-0.0002262592315673828,
-0.0030040740966796875,
-0.0288238525390625,
-0.01800537109375,
-0.031494140625,
-0.00843048095703125,
-0.029327392578125,
-0.017608642578125,
-0.004505157470703125,
-0.0131378173828125,
-0.017791748046875,
0.0211029052734375,
-0.0024089813232421875,
-0.01528167724609375,
0.000041484832763671875,
-0.0247039794921875,
0.0234832763671875,
-0.00044035911560058594,
-0.00423431396484375,
-0.01012420654296875,
0.02392578125,
-0.018035888671875,
-0.012176513671875,
-0.004306793212890625,
0.0013952255249023438,
0.003574371337890625,
0.0287017822265625,
-0.00899505615234375,
0.018463134765625,
0.00685882568359375,
0.0323486328125,
-0.0019512176513671875,
-0.049102783203125,
0.002593994140625,
-0.00846099853515625,
-0.0187530517578125,
0.01229095458984375,
-0.0127105712890625,
-0.00665283203125,
-0.0137939453125,
-0.0229949951171875,
0.0117950439453125,
0.028656005859375,
0.0306243896484375,
-0.02716064453125,
0.0171966552734375,
-0.00461578369140625,
0.0005202293395996094,
0.0266265869140625,
-0.01319122314453125,
0.005680084228515625,
0.004116058349609375,
-0.0244293212890625,
-0.0396728515625,
0.025604248046875,
0.0265655517578125,
0.0099334716796875,
-0.0265350341796875,
-0.0202178955078125,
-0.03375244140625,
-0.0243072509765625,
0.0169525146484375,
-0.0008835792541503906,
-0.0216827392578125,
-0.00226593017578125,
0.00815582275390625,
-0.01335906982421875,
0.0255584716796875,
-0.0016002655029296875,
0.02337646484375,
0.0016546249389648438,
-0.0234527587890625,
0.0138702392578125,
-0.006183624267578125,
0.0025310516357421875,
0.01250457763671875,
-0.0059814453125,
0.0096282958984375,
-0.00568389892578125,
0.0024318695068359375,
0.0031948089599609375,
0.020172119140625,
0.005779266357421875,
0.0215911865234375,
-0.039031982421875,
0.00589752197265625,
-0.040863037109375,
-0.00699615478515625,
-0.0261688232421875,
-0.01000213623046875,
0.0020275115966796875,
-0.0018463134765625,
-0.0150909423828125,
-0.0219268798828125,
-0.001186370849609375,
-0.0052947998046875,
-0.0200653076171875,
0.019683837890625,
0.0220794677734375,
0.0391845703125,
0.01265716552734375,
0.0241851806640625,
-0.0179443359375,
0.0247344970703125,
-0.0137176513671875,
-0.030059814453125,
-0.006439208984375,
0.005462646484375,
-0.034423828125,
-0.026031494140625,
-0.0118255615234375,
0.0076904296875,
0.048095703125,
0.007083892822265625,
-0.0002617835998535156,
0.0008807182312011719,
0.00621795654296875,
0.0229644775390625,
-0.00656890869140625,
-0.00008696317672729492,
-0.0103912353515625,
0.0251007080078125,
-0.0003867149353027344,
0.00531005859375,
-0.02923583984375,
-0.00514984130859375,
-0.0249176025390625,
-0.0007739067077636719,
-0.018585205078125,
0.059722900390625,
0.011627197265625,
-0.0306243896484375,
0.0272064208984375,
-0.05560302734375,
0.0019311904907226562,
-0.00478363037109375,
-0.0008873939514160156,
-0.000843048095703125,
0.026763916015625,
0.0068206787109375,
0.0306854248046875,
-0.00540924072265625,
-0.0023212432861328125,
0.0202484130859375,
0.012420654296875,
-0.01210784912109375,
-0.0116424560546875,
0.00833892822265625,
0.0014257431030273438,
0.0243988037109375,
0.011627197265625,
0.013641357421875,
-0.0238037109375,
-0.0276031494140625,
0.034912109375,
0.00817108154296875,
-0.0266876220703125,
0.017608642578125,
-0.029449462890625,
0.03533935546875,
0.044464111328125,
0.031341552734375,
0.0077667236328125,
-0.024658203125,
-0.0257110595703125,
0.00751495361328125,
0.0300750732421875,
-0.0033626556396484375,
-0.0096282958984375,
0.00978851318359375,
-0.0357666015625,
-0.01180267333984375,
-0.029754638671875,
0.0230255126953125,
-0.00739288330078125,
-0.01416015625,
0.0286102294921875,
-0.031158447265625,
0.009307861328125,
-0.0131683349609375,
-0.0207977294921875,
-0.015167236328125,
-0.032470703125,
-0.01548004150390625,
0.01262664794921875,
-0.0179595947265625,
0.0033245086669921875,
-0.0155487060546875,
0.0250701904296875,
-0.026214599609375,
-0.029541015625,
0.0054931640625,
0.0175933837890625,
0.02215576171875,
-0.012969970703125,
0.00490570068359375,
-0.00914764404296875,
0.000025451183319091797,
0.0266876220703125,
-0.0006651878356933594,
0.01267242431640625,
0.0154571533203125,
0.00754547119140625,
-0.004802703857421875,
0.0147552490234375,
0.03662109375,
-0.007221221923828125,
-0.03375244140625,
0.00424957275390625,
-0.0011816024780273438,
0.0159454345703125,
0.0006966590881347656,
-0.0285797119140625,
-0.031646728515625,
0.01419830322265625,
0.0283355712890625,
-0.00843048095703125,
-0.0153961181640625,
0.007251739501953125,
0.007297515869140625,
0.00759124755859375,
0.01416778564453125,
-0.01084136962890625,
0.0010824203491210938,
0.00775909423828125,
-0.0155792236328125,
0.031524658203125
] |
ours_559
|
The answer is \( 60 \).
We need to find the number of positive integers \( a \) such that the coefficient of \( x^a \) is zero. The expression can be rewritten as finding the number of positive integers \( a \) that cannot be expressed in the form \( 7m + 11n \) where \( 0 \leq m \leq 11 \) and \( 0 \leq n \leq 7 \).
The sum of the coefficients is \( 8 \times 12 = 96 \) (by substituting \( x = 1 \) into the expression). Since the coefficient of \( x^{77} \) is \( 2 \) and all other nonzero coefficients are \( 1 \), there are \( 96 - 1 = 95 \) distinct nonzero coefficients.
Thus, there are \( 155 - 95 = 60 \) values of \( a \) for which the coefficient of \( x^a \) is zero.
\(\boxed{60}\)
|
60
|
{
"competition": "us_comps",
"dataset": "Ours",
"posts": null,
"source": "OMOSoln2.md"
}
|
How many positive integers \( a \) with \( a \leq 154 \) are there such that the coefficient of \( x^{a} \) in the expansion of
\[
\left(1+x^{7}+x^{14}+\cdots+x^{77}\right)\left(1+x^{11}+x^{22}+\cdots+x^{77}\right)
\]
is zero?
|
[
"/Mathematics/DiscreteMathematics/Combinatorics/Enumeration",
"/Mathematics/DiscreteMathematics/GeneralDiscreteMathematics/DiscreteMath",
"/Mathematics/DiscreteMathematics/GeneralDiscreteMathematics/DiscreteMathematics",
"/Mathematics/NumberTheory/DiophantineEquations/CoinProblem",
"/Mathematics/NumberTheory/DiophantineEquations/FrobeniusCoinProblem",
"/Mathematics/NumberTheory/DiophantineEquations/FrobeniusProblem",
"/Mathematics/NumberTheory/GeneralNumberTheory/AdditiveNumberTheory",
"/Mathematics/NumberTheory/GeneralNumberTheory/ElementaryMethods",
"/Mathematics/NumberTheory/GeneralNumberTheory/ElementaryNumberTheory",
"/Mathematics/NumberTheory/GeneralNumberTheory/NumberTheory",
"/Mathematics/NumberTheory/GeneratingFunctions/GeneratingFunction"
] |
Recognize that a non‑zero coefficient occurs exactly when a can be written as 7m+11n with 0≤m≤11 and 0≤n≤7, then count the integers a≤154 that lack such a representation.
|
[
0.00007778406143188477,
-0.0225067138671875,
0.01369476318359375,
-0.00537109375,
0.0006079673767089844,
-0.01099395751953125,
-0.0204620361328125,
-0.032318115234375,
0.0095977783203125,
-0.05743408203125,
0.03277587890625,
-0.039794921875,
-0.0018558502197265625,
0.00420379638671875,
-0.046630859375,
0.0028228759765625,
0.053253173828125,
0.01187896728515625,
0.040374755859375,
-0.0009617805480957031,
-0.0052947998046875,
0.01393890380859375,
-0.048828125,
0.043304443359375,
-0.00490570068359375,
-0.00287628173828125,
-0.021881103515625,
0.01383209228515625,
0.005901336669921875,
0.002460479736328125,
-0.00791168212890625,
-0.0010480880737304688,
0.0024776458740234375,
-0.03375244140625,
0.0033016204833984375,
-0.008209228515625,
0.0233917236328125,
-0.0033206939697265625,
0.0212860107421875,
-0.0308685302734375,
-0.017852783203125,
-0.0000032186508178710938,
-0.0090484619140625,
-0.01546478271484375,
0.0105743408203125,
0.003246307373046875,
-0.0036296844482421875,
0.01092529296875,
-0.00447845458984375,
-0.01067352294921875,
-0.006744384765625,
0.0036163330078125,
-0.0232696533203125,
-0.00982666015625,
-0.04095458984375,
-0.05474853515625,
-0.00704193115234375,
0.00627899169921875,
-0.041046142578125,
-0.030364990234375,
-0.0040130615234375,
-0.0008025169372558594,
-0.03009033203125,
-0.0171966552734375,
-0.000038504600524902344,
0.0010557174682617188,
0.00008553266525268555,
-0.0350341796875,
0.00803375244140625,
-0.005950927734375,
-0.0225830078125,
-0.0187530517578125,
-0.017425537109375,
0.0250244140625,
0.0308074951171875,
-0.006618499755859375,
-0.00453948974609375,
0.0226287841796875,
0.001636505126953125,
0.01035308837890625,
0.00780487060546875,
0.01024627685546875,
0.01050567626953125,
-0.01535797119140625,
0.0044708251953125,
-0.05218505859375,
0.005321502685546875,
0.007534027099609375,
0.046051025390625,
-0.0012950897216796875,
-0.00635528564453125,
0.020050048828125,
0.0289459228515625,
-0.005859375,
-0.007289886474609375,
0.0028514862060546875,
0.0137176513671875,
-0.00583648681640625,
-0.003536224365234375,
0.01480865478515625,
-0.0080413818359375,
-0.0169219970703125,
0.01343536376953125,
-0.002841949462890625,
-0.05145263671875,
-0.0222320556640625,
0.005443572998046875,
0.00983428955078125,
-0.006786346435546875,
-0.0048065185546875,
0.0014123916625976562,
0.006591796875,
-0.0038814544677734375,
-0.0008606910705566406,
0.0010547637939453125,
-0.004856109619140625,
0.00864410400390625,
-0.01503753662109375,
-0.0292510986328125,
-0.021270751953125,
-0.00630950927734375,
0.00731658935546875,
0.0036220550537109375,
0.016845703125,
0.0127716064453125,
0.004810333251953125,
-0.01203155517578125,
-0.016387939453125,
-0.01390838623046875,
-0.0077056884765625,
0.0040283203125,
0.00041675567626953125,
-0.0094451904296875,
-0.0198974609375,
-0.0386962890625,
-0.007732391357421875,
-0.008148193359375,
-0.0175933837890625,
0.0035305023193359375,
-0.00579833984375,
-0.011566162109375,
-0.01580810546875,
0.005565643310546875,
0.0122833251953125,
-0.0166015625,
-0.004230499267578125,
-0.01352691650390625,
-0.0233001708984375,
-0.007110595703125,
-0.01519775390625,
0.0202178955078125,
-0.004077911376953125,
-0.019927978515625,
0.0181121826171875,
-0.00016999244689941406,
0.01071929931640625,
0.0190582275390625,
0.016510009765625,
-0.006435394287109375,
0.031402587890625,
0.0299072265625,
0.00930023193359375,
0.01276397705078125,
0.019439697265625,
0.0045013427734375,
-0.0211639404296875,
-0.00481414794921875,
-0.004199981689453125,
-0.0213775634765625,
0.0021495819091796875,
0.014495849609375,
0.00615692138671875,
0.006717681884765625,
-0.010406494140625,
0.0189361572265625,
-0.002620697021484375,
-0.004810333251953125,
0.01248931884765625,
-0.005420684814453125,
0.0222320556640625,
0.003635406494140625,
-0.0218048095703125,
0.01336669921875,
0.0028743743896484375,
-0.0016117095947265625,
-0.00328826904296875,
0.000514984130859375,
0.003570556640625,
0.0102691650390625,
0.0130767822265625,
-0.01007080078125,
-0.0257568359375,
-0.0244293212890625,
0.020416259765625,
-0.007053375244140625,
-0.001461029052734375,
0.006755828857421875,
-0.005893707275390625,
0.0278472900390625,
0.00403594970703125,
-0.01168060302734375,
0.0177459716796875,
0.0010156631469726562,
-0.0096588134765625,
0.0208740234375,
-0.01174163818359375,
-0.021453857421875,
-0.00036215782165527344,
0.01666259765625,
-0.012237548828125,
0.002044677734375,
-0.0107879638671875,
-0.015350341796875,
-0.042694091796875,
-0.0291290283203125,
-0.0052032470703125,
-0.01238250732421875,
0.006801605224609375,
0.01480865478515625,
-0.024322509765625,
0.00225067138671875,
0.024383544921875,
-0.0165557861328125,
0.004726409912109375,
-0.039215087890625,
-0.00616455078125,
0.0024204254150390625,
0.001232147216796875,
-0.00189971923828125,
0.015350341796875,
0.04498291015625,
0.004650115966796875,
-0.0224761962890625,
0.0126190185546875,
0.0019512176513671875,
-0.00274658203125,
-0.0006160736083984375,
-0.02099609375,
-0.005092620849609375,
0.01061248779296875,
0.0114593505859375,
0.000545501708984375,
0.021148681640625,
-0.0120391845703125,
0.0019664764404296875,
-0.01067352294921875,
0.01291656494140625,
-0.006122589111328125,
0.028472900390625,
0.0010995864868164062,
-0.0302734375,
0.00946807861328125,
-0.00982666015625,
-0.01055908203125,
0.0139617919921875,
-0.00539398193359375,
-0.003612518310546875,
0.03973388671875,
-0.0078887939453125,
-0.006923675537109375,
0.008331298828125,
-0.0195159912109375,
0.0009741783142089844,
-0.02252197265625,
-0.003353118896484375,
0.0015268325805664062,
0.0165252685546875,
0.00106048583984375,
-0.0011653900146484375,
-0.00016939640045166016,
0.034637451171875,
-0.005268096923828125,
-0.005619049072265625,
-0.01235198974609375,
0.0160369873046875,
0.01325225830078125,
-0.0185089111328125,
0.002109527587890625,
-0.0026798248291015625,
-0.01050567626953125,
0.005634307861328125,
-0.0102081298828125,
0.00862884521484375,
0.0066375732421875,
-0.0248565673828125,
-0.01006317138671875,
0.01483154296875,
-0.036590576171875,
0.0115509033203125,
-0.00919342041015625,
0.027496337890625,
0.0081634521484375,
-0.0215606689453125,
-0.00872802734375,
0.036285400390625,
-0.027984619140625,
-0.00476837158203125,
-0.0246124267578125,
0.031524658203125,
0.002582550048828125,
0.0298919677734375,
-0.0106048583984375,
-0.004978179931640625,
-0.0191497802734375,
0.0006203651428222656,
0.01160430908203125,
-0.0006413459777832031,
-0.00829315185546875,
-0.01480865478515625,
-0.007778167724609375,
-0.005229949951171875,
0.005092620849609375,
-0.00506591796875,
0.0006451606750488281,
-0.004543304443359375,
-0.0221405029296875,
0.017303466796875,
0.0143585205078125,
-0.0018930435180664062,
0.023956298828125,
-0.004913330078125,
0.0242919921875,
-0.032958984375,
-0.01044464111328125,
-0.021697998046875,
0.006561279296875,
0.018463134765625,
-0.005748748779296875,
-0.06072998046875,
0.053741455078125,
-0.034027099609375,
-0.01430511474609375,
-0.0153045654296875,
-0.050506591796875,
-0.00933074951171875,
0.018463134765625,
-0.006317138671875,
0.01056671142578125,
-0.01071929931640625,
-0.023101806640625,
-0.00791168212890625,
-0.0200653076171875,
-0.01192474365234375,
0.0284881591796875,
-0.0116119384765625,
0.007030487060546875,
-0.0200042724609375,
0.013275146484375,
-0.006023406982421875,
-0.0064544677734375,
0.00888824462890625,
0.0171966552734375,
-0.01303863525390625,
0.0230712890625,
-0.046173095703125,
0.01430511474609375,
-0.009002685546875,
-0.007610321044921875,
-0.00066375732421875,
0.031524658203125,
0.0099945068359375,
-0.0029010772705078125,
0.005126953125,
0.004268646240234375,
-0.01427459716796875,
0.0003705024719238281,
-0.01110076904296875,
0.0203857421875,
-0.0014104843139648438,
-0.0196380615234375,
-0.0178375244140625,
-0.031402587890625,
0.003650665283203125,
0.0017251968383789062,
-0.0267181396484375,
-0.01087188720703125,
0.0226898193359375,
0.0099334716796875,
-0.012542724609375,
-0.004238128662109375,
-0.0148773193359375,
0.007678985595703125,
-0.012939453125,
0.019805908203125,
-0.009918212890625,
-0.01090240478515625,
-0.015625,
-0.045806884765625,
-0.00444793701171875,
0.039581298828125,
-0.028106689453125,
-0.007106781005859375,
-0.007701873779296875,
0.005443572998046875,
0.0283203125,
-0.0367431640625,
-0.01117706298828125,
0.02801513671875,
0.040679931640625,
-0.04290771484375,
0.02069091796875,
-0.01129150390625,
-0.014617919921875,
-0.01517486572265625,
0.0225830078125,
-0.01434326171875,
0.01517486572265625,
-0.049774169921875,
-0.0247344970703125,
-0.007049560546875,
-0.01024627685546875,
0.02850341796875,
-0.007266998291015625,
-0.031341552734375,
0.0022525787353515625,
-0.01354217529296875,
0.0198974609375,
-0.00498199462890625,
-0.03863525390625,
-0.01248931884765625,
-0.01366424560546875,
-0.0167083740234375,
0.037017822265625,
-0.0017995834350585938,
0.007205963134765625,
0.0120697021484375,
-0.0270843505859375,
0.0010290145874023438,
-0.01824951171875,
-0.0020656585693359375,
-0.0021991729736328125,
-0.016510009765625,
0.018463134765625,
0.0272369384765625,
0.00939178466796875,
0.01678466796875,
0.01708984375,
-0.0107269287109375,
-0.0144805908203125,
0.00974273681640625,
-0.0141448974609375,
-0.0007653236389160156,
-0.004486083984375,
-0.01421356201171875,
-0.00392913818359375,
0.006683349609375,
0.006160736083984375,
0.0295867919921875,
-0.03326416015625,
0.0208282470703125,
-0.0183868408203125,
0.007038116455078125,
-0.0421142578125,
-0.0193023681640625,
-0.0202789306640625,
0.016448974609375,
0.022064208984375,
-0.0007448196411132812,
-0.008697509765625,
-0.0299835205078125,
-0.0169830322265625,
0.019744873046875,
-0.01279449462890625,
-0.0169219970703125,
-0.0276641845703125,
0.0006160736083984375,
-0.0008554458618164062,
0.01995849609375,
0.007282257080078125,
-0.0179443359375,
0.004730224609375,
-0.004322052001953125,
0.01128387451171875,
-0.0193328857421875,
-0.0303192138671875,
0.0272369384765625,
-0.00757598876953125,
0.01302337646484375,
-0.01108551025390625,
-0.010528564453125,
0.015777587890625,
0.0107269287109375,
-0.01739501953125,
0.025787353515625,
-0.0168304443359375,
0.0253448486328125,
0.031097412109375,
0.0150604248046875,
-0.033935546875,
0.00750732421875,
0.019287109375,
0.035003662109375,
-0.0242156982421875,
-0.0263214111328125,
0.01611328125,
0.0006098747253417969,
0.0019330978393554688,
0.02203369140625,
-0.0218658447265625,
0.001506805419921875,
0.01513671875,
-0.070068359375,
0.0290374755859375,
-0.016021728515625,
0.00012636184692382812,
-0.006526947021484375,
0.043426513671875,
0.0008568763732910156,
-0.0013427734375,
0.0004703998565673828,
0.0220489501953125,
0.019622802734375,
0.0093994140625,
-0.036285400390625,
0.004116058349609375,
0.0033283233642578125,
0.004627227783203125,
-0.0300140380859375,
0.00948333740234375,
0.0175628662109375,
-0.0104827880859375,
0.01024627685546875,
0.006649017333984375,
-0.003871917724609375,
0.0308837890625,
0.0065460205078125,
-0.000024318695068359375,
-0.04669189453125,
-0.003421783447265625,
-0.002529144287109375,
0.007770538330078125,
-0.01470184326171875,
0.0125885009765625,
-0.0061492919921875,
-0.0233306884765625,
0.027862548828125,
-0.0103912353515625,
-0.00762939453125,
0.004825592041015625,
0.0209197998046875,
-0.0211944580078125,
0.007354736328125,
0.006389617919921875,
-0.0283355712890625,
-0.01275634765625,
-0.04534912109375,
-0.007415771484375,
-0.006526947021484375,
-0.04327392578125,
0.029449462890625,
0.013580322265625,
0.0010929107666015625,
0.0275421142578125,
-0.01175689697265625,
-0.0699462890625,
-0.00013017654418945312,
0.02056884765625,
0.007389068603515625,
-0.0216827392578125,
-0.01861572265625,
0.006961822509765625,
0.0290374755859375,
-0.0154876708984375,
0.004184722900390625,
-0.0016794204711914062,
-0.0300750732421875,
-0.010040283203125,
0.0026798248291015625,
-0.006336212158203125,
0.0011034011840820312,
-0.0147552490234375,
0.004199981689453125,
-0.02960205078125,
0.0289764404296875,
-0.0038738250732421875,
0.005748748779296875,
-0.035797119140625,
0.0290069580078125,
0.015228271484375,
-0.049835205078125,
-0.01213836669921875,
0.0196075439453125,
-0.0212249755859375,
0.0169525146484375,
0.020599365234375,
-0.014404296875,
-0.00504302978515625,
-0.0113983154296875,
0.002834320068359375,
-0.012908935546875,
0.0012769699096679688,
0.03155517578125,
0.0026874542236328125,
-0.0006947517395019531,
-0.002017974853515625,
-0.00872802734375,
0.052642822265625,
-0.035858154296875,
0.004894256591796875,
0.007904052734375,
0.0034694671630859375,
0.0029430389404296875,
0.01763916015625,
0.0225067138671875,
-0.043731689453125,
0.004657745361328125,
0.0170440673828125,
0.0293121337890625,
-0.0022296905517578125,
0.00815582275390625,
0.019317626953125,
-0.027191162109375,
0.0210418701171875,
-0.009613037109375,
0.0321044921875,
0.0233917236328125,
-0.0232391357421875,
-0.01261138916015625,
0.021697998046875,
-0.01206207275390625,
-0.0021038055419921875,
0.0068359375,
-0.00804901123046875,
0.0011959075927734375,
0.028472900390625,
0.0164794921875,
0.031494140625,
-0.0107269287109375,
0.0018911361694335938,
0.0014400482177734375,
-0.0296630859375,
-0.0020923614501953125,
-0.0283050537109375,
-0.006778717041015625,
-0.01239776611328125,
0.01047515869140625,
0.0086669921875,
0.016510009765625,
0.006534576416015625,
-0.0164794921875,
0.00937652587890625,
0.0277099609375,
-0.0017185211181640625,
-0.0129852294921875,
-0.007717132568359375,
-0.00007271766662597656,
-0.0206451416015625,
0.0034465789794921875,
0.0029773712158203125,
-0.0038394927978515625,
-0.036285400390625,
0.0003108978271484375,
0.01561737060546875,
0.004451751708984375,
-0.037750244140625,
-0.01082611083984375,
-0.003475189208984375,
0.002105712890625,
-0.03369140625,
-0.00453948974609375,
0.0218048095703125,
-0.00469970703125,
-0.0008816719055175781,
0.0002796649932861328,
-0.020294189453125,
-0.00624847412109375,
0.0006046295166015625,
0.00490570068359375,
-0.0058746337890625,
-0.0245513916015625,
0.028472900390625,
-0.041046142578125,
0.0204315185546875,
-0.0309906005859375,
0.0001671314239501953,
-0.034912109375,
-0.0149383544921875,
0.0141754150390625,
0.0386962890625,
0.0310211181640625,
0.007659912109375,
0.01617431640625,
0.0028743743896484375,
0.004505157470703125,
0.01456451416015625,
0.0247955322265625,
-0.003238677978515625,
-0.032012939453125,
0.0078277587890625,
0.0234375,
0.00415802001953125,
-0.00827789306640625,
-0.0164642333984375,
-0.00867462158203125,
-0.003665924072265625,
-0.01184844970703125,
0.0102081298828125,
0.0112762451171875,
-0.0259246826171875,
-0.0005245208740234375,
0.0270843505859375,
0.010467529296875,
0.034027099609375,
0.0029888153076171875,
-0.01105499267578125,
0.0033130645751953125,
-0.04736328125,
0.0170440673828125,
-0.01230621337890625,
0.0330810546875,
-0.0230560302734375,
0.011993408203125,
-0.0234527587890625,
-0.0170135498046875,
-0.00360107421875,
0.01282501220703125,
0.06787109375,
-0.01120758056640625,
0.0200042724609375,
-0.01189422607421875,
-0.01413726806640625,
0.02349853515625,
0.00025081634521484375,
-0.01995849609375,
0.033599853515625,
0.0180511474609375,
0.0066680908203125,
-0.037200927734375,
-0.04193115234375,
-0.0153045654296875,
-0.022735595703125,
0.00063323974609375,
0.02154541015625,
-0.0193023681640625,
0.0118560791015625,
-0.024932861328125,
-0.01250457763671875,
-0.050384521484375,
0.0274200439453125,
-0.00937652587890625,
0.016571044921875,
-0.0201263427734375,
0.0197296142578125,
-0.00603485107421875,
0.0157623291015625,
-0.005889892578125,
0.0284881591796875,
-0.0016336441040039062,
0.019256591796875,
-0.014556884765625,
0.042144775390625,
0.005035400390625,
-0.01178741455078125,
-0.046905517578125,
0.00826263427734375,
-0.00891876220703125,
0.0205230712890625,
-0.021575927734375,
-0.00197601318359375,
0.0116729736328125,
-0.07794189453125,
0.0024394989013671875,
-0.01433563232421875,
-0.012542724609375,
0.044830322265625,
-0.01377105712890625,
0.01654052734375,
0.003814697265625,
0.003658294677734375,
0.060882568359375,
-0.0311126708984375,
-0.005664825439453125,
0.031646728515625,
0.0153350830078125,
0.00435638427734375,
-0.00852203369140625,
-0.0214385986328125,
0.01062774658203125,
0.053863525390625,
-0.01189422607421875,
-0.0170440673828125,
0.0100555419921875,
-0.004581451416015625,
0.003204345703125,
-0.04644775390625,
0.01529693603515625,
0.037628173828125,
-0.034912109375,
-0.01181793212890625,
-0.01125335693359375,
0.02423095703125,
0.0162353515625,
0.003330230712890625,
0.00469970703125,
-0.032623291015625,
-0.00531005859375,
-0.01108551025390625,
-0.02362060546875,
-0.052825927734375,
0.00970458984375,
-0.004909515380859375,
0.00212860107421875,
-0.005611419677734375,
0.004974365234375,
0.00040149688720703125,
0.01009368896484375,
0.017669677734375,
0.0009603500366210938,
-0.018280029296875,
0.006542205810546875,
-0.0165557861328125,
0.005985260009765625,
-0.0196075439453125,
-0.0147552490234375,
0.02069091796875,
-0.00030541419982910156,
0.00506591796875,
-0.0140228271484375,
-0.00396728515625,
0.0296630859375,
-0.01403045654296875,
0.016021728515625,
0.004932403564453125,
-0.004650115966796875,
-0.044952392578125,
0.0117340087890625,
0.0183563232421875,
-0.01287841796875,
0.0117645263671875,
-0.0078887939453125,
0.01206207275390625,
-0.0237884521484375,
-0.029571533203125,
0.01425933837890625,
-0.01467132568359375,
-0.0013380050659179688,
-0.00821685791015625,
0.025360107421875,
0.001995086669921875,
0.0056915283203125,
0.007801055908203125,
0.03717041015625,
0.0024852752685546875,
-0.0180206298828125,
0.0299530029296875,
0.0007004737854003906,
-0.0057525634765625,
0.0231781005859375,
-0.0239410400390625,
0.00710296630859375,
-0.01468658447265625,
0.00606536865234375,
-0.00586700439453125,
0.01268768310546875,
0.0004444122314453125,
-0.003170013427734375,
-0.0130767822265625,
0.004421234130859375,
0.00807952880859375,
0.0070037841796875,
-0.0263671875,
0.001190185546875,
0.012847900390625,
-0.036590576171875,
-0.003467559814453125,
-0.0011014938354492188,
0.009979248046875,
-0.01190948486328125,
-0.007518768310546875,
0.00826263427734375,
0.014739990234375,
-0.016937255859375,
0.04046630859375,
-0.005550384521484375,
0.001064300537109375,
0.01160430908203125,
0.008544921875,
-0.01236724853515625,
0.0206298828125,
0.01346588134765625,
0.033966064453125,
-0.058685302734375,
-0.006511688232421875,
0.0137176513671875,
-0.023773193359375,
-0.0057525634765625,
0.019439697265625,
0.0163726806640625,
-0.0190887451171875,
0.00351715087890625,
-0.0256195068359375,
-0.0062103271484375,
-0.008270263671875,
-0.0284881591796875,
0.0217742919921875,
0.01149749755859375,
-0.0006809234619140625,
-0.01457977294921875,
-0.0240631103515625,
-0.038116455078125,
-0.0230712890625,
0.0024089813232421875,
0.01290130615234375,
0.01242828369140625,
-0.042633056640625,
-0.0017833709716796875,
0.0113067626953125,
-0.01471710205078125,
-0.0002589225769042969,
0.04949951171875,
-0.02532958984375,
0.0187530517578125,
-0.0204620361328125,
0.0170135498046875,
-0.00519561767578125,
0.00609588623046875,
0.0010251998901367188,
0.0209503173828125,
0.02130126953125,
-0.01396942138671875,
-0.007549285888671875,
-0.00372314453125,
-0.02972412109375,
-0.018157958984375,
-0.004558563232421875,
0.0134735107421875,
0.00830078125,
0.02447509765625,
-0.0017614364624023438,
-0.0216217041015625,
0.01070404052734375,
0.0295867919921875,
-0.01727294921875,
0.0218353271484375,
0.022216796875,
0.0117645263671875,
0.00948333740234375,
-0.025482177734375,
0.0161895751953125,
0.0469970703125,
0.0137481689453125,
0.0283966064453125,
-0.00438690185546875,
0.0241851806640625,
0.0172271728515625,
0.00226593017578125,
0.003597259521484375,
0.004230499267578125,
-0.0384521484375,
-0.0141448974609375,
-0.0207366943359375,
0.003688812255859375,
-0.0100555419921875,
0.02783203125,
-0.0135650634765625,
0.03131103515625,
0.01995849609375,
-0.035919189453125,
0.00959014892578125,
-0.0201263427734375,
-0.0005145072937011719,
0.01204681396484375,
-0.021392822265625,
-0.0219879150390625,
-0.03924560546875,
-0.0129241943359375,
-0.00628662109375,
0.01812744140625,
-0.0011548995971679688,
0.023193359375,
-0.00978851318359375,
-0.00604248046875,
0.00926971435546875,
-0.0262603759765625,
-0.0105438232421875,
0.0309600830078125,
0.003498077392578125,
0.034759521484375,
0.0037746429443359375,
0.0161590576171875,
-0.052703857421875,
0.0234832763671875,
-0.0128021240234375,
0.0044097900390625,
0.01555633544921875,
0.02825927734375,
-0.014923095703125,
-0.036773681640625,
-0.00677490234375,
-0.041015625,
-0.0308685302734375,
0.0017099380493164062,
-0.00004088878631591797,
0.002346038818359375,
-0.0093994140625,
0.01465606689453125,
-0.005802154541015625,
-0.01438140869140625,
0.0011758804321289062,
0.006130218505859375,
-0.0283050537109375,
-0.014312744140625,
-0.0204925537109375,
-0.00408172607421875,
0.043731689453125,
-0.0249176025390625,
0.03253173828125,
-0.01291656494140625,
0.015655517578125,
0.019683837890625,
0.00574493408203125,
-0.01177978515625,
0.0281982421875,
0.0025787353515625,
-0.0382080078125,
0.0001099705696105957,
-0.023468017578125,
-0.009857177734375,
-0.00775909423828125,
-0.0037784576416015625,
0.004825592041015625,
0.0223236083984375,
-0.0418701171875,
-0.0239410400390625,
0.0017538070678710938,
0.003238677978515625,
-0.005710601806640625,
0.0005459785461425781,
0.01050567626953125,
0.01971435546875,
-0.02349853515625,
0.0029773712158203125,
0.039459228515625,
0.003696441650390625,
0.005634307861328125,
-0.01332855224609375,
0.022064208984375,
0.0007033348083496094,
0.04669189453125,
0.0087738037109375,
0.0050811767578125,
-0.0146636962890625,
0.035736083984375,
-0.0009050369262695312,
-0.0001723766326904297,
0.0038166046142578125,
-0.018890380859375,
-0.00020742416381835938,
0.006191253662109375,
-0.0096435546875,
-0.002803802490234375,
-0.030731201171875,
-0.029693603515625,
-0.00975799560546875,
-0.00788116455078125,
0.011260986328125,
0.0266265869140625,
-0.045196533203125,
0.025848388671875,
0.03253173828125,
0.003719329833984375,
0.0128326416015625,
-0.0301055908203125,
-0.029815673828125,
-0.00231170654296875,
-0.0240325927734375,
-0.043243408203125,
-0.0011911392211914062,
0.009307861328125,
-0.006256103515625,
-0.00836181640625,
-0.0279083251953125,
-0.00678253173828125,
-0.0204925537109375,
0.0195465087890625,
0.040130615234375,
-0.0184173583984375,
-0.00021910667419433594,
-0.044647216796875,
0.0426025390625,
-0.01322174072265625,
-0.0269927978515625,
-0.00254058837890625,
0.0018520355224609375,
0.00888824462890625,
0.0211181640625,
-0.0183563232421875,
0.01776123046875,
0.041748046875,
0.01195526123046875,
0.0013647079467773438,
-0.0116424560546875,
-0.00972747802734375,
0.0312042236328125,
0.0036983489990234375,
-0.037017822265625,
0.0155792236328125,
0.031982421875,
0.006252288818359375,
0.0017366409301757812,
-0.01233673095703125,
0.026275634765625,
-0.0108489990234375,
0.005916595458984375,
0.0115814208984375,
-0.0033283233642578125,
-0.004978179931640625,
0.005115509033203125,
0.00836181640625,
-0.0269317626953125,
0.01507568359375,
-0.0241546630859375,
0.02752685546875,
-0.0036182403564453125,
-0.0139007568359375,
-0.00576019287109375,
-0.069091796875,
-0.029144287109375,
-0.0190582275390625,
-0.030670166015625,
-0.0030727386474609375,
0.0526123046875,
-0.01800537109375,
0.049560546875,
0.017303466796875,
-0.01175689697265625,
0.0016126632690429688,
0.00911712646484375,
-0.003658294677734375,
-0.00696563720703125,
-0.0272979736328125,
0.0197296142578125,
-0.0211639404296875,
-0.01544189453125,
0.01222991943359375,
-0.01348876953125,
-0.020050048828125,
0.0207061767578125,
0.006641387939453125,
-0.0030155181884765625,
0.01314544677734375,
-0.01036834716796875,
-0.043701171875,
-0.00365447998046875,
-0.009918212890625,
0.00201416015625,
-0.005130767822265625,
-0.02252197265625,
0.0211181640625,
0.01953125,
-0.00691986083984375,
0.0260772705078125,
-0.03228759765625,
0.01155853271484375,
0.00646209716796875,
-0.01145172119140625,
-0.0150299072265625,
-0.01256561279296875,
-0.0013170242309570312,
-0.0225982666015625,
-0.0011806488037109375,
-0.02923583984375,
0.0243988037109375,
0.0164947509765625,
-0.0206756591796875,
-0.0260772705078125,
-0.007198333740234375,
0.048095703125,
-0.03363037109375,
0.0180511474609375,
-0.01035308837890625,
-0.0281982421875,
0.01076507568359375,
-0.00833892822265625,
0.0309295654296875,
0.003543853759765625,
0.032745361328125,
-0.044525146484375,
-0.025909423828125,
-0.004993438720703125,
-0.034393310546875,
-0.0023365020751953125,
-0.013824462890625,
-0.007598876953125,
-0.025238037109375,
-0.01064300537109375,
-0.01690673828125,
-0.00736236572265625,
-0.013458251953125,
-0.0049896240234375,
0.0050048828125,
-0.006183624267578125,
-0.0164642333984375,
0.00623321533203125,
0.00040435791015625,
0.020477294921875,
-0.014984130859375,
0.031494140625,
0.01152801513671875,
-0.01177215576171875,
-0.0341796875,
-0.006816864013671875,
-0.046173095703125,
-0.032318115234375,
-0.01142120361328125,
0.007045745849609375,
0.000010371208190917969,
0.01410675048828125,
-0.0014247894287109375,
0.005542755126953125,
-0.031524658203125,
-0.0191192626953125,
-0.00720977783203125,
-0.00495147705078125,
0.004241943359375,
0.0007529258728027344,
0.0208282470703125,
-0.017822265625,
-0.0106658935546875,
-0.0173187255859375,
-0.0136260986328125,
-0.006389617919921875,
0.022918701171875,
-0.0106964111328125,
-0.0228118896484375,
-0.003131866455078125,
0.004337310791015625,
0.00986480712890625,
0.0082244873046875,
-0.019866943359375,
0.00742340087890625,
0.018310546875,
-0.0203857421875,
0.0477294921875,
0.00695037841796875,
-0.00638580322265625,
-0.0028667449951171875,
0.04107666015625,
0.0137481689453125,
0.00484466552734375,
-0.00850677490234375,
-0.0036029815673828125,
-0.0077362060546875,
0.04144287109375,
0.01508331298828125,
-0.025848388671875,
-0.0465087890625,
-0.0096282958984375,
-0.0081939697265625,
-0.00785064697265625,
-0.005695343017578125,
0.004573822021484375,
-0.0036773681640625,
-0.01287841796875,
-0.01364898681640625,
-0.0252838134765625,
0.01788330078125,
0.0030384063720703125,
-0.0259246826171875,
-0.00789642333984375,
0.0003409385681152344,
0.006511688232421875,
-0.034027099609375,
0.00977325439453125,
0.001865386962890625,
-0.0148162841796875,
0.00275421142578125,
0.012664794921875,
-0.048797607421875,
0.0008711814880371094,
0.0189971923828125,
-0.01494598388671875,
0.04046630859375,
0.00835418701171875,
-0.00604248046875,
-0.0026798248291015625,
-0.0304718017578125,
-0.0328369140625,
0.0168609619140625,
-0.029754638671875,
-0.0242919921875,
0.01922607421875,
0.03863525390625,
-0.0192413330078125,
-0.0203399658203125,
-0.00960540771484375,
0.00015783309936523438,
-0.002288818359375,
-0.02447509765625,
0.008056640625,
-0.0179443359375,
-0.0478515625,
-0.02862548828125,
0.02288818359375,
0.020751953125,
0.01258087158203125,
0.001369476318359375,
0.0056304931640625,
0.007045745849609375,
0.01296234130859375,
-0.00859832763671875,
-0.037139892578125,
-0.0145416259765625,
-0.0042877197265625,
-0.0157928466796875,
0.027130126953125,
0.030242919921875,
-0.0073089599609375,
-0.0229034423828125,
0.00670623779296875,
0.0079345703125,
0.0258941650390625,
0.011138916015625,
-0.0071868896484375,
0.046173095703125,
0.00563812255859375,
-0.0181427001953125,
-0.01250457763671875,
-0.0325927734375,
-0.004108428955078125,
0.0119781494140625,
0.0238037109375,
-0.004947662353515625,
0.01403045654296875,
-0.0216522216796875,
-0.0051422119140625,
-0.02227783203125,
-0.00870513916015625,
-0.0240936279296875,
-0.04083251953125,
-0.014678955078125,
-0.0130462646484375,
-0.0258026123046875,
-0.00518798828125,
0.0014791488647460938,
0.01399993896484375,
0.003276824951171875,
0.0021305084228515625,
0.019287109375,
-0.02996826171875,
0.002197265625,
0.0482177734375,
-0.011505126953125,
-0.0038089752197265625,
-0.023284912109375,
0.01123046875,
0.0005908012390136719,
0.01104736328125,
-0.004566192626953125,
-0.033233642578125,
-0.0088958740234375,
0.006626129150390625,
-0.052398681640625,
0.00927734375,
-0.0116729736328125,
-0.023162841796875,
-0.005901336669921875,
-0.018310546875,
0.00910186767578125,
-0.0186920166015625,
0.0330810546875,
-0.022705078125,
0.01355743408203125,
0.0064544677734375,
0.018585205078125,
-0.00022220611572265625,
-0.01439666748046875,
0.00418853759765625,
0.01494598388671875,
0.002338409423828125,
-0.0254974365234375,
0.002506256103515625,
-0.018035888671875,
0.0106964111328125,
0.0156402587890625,
0.00478363037109375,
-0.04278564453125,
-0.006755828857421875,
-0.006526947021484375,
-0.002971649169921875,
-0.0147552490234375,
-0.01885986328125,
-0.0003960132598876953,
-0.00543975830078125,
0.027099609375,
0.024505615234375,
0.0151824951171875,
0.0226898193359375,
-0.01450347900390625,
-0.043212890625,
-0.00020754337310791016,
0.002475738525390625,
-0.016571044921875,
0.005779266357421875,
-0.032379150390625,
0.023162841796875,
-0.01076507568359375,
0.01354217529296875,
0.0024051666259765625,
0.04339599609375,
0.03070068359375,
0.00998687744140625,
-0.01245880126953125,
0.008880615234375,
0.0247955322265625,
-0.0029087066650390625,
-0.006496429443359375,
-0.0175933837890625,
-0.003253936767578125,
-0.0030384063720703125,
-0.0089263916015625,
0.00774383544921875,
-0.042755126953125,
-0.01033782958984375,
0.01097869873046875,
-0.015869140625,
-0.022705078125,
0.00852203369140625,
-0.01303863525390625,
-0.01229095458984375,
0.00001609325408935547,
-0.01091766357421875,
-0.0128173828125,
-0.0165557861328125,
0.00799560546875,
-0.01168060302734375,
-0.00797271728515625,
-0.0104827880859375,
-0.0164947509765625,
-0.00717926025390625,
-0.00936126708984375,
-0.0142974853515625,
-0.03521728515625,
-0.00902557373046875,
-0.01418304443359375,
-0.0157318115234375,
0.0232696533203125,
-0.0196380615234375,
0.01438140869140625,
0.002475738525390625,
-0.0238037109375,
-0.00920867919921875,
-0.020294189453125,
-0.040496826171875,
-0.01824951171875,
0.009735107421875,
-0.00107574462890625,
0.046722412109375,
-0.01404571533203125,
-0.0228729248046875,
-0.038177490234375,
-0.0301666259765625,
-0.0107574462890625,
-0.0228271484375,
0.021331787109375,
0.002105712890625,
-0.0219268798828125,
-0.036956787109375,
0.00753021240234375,
-0.0012826919555664062,
-0.019561767578125,
-0.007274627685546875,
0.0079345703125,
0.036651611328125,
0.0198974609375,
-0.0249786376953125,
-0.005664825439453125,
0.0341796875,
0.0242462158203125,
-0.01336669921875,
-0.0017375946044921875,
-0.04046630859375,
-0.019500732421875,
-0.00374603271484375,
0.005802154541015625,
0.006893157958984375,
0.00791168212890625,
-0.0112152099609375,
0.0093841552734375,
-0.05291748046875,
0.0098876953125,
0.00827789306640625,
0.06256103515625,
-0.0001405477523803711,
-0.02667236328125,
-0.00251007080078125,
-0.0005850791931152344,
-0.00154876708984375,
0.006072998046875,
0.00970458984375,
-0.003986358642578125,
-0.014923095703125,
-0.0173797607421875,
0.0235137939453125,
0.024505615234375,
-0.00222015380859375,
-0.002437591552734375,
0.0038661956787109375,
-0.01302337646484375,
0.0531005859375,
-0.0108642578125,
-0.0019426345825195312,
0.00643157958984375,
-0.01398468017578125,
0.00406646728515625,
0.003643035888671875,
0.01189422607421875,
-0.02520751953125,
-0.00995635986328125,
-0.01027679443359375,
0.00998687744140625,
0.001247406005859375,
0.0008840560913085938,
0.0151519775390625,
-0.0074310302734375,
-0.005496978759765625,
-0.017120361328125,
0.0255889892578125,
-0.03631591796875,
0.01284027099609375,
0.0289764404296875,
-0.002674102783203125,
-0.0068206787109375,
0.0128173828125,
-0.00768280029296875,
-0.041595458984375,
-0.001949310302734375,
0.028533935546875,
0.00799560546875,
-0.021240234375,
0.00638580322265625,
-0.0181884765625,
0.004909515380859375,
0.026092529296875,
0.017791748046875,
0.00841522216796875,
0.045867919921875,
0.0189208984375,
-0.008819580078125,
0.041656494140625,
0.006866455078125,
0.007740020751953125,
-0.00794219970703125,
0.01531982421875,
-0.0081939697265625,
0.02777099609375,
0.00620269775390625,
0.00443267822265625,
0.03729248046875,
0.01593017578125,
-0.000492095947265625,
-0.0124969482421875,
-0.0218353271484375,
-0.028778076171875,
-0.01313018798828125,
0.01068115234375,
-0.01177978515625,
0.04107666015625,
0.022705078125,
-0.0214691162109375,
-0.0122528076171875,
0.00019824504852294922,
-0.002666473388671875,
0.0160980224609375,
-0.017822265625,
0.0243682861328125,
0.00319671630859375,
0.026702880859375,
0.023345947265625,
-0.00406646728515625,
0.0008101463317871094,
-0.0023517608642578125,
-0.050933837890625,
0.02069091796875,
-0.00701141357421875,
0.0133056640625,
-0.012115478515625,
-0.00286865234375,
0.0213775634765625,
0.027099609375,
-0.01548004150390625,
-0.03228759765625,
-0.0164947509765625,
-0.034820556640625,
0.00925445556640625,
-0.023681640625,
0.00792694091796875,
0.00775146484375,
-0.027435302734375,
-0.00971221923828125,
0.01776123046875,
0.001781463623046875,
-0.0269927978515625,
-0.030120849609375,
-0.0170440673828125,
-0.017303466796875,
0.026824951171875,
0.004192352294921875,
0.04071044921875,
0.02374267578125,
0.0159759521484375,
0.00498199462890625,
0.0106048583984375,
0.0157623291015625,
-0.003108978271484375,
-0.00522613525390625,
-0.00547027587890625,
-0.0274810791015625,
-0.0169525146484375,
0.01263427734375,
0.00893402099609375,
-0.005748748779296875,
0.037933349609375,
-0.00872039794921875,
0.0171051025390625,
0.0305023193359375,
-0.01177978515625,
-0.0116424560546875,
0.0019350051879882812,
-0.008880615234375,
0.038116455078125,
-0.0096435546875,
0.01071929931640625,
-0.0265960693359375,
0.033233642578125,
0.00623321533203125,
-0.016357421875,
-0.0142059326171875,
-0.022796630859375,
0.0002522468566894531,
0.014007568359375,
-0.0289459228515625,
0.00191497802734375,
0.0276947021484375,
-0.0018491744995117188,
-0.020416259765625,
-0.0265045166015625,
0.01305389404296875,
-0.0071563720703125,
0.0158233642578125,
-0.01110076904296875,
-0.0298309326171875,
0.0074920654296875,
-0.013885498046875,
-0.00995635986328125,
0.0121612548828125,
-0.0026302337646484375,
0.0273284912109375,
-0.007045745849609375,
-0.0171966552734375,
-0.0078125,
-0.006378173828125,
0.055999755859375,
-0.0211944580078125,
-0.002033233642578125,
-0.01293182373046875,
-0.006439208984375,
0.00878143310546875,
0.0192108154296875,
-0.009490966796875,
0.00542449951171875,
-0.01309967041015625,
0.0251312255859375,
0.039764404296875,
0.007305145263671875,
0.0211029052734375,
0.0084075927734375,
0.0029811859130859375,
-0.00006246566772460938,
0.03302001953125,
-0.02630615234375,
-0.01500701904296875,
0.0170135498046875,
0.043853759765625,
-0.0172271728515625,
-0.0026760101318359375,
-0.016815185546875,
-0.045440673828125,
0.0008153915405273438,
-0.01305389404296875,
0.036895751953125,
-0.017822265625,
-0.0069732666015625,
-0.004001617431640625,
0.004608154296875,
0.01331329345703125,
0.0213623046875,
0.01105499267578125,
0.00940704345703125,
0.0172119140625,
0.0029392242431640625,
0.009307861328125,
-0.0125885009765625,
0.02081298828125,
0.025146484375,
-0.0106658935546875,
-0.0023326873779296875,
0.0125579833984375,
0.038177490234375,
0.0027637481689453125,
-0.0020389556884765625,
0.01165771484375,
0.0169219970703125,
-0.0300140380859375,
0.00972747802734375,
0.0282135009765625,
-0.00058746337890625,
0.005474090576171875,
-0.00415802001953125,
-0.0033092498779296875,
0.0123443603515625,
-0.058685302734375,
-0.0279998779296875,
0.045440673828125,
-0.020904541015625,
-0.0286102294921875,
0.0035419464111328125,
0.008636474609375,
-0.0270538330078125,
0.0164794921875,
-0.0025348663330078125,
0.005207061767578125,
-0.005619049072265625,
0.0172576904296875,
0.026092529296875,
0.004856109619140625,
0.002696990966796875,
-0.042144775390625,
0.0046234130859375,
-0.003917694091796875,
0.006282806396484375,
0.027008056640625,
0.005825042724609375,
-0.00848388671875,
0.0095062255859375,
-0.0060577392578125,
-0.009674072265625,
-0.0292816162109375,
-0.039276123046875,
0.0011138916015625,
0.0231170654296875,
-0.005413055419921875,
-0.0182037353515625,
-0.01163482666015625,
0.0024871826171875,
0.0087890625,
-0.0384521484375,
-0.01024627685546875,
0.005901336669921875,
-0.0090484619140625,
0.00997161865234375,
-0.0151824951171875,
-0.0035305023193359375,
-0.04498291015625,
-0.0132598876953125,
-0.018951416015625,
0.00701141357421875,
-0.020263671875,
-0.0021495819091796875,
0.01174163818359375,
-0.01244354248046875,
-0.01439666748046875,
0.024810791015625,
0.0011034011840820312,
0.02203369140625,
-0.01137542724609375,
-0.0205078125,
-0.0165252685546875,
-0.00983428955078125,
-0.00730133056640625,
0.0028095245361328125,
-0.0148468017578125,
0.004688262939453125,
0.0202178955078125,
0.020751953125,
-0.003055572509765625,
0.01097869873046875,
0.0019168853759765625,
-0.004848480224609375,
0.019927978515625,
0.0203704833984375,
-0.0000591278076171875,
0.040679931640625,
0.006603240966796875,
0.0137176513671875,
0.021087646484375,
-0.01190185546875,
0.02899169921875,
0.0090789794921875,
0.0190887451171875,
0.006771087646484375,
-0.034454345703125,
0.0273590087890625,
-0.01010894775390625,
-0.0007300376892089844,
0.0212249755859375,
-0.01107025146484375,
-0.0090484619140625,
0.0018911361694335938,
-0.0010862350463867188,
-0.004177093505859375,
0.01267242431640625,
0.0251617431640625,
0.0089874267578125,
0.01456451416015625,
-0.0098419189453125,
-0.03082275390625,
-0.00936126708984375,
-0.01192474365234375,
-0.0167694091796875,
-0.01251220703125,
0.031890869140625,
0.0031642913818359375,
-0.00421142578125,
-0.030670166015625,
-0.0269317626953125,
0.01275634765625,
0.02764892578125,
-0.0034885406494140625,
0.00730133056640625,
-0.01366424560546875,
0.0099639892578125,
-0.00589752197265625,
-0.042205810546875,
0.0167388916015625,
0.0130157470703125,
0.00325775146484375,
-0.0007476806640625,
-0.00482177734375,
0.027435302734375,
-0.0016994476318359375,
0.0155487060546875,
-0.0233612060546875,
-0.042266845703125,
0.016357421875,
-0.0191497802734375,
0.01189422607421875,
-0.0179443359375,
-0.004550933837890625,
0.034210205078125,
0.00438690185546875,
0.0226287841796875,
-0.01763916015625,
0.0152587890625,
0.0157470703125,
-0.0223541259765625,
0.01032257080078125,
-0.0148162841796875,
0.0094146728515625,
-0.005779266357421875,
0.0194854736328125,
-0.00687408447265625,
-0.01293182373046875,
-0.011566162109375,
0.0280303955078125,
-0.00542449951171875,
-0.0083770751953125,
0.005947113037109375,
0.006683349609375,
-0.002838134765625,
0.014556884765625,
-0.03790283203125,
0.011444091796875,
-0.04608154296875,
-0.00848388671875,
-0.01187896728515625,
-0.00618743896484375,
-0.00455474853515625,
-0.0307159423828125,
-0.0073394775390625,
0.03851318359375,
0.004917144775390625,
-0.002872467041015625,
0.00534820556640625,
-0.006862640380859375,
-0.0198211669921875,
-0.007781982421875,
0.01751708984375,
0.043212890625,
0.01273345947265625,
-0.01287078857421875,
0.0212554931640625,
0.0257415771484375,
0.0032901763916015625,
-0.0217437744140625,
0.01486968994140625,
0.01100921630859375,
0.0034942626953125,
0.001964569091796875,
0.022430419921875,
-0.004604339599609375,
0.01007080078125,
0.0113677978515625,
-0.0269012451171875,
0.0010099411010742188,
-0.0029239654541015625,
-0.01389312744140625,
-0.002025604248046875,
-0.0271148681640625,
-0.014129638671875,
-0.01824951171875,
0.007904052734375,
-0.009002685546875,
-0.003963470458984375,
-0.0171051025390625,
0.007373809814453125,
-0.020965576171875,
-0.0307769775390625,
0.01320648193359375,
-0.0033721923828125,
0.01509857177734375,
0.00014460086822509766,
-0.0311126708984375,
-0.0166778564453125,
0.006458282470703125,
0.00565338134765625,
0.0258941650390625,
-0.000827789306640625,
-0.023468017578125,
0.01395416259765625,
-0.01079559326171875,
-0.0260772705078125,
0.001239776611328125,
0.0009679794311523438,
-0.00855255126953125,
-0.001079559326171875,
-0.031951904296875,
0.020751953125,
-0.0285491943359375,
0.0036449432373046875,
0.0160980224609375,
0.041717529296875,
-0.007476806640625,
-0.0010204315185546875,
-0.000614166259765625,
-0.0009722709655761719,
-0.0060272216796875,
-0.007472991943359375,
0.0074920654296875,
0.004894256591796875,
0.0172576904296875,
-0.00592041015625,
0.0017032623291015625,
-0.0261688232421875,
-0.0252227783203125,
-0.012054443359375,
0.00542449951171875,
0.0023899078369140625,
0.005096435546875,
-0.0020008087158203125,
-0.00008052587509155273,
-0.006160736083984375,
0.008636474609375,
-0.0245819091796875,
-0.016876220703125,
0.003124237060546875,
-0.02117919921875,
-0.02734375,
-0.0078125,
0.03668212890625,
0.00839996337890625,
-0.022491455078125,
-0.007358551025390625,
-0.053070068359375,
-0.01201629638671875,
-0.01311492919921875,
0.022979736328125,
-0.06683349609375,
-0.0291595458984375,
-0.0034637451171875,
0.002101898193359375,
-0.01123809814453125,
0.036895751953125,
-0.00746917724609375,
0.024322509765625,
-0.0213165283203125,
0.0058135986328125,
0.01849365234375,
0.0005331039428710938,
-0.0191192626953125,
-0.042266845703125,
-0.026275634765625,
-0.01253509521484375,
-0.008453369140625,
-0.00768280029296875,
0.002933502197265625,
0.00799560546875,
-0.004730224609375,
0.005970001220703125,
0.025115966796875,
-0.007091522216796875,
-0.0294189453125,
-0.0029354095458984375,
0.01348876953125,
0.0041961669921875,
0.0118560791015625,
0.01290130615234375,
-0.006988525390625,
0.01515960693359375,
-0.009613037109375,
0.00043010711669921875,
0.01169586181640625,
0.0220489501953125,
-0.01776123046875,
0.0033740997314453125,
-0.038177490234375,
0.0042724609375,
0.01837158203125,
0.0003867149353027344,
-0.005664825439453125,
0.0098419189453125,
-0.016815185546875,
-0.0138702392578125,
-0.01038360595703125,
-0.00927734375,
-0.004425048828125,
-0.035064697265625,
-0.00909423828125,
0.01334381103515625,
0.003871917724609375,
0.007213592529296875,
0.0010223388671875,
-0.01154327392578125,
-0.0341796875,
-0.0220947265625,
0.039337158203125,
-0.00885009765625,
-0.00970458984375,
-0.0251312255859375,
-0.01552581787109375,
0.02874755859375,
-0.0219268798828125,
0.02288818359375,
0.01288604736328125,
-0.009368896484375,
-0.0010890960693359375,
0.01788330078125,
0.042755126953125,
0.0247344970703125,
-0.011688232421875,
-0.0111846923828125,
-0.022735595703125,
-0.010040283203125,
0.02447509765625,
-0.020965576171875,
-0.005756378173828125,
0.029937744140625,
-0.0096893310546875,
-0.00577545166015625,
-0.00982666015625,
0.0219268798828125,
0.01641845703125,
0.034820556640625,
-0.00859832763671875,
-0.02813720703125,
-0.041534423828125,
0.002857208251953125,
-0.00057220458984375,
-0.01446533203125,
0.01187896728515625,
0.004550933837890625,
-0.01084136962890625,
0.0292205810546875,
-0.007114410400390625,
0.01055145263671875,
0.01180267333984375,
-0.0302276611328125,
-0.020263671875,
-0.026824951171875,
0.013092041015625,
-0.0187835693359375,
0.0169525146484375,
0.0235595703125,
0.051483154296875,
0.0077362060546875,
0.0123291015625,
0.0155792236328125,
0.01451873779296875,
-0.0099029541015625,
0.014923095703125,
-0.02618408203125,
0.0021820068359375,
0.0102996826171875,
-0.0029926300048828125,
0.03314208984375,
-0.01435089111328125,
-0.01959228515625,
0.00261688232421875,
0.0101165771484375,
0.00946044921875,
-0.00357818603515625,
-0.010498046875,
-0.01045989990234375,
0.0242767333984375,
-0.0003407001495361328,
-0.040863037109375,
-0.008636474609375,
-0.0240020751953125,
0.039306640625,
-0.01062774658203125,
-0.0170135498046875,
0.041015625,
0.005401611328125,
-0.030731201171875,
-0.005008697509765625,
0.02679443359375,
-0.00513458251953125,
-0.00046944618225097656,
-0.0116729736328125,
-0.027130126953125,
-0.037445068359375,
-0.01119232177734375,
0.035980224609375,
-0.01407623291015625,
0.0374755859375,
-0.00959014892578125,
-0.004032135009765625,
-0.04119873046875,
-0.00832366943359375,
-0.00041413307189941406,
0.0056610107421875,
0.0135345458984375,
-0.0157470703125,
0.0076751708984375,
0.01183319091796875,
-0.00246429443359375,
0.005802154541015625,
0.01177215576171875,
0.003833770751953125,
0.0164031982421875,
-0.030364990234375,
0.031982421875,
0.0089111328125,
-0.0170135498046875,
-0.04058837890625,
-0.01367950439453125,
0.0323486328125,
-0.0209197998046875,
-0.0174560546875,
0.0189666748046875,
0.02685546875,
-0.00592041015625,
0.020751953125,
-0.004734039306640625,
-0.002056121826171875,
-0.018829345703125,
0.0262603759765625,
-0.0017137527465820312,
0.033843994140625,
0.00792694091796875,
-0.01053619384765625,
0.0214080810546875,
-0.033905029296875,
-0.030181884765625,
0.0144195556640625,
0.023162841796875,
-0.0010509490966796875,
0.0014581680297851562,
-0.0122833251953125,
0.025543212890625,
0.04718017578125,
-0.0316162109375,
-0.007381439208984375,
-0.020233154296875,
-0.01024627685546875,
-0.0022220611572265625,
-0.0182647705078125,
0.00988006591796875,
0.001560211181640625,
0.00655364990234375,
-0.00579833984375,
0.002574920654296875,
-0.0184783935546875,
0.00478363037109375,
0.005336761474609375,
0.005390167236328125,
-0.0121612548828125,
0.030914306640625,
0.007198333740234375,
-0.01493072509765625,
0.021240234375,
0.03436279296875,
-0.024078369140625,
0.0196533203125,
0.026580810546875,
-0.0016412734985351562,
-0.00791168212890625,
0.0271148681640625,
0.01354217529296875,
-0.00006908178329467773,
-0.004955291748046875,
0.00630950927734375,
0.0098724365234375,
0.017333984375,
-0.02081298828125,
-0.005504608154296875,
-0.0213623046875,
-0.0014352798461914062,
-0.0262603759765625,
-0.024810791015625,
0.0248565673828125,
0.009918212890625,
-0.0027332305908203125,
-0.01453399658203125,
0.01025390625,
-0.0122833251953125,
-0.0036945343017578125,
-0.04931640625,
-0.00023126602172851562,
0.012847900390625,
0.00896453857421875,
0.029022216796875,
-0.04180908203125,
0.016204833984375,
0.0228271484375,
0.01340484619140625,
-0.004730224609375,
-0.006977081298828125,
0.022186279296875,
-0.0218963623046875,
-0.00829315185546875,
-0.01044464111328125,
0.03924560546875,
-0.01690673828125,
-0.01128387451171875,
-0.01434326171875,
0.01093292236328125,
0.032257080078125,
0.02069091796875,
0.02435302734375,
0.012237548828125,
0.0083770751953125,
0.0227203369140625,
0.02313232421875,
-0.0075225830078125,
0.01403045654296875,
-0.00897216796875,
0.041778564453125,
0.0242919921875,
0.007549285888671875,
-0.0194091796875,
0.0203399658203125,
-0.0380859375,
-0.0011196136474609375,
-0.0014715194702148438,
-0.032989501953125,
0.0179290771484375,
0.01555633544921875,
0.02215576171875,
0.02032470703125,
-0.02294921875,
0.039398193359375,
-0.0333251953125,
-0.04547119140625,
0.033966064453125,
-0.00751495361328125,
-0.016357421875,
0.01200103759765625,
0.0160675048828125,
-0.00588226318359375,
-0.0021572113037109375,
0.016632080078125,
0.00936126708984375,
-0.01434326171875,
0.006053924560546875,
0.006847381591796875,
0.034881591796875,
-0.00792694091796875,
-0.00720977783203125,
-0.016693115234375,
0.0236968994140625,
-0.00815582275390625,
0.0132904052734375,
0.0196380615234375,
0.0032100677490234375,
-0.017822265625,
0.0221099853515625,
0.0173187255859375,
-0.00318145751953125,
0.0015659332275390625,
-0.00826263427734375,
0.01151275634765625,
0.0090179443359375,
0.002567291259765625,
0.038360595703125,
0.00402069091796875,
0.00597381591796875,
0.01378631591796875,
0.0207366943359375,
-0.0022068023681640625,
0.033050537109375,
0.00040030479431152344,
0.02777099609375,
0.008148193359375,
0.0244293212890625,
0.0007290840148925781,
0.01058197021484375,
-0.001667022705078125,
0.01279449462890625,
0.0017490386962890625,
0.0156097412109375,
-0.0238189697265625,
-0.004062652587890625,
-0.00920867919921875,
-0.015655517578125,
0.003917694091796875,
0.00699615478515625,
-0.026763916015625,
0.0287933349609375,
-0.002170562744140625,
0.00787353515625,
0.034912109375,
0.003326416015625,
0.0013132095336914062,
-0.01100921630859375,
-0.006000518798828125,
-0.0017309188842773438,
-0.01617431640625,
0.01500701904296875,
-0.007080078125,
-0.0131378173828125,
-0.0182952880859375,
0.0026035308837890625,
0.041015625,
-0.03228759765625,
0.017425537109375,
-0.038787841796875,
-0.019256591796875,
0.01556396484375,
0.003810882568359375,
0.04766845703125,
-0.036712646484375,
0.032440185546875,
0.003894805908203125,
0.0089263916015625,
-0.01248931884765625,
0.0128326416015625,
-0.038330078125,
0.00011688470840454102,
0.0102996826171875,
-0.0109100341796875,
0.0004177093505859375,
-0.0019588470458984375,
0.002197265625,
-0.0026798248291015625,
0.000514984130859375,
0.026092529296875,
-0.006832122802734375,
0.0021305084228515625,
-0.0280609130859375,
-0.01213836669921875,
0.0022640228271484375,
-0.0161895751953125,
0.0021724700927734375,
-0.017059326171875,
-0.01235198974609375,
-0.038116455078125,
-0.020721435546875,
0.0001245737075805664,
-0.01702880859375,
0.007537841796875,
0.0207366943359375,
0.01085662841796875,
0.01004791259765625,
-0.04412841796875,
0.0280303955078125,
-0.002666473388671875,
-0.00743865966796875,
-0.00684356689453125,
-0.026214599609375,
0.0001595020294189453,
0.03424072265625,
0.01335906982421875,
-0.0175933837890625,
-0.033935546875,
0.01529693603515625,
0.035797119140625,
-0.0278472900390625,
0.01384735107421875,
0.01140594482421875,
0.032989501953125,
0.01068878173828125,
-0.021759033203125,
0.0003902912139892578,
-0.0258331298828125,
0.0118255615234375,
-0.00788116455078125,
-0.0176239013671875,
0.0001513957977294922,
0.017333984375,
-0.00420379638671875,
0.01322174072265625,
-0.0316162109375,
0.021820068359375,
0.01413726806640625,
0.0120391845703125,
0.00958251953125,
-0.006595611572265625,
-0.01666259765625,
-0.02423095703125,
0.05029296875,
0.031768798828125,
-0.01110076904296875,
-0.01995849609375,
-0.0240936279296875,
-0.021392822265625,
0.0002548694610595703,
0.023773193359375,
-0.00028061866760253906,
-0.01166534423828125,
0.006397247314453125,
0.00015056133270263672,
-0.036346435546875,
0.015716552734375,
0.006710052490234375,
-0.0002684593200683594,
-0.011199951171875,
0.00730133056640625,
0.004718780517578125,
-0.005146026611328125,
0.0248260498046875,
-0.02471923828125,
0.0025997161865234375,
0.0289154052734375,
0.00038051605224609375,
-0.006969451904296875,
0.022613525390625,
-0.0095672607421875,
-0.0071258544921875,
-0.006191253662109375,
-0.006610870361328125,
0.0007505416870117188,
0.019256591796875,
-0.0202484130859375,
-0.006732940673828125,
0.001251220703125,
-0.0269317626953125,
-0.007106781005859375,
-0.0172882080078125,
0.00411224365234375,
0.0031566619873046875,
0.01251983642578125,
0.0303497314453125,
0.00347137451171875,
0.0203704833984375,
0.005401611328125,
-0.00384521484375,
0.0301666259765625,
0.0016279220581054688,
0.031768798828125,
0.004375457763671875,
-0.006061553955078125,
-0.0308685302734375,
0.02752685546875,
0.04022216796875,
-0.0057220458984375,
-0.002117156982421875,
0.02166748046875,
-0.03228759765625,
-0.03515625,
-0.0009446144104003906,
-0.04205322265625,
0.0115814208984375,
-0.01629638671875,
-0.03973388671875,
-0.057769775390625,
-0.027008056640625,
0.033966064453125,
-0.00855255126953125,
0.001285552978515625,
0.0198211669921875,
-0.0202178955078125,
-0.014373779296875,
0.01593017578125,
-0.05218505859375,
-0.02008056640625,
0.007045745849609375,
-0.0215911865234375,
-0.0170135498046875,
0.0019397735595703125,
0.00036716461181640625,
-0.02935791015625,
-0.017578125,
0.0029544830322265625,
0.00539398193359375,
-0.0296478271484375,
-0.00830841064453125,
-0.002681732177734375,
0.0059967041015625,
0.0174560546875,
-0.05987548828125,
-0.0053558349609375,
0.0017366409301757812,
-0.01251983642578125,
-0.01013946533203125,
0.0032749176025390625,
-0.019134521484375,
0.0018711090087890625,
-0.01096343994140625,
0.01099395751953125,
0.0037708282470703125,
-0.02532958984375,
-0.0008101463317871094,
0.0025959014892578125,
0.0087432861328125,
-0.01009368896484375,
-0.00908660888671875,
0.0005245208740234375,
-0.016448974609375,
0.0021228790283203125,
-0.022613525390625,
-0.022308349609375,
-0.00927734375,
0.01291656494140625,
0.0006237030029296875,
-0.0268096923828125,
0.0203857421875,
-0.01457977294921875,
0.01473236083984375,
0.044525146484375,
-0.01255035400390625,
0.0084228515625,
-0.0100860595703125,
-0.0011529922485351562,
0.01222991943359375,
-0.0099639892578125,
0.021759033203125,
0.0265960693359375,
0.04913330078125,
0.01435089111328125,
0.0097503662109375,
-0.022857666015625,
-0.0736083984375,
-0.026641845703125,
0.00949859619140625,
-0.0024852752685546875,
0.0229034423828125,
-0.02667236328125,
-0.0059967041015625,
-0.026947021484375,
0.01025390625,
0.04010009765625,
-0.005695343017578125,
0.005298614501953125,
0.004947662353515625,
-0.0245819091796875,
0.0007290840148925781,
0.015777587890625,
0.0192108154296875,
-0.031402587890625,
-0.0030994415283203125,
-0.007061004638671875,
-0.0097198486328125,
-0.0016298294067382812,
0.0352783203125,
-0.0015001296997070312,
0.00249481201171875,
0.004871368408203125,
0.004398345947265625,
0.0224761962890625
] |
ours_560
|
The answer is \(280\).
Call a \(k\)-string a string of moves that start and end at the origin, without passing through the origin other than at its endpoints.
1. **8-string paths**: The frog traces out a polyomino. There are 3 polyominoes in this case: a \(2 \times 2\) square, a straight segment with 3 unit squares, and an L shape. The square can be rotated in 1 way, the straight segment in 2 ways, and the L in 4 ways. For each polyomino and orientation, the origin of the coordinate system can be placed at 8 positions on the boundary, and given the polyomino, orientation, and origin location, there are 2 ways to traverse the path. This gives \(2 \times 8 \times (1+2+4) = 112\) paths.
2. **6-string paths**: The path is a dangling line segment attached to a polyomino, specifically a domino with a dangling segment. The domino has 2 possible orientations. For each orientation, there are 6 places to put the origin. If the origin is at a vertex, there are 4 places it could go, and the dangling segment has 2 possible directions. There are 2 ways to choose the traversal order (segment first or domino first), and there are 2 ways to traverse the domino. Thus, there are \(4 \times 2 \times 2 \times 2 = 32\) paths. If the origin is not at a vertex, there are 2 places it could go, and the dangling segment has 1 possible direction. Again, there are 2 ways to choose traversal order and 2 ways to traverse the domino, giving \(2 \times 2 \times 2 = 8\) paths. With 2 orientations of the domino, we have \(2 \times (32+8) = 80\) paths.
3. **4-string and 2-string paths**: There are three cases:
- Two 4-strings: Two unit squares attached at a corner. There are 2 ways to choose the orientation of the squares, and 8 ways to traverse each orientation, for 16 paths.
- One 4-string and two 2-strings: Two dangling line segments attached to one corner of a unit square. There are 4 orientations, 2 ways to traverse the square, and \(3! = 6\) ways to choose the order of the square and segments. This gives \(4 \cdot 2 \cdot 6 = 48\) paths.
- Four 2-strings: A star shape. There are \(4! = 24\) ways to choose the order of the stars.
Adding these, the total number of paths is \(112 + 80 + 16 + 48 + 24 = 280\).
\(\boxed{280}\)
|
280
|
{
"competition": "us_comps",
"dataset": "Ours",
"posts": null,
"source": "OMOSoln2.md"
}
|
The Lattice Point Jumping Frog jumps between lattice points in a coordinate plane that are exactly 1 unit apart. The Lattice Point Jumping Frog starts at the origin and makes 8 jumps, ending at the origin. Additionally, it never lands on a point other than the origin more than once. How many possible paths could the frog have taken?
## Clarifications:
- The Lattice Jumping Frog is allowed to visit the origin more than twice.
- The path of the Lattice Jumping Frog is an ordered path, that is, the order in which the Lattice Jumping Frog performs its jumps matters.
|
[
"/Mathematics/DiscreteMathematics/Combinatorics/Enumeration",
"/Mathematics/DiscreteMathematics/Combinatorics/LatticePathsandPolygons",
"/Mathematics/DiscreteMathematics/GeneralDiscreteMathematics/DiscreteMath",
"/Mathematics/DiscreteMathematics/GeneralDiscreteMathematics/DiscreteMathematics",
"/Mathematics/DiscreteMathematics/GeneralDiscreteMathematics/FiniteMathematics",
"/Mathematics/RecreationalMathematics/Puzzles/Puzzle"
] |
Decompose the 8‑step closed walk into non‑overlapping k‑strings (subloops) that correspond to distinct polyomino shapes and count all shape, orientation, origin placement, and traversal order possibilities.
|
[
0.00008213520050048828,
-0.036834716796875,
0.047698974609375,
-0.044281005859375,
0.0005426406860351562,
0.00023412704467773438,
0.023468017578125,
-0.038848876953125,
0.005733489990234375,
0.048095703125,
0.03118896484375,
-0.00638580322265625,
-0.003692626953125,
0.0204925537109375,
-0.0154266357421875,
-0.033966064453125,
0.03961181640625,
0.0292816162109375,
-0.042938232421875,
0.004520416259765625,
-0.01641845703125,
-0.07745361328125,
-0.031158447265625,
0.05364990234375,
-0.034454345703125,
-0.012908935546875,
-0.0152130126953125,
-0.0169677734375,
-0.03399658203125,
0.022705078125,
-0.075439453125,
0.00632476806640625,
0.03448486328125,
-0.006816864013671875,
0.002285003662109375,
0.00919342041015625,
0.0394287109375,
0.00452423095703125,
-0.0198516845703125,
-0.0225372314453125,
-0.0120391845703125,
-0.0243988037109375,
0.02349853515625,
0.010009765625,
-0.01165771484375,
0.026611328125,
-0.0025997161865234375,
0.0223541259765625,
-0.0197906494140625,
-0.00931549072265625,
-0.00658416748046875,
0.01033782958984375,
-0.005733489990234375,
-0.0163421630859375,
-0.032989501953125,
-0.035064697265625,
-0.031402587890625,
-0.00133514404296875,
-0.007663726806640625,
0.0300750732421875,
0.004222869873046875,
0.017669677734375,
-0.019775390625,
-0.00661468505859375,
-0.00803375244140625,
-0.0092926025390625,
-0.00487518310546875,
0.0017938613891601562,
0.0055694580078125,
-0.019561767578125,
-0.006687164306640625,
-0.02105712890625,
-0.0185089111328125,
0.01490020751953125,
0.0073699951171875,
-0.0150146484375,
-0.011505126953125,
0.0054168701171875,
0.034912109375,
0.0084991455078125,
0.026123046875,
-0.01184844970703125,
0.01690673828125,
-0.01885986328125,
0.006999969482421875,
0.027923583984375,
0.0157928466796875,
-0.0161285400390625,
0.0245361328125,
-0.00142669677734375,
-0.0013437271118164062,
-0.010040283203125,
-0.0218505859375,
0.0148468017578125,
-0.0086212158203125,
0.015045166015625,
0.0008206367492675781,
-0.0156707763671875,
-0.00978851318359375,
-0.0014209747314453125,
-0.00676727294921875,
-0.006748199462890625,
0.0190277099609375,
0.00737762451171875,
-0.006927490234375,
-0.0107269287109375,
-0.01385498046875,
-0.00194549560546875,
-0.007354736328125,
0.01175689697265625,
0.0009055137634277344,
0.0008296966552734375,
0.0176544189453125,
0.0391845703125,
0.01031494140625,
0.0021686553955078125,
-0.01412200927734375,
-0.002155303955078125,
-0.0062408447265625,
-0.0284576416015625,
0.0140533447265625,
0.020050048828125,
0.00719451904296875,
0.0041351318359375,
0.01428985595703125,
-0.033477783203125,
0.00041031837463378906,
-0.0028057098388671875,
-0.0136260986328125,
0.004413604736328125,
0.0118560791015625,
0.00579071044921875,
0.0022792816162109375,
-0.0301513671875,
-0.032196044921875,
-0.0258331298828125,
0.0098724365234375,
-0.02288818359375,
0.0004794597625732422,
-0.0204620361328125,
0.0129852294921875,
-0.0193328857421875,
0.007579803466796875,
-0.026763916015625,
-0.012542724609375,
0.033294677734375,
-0.0131988525390625,
-0.035186767578125,
0.0079498291015625,
0.01122283935546875,
-0.030364990234375,
0.009735107421875,
0.006805419921875,
0.0020160675048828125,
-0.0023784637451171875,
0.000034809112548828125,
0.00299072265625,
-0.01329803466796875,
0.0288543701171875,
0.0220489501953125,
0.0031986236572265625,
-0.007427215576171875,
0.0433349609375,
0.036346435546875,
0.0061492919921875,
0.0243988037109375,
0.0059814453125,
0.00485992431640625,
-0.00870513916015625,
0.025970458984375,
0.0024890899658203125,
-0.0204925537109375,
0.027374267578125,
-0.037017822265625,
0.008056640625,
0.007511138916015625,
0.00742340087890625,
0.01544189453125,
-0.0188446044921875,
0.00545501708984375,
0.0030422210693359375,
-0.05596923828125,
0.00785064697265625,
0.03265380859375,
0.005481719970703125,
-0.0108184814453125,
-0.006870269775390625,
0.0146331787109375,
0.03094482421875,
0.0005588531494140625,
0.0165863037109375,
-0.03436279296875,
0.00968170166015625,
-0.0012083053588867188,
0.005123138427734375,
0.005367279052734375,
-0.01947021484375,
0.00799560546875,
0.026519775390625,
0.0014247894287109375,
-0.0201263427734375,
0.009307861328125,
-0.006649017333984375,
0.00943756103515625,
-0.0101318359375,
0.0198822021484375,
0.003936767578125,
-0.01346588134765625,
0.0148773193359375,
-0.0147705078125,
-0.004055023193359375,
-0.039581298828125,
-0.027496337890625,
-0.07073974609375,
0.005710601806640625,
0.0004019737243652344,
-0.017578125,
-0.01305389404296875,
0.03369140625,
-0.0305023193359375,
-0.00033283233642578125,
0.0036220550537109375,
-0.003665924072265625,
0.01424407958984375,
0.0007791519165039062,
-0.01474761962890625,
0.00868988037109375,
0.00617218017578125,
-0.0038852691650390625,
-0.0007033348083496094,
0.0177001953125,
0.007106781005859375,
-0.003551483154296875,
-0.0229339599609375,
0.0037860870361328125,
-0.0034999847412109375,
0.01175689697265625,
-0.0220489501953125,
-0.0010986328125,
0.009521484375,
0.031158447265625,
0.00731658935546875,
-0.023193359375,
-0.008636474609375,
-0.00965118408203125,
0.003917694091796875,
-0.003025054931640625,
0.016845703125,
0.01165771484375,
-0.015869140625,
-0.0195770263671875,
0.0198822021484375,
0.00919342041015625,
-0.024505615234375,
-0.01739501953125,
-0.00858306884765625,
-0.00988006591796875,
0.01824951171875,
-0.0083465576171875,
0.020233154296875,
-0.01058197021484375,
0.0240936279296875,
0.00836181640625,
-0.001224517822265625,
-0.0095062255859375,
-0.031341552734375,
-0.01407623291015625,
0.00917816162109375,
-0.0010328292846679688,
-0.006374359130859375,
0.032867431640625,
0.00968170166015625,
0.010345458984375,
-0.0003025531768798828,
0.004856109619140625,
-0.00373077392578125,
-0.006587982177734375,
0.0140838623046875,
0.0253753662109375,
-0.005199432373046875,
0.02618408203125,
-0.00444793701171875,
0.00902557373046875,
0.003650665283203125,
0.00917816162109375,
-0.02154541015625,
-0.056121826171875,
-0.006847381591796875,
-0.0228271484375,
0.01947021484375,
0.0149383544921875,
-0.020538330078125,
0.0002770423889160156,
-0.0222015380859375,
0.0054931640625,
-0.061798095703125,
-0.0105133056640625,
0.01032257080078125,
0.006317138671875,
-0.01279449462890625,
0.0084686279296875,
-0.0188446044921875,
0.0096893310546875,
0.045318603515625,
0.0099029541015625,
0.057525634765625,
-0.00768280029296875,
0.002361297607421875,
0.00173187255859375,
-0.0046844482421875,
-0.021209716796875,
0.041229248046875,
0.0015802383422851562,
-0.01485443115234375,
0.005344390869140625,
-0.01031494140625,
0.0042266845703125,
0.00792694091796875,
-0.00606536865234375,
-0.006900787353515625,
0.019500732421875,
-0.008148193359375,
0.0194549560546875,
0.00018525123596191406,
0.0396728515625,
0.01247406005859375,
0.016143798828125,
-0.01355743408203125,
-0.0237579345703125,
-0.006412506103515625,
-0.030029296875,
0.01474761962890625,
-0.00211334228515625,
-0.00798797607421875,
-0.01499176025390625,
0.029327392578125,
-0.012908935546875,
0.04046630859375,
-0.01229095458984375,
0.012420654296875,
-0.03662109375,
0.009918212890625,
0.03411865234375,
0.0070648193359375,
0.00601959228515625,
0.0204315185546875,
-0.0167694091796875,
-0.019500732421875,
-0.001129150390625,
0.004344940185546875,
0.00420379638671875,
0.03021240234375,
0.0178680419921875,
0.0003192424774169922,
-0.0325927734375,
0.00984954833984375,
0.0015163421630859375,
-0.0177764892578125,
-0.00795745849609375,
0.028656005859375,
-0.01245880126953125,
-0.00691986083984375,
0.0163726806640625,
-0.0098419189453125,
0.02178955078125,
-0.0009694099426269531,
-0.01490020751953125,
0.005496978759765625,
-0.041839599609375,
-0.01125335693359375,
-0.019134521484375,
-0.00859832763671875,
0.0032825469970703125,
-0.016326904296875,
-0.0142364501953125,
0.020599365234375,
0.034759521484375,
-0.036346435546875,
-0.0263824462890625,
-0.01229095458984375,
0.00412750244140625,
0.040496826171875,
0.008056640625,
0.01407623291015625,
-0.0005884170532226562,
0.01447296142578125,
-0.01508331298828125,
-0.0288238525390625,
-0.040863037109375,
0.013275146484375,
-0.0117645263671875,
-0.005619049072265625,
-0.0018606185913085938,
-0.00333404541015625,
-0.0230560302734375,
-0.0038394927978515625,
-0.0116729736328125,
-0.005504608154296875,
0.033966064453125,
-0.0274200439453125,
0.0009198188781738281,
-0.01416778564453125,
-0.00870513916015625,
0.0169677734375,
0.01033782958984375,
-0.003101348876953125,
0.004131317138671875,
0.00046896934509277344,
-0.0051422119140625,
0.01329803466796875,
-0.0004138946533203125,
0.0138092041015625,
0.01224517822265625,
-0.0160064697265625,
0.0272064208984375,
0.0340576171875,
0.0233001708984375,
-0.01113128662109375,
-0.0028972625732421875,
-0.014617919921875,
-0.0143890380859375,
-0.002643585205078125,
-0.0002593994140625,
-0.003833770751953125,
0.0220947265625,
0.005863189697265625,
-0.03399658203125,
0.02532958984375,
0.0216522216796875,
0.0005083084106445312,
-0.02587890625,
0.027679443359375,
0.020263671875,
0.03704833984375,
0.00412750244140625,
0.0516357421875,
0.030731201171875,
0.007686614990234375,
-0.04595947265625,
0.0195159912109375,
-0.01187896728515625,
0.01355743408203125,
0.005542755126953125,
-0.016937255859375,
0.019561767578125,
0.0002574920654296875,
0.0257415771484375,
0.00516510009765625,
-0.012359619140625,
0.013763427734375,
-0.01030731201171875,
-0.03179931640625,
0.025360107421875,
0.005584716796875,
-0.01346588134765625,
0.04730224609375,
0.0222625732421875,
0.006298065185546875,
-0.0021228790283203125,
0.004547119140625,
0.005573272705078125,
-0.0113372802734375,
-0.045928955078125,
-0.023468017578125,
-0.04351806640625,
0.0008211135864257812,
-0.0102691650390625,
-0.0197906494140625,
0.061981201171875,
-0.0411376953125,
-0.00293731689453125,
-0.039642333984375,
-0.021759033203125,
-0.0033054351806640625,
-0.0221099853515625,
0.00943756103515625,
0.0523681640625,
0.00844573974609375,
-0.0435791015625,
-0.0162506103515625,
0.05718994140625,
0.0295257568359375,
0.01224517822265625,
0.048583984375,
-0.01140594482421875,
-0.046661376953125,
0.035430908203125,
0.02801513671875,
-0.0021152496337890625,
-0.032318115234375,
0.0238800048828125,
0.0247344970703125,
-0.018829345703125,
-0.025177001953125,
0.0174407958984375,
0.0084228515625,
0.00922393798828125,
-0.0009794235229492188,
-0.0158233642578125,
0.0157928466796875,
0.035003662109375,
-0.005237579345703125,
-0.0093536376953125,
0.0411376953125,
0.0055694580078125,
0.01107025146484375,
0.04510498046875,
0.006580352783203125,
0.0204925537109375,
0.00614166259765625,
0.0139923095703125,
-0.012603759765625,
0.0117034912109375,
-0.0214691162109375,
-0.0036907196044921875,
-0.004917144775390625,
0.042266845703125,
0.01282501220703125,
-0.0202178955078125,
0.00893402099609375,
-0.0258941650390625,
0.0252532958984375,
-0.0032787322998046875,
0.01165008544921875,
0.01047515869140625,
0.030548095703125,
0.01128387451171875,
-0.00203704833984375,
-0.01470184326171875,
0.006626129150390625,
0.0021419525146484375,
-0.0271453857421875,
0.00017344951629638672,
-0.00864410400390625,
0.00025010108947753906,
-0.0019683837890625,
-0.0046234130859375,
-0.034942626953125,
0.0006122589111328125,
0.020538330078125,
-0.0033473968505859375,
0.017669677734375,
0.022125244140625,
-0.0121917724609375,
0.0151519775390625,
0.0192413330078125,
0.04217529296875,
0.0241546630859375,
-0.03875732421875,
0.005908966064453125,
-0.0120849609375,
-0.002166748046875,
-0.0292816162109375,
0.02825927734375,
-0.0130767822265625,
0.00847625732421875,
0.003528594970703125,
0.0007419586181640625,
-0.027618408203125,
0.02203369140625,
-0.031768798828125,
0.007236480712890625,
0.00962066650390625,
-0.004199981689453125,
0.045166015625,
-0.004955291748046875,
-0.0093994140625,
0.0068511962890625,
0.01198577880859375,
-0.040435791015625,
-0.0323486328125,
-0.0160980224609375,
0.006465911865234375,
0.01105499267578125,
-0.034759521484375,
0.0129547119140625,
0.00030112266540527344,
-0.0308990478515625,
-0.016204833984375,
-0.03662109375,
0.004974365234375,
0.028076171875,
-0.030853271484375,
0.0218353271484375,
-0.01168060302734375,
-0.0284881591796875,
-0.01125335693359375,
-0.007297515869140625,
-0.0146026611328125,
0.01064300537109375,
-0.0244903564453125,
0.0220947265625,
0.0063629150390625,
0.013092041015625,
-0.011566162109375,
-0.0133056640625,
-0.0026378631591796875,
-0.0024318695068359375,
-0.03106689453125,
-0.0004317760467529297,
0.037750244140625,
-0.006771087646484375,
-0.034332275390625,
-0.0084381103515625,
0.03472900390625,
0.01374053955078125,
-0.0303192138671875,
0.00897979736328125,
0.00847625732421875,
-0.004913330078125,
0.0008544921875,
-0.0280914306640625,
-0.019683837890625,
-0.01197052001953125,
0.036895751953125,
-0.0230560302734375,
-0.01018524169921875,
0.032958984375,
0.0074462890625,
0.0010280609130859375,
-0.02227783203125,
0.0069580078125,
-0.0049591064453125,
0.026214599609375,
0.01049041748046875,
-0.02880859375,
0.037750244140625,
0.0018053054809570312,
-0.00033926963806152344,
-0.01007080078125,
-0.03997802734375,
-0.0178375244140625,
0.02337646484375,
0.007049560546875,
-0.005950927734375,
-0.0171966552734375,
-0.01259613037109375,
-0.00739288330078125,
0.0058441162109375,
0.018035888671875,
-0.00998687744140625,
0.0292205810546875,
0.01515960693359375,
-0.01551055908203125,
-0.004985809326171875,
0.0203094482421875,
0.021331787109375,
-0.006023406982421875,
-0.01354217529296875,
-0.01178741455078125,
-0.0140533447265625,
-0.0025272369384765625,
-0.00887298583984375,
0.00213623046875,
-0.005313873291015625,
0.00785064697265625,
-0.025482177734375,
0.006702423095703125,
0.0064544677734375,
-0.0127105712890625,
0.0300750732421875,
0.0225677490234375,
-0.01018524169921875,
0.0087432861328125,
-0.008331298828125,
-0.0140838623046875,
0.036895751953125,
0.032989501953125,
-0.0034027099609375,
-0.00958251953125,
0.046966552734375,
-0.01192474365234375,
-0.005512237548828125,
-0.01483154296875,
0.021087646484375,
-0.016387939453125,
-0.0188446044921875,
-0.00823974609375,
0.02093505859375,
-0.00818634033203125,
0.01085662841796875,
0.01068878173828125,
0.040496826171875,
-0.0031452178955078125,
0.0191192626953125,
0.0114898681640625,
0.004261016845703125,
-0.0026569366455078125,
0.009124755859375,
-0.004390716552734375,
-0.0198516845703125,
-0.0175933837890625,
-0.0360107421875,
-0.00812530517578125,
0.0185089111328125,
-0.0084075927734375,
-0.00267791748046875,
-0.007312774658203125,
-0.029937744140625,
0.0098114013671875,
0.044097900390625,
0.00136566162109375,
-0.0028533935546875,
0.017608642578125,
-0.014739990234375,
-0.037078857421875,
-0.02093505859375,
-0.00978851318359375,
-0.019927978515625,
0.0003135204315185547,
-0.0399169921875,
-0.0199737548828125,
0.0187225341796875,
-0.0233306884765625,
0.01143646240234375,
0.00717926025390625,
0.0191192626953125,
0.006969451904296875,
0.025543212890625,
0.0244598388671875,
-0.013397216796875,
-0.004985809326171875,
-0.0300445556640625,
-0.004547119140625,
0.0116119384765625,
-0.005832672119140625,
-0.03564453125,
-0.00984954833984375,
-0.036224365234375,
-0.02667236328125,
0.0233612060546875,
0.02239990234375,
-0.005847930908203125,
0.02093505859375,
-0.06622314453125,
-0.0704345703125,
0.0019588470458984375,
-0.055633544921875,
-0.0129241943359375,
-0.030242919921875,
0.031585693359375,
0.01100921630859375,
0.0005125999450683594,
-0.01105499267578125,
-0.01328277587890625,
-0.009765625,
0.02728271484375,
0.00922393798828125,
0.0017728805541992188,
0.02410888671875,
0.0390625,
0.01296234130859375,
0.0184783935546875,
-0.03106689453125,
0.0018854141235351562,
0.035308837890625,
0.028228759765625,
-0.01438140869140625,
-0.00714111328125,
-0.01010894775390625,
-0.05706787109375,
0.00200653076171875,
-0.01320648193359375,
-0.025177001953125,
0.027557373046875,
0.0309295654296875,
0.01102447509765625,
0.0000826716423034668,
-0.009735107421875,
-0.007503509521484375,
-0.032257080078125,
-0.0025157928466796875,
0.045196533203125,
0.0215911865234375,
0.0159759521484375,
-0.0333251953125,
-0.043609619140625,
0.00958251953125,
0.01412200927734375,
-0.029388427734375,
-0.01145172119140625,
-0.0003731250762939453,
-0.01953125,
0.0026912689208984375,
-0.01096343994140625,
0.01253509521484375,
-0.01186370849609375,
-0.01318359375,
-0.0140533447265625,
0.0038433074951171875,
0.0031681060791015625,
0.0262908935546875,
0.0252685546875,
-0.045257568359375,
0.0040130615234375,
-0.00965118408203125,
0.0447998046875,
-0.056671142578125,
-0.0164031982421875,
0.05517578125,
-0.0304718017578125,
0.0172271728515625,
0.0020694732666015625,
0.0282440185546875,
0.032135009765625,
0.00283050537109375,
0.002017974853515625,
-0.00914764404296875,
-0.0030384063720703125,
0.00855255126953125,
0.01297760009765625,
0.004070281982421875,
-0.007747650146484375,
-0.0146636962890625,
-0.0002758502960205078,
0.0252532958984375,
-0.00563812255859375,
0.01352691650390625,
0.0131683349609375,
0.0308074951171875,
-0.00597381591796875,
0.010894775390625,
0.016204833984375,
-0.0019073486328125,
-0.032196044921875,
0.01395416259765625,
0.0031871795654296875,
-0.0175018310546875,
0.005428314208984375,
0.01265716552734375,
-0.0251312255859375,
0.021026611328125,
-0.01096343994140625,
0.0019321441650390625,
0.0164947509765625,
-0.013946533203125,
0.00021708011627197266,
-0.01180267333984375,
0.0134735107421875,
-0.036651611328125,
-0.0246734619140625,
0.04351806640625,
-0.01076507568359375,
-0.0036373138427734375,
0.02374267578125,
0.0158233642578125,
-0.0188446044921875,
-0.0186920166015625,
0.01210784912109375,
0.019622802734375,
-0.008758544921875,
0.0271453857421875,
-0.004863739013671875,
0.00501251220703125,
0.000522613525390625,
0.00907135009765625,
0.009674072265625,
0.00521087646484375,
-0.00128936767578125,
0.027740478515625,
0.01021575927734375,
-0.03411865234375,
0.0088653564453125,
-0.01715087890625,
-0.01513671875,
0.00852203369140625,
-0.004383087158203125,
-0.038909912109375,
0.006397247314453125,
0.0200653076171875,
0.006847381591796875,
0.0229949951171875,
0.0213623046875,
0.024871826171875,
-0.0095977783203125,
-0.0211334228515625,
0.00847625732421875,
-0.0360107421875,
0.02545166015625,
0.018341064453125,
-0.005825042724609375,
-0.03192138671875,
-0.01525115966796875,
-0.0264434814453125,
-0.007221221923828125,
0.00445556640625,
0.027435302734375,
0.02984619140625,
0.01806640625,
0.005176544189453125,
0.006252288818359375,
-0.0139007568359375,
0.0029430389404296875,
-0.019989013671875,
0.04754638671875,
-0.016204833984375,
0.0206756591796875,
-0.0157928466796875,
0.031158447265625,
-0.07611083984375,
-0.053863525390625,
-0.0127410888671875,
-0.0196380615234375,
0.036895751953125,
-0.007587432861328125,
-0.01403045654296875,
0.005096435546875,
-0.022552490234375,
0.01476287841796875,
-0.00991058349609375,
0.01641845703125,
-0.020965576171875,
0.0034942626953125,
-0.01105499267578125,
-0.0091552734375,
-0.004611968994140625,
0.018524169921875,
0.032135009765625,
0.00667572021484375,
-0.00653839111328125,
0.007465362548828125,
0.007114410400390625,
-0.0113067626953125,
-0.0168304443359375,
0.027252197265625,
-0.0213470458984375,
0.01216888427734375,
-0.0051422119140625,
0.002429962158203125,
0.01103973388671875,
-0.0244140625,
0.027557373046875,
-0.01340484619140625,
0.00859832763671875,
0.0200653076171875,
0.0237274169921875,
-0.038116455078125,
-0.019866943359375,
0.006069183349609375,
-0.00922393798828125,
0.003139495849609375,
0.007419586181640625,
-0.00911712646484375,
0.00850677490234375,
0.0147552490234375,
0.0145263671875,
-0.008331298828125,
-0.01206207275390625,
0.005687713623046875,
-0.0325927734375,
-0.03643798828125,
0.0023784637451171875,
0.00992584228515625,
0.0149688720703125,
-0.0078887939453125,
-0.003139495849609375,
-0.02545166015625,
-0.0255279541015625,
0.0022716522216796875,
-0.006534576416015625,
-0.019317626953125,
0.005336761474609375,
-0.031585693359375,
-0.01241302490234375,
-0.0241851806640625,
-0.00925445556640625,
-0.0178375244140625,
-0.01117706298828125,
0.016998291015625,
0.001529693603515625,
-0.0135650634765625,
0.0211944580078125,
0.0171356201171875,
0.0024318695068359375,
-0.04254150390625,
0.0239105224609375,
-0.021240234375,
0.006092071533203125,
0.020416259765625,
-0.005916595458984375,
-0.0301361083984375,
0.00033164024353027344,
0.004146575927734375,
0.020843505859375,
0.0134735107421875,
0.00775146484375,
-0.0008687973022460938,
-0.037445068359375,
-0.0018720626831054688,
-0.0178985595703125,
-0.01082611083984375,
0.01308441162109375,
0.01277923583984375,
0.02154541015625,
-0.0142974853515625,
-0.00823974609375,
-0.0217132568359375,
0.01776123046875,
0.016845703125,
0.02191162109375,
-0.016387939453125,
-0.006961822509765625,
0.0264892578125,
0.03143310546875,
0.006656646728515625,
-0.038665771484375,
-0.0162506103515625,
0.0226898193359375,
0.00669097900390625,
0.0134429931640625,
0.002307891845703125,
0.0020847320556640625,
-0.032379150390625,
-0.031341552734375,
-0.01108551025390625,
-0.02130126953125,
0.01959228515625,
-0.020538330078125,
-0.04302978515625,
-0.012115478515625,
0.0021724700927734375,
0.01035308837890625,
-0.0272674560546875,
0.00795745849609375,
0.01361846923828125,
-0.019989013671875,
-0.0202484130859375,
0.008880615234375,
-0.00768280029296875,
0.0262603759765625,
0.00751495361328125,
-0.037078857421875,
0.0218048095703125,
0.00795745849609375,
-0.0116424560546875,
0.006427764892578125,
-0.0184326171875,
0.0163421630859375,
-0.0281524658203125,
-0.0198516845703125,
-0.0309295654296875,
0.03363037109375,
0.0257568359375,
-0.006435394287109375,
-0.016204833984375,
-0.046722412109375,
0.025634765625,
0.00974273681640625,
-0.00472259521484375,
-0.039215087890625,
0.0170135498046875,
0.0026912689208984375,
-0.02581787109375,
-0.0278472900390625,
-0.004726409912109375,
-0.0081024169921875,
0.00913238525390625,
-0.009796142578125,
0.0128631591796875,
0.02197265625,
-0.0023746490478515625,
0.0186309814453125,
-0.009307861328125,
-0.0245208740234375,
0.028564453125,
0.00007975101470947266,
-0.0000902414321899414,
0.0189056396484375,
0.019256591796875,
0.0293426513671875,
-0.0240478515625,
0.0287628173828125,
-0.00821685791015625,
-0.00287628173828125,
0.0200958251953125,
0.0028839111328125,
0.0301055908203125,
0.019073486328125,
-0.0229949951171875,
0.0011644363403320312,
-0.0007805824279785156,
-0.0014734268188476562,
-0.031524658203125,
-0.0015201568603515625,
0.020965576171875,
0.0009603500366210938,
0.009429931640625,
0.0194091796875,
0.03826904296875,
0.0164642333984375,
-0.0230560302734375,
0.00771331787109375,
-0.0244293212890625,
0.0445556640625,
-0.0012388229370117188,
-0.0124359130859375,
0.0097198486328125,
0.0021686553955078125,
0.0255126953125,
0.004367828369140625,
0.01399993896484375,
0.0277862548828125,
-0.036224365234375,
-0.01444244384765625,
0.0017337799072265625,
0.0026702880859375,
-0.0206451416015625,
0.0225677490234375,
-0.017242431640625,
0.00127410888671875,
0.004749298095703125,
0.0174407958984375,
0.0138092041015625,
-0.00823211669921875,
0.01367950439453125,
0.03594970703125,
-0.0194244384765625,
-0.0167694091796875,
0.0141143798828125,
-0.00424957275390625,
-0.031585693359375,
0.00579833984375,
-0.00011867284774780273,
0.006870269775390625,
-0.009185791015625,
-0.00711822509765625,
0.0171661376953125,
-0.029632568359375,
-0.04132080078125,
0.0220947265625,
-0.059967041015625,
0.0148773193359375,
0.0361328125,
-0.00014841556549072266,
0.0267791748046875,
0.00933074951171875,
-0.0170745849609375,
-0.007808685302734375,
0.00888824462890625,
-0.019500732421875,
0.00229644775390625,
0.01514434814453125,
-0.017242431640625,
0.0043792724609375,
-0.04510498046875,
-0.0159759521484375,
-0.0037975311279296875,
0.0161895751953125,
0.024169921875,
-0.0439453125,
-0.0250244140625,
0.045928955078125,
-0.0133209228515625,
0.0287628173828125,
-0.022369384765625,
-0.0411376953125,
0.007648468017578125,
-0.00707244873046875,
0.0128021240234375,
0.00942230224609375,
-0.0010652542114257812,
-0.0213470458984375,
0.00514984130859375,
0.00909423828125,
-0.01910400390625,
-0.0088348388671875,
-0.039031982421875,
0.024627685546875,
-0.034881591796875,
0.01123809814453125,
-0.036712646484375,
0.00928497314453125,
0.006114959716796875,
0.0016241073608398438,
0.00470733642578125,
-0.0247039794921875,
0.024658203125,
-0.017852783203125,
-0.034881591796875,
0.031890869140625,
-0.0028896331787109375,
0.01235198974609375,
0.01485443115234375,
0.015655517578125,
-0.00792694091796875,
-0.0051422119140625,
0.00960540771484375,
0.0209197998046875,
-0.002750396728515625,
-0.0235748291015625,
-0.0125274658203125,
-0.017181396484375,
0.027587890625,
-0.00011110305786132812,
-0.024505615234375,
-0.02557373046875,
-0.001689910888671875,
-0.007198333740234375,
0.025177001953125,
-0.020050048828125,
-0.0129547119140625,
0.0296783447265625,
-0.0101165771484375,
-0.004009246826171875,
-0.01280975341796875,
-0.0244598388671875,
-0.0006318092346191406,
0.002651214599609375,
-0.01105499267578125,
0.00391387939453125,
-0.027252197265625,
-0.03076171875,
-0.0206146240234375,
-0.00807952880859375,
0.037200927734375,
0.0158538818359375,
0.0217437744140625,
-0.01410675048828125,
-0.0002818107604980469,
-0.0419921875,
0.023956298828125,
0.00881195068359375,
-0.0165557861328125,
0.0188751220703125,
-0.01065826416015625,
-0.0106201171875,
-0.01898193359375,
-0.00628662109375,
-0.0021991729736328125,
0.00792694091796875,
0.0249481201171875,
0.0081939697265625,
-0.0085601806640625,
0.01776123046875,
-0.0093536376953125,
-0.01280975341796875,
0.00455474853515625,
0.00511932373046875,
-0.00858306884765625,
0.033966064453125,
-0.0293731689453125,
0.003780364990234375,
0.0233306884765625,
0.0006809234619140625,
-0.0016279220581054688,
-0.01403045654296875,
-0.02313232421875,
0.01412200927734375,
-0.00769805908203125,
0.0102996826171875,
0.003582000732421875,
0.031951904296875,
0.0257568359375,
0.01055145263671875,
0.0010786056518554688,
-0.00921630859375,
0.0241851806640625,
-0.002124786376953125,
-0.022247314453125,
-0.021392822265625,
-0.01727294921875,
0.012420654296875,
0.002414703369140625,
-0.019317626953125,
-0.012481689453125,
0.0029850006103515625,
0.0223388671875,
-0.026763916015625,
0.007511138916015625,
0.00901031494140625,
0.00943756103515625,
0.016510009765625,
-0.012298583984375,
-0.01410675048828125,
0.017486572265625,
-0.0038013458251953125,
0.020172119140625,
-0.0183563232421875,
-0.00562286376953125,
-0.01134490966796875,
-0.011199951171875,
0.0057525634765625,
-0.0160369873046875,
-0.01947021484375,
-0.0202178955078125,
-0.024322509765625,
-0.01424407958984375,
0.01214599609375,
-0.00884246826171875,
0.0124053955078125,
0.002063751220703125,
-0.0006780624389648438,
-0.004581451416015625,
0.0073394775390625,
-0.05908203125,
0.01458740234375,
-0.0062103271484375,
0.01065826416015625,
0.00311279296875,
0.03070068359375,
0.011199951171875,
-0.0056304931640625,
0.00109100341796875,
-0.00725555419921875,
-0.002666473388671875,
-0.01255035400390625,
0.02813720703125,
-0.0013608932495117188,
-0.0011816024780273438,
-0.035064697265625,
0.0143585205078125,
-0.012786865234375,
-0.00677490234375,
-0.00696563720703125,
0.03350830078125,
-0.002605438232421875,
-0.001453399658203125,
0.0010995864868164062,
-0.0203399658203125,
-0.00447845458984375,
0.0013065338134765625,
0.036346435546875,
0.0130157470703125,
0.02996826171875,
0.004894256591796875,
0.014801025390625,
-0.018951416015625,
0.0198516845703125,
0.0186004638671875,
-0.01482391357421875,
0.0012941360473632812,
0.0126495361328125,
-0.023834228515625,
0.039642333984375,
0.01302337646484375,
0.006778717041015625,
0.0270538330078125,
-0.0167694091796875,
0.03582763671875,
-0.0162353515625,
-0.0267486572265625,
0.031402587890625,
0.00794219970703125,
-0.01233673095703125,
-0.0171051025390625,
0.031646728515625,
0.0005612373352050781,
0.0244140625,
-0.0250091552734375,
-0.03546142578125,
0.0159759521484375,
0.01122283935546875,
-0.004383087158203125,
0.036895751953125,
-0.0011339187622070312,
0.00799560546875,
-0.006488800048828125,
0.00855255126953125,
0.035491943359375,
-0.012725830078125,
0.03338623046875,
-0.0279693603515625,
0.0018205642700195312,
-0.04107666015625,
-0.0031566619873046875,
-0.00052642822265625,
-0.004001617431640625,
0.005588531494140625,
0.023651123046875,
-0.01157379150390625,
-0.0196685791015625,
-0.020416259765625,
0.007602691650390625,
0.0034332275390625,
-0.01032257080078125,
-0.0006089210510253906,
-0.00567626953125,
-0.01560211181640625,
-0.00548553466796875,
-0.0216522216796875,
-0.00989532470703125,
0.007678985595703125,
-0.007495880126953125,
0.0203399658203125,
0.00434112548828125,
0.0014410018920898438,
-0.01263427734375,
0.01161956787109375,
0.0123748779296875,
-0.0150604248046875,
-0.00411224365234375,
-0.033599853515625,
-0.038970947265625,
0.0076446533203125,
-0.00891876220703125,
-0.03790283203125,
-0.01329803466796875,
0.0265655517578125,
-0.008941650390625,
-0.012420654296875,
0.0150909423828125,
-0.0008435249328613281,
-0.01134490966796875,
0.01319122314453125,
0.0269927978515625,
0.01287841796875,
-0.0227813720703125,
-0.0150299072265625,
0.00774383544921875,
-0.0268402099609375,
0.0060272216796875,
0.0053253173828125,
0.0038356781005859375,
-0.00728607177734375,
-0.003498077392578125,
-0.010467529296875,
0.00794219970703125,
0.00908660888671875,
0.02001953125,
0.0054473876953125,
0.0032787322998046875,
0.0384521484375,
-0.00013709068298339844,
0.0175628662109375,
-0.032958984375,
0.00531768798828125,
-0.01471710205078125,
-0.00640869140625,
-0.0027637481689453125,
-0.00830078125,
-0.0014715194702148438,
-0.0245819091796875,
-0.025115966796875,
-0.005687713623046875,
0.0184478759765625,
-0.00537109375,
0.0218658447265625,
0.0021648406982421875,
0.01861572265625,
0.0020084381103515625,
0.04351806640625,
0.00643157958984375,
0.00910186767578125,
-0.0046539306640625,
-0.007549285888671875,
0.004703521728515625,
0.01043701171875,
0.03240966796875,
-0.051483154296875,
-0.003925323486328125,
0.00823211669921875,
-0.01312255859375,
0.0011425018310546875,
-0.01380157470703125,
-0.004505157470703125,
-0.0323486328125,
-0.019805908203125,
-0.00897216796875,
-0.018768310546875,
-0.026580810546875,
-0.0101776123046875,
0.00836944580078125,
-0.020904541015625,
-0.0020427703857421875,
0.01715087890625,
-0.0133056640625,
-0.0303802490234375,
0.01873779296875,
0.014312744140625,
-0.017364501953125,
-0.03704833984375,
0.022979736328125,
-0.0250091552734375,
0.024658203125,
0.029510498046875,
-0.0015153884887695312,
-0.032135009765625,
-0.006591796875,
0.0087432861328125,
-0.0021209716796875,
0.0262603759765625,
0.0208282470703125,
-0.00852203369140625,
0.0107879638671875,
-0.011138916015625,
0.016204833984375,
-0.026885986328125,
0.040618896484375,
0.012939453125,
0.021697998046875,
-0.01439666748046875,
0.006679534912109375,
0.01348876953125,
0.032073974609375,
0.038543701171875,
0.026611328125,
0.0185089111328125,
-0.01983642578125,
-0.004589080810546875,
0.018463134765625,
0.020721435546875,
0.0230255126953125,
0.00534820556640625,
-0.0057830810546875,
-0.0297698974609375,
-0.0303802490234375,
0.012298583984375,
-0.0006771087646484375,
0.005176544189453125,
-0.0040435791015625,
-0.016876220703125,
-0.012237548828125,
0.00994873046875,
0.0166778564453125,
-0.01004791259765625,
0.00942230224609375,
-0.01953125,
0.00615692138671875,
-0.00772857666015625,
-0.016143798828125,
0.0167694091796875,
-0.003082275390625,
-0.03863525390625,
0.0014581680297851562,
0.008087158203125,
-0.0193634033203125,
0.00799560546875,
0.0005092620849609375,
0.0291748046875,
0.0012331008911132812,
-0.01177978515625,
-0.030853271484375,
0.005352020263671875,
-0.01898193359375,
0.0180816650390625,
-0.020263671875,
0.004848480224609375,
-0.0105743408203125,
0.0241851806640625,
-0.00850677490234375,
-0.014617919921875,
-0.0014019012451171875,
-0.01045989990234375,
0.0013227462768554688,
0.0202484130859375,
-0.015411376953125,
0.0050201416015625,
0.0181121826171875,
0.0108642578125,
-0.021820068359375,
0.0207366943359375,
-0.012481689453125,
-0.018646240234375,
-0.018798828125,
-0.03900146484375,
0.007022857666015625,
0.013427734375,
0.01016998291015625,
-0.0171966552734375,
0.0033111572265625,
-0.01134490966796875,
0.021942138671875,
-0.00897216796875,
0.00576019287109375,
0.0033893585205078125,
-0.01953125,
0.004070281982421875,
0.003192901611328125,
0.003162384033203125,
-0.00836944580078125,
0.0258026123046875,
0.0199432373046875,
-0.0002187490463256836,
-0.00690460205078125,
-0.00524139404296875,
-0.006160736083984375,
-0.0139923095703125,
-0.0018262863159179688,
-0.0047607421875,
-0.0137176513671875,
0.015777587890625,
-0.0240020751953125,
0.0240631103515625,
0.005176544189453125,
0.01387786865234375,
-0.004199981689453125,
-0.003002166748046875,
0.008209228515625,
-0.019134521484375,
-0.0282745361328125,
0.030731201171875,
0.01373291015625,
-0.0016489028930664062,
-0.014923095703125,
-0.0233917236328125,
-0.00855255126953125,
0.043060302734375,
-0.003376007080078125,
0.0211334228515625,
-0.004695892333984375,
0.01129913330078125,
-0.0208892822265625,
0.0202178955078125,
0.0286712646484375,
0.016143798828125,
-0.0362548828125,
0.0164337158203125,
-0.0261993408203125,
-0.0017309188842773438,
0.0176544189453125,
-0.0035305023193359375,
0.0029621124267578125,
0.00823211669921875,
-0.00963592529296875,
-0.037384033203125,
-0.0161285400390625,
0.00806427001953125,
0.01305389404296875,
-0.007171630859375,
0.01181793212890625,
0.0784912109375,
-0.0034389495849609375,
-0.010040283203125,
0.01447296142578125,
0.0212249755859375,
0.006191253662109375,
-0.022430419921875,
0.0248260498046875,
-0.02020263671875,
-0.0036773681640625,
-0.0008435249328613281,
0.00934600830078125,
-0.04644775390625,
0.00804901123046875,
-0.0031986236572265625,
-0.0313720703125,
-0.0193939208984375,
0.021026611328125,
-0.015472412109375,
-0.028533935546875,
0.0164642333984375,
-0.0142364501953125,
-0.0218963623046875,
-0.018280029296875,
0.004085540771484375,
0.0018625259399414062,
0.04302978515625,
0.0220947265625,
0.03387451171875,
-0.044036865234375,
-0.01010894775390625,
-0.004634857177734375,
-0.0017528533935546875,
-0.01275634765625,
0.0221710205078125,
-0.007556915283203125,
-0.0027637481689453125,
-0.021209716796875,
-0.0010480880737304688,
0.019073486328125,
0.03509521484375,
0.032562255859375,
0.045440673828125,
0.0130767822265625,
0.006572723388671875,
0.00893402099609375,
0.00853729248046875,
0.038116455078125,
0.0197906494140625,
0.01270294189453125,
-0.003055572509765625,
-0.037811279296875,
-0.005817413330078125,
0.0241241455078125,
-0.0022830963134765625,
-0.00408172607421875,
0.0206146240234375,
-0.006847381591796875,
-0.007045745849609375,
-0.009002685546875,
-0.005931854248046875,
-0.01580810546875,
0.021942138671875,
0.01007080078125,
-0.0252838134765625,
0.005962371826171875,
-0.0011138916015625,
-0.0029315948486328125,
0.019561767578125,
-0.0137176513671875,
0.0189666748046875,
-0.032379150390625,
-0.01506805419921875,
-0.007343292236328125,
0.00006121397018432617,
0.006549835205078125,
0.01203155517578125,
-0.011871337890625,
-0.0286407470703125,
-0.0271453857421875,
0.021881103515625,
0.0156402587890625,
0.0166015625,
0.0037937164306640625,
0.0040130615234375,
-0.0002689361572265625,
-0.0012636184692382812,
-0.0189208984375,
-0.02862548828125,
-0.00830841064453125,
0.0399169921875,
-0.023773193359375,
0.00666046142578125,
-0.00556182861328125,
0.0170135498046875,
0.006427764892578125,
0.015655517578125,
-0.002597808837890625,
0.002223968505859375,
-0.0141754150390625,
0.015899658203125,
-0.00528717041015625,
0.0013885498046875,
-0.00601959228515625,
0.00405120849609375,
-0.00876617431640625,
0.019866943359375,
0.0052032470703125,
0.001495361328125,
0.024993896484375,
0.01131439208984375,
0.02569580078125,
0.0009045600891113281,
-0.00891876220703125,
-0.025665283203125,
0.0017910003662109375,
0.034759521484375,
-0.01727294921875,
-0.0255584716796875,
-0.00473785400390625,
0.03839111328125,
0.01751708984375,
-0.0130462646484375,
-0.01548004150390625,
0.010162353515625,
-0.0161285400390625,
-0.00823211669921875,
0.01416778564453125,
-0.005329132080078125,
0.048736572265625,
0.020599365234375,
-0.0212554931640625,
0.0226287841796875,
0.003673553466796875,
-0.00479888916015625,
0.0190277099609375,
-0.0004668235778808594,
-0.01132965087890625,
-0.0126953125,
0.0191192626953125,
0.01641845703125,
-0.019287109375,
-0.0318603515625,
0.0045318603515625,
0.004730224609375,
-0.0081024169921875,
0.0081787109375,
0.005443572998046875,
-0.0092010498046875,
-0.00510406494140625,
0.018524169921875,
-0.011016845703125,
-0.0086822509765625,
0.02691650390625,
-0.0040435791015625,
-0.0194244384765625,
0.0065765380859375,
-0.03759765625,
0.01119232177734375,
0.01378631591796875,
-0.009552001953125,
-0.020477294921875,
0.0293121337890625,
-0.025421142578125,
-0.00858306884765625,
0.006191253662109375,
0.0108642578125,
-0.0280914306640625,
0.0195465087890625,
0.0127716064453125,
-0.0149078369140625,
0.0111541748046875,
-0.006275177001953125,
0.023834228515625,
0.0185089111328125,
0.0209808349609375,
-0.0003638267517089844,
0.0084991455078125,
-0.00311279296875,
0.0307464599609375,
0.01108551025390625,
-0.0007071495056152344,
0.0018224716186523438,
-0.0009183883666992188,
0.0248565673828125,
0.00864410400390625,
-0.00722503662109375,
-0.007724761962890625,
0.0001176595687866211,
0.0051116943359375,
0.0087127685546875,
0.01059722900390625,
-0.02459716796875,
-0.0282440185546875,
-0.017578125,
0.00981903076171875,
0.049713134765625,
0.00711822509765625,
0.004650115966796875,
0.01322174072265625,
-0.03106689453125,
0.0272216796875,
-0.028656005859375,
-0.035614013671875,
0.03338623046875,
-0.00827789306640625,
0.0116729736328125,
-0.0245208740234375,
-0.00936126708984375,
0.060089111328125,
-0.026702880859375,
-0.031982421875,
-0.0161285400390625,
-0.0204315185546875,
0.034942626953125,
0.015655517578125,
0.0010890960693359375,
-0.0157318115234375,
0.0296783447265625,
-0.01654052734375,
0.0122528076171875,
-0.0014982223510742188,
-0.017791748046875,
0.00640106201171875,
0.0178680419921875,
0.0147247314453125,
0.005279541015625,
0.0004291534423828125,
-0.00537872314453125,
0.02081298828125,
0.0034027099609375,
-0.0299072265625,
0.0008788108825683594,
0.00693511962890625,
-0.0156402587890625,
-0.007236480712890625,
0.0181121826171875,
0.015869140625,
0.005023956298828125,
0.00336456298828125,
0.013824462890625,
-0.00293731689453125,
0.009796142578125,
-0.0318603515625,
-0.022796630859375,
-0.022064208984375,
-0.0032482147216796875,
0.0055389404296875,
0.0031261444091796875,
-0.015472412109375,
0.0017023086547851562,
-0.00182342529296875,
-0.04620361328125,
-0.02154541015625,
0.0207672119140625,
-0.01451873779296875,
0.004344940185546875,
0.0249176025390625,
0.0088653564453125,
-0.0201263427734375,
0.019378662109375,
0.01520538330078125,
0.01201629638671875,
-0.00136566162109375,
-0.01702880859375,
0.0299072265625,
-0.0014400482177734375,
0.021575927734375,
0.0011453628540039062,
0.005146026611328125,
0.00450897216796875,
0.003932952880859375,
-0.01209259033203125,
0.0012865066528320312,
0.0112457275390625,
-0.008056640625,
-0.0059661865234375,
-0.0031452178955078125,
0.011199951171875,
0.0007448196411132812,
0.0170440673828125,
0.001445770263671875,
-0.01114654541015625,
0.001728057861328125,
-0.004901885986328125,
-0.0023708343505859375,
0.0297088623046875,
-0.0072174072265625,
0.0131072998046875,
-0.00641632080078125,
-0.0198822021484375,
-0.0272216796875,
-0.0300140380859375,
-0.007598876953125,
0.01033782958984375,
0.0247955322265625,
0.0178375244140625,
0.07415771484375,
-0.0059051513671875,
0.02056884765625,
-0.00836944580078125,
0.01000213623046875,
0.008819580078125,
-0.01380157470703125,
0.0160675048828125,
-0.00421142578125,
-0.0214996337890625,
-0.01142120361328125,
-0.0026416778564453125,
-0.0232391357421875,
0.027069091796875,
0.0023784637451171875,
0.0269927978515625,
0.0041656494140625,
0.007183074951171875,
0.01251983642578125,
0.0056304931640625,
0.00536346435546875,
0.008819580078125,
0.005962371826171875,
0.0005979537963867188,
0.0274658203125,
-0.020111083984375,
-0.00891876220703125,
0.000044226646423339844,
0.007396697998046875,
0.031280517578125,
-0.0004456043243408203,
0.0211334228515625,
0.01021575927734375,
-0.0018491744995117188,
-0.0074920654296875,
-0.01763916015625,
-0.04632568359375,
-0.023651123046875,
-0.002750396728515625,
0.035675048828125,
-0.027740478515625,
-0.004192352294921875,
0.048004150390625,
-0.003437042236328125,
-0.01507568359375,
0.0011053085327148438,
-0.049652099609375,
-0.00807952880859375,
-0.0207672119140625,
0.0301513671875,
-0.032135009765625,
-0.03399658203125,
0.00662994384765625,
-0.01922607421875,
-0.00421905517578125,
-0.01465606689453125,
0.005252838134765625,
-0.018280029296875,
-0.0236053466796875,
-0.005992889404296875,
0.011138916015625,
0.01209259033203125,
-0.0234527587890625,
-0.01155853271484375,
0.00568389892578125,
0.001247406005859375,
-0.01384735107421875,
-0.0011854171752929688,
-0.007465362548828125,
0.032958984375,
0.0174407958984375,
0.01271820068359375,
-0.0030841827392578125,
-0.005542755126953125,
0.0017938613891601562,
-0.0017986297607421875,
0.00616455078125,
-0.0020847320556640625,
0.0305633544921875,
0.028350830078125,
0.001964569091796875,
-0.01314544677734375,
-0.01358795166015625,
-0.00914764404296875,
0.004913330078125,
0.041015625,
0.017547607421875,
0.0011005401611328125,
0.0126800537109375,
0.0096893310546875,
-0.0048828125,
0.00850677490234375,
0.00019979476928710938,
-0.00821685791015625,
-0.058349609375,
0.003505706787109375,
0.00901031494140625,
0.0000362396240234375,
-0.002685546875,
-0.02117919921875,
0.0090789794921875,
-0.0032634735107421875,
-0.0016756057739257812,
0.01427459716796875,
0.01154327392578125,
0.0215301513671875,
-0.0209197998046875,
-0.036590576171875,
-0.00916290283203125,
-0.0025043487548828125,
-0.01232147216796875,
-0.000029265880584716797,
-0.00997161865234375,
0.006984710693359375,
-0.00754547119140625,
0.0256500244140625,
0.03533935546875,
0.027587890625,
-0.00830841064453125,
0.00830078125,
0.0025005340576171875,
0.0168609619140625,
-0.0022945404052734375,
-0.006587982177734375,
-0.00919342041015625,
0.01739501953125,
0.0261688232421875,
-0.016510009765625,
-0.03558349609375,
-0.006256103515625,
-0.0105133056640625,
-0.0210723876953125,
-0.01137542724609375,
0.005672454833984375,
0.0253448486328125,
0.006862640380859375,
-0.002201080322265625,
0.00504302978515625,
-0.006404876708984375,
-0.00688934326171875,
-0.01409912109375,
0.0005116462707519531,
-0.00566864013671875,
-0.0010366439819335938,
-0.003574371337890625,
0.0161895751953125,
-0.00498199462890625,
0.040374755859375,
0.0180816650390625,
-0.061187744140625,
-0.0135498046875,
-0.0096588134765625,
-0.0101776123046875,
-0.041534423828125,
0.02008056640625,
-0.01971435546875,
0.0115814208984375,
0.0034332275390625,
-0.00936126708984375,
0.00909423828125,
0.019195556640625,
0.0067291259765625,
0.0031719207763671875,
-0.023712158203125,
0.0198822021484375,
0.037017822265625,
0.036102294921875,
0.01110076904296875,
0.01200103759765625,
-0.0234222412109375,
0.01690673828125,
0.004428863525390625,
-0.0283050537109375,
-0.00832366943359375,
0.036468505859375,
-0.021881103515625,
-0.0158233642578125,
0.01447296142578125,
-0.0289459228515625,
-0.005916595458984375,
-0.0009670257568359375,
0.017730712890625,
-0.00861358642578125,
0.0038814544677734375,
-0.0186920166015625,
0.00396728515625,
0.00736236572265625,
-0.006435394287109375,
0.00910186767578125,
0.04473876953125,
-0.004123687744140625,
0.014862060546875,
0.00200653076171875,
-0.0245361328125,
-0.028961181640625,
-0.005542755126953125,
0.0310516357421875,
0.0223388671875,
0.01629638671875,
0.0192718505859375,
-0.043121337890625,
-0.006031036376953125,
-0.0025920867919921875,
0.03009033203125,
0.00372314453125,
-0.016326904296875,
0.00601959228515625,
-0.019317626953125,
-0.01416015625,
0.02880859375,
-0.0194854736328125,
-0.0063629150390625,
-0.0167999267578125,
0.007457733154296875,
-0.0181884765625,
-0.0196685791015625,
-0.0215606689453125,
0.00675201416015625,
0.02490234375,
0.017608642578125,
-0.020599365234375,
-0.0283050537109375,
0.034393310546875,
-0.00637054443359375,
-0.02947998046875,
0.007740020751953125,
0.0183868408203125,
0.0153961181640625,
0.0245819091796875,
0.01435089111328125,
0.018096923828125,
0.0169525146484375,
0.0173492431640625,
-0.007099151611328125,
-0.00022554397583007812,
-0.0019931793212890625,
0.0158233642578125,
-0.00897979736328125,
0.0171966552734375,
0.023590087890625,
-0.024932861328125,
-0.020843505859375,
0.020965576171875,
0.0205535888671875,
-0.005008697509765625,
-0.007415771484375,
-0.0277099609375,
0.04266357421875,
-0.03289794921875,
-0.006122589111328125,
-0.0010223388671875,
0.0025424957275390625,
0.004184722900390625,
-0.0174713134765625,
-0.0021457672119140625,
-0.00655364990234375,
0.01129150390625,
-0.00516510009765625,
0.007080078125,
-0.0080413818359375,
0.0136260986328125,
0.01294708251953125,
0.016510009765625,
0.012603759765625,
0.0287933349609375,
-0.00682830810546875,
0.039031982421875,
0.0016469955444335938,
0.0300140380859375,
-0.01468658447265625,
0.0117950439453125,
0.021148681640625,
0.005603790283203125,
-0.0033245086669921875,
-0.0168609619140625,
0.039306640625,
-0.01220703125,
-0.0163726806640625,
0.010162353515625,
0.022613525390625,
-0.01158905029296875,
0.0260009765625,
-0.020721435546875,
0.014556884765625,
-0.0209197998046875,
0.0042266845703125,
0.0268096923828125,
0.009918212890625,
-0.0103912353515625,
-0.0042724609375,
0.022979736328125,
0.0009222030639648438,
-0.003208160400390625,
0.0019664764404296875,
0.005863189697265625,
-0.0169219970703125,
0.0294952392578125,
0.0173187255859375,
0.0022754669189453125,
0.0257110595703125,
-0.025634765625,
0.017120361328125,
0.0247955322265625,
-0.0044708251953125,
0.021575927734375,
0.042266845703125,
-0.041473388671875,
-0.00244140625,
-0.02532958984375,
0.0157928466796875,
0.002704620361328125,
-0.017822265625,
0.031341552734375,
0.01318359375,
0.015106201171875,
0.0177001953125,
-0.007843017578125,
0.0308990478515625,
0.01309967041015625,
-0.0169677734375,
-0.0046539306640625,
0.0171356201171875,
0.01218414306640625,
-0.0226593017578125,
-0.0012454986572265625,
-0.0194854736328125,
-0.051055908203125,
-0.00742340087890625,
-0.01275634765625,
-0.0014657974243164062,
0.00643157958984375,
-0.0011081695556640625,
-0.026397705078125,
-0.0096282958984375,
0.004299163818359375,
-0.01214599609375,
0.0007343292236328125,
0.0068511962890625,
-0.0283050537109375,
0.0008587837219238281,
-0.00432586669921875,
-0.01369476318359375,
-0.006397247314453125,
-0.0228424072265625,
0.0253753662109375,
0.0178375244140625,
0.00931549072265625,
-0.010589599609375,
-0.01490020751953125,
0.007434844970703125,
-0.0204925537109375,
-0.03326416015625,
-0.004974365234375,
-0.028656005859375,
-0.0182342529296875,
0.015655517578125,
-0.0154876708984375,
0.00045108795166015625,
-0.0014019012451171875,
-0.00835418701171875,
-0.0048370361328125,
0.0008559226989746094,
-0.006561279296875,
0.01369476318359375,
-0.017242431640625,
-0.005062103271484375,
-0.01776123046875,
0.0504150390625,
-0.0221099853515625,
-0.0266876220703125,
0.0162811279296875,
0.01123809814453125,
0.00577545166015625,
0.039154052734375,
-0.03167724609375,
0.005611419677734375,
-0.03424072265625,
-0.0307769775390625,
-0.0181732177734375,
-0.003711700439453125,
-0.0015392303466796875,
-0.003635406494140625,
-0.0098724365234375,
-0.00384521484375,
-0.005023956298828125,
0.035400390625,
0.0087432861328125,
0.01421356201171875,
-0.0299835205078125,
-0.0213165283203125,
-0.01161956787109375,
-0.0037784576416015625,
0.0372314453125,
-0.039398193359375,
-0.0069427490234375,
0.00690460205078125,
0.004489898681640625,
-0.036956787109375,
0.01511383056640625,
0.03448486328125,
0.010406494140625,
0.0035228729248046875,
0.0133819580078125,
-0.020050048828125,
0.0218353271484375,
0.0148468017578125,
-0.004547119140625,
-0.0241851806640625,
0.01708984375,
-0.01265716552734375,
0.0269622802734375,
-0.0034465789794921875,
-0.006114959716796875,
0.0031528472900390625,
-0.040679931640625,
0.00197601318359375,
-0.007598876953125,
-0.0196380615234375,
-0.0179595947265625,
-0.01137542724609375,
-0.01323699951171875,
-0.0243377685546875,
0.005401611328125,
-0.021575927734375,
-0.01226806640625,
-0.003688812255859375,
0.0102386474609375,
0.0166778564453125,
0.0037326812744140625,
-0.035552978515625,
-0.00714874267578125,
0.01319122314453125,
0.0220794677734375,
-0.022979736328125,
0.004192352294921875,
-0.01251983642578125,
0.001033782958984375,
-0.005031585693359375,
-0.0023040771484375,
0.03558349609375,
-0.04034423828125,
0.01052093505859375,
-0.03009033203125,
0.0097198486328125,
-0.01230621337890625,
-0.0023212432861328125,
0.037567138671875,
-0.034637451171875,
-0.004352569580078125,
-0.018585205078125,
-0.018890380859375,
-0.0181884765625,
-0.0164947509765625,
-0.004978179931640625,
0.01030731201171875,
-0.0013818740844726562,
-0.02728271484375,
-0.0224456787109375,
0.024627685546875,
0.02166748046875,
-0.0038394927978515625,
0.0089874267578125,
0.048126220703125,
0.003269195556640625,
0.034271240234375,
-0.0186920166015625,
0.0088653564453125,
-0.00658416748046875,
0.0010013580322265625,
0.02203369140625,
0.0157318115234375,
0.04443359375,
0.01251983642578125,
0.031463623046875,
0.00652313232421875,
-0.0162811279296875,
0.034698486328125,
0.0228118896484375,
-0.00946807861328125,
0.0110626220703125,
-0.0020751953125,
-0.0293121337890625,
-0.00504302978515625,
0.0032215118408203125,
-0.0123748779296875,
0.01568603515625,
-0.004024505615234375,
-0.0308837890625,
0.0015249252319335938,
0.00907135009765625,
0.003765106201171875,
-0.01103973388671875,
0.0204315185546875,
-0.00408935546875,
0.0179290771484375,
-0.0196075439453125,
0.0198974609375,
0.007556915283203125,
-0.01497650146484375,
-0.0022430419921875,
0.00270843505859375,
-0.00943756103515625,
0.0063629150390625,
-0.006862640380859375,
-0.0076751708984375,
0.0113983154296875,
0.0134735107421875,
0.016876220703125,
-0.02685546875,
0.0445556640625,
0.01343536376953125,
-0.0154571533203125,
0.00919342041015625,
0.005474090576171875,
-0.017608642578125,
0.052703857421875,
-0.0024871826171875,
0.0171356201171875,
-0.01502227783203125,
0.0038204193115234375,
0.0002319812774658203,
-0.030548095703125,
-0.012237548828125,
0.013702392578125,
-0.028472900390625,
0.004711151123046875,
0.0018281936645507812,
0.0013322830200195312,
-0.0032939910888671875,
0.01270294189453125,
0.0181732177734375,
0.002140045166015625,
0.004047393798828125,
-0.00571441650390625,
-0.034149169921875,
-0.002803802490234375,
0.046661376953125,
0.008819580078125,
0.0002651214599609375,
0.0203704833984375,
-0.0019102096557617188,
-0.0255889892578125,
0.01180267333984375,
0.01373291015625,
-0.028839111328125,
0.002002716064453125,
0.018707275390625,
-0.0266571044921875,
-0.0259857177734375,
0.0034008026123046875,
0.01331329345703125,
-0.01102447509765625,
0.0168609619140625,
0.00676727294921875,
-0.00843048095703125,
-0.00690460205078125,
0.0090484619140625,
-0.037078857421875,
-0.0003974437713623047,
0.0212554931640625,
0.007732391357421875,
-0.0244903564453125,
0.028900146484375,
0.046539306640625,
0.010589599609375,
-0.0003085136413574219,
-0.006557464599609375,
-0.01044464111328125,
-0.0185089111328125,
-0.0189056396484375,
-0.00982666015625,
-0.0014209747314453125,
-0.010345458984375,
-0.006153106689453125,
0.035064697265625,
0.00922393798828125,
0.0079345703125,
-0.0153350830078125,
-0.00897979736328125,
-0.024871826171875,
-0.0285491943359375,
0.015655517578125,
-0.029693603515625,
0.03057861328125,
-0.034454345703125,
-0.004108428955078125,
-0.0027923583984375,
-0.003131866455078125,
-0.007293701171875,
-0.00795745849609375,
-0.012054443359375,
0.0062255859375,
0.037353515625,
-0.0193023681640625,
-0.01290130615234375,
-0.025054931640625,
-0.02020263671875,
-0.0115203857421875,
0.0211944580078125,
0.0153045654296875,
-0.020721435546875,
0.00222015380859375,
0.0266265869140625,
-0.03253173828125,
0.036651611328125,
0.01027679443359375,
0.01192474365234375,
-0.003574371337890625,
-0.0121612548828125,
0.006664276123046875,
-0.004016876220703125,
0.002002716064453125,
-0.010894775390625,
0.01221466064453125,
0.033905029296875,
-0.02447509765625,
0.048675537109375,
0.01238250732421875,
-0.012969970703125,
0.022369384765625,
0.0268096923828125,
0.0279998779296875,
-0.002773284912109375,
-0.011444091796875,
0.021484375,
0.010162353515625,
-0.005779266357421875,
-0.0188751220703125,
0.0102386474609375,
-0.0179443359375,
0.004100799560546875,
0.0128173828125,
-0.023284912109375,
0.003971099853515625,
0.00005120038986206055,
0.01708984375,
-0.006954193115234375,
0.031158447265625,
-0.001953125,
0.0195465087890625,
-0.00124359130859375,
0.027679443359375,
-0.0016832351684570312
] |
ours_561
|
Let \( AD \) intersect \( MN \) at \( Q \), and let \( MN \) intersect \( BO \) at \( P \). Since \( BO = OP \) and \( MN \parallel BC \), it follows that \( QO = OD \). We also have \( AQ = QD \), so \( AD = \frac{4}{3} AO = 444 \).
\(\boxed{444}\)
|
444
|
{
"competition": "us_comps",
"dataset": "Ours",
"posts": null,
"source": "OMOSoln2.md"
}
|
Let \( \triangle ABC \) be a triangle inscribed in circle \(\Gamma\), centered at \( O \) with radius \( 333 \). Let \( M \) be the midpoint of \( AB \), \( N \) be the midpoint of \( AC \), and \( D \) be the point where line \( AO \) intersects \( BC \). Given that lines \( MN \) and \( BO \) concur on \(\Gamma\) and that \( BC = 665 \), find the length of segment \( AD \).
|
[
"/Mathematics/Geometry/Distance/Point-PointDistance2-Dimensional",
"/Mathematics/Geometry/GeneralGeometry/EuclideanGeometry",
"/Mathematics/Geometry/GeneralGeometry/Geometry",
"/Mathematics/Geometry/PlaneGeometry/Circles/Circle",
"/Mathematics/Geometry/PlaneGeometry/Circles/Circumcenter",
"/Mathematics/Geometry/PlaneGeometry/Circles/Radius",
"/Mathematics/Geometry/PlaneGeometry/CircularTriangles/CircularTriangle",
"/Mathematics/Geometry/PlaneGeometry/Triangles/Cevians",
"/Mathematics/Geometry/PlaneGeometry/Triangles/TriangleLines",
"/Mathematics/Geometry/PlaneGeometry/Triangles/TrianglePoints",
"/Mathematics/Geometry/Points/Midpoint"
] |
Use MN ∥ BC and BO = OP to get QO = OD, which gives AD = 4/3·AO.
|
[
-0.0001430511474609375,
-0.0321044921875,
0.0229034423828125,
0.021728515625,
-0.00030684471130371094,
0.032135009765625,
-0.0042877197265625,
0.050689697265625,
-0.0015802383422851562,
-0.058258056640625,
-0.00768280029296875,
0.026641845703125,
-0.005023956298828125,
0.029937744140625,
-0.004352569580078125,
-0.0025119781494140625,
0.0191802978515625,
-0.02001953125,
0.031463623046875,
-0.0010061264038085938,
-0.01025390625,
0.00621795654296875,
-0.045318603515625,
-0.0283660888671875,
0.0089874267578125,
-0.0121612548828125,
-0.0220794677734375,
-0.00396728515625,
-0.006687164306640625,
0.035614013671875,
0.00366973876953125,
0.019989013671875,
0.0085601806640625,
-0.0150146484375,
-0.0006213188171386719,
-0.00023221969604492188,
-0.0020904541015625,
0.0019168853759765625,
-0.02655029296875,
-0.05157470703125,
0.0227813720703125,
-0.0124053955078125,
0.0065765380859375,
0.03204345703125,
0.024383544921875,
0.0282135009765625,
-0.005741119384765625,
-0.0072021484375,
-0.00881195068359375,
0.0031223297119140625,
0.0042877197265625,
0.007511138916015625,
-0.03778076171875,
-0.006622314453125,
-0.005908966064453125,
-0.052459716796875,
-0.0216217041015625,
0.0029697418212890625,
-0.003215789794921875,
-0.04083251953125,
0.0030460357666015625,
0.031951904296875,
-0.0083770751953125,
-0.0069427490234375,
-0.0026073455810546875,
-0.00024187564849853516,
-0.031707763671875,
-0.038055419921875,
-0.00403594970703125,
-0.01678466796875,
0.034332275390625,
-0.032379150390625,
0.006900787353515625,
-0.0022296905517578125,
-0.01047515869140625,
-0.00852203369140625,
-0.01255035400390625,
-0.00024437904357910156,
-0.021759033203125,
0.003917694091796875,
0.0026988983154296875,
-0.00493621826171875,
0.006938934326171875,
-0.0088043212890625,
0.0234222412109375,
-0.0089874267578125,
-0.032989501953125,
-0.0014429092407226562,
0.047027587890625,
-0.0103302001953125,
0.01187896728515625,
-0.01453399658203125,
-0.0112152099609375,
-0.002437591552734375,
-0.004161834716796875,
0.00563812255859375,
-0.005062103271484375,
-0.0092926025390625,
-0.0216827392578125,
0.006488800048828125,
-0.01230621337890625,
0.002109527587890625,
-0.0234375,
-0.028594970703125,
0.0159454345703125,
-0.0179443359375,
-0.0054931640625,
0.0031452178955078125,
-0.023712158203125,
-0.0006909370422363281,
0.0033702850341796875,
-0.005218505859375,
0.041961669921875,
0.03656005859375,
0.00844573974609375,
-0.0289154052734375,
0.01557159423828125,
0.0208740234375,
0.00664520263671875,
0.0239715576171875,
0.005558013916015625,
0.00905609130859375,
0.006542205810546875,
0.043975830078125,
-0.00225067138671875,
-0.01494598388671875,
-0.0023193359375,
-0.030609130859375,
-0.0301361083984375,
-0.006137847900390625,
0.0235748291015625,
-0.00031757354736328125,
-0.037841796875,
-0.02691650390625,
0.00345611572265625,
-0.00893402099609375,
-0.01531219482421875,
0.01084136962890625,
-0.0171356201171875,
-0.01464080810546875,
-0.00925445556640625,
-0.004405975341796875,
0.021484375,
-0.07196044921875,
0.0136871337890625,
-0.06439208984375,
-0.01078033447265625,
-0.003925323486328125,
0.00714111328125,
0.01084136962890625,
-0.015838623046875,
0.01351165771484375,
0.0171051025390625,
-0.004146575927734375,
-0.01788330078125,
-0.0017757415771484375,
-0.0028247833251953125,
0.03314208984375,
0.01378631591796875,
0.0027923583984375,
-0.00788116455078125,
-0.0197296142578125,
0.01485443115234375,
0.0023956298828125,
-0.007495880126953125,
-0.0204620361328125,
-0.0204010009765625,
-0.00164794921875,
-0.043548583984375,
-0.01430511474609375,
0.01465606689453125,
0.01409912109375,
0.0035991668701171875,
-0.0184326171875,
-0.0066070556640625,
-0.0012416839599609375,
0.005565643310546875,
0.0044403076171875,
-0.0226287841796875,
0.0256195068359375,
-0.003406524658203125,
0.0007224082946777344,
-0.0022983551025390625,
0.00958251953125,
0.015716552734375,
0.005977630615234375,
0.00823974609375,
-0.0207977294921875,
-0.006580352783203125,
0.01239776611328125,
-0.01366424560546875,
-0.029327392578125,
-0.0007648468017578125,
0.002147674560546875,
0.029632568359375,
0.0212554931640625,
-0.02325439453125,
0.0121307373046875,
0.0171661376953125,
0.001697540283203125,
-0.015655517578125,
-0.0245208740234375,
0.015625,
0.00809478759765625,
-0.01349639892578125,
-0.007007598876953125,
-0.005084991455078125,
0.0114288330078125,
-0.006343841552734375,
0.007495880126953125,
0.00861358642578125,
0.035980224609375,
-0.0009036064147949219,
0.0214385986328125,
0.0087432861328125,
-0.0245208740234375,
-0.01035308837890625,
0.00965118408203125,
-0.00201416015625,
0.0173492431640625,
0.0199127197265625,
-0.00868988037109375,
0.0036029815673828125,
-0.0168304443359375,
-0.012359619140625,
-0.005767822265625,
0.00933074951171875,
-0.0244598388671875,
0.0081787109375,
0.0020275115966796875,
-0.0106353759765625,
0.0107879638671875,
-0.0191802978515625,
-0.0038394927978515625,
-0.003498077392578125,
-0.0016717910766601562,
-0.02728271484375,
-0.01226043701171875,
-0.003620147705078125,
-0.0059967041015625,
0.042327880859375,
-0.01230621337890625,
-0.006481170654296875,
-0.00818634033203125,
0.000980377197265625,
0.01068878173828125,
0.0110015869140625,
-0.01702880859375,
-0.00881195068359375,
-0.0210418701171875,
-0.037872314453125,
0.0117034912109375,
0.006526947021484375,
-0.010498046875,
-0.008819580078125,
0.0190887451171875,
0.004894256591796875,
0.0037288665771484375,
-0.005496978759765625,
0.00399017333984375,
-0.00955963134765625,
0.0004532337188720703,
0.0025653839111328125,
-0.017547607421875,
-0.005535125732421875,
0.0411376953125,
-0.01203155517578125,
0.01543426513671875,
0.006366729736328125,
-0.0018072128295898438,
0.0341796875,
-0.01300811767578125,
-0.0074005126953125,
0.007328033447265625,
-0.004638671875,
-0.007381439208984375,
-0.0192108154296875,
0.0206451416015625,
0.0035114288330078125,
0.0142822265625,
-0.003002166748046875,
-0.00927734375,
-0.04412841796875,
0.0024242401123046875,
0.0164337158203125,
0.0028820037841796875,
0.006717681884765625,
-0.029937744140625,
-0.007450103759765625,
0.0228118896484375,
-0.0013828277587890625,
0.01561737060546875,
-0.017608642578125,
-0.024017333984375,
0.040313720703125,
0.0007696151733398438,
-0.01038360595703125,
0.0024013519287109375,
0.01947021484375,
0.00030517578125,
0.0215911865234375,
-0.01465606689453125,
-0.00768280029296875,
0.0000349879264831543,
-0.005527496337890625,
0.0341796875,
0.006946563720703125,
0.01107025146484375,
-0.0240631103515625,
-0.0088348388671875,
0.0018815994262695312,
-0.0029582977294921875,
0.016326904296875,
-0.01253509521484375,
-0.02276611328125,
-0.00677490234375,
-0.0129241943359375,
-0.0003094673156738281,
-0.005939483642578125,
0.021697998046875,
0.0194549560546875,
0.037200927734375,
0.019775390625,
0.0029735565185546875,
0.04803466796875,
-0.0206146240234375,
0.0202484130859375,
-0.0028629302978515625,
0.036712646484375,
0.0170135498046875,
-0.008575439453125,
0.00727081298828125,
0.0025920867919921875,
-0.03118896484375,
-0.0093536376953125,
0.01507568359375,
0.01250457763671875,
0.0172119140625,
0.00635528564453125,
0.0009937286376953125,
0.0086822509765625,
0.011566162109375,
0.05267333984375,
-0.0697021484375,
-0.04302978515625,
0.00235748291015625,
-0.0193023681640625,
0.0262298583984375,
-0.06146240234375,
-0.0240478515625,
0.01268768310546875,
0.0005893707275390625,
0.033355712890625,
0.015289306640625,
-0.00997161865234375,
-0.0092315673828125,
0.007480621337890625,
-0.0012960433959960938,
0.0090179443359375,
-0.01415252685546875,
-0.00261688232421875,
-0.03448486328125,
-0.008819580078125,
0.0225067138671875,
-0.01413726806640625,
-0.01450347900390625,
0.01032257080078125,
0.0015687942504882812,
-0.0450439453125,
-0.00995635986328125,
0.01360321044921875,
-0.00989532470703125,
0.00685882568359375,
0.006366729736328125,
0.0248565673828125,
0.01236724853515625,
-0.0179443359375,
0.0108184814453125,
-0.01116180419921875,
-0.00719451904296875,
-0.0025234222412109375,
-0.0159759521484375,
0.01384735107421875,
0.02685546875,
-0.02130126953125,
-0.000988006591796875,
0.0244140625,
-0.0190887451171875,
0.029327392578125,
0.012054443359375,
0.0013303756713867188,
-0.0112457275390625,
-0.006443023681640625,
-0.02685546875,
-0.024505615234375,
0.004886627197265625,
-0.003704071044921875,
0.01398468017578125,
0.032928466796875,
0.0013170242309570312,
-0.036224365234375,
-0.01488494873046875,
0.0240478515625,
-0.01123809814453125,
0.0028629302978515625,
-0.00740814208984375,
0.0002467632293701172,
-0.00583648681640625,
0.01739501953125,
0.035491943359375,
-0.0090484619140625,
0.0011510848999023438,
-0.007171630859375,
-0.0186004638671875,
-0.0226287841796875,
0.01812744140625,
-0.0306549072265625,
0.00042939186096191406,
-0.0187835693359375,
-0.0113677978515625,
0.004062652587890625,
-0.013427734375,
0.0237884521484375,
-0.0190277099609375,
0.0222015380859375,
-0.0175323486328125,
-0.0107269287109375,
0.048065185546875,
-0.0017518997192382812,
-0.02130126953125,
0.02313232421875,
-0.001499176025390625,
-0.01543426513671875,
0.003864288330078125,
-0.0014486312866210938,
0.005290985107421875,
0.0479736328125,
-0.007350921630859375,
0.00000959634780883789,
0.021331787109375,
0.029632568359375,
-0.006832122802734375,
-0.003437042236328125,
-0.013885498046875,
-0.005466461181640625,
0.01020050048828125,
0.0033092498779296875,
0.0156402587890625,
-0.0003247261047363281,
0.00428009033203125,
-0.0010919570922851562,
-0.034210205078125,
0.021820068359375,
-0.01331329345703125,
-0.0130615234375,
0.00868988037109375,
0.00859832763671875,
-0.0162506103515625,
-0.00879669189453125,
0.042877197265625,
-0.017822265625,
0.01497650146484375,
-0.0030918121337890625,
0.004230499267578125,
-0.007503509521484375,
-0.006641387939453125,
-0.00386810302734375,
0.007305145263671875,
0.029449462890625,
0.0036029815673828125,
-0.01898193359375,
-0.0217132568359375,
-0.005069732666015625,
-0.03741455078125,
-0.0180816650390625,
0.033233642578125,
-0.0207061767578125,
-0.01263427734375,
0.0146636962890625,
0.01568603515625,
-0.0341796875,
-0.006748199462890625,
0.0007076263427734375,
-0.00693511962890625,
-0.01010894775390625,
0.00911712646484375,
0.01143646240234375,
-0.0012159347534179688,
0.00861358642578125,
-0.045166015625,
-0.01117706298828125,
-0.004791259765625,
-0.013763427734375,
-0.0272064208984375,
-0.0290679931640625,
-0.012939453125,
0.025970458984375,
-0.00021004676818847656,
-0.0034046173095703125,
-0.021514892578125,
0.0413818359375,
-0.021148681640625,
-0.028839111328125,
0.025543212890625,
0.016265869140625,
-0.0638427734375,
0.0164794921875,
0.005218505859375,
0.0090484619140625,
0.004901885986328125,
-0.006908416748046875,
0.018829345703125,
0.01541900634765625,
-0.0247802734375,
0.01493072509765625,
0.01348876953125,
-0.01119232177734375,
-0.03289794921875,
0.017730712890625,
0.039886474609375,
-0.0182647705078125,
0.00476837158203125,
-0.01043701171875,
0.0012674331665039062,
0.01389312744140625,
0.0299530029296875,
-0.0005831718444824219,
-0.0218658447265625,
0.0219268798828125,
0.0034503936767578125,
-0.006641387939453125,
0.0020122528076171875,
-0.043792724609375,
0.001880645751953125,
0.0018339157104492188,
-0.004329681396484375,
-0.02508544921875,
0.00286102294921875,
0.01016998291015625,
-0.00618743896484375,
-0.0009350776672363281,
0.00949859619140625,
-0.0035762786865234375,
-0.001323699951171875,
0.0236968994140625,
0.01129913330078125,
-0.027679443359375,
0.00023055076599121094,
0.0222015380859375,
0.008697509765625,
-0.01436614990234375,
-0.0096893310546875,
-0.034210205078125,
0.00766754150390625,
-0.0208587646484375,
0.038909912109375,
0.0032806396484375,
0.0197296142578125,
-0.0066070556640625,
0.01556396484375,
-0.0017795562744140625,
-0.0216064453125,
0.0242919921875,
-0.01548004150390625,
-0.026336669921875,
0.0194549560546875,
-0.00844573974609375,
0.005832672119140625,
-0.0240936279296875,
-0.0122222900390625,
0.00574493408203125,
-0.0107269287109375,
0.02227783203125,
-0.00888824462890625,
0.036590576171875,
-0.0287322998046875,
0.00688934326171875,
-0.006656646728515625,
0.0142974853515625,
0.004302978515625,
0.0121612548828125,
0.046142578125,
-0.01473236083984375,
-0.0118560791015625,
-0.0091400146484375,
0.01105499267578125,
0.0274810791015625,
0.01230621337890625,
-0.00787353515625,
-0.0164031982421875,
-0.0095977783203125,
0.0125274658203125,
0.03131103515625,
-0.013702392578125,
-0.0288238525390625,
-0.0169525146484375,
0.018768310546875,
-0.0218048095703125,
0.03314208984375,
0.0298919677734375,
-0.020782470703125,
-0.0012578964233398438,
-0.005893707275390625,
0.0264739990234375,
0.01535797119140625,
-0.01177978515625,
-0.02447509765625,
0.014404296875,
0.01308441162109375,
0.0139923095703125,
-0.0141754150390625,
-0.0298614501953125,
0.00432586669921875,
0.0105438232421875,
0.01343536376953125,
-0.007755279541015625,
-0.020538330078125,
-0.010101318359375,
-0.004180908203125,
-0.01139068603515625,
0.01160430908203125,
0.0021266937255859375,
0.006999969482421875,
0.0062103271484375,
-0.0019207000732421875,
-0.0265960693359375,
-0.0241851806640625,
-0.042449951171875,
0.0280914306640625,
-0.037078857421875,
-0.0197906494140625,
-0.005523681640625,
-0.0010404586791992188,
0.01032257080078125,
0.006351470947265625,
-0.0237884521484375,
-0.0016584396362304688,
0.019775390625,
-0.00453948974609375,
0.0182342529296875,
0.00946807861328125,
0.01617431640625,
0.01036834716796875,
-0.0386962890625,
-0.0201416015625,
0.00658416748046875,
-0.027435302734375,
-0.00493621826171875,
0.00894927978515625,
0.0173797607421875,
0.00484466552734375,
-0.00841522216796875,
0.02874755859375,
0.0233612060546875,
0.0077056884765625,
-0.0126495361328125,
-0.0015687942504882812,
-0.0014133453369140625,
0.03509521484375,
0.00902557373046875,
-0.01197052001953125,
-0.007617950439453125,
0.0074615478515625,
-0.00075531005859375,
0.01329803466796875,
0.0021610260009765625,
-0.041473388671875,
-0.014251708984375,
0.0025501251220703125,
0.023193359375,
-0.0251922607421875,
-0.004680633544921875,
0.0019464492797851562,
-0.02056884765625,
-0.046295166015625,
0.0103759765625,
-0.016693115234375,
0.035858154296875,
0.00234222412109375,
-0.007781982421875,
-0.0106201171875,
-0.004375457763671875,
0.025604248046875,
-0.01024627685546875,
-0.02886962890625,
0.06451416015625,
0.003757476806640625,
-0.0027256011962890625,
-0.0200042724609375,
-0.01226806640625,
0.00103759765625,
0.006710052490234375,
-0.0242156982421875,
0.000025033950805664062,
-0.0033054351806640625,
0.0200347900390625,
0.0261993408203125,
0.0015153884887695312,
-0.008514404296875,
-0.0160980224609375,
0.01172637939453125,
-0.016204833984375,
0.010650634765625,
0.0026493072509765625,
-0.0104522705078125,
-0.017059326171875,
-0.0004916191101074219,
0.0294342041015625,
-0.0321044921875,
-0.004840850830078125,
-0.023590087890625,
-0.014190673828125,
-0.0142974853515625,
-0.0186004638671875,
-0.03216552734375,
-0.0413818359375,
-0.0305328369140625,
0.0094146728515625,
0.00899505615234375,
0.00539398193359375,
-0.02197265625,
0.00801849365234375,
-0.0304412841796875,
0.0002579689025878906,
-0.004150390625,
0.0140838623046875,
-0.0234375,
-0.0090179443359375,
-0.01568603515625,
0.023101806640625,
0.039520263671875,
-0.01198577880859375,
0.00997161865234375,
0.0022068023681640625,
-0.006610870361328125,
-0.022735595703125,
-0.0156707763671875,
-0.036651611328125,
-0.0172119140625,
0.00021505355834960938,
0.051239013671875,
-0.003963470458984375,
0.004886627197265625,
-0.0258026123046875,
-0.005268096923828125,
-0.007602691650390625,
-0.0019092559814453125,
-0.041839599609375,
0.03521728515625,
-0.00896453857421875,
0.0156707763671875,
0.0064849853515625,
-0.024993896484375,
0.01105499267578125,
-0.0008716583251953125,
-0.018310546875,
-0.01038360595703125,
-0.0206756591796875,
-0.0035495758056640625,
0.0027942657470703125,
-0.0298919677734375,
-0.0016775131225585938,
0.02020263671875,
-0.0195770263671875,
-0.01123046875,
0.007328033447265625,
-0.00768280029296875,
0.013946533203125,
0.0030384063720703125,
0.0183258056640625,
0.0173187255859375,
-0.007282257080078125,
0.01247406005859375,
-0.017333984375,
-0.01122283935546875,
0.0014810562133789062,
-0.048004150390625,
-0.0044403076171875,
-0.0006613731384277344,
-0.004581451416015625,
-0.0029277801513671875,
0.0085906982421875,
-0.006587982177734375,
0.03765869140625,
-0.034912109375,
0.0072784423828125,
-0.0091705322265625,
0.000492095947265625,
0.01325225830078125,
-0.047119140625,
0.0184783935546875,
-0.01491546630859375,
0.0005526542663574219,
-0.0256195068359375,
-0.00626373291015625,
-0.003307342529296875,
0.0110931396484375,
-0.01654052734375,
-0.026153564453125,
-0.015625,
0.0027523040771484375,
-0.0306396484375,
-0.01331329345703125,
0.0147857666015625,
0.0215301513671875,
0.01517486572265625,
0.0051116943359375,
0.0112762451171875,
-0.0167694091796875,
-0.004978179931640625,
0.023834228515625,
-0.040802001953125,
-0.0011053085327148438,
0.003635406494140625,
-0.0004367828369140625,
-0.00782012939453125,
0.018280029296875,
0.01491546630859375,
-0.0218353271484375,
-0.01299285888671875,
-0.00957489013671875,
0.0284423828125,
-0.012054443359375,
0.006122589111328125,
-0.014739990234375,
-0.0098114013671875,
0.0242462158203125,
0.018707275390625,
-0.0017070770263671875,
-0.0189971923828125,
0.0160369873046875,
0.0020275115966796875,
-0.016876220703125,
0.01412200927734375,
-0.0589599609375,
0.0066070556640625,
0.00640106201171875,
0.00975799560546875,
-0.0258941650390625,
-0.029876708984375,
0.05108642578125,
-0.0252227783203125,
0.0288848876953125,
0.01241302490234375,
0.04034423828125,
-0.02459716796875,
-0.0224151611328125,
0.0139007568359375,
-0.01198577880859375,
0.0037631988525390625,
0.007144927978515625,
-0.00423431396484375,
-0.0176544189453125,
0.025665283203125,
-0.01947021484375,
0.01422119140625,
-0.020111083984375,
0.0001398324966430664,
0.00988006591796875,
-0.02056884765625,
0.023895263671875,
-0.01849365234375,
0.0100860595703125,
0.0238800048828125,
0.00273895263671875,
-0.021270751953125,
-0.021575927734375,
-0.015838623046875,
0.054840087890625,
0.02252197265625,
0.046234130859375,
-0.0247802734375,
-0.005199432373046875,
0.0221099853515625,
0.02276611328125,
0.040374755859375,
-0.007213592529296875,
-0.009185791015625,
0.046722412109375,
0.0269927978515625,
0.0032253265380859375,
-0.006160736083984375,
-0.0017976760864257812,
0.005214691162109375,
-0.017181396484375,
0.0019683837890625,
0.0143280029296875,
-0.01363372802734375,
-0.014434814453125,
-0.01371002197265625,
-0.01508331298828125,
-0.01055908203125,
-0.003387451171875,
-0.007617950439453125,
0.038482666015625,
-0.037841796875,
-0.0079498291015625,
-0.0205841064453125,
0.02716064453125,
-0.03253173828125,
0.0014896392822265625,
0.017822265625,
-0.0050506591796875,
-0.0175628662109375,
0.0113983154296875,
-0.0128631591796875,
-0.01128387451171875,
-0.007404327392578125,
0.043853759765625,
0.0268096923828125,
-0.00046825408935546875,
0.013458251953125,
-0.0007266998291015625,
-0.0009617805480957031,
-0.021331787109375,
-0.005039215087890625,
-0.01346588134765625,
-0.0153350830078125,
0.00775909423828125,
-0.0024394989013671875,
0.003204345703125,
0.01541900634765625,
-0.008941650390625,
-0.0005879402160644531,
0.0282135009765625,
0.00972747802734375,
0.019439697265625,
0.006748199462890625,
-0.0266265869140625,
-0.0026950836181640625,
-0.023162841796875,
0.0386962890625,
-0.01316070556640625,
0.00251007080078125,
0.00009506940841674805,
0.01450347900390625,
-0.0009646415710449219,
0.00518798828125,
0.0031490325927734375,
-0.0119476318359375,
0.0122833251953125,
0.00592041015625,
-0.002017974853515625,
0.0005679130554199219,
-0.0053558349609375,
0.0006737709045410156,
0.005695343017578125,
0.0147552490234375,
0.00406646728515625,
-0.036041259765625,
-0.00301361083984375,
0.01187896728515625,
-0.0024089813232421875,
-0.012847900390625,
0.003620147705078125,
0.007274627685546875,
-0.010040283203125,
0.0184783935546875,
-0.003459930419921875,
-0.01363372802734375,
0.0168914794921875,
0.0201568603515625,
0.006328582763671875,
0.042572021484375,
0.0006670951843261719,
0.00775146484375,
-0.0086669921875,
0.04254150390625,
0.012298583984375,
-0.00708770751953125,
0.005107879638671875,
0.006633758544921875,
-0.024566650390625,
-0.045928955078125,
-0.035400390625,
0.005680084228515625,
0.005645751953125,
0.0143890380859375,
0.06085205078125,
0.0014209747314453125,
-0.03204345703125,
0.048126220703125,
-0.013885498046875,
0.0078582763671875,
0.0055084228515625,
0.0235595703125,
0.0155487060546875,
0.0257720947265625,
0.039520263671875,
-0.0024890899658203125,
-0.016143798828125,
0.0230255126953125,
-0.0005326271057128906,
0.012054443359375,
-0.011505126953125,
0.01898193359375,
0.01495361328125,
-0.0270538330078125,
0.01715087890625,
-0.03546142578125,
-0.0263824462890625,
0.0081634521484375,
0.01126861572265625,
-0.0014934539794921875,
-0.007350921630859375,
-0.0157318115234375,
-0.005062103271484375,
0.033782958984375,
-0.002582550048828125,
0.004924774169921875,
-0.043609619140625,
0.0107269287109375,
0.0010766983032226562,
0.0105133056640625,
-0.029632568359375,
0.0296630859375,
0.017486572265625,
0.056732177734375,
-0.0256195068359375,
0.01110076904296875,
0.0098114013671875,
-0.0176544189453125,
-0.037994384765625,
-0.0227508544921875,
0.0347900390625,
-0.0142059326171875,
0.007080078125,
-0.027008056640625,
-0.00897979736328125,
0.00911712646484375,
-0.01332855224609375,
0.0430908203125,
-0.01439666748046875,
0.0024852752685546875,
-0.0277252197265625,
-0.01409912109375,
0.00417327880859375,
-0.02777099609375,
0.03387451171875,
-0.0164031982421875,
-0.022369384765625,
-0.0067291259765625,
-0.0208587646484375,
-0.01361846923828125,
-0.0245361328125,
0.02752685546875,
0.018310546875,
-0.0091400146484375,
0.00756072998046875,
-0.00909423828125,
0.0284576416015625,
0.012786865234375,
-0.049896240234375,
-0.00969696044921875,
0.00003361701965332031,
0.012664794921875,
-0.0198211669921875,
-0.01401519775390625,
-0.0203399658203125,
-0.007678985595703125,
0.027984619140625,
-0.046630859375,
-0.00505828857421875,
-0.01525115966796875,
0.023223876953125,
0.01165008544921875,
-0.006465911865234375,
-0.00688934326171875,
0.0008492469787597656,
0.007843017578125,
-0.06329345703125,
0.01971435546875,
-0.017669677734375,
0.01378631591796875,
0.005069732666015625,
-0.0269317626953125,
0.00621795654296875,
-0.033233642578125,
-0.00824737548828125,
-0.0175933837890625,
0.0035839080810546875,
0.009063720703125,
-0.0157623291015625,
-0.0150604248046875,
0.0276947021484375,
-0.005275726318359375,
-0.00286102294921875,
-0.0272674560546875,
0.0192108154296875,
-0.0124053955078125,
0.02008056640625,
-0.007022857666015625,
-0.005870819091796875,
-0.029541015625,
-0.007289886474609375,
-0.0246124267578125,
0.0009622573852539062,
0.0267333984375,
0.02288818359375,
0.0016183853149414062,
-0.0074462890625,
0.00534820556640625,
0.0084991455078125,
0.006061553955078125,
0.0017309188842773438,
-0.021759033203125,
-0.029632568359375,
0.02789306640625,
0.00202178955078125,
-0.0007538795471191406,
-0.015655517578125,
0.00799560546875,
0.0242462158203125,
0.0302886962890625,
-0.0133514404296875,
-0.0228424072265625,
-0.00688934326171875,
0.0008139610290527344,
0.019073486328125,
-0.0211181640625,
0.00489044189453125,
0.01561737060546875,
0.01215362548828125,
0.032928466796875,
-0.0382080078125,
-0.0162200927734375,
-0.02349853515625,
-0.00032210350036621094,
-0.02569580078125,
-0.019500732421875,
-0.0160675048828125,
-0.0003991127014160156,
0.00875091552734375,
-0.029022216796875,
-0.00959014892578125,
0.03778076171875,
0.007305145263671875,
0.016265869140625,
0.0198211669921875,
0.0036449432373046875,
-0.0201263427734375,
0.017364501953125,
0.0134735107421875,
-0.0248870849609375,
-0.0196990966796875,
-0.01806640625,
-0.0118255615234375,
-0.003078460693359375,
0.0034351348876953125,
0.0006074905395507812,
-0.01175689697265625,
-0.017242431640625,
0.0030002593994140625,
-0.0180816650390625,
0.00215911865234375,
-0.01320648193359375,
-0.011444091796875,
0.006404876708984375,
-0.0032138824462890625,
0.0188446044921875,
0.0182647705078125,
0.00494384765625,
0.056793212890625,
0.0095672607421875,
0.0025482177734375,
0.0231781005859375,
0.00750732421875,
0.00879669189453125,
-0.006862640380859375,
0.0124969482421875,
0.0126800537109375,
0.00720977783203125,
0.02532958984375,
0.0060272216796875,
0.0284576416015625,
-0.0063934326171875,
0.004177093505859375,
-0.0291595458984375,
-0.00948333740234375,
-0.006107330322265625,
-0.025909423828125,
0.052093505859375,
0.0258331298828125,
0.004550933837890625,
0.01363372802734375,
-0.0163116455078125,
0.0007462501525878906,
-0.0165863037109375,
-0.01157379150390625,
0.017303466796875,
-0.00461578369140625,
-0.01641845703125,
-0.00637054443359375,
0.023651123046875,
0.0243377685546875,
0.009857177734375,
-0.0211639404296875,
-0.002292633056640625,
-0.041107177734375,
-0.0248565673828125,
-0.0233306884765625,
-0.00244903564453125,
-0.01092529296875,
-0.01367950439453125,
0.00885009765625,
0.01137542724609375,
0.0007357597351074219,
0.0653076171875,
-0.021942138671875,
0.02178955078125,
0.022857666015625,
0.007144927978515625,
-0.003025054931640625,
-0.0147552490234375,
-0.017822265625,
-0.0164642333984375,
-0.007537841796875,
-0.00928497314453125,
0.0148773193359375,
-0.025482177734375,
0.007602691650390625,
0.00701141357421875,
0.0240631103515625,
0.006519317626953125,
-0.00441741943359375,
0.00344085693359375,
-0.02606201171875,
0.004116058349609375,
-0.00101470947265625,
0.0253143310546875,
0.0168609619140625,
0.00408172607421875,
-0.0161895751953125,
0.02069091796875,
0.0163421630859375,
-0.014862060546875,
-0.0029468536376953125,
0.0200958251953125,
-0.0223541259765625,
0.0221405029296875,
-0.003582000732421875,
0.0157623291015625,
0.01214599609375,
0.00603485107421875,
0.0634765625,
-0.018310546875,
-0.033294677734375,
0.00106048583984375,
-0.02020263671875,
0.0264434814453125,
-0.032958984375,
0.0012845993041992188,
-0.0301666259765625,
0.0021800994873046875,
0.005767822265625,
0.00908660888671875,
0.0164947509765625,
0.0256500244140625,
0.005321502685546875,
-0.029815673828125,
-0.0183258056640625,
-0.00576019287109375,
-0.00809478759765625,
-0.033782958984375,
-0.007415771484375,
-0.026458740234375,
-0.00588226318359375,
0.0439453125,
0.01739501953125,
0.01261138916015625,
0.0025768280029296875,
0.03045654296875,
0.005870819091796875,
0.02337646484375,
0.0196685791015625,
-0.0166473388671875,
-0.0178985595703125,
-0.043548583984375,
0.0096893310546875,
0.0013484954833984375,
0.0038509368896484375,
0.017181396484375,
0.038421630859375,
-0.00989532470703125,
-0.0168304443359375,
-0.01297760009765625,
-0.020660400390625,
0.019622802734375,
0.0085601806640625,
0.006015777587890625,
-0.00022542476654052734,
0.06427001953125,
0.005573272705078125,
0.044769287109375,
-0.033447265625,
-0.02783203125,
-0.030792236328125,
0.0212860107421875,
0.036407470703125,
-0.0209808349609375,
0.0022830963134765625,
-0.00852203369140625,
-0.01332855224609375,
-0.0215911865234375,
0.006801605224609375,
-0.024566650390625,
0.01300048828125,
0.006473541259765625,
0.017303466796875,
0.0006489753723144531,
0.0440673828125,
-0.018035888671875,
-0.0012149810791015625,
0.027618408203125,
0.00594329833984375,
0.001987457275390625,
-0.0020732879638671875,
-0.0278167724609375,
0.00917816162109375,
0.01297760009765625,
0.015869140625,
-0.01512908935546875,
-0.038543701171875,
-0.00247955322265625,
-0.006580352783203125,
-0.004383087158203125,
0.009124755859375,
-0.0268402099609375,
-0.00865936279296875,
-0.0404052734375,
-0.006366729736328125,
-0.029876708984375,
-0.001636505126953125,
-0.01337432861328125,
0.004669189453125,
0.002941131591796875,
0.0157470703125,
0.003543853759765625,
0.00586700439453125,
-0.0004322528839111328,
0.0018682479858398438,
0.00606536865234375,
-0.00377655029296875,
0.004016876220703125,
0.025787353515625,
-0.00872802734375,
-0.0093841552734375,
0.0025577545166015625,
-0.023345947265625,
-0.01355743408203125,
0.0062713623046875,
0.00901031494140625,
0.01013946533203125,
0.0550537109375,
-0.03704833984375,
-0.017181396484375,
-0.0035533905029296875,
0.00646209716796875,
-0.0141143798828125,
0.0233612060546875,
0.0005578994750976562,
0.0024662017822265625,
0.013031005859375,
-0.011566162109375,
0.00963592529296875,
-0.032440185546875,
0.0042724609375,
-0.0128936767578125,
-0.020111083984375,
-0.0255584716796875,
-0.0218048095703125,
0.0268707275390625,
0.04376220703125,
-0.007781982421875,
0.025787353515625,
-0.0272674560546875,
-0.002941131591796875,
-0.0167236328125,
0.0167083740234375,
-0.002735137939453125,
0.0171051025390625,
-0.0030307769775390625,
0.006267547607421875,
-0.016326904296875,
0.016357421875,
0.0159759521484375,
-0.0137786865234375,
0.0016088485717773438,
-0.0043182373046875,
-0.018707275390625,
0.01299285888671875,
-0.000530242919921875,
-0.0262298583984375,
0.0159454345703125,
0.025421142578125,
-0.0033893585205078125,
0.032806396484375,
-0.0198211669921875,
-0.005489349365234375,
0.0233612060546875,
0.01253509521484375,
-0.01412200927734375,
0.0015878677368164062,
-0.00011456012725830078,
0.022308349609375,
-0.005146026611328125,
0.004787445068359375,
-0.007770538330078125,
0.041839599609375,
0.015838623046875,
-0.007770538330078125,
-0.00029921531677246094,
0.00040650367736816406,
-0.01526641845703125,
-0.006717681884765625,
-0.01213836669921875,
-0.019805908203125,
-0.01522064208984375,
-0.0228271484375,
-0.0169677734375,
0.01366424560546875,
0.0239105224609375,
-0.0012712478637695312,
-0.031402587890625,
-0.007171630859375,
-0.0021228790283203125,
0.0077362060546875,
0.002532958984375,
-0.009063720703125,
0.012786865234375,
-0.01215362548828125,
-0.019134521484375,
-0.0181427001953125,
0.0228424072265625,
0.0180511474609375,
0.01568603515625,
0.030303955078125,
0.01751708984375,
0.024871826171875,
0.0008068084716796875,
-0.013458251953125,
-0.005771636962890625,
0.010894775390625,
-0.0120086669921875,
0.00926971435546875,
0.016082763671875,
-0.0163421630859375,
-0.019500732421875,
0.00937652587890625,
-0.0169830322265625,
-0.00241851806640625,
-0.047149658203125,
-0.03656005859375,
-0.00952911376953125,
0.0142059326171875,
0.0101776123046875,
-0.010040283203125,
0.0254058837890625,
0.0192413330078125,
-0.047698974609375,
0.004611968994140625,
-0.0222015380859375,
-0.004062652587890625,
0.0153350830078125,
-0.017486572265625,
0.013671875,
0.006439208984375,
0.0274658203125,
0.006649017333984375,
0.013519287109375,
-0.0278472900390625,
0.00852203369140625,
0.005367279052734375,
0.0088348388671875,
0.00934600830078125,
-0.0230712890625,
0.0229034423828125,
-0.009979248046875,
0.023834228515625,
-0.0017499923706054688,
0.0166473388671875,
-0.002162933349609375,
0.0172119140625,
-0.00875091552734375,
-0.0206756591796875,
-0.0008077621459960938,
0.0042266845703125,
0.00470733642578125,
0.00780487060546875,
-0.033203125,
0.0049591064453125,
0.003307342529296875,
0.035736083984375,
0.00029349327087402344,
0.025787353515625,
0.01898193359375,
-0.00879669189453125,
-0.0018367767333984375,
-0.010955810546875,
-0.03411865234375,
0.022674560546875,
0.036468505859375,
0.0217742919921875,
0.023193359375,
0.026885986328125,
-0.04302978515625,
0.01425933837890625,
-0.0192108154296875,
0.003513336181640625,
-0.0152435302734375,
0.005268096923828125,
-0.0031299591064453125,
-0.0096893310546875,
0.0292510986328125,
-0.03399658203125,
0.015625,
-0.01233673095703125,
-0.006072998046875,
-0.0232391357421875,
-0.0231475830078125,
0.03216552734375,
0.005344390869140625,
-0.00542449951171875,
0.03424072265625,
0.0107879638671875,
-0.01739501953125,
0.02801513671875,
0.00884246826171875,
0.01560211181640625,
0.010467529296875,
0.0079498291015625,
-0.0196990966796875,
0.0117645263671875,
0.0006737709045410156,
0.003108978271484375,
-0.0247344970703125,
-0.0098419189453125,
-0.007053375244140625,
0.00815582275390625,
-0.0345458984375,
0.004795074462890625,
0.00635528564453125,
0.00782012939453125,
0.040924072265625,
0.022430419921875,
0.0142669677734375,
-0.004184722900390625,
-0.006832122802734375,
0.0136260986328125,
0.007694244384765625,
0.0526123046875,
-0.0240325927734375,
-0.007049560546875,
0.0019102096557617188,
-0.0215911865234375,
0.0175933837890625,
-0.013641357421875,
0.0219268798828125,
-0.040283203125,
-0.01617431640625,
-0.012237548828125,
0.06488037109375,
-0.0158233642578125,
-0.0052337646484375,
-0.0235748291015625,
-0.032623291015625,
0.0013437271118164062,
0.0005927085876464844,
-0.0237884521484375,
-0.00946807861328125,
0.002086639404296875,
0.0193634033203125,
-0.0006794929504394531,
-0.00012862682342529297,
0.0157623291015625,
0.0186614990234375,
-0.001983642578125,
-0.002613067626953125,
0.00449371337890625,
-0.0115966796875,
0.0311279296875,
-0.01235198974609375,
0.01265716552734375,
0.037872314453125,
0.0517578125,
-0.002910614013671875,
0.00489044189453125,
0.03216552734375,
-0.01459503173828125,
-0.022186279296875,
0.004535675048828125,
0.0020008087158203125,
0.0187225341796875,
-0.0263519287109375,
0.004291534423828125,
-0.0206756591796875,
0.0181121826171875,
0.01494598388671875,
0.029083251953125,
0.0127105712890625,
-0.002742767333984375,
0.0294036865234375,
-0.00511932373046875,
-0.007480621337890625,
0.0142974853515625,
0.01873779296875,
-0.004871368408203125,
0.01336669921875,
-0.02093505859375,
0.01788330078125,
0.00630950927734375,
0.0055084228515625,
0.0172882080078125,
0.0117340087890625,
0.0035266876220703125,
0.024169921875,
0.0261688232421875,
0.027252197265625,
-0.027313232421875,
-0.0017271041870117188,
0.0110321044921875,
-0.0165557861328125,
-0.007755279541015625,
-0.0014162063598632812,
-0.00632476806640625,
0.0189361572265625,
0.0125732421875,
-0.0030803680419921875,
-0.0095062255859375,
-0.0240478515625,
0.0018854141235351562,
0.001544952392578125,
0.009857177734375,
-0.00011134147644042969,
-0.0450439453125,
-0.017578125,
-0.0133819580078125,
-0.0012025833129882812,
0.01334381103515625,
0.0145111083984375,
0.00655364990234375,
-0.0010843276977539062,
0.047821044921875,
-0.0272064208984375,
-0.01047515869140625,
-0.00670623779296875,
-0.005626678466796875,
0.0181427001953125,
0.017730712890625,
-0.01197052001953125,
-0.004741668701171875,
0.0214691162109375,
0.0217742919921875,
0.0172576904296875,
0.040771484375,
-0.0014410018920898438,
-0.00736236572265625,
-0.0197601318359375,
-0.003326416015625,
0.01654052734375,
0.0113525390625,
0.0170440673828125,
0.0016508102416992188,
0.006633758544921875,
0.01361083984375,
-0.024993896484375,
-0.01209259033203125,
0.0013284683227539062,
-0.01540374755859375,
-0.04034423828125,
0.0123748779296875,
-0.0010433197021484375,
0.0045318603515625,
-0.00506591796875,
-0.01300048828125,
-0.0163116455078125,
-0.00684356689453125,
0.00281524658203125,
0.007236480712890625,
0.0166473388671875,
0.0109100341796875,
-0.04583740234375,
-0.0232086181640625,
0.01004791259765625,
-0.01078033447265625,
-0.01316070556640625,
-0.0173492431640625,
-0.0196380615234375,
-0.001453399658203125,
0.0110321044921875,
0.02130126953125,
-0.0164337158203125,
-0.0227508544921875,
0.0287933349609375,
0.020172119140625,
0.01387786865234375,
0.0285491943359375,
0.01513671875,
-0.038787841796875,
0.0212860107421875,
-0.00299072265625,
0.0296173095703125,
0.0008444786071777344,
-0.0328369140625,
0.010650634765625,
-0.0167694091796875,
-0.048797607421875,
-0.00974273681640625,
-0.023284912109375,
-0.0249176025390625,
0.033050537109375,
-0.025848388671875,
0.0034656524658203125,
-0.005451202392578125,
0.005870819091796875,
0.029083251953125,
0.0066680908203125,
0.0244140625,
-0.0219268798828125,
0.011077880859375,
-0.00258636474609375,
-0.00913238525390625,
0.018402099609375,
0.022491455078125,
0.0377197265625,
-0.0003414154052734375,
0.0238494873046875,
-0.046539306640625,
-0.0428466796875,
0.0229034423828125,
0.0211639404296875,
-0.005939483642578125,
-0.0130462646484375,
-0.0205230712890625,
-0.0252685546875,
-0.056854248046875,
0.0088653564453125,
0.004116058349609375,
-0.0111846923828125,
0.026397705078125,
-0.0254058837890625,
0.04241943359375,
-0.00453948974609375,
0.0283355712890625,
0.00775909423828125,
-0.0113525390625,
0.00836181640625,
0.04217529296875,
0.01885986328125,
0.005290985107421875,
-0.0240631103515625,
0.006603240966796875,
0.01157379150390625,
-0.01080322265625,
-0.02313232421875,
-0.003391265869140625,
0.009613037109375,
0.0027904510498046875,
-0.006366729736328125,
-0.0194244384765625,
0.0287322998046875,
-0.01456451416015625,
0.0144195556640625,
-0.030059814453125,
0.011077880859375,
-0.002674102783203125,
-0.00705718994140625,
-0.0013914108276367188,
-0.004764556884765625,
-0.017547607421875,
0.011627197265625,
0.017486572265625,
0.02435302734375,
-0.0007557868957519531,
0.00273895263671875,
-0.0014734268188476562,
0.00634765625,
-0.020721435546875,
-0.030548095703125,
-0.01442718505859375,
-0.01038360595703125,
-0.001712799072265625,
-0.0128326416015625,
0.00445556640625,
0.020965576171875,
0.0169830322265625,
-0.0011997222900390625,
-0.0277557373046875,
-0.0195159912109375,
-0.0088043212890625,
0.00948333740234375,
0.01168060302734375,
-0.014404296875,
-0.0309906005859375,
-0.00511932373046875,
-0.0132904052734375,
-0.0063629150390625,
-0.020233154296875,
-0.0289154052734375,
0.034088134765625,
0.0275421142578125,
0.003936767578125,
-0.01316070556640625,
-0.0191802978515625,
0.020751953125,
0.03302001953125,
-0.01444244384765625,
-0.01082611083984375,
0.0250244140625,
-0.0160980224609375,
0.0032978057861328125,
-0.01438140869140625,
-0.0264129638671875,
0.0157470703125,
-0.024871826171875,
-0.0011491775512695312,
0.0009264945983886719,
0.0170440673828125,
-0.01526641845703125,
-0.00377655029296875,
0.0014324188232421875,
-0.01552581787109375,
-0.0122833251953125,
-0.051300048828125,
-0.00785064697265625,
-0.0029888153076171875,
-0.012939453125,
0.0217437744140625,
-0.037322998046875,
0.012786865234375,
0.007488250732421875,
0.016448974609375,
-0.0189666748046875,
0.0001773834228515625,
0.0211639404296875,
0.00421142578125,
-0.01434326171875,
-0.003147125244140625,
0.02001953125,
-0.0211029052734375,
0.019622802734375,
0.03399658203125,
0.0186309814453125,
0.00971221923828125,
0.031280517578125,
-0.0002071857452392578,
0.01004791259765625,
0.01493072509765625,
0.01340484619140625,
0.0240325927734375,
-0.0219268798828125,
0.00696563720703125,
-0.01275634765625,
0.0228729248046875,
-0.01134490966796875,
0.007671356201171875,
-0.00138092041015625,
0.0177764892578125,
-0.02716064453125,
-0.0180511474609375,
0.03643798828125,
-0.028778076171875,
0.01442718505859375,
-0.01497650146484375,
-0.0038356781005859375,
0.0162811279296875,
-0.0007581710815429688,
-0.0150146484375,
-0.01090240478515625,
-0.00296783447265625,
-0.02935791015625,
-0.031829833984375,
0.01708984375,
-0.044708251953125,
-0.01499176025390625,
0.00650787353515625,
0.0141448974609375,
0.01177978515625,
0.01995849609375,
0.01824951171875,
-0.005794525146484375,
-0.01983642578125,
-0.0122833251953125,
0.0212554931640625,
0.004638671875,
0.01076507568359375,
0.018402099609375,
0.00557708740234375,
0.029876708984375,
0.014007568359375,
0.01861572265625,
0.00968170166015625,
-0.002246856689453125,
0.036376953125,
0.00173187255859375,
0.00626373291015625,
-0.0095672607421875,
0.00801849365234375,
-0.016937255859375,
0.010711669921875,
-0.01056671142578125,
-0.01528167724609375,
0.0158233642578125,
0.04046630859375,
-0.0078277587890625,
0.0167388916015625,
-0.0158233642578125,
-0.01397705078125,
-0.006927490234375,
0.0189208984375,
0.003459930419921875,
-0.0021572113037109375,
-0.023590087890625,
0.015869140625,
-0.01392364501953125,
0.020660400390625,
-0.0247039794921875,
0.0338134765625,
-0.06317138671875,
0.01171875,
-0.0169830322265625,
-0.023223876953125,
0.033660888671875,
0.0016803741455078125,
0.0079803466796875,
-0.021820068359375,
-0.02349853515625,
-0.014495849609375,
0.0239410400390625,
0.0018768310546875,
0.019256591796875,
0.00029969215393066406,
0.041107177734375,
-0.031463623046875,
-0.0071868896484375,
0.006267547607421875,
-0.0163116455078125,
-0.013580322265625,
0.007427215576171875,
-0.0240020751953125,
-0.00139617919921875,
-0.005847930908203125,
-0.04388427734375,
-0.0447998046875,
0.005466461181640625,
-0.012664794921875,
0.00736236572265625,
-0.0231170654296875,
0.01508331298828125,
-0.005718231201171875,
0.0236968994140625,
-0.0207061767578125,
0.0017328262329101562,
0.01428985595703125,
-0.0166015625,
-0.0179443359375,
0.0011119842529296875,
0.00911712646484375,
0.005199432373046875,
0.052642822265625,
0.022003173828125,
0.01157379150390625,
-0.054534912109375,
-0.0008063316345214844,
-0.0252838134765625,
-0.0191497802734375,
-0.00443267822265625,
-0.006084442138671875,
-0.0060577392578125,
-0.0219268798828125,
-0.00661468505859375,
-0.024993896484375,
-0.006298065185546875,
-0.014251708984375,
0.024627685546875,
-0.002292633056640625,
0.0303192138671875,
0.0007605552673339844,
0.00766754150390625,
-0.0282440185546875,
0.006237030029296875,
-0.0179901123046875,
-0.027069091796875,
-0.00913238525390625,
0.007965087890625,
-0.03094482421875,
0.033203125,
-0.004459381103515625,
-0.016326904296875,
0.00673675537109375,
0.04608154296875,
-0.0301055908203125,
-0.0077362060546875,
0.03765869140625,
0.0112152099609375,
-0.003177642822265625,
-0.0003345012664794922,
0.01114654541015625,
0.001983642578125,
-0.0123138427734375,
-0.0244293212890625,
-0.00848388671875,
0.046356201171875,
0.01451873779296875,
0.01264190673828125,
0.00011497735977172852,
-0.0212860107421875,
-0.04302978515625,
0.01312255859375,
-0.029998779296875,
0.021148681640625,
-0.005161285400390625,
0.03228759765625,
0.033416748046875,
-0.0196990966796875,
-0.01068878173828125,
-0.007106781005859375,
-0.003025054931640625,
0.01537322998046875,
-0.0056610107421875,
0.0183563232421875,
-0.0258636474609375,
-0.0231475830078125,
0.01050567626953125,
0.035888671875,
-0.0183563232421875,
-0.0268707275390625,
0.035430908203125,
0.014801025390625,
0.00662994384765625,
0.005649566650390625,
-0.032806396484375,
0.0084228515625,
0.0069580078125,
0.0147857666015625,
0.026031494140625,
0.000988006591796875,
0.00801849365234375,
-0.001678466796875,
-0.053131103515625,
0.0064697265625,
0.023895263671875,
-0.004306793212890625,
0.0263519287109375,
0.01373291015625,
0.01186370849609375,
0.04827880859375,
0.01068115234375,
-0.00238037109375,
-0.01873779296875,
0.01267242431640625,
0.0100860595703125,
-0.0455322265625,
-0.05615234375,
-0.00997161865234375,
0.023651123046875,
0.0138397216796875,
-0.028839111328125,
0.00849151611328125,
-0.006839752197265625,
-0.00814056396484375,
0.0204925537109375,
0.01025390625,
0.010528564453125,
0.029998779296875,
-0.01055908203125,
-0.0245361328125,
-0.00438690185546875,
-0.0126190185546875,
-0.006343841552734375,
0.022979736328125,
-0.00662994384765625,
-0.060089111328125,
-0.03790283203125,
0.01100921630859375,
0.0426025390625,
-0.02618408203125,
-0.02294921875,
-0.00968170166015625,
0.0225677490234375,
-0.048553466796875,
-0.0196533203125,
0.006649017333984375,
-0.001934051513671875,
0.04443359375,
-0.00980377197265625,
-0.0175628662109375,
0.0159149169921875,
-0.02056884765625,
-0.034027099609375,
-0.036376953125,
-0.01727294921875,
-0.029541015625,
-0.002933502197265625,
0.00940704345703125,
0.005207061767578125,
0.005123138427734375,
0.00775909423828125,
-0.0153350830078125,
0.0078277587890625,
0.024261474609375,
-0.01317596435546875,
0.0005741119384765625,
0.0061187744140625,
-0.0016355514526367188,
-0.022003173828125,
0.040557861328125,
-0.0296478271484375,
-0.00537109375,
0.004634857177734375,
-0.0318603515625,
0.0163726806640625,
-0.006748199462890625,
-0.0170135498046875,
0.036285400390625,
0.0050811767578125,
0.04730224609375,
-0.0186767578125,
0.0286102294921875,
0.0132598876953125,
-0.01210784912109375,
0.0306243896484375,
0.01241302490234375,
-0.005870819091796875,
-0.01529693603515625,
0.027008056640625,
-0.0035724639892578125,
0.02716064453125,
0.04937744140625,
-0.0038928985595703125,
-0.0158233642578125,
0.0244140625,
-0.00713348388671875,
-0.040252685546875,
0.01078033447265625,
0.01012420654296875,
0.02349853515625,
-0.00899505615234375,
-0.0219573974609375,
0.007709503173828125,
-0.011016845703125,
0.005207061767578125,
0.0181884765625,
0.01153564453125,
0.0113677978515625,
0.005077362060546875,
0.016693115234375,
0.031280517578125,
0.06402587890625,
0.01067352294921875,
0.0251312255859375,
0.0233154296875,
-0.032958984375,
0.01629638671875,
0.0298309326171875,
-0.057037353515625,
-0.00716400146484375,
-0.01473236083984375,
0.0036640167236328125,
0.0033111572265625,
0.003978729248046875,
-0.01812744140625,
0.00677490234375,
-0.0018444061279296875,
-0.001132965087890625,
-0.00908660888671875,
-0.0316162109375,
0.0109710693359375,
0.02313232421875,
0.0030879974365234375,
0.01056671142578125,
-0.0157470703125,
-0.01458740234375,
-0.0242462158203125,
0.00640106201171875,
0.00482940673828125,
0.00777435302734375,
-0.013275146484375,
-0.008331298828125,
0.00313568115234375,
0.00606536865234375,
0.006927490234375,
-0.01435089111328125,
0.017974853515625,
0.00662994384765625,
0.0010385513305664062,
-0.029632568359375,
0.00458526611328125,
0.041534423828125,
-0.0096893310546875,
-0.007537841796875,
-0.019012451171875,
0.018157958984375,
0.0311431884765625,
-0.00685882568359375,
0.059814453125,
-0.004268646240234375,
-0.01155853271484375,
-0.000934600830078125,
-0.00817108154296875,
0.0031642913818359375,
-0.028778076171875,
0.00811767578125,
0.0050506591796875,
-0.004993438720703125,
-0.0218963623046875,
0.00908660888671875,
-0.0019989013671875,
0.02099609375,
-0.0279388427734375,
-0.0002765655517578125,
-0.0188140869140625,
-0.004619598388671875,
0.0029315948486328125,
0.0275115966796875,
-0.01511383056640625,
0.003299713134765625,
-0.0084381103515625,
-0.01523590087890625,
-0.004161834716796875,
-0.0278778076171875,
-0.005329132080078125,
0.01439666748046875,
-0.037261962890625,
0.01499176025390625,
-0.02960205078125,
-0.0060882568359375,
0.006439208984375,
0.00917816162109375,
0.01181793212890625,
0.0037174224853515625,
0.0219268798828125,
0.0181427001953125,
-0.00360870361328125,
-0.00868988037109375,
0.024871826171875,
-0.043487548828125,
0.027984619140625,
-0.020751953125,
0.00579071044921875,
-0.005504608154296875,
0.0114898681640625,
-0.01554107666015625,
0.0234527587890625,
-0.021209716796875,
-0.0288543701171875,
-0.030731201171875,
-0.013641357421875,
0.009796142578125,
-0.005840301513671875,
-0.0216522216796875,
-0.01175689697265625,
0.011383056640625,
0.0214080810546875,
0.01247406005859375,
-0.0146026611328125,
-0.0214691162109375,
-0.023590087890625,
-0.018798828125,
0.0172576904296875,
-0.01514434814453125,
0.0211334228515625,
-0.0085296630859375,
0.003063201904296875,
0.0038299560546875,
-0.0035400390625,
0.012908935546875,
0.0012607574462890625,
-0.024627685546875,
-0.0013380050659179688,
0.005596160888671875,
0.039642333984375,
0.00609588623046875,
-0.025360107421875,
-0.00478363037109375,
0.0308837890625,
-0.00017440319061279297,
-0.00469970703125,
0.005397796630859375,
-0.0206298828125,
-0.0194244384765625,
-0.0106353759765625,
-0.0168914794921875,
-0.02703857421875,
-0.003925323486328125,
0.00856781005859375,
-0.004703521728515625,
-0.0167083740234375,
0.0057525634765625,
0.0221710205078125,
0.0044708251953125,
0.0159454345703125,
0.01495361328125,
0.00047016143798828125,
-0.019866943359375,
0.031036376953125,
0.0307464599609375,
0.0212554931640625,
0.0120086669921875,
0.022552490234375,
-0.01371002197265625,
0.0127716064453125,
0.02569580078125,
-0.01464080810546875,
0.034271240234375,
0.0029125213623046875,
0.006633758544921875,
-0.0261383056640625,
-0.0457763671875,
-0.0006585121154785156,
0.01506805419921875,
-0.046173095703125,
0.0007848739624023438,
0.00345611572265625,
-0.004283905029296875,
-0.01340484619140625,
0.002513885498046875,
-0.008026123046875,
-0.005962371826171875,
0.01154327392578125,
0.0003151893615722656,
-0.0237579345703125,
-0.037353515625,
-0.002117156982421875,
-0.038238525390625,
0.0190887451171875,
0.00865936279296875,
-0.006877899169921875,
0.02984619140625,
-0.022552490234375,
-0.0016317367553710938,
0.003124237060546875,
-0.0273895263671875,
0.00782012939453125,
-0.00527191162109375,
0.0171661376953125,
0.01343536376953125,
-0.0016069412231445312,
-0.0222015380859375,
0.019378662109375,
-0.032257080078125,
-0.0299072265625,
0.00634765625,
0.02899169921875,
0.024993896484375,
-0.009674072265625,
-0.005130767822265625,
0.0143585205078125,
0.0184173583984375,
0.019775390625,
0.0016565322875976562,
-0.0005316734313964844,
-0.00927734375,
-0.00536346435546875,
-0.035369873046875,
-0.031707763671875,
-0.00140380859375,
-0.005245208740234375,
0.005275726318359375,
-0.024261474609375,
-0.00412750244140625,
0.01552581787109375,
-0.0017757415771484375,
0.0099945068359375,
-0.0275115966796875,
0.0095977783203125,
0.00658416748046875,
-0.0026702880859375,
0.0173187255859375,
0.0291900634765625,
0.043121337890625,
0.0027561187744140625,
-0.0316162109375,
0.01215362548828125,
0.01080322265625,
0.02655029296875,
0.0153045654296875,
-0.02203369140625,
0.0135955810546875,
0.00507354736328125,
0.0180816650390625,
0.0075225830078125,
-0.00913238525390625,
-0.01139068603515625,
-0.01027679443359375,
0.00362396240234375,
0.01837158203125,
-0.0168304443359375,
0.0295257568359375,
-0.0009474754333496094,
0.01076507568359375,
0.026153564453125,
0.002410888671875,
0.04144287109375,
-0.0015468597412109375,
-0.011749267578125,
-0.0128326416015625,
0.005435943603515625,
0.005222320556640625,
0.041015625,
0.036376953125,
0.0015392303466796875,
0.03094482421875,
-0.0019664764404296875,
-0.0207366943359375,
0.01727294921875,
-0.0298004150390625,
0.03729248046875,
0.00905609130859375,
-0.0119781494140625,
0.03271484375,
-0.003734588623046875,
-0.032806396484375,
0.0262298583984375,
-0.031280517578125,
-0.0110015869140625,
-0.00818634033203125,
0.016082763671875,
-0.035919189453125,
0.0007891654968261719,
0.010406494140625,
0.006771087646484375,
0.00728607177734375,
0.022705078125,
0.0006017684936523438,
0.0025463104248046875,
0.005340576171875,
0.0235137939453125,
-0.0160675048828125,
0.0229339599609375,
-0.018402099609375,
0.03924560546875,
0.0158843994140625,
0.0080413818359375,
-0.0036773681640625,
0.0005960464477539062,
0.0206756591796875,
0.01435089111328125,
-0.0175323486328125,
0.004199981689453125,
-0.0020389556884765625,
0.0009207725524902344,
0.024078369140625,
0.01611328125,
0.00786590576171875,
0.06036376953125,
-0.03411865234375,
0.0311126708984375,
0.016357421875,
-0.0206146240234375,
-0.023162841796875,
-0.030120849609375,
-0.00876617431640625,
0.01404571533203125,
-0.014678955078125,
0.0193939208984375,
0.024078369140625,
0.00624847412109375,
-0.0177764892578125,
-0.025115966796875,
0.038421630859375,
-0.0111541748046875,
0.00013506412506103516,
0.0010900497436523438,
-0.0028209686279296875,
-0.0035762786865234375,
-0.009674072265625,
-0.00023627281188964844,
-0.00124359130859375,
-0.01200103759765625,
0.032806396484375,
-0.01239776611328125,
-0.00647735595703125,
-0.003509521484375,
-0.017242431640625,
-0.0259246826171875,
0.021331787109375,
-0.006107330322265625,
-0.0116424560546875,
0.0275421142578125,
-0.008392333984375,
-0.00437164306640625,
0.0146484375,
-0.01140594482421875,
-0.0242156982421875,
-0.007625579833984375,
-0.0151824951171875,
0.017547607421875,
-0.006587982177734375,
-0.040740966796875,
-0.04461669921875,
-0.0191192626953125,
0.019500732421875,
-0.002620697021484375,
-0.0001621246337890625,
0.005428314208984375,
-0.036041259765625,
-0.01097869873046875,
-0.002208709716796875,
0.0016345977783203125,
0.008636474609375,
-0.027740478515625,
-0.00555419921875,
-0.0122222900390625,
0.0216522216796875,
-0.0166015625,
-0.0006122589111328125,
-0.035369873046875,
0.01488494873046875,
-0.0185699462890625,
-0.01390838623046875,
-0.0185699462890625,
-0.003353118896484375,
-0.029632568359375,
-0.0283050537109375,
0.004489898681640625,
0.0294342041015625,
-0.03692626953125,
-0.02374267578125,
0.01690673828125,
-0.015869140625,
-0.005481719970703125,
0.00461578369140625,
-0.016204833984375,
0.0012989044189453125,
-0.0090484619140625,
-0.008758544921875,
0.007480621337890625,
0.023651123046875,
-0.020721435546875,
0.0098876953125,
0.02685546875,
-0.01180267333984375,
-0.024261474609375,
0.0294342041015625,
0.004810333251953125,
0.03826904296875,
-0.03497314453125,
-0.019805908203125,
-0.0018758773803710938,
0.0015048980712890625,
0.0140228271484375,
0.00592041015625,
-0.00690460205078125,
-0.01336669921875,
-0.01171112060546875,
0.0040435791015625,
-0.003345489501953125,
0.0208892822265625,
0.00943756103515625,
0.00655364990234375,
-0.0116424560546875,
0.01146697998046875,
-0.004253387451171875,
0.006145477294921875,
0.0207366943359375,
-0.00482940673828125,
-0.0164031982421875,
0.02642822265625,
0.015289306640625
] |
ours_562
|
Using partial fractions, we have
\[
\frac{a_{i-1}}{a_{i}^{2}-a_{i-1}^{2}}=\frac{1}{2}\left(\frac{1}{a_{i}-a_{i-1}}-\frac{1}{a_{i}+a_{i-1}}\right)
\]
By the recurrence relation, \(a_{i}+a_{i-1}=a_{i+1}-a_{i}\). Thus, we can write
\[
S=\sum_{i=1}^{\infty} \frac{1}{2}\left(\frac{1}{a_{i}-a_{i-1}}-\frac{1}{a_{i+1}-a_{i}}\right)=\frac{1}{2\left(a_{1}-a_{0}\right)}=\frac{1}{3620}
\]
Therefore, \(\frac{1}{S} = 3620\).
\(\boxed{3620}\)
|
3620
|
{
"competition": "us_comps",
"dataset": "Ours",
"posts": null,
"source": "OMOSoln2.md"
}
|
The sequence \(\{a_{n}\}\) satisfies \(a_{0}=201\), \(a_{1}=2011\), and \(a_{n}=2 a_{n-1}+a_{n-2}\) for all \(n \geq 2\). Let
\[
S=\sum_{i=1}^{\infty} \frac{a_{i-1}}{a_{i}^{2}-a_{i-1}^{2}}
\]
What is \(\frac{1}{S}\)?
|
[
"/Mathematics/Algebra/NumberTheory/Integers/Integer",
"/Mathematics/Algebra/NumberTheory/Integers/PositiveInteger",
"/Mathematics/Algebra/NumberTheory/Integers/Z",
"/Mathematics/Algebra/NumberTheory/Integers/Z-Plus",
"/Mathematics/Algebra/NumberTheory/Sequences/IntegerSequence",
"/Mathematics/Algebra/NumberTheory/Sequences/Sequence",
"/Mathematics/Algebra/Sums/TelescopingSeries",
"/Mathematics/Algebra/Sums/TelescopingSum",
"/Mathematics/DiscreteMathematics/RecurrenceEquations/LinearRecurrenceEquation",
"/Mathematics/DiscreteMathematics/RecurrenceEquations/RecurrenceEquation",
"/Mathematics/DiscreteMathematics/RecurrenceEquations/RecurrenceRelation",
"/Mathematics/DiscreteMathematics/RecurrenceEquations/RecursiveSequence"
] |
Express each term as a difference of reciprocals of successive differences using partial fractions and the recurrence, yielding a telescoping series.
|
[
-0.00010532140731811523,
0.003826141357421875,
0.06317138671875,
0.042938232421875,
-0.0004177093505859375,
0.0172882080078125,
0.00330352783203125,
-0.0020427703857421875,
-0.000010848045349121094,
-0.01552581787109375,
0.0092315673828125,
-0.0595703125,
-0.003704071044921875,
0.02191162109375,
-0.0207061767578125,
-0.01511383056640625,
0.01016998291015625,
0.015777587890625,
0.041473388671875,
-0.002765655517578125,
-0.002429962158203125,
-0.018157958984375,
-0.060333251953125,
0.029541015625,
-0.06500244140625,
0.0022449493408203125,
-0.00860595703125,
-0.01303863525390625,
0.0276336669921875,
0.01311492919921875,
-0.0193328857421875,
-0.024688720703125,
0.01517486572265625,
-0.01458740234375,
-0.0009431838989257812,
-0.0104827880859375,
0.023651123046875,
-0.0092926025390625,
0.006587982177734375,
-0.0277252197265625,
0.00656890869140625,
0.035064697265625,
-0.0092620849609375,
0.00946807861328125,
0.006103515625,
-0.01114654541015625,
-0.0007386207580566406,
-0.01404571533203125,
0.00804901123046875,
0.0115966796875,
-0.0097808837890625,
0.00698089599609375,
-0.01678466796875,
-0.00926971435546875,
-0.029510498046875,
-0.056182861328125,
0.00981903076171875,
-0.00023853778839111328,
-0.0201873779296875,
-0.04656982421875,
-0.005809783935546875,
0.013916015625,
0.002140045166015625,
0.01125335693359375,
-0.001171112060546875,
-0.01407623291015625,
0.0189361572265625,
-0.01377105712890625,
-0.001789093017578125,
0.01435089111328125,
0.037628173828125,
-0.0097503662109375,
-0.010711669921875,
0.0335693359375,
0.029205322265625,
-0.009552001953125,
-0.027374267578125,
0.004791259765625,
0.038116455078125,
0.014892578125,
-0.0097503662109375,
0.0049285888671875,
0.004711151123046875,
0.00695037841796875,
-0.006237030029296875,
-0.00461578369140625,
-0.044769287109375,
0.0043487548828125,
0.04656982421875,
-0.0108642578125,
0.0037631988525390625,
-0.0136260986328125,
0.0186309814453125,
-0.0194091796875,
-0.004230499267578125,
-0.0004227161407470703,
0.0189208984375,
-0.00896453857421875,
-0.026824951171875,
0.00594329833984375,
-0.01898193359375,
0.0010776519775390625,
0.020172119140625,
-0.0112152099609375,
-0.02130126953125,
0.0009336471557617188,
-0.023284912109375,
0.0013341903686523438,
-0.01154327392578125,
-0.0090484619140625,
0.0132598876953125,
-0.01474761962890625,
0.0182952880859375,
0.01461029052734375,
-0.0243377685546875,
0.01605224609375,
0.0078277587890625,
0.00971221923828125,
0.00048041343688964844,
-0.00920867919921875,
0.00751495361328125,
0.0135345458984375,
0.023773193359375,
0.02117919921875,
0.007183074951171875,
0.017486572265625,
-0.01409149169921875,
0.00241851806640625,
0.0027904510498046875,
-0.0031795501708984375,
0.001148223876953125,
-0.01678466796875,
-0.03253173828125,
-0.041168212890625,
-0.089599609375,
-0.007404327392578125,
-0.006328582763671875,
-0.02508544921875,
-0.005657196044921875,
-0.01959228515625,
0.01131439208984375,
0.00719451904296875,
0.005207061767578125,
0.006114959716796875,
-0.010101318359375,
0.008941650390625,
0.0152435302734375,
-0.0152740478515625,
0.0122528076171875,
-0.00738525390625,
0.0260467529296875,
0.00377655029296875,
0.0031528472900390625,
-0.0020656585693359375,
0.00847625732421875,
0.0216522216796875,
0.01727294921875,
-0.004329681396484375,
-0.014251708984375,
-0.0013589859008789062,
0.00628662109375,
0.00261688232421875,
-0.0267486572265625,
0.0176239013671875,
-0.003437042236328125,
-0.021209716796875,
-0.0171051025390625,
-0.018646240234375,
-0.0007061958312988281,
-0.0004611015319824219,
0.003986358642578125,
0.00885772705078125,
0.002979278564453125,
-0.0097503662109375,
-0.0087127685546875,
0.0179901123046875,
-0.0298309326171875,
-0.00933837890625,
0.006198883056640625,
0.00836181640625,
0.013275146484375,
-0.045196533203125,
-0.032196044921875,
-0.01336669921875,
0.0288543701171875,
-0.011444091796875,
0.0031032562255859375,
0.003177642822265625,
0.02581787109375,
0.0325927734375,
0.0103607177734375,
0.005035400390625,
0.0019855499267578125,
0.002246856689453125,
-0.0127105712890625,
-0.0003383159637451172,
-0.01052093505859375,
0.0189971923828125,
0.0205230712890625,
0.0004901885986328125,
-0.003936767578125,
0.01395416259765625,
-0.0009112358093261719,
0.01010894775390625,
0.00213623046875,
-0.006145477294921875,
0.002208709716796875,
-0.007678985595703125,
-0.00665283203125,
0.0017881393432617188,
0.00665283203125,
-0.01806640625,
-0.005031585693359375,
-0.0243988037109375,
-0.0183868408203125,
-0.0208587646484375,
-0.01029205322265625,
-0.00858306884765625,
0.005523681640625,
0.004787445068359375,
0.005939483642578125,
0.031585693359375,
0.0182647705078125,
-0.00933837890625,
-0.0294036865234375,
0.0063629150390625,
0.006900787353515625,
-0.01085662841796875,
-0.004253387451171875,
0.0229339599609375,
0.0179443359375,
0.024017333984375,
-0.011566162109375,
-0.0170745849609375,
0.0085601806640625,
0.02569580078125,
-0.01313018798828125,
-0.0025577545166015625,
-0.01108551025390625,
-0.020050048828125,
-0.0302886962890625,
-0.0189971923828125,
0.0184783935546875,
-0.0110015869140625,
0.0140533447265625,
0.0033397674560546875,
-0.004962921142578125,
-0.000713348388671875,
-0.0010166168212890625,
-0.0037212371826171875,
-0.006366729736328125,
-0.0016698837280273438,
-0.020355224609375,
-0.007244110107421875,
-0.0023021697998046875,
0.0149993896484375,
0.00977325439453125,
-0.0087890625,
-0.0008955001831054688,
0.04638671875,
0.0093994140625,
-0.0189208984375,
-0.0153656005859375,
0.0107574462890625,
-0.015869140625,
0.026763916015625,
-0.01393890380859375,
-0.01043701171875,
0.03375244140625,
0.0004181861877441406,
0.050384521484375,
-0.0175628662109375,
-0.0039215087890625,
-0.011810302734375,
-0.0281524658203125,
-0.03436279296875,
-0.021575927734375,
0.0027065277099609375,
-0.004730224609375,
0.004852294921875,
-0.005191802978515625,
-0.023773193359375,
0.0031490325927734375,
0.004852294921875,
0.004726409912109375,
0.006649017333984375,
0.0004374980926513672,
-0.0171051025390625,
0.0007281303405761719,
-0.0089569091796875,
0.0031299591064453125,
-0.01444244384765625,
-0.006366729736328125,
-0.002315521240234375,
0.04998779296875,
-0.0254669189453125,
0.01406097412109375,
0.01059722900390625,
-0.00711822509765625,
-0.01195526123046875,
0.02874755859375,
-0.0066070556640625,
0.0119476318359375,
-0.0234222412109375,
0.02313232421875,
0.0027828216552734375,
-0.0010232925415039062,
-0.007232666015625,
-0.041595458984375,
-0.0157318115234375,
0.0280303955078125,
0.0021038055419921875,
-0.00809478759765625,
-0.01140594482421875,
-0.030609130859375,
-0.0210723876953125,
0.0032329559326171875,
-0.0027618408203125,
-0.01351165771484375,
-0.016204833984375,
0.00018584728240966797,
0.0135498046875,
0.0092315673828125,
0.01068878173828125,
-0.004932403564453125,
-0.00568389892578125,
0.01837158203125,
0.0024013519287109375,
0.017578125,
0.01300048828125,
-0.054107666015625,
0.0228424072265625,
0.0181732177734375,
-0.00585174560546875,
-0.0027370452880859375,
-0.003032684326171875,
0.00279998779296875,
0.0089874267578125,
-0.0031948089599609375,
0.0040435791015625,
0.0155487060546875,
-0.006191253662109375,
-0.006561279296875,
-0.0225982666015625,
-0.0291595458984375,
-0.00010329484939575195,
-0.0055389404296875,
0.01274871826171875,
-0.0005640983581542969,
0.0259552001953125,
0.01751708984375,
0.007511138916015625,
0.0006136894226074219,
-0.00634765625,
-0.0238037109375,
0.00014984607696533203,
-0.0165252685546875,
0.007373809814453125,
0.0003921985626220703,
0.0179290771484375,
0.004413604736328125,
-0.01318359375,
-0.0133514404296875,
0.0196990966796875,
0.00839996337890625,
-0.00826263427734375,
-0.03472900390625,
0.0115814208984375,
-0.0430908203125,
0.00933074951171875,
0.0064849853515625,
-0.006710052490234375,
0.01439666748046875,
-0.006069183349609375,
0.00830078125,
-0.006008148193359375,
-0.018463134765625,
-0.004547119140625,
-0.0030956268310546875,
-0.00736236572265625,
-0.018096923828125,
0.0303497314453125,
-0.0322265625,
0.012603759765625,
0.0035724639892578125,
-0.0163726806640625,
0.0166015625,
-0.06048583984375,
-0.04644775390625,
0.01116180419921875,
-0.0152435302734375,
-0.006198883056640625,
0.0047760009765625,
0.00446319580078125,
-0.0621337890625,
-0.00597381591796875,
-0.00836181640625,
-0.022064208984375,
0.03131103515625,
-0.00727081298828125,
0.008209228515625,
-0.03143310546875,
-0.039031982421875,
0.03924560546875,
0.0055694580078125,
-0.00397491455078125,
-0.007415771484375,
-0.01285552978515625,
-0.0247344970703125,
0.0035037994384765625,
0.0166473388671875,
0.030242919921875,
0.03302001953125,
-0.0022258758544921875,
-0.00554656982421875,
0.00609588623046875,
0.0001742839813232422,
-0.0396728515625,
0.00330352783203125,
-0.0107269287109375,
-0.0092010498046875,
-0.01061248779296875,
0.0223541259765625,
0.0254669189453125,
0.0168609619140625,
0.0100250244140625,
-0.003787994384765625,
0.0064239501953125,
-0.005153656005859375,
0.006458282470703125,
-0.0024700164794921875,
-0.01515960693359375,
0.01751708984375,
0.008392333984375,
0.0032520294189453125,
0.0005097389221191406,
-0.0298309326171875,
0.01259613037109375,
-0.00811767578125,
0.00919342041015625,
-0.025726318359375,
0.0008320808410644531,
0.0019502639770507812,
0.0135955810546875,
-0.03680419921875,
0.0009007453918457031,
-0.00345611572265625,
0.0272064208984375,
-0.029571533203125,
0.0140533447265625,
-0.006317138671875,
0.0269927978515625,
0.004817962646484375,
-0.0170745849609375,
0.00382232666015625,
0.061798095703125,
0.036712646484375,
0.0003306865692138672,
-0.004119873046875,
-0.010345458984375,
0.0201416015625,
0.0232086181640625,
-0.0025157928466796875,
0.0087890625,
-0.0126495361328125,
-0.0006833076477050781,
-0.0167236328125,
0.0005960464477539062,
-0.001041412353515625,
0.0009794235229492188,
-0.0003838539123535156,
-0.00823211669921875,
0.02392578125,
-0.008880615234375,
-0.039306640625,
0.04644775390625,
-0.0123748779296875,
0.025177001953125,
-0.00632476806640625,
-0.016632080078125,
-0.0025386810302734375,
-0.0128021240234375,
-0.0043487548828125,
0.0141448974609375,
-0.0005135536193847656,
0.04107666015625,
0.01898193359375,
-0.019683837890625,
-0.002529144287109375,
-0.0009822845458984375,
0.002674102783203125,
0.01236724853515625,
-0.005157470703125,
-0.033843994140625,
-0.042694091796875,
0.00710296630859375,
0.010772705078125,
0.00849151611328125,
-0.016143798828125,
-0.0107421875,
-0.0162811279296875,
-0.050506591796875,
-0.022674560546875,
0.0187225341796875,
-0.0003371238708496094,
-0.053955078125,
0.0116729736328125,
0.024169921875,
0.033721923828125,
0.015838623046875,
0.01274871826171875,
-0.006351470947265625,
-0.00510406494140625,
-0.025177001953125,
0.02349853515625,
0.0277099609375,
0.0114593505859375,
0.023345947265625,
-0.006572723388671875,
0.01113128662109375,
-0.0116729736328125,
0.005970001220703125,
0.02496337890625,
-0.0269775390625,
0.024627685546875,
-0.0181732177734375,
0.010406494140625,
-0.026885986328125,
0.03375244140625,
0.0245819091796875,
-0.00597381591796875,
-0.068115234375,
0.01995849609375,
0.01096343994140625,
0.006744384765625,
-0.00756072998046875,
-0.006710052490234375,
-0.0015277862548828125,
-0.028778076171875,
0.0019350051879882812,
-0.0253753662109375,
-0.0007352828979492188,
-0.03204345703125,
-0.02716064453125,
-0.02325439453125,
-0.00298309326171875,
0.0141143798828125,
0.020233154296875,
-0.0100555419921875,
0.01328277587890625,
0.00899505615234375,
0.0125579833984375,
0.0233306884765625,
-0.01256561279296875,
-0.007404327392578125,
0.008209228515625,
-0.002544403076171875,
-0.024200439453125,
-0.01995849609375,
0.002269744873046875,
0.02630615234375,
0.0103302001953125,
0.0256805419921875,
-0.0038585662841796875,
-0.00958251953125,
0.00872039794921875,
-0.0014190673828125,
-0.01282501220703125,
-0.0164794921875,
-0.0489501953125,
0.008056640625,
-0.0006799697875976562,
-0.00027632713317871094,
-0.0042877197265625,
-0.01256561279296875,
-0.034454345703125,
-0.0029888153076171875,
0.013519287109375,
0.032470703125,
-0.026214599609375,
0.0252227783203125,
0.0116119384765625,
0.00003463029861450195,
0.01345062255859375,
0.0029163360595703125,
0.004680633544921875,
0.02130126953125,
-0.0209197998046875,
-0.01039886474609375,
0.0086822509765625,
-0.0075531005859375,
-0.0106964111328125,
-0.044097900390625,
0.0013446807861328125,
-0.02996826171875,
0.00492095947265625,
-0.01392364501953125,
-0.0018281936645507812,
-0.01313018798828125,
-0.024993896484375,
0.00983428955078125,
0.009490966796875,
-0.01506805419921875,
-0.0059967041015625,
-0.022796630859375,
0.0101776123046875,
-0.03472900390625,
0.01708984375,
0.0034542083740234375,
-0.006622314453125,
-0.01403045654296875,
0.0044097900390625,
-0.02294921875,
-0.0008711814880371094,
0.00681304931640625,
0.0173187255859375,
0.004131317138671875,
-0.0011339187622070312,
0.0002593994140625,
0.0026264190673828125,
-0.01490020751953125,
-0.004787445068359375,
-0.0160675048828125,
0.004425048828125,
-0.045684814453125,
0.0007600784301757812,
0.016326904296875,
-0.036834716796875,
-0.01425933837890625,
0.0001252889633178711,
-0.014556884765625,
-0.041290283203125,
-0.01183319091796875,
-0.018951416015625,
-0.0093841552734375,
-0.01399993896484375,
-0.050994873046875,
0.0191650390625,
-0.01317596435546875,
-0.00444793701171875,
0.0150909423828125,
0.022308349609375,
0.01568603515625,
-0.0548095703125,
0.0181121826171875,
-0.0038394927978515625,
-0.00887298583984375,
-0.02142333984375,
-0.0171661376953125,
0.008026123046875,
-0.0248260498046875,
-0.013092041015625,
0.006519317626953125,
0.0181121826171875,
-0.00038123130798339844,
-0.0029888153076171875,
0.0037059783935546875,
-0.03607177734375,
0.0175628662109375,
-0.0184326171875,
0.002941131591796875,
-0.000514984130859375,
0.009246826171875,
-0.012451171875,
-0.0173187255859375,
-0.0206451416015625,
-0.0204620361328125,
-0.0330810546875,
0.010833740234375,
-0.0203857421875,
0.013153076171875,
0.00881195068359375,
0.03204345703125,
-0.006580352783203125,
-0.005710601806640625,
0.025146484375,
0.00992584228515625,
-0.020721435546875,
0.0172576904296875,
0.044036865234375,
0.01861572265625,
0.026947021484375,
0.0215911865234375,
0.003826141357421875,
0.0247039794921875,
0.0325927734375,
0.004611968994140625,
0.0160980224609375,
0.0112457275390625,
-0.00586700439453125,
-0.0194091796875,
0.005947113037109375,
-0.0091400146484375,
0.00789642333984375,
0.008209228515625,
-0.01355743408203125,
-0.0013341903686523438,
-0.01454925537109375,
-0.0105133056640625,
-0.0021228790283203125,
-0.0196380615234375,
-0.018768310546875,
0.02105712890625,
0.0093841552734375,
0.00600433349609375,
-0.0261077880859375,
0.004337310791015625,
-0.0177001953125,
-0.04815673828125,
0.0116424560546875,
-0.0379638671875,
-0.031982421875,
-0.01727294921875,
-0.006114959716796875,
-0.01409149169921875,
0.0092315673828125,
-0.00682830810546875,
0.0096893310546875,
-0.0053253173828125,
-0.0141754150390625,
-0.052001953125,
-0.000009119510650634766,
-0.021820068359375,
-0.024627685546875,
0.0200958251953125,
-0.002079010009765625,
-0.017974853515625,
-0.01430511474609375,
-0.051025390625,
0.010223388671875,
0.006359100341796875,
-0.017669677734375,
0.00943756103515625,
0.003692626953125,
0.0229339599609375,
-0.00434112548828125,
0.0247650146484375,
-0.0178375244140625,
0.0244903564453125,
0.005931854248046875,
0.046966552734375,
0.009490966796875,
0.01617431640625,
0.0015592575073242188,
-0.0217437744140625,
-0.0131378173828125,
0.007061004638671875,
-0.0016965866088867188,
-0.007625579833984375,
0.0099334716796875,
0.02203369140625,
0.004016876220703125,
-0.0177764892578125,
-0.043426513671875,
-0.01152801513671875,
-0.01342010498046875,
0.0204010009765625,
-0.0211029052734375,
-0.0113677978515625,
0.0290679931640625,
-0.058929443359375,
-0.0019197463989257812,
-0.01019287109375,
-0.0170440673828125,
0.007709503173828125,
-0.01326751708984375,
0.0255889892578125,
-0.0190277099609375,
-0.004913330078125,
-0.0006718635559082031,
-0.0230865478515625,
-0.013427734375,
-0.01369476318359375,
-0.019439697265625,
-0.001216888427734375,
-0.004947662353515625,
-0.0279541015625,
-0.012359619140625,
0.0258636474609375,
-0.0019512176513671875,
0.019622802734375,
-0.0191192626953125,
-0.0054168701171875,
0.007537841796875,
-0.02154541015625,
-0.000850677490234375,
-0.000885009765625,
-0.0064239501953125,
0.0141143798828125,
0.01526641845703125,
0.031463623046875,
0.0033245086669921875,
0.0340576171875,
0.00408935546875,
-0.0221405029296875,
0.00629425048828125,
0.003814697265625,
-0.015655517578125,
-0.0273284912109375,
-0.012054443359375,
0.03662109375,
-0.014251708984375,
0.0022678375244140625,
0.020721435546875,
-0.00957489013671875,
0.00769805908203125,
0.0289459228515625,
-0.01519012451171875,
-0.01059722900390625,
0.010101318359375,
0.003376007080078125,
0.018035888671875,
0.0148468017578125,
-0.01508331298828125,
-0.01479339599609375,
-0.0396728515625,
0.01300811767578125,
0.0061187744140625,
0.01189422607421875,
0.0083160400390625,
-0.031097412109375,
0.0226593017578125,
0.01108551025390625,
-0.011383056640625,
0.00592041015625,
-0.0003113746643066406,
-0.00388336181640625,
0.03863525390625,
0.027191162109375,
0.015960693359375,
0.005859375,
0.00846099853515625,
-0.0021190643310546875,
0.0160064697265625,
0.0002613067626953125,
0.00635528564453125,
-0.01837158203125,
0.01611328125,
0.0023651123046875,
-0.0175628662109375,
0.0133209228515625,
0.0310516357421875,
0.001255035400390625,
-0.01201629638671875,
-0.01016998291015625,
-0.01285552978515625,
-0.04400634765625,
-0.0120086669921875,
0.01375579833984375,
-0.0281982421875,
0.0063018798828125,
0.023651123046875,
-0.0157928466796875,
-0.006122589111328125,
-0.00933074951171875,
0.02154541015625,
0.0128631591796875,
0.0035400390625,
-0.030731201171875,
-0.035064697265625,
-0.0228424072265625,
-0.0267791748046875,
0.01442718505859375,
0.006504058837890625,
-0.00974273681640625,
0.02215576171875,
-0.0193939208984375,
-0.0143890380859375,
0.026824951171875,
-0.0070953369140625,
0.0188751220703125,
0.03070068359375,
0.02899169921875,
-0.004241943359375,
-0.02001953125,
0.0135498046875,
0.0149993896484375,
0.0247802734375,
0.0250701904296875,
0.040618896484375,
0.01107025146484375,
-0.0036029815673828125,
-0.019927978515625,
-0.0005216598510742188,
-0.0292510986328125,
-0.01239776611328125,
-0.002994537353515625,
0.027557373046875,
0.0083465576171875,
-0.06024169921875,
-0.033477783203125,
-0.008148193359375,
0.0003914833068847656,
-0.0384521484375,
0.01013946533203125,
-0.0013275146484375,
0.0270843505859375,
-0.00821685791015625,
-0.0010738372802734375,
-0.049713134765625,
0.0235595703125,
0.004940032958984375,
0.00643157958984375,
-0.018463134765625,
-0.046630859375,
-0.02117919921875,
-0.032958984375,
-0.00539398193359375,
0.0251312255859375,
0.0269317626953125,
0.006072998046875,
0.0372314453125,
0.007259368896484375,
0.0265655517578125,
-0.035003662109375,
-0.00341796875,
-0.014984130859375,
0.02825927734375,
-0.0357666015625,
0.02117919921875,
0.01247406005859375,
0.029388427734375,
-0.023956298828125,
0.00408172607421875,
0.0177459716796875,
0.02178955078125,
0.01025390625,
0.016845703125,
-0.060516357421875,
0.007671356201171875,
-0.03814697265625,
0.0237884521484375,
-0.023529052734375,
-0.043487548828125,
0.00579071044921875,
0.0445556640625,
-0.0194854736328125,
0.00850677490234375,
-0.005222320556640625,
-0.00392913818359375,
-0.0210418701171875,
-0.005741119384765625,
-0.0004935264587402344,
0.007526397705078125,
0.0300445556640625,
0.0034809112548828125,
-0.005184173583984375,
0.01122283935546875,
-0.02239990234375,
-0.0193939208984375,
0.01366424560546875,
0.0016574859619140625,
0.02667236328125,
0.0341796875,
-0.01033782958984375,
0.01377105712890625,
-0.0243682861328125,
-0.0009341239929199219,
0.00882720947265625,
-0.002887725830078125,
-0.005268096923828125,
-0.0012025833129882812,
-0.042816162109375,
-0.012603759765625,
0.0033931732177734375,
-0.00909423828125,
0.0182952880859375,
-0.007305145263671875,
0.00965118408203125,
0.0179901123046875,
-0.0176849365234375,
-0.0242462158203125,
-0.00421905517578125,
-0.0106201171875,
0.0150604248046875,
-0.003856658935546875,
0.005710601806640625,
0.01220703125,
0.002193450927734375,
0.01201629638671875,
0.0033969879150390625,
-0.00917816162109375,
-0.016265869140625,
-0.0071868896484375,
-0.02325439453125,
0.033660888671875,
0.01666259765625,
-0.024932861328125,
0.0305633544921875,
-0.024017333984375,
-0.008636474609375,
0.04052734375,
-0.006206512451171875,
0.03240966796875,
-0.034759521484375,
-0.0268707275390625,
-0.0008492469787597656,
-0.0230255126953125,
0.0318603515625,
0.01027679443359375,
-0.00693511962890625,
-0.0004811286926269531,
-0.0157928466796875,
0.006504058837890625,
0.0244140625,
0.01245880126953125,
0.018798828125,
0.0178070068359375,
0.0033092498779296875,
-0.0009255409240722656,
0.0068359375,
-0.031585693359375,
-0.0007920265197753906,
-0.02655029296875,
-0.0221099853515625,
-0.0004954338073730469,
0.00820159912109375,
0.003986358642578125,
-0.050323486328125,
-0.013671875,
0.0006561279296875,
-0.00669097900390625,
-0.050567626953125,
-0.006244659423828125,
0.0028057098388671875,
0.0130615234375,
-0.01137542724609375,
0.0170745849609375,
0.0216064453125,
0.030364990234375,
0.009124755859375,
-0.00794219970703125,
0.00362396240234375,
-0.01312255859375,
0.0200958251953125,
-0.02838134765625,
-0.0098419189453125,
-0.0011701583862304688,
0.025054931640625,
0.00853729248046875,
-0.004878997802734375,
0.04315185546875,
0.008758544921875,
0.00341033935546875,
0.040069580078125,
-0.00550079345703125,
0.0167999267578125,
0.0168609619140625,
-0.03643798828125,
0.00107574462890625,
0.0013113021850585938,
0.0311279296875,
-0.039306640625,
-0.007801055908203125,
0.0286407470703125,
0.0208892822265625,
0.019378662109375,
-0.0225830078125,
0.0197601318359375,
0.016143798828125,
-0.00543975830078125,
-0.00934600830078125,
-0.0212249755859375,
-0.03118896484375,
-0.021484375,
0.02301025390625,
-0.0165252685546875,
-0.01284027099609375,
0.01291656494140625,
0.0292510986328125,
-0.0022678375244140625,
-0.00846099853515625,
0.030303955078125,
-0.004299163818359375,
0.01316070556640625,
-0.0236053466796875,
0.01441192626953125,
-0.010986328125,
-0.038970947265625,
-0.003818511962890625,
-0.00583648681640625,
0.00039315223693847656,
-0.040313720703125,
0.0077667236328125,
0.02264404296875,
-0.019439697265625,
-0.0033626556396484375,
-0.00606536865234375,
0.038848876953125,
-0.0223388671875,
-0.0157623291015625,
-0.00380706787109375,
0.012725830078125,
-0.0005197525024414062,
0.0008225440979003906,
-0.0416259765625,
-0.005435943603515625,
-0.005443572998046875,
0.01178741455078125,
-0.0003616809844970703,
0.026336669921875,
0.0272979736328125,
-0.02056884765625,
0.00860595703125,
0.008880615234375,
-0.01641845703125,
0.01422882080078125,
0.004726409912109375,
0.0184783935546875,
-0.00634765625,
0.028656005859375,
0.038726806640625,
0.006397247314453125,
0.0300750732421875,
0.0096893310546875,
0.0027217864990234375,
-0.025909423828125,
-0.00846099853515625,
0.007450103759765625,
-0.01012420654296875,
-0.021575927734375,
0.0295562744140625,
0.0025634765625,
-0.0223388671875,
0.00496673583984375,
-0.00492095947265625,
0.01451873779296875,
-0.0396728515625,
-0.0050506591796875,
0.013671875,
0.0201263427734375,
0.0220947265625,
0.005527496337890625,
-0.0154266357421875,
0.01406097412109375,
-0.0083770751953125,
-0.0255584716796875,
-0.02392578125,
0.00946807861328125,
-0.0020465850830078125,
0.00839996337890625,
0.0012760162353515625,
-0.005413055419921875,
-0.0129852294921875,
-0.015167236328125,
0.02581787109375,
-0.0093994140625,
0.0016241073608398438,
0.0146331787109375,
0.0027141571044921875,
0.007625579833984375,
0.0171051025390625,
-0.015289306640625,
0.00194549560546875,
0.0016155242919921875,
-0.006053924560546875,
-0.03778076171875,
0.00394439697265625,
-0.010406494140625,
-0.019805908203125,
0.01551055908203125,
0.0106201171875,
0.0082855224609375,
-0.01605224609375,
-0.0114593505859375,
0.0018711090087890625,
-0.005741119384765625,
0.019805908203125,
-0.049102783203125,
0.00896453857421875,
0.0009579658508300781,
-0.03515625,
0.00801849365234375,
-0.0200653076171875,
-0.0144195556640625,
0.003925323486328125,
0.00861358642578125,
-0.0256195068359375,
-0.0149383544921875,
-0.0204010009765625,
-0.0209808349609375,
0.01113128662109375,
-0.0025157928466796875,
-0.0177001953125,
-0.0195159912109375,
-0.0279998779296875,
-0.0141448974609375,
-0.00504302978515625,
0.0282135009765625,
0.026580810546875,
0.0133514404296875,
-0.00811767578125,
-0.055755615234375,
-0.0094451904296875,
0.003681182861328125,
0.0193023681640625,
-0.030426025390625,
-0.02276611328125,
0.01166534423828125,
0.0162506103515625,
0.0017547607421875,
-0.0005950927734375,
-0.02105712890625,
-0.0243682861328125,
-0.0052337646484375,
0.0241851806640625,
-0.030975341796875,
0.0038089752197265625,
-0.022308349609375,
0.0124969482421875,
-0.021484375,
-0.0157623291015625,
0.006134033203125,
-0.016021728515625,
0.016021728515625,
-0.01110076904296875,
0.026519775390625,
0.02484130859375,
-0.0284423828125,
-0.02960205078125,
0.01099395751953125,
-0.039764404296875,
0.00567626953125,
-0.01105499267578125,
-0.0007266998291015625,
0.01103973388671875,
-0.01104736328125,
0.0325927734375,
0.0007848739624023438,
0.0158843994140625,
-0.016265869140625,
-0.01045989990234375,
-0.00327301025390625,
0.03778076171875,
-0.0200653076171875,
-0.0158233642578125,
0.0196990966796875,
0.05572509765625,
-0.01331329345703125,
0.0262298583984375,
-0.006702423095703125,
0.0161285400390625,
0.00445556640625,
0.0162353515625,
0.01959228515625,
-0.020263671875,
-0.05889892578125,
0.00562286376953125,
-0.0299224853515625,
0.0086822509765625,
0.00934600830078125,
0.0127410888671875,
-0.01268768310546875,
-0.031005859375,
-0.0006766319274902344,
-0.019378662109375,
0.0259246826171875,
-0.0008697509765625,
-0.0066680908203125,
-0.018341064453125,
-0.037506103515625,
-0.01265716552734375,
-0.01313018798828125,
-0.00797271728515625,
0.0167388916015625,
-0.0030384063720703125,
0.01358795166015625,
0.0280609130859375,
-0.000024020671844482422,
0.00872802734375,
0.023529052734375,
0.00780487060546875,
0.0149078369140625,
0.044891357421875,
0.01312255859375,
0.037353515625,
-0.0098114013671875,
-0.0147552490234375,
-0.0196990966796875,
-0.0031070709228515625,
-0.015228271484375,
0.03717041015625,
0.01338958740234375,
0.019134521484375,
-0.0031871795654296875,
-0.014739990234375,
-0.0223846435546875,
-0.026153564453125,
0.005634307861328125,
0.001605987548828125,
-0.0016336441040039062,
-0.004833221435546875,
-0.0010042190551757812,
0.027984619140625,
0.0217742919921875,
0.006378173828125,
0.0027828216552734375,
-0.0034999847412109375,
-0.0024776458740234375,
0.000019669532775878906,
-0.03997802734375,
-0.036712646484375,
0.0056915283203125,
0.0007147789001464844,
-0.04608154296875,
-0.0277862548828125,
0.0142822265625,
-0.0257720947265625,
-0.005863189697265625,
-0.0196380615234375,
-0.008209228515625,
0.003513336181640625,
-0.00830841064453125,
0.020721435546875,
-0.0164337158203125,
-0.0153961181640625,
-0.0178680419921875,
0.009246826171875,
-0.040130615234375,
-0.0028018951416015625,
-0.0261993408203125,
-0.00485992431640625,
-0.0191192626953125,
0.0135345458984375,
0.005573272705078125,
0.0053253173828125,
-0.0095672607421875,
0.0006279945373535156,
-0.01213836669921875,
0.00366973876953125,
0.02313232421875,
0.0177459716796875,
-0.01244354248046875,
-0.027862548828125,
-0.00392913818359375,
0.01203155517578125,
-0.005458831787109375,
0.01415252685546875,
0.0225677490234375,
-0.0227203369140625,
-0.016815185546875,
-0.0079193115234375,
-0.0265655517578125,
-0.0010280609130859375,
0.004669189453125,
-0.0044097900390625,
-0.0224761962890625,
0.01751708984375,
0.045257568359375,
-0.006862640380859375,
-0.01131439208984375,
0.0174560546875,
0.01171112060546875,
0.0284271240234375,
-0.0120849609375,
-0.01006317138671875,
-0.00621795654296875,
0.02288818359375,
0.00466156005859375,
0.04473876953125,
-0.01343536376953125,
-0.0208587646484375,
0.0369873046875,
-0.01146697998046875,
0.04296875,
0.02001953125,
-0.0187835693359375,
0.0020084381103515625,
-0.0019083023071289062,
-0.0202484130859375,
-0.037750244140625,
-0.0164031982421875,
0.01397705078125,
-0.00046515464782714844,
0.01016998291015625,
0.02557373046875,
-0.051239013671875,
-0.00222015380859375,
-0.0150604248046875,
0.00933837890625,
0.00748443603515625,
-0.0218658447265625,
-0.00463104248046875,
-0.0159149169921875,
0.03265380859375,
0.0340576171875,
0.005504608154296875,
0.0289154052734375,
0.021636962890625,
-0.03167724609375,
0.01537322998046875,
-0.00829315185546875,
-0.01763916015625,
-0.00836944580078125,
0.002483367919921875,
-0.0180206298828125,
0.005672454833984375,
-0.0250701904296875,
-0.021270751953125,
0.0224456787109375,
0.01071929931640625,
-0.0124053955078125,
0.005397796630859375,
0.01971435546875,
-0.001201629638671875,
-0.0185089111328125,
-0.0140533447265625,
0.01953125,
-0.007625579833984375,
0.01439666748046875,
0.003269195556640625,
-0.0288848876953125,
-0.00901031494140625,
-0.031646728515625,
0.016265869140625,
-0.020904541015625,
-0.017303466796875,
-0.00018739700317382812,
0.006458282470703125,
0.01025390625,
0.020782470703125,
0.00406646728515625,
-0.00208282470703125,
-0.0299224853515625,
-0.008758544921875,
-0.005771636962890625,
0.0005369186401367188,
0.0018167495727539062,
-0.0259246826171875,
-0.01666259765625,
-0.00824737548828125,
-0.00946044921875,
0.012481689453125,
-0.0164031982421875,
-0.0265655517578125,
0.0082855224609375,
-0.004627227783203125,
-0.00902557373046875,
-0.004489898681640625,
-0.00919342041015625,
-0.0109710693359375,
-0.0031757354736328125,
0.004978179931640625,
-0.023895263671875,
-0.01215362548828125,
0.0247802734375,
0.0178680419921875,
0.00026345252990722656,
0.01145172119140625,
-0.0124969482421875,
-0.0247955322265625,
-0.0233917236328125,
0.015960693359375,
0.0084228515625,
0.0302886962890625,
-0.00463104248046875,
-0.010498046875,
0.0274810791015625,
0.0304107666015625,
-0.01023101806640625,
-0.01195526123046875,
-0.022857666015625,
0.01276397705078125,
-0.0031757354736328125,
0.029510498046875,
-0.022796630859375,
0.006893157958984375,
0.021026611328125,
0.042510986328125,
0.01263427734375,
0.00641632080078125,
-0.01393890380859375,
0.020416259765625,
-0.0286407470703125,
-0.008697509765625,
0.0050811767578125,
0.03912353515625,
-0.006877899169921875,
0.00630950927734375,
-0.0455322265625,
-0.0153045654296875,
0.03680419921875,
0.0306396484375,
0.0020771026611328125,
-0.0140533447265625,
-0.0267791748046875,
0.01739501953125,
0.00888824462890625,
-0.0194091796875,
0.00438690185546875,
-0.01812744140625,
-0.0171966552734375,
-0.0129241943359375,
0.036865234375,
0.03125,
-0.0285491943359375,
-0.03375244140625,
-0.04254150390625,
-0.034393310546875,
0.006572723388671875,
-0.00469970703125,
0.00551605224609375,
0.003955841064453125,
-0.035430908203125,
0.053924560546875,
-0.00433349609375,
0.0255584716796875,
0.0204010009765625,
-0.006000518798828125,
-0.014801025390625,
0.01422882080078125,
0.0016040802001953125,
0.005092620849609375,
0.04010009765625,
-0.031768798828125,
-0.005077362060546875,
0.02947998046875,
-0.01922607421875,
-0.0259246826171875,
-0.035369873046875,
0.03924560546875,
0.001140594482421875,
0.0150909423828125,
0.0126190185546875,
0.03118896484375,
-0.050537109375,
-0.006153106689453125,
-0.02081298828125,
0.000045359134674072266,
0.00928497314453125,
0.001708984375,
-0.019927978515625,
-0.01100921630859375,
0.0153656005859375,
-0.0008678436279296875,
0.00453948974609375,
-0.01666259765625,
0.00199127197265625,
-0.0034027099609375,
0.0050811767578125,
0.01318359375,
-0.01111602783203125,
-0.01251220703125,
-0.0178375244140625,
0.0191192626953125,
-0.0098724365234375,
0.00945281982421875,
0.032318115234375,
0.0212554931640625,
0.0210418701171875,
0.047698974609375,
-0.007724761962890625,
-0.00966644287109375,
0.002109527587890625,
-0.014068603515625,
0.004871368408203125,
-0.0028324127197265625,
0.03240966796875,
-0.01197052001953125,
-0.02783203125,
0.0167999267578125,
0.0157623291015625,
0.0152130126953125,
0.0157928466796875,
-0.001407623291015625,
-0.00957489013671875,
-0.0142364501953125,
0.007663726806640625,
0.00630950927734375,
-0.01690673828125,
0.004581451416015625,
0.014862060546875,
-0.00875091552734375,
0.0025386810302734375,
-0.002986907958984375,
0.0151214599609375,
0.03277587890625,
-0.033294677734375,
-0.0059814453125,
-0.0021762847900390625,
0.0085296630859375,
-0.0156707763671875,
-0.00428009033203125,
0.00931549072265625,
0.038055419921875,
-0.0165863037109375,
-0.005096435546875,
0.055419921875,
-0.01104736328125,
0.00847625732421875,
0.0209808349609375,
0.0023956298828125,
0.004444122314453125,
0.00469207763671875,
-0.0168304443359375,
-0.0077056884765625,
0.0128936767578125,
-0.0257110595703125,
0.0265350341796875,
0.00284576416015625,
-0.007511138916015625,
0.0156402587890625,
-0.015655517578125,
-0.001926422119140625,
-0.022735595703125,
0.0215911865234375,
0.017730712890625,
-0.0145263671875,
0.006572723388671875,
0.00897979736328125,
-0.007251739501953125,
-0.02252197265625,
0.0008392333984375,
0.0022411346435546875,
0.01432037353515625,
0.061614990234375,
0.0223846435546875,
0.032745361328125,
-0.0031566619873046875,
0.00313568115234375,
0.0263824462890625,
0.01027679443359375,
-0.0036067962646484375,
-0.0240478515625,
0.0288543701171875,
0.003448486328125,
0.0029449462890625,
0.000865936279296875,
-0.016876220703125,
-0.04840087890625,
0.035919189453125,
-0.015625,
-0.007724761962890625,
0.0390625,
-0.02166748046875,
-0.025848388671875,
0.0224456787109375,
0.0159454345703125,
-0.01812744140625,
0.0002446174621582031,
-0.01245880126953125,
-0.0230865478515625,
0.016571044921875,
-0.06427001953125,
-0.047027587890625,
0.0283203125,
-0.0023059844970703125,
-0.00460052490234375,
0.0007352828979492188,
-0.0019502639770507812,
-0.005756378173828125,
0.00848388671875,
-0.00604248046875,
-0.0016717910766601562,
0.0083770751953125,
-0.014373779296875,
-0.003948211669921875,
0.00447845458984375,
0.0004680156707763672,
-0.007556915283203125,
-0.0125274658203125,
0.0043487548828125,
-0.00032830238342285156,
-0.017425537109375,
-0.025848388671875,
0.0214996337890625,
-0.00473785400390625,
0.0140380859375,
-0.0149993896484375,
-0.01202392578125,
-0.008392333984375,
0.0007371902465820312,
-0.000301361083984375,
0.00048065185546875,
-0.0125885009765625,
0.0052947998046875,
-0.00562286376953125,
0.0116729736328125,
-0.0111236572265625,
-0.0174560546875,
0.04351806640625,
-0.016845703125,
0.0141143798828125,
0.016021728515625,
-0.0242919921875,
-0.024078369140625,
0.0118560791015625,
0.00534820556640625,
0.0214385986328125,
0.016021728515625,
0.052886962890625,
-0.011260986328125,
-0.0025691986083984375,
0.0163421630859375,
0.051025390625,
0.0229644775390625,
-0.00414276123046875,
-0.0152435302734375,
-0.005748748779296875,
-0.0269012451171875,
0.03466796875,
-0.0038509368896484375,
-0.007160186767578125,
-0.0131988525390625,
0.04156494140625,
0.0202484130859375,
-0.01690673828125,
0.008819580078125,
-0.0059356689453125,
0.015838623046875,
0.0037384033203125,
0.003467559814453125,
-0.0164642333984375,
0.00505828857421875,
-0.016265869140625,
0.006504058837890625,
0.0166778564453125,
0.023406982421875,
0.0022678375244140625,
-0.039459228515625,
-0.00992584228515625,
-0.01361083984375,
-0.01428985595703125,
0.00231170654296875,
0.0135650634765625,
-0.01461029052734375,
0.006214141845703125,
0.0000553131103515625,
0.00231170654296875,
0.005245208740234375,
0.01323699951171875,
0.01474761962890625,
0.01715087890625,
0.007450103759765625,
0.04241943359375,
-0.021240234375,
0.03485107421875,
-0.003841400146484375,
-0.0159454345703125,
-0.0120849609375,
-0.01806640625,
0.021820068359375,
0.004039764404296875,
-0.006519317626953125,
0.004528045654296875,
0.01064300537109375,
-0.00130462646484375,
0.01274871826171875,
0.046295166015625,
-0.0191497802734375,
0.01593017578125,
-0.0190277099609375,
0.00870513916015625,
0.0089111328125,
-0.0244903564453125,
0.001903533935546875,
-0.036712646484375,
-0.0131988525390625,
-0.0149383544921875,
-0.002696990966796875,
-0.0213470458984375,
-0.014190673828125,
0.023101806640625,
-0.01245880126953125,
0.00925445556640625,
-0.0227813720703125,
0.0275115966796875,
-0.019622802734375,
-0.004711151123046875,
-0.0187225341796875,
-0.01103973388671875,
0.00428009033203125,
0.032318115234375,
0.0040435791015625,
0.0257568359375,
0.00946044921875,
0.03717041015625,
-0.0170745849609375,
-0.0024013519287109375,
-0.00136566162109375,
0.004306793212890625,
0.027740478515625,
0.0367431640625,
-0.01383209228515625,
-0.011505126953125,
0.01006317138671875,
-0.0013837814331054688,
-0.0028438568115234375,
-0.01554107666015625,
-0.0023059844970703125,
-0.01384735107421875,
-0.005077362060546875,
-0.0162353515625,
-0.0271148681640625,
-0.01320648193359375,
-0.01096343994140625,
0.0117645263671875,
0.0016803741455078125,
-0.01392364501953125,
0.0076446533203125,
0.00704193115234375,
0.01395416259765625,
0.0033855438232421875,
0.00748443603515625,
-0.0106048583984375,
0.01078033447265625,
-0.023956298828125,
0.0035648345947265625,
-0.01064300537109375,
-0.0157928466796875,
-0.022613525390625,
0.020263671875,
-0.00037741661071777344,
0.0151214599609375,
-0.0088958740234375,
-0.0223236083984375,
-0.0101318359375,
0.0037384033203125,
-0.03472900390625,
-0.005870819091796875,
-0.0220184326171875,
0.0261688232421875,
0.00186920166015625,
-0.0211334228515625,
-0.01531219482421875,
0.00302886962890625,
0.0225372314453125,
-0.027679443359375,
0.0117950439453125,
0.0203704833984375,
0.0123748779296875,
0.0025196075439453125,
0.0141754150390625,
0.0024471282958984375,
0.0288848876953125,
0.01885986328125,
-0.0196380615234375,
0.006866455078125,
0.0028934478759765625,
0.0284271240234375,
-0.00908660888671875,
0.042694091796875,
-0.029266357421875,
-0.0012073516845703125,
0.0204925537109375,
0.0032806396484375,
0.0198974609375,
0.00971221923828125,
-0.0081329345703125,
0.01232147216796875,
0.006137847900390625,
-0.028533935546875,
-0.0011358261108398438,
-0.00891876220703125,
-0.0098114013671875,
-0.00991058349609375,
-0.00286102294921875,
0.016082763671875,
0.031829833984375,
0.01251220703125,
0.0309295654296875,
-0.00402069091796875,
-0.03369140625,
0.016815185546875,
-0.0008068084716796875,
-0.00970458984375,
-0.0251007080078125,
-0.0111846923828125,
-0.0203399658203125,
0.01291656494140625,
0.01239776611328125,
-0.01490020751953125,
-0.007160186767578125,
-0.01543426513671875,
0.033660888671875,
-0.0081787109375,
-0.064697265625,
0.0005636215209960938,
-0.00339508056640625,
0.0190277099609375,
-0.0124664306640625,
0.01397705078125,
0.0252532958984375,
0.008026123046875,
-0.0088958740234375,
0.011474609375,
0.0215606689453125,
-0.0109405517578125,
-0.032867431640625,
-0.0279541015625,
0.0036487579345703125,
0.0204315185546875,
0.038726806640625,
-0.007663726806640625,
0.01482391357421875,
0.0100250244140625,
-0.014556884765625,
0.0037403106689453125,
0.0052032470703125,
0.019683837890625,
-0.0193328857421875,
0.028076171875,
-0.02032470703125,
-0.0248565673828125,
-0.032501220703125,
-0.0037593841552734375,
0.0159912109375,
-0.0013980865478515625,
0.0305328369140625,
0.00963592529296875,
0.00522613525390625,
-0.0277099609375,
-0.040618896484375,
0.0082855224609375,
-0.003894805908203125,
0.05804443359375,
0.01898193359375,
-0.01332855224609375,
-0.0301055908203125,
-0.0004305839538574219,
-0.00455474853515625,
-0.00913238525390625,
0.0238494873046875,
-0.0033435821533203125,
0.01611328125,
0.031524658203125,
-0.0042572021484375,
-0.01445770263671875,
0.0236968994140625,
0.00429534912109375,
-0.0328369140625,
0.022857666015625,
0.01229095458984375,
-0.0284576416015625,
-0.006591796875,
-0.034210205078125,
-0.0258026123046875,
0.006427764892578125,
-0.004344940185546875,
-0.016632080078125,
-0.0147247314453125,
-0.0186767578125,
0.033477783203125,
0.00299835205078125,
0.005931854248046875,
-0.042449951171875,
-0.0008292198181152344,
-0.01181793212890625,
0.0302734375,
-0.03216552734375,
-0.0204315185546875,
-0.024169921875,
0.00742340087890625,
-0.00366973876953125,
0.01015472412109375,
0.00835418701171875,
0.0172882080078125,
0.0015802383422851562,
0.055572509765625,
-0.014068603515625,
-0.0015773773193359375,
-0.0070343017578125,
-0.006305694580078125,
-0.0143280029296875,
-0.01074981689453125,
0.0305328369140625,
-0.003238677978515625,
-0.02777099609375,
-0.0219573974609375,
-0.039764404296875,
0.0021343231201171875,
0.00955963134765625,
-0.01215362548828125,
0.0158233642578125,
0.02789306640625,
-0.04644775390625,
-0.01165771484375,
0.01032257080078125,
0.0015163421630859375,
-0.0030803680419921875,
0.00206756591796875,
-0.025146484375,
0.0304412841796875,
-0.0218353271484375,
0.0061798095703125,
-0.007221221923828125,
0.0015821456909179688,
-0.020355224609375,
0.014923095703125,
-0.001781463623046875,
0.0008420944213867188,
-0.02789306640625,
-0.00968170166015625,
0.005161285400390625,
0.006626129150390625,
0.006092071533203125,
0.007720947265625,
0.02386474609375,
0.00984954833984375,
-0.01229095458984375,
0.011993408203125,
0.0323486328125,
0.0122528076171875,
-0.02764892578125,
0.0195159912109375,
0.0277099609375,
-0.003986358642578125,
0.025115966796875,
-0.0009732246398925781,
-0.02264404296875,
-0.0004799365997314453,
-0.03326416015625,
0.00830078125,
0.004650115966796875,
-0.00875091552734375,
0.03338623046875,
-0.018768310546875,
-0.008941650390625,
0.0006875991821289062,
0.0145111083984375,
-0.019927978515625,
0.00034546852111816406,
-0.00262451171875,
-0.00545501708984375,
-0.0160980224609375,
0.004543304443359375,
-0.0120086669921875,
-0.005550384521484375,
-0.039794921875,
-0.00859832763671875,
-0.0168304443359375,
-0.043212890625,
0.03228759765625,
0.017974853515625,
0.0162506103515625,
0.03173828125,
-0.0252532958984375,
-0.0025272369384765625,
0.004364013671875,
0.010009765625,
0.0054473876953125,
0.00653839111328125,
-0.000885009765625,
0.00191497802734375,
-0.027984619140625,
-0.0301055908203125,
0.0202484130859375,
0.0225067138671875,
0.002964019775390625,
0.0286712646484375,
-0.0159454345703125,
-0.00244903564453125,
0.004703521728515625,
-0.0035572052001953125,
-0.04400634765625,
0.0035457611083984375,
0.0145263671875,
0.0076141357421875,
-0.01035308837890625,
0.033172607421875,
-0.032318115234375,
-0.01531982421875,
0.01329803466796875,
-0.009124755859375,
-0.0159454345703125,
0.0638427734375,
-0.03369140625,
-0.025054931640625,
-0.0478515625,
0.00814056396484375,
0.00481414794921875,
0.00530242919921875,
-0.012115478515625,
0.0106964111328125,
0.0184478759765625,
-0.00897979736328125,
0.00423431396484375,
0.00848388671875,
0.003269195556640625,
0.00262451171875,
-0.0121917724609375,
-0.0095672607421875,
0.0173797607421875,
0.006282806396484375,
0.0129547119140625,
-0.017578125,
-0.01180267333984375,
0.0190277099609375,
0.0237274169921875,
-0.0168304443359375,
-0.037445068359375,
0.00800323486328125,
0.00769805908203125,
0.01116180419921875,
0.003681182861328125,
-0.0216522216796875,
0.020904541015625,
0.022735595703125,
0.036773681640625,
-0.042388916015625,
-0.003490447998046875,
0.0254364013671875,
-0.01131439208984375,
-0.030303955078125,
0.00226593017578125,
-0.00983428955078125,
0.01357269287109375,
-0.01369476318359375,
0.016265869140625,
0.022125244140625,
-0.0180511474609375,
-0.0008826255798339844,
0.0271453857421875,
-0.0035400390625,
0.0136566162109375,
-0.01013946533203125,
0.013275146484375,
-0.031219482421875,
-0.0196990966796875,
-0.0239410400390625,
-0.00728607177734375,
0.01357269287109375,
0.017333984375,
0.009490966796875,
-0.033966064453125,
0.0015077590942382812,
0.0003483295440673828,
0.00876617431640625,
-0.01409912109375,
0.04241943359375,
-0.0012769699096679688,
0.01230621337890625,
0.0323486328125,
-0.006664276123046875,
-0.00749969482421875,
0.0224151611328125,
0.05596923828125,
-0.0027790069580078125,
-0.0156402587890625,
0.0027294158935546875,
-0.033447265625,
-0.0096588134765625,
0.022705078125,
-0.0146942138671875,
0.00012540817260742188,
0.00789642333984375,
-0.0134124755859375,
0.0145111083984375,
0.0043182373046875,
0.00446319580078125,
-0.0299072265625,
0.0211944580078125,
-0.02203369140625,
-0.017578125,
0.0175018310546875,
0.00397491455078125,
-0.00583648681640625,
-0.0260162353515625,
-0.0107421875,
0.0232086181640625,
0.01105499267578125,
-0.0000388026237487793,
-0.032684326171875,
-0.0223846435546875,
-0.0240478515625,
-0.01074981689453125,
-0.01502227783203125,
-0.028778076171875,
-0.0006585121154785156,
-0.0019378662109375,
-0.009033203125,
0.0243988037109375,
0.007633209228515625,
-0.0099639892578125,
0.00518035888671875,
-0.0246124267578125,
-0.030487060546875,
0.050689697265625,
0.0038204193115234375,
-0.0284423828125,
0.0168304443359375,
0.0143585205078125,
-0.03472900390625,
0.0025463104248046875,
0.02972412109375,
-0.01503753662109375,
0.003936767578125,
0.0224609375,
0.043609619140625,
-0.0181732177734375,
0.01485443115234375,
-0.02850341796875,
0.017059326171875,
0.00970458984375,
0.004985809326171875,
-0.029937744140625,
0.02642822265625,
0.00989532470703125,
-0.016326904296875,
0.001346588134765625,
0.0168304443359375,
0.03350830078125,
-0.0274810791015625,
-0.015411376953125,
0.026702880859375,
-0.0109100341796875,
-0.02789306640625,
-0.03759765625,
0.0025806427001953125,
-0.00438690185546875,
-0.01259613037109375,
0.039215087890625,
-0.0258636474609375,
0.0157928466796875,
0.0017852783203125,
-0.0165252685546875,
-0.0107879638671875,
0.0149688720703125,
-0.026214599609375,
-0.0120086669921875,
-0.002910614013671875,
-0.02294921875,
-0.0113677978515625,
0.004398345947265625,
0.00372314453125,
-0.01486968994140625,
0.0017452239990234375,
0.0195770263671875,
-0.0005431175231933594,
0.00850677490234375,
0.00650787353515625,
0.0281982421875,
0.002552032470703125,
0.001102447509765625,
-0.016265869140625,
0.01715087890625,
-0.002880096435546875,
0.01303863525390625,
-0.009124755859375,
0.0187530517578125,
-0.032928466796875,
0.024444580078125,
-0.0201263427734375,
-0.02734375,
-0.008056640625,
-0.0112457275390625,
0.001064300537109375,
-0.0243988037109375,
0.01788330078125,
-0.002170562744140625,
-0.032196044921875,
0.0001608133316040039,
-0.004425048828125,
-0.0188446044921875,
0.019500732421875,
-0.040771484375,
-0.01727294921875,
-0.016937255859375,
-0.005428314208984375,
0.0022678375244140625,
0.017120361328125,
0.019744873046875,
-0.0165252685546875,
-0.0128936767578125,
-0.010223388671875,
0.0313720703125,
0.01580810546875,
-0.00039887428283691406,
-0.0243988037109375,
-0.0302276611328125,
0.02117919921875,
0.0158538818359375,
0.0128326416015625,
-0.00678253173828125,
-0.020416259765625,
0.0001970529556274414,
-0.00771331787109375,
-0.01235198974609375,
-0.0218658447265625,
0.014495849609375,
0.0218505859375,
-0.027801513671875,
-0.014739990234375,
-0.04156494140625,
0.01160430908203125,
-0.0008358955383300781,
0.000035643577575683594,
0.0019512176513671875,
0.04571533203125,
-0.02166748046875,
0.009063720703125,
-0.00984954833984375,
0.032257080078125,
0.0191650390625,
0.04345703125,
0.00531005859375,
0.0184326171875,
0.026947021484375,
0.007110595703125,
-0.0003311634063720703,
0.042022705078125,
-0.0010156631469726562,
0.01407623291015625,
0.0010356903076171875,
0.0036468505859375,
-0.01297760009765625,
-0.0289459228515625,
0.004085540771484375,
0.003170013427734375,
0.0170440673828125,
0.03472900390625,
0.005828857421875,
0.0029544830322265625,
0.01239013671875,
-0.0293121337890625,
-0.01904296875,
0.01161956787109375,
0.00510406494140625,
-0.0247802734375,
0.01557159423828125,
-0.036590576171875,
-0.036773681640625,
0.0198822021484375,
0.0008769035339355469,
-0.012939453125,
-0.008544921875,
-0.006134033203125,
-0.0151824951171875,
-0.004619598388671875,
-0.0033512115478515625,
0.01971435546875,
-0.032562255859375,
0.00879669189453125,
-0.005947113037109375,
-0.0288848876953125,
-0.0191497802734375,
-0.0020618438720703125,
0.0169525146484375,
0.0030879974365234375,
0.021728515625,
-0.007595062255859375,
0.0173187255859375,
-0.006450653076171875,
-0.010833740234375,
-0.00258636474609375,
0.01113128662109375,
0.0230865478515625,
-0.01418304443359375,
0.00933837890625,
-0.0104217529296875,
0.001163482666015625,
0.007602691650390625,
-0.0013294219970703125,
0.01016998291015625,
-0.0256195068359375,
-0.01041412353515625,
-0.023651123046875,
-0.0246734619140625,
-0.004245758056640625,
-0.042144775390625,
-0.01505279541015625,
0.0100555419921875,
-0.0146942138671875,
-0.004486083984375,
0.0170745849609375,
0.01369476318359375,
0.0120391845703125,
-0.016845703125,
0.01560211181640625,
0.04803466796875,
0.0278778076171875,
0.014617919921875,
-0.0271759033203125,
-0.006988525390625,
-0.0261383056640625,
0.02294921875,
0.06494140625,
-0.03961181640625,
0.03253173828125,
0.00623321533203125,
0.034759521484375,
0.028533935546875,
-0.01468658447265625,
0.00580596923828125,
-0.0037479400634765625,
-0.01395416259765625,
-0.033538818359375,
0.0026721954345703125,
0.01300048828125,
0.0396728515625,
0.0213470458984375,
0.002010345458984375,
0.01326751708984375,
-0.004940032958984375,
0.004726409912109375,
0.0174713134765625,
-0.00472259521484375,
0.0155792236328125,
-0.0020923614501953125,
-0.0052642822265625,
0.042633056640625,
-0.00582122802734375,
0.0193328857421875,
-0.005702972412109375,
-0.01678466796875,
0.0015573501586914062,
0.033905029296875,
0.0074005126953125,
0.0070648193359375,
-0.0041351318359375,
0.01325225830078125,
0.01438140869140625,
-0.044708251953125,
0.00876617431640625,
0.0014028549194335938,
0.0191192626953125,
0.0198822021484375,
-0.01447296142578125,
-0.036376953125,
0.01207733154296875,
0.03680419921875,
-0.0183868408203125,
0.005817413330078125,
0.017120361328125,
-0.025421142578125,
-0.015167236328125,
-0.005733489990234375,
-0.004428863525390625,
-0.0295257568359375,
-0.024688720703125,
-0.01450347900390625,
-0.00885009765625,
0.04327392578125,
0.011505126953125,
-0.0108184814453125,
0.013519287109375,
0.0271148681640625,
-0.041717529296875,
-0.023406982421875,
0.02642822265625,
-0.0012302398681640625,
-0.029083251953125,
-0.019622802734375,
0.004680633544921875,
0.0250701904296875,
0.033538818359375,
0.022064208984375,
0.0132598876953125,
-0.00852203369140625,
0.00672149658203125,
0.0261688232421875,
0.01395416259765625,
-0.005672454833984375,
0.0038776397705078125,
0.00734710693359375,
-0.041351318359375,
0.01922607421875,
0.020721435546875,
-0.02349853515625,
0.009918212890625,
-0.0152435302734375,
0.005847930908203125,
0.037078857421875,
0.02032470703125,
-0.005523681640625,
-0.0394287109375,
-0.0057373046875,
0.0217437744140625,
0.0009212493896484375,
0.0003254413604736328,
0.020599365234375,
0.0023193359375,
-0.0426025390625,
0.0040130615234375,
-0.014129638671875,
-0.0291900634765625,
0.0227813720703125,
-0.00954437255859375,
0.00966644287109375,
0.00847625732421875,
0.0103759765625,
0.036529541015625,
-0.017333984375,
0.01320648193359375,
-0.0258636474609375,
-0.0217132568359375,
0.0200958251953125,
0.01715087890625,
0.024017333984375,
-0.06378173828125,
-0.0029048919677734375,
-0.0232391357421875,
-0.013214111328125,
-0.0189056396484375,
0.00411224365234375,
-0.0149688720703125,
-0.043670654296875,
0.019012451171875,
0.006103515625,
0.03021240234375,
0.0087738037109375,
0.0035762786865234375,
-0.0226593017578125,
-0.0260162353515625,
0.021820068359375,
0.004909515380859375,
-0.0182647705078125,
-0.0128173828125,
-0.01354217529296875,
0.01506805419921875,
0.01224517822265625,
-0.0052947998046875,
0.01084136962890625,
-0.017242431640625,
-0.015899658203125,
-0.00484466552734375,
0.0225067138671875,
-0.0132598876953125,
0.002216339111328125,
-0.01666259765625,
-0.014068603515625,
-0.0132293701171875,
-0.01245880126953125,
0.01483917236328125,
-0.01047515869140625,
0.0275726318359375,
-0.0169525146484375,
0.0270233154296875,
-0.00405120849609375,
0.01222991943359375,
0.0291595458984375,
0.01352691650390625,
-0.0010976791381835938,
-0.01232147216796875,
0.0285491943359375,
0.027069091796875,
0.00019729137420654297,
-0.01385498046875,
-0.0323486328125,
-0.001800537109375,
-0.019622802734375,
0.0192108154296875,
0.04449462890625,
0.0134124755859375,
-0.02618408203125,
-0.003131866455078125,
0.03253173828125,
-0.004749298095703125,
0.0105743408203125,
-0.01251220703125,
0.0198974609375,
-0.02532958984375,
-0.0018739700317382812,
0.01018524169921875,
0.019927978515625,
-0.01300048828125,
-0.0080413818359375,
-0.047027587890625,
0.01904296875,
-0.0038051605224609375
] |
ours_563
|
For one envelope, your expected winnings are $500$. For two envelopes, open one. If it has over $500$, you should keep it; otherwise, discard it. Hence, your expected winnings should be \(\frac{1}{2} \cdot 750 + \frac{1}{2} \cdot 500 = 625\).
With three envelopes, if the first envelope has over $625$, you should keep it; otherwise, discard it. Thus, the expected winnings are \(\frac{3}{8} \cdot \frac{625 + 1000}{2} + \frac{5}{8} \cdot 625 = \frac{11125}{16} = 695 + \frac{5}{16}\). Therefore, \(\lfloor E \rfloor = 695\).
\(\boxed{695}\)
|
695
|
{
"competition": "us_comps",
"dataset": "Ours",
"posts": null,
"source": "OMOSoln2.md"
}
|
You are playing a game in which you have 3 envelopes, each containing a uniformly random amount of money between $0$ and $1000$ dollars. (That is, for any real $0 \leq a < b \leq 1000$, the probability that the amount of money in a given envelope is between $a$ and $b$ is $\frac{b-a}{1000}$.) At any step, you take an envelope and look at its contents. You may choose either to keep the envelope, at which point you finish, or discard it and repeat the process with one less envelope. If you play to optimize your expected winnings, your expected winnings will be $E$. What is $\lfloor E\rfloor$, the greatest integer less than or equal to $E$?
|
[
"/Mathematics/ProbabilityandStatistics/Probability/ProbabilityAxioms",
"/Mathematics/ProbabilityandStatistics/Probability/ProbabilityMeasure",
"/Mathematics/ProbabilityandStatistics/Probability/ProbabilitySpace",
"/Mathematics/ProbabilityandStatistics/StatisticalDistributions/ContinuousDistributions/UniformDistribution",
"/Mathematics/ProbabilityandStatistics/StatisticalDistributions/ContinuousDistributions/UniformVariate"
] |
Use the optimal expected value of the remaining envelopes as a threshold to decide whether to keep or discard each observed amount.
|
[
-0.0002111196517944336,
0.0279388427734375,
0.040130615234375,
0.01934814453125,
-0.001323699951171875,
0.0245513916015625,
0.07000732421875,
-0.03863525390625,
0.001861572265625,
-0.016632080078125,
-0.025787353515625,
-0.08233642578125,
-0.003570556640625,
-0.058807373046875,
-0.02642822265625,
-0.0016613006591796875,
-0.0120086669921875,
0.016693115234375,
0.0236053466796875,
0.0023822784423828125,
-0.00827789306640625,
-0.0287628173828125,
-0.00782012939453125,
-0.00457000732421875,
-0.035186767578125,
-0.02935791015625,
-0.01282501220703125,
-0.0084991455078125,
0.007534027099609375,
-0.00701141357421875,
-0.009796142578125,
0.006076812744140625,
0.0263824462890625,
-0.01216888427734375,
-0.001163482666015625,
0.0206298828125,
0.0037441253662109375,
-0.005283355712890625,
-0.0137481689453125,
0.024658203125,
-0.002193450927734375,
0.0263824462890625,
0.0198822021484375,
0.02264404296875,
-0.01207733154296875,
0.0235595703125,
-0.0037746429443359375,
-0.006946563720703125,
-0.0108795166015625,
-0.00927734375,
-0.00035071372985839844,
-0.0002903938293457031,
0.03338623046875,
-0.0126800537109375,
0.01461029052734375,
-0.06878662109375,
0.005596160888671875,
-0.0033206939697265625,
0.005580902099609375,
-0.0263824462890625,
-0.0062408447265625,
-0.006641387939453125,
0.025482177734375,
0.0198822021484375,
-0.005825042724609375,
-0.007556915283203125,
-0.0154266357421875,
-0.0535888671875,
0.006412506103515625,
0.00435638427734375,
0.035980224609375,
-0.0214691162109375,
-0.02789306640625,
0.0033664703369140625,
0.0302581787109375,
-0.0221099853515625,
-0.00783538818359375,
0.00305938720703125,
0.0256195068359375,
0.0247802734375,
0.00818634033203125,
0.0207977294921875,
-0.0001499652862548828,
0.0189361572265625,
0.01470184326171875,
0.0212860107421875,
0.01169586181640625,
-0.0156707763671875,
0.0189666748046875,
-0.0026073455810546875,
0.01160430908203125,
0.0445556640625,
0.013031005859375,
-0.0096893310546875,
-0.00749969482421875,
0.015777587890625,
-0.0002446174621582031,
-0.0110015869140625,
-0.0209503173828125,
0.01296234130859375,
-0.0177001953125,
-0.004856109619140625,
0.02471923828125,
-0.0163116455078125,
-0.035888671875,
0.009735107421875,
-0.01430511474609375,
-0.01529693603515625,
-0.0037326812744140625,
0.0060577392578125,
0.0019102096557617188,
0.0026493072509765625,
-0.002750396728515625,
-0.004924774169921875,
0.01540374755859375,
0.008941650390625,
-0.015716552734375,
-0.0189361572265625,
-0.00843048095703125,
-0.0037326812744140625,
0.0092620849609375,
0.018218994140625,
-0.00109100341796875,
0.0016355514526367188,
-0.00551605224609375,
0.0096893310546875,
-0.00836181640625,
0.01149749755859375,
0.0123443603515625,
0.004093170166015625,
-0.0018768310546875,
-0.00939178466796875,
-0.050628662109375,
0.0034847259521484375,
-0.047698974609375,
0.007843017578125,
0.0086212158203125,
0.006275177001953125,
-0.023284912109375,
0.01325225830078125,
0.01507568359375,
-0.002849578857421875,
0.004062652587890625,
0.01209259033203125,
-0.0157470703125,
0.0089569091796875,
0.003696441650390625,
-0.0307159423828125,
0.001750946044921875,
-0.0015716552734375,
-0.0036220550537109375,
-0.0010671615600585938,
-0.0179595947265625,
0.0129852294921875,
0.0023670196533203125,
-0.00511932373046875,
-0.0005383491516113281,
-0.003948211669921875,
-0.0181732177734375,
-0.0033626556396484375,
-0.00920867919921875,
-0.01348114013671875,
0.0208740234375,
0.0509033203125,
-0.007396697998046875,
0.01360321044921875,
0.020172119140625,
0.0016431808471679688,
-0.02191162109375,
0.02239990234375,
0.0008697509765625,
0.0018787384033203125,
0.0026092529296875,
-0.01090240478515625,
-0.019866943359375,
0.01163482666015625,
-0.0016164779663085938,
-0.046783447265625,
-0.011383056640625,
0.0100555419921875,
-0.01349639892578125,
0.0208892822265625,
0.040496826171875,
0.0204925537109375,
0.00330352783203125,
0.0307159423828125,
-0.00023615360260009766,
-0.004764556884765625,
0.018280029296875,
0.0008115768432617188,
-0.0124053955078125,
0.01486968994140625,
-0.0029296875,
-0.00768280029296875,
-0.006694793701171875,
0.021392822265625,
-0.017425537109375,
-0.00655364990234375,
0.045684814453125,
0.0081329345703125,
0.0162200927734375,
-0.0036106109619140625,
-0.029693603515625,
-0.01155853271484375,
0.00476837158203125,
-0.0128326416015625,
0.01386260986328125,
0.006805419921875,
0.00214385986328125,
0.00795745849609375,
-0.00243377685546875,
0.0066680908203125,
-0.004772186279296875,
-0.0243072509765625,
0.0033817291259765625,
0.006893157958984375,
0.004047393798828125,
-0.0122222900390625,
0.006683349609375,
-0.03106689453125,
-0.00687408447265625,
0.01340484619140625,
0.01090240478515625,
-0.0139617919921875,
-0.0303802490234375,
0.004238128662109375,
-0.00963592529296875,
-0.007572174072265625,
0.0105438232421875,
-0.02130126953125,
0.0283050537109375,
0.01181793212890625,
-0.0005311965942382812,
-0.0011911392211914062,
0.00847625732421875,
0.0210418701171875,
-0.005428314208984375,
-0.00954437255859375,
0.02191162109375,
-0.0004730224609375,
0.015869140625,
-0.012908935546875,
0.00714874267578125,
0.00936126708984375,
0.01529693603515625,
-0.0226898193359375,
-0.00957489013671875,
-0.01215362548828125,
0.00396728515625,
-0.00994110107421875,
-0.0084686279296875,
0.0164642333984375,
-0.01137542724609375,
-0.0194854736328125,
0.0039825439453125,
0.0169525146484375,
0.0036373138427734375,
-0.023773193359375,
-0.0050201416015625,
-0.015655517578125,
-0.01016998291015625,
-0.010009765625,
0.0073699951171875,
0.01123809814453125,
-0.00004279613494873047,
0.04656982421875,
0.0047149658203125,
0.01324462890625,
-0.003383636474609375,
-0.00006330013275146484,
0.01496124267578125,
-0.007415771484375,
-0.00037288665771484375,
0.0045318603515625,
0.0298919677734375,
-0.0190887451171875,
0.00959014892578125,
0.0029621124267578125,
0.0025482177734375,
0.0202789306640625,
-0.006221771240234375,
-0.018768310546875,
-0.01131439208984375,
0.00335693359375,
0.01175689697265625,
-0.0038299560546875,
-0.0107879638671875,
-0.0172576904296875,
-0.0236968994140625,
0.027374267578125,
-0.01454925537109375,
0.0224609375,
-0.0121612548828125,
0.00106048583984375,
-0.01207733154296875,
-0.032958984375,
0.015045166015625,
0.00852203369140625,
0.0192718505859375,
-0.0121612548828125,
0.0007252693176269531,
-0.0048828125,
-0.0122833251953125,
0.01296234130859375,
-0.006450653076171875,
0.0254058837890625,
0.019317626953125,
-0.002376556396484375,
0.010223388671875,
-0.02703857421875,
0.0059661865234375,
0.007781982421875,
-0.00643157958984375,
0.00412750244140625,
-0.01389312744140625,
-0.051055908203125,
0.0179443359375,
-0.0027408599853515625,
0.004451751708984375,
0.0015964508056640625,
-0.0151519775390625,
-0.02581787109375,
-0.024322509765625,
0.00731658935546875,
0.0070648193359375,
0.0081329345703125,
0.01364898681640625,
0.0207366943359375,
-0.0048065185546875,
0.0171051025390625,
0.032196044921875,
0.03094482421875,
0.00638580322265625,
-0.00611114501953125,
0.004222869873046875,
0.036224365234375,
0.018707275390625,
0.027191162109375,
0.003936767578125,
-0.0098724365234375,
-0.026336669921875,
0.003139495849609375,
-0.0293731689453125,
-0.030120849609375,
0.01451873779296875,
0.0165252685546875,
0.00832366943359375,
-0.00890350341796875,
-0.01480865478515625,
0.0006852149963378906,
0.0146026611328125,
0.0229644775390625,
0.007610321044921875,
0.00920867919921875,
-0.0202484130859375,
0.015960693359375,
-0.01035308837890625,
0.01149749755859375,
0.04266357421875,
-0.005023956298828125,
0.01441192626953125,
-0.015869140625,
-0.016143798828125,
0.0190887451171875,
-0.0167388916015625,
-0.009368896484375,
-0.0177001953125,
-0.01148223876953125,
-0.0230865478515625,
-0.00814056396484375,
0.007427215576171875,
-0.00399017333984375,
0.029022216796875,
0.007778167724609375,
-0.0251617431640625,
0.0283203125,
-0.0111541748046875,
0.003261566162109375,
0.00803375244140625,
0.00731658935546875,
-0.0260009765625,
0.04388427734375,
-0.006443023681640625,
0.01849365234375,
-0.0189971923828125,
-0.006618499755859375,
0.0192108154296875,
0.013824462890625,
-0.0173187255859375,
-0.006683349609375,
-0.005321502685546875,
0.0190277099609375,
-0.0025806427001953125,
-0.01165771484375,
0.0165252685546875,
-0.0195770263671875,
0.001468658447265625,
-0.00022363662719726562,
0.045928955078125,
-0.00713348388671875,
-0.020751953125,
0.00469207763671875,
-0.032958984375,
0.041473388671875,
-0.00250244140625,
0.0122528076171875,
0.00441741943359375,
-0.01141357421875,
-0.0157318115234375,
0.0009455680847167969,
-0.024871826171875,
-0.0092620849609375,
0.00833892822265625,
0.0275115966796875,
-0.0173797607421875,
0.0235443115234375,
0.01291656494140625,
0.00417327880859375,
-0.024810791015625,
-0.00475311279296875,
-0.0114593505859375,
-0.0105743408203125,
-0.05181884765625,
-0.0222320556640625,
0.0262298583984375,
0.01453399658203125,
-0.0012025833129882812,
0.0305938720703125,
-0.04364013671875,
0.04046630859375,
0.007038116455078125,
-0.005535125732421875,
-0.02197265625,
0.019775390625,
-0.01064300537109375,
0.048675537109375,
0.0084381103515625,
0.0135040283203125,
-0.035980224609375,
-0.00835418701171875,
0.0074615478515625,
0.0083160400390625,
0.0003306865692138672,
-0.0244903564453125,
-0.028289794921875,
0.002635955810546875,
-0.0041656494140625,
0.00014483928680419922,
0.0149993896484375,
-0.000507354736328125,
0.0008435249328613281,
-0.030609130859375,
0.008544921875,
-0.0247039794921875,
-0.038543701171875,
0.00888824462890625,
0.030181884765625,
-0.014801025390625,
-0.006420135498046875,
-0.042205810546875,
-0.0299530029296875,
-0.004825592041015625,
0.006649017333984375,
-0.0347900390625,
0.0157928466796875,
-0.0005078315734863281,
-0.005939483642578125,
-0.0005307197570800781,
-0.003429412841796875,
0.028564453125,
-0.0185089111328125,
-0.0081024169921875,
-0.00942230224609375,
-0.0121002197265625,
-0.0256500244140625,
0.0443115234375,
-0.016204833984375,
0.030517578125,
-0.0272674560546875,
-0.019195556640625,
0.01517486572265625,
-0.006603240966796875,
0.007534027099609375,
0.08062744140625,
0.004486083984375,
-0.0015344619750976562,
-0.002044677734375,
0.00009161233901977539,
-0.0309295654296875,
0.0119781494140625,
0.0048065185546875,
0.0179901123046875,
0.0024204254150390625,
-0.043701171875,
-0.007083892822265625,
0.013214111328125,
0.01541900634765625,
-0.007564544677734375,
-0.00595855712890625,
-0.0229949951171875,
0.005908966064453125,
0.01105499267578125,
-0.0010747909545898438,
-0.01357269287109375,
0.0077362060546875,
-0.0191802978515625,
0.02728271484375,
0.00887298583984375,
-0.006320953369140625,
0.01207733154296875,
0.01062774658203125,
0.01898193359375,
0.013519287109375,
-0.040863037109375,
0.0178680419921875,
0.0219268798828125,
0.00934600830078125,
-0.0411376953125,
0.0035419464111328125,
0.0279693603515625,
-0.041168212890625,
0.0236358642578125,
0.04302978515625,
-0.01024627685546875,
-0.026611328125,
0.01031494140625,
0.005237579345703125,
0.035003662109375,
0.0154266357421875,
0.01300811767578125,
-0.021759033203125,
-0.013153076171875,
0.029022216796875,
-0.02740478515625,
-0.022705078125,
-0.006671905517578125,
0.003021240234375,
0.0477294921875,
-0.004383087158203125,
0.035614013671875,
0.0133056640625,
0.0010471343994140625,
-0.00328826904296875,
-0.0152130126953125,
-0.00846099853515625,
-0.0406494140625,
0.0038166046142578125,
-0.025421142578125,
-0.007595062255859375,
-0.0193328857421875,
0.0136871337890625,
0.0195465087890625,
0.038543701171875,
-0.004055023193359375,
-0.0101165771484375,
0.023895263671875,
0.0008034706115722656,
0.032745361328125,
0.007564544677734375,
0.0036640167236328125,
-0.01000213623046875,
0.0061798095703125,
-0.01003265380859375,
-0.00030350685119628906,
-0.0133514404296875,
0.004940032958984375,
-0.01318359375,
0.053741455078125,
-0.015106201171875,
-0.04736328125,
0.0226287841796875,
-0.010009765625,
-0.00262451171875,
0.0294189453125,
0.0035114288330078125,
0.0020275115966796875,
0.02178955078125,
0.005001068115234375,
0.002254486083984375,
-0.035919189453125,
0.006404876708984375,
0.01291656494140625,
0.017852783203125,
-0.0203704833984375,
0.0139007568359375,
-0.0052947998046875,
0.0024471282958984375,
0.01910400390625,
0.006420135498046875,
-0.00286102294921875,
-0.0016126632690429688,
0.007694244384765625,
0.0276031494140625,
0.01044464111328125,
-0.01593017578125,
-0.039947509765625,
-0.038299560546875,
-0.0144805908203125,
0.00681304931640625,
0.0026378631591796875,
-0.006778717041015625,
-0.0058746337890625,
0.0012378692626953125,
0.01534271240234375,
0.01282501220703125,
0.018157958984375,
0.01111602783203125,
0.008026123046875,
-0.0257415771484375,
0.033355712890625,
0.004245758056640625,
-0.006282806396484375,
-0.03460693359375,
0.01459503173828125,
-0.003509521484375,
0.026519775390625,
-0.026458740234375,
-0.02532958984375,
-0.01348114013671875,
-0.0271148681640625,
0.0063934326171875,
-0.022735595703125,
0.0024623870849609375,
0.005706787109375,
-0.004436492919921875,
0.0254669189453125,
-0.0045623779296875,
-0.00711822509765625,
-0.0183868408203125,
-0.01837158203125,
0.01038360595703125,
-0.007648468017578125,
-0.00939178466796875,
0.004955291748046875,
0.0009069442749023438,
-0.0127716064453125,
-0.033416748046875,
-0.00341796875,
-0.01358795166015625,
-0.00019478797912597656,
0.0003361701965332031,
-0.00885009765625,
0.045166015625,
-0.08538818359375,
-0.032257080078125,
-0.007259368896484375,
0.0007567405700683594,
0.0208892822265625,
-0.0171661376953125,
0.0051116943359375,
-0.0273284912109375,
0.0069732666015625,
-0.0005068778991699219,
-0.007556915283203125,
-0.0360107421875,
-0.01523590087890625,
-0.0208892822265625,
-0.034759521484375,
0.036468505859375,
-0.0136871337890625,
0.005367279052734375,
-0.01338958740234375,
0.02154541015625,
0.01971435546875,
-0.040618896484375,
-0.04559326171875,
0.00850677490234375,
-0.0116424560546875,
-0.0033168792724609375,
0.0028972625732421875,
-0.0394287109375,
0.00345611572265625,
0.02008056640625,
0.005252838134765625,
0.018310546875,
-0.0035114288330078125,
-0.008453369140625,
-0.0223541259765625,
-0.023956298828125,
0.0078582763671875,
-0.01444244384765625,
-0.0084075927734375,
0.049346923828125,
-0.0137481689453125,
-0.0223846435546875,
0.053863525390625,
0.004825592041015625,
0.0186309814453125,
0.0291595458984375,
0.0186614990234375,
0.0131072998046875,
-0.0251617431640625,
0.0157012939453125,
0.036529541015625,
0.0214691162109375,
-0.0167694091796875,
0.00670623779296875,
-0.0021610260009765625,
-0.00720977783203125,
-0.021575927734375,
-0.0038585662841796875,
-0.0187835693359375,
0.004177093505859375,
-0.0009183883666992188,
0.01143646240234375,
-0.01509857177734375,
-0.00524139404296875,
0.018951416015625,
-0.02484130859375,
0.0123138427734375,
0.0101165771484375,
-0.0013370513916015625,
-0.01824951171875,
0.0203399658203125,
-0.01189422607421875,
0.0071258544921875,
0.01593017578125,
-0.0100250244140625,
-0.0019502639770507812,
0.00533294677734375,
-0.057098388671875,
0.00753021240234375,
-0.010772705078125,
0.0109710693359375,
0.009063720703125,
-0.009735107421875,
-0.00797271728515625,
-0.0211181640625,
-0.0177459716796875,
0.01082611083984375,
0.0133209228515625,
-0.01555633544921875,
0.0193634033203125,
-0.0005345344543457031,
-0.007411956787109375,
0.00247955322265625,
-0.018829345703125,
-0.037872314453125,
0.01523590087890625,
-0.007843017578125,
0.03271484375,
0.001842498779296875,
0.007274627685546875,
-0.0264892578125,
-0.00382232666015625,
0.0089569091796875,
-0.02508544921875,
0.035491943359375,
0.0280914306640625,
-0.002231597900390625,
-0.0146026611328125,
0.0018520355224609375,
0.0174102783203125,
0.0148162841796875,
-0.022064208984375,
0.04595947265625,
-0.0028705596923828125,
0.0323486328125,
0.010986328125,
-0.0012331008911132812,
0.01270294189453125,
0.021240234375,
0.008087158203125,
-0.0307769775390625,
-0.014739990234375,
-0.006984710693359375,
-0.023590087890625,
-0.02178955078125,
0.01094818115234375,
0.01215362548828125,
-0.031158447265625,
-0.0308074951171875,
-0.0183868408203125,
-0.00527191162109375,
0.0253143310546875,
0.0035343170166015625,
-0.044677734375,
-0.0193023681640625,
-0.0218353271484375,
0.0071563720703125,
-0.0121002197265625,
-0.042144775390625,
0.0284881591796875,
0.047332763671875,
0.0308074951171875,
0.0151824951171875,
-0.025604248046875,
-0.018829345703125,
0.0086669921875,
-0.00038170814514160156,
0.0304107666015625,
-0.0219268798828125,
0.0174102783203125,
0.01947021484375,
0.00331878662109375,
-0.0260772705078125,
-0.01366424560546875,
-0.041534423828125,
-0.03363037109375,
0.0265960693359375,
0.002166748046875,
-0.0069122314453125,
-0.01316070556640625,
0.035003662109375,
0.0180816650390625,
-0.031341552734375,
0.0196685791015625,
0.01447296142578125,
-0.0308837890625,
0.0162506103515625,
-0.00644683837890625,
-0.01403045654296875,
-0.005672454833984375,
0.0243682861328125,
0.0195465087890625,
-0.0264434814453125,
0.02667236328125,
-0.004123687744140625,
0.0106353759765625,
-0.0116424560546875,
0.01568603515625,
0.0218963623046875,
0.0016841888427734375,
-0.006900787353515625,
0.023529052734375,
-0.0147552490234375,
-0.00931549072265625,
-0.04034423828125,
-0.0196990966796875,
-0.002838134765625,
0.006011962890625,
0.006282806396484375,
-0.020355224609375,
0.00439453125,
-0.003330230712890625,
-0.01580810546875,
-0.052398681640625,
-0.00489044189453125,
-0.027923583984375,
-0.0206146240234375,
0.017913818359375,
-0.01111602783203125,
0.0206298828125,
-0.0054931640625,
-0.00970458984375,
-0.026641845703125,
0.044342041015625,
-0.0025386810302734375,
0.0175323486328125,
0.0167083740234375,
0.00939178466796875,
0.0433349609375,
-0.0161590576171875,
0.0380859375,
0.050750732421875,
0.0284423828125,
0.044525146484375,
0.0159912109375,
-0.01325225830078125,
-0.007793426513671875,
0.0054931640625,
-0.004894256591796875,
-0.0007328987121582031,
-0.0003921985626220703,
-0.0018663406372070312,
-0.0192413330078125,
0.0190887451171875,
-0.01136016845703125,
0.02978515625,
-0.0189361572265625,
-0.002063751220703125,
-0.01611328125,
0.025360107421875,
0.044097900390625,
-0.002147674560546875,
0.033538818359375,
0.0235137939453125,
-0.0003559589385986328,
0.03753662109375,
-0.033843994140625,
0.0249481201171875,
-0.00789642333984375,
0.01029205322265625,
0.0204620361328125,
-0.015380859375,
-0.035888671875,
0.0244140625,
-0.0419921875,
-0.0197296142578125,
-0.004306793212890625,
0.01824951171875,
-0.00467681884765625,
-0.022796630859375,
-0.004058837890625,
0.0143585205078125,
-0.027862548828125,
-0.0166015625,
-0.02337646484375,
0.01517486572265625,
-0.01284027099609375,
-0.0166168212890625,
-0.023468017578125,
-0.01242828369140625,
0.001129150390625,
0.0190887451171875,
-0.0142364501953125,
-0.023834228515625,
0.00795745849609375,
-0.0249786376953125,
-0.0095062255859375,
0.003635406494140625,
0.035491943359375,
0.00013554096221923828,
0.032196044921875,
-0.0350341796875,
-0.01837158203125,
-0.029449462890625,
0.007404327392578125,
-0.01068115234375,
0.038787841796875,
0.0238800048828125,
-0.01047515869140625,
-0.01514434814453125,
-0.036163330078125,
-0.017578125,
-0.0302276611328125,
0.011932373046875,
-0.009368896484375,
-0.03997802734375,
0.00948333740234375,
-0.0161285400390625,
0.031219482421875,
0.0134429931640625,
0.01013946533203125,
0.00018489360809326172,
-0.022125244140625,
0.00527191162109375,
0.0037708282470703125,
0.0030231475830078125,
0.001010894775390625,
0.0067901611328125,
0.0213470458984375,
-0.01308441162109375,
-0.0101776123046875,
-0.00821685791015625,
0.0011386871337890625,
0.0292510986328125,
0.007686614990234375,
-0.0205841064453125,
0.0176849365234375,
-0.02569580078125,
0.01381683349609375,
-0.0289154052734375,
-0.00447845458984375,
-0.0196685791015625,
0.0029048919677734375,
-0.0251312255859375,
-0.0212249755859375,
-0.01035308837890625,
-0.0199432373046875,
0.016632080078125,
-0.0106964111328125,
-0.019134521484375,
0.019073486328125,
0.0252838134765625,
0.06805419921875,
0.005779266357421875,
-0.0229034423828125,
-0.004047393798828125,
0.004756927490234375,
-0.0276031494140625,
-0.004608154296875,
-0.0196533203125,
-0.03271484375,
-0.01605224609375,
-0.00632476806640625,
-0.02386474609375,
0.0110931396484375,
0.04742431640625,
0.036651611328125,
-0.04656982421875,
-0.01324462890625,
0.037109375,
-0.01036834716796875,
0.0190887451171875,
0.01141357421875,
0.025177001953125,
-0.01187896728515625,
0.01190185546875,
0.0016765594482421875,
0.0171966552734375,
0.0007104873657226562,
-0.042938232421875,
0.0174560546875,
0.004871368408203125,
0.0306854248046875,
-0.013641357421875,
-0.0017948150634765625,
0.0019207000732421875,
-0.0004436969757080078,
0.0079193115234375,
0.036407470703125,
0.015899658203125,
-0.01284027099609375,
0.0139617919921875,
-0.0222015380859375,
0.00531768798828125,
-0.00527191162109375,
0.037200927734375,
0.0157012939453125,
-0.00743865966796875,
0.0201263427734375,
0.00492095947265625,
0.0272369384765625,
-0.0255126953125,
-0.0224761962890625,
-0.00508880615234375,
-0.0012731552124023438,
-0.042877197265625,
0.0204620361328125,
-0.011962890625,
-0.0245361328125,
-0.02374267578125,
-0.0015106201171875,
0.01239776611328125,
-0.023162841796875,
0.03375244140625,
-0.00708770751953125,
0.0030574798583984375,
-0.00799560546875,
0.021392822265625,
-0.0228729248046875,
-0.03240966796875,
0.022186279296875,
-0.0049285888671875,
0.004543304443359375,
0.02081298828125,
0.0245361328125,
0.01971435546875,
0.01462554931640625,
0.01666259765625,
0.0181732177734375,
0.00702667236328125,
-0.0195159912109375,
-0.0242767333984375,
-0.0311279296875,
-0.005771636962890625,
-0.01331329345703125,
-0.0221099853515625,
0.03173828125,
-0.00395965576171875,
-0.0030040740966796875,
-0.00811004638671875,
-0.028106689453125,
0.0300140380859375,
-0.00722503662109375,
-0.0008835792541503906,
0.02545166015625,
0.015106201171875,
0.06207275390625,
0.02349853515625,
-0.02032470703125,
-0.0160369873046875,
-0.040496826171875,
-0.01044464111328125,
0.0229034423828125,
-0.0167236328125,
-0.03070068359375,
-0.005039215087890625,
0.0462646484375,
-0.0758056640625,
0.0068359375,
0.021453857421875,
-0.00506591796875,
-0.006710052490234375,
-0.053680419921875,
0.018524169921875,
0.0017118453979492188,
0.001018524169921875,
0.042449951171875,
-0.0400390625,
-0.01496124267578125,
-0.0227508544921875,
0.0008387565612792969,
0.034027099609375,
0.0050811767578125,
0.0166778564453125,
-0.01239013671875,
-0.0235443115234375,
0.0204315185546875,
-0.00392913818359375,
0.005313873291015625,
0.0244293212890625,
0.0063629150390625,
0.0196685791015625,
-0.02294921875,
-0.0075531005859375,
0.0177001953125,
-0.004344940185546875,
0.01474761962890625,
-0.007556915283203125,
0.03594970703125,
0.0254669189453125,
0.0005192756652832031,
-0.009613037109375,
-0.01439666748046875,
0.01251220703125,
0.035491943359375,
0.006229400634765625,
-0.000881195068359375,
-0.048095703125,
0.01436614990234375,
0.0081787109375,
0.0499267578125,
-0.031219482421875,
-0.00534820556640625,
-0.0090789794921875,
-0.038482666015625,
-0.036041259765625,
0.0142669677734375,
-0.01059722900390625,
0.0265350341796875,
-0.0009183883666992188,
0.01363372802734375,
-0.003726959228515625,
0.005626678466796875,
0.011474609375,
0.00811767578125,
0.005397796630859375,
0.003467559814453125,
0.0130767822265625,
0.011077880859375,
-0.01140594482421875,
-0.012542724609375,
0.0021839141845703125,
-0.0216522216796875,
0.00167083740234375,
0.004436492919921875,
-0.0006289482116699219,
0.00372314453125,
-0.0248260498046875,
0.05267333984375,
-0.0031337738037109375,
-0.026824951171875,
-0.00984954833984375,
-0.021942138671875,
0.0144195556640625,
-0.015960693359375,
0.0421142578125,
-0.0003764629364013672,
-0.01090240478515625,
0.0279388427734375,
-0.00949859619140625,
-0.0027675628662109375,
-0.018310546875,
0.003368377685546875,
-0.0133056640625,
-0.005558013916015625,
-0.0123443603515625,
0.03558349609375,
0.01861572265625,
-0.003192901611328125,
0.01495361328125,
-0.0084686279296875,
-0.005069732666015625,
0.0257110595703125,
-0.0297393798828125,
-0.018890380859375,
-0.0036296844482421875,
0.07720947265625,
0.01251220703125,
-0.0159912109375,
0.0151214599609375,
-0.01617431640625,
0.01169586181640625,
0.0242156982421875,
0.0195159912109375,
0.01453399658203125,
0.003398895263671875,
-0.0219268798828125,
-0.023651123046875,
0.0254058837890625,
0.00870513916015625,
-0.00908660888671875,
0.018798828125,
-0.004535675048828125,
0.0007801055908203125,
-0.0272674560546875,
-0.0101470947265625,
-0.047332763671875,
-0.0196685791015625,
-0.007717132568359375,
0.00420379638671875,
-0.0171661376953125,
0.0243377685546875,
-0.003936767578125,
-0.027557373046875,
0.0009889602661132812,
-0.017059326171875,
-0.001399993896484375,
0.0175323486328125,
-0.01337432861328125,
-0.0010433197021484375,
-0.001392364501953125,
-0.0015506744384765625,
0.017730712890625,
-0.0029754638671875,
0.0498046875,
0.0031528472900390625,
0.034912109375,
0.0194244384765625,
0.0003876686096191406,
0.01605224609375,
0.00618743896484375,
-0.004535675048828125,
0.01045989990234375,
-0.0056304931640625,
0.0077056884765625,
-0.0238189697265625,
-0.021697998046875,
0.0085296630859375,
0.0107269287109375,
0.003345489501953125,
-0.01480865478515625,
0.0191192626953125,
-0.0175628662109375,
0.00196075439453125,
0.04290771484375,
0.004726409912109375,
0.01502227783203125,
0.034454345703125,
0.00949859619140625,
0.020904541015625,
0.01336669921875,
-0.014495849609375,
0.0157470703125,
0.00011497735977172852,
0.019805908203125,
0.0136871337890625,
0.0078887939453125,
0.0153656005859375,
0.039031982421875,
-0.0014333724975585938,
0.00888824462890625,
0.059173583984375,
0.0015306472778320312,
-0.0289459228515625,
0.0094757080078125,
-0.01114654541015625,
0.0145111083984375,
0.018646240234375,
0.03778076171875,
-0.0250244140625,
0.006519317626953125,
0.004673004150390625,
-0.0150299072265625,
0.0136260986328125,
-0.007228851318359375,
-0.0168304443359375,
-0.01544952392578125,
-0.04595947265625,
-0.022186279296875,
0.01064300537109375,
-0.0017261505126953125,
0.001434326171875,
-0.01404571533203125,
0.017669677734375,
0.00878143310546875,
0.032379150390625,
0.0092010498046875,
0.043487548828125,
0.03436279296875,
-0.00630950927734375,
0.01226806640625,
0.00263214111328125,
0.0060272216796875,
0.0014333724975585938,
-0.0362548828125,
0.007274627685546875,
-0.0171966552734375,
-0.048858642578125,
0.0230560302734375,
-0.007843017578125,
0.0157623291015625,
-0.01241302490234375,
-0.006412506103515625,
-0.033355712890625,
0.01070404052734375,
-0.0007762908935546875,
-0.0061798095703125,
0.040130615234375,
0.0143890380859375,
0.00681304931640625,
0.01959228515625,
0.007312774658203125,
-0.00959014892578125,
0.00720977783203125,
-0.019500732421875,
0.059295654296875,
0.0027599334716796875,
-0.006053924560546875,
0.015899658203125,
-0.0205230712890625,
-0.003894805908203125,
-0.0106658935546875,
-0.061370849609375,
0.005825042724609375,
-0.02227783203125,
-0.00205230712890625,
-0.00015687942504882812,
0.02947998046875,
0.00865936279296875,
0.033782958984375,
-0.01080322265625,
-0.0037555694580078125,
0.00634765625,
0.0223388671875,
-0.0205535888671875,
0.0226287841796875,
0.01305389404296875,
-0.01161956787109375,
0.01136016845703125,
-0.000888824462890625,
-0.00591278076171875,
0.0098114013671875,
-0.0132598876953125,
-0.0278472900390625,
0.002956390380859375,
0.0005145072937011719,
0.01058197021484375,
-0.005947113037109375,
-0.0170745849609375,
-0.0160064697265625,
-0.005817413330078125,
-0.0028667449951171875,
-0.0006213188171386719,
0.01490020751953125,
0.02984619140625,
0.0195159912109375,
-0.0047760009765625,
0.01010894775390625,
0.033203125,
-0.0119781494140625,
0.0009765625,
0.02532958984375,
0.0140533447265625,
-0.04486083984375,
0.0283660888671875,
0.007503509521484375,
-0.0335693359375,
-0.0011463165283203125,
-0.009857177734375,
-0.0084686279296875,
0.02374267578125,
-0.003192901611328125,
-0.016754150390625,
-0.0097198486328125,
-0.0200958251953125,
0.018585205078125,
0.0034313201904296875,
0.02020263671875,
-0.0300140380859375,
-0.0197601318359375,
-0.0309906005859375,
0.031829833984375,
0.0036468505859375,
0.0092010498046875,
0.01317596435546875,
0.0017995834350585938,
-0.01519012451171875,
-0.0103912353515625,
0.034576416015625,
-0.01065826416015625,
0.0020122528076171875,
0.0037441253662109375,
-0.01473236083984375,
-0.013519287109375,
-0.006298065185546875,
-0.0230560302734375,
-0.004230499267578125,
0.0006070137023925781,
-0.0111846923828125,
0.0117645263671875,
-0.002208709716796875,
-0.0018968582153320312,
0.0181427001953125,
-0.0301666259765625,
0.0244903564453125,
-0.007770538330078125,
0.0225677490234375,
-0.0243377685546875,
0.0013885498046875,
-0.0195159912109375,
-0.03363037109375,
-0.00640106201171875,
-0.0171051025390625,
-0.005901336669921875,
-0.004638671875,
0.01023101806640625,
0.0292510986328125,
-0.002704620361328125,
0.01531982421875,
-0.004608154296875,
-0.00676727294921875,
-0.004856109619140625,
-0.04754638671875,
0.0214996337890625,
-0.01873779296875,
-0.0033550262451171875,
-0.001605987548828125,
-0.023101806640625,
0.01143646240234375,
-0.01453399658203125,
-0.044769287109375,
0.0027561187744140625,
-0.039215087890625,
-0.0161590576171875,
-0.02288818359375,
-0.00606536865234375,
0.0131378173828125,
-0.0006093978881835938,
0.01922607421875,
-0.01873779296875,
0.017425537109375,
-0.025848388671875,
0.00655364990234375,
0.046783447265625,
0.0129241943359375,
0.0263671875,
0.0201416015625,
0.0186004638671875,
0.0030879974365234375,
0.010009765625,
-0.01227569580078125,
-0.0036487579345703125,
-0.0168304443359375,
0.005809783935546875,
0.0127716064453125,
0.0209197998046875,
0.00836944580078125,
-0.039276123046875,
0.0179290771484375,
0.0024433135986328125,
0.00858306884765625,
-0.0005674362182617188,
0.0202178955078125,
-0.0108642578125,
-0.0113067626953125,
0.00815582275390625,
-0.01422882080078125,
0.023712158203125,
-0.00562286376953125,
-0.006458282470703125,
-0.0101318359375,
0.004299163818359375,
-0.019683837890625,
0.006687164306640625,
0.00438690185546875,
-0.002986907958984375,
-0.0115509033203125,
0.0165252685546875,
0.01849365234375,
0.0010881423950195312,
-0.00914764404296875,
0.0105438232421875,
-0.036376953125,
-0.025177001953125,
-0.0028076171875,
-0.0294952392578125,
0.0097808837890625,
-0.0279083251953125,
0.0185546875,
-0.00991058349609375,
-0.0206451416015625,
-0.01288604736328125,
0.01462554931640625,
-0.00678253173828125,
0.00611114501953125,
0.015411376953125,
-0.02410888671875,
-0.038787841796875,
0.011260986328125,
0.00910186767578125,
-0.0014295578002929688,
-0.01428985595703125,
-0.019378662109375,
0.004436492919921875,
-0.007049560546875,
-0.01361846923828125,
0.0059356689453125,
-0.0164947509765625,
-0.0305938720703125,
0.035491943359375,
0.001430511474609375,
0.0242156982421875,
-0.030548095703125,
-0.0201568603515625,
0.0036678314208984375,
0.006610870361328125,
-0.04742431640625,
0.01345062255859375,
0.0219573974609375,
0.001956939697265625,
0.01071929931640625,
0.01031494140625,
-0.0211181640625,
0.01544952392578125,
-0.0130462646484375,
0.037261962890625,
-0.0408935546875,
-0.018768310546875,
-0.00823974609375,
0.0019435882568359375,
-0.0088348388671875,
-0.00832366943359375,
-0.00997161865234375,
0.023040771484375,
0.022796630859375,
-0.0272674560546875,
-0.001094818115234375,
-0.00821685791015625,
-0.0010709762573242188,
0.01568603515625,
0.02294921875,
-0.004451751708984375,
-0.0204010009765625,
0.0183563232421875,
0.0080413818359375,
0.00897216796875,
-0.0021114349365234375,
0.027191162109375,
0.0016012191772460938,
0.0157318115234375,
0.0260162353515625,
-0.029266357421875,
-0.0027446746826171875,
-0.0406494140625,
-0.036590576171875,
0.0128326416015625,
-0.00989532470703125,
0.0270538330078125,
-0.013427734375,
0.0220489501953125,
0.0020236968994140625,
0.006160736083984375,
-0.002216339111328125,
0.004238128662109375,
0.02423095703125,
0.004581451416015625,
-0.007366180419921875,
-0.0047760009765625,
-0.0309600830078125,
0.0155181884765625,
0.0364990234375,
-0.0218505859375,
0.0386962890625,
0.01006317138671875,
0.023162841796875,
-0.0162811279296875,
-0.00528717041015625,
0.0244140625,
0.0209197998046875,
-0.0259857177734375,
-0.0028972625732421875,
0.0166778564453125,
0.003238677978515625,
0.00909423828125,
0.03021240234375,
-0.01788330078125,
0.0024089813232421875,
-0.019775390625,
-0.01036834716796875,
-0.0157928466796875,
-0.01165771484375,
0.01297760009765625,
-0.012603759765625,
0.018463134765625,
0.004535675048828125,
-0.00603485107421875,
0.010894775390625,
0.01070404052734375,
-0.01251220703125,
0.01239776611328125,
0.01490020751953125,
0.0477294921875,
0.0199127197265625,
-0.0276947021484375,
0.034271240234375,
0.01134490966796875,
-0.006011962890625,
-0.006473541259765625,
-0.0026264190673828125,
0.034912109375,
0.0265960693359375,
0.004238128662109375,
-0.0022258758544921875,
0.0499267578125,
0.007114410400390625,
0.0419921875,
-0.0277557373046875,
0.004978179931640625,
0.0124053955078125,
-0.0002028942108154297,
0.0151824951171875,
-0.0099945068359375,
-0.00013399124145507812,
0.043731689453125,
-0.004817962646484375,
-0.019744873046875,
-0.0278472900390625,
0.00274658203125,
0.0073089599609375,
0.016021728515625,
0.015838623046875,
-0.00783538818359375,
0.0005559921264648438,
0.027374267578125,
0.016815185546875,
-0.0088043212890625,
0.0211944580078125,
0.007457733154296875,
0.0017261505126953125,
0.0285491943359375,
0.00864410400390625,
0.01157379150390625,
0.001705169677734375,
-0.0032253265380859375,
-0.03778076171875,
-0.01036834716796875,
-0.0258636474609375,
0.019683837890625,
-0.0021572113037109375,
-0.01313018798828125,
0.02093505859375,
-0.0147705078125,
-0.02960205078125,
0.01215362548828125,
0.043487548828125,
0.0142669677734375,
0.016021728515625,
0.0274658203125,
-0.01177215576171875,
0.00907135009765625,
-0.0357666015625,
-0.044464111328125,
0.0183258056640625,
-0.01526641845703125,
0.0408935546875,
0.00481414794921875,
-0.027099609375,
0.0309600830078125,
-0.005229949951171875,
0.0222320556640625,
0.005588531494140625,
0.0206451416015625,
0.01543426513671875,
-0.0180511474609375,
-0.0089263916015625,
-0.0279541015625,
-0.036590576171875,
0.01055908203125,
-0.011505126953125,
-0.0038585662841796875,
0.00327301025390625,
0.020782470703125,
0.01503753662109375,
-0.023223876953125,
0.021026611328125,
-0.01332855224609375,
0.0150604248046875,
0.01329803466796875,
-0.005672454833984375,
0.0012636184692382812,
0.033660888671875,
-0.0222625732421875,
-0.013641357421875,
-0.055999755859375,
0.05438232421875,
0.0143280029296875,
-0.000560760498046875,
-0.00264739990234375,
-0.00362396240234375,
-0.00321197509765625,
-0.0127410888671875,
-0.0013971328735351562,
-0.0193328857421875,
0.0184173583984375,
-0.01224517822265625,
0.020355224609375,
-0.006061553955078125,
0.048980712890625,
0.03387451171875,
-0.01259613037109375,
0.001888275146484375,
-0.01493072509765625,
-0.004123687744140625,
-0.000335693359375,
0.01013946533203125,
-0.01410675048828125,
0.0258026123046875,
-0.0154571533203125,
0.007640838623046875,
-0.019927978515625,
-0.0281219482421875,
0.0158843994140625,
0.0172271728515625,
0.0150299072265625,
0.01020050048828125,
-0.03662109375,
-0.013763427734375,
0.050750732421875,
0.008544921875,
0.01338958740234375,
-0.0176544189453125,
0.021514892578125,
0.01462554931640625,
-0.004726409912109375,
-0.004360198974609375,
0.005214691162109375,
-0.0196075439453125,
0.0283660888671875,
-0.00275421142578125,
0.007808685302734375,
0.02313232421875,
0.042022705078125,
-0.00823974609375,
-0.0193023681640625,
0.0158233642578125,
0.0031719207763671875,
0.021270751953125,
-0.005496978759765625,
0.005046844482421875,
-0.0280914306640625,
0.006687164306640625,
0.0005011558532714844,
-0.0263214111328125,
0.028533935546875,
-0.031158447265625,
-0.022674560546875,
-0.0187835693359375,
-0.0117034912109375,
-0.0290985107421875,
0.0197601318359375,
0.034210205078125,
0.0106201171875,
-0.021881103515625,
-0.005100250244140625,
0.022674560546875,
0.0087738037109375,
0.0186767578125,
-0.034088134765625,
0.024383544921875,
-0.0025615692138671875,
0.04803466796875,
-0.030029296875,
0.008148193359375,
0.004215240478515625,
0.0190887451171875,
0.022491455078125,
0.006519317626953125,
0.0194549560546875,
0.006069183349609375,
0.0158843994140625,
-0.011322021484375,
0.0013914108276367188,
-0.017852783203125,
0.01546478271484375,
-0.00583648681640625,
-0.0272216796875,
-0.01776123046875,
0.0005660057067871094,
-0.0008759498596191406,
0.021575927734375,
-0.0087432861328125,
0.01081085205078125,
-0.0000012516975402832031,
0.00225830078125,
0.0167083740234375,
-0.0255889892578125,
0.009033203125,
-0.02386474609375,
-0.00823974609375,
-0.019012451171875,
0.0285186767578125,
0.005985260009765625,
-0.026458740234375,
-0.00881195068359375,
-0.00374603271484375,
0.02496337890625,
-0.01971435546875,
-0.0109100341796875,
-0.0142822265625,
-0.02496337890625,
0.00695037841796875,
0.005092620849609375,
-0.000789642333984375,
-0.00627899169921875,
0.005001068115234375,
-0.00736236572265625,
0.006328582763671875,
-0.023834228515625,
0.0242156982421875,
0.0009465217590332031,
-0.0276336669921875,
0.01345062255859375,
-0.0247650146484375,
0.02093505859375,
-0.0389404296875,
0.0188446044921875,
0.0005574226379394531,
0.01345062255859375,
0.0325927734375,
-0.0011138916015625,
-0.002269744873046875,
-0.00019931793212890625,
0.001678466796875,
0.019378662109375,
0.0137939453125,
-0.036956787109375,
-0.0125885009765625,
0.0011949539184570312,
0.0163421630859375,
-0.022125244140625,
-0.0172576904296875,
0.00418853759765625,
0.01210784912109375,
0.040283203125,
-0.003604888916015625,
-0.0245819091796875,
0.037628173828125,
0.018218994140625,
0.0028400421142578125,
-0.019317626953125,
-0.009979248046875,
0.0026569366455078125,
-0.0207977294921875,
-0.0030059814453125,
-0.0085906982421875,
0.008148193359375,
0.018096923828125,
0.0016622543334960938,
0.00872039794921875,
-0.0193939208984375,
0.059478759765625,
0.0034027099609375,
-0.022216796875,
0.022674560546875,
0.0146484375,
-0.0036907196044921875,
0.0261077880859375,
0.0123138427734375,
-0.038299560546875,
-0.0012788772583007812,
0.01404571533203125,
-0.005107879638671875,
0.0105438232421875,
-0.01514434814453125,
-0.018798828125,
0.006175994873046875,
0.022125244140625,
-0.0089874267578125,
-0.0206451416015625,
0.006134033203125,
0.007022857666015625,
0.007228851318359375,
0.0110015869140625,
0.0269775390625,
-0.0203399658203125,
-0.00524139404296875,
0.017547607421875,
0.037200927734375,
-0.0124664306640625,
0.00908660888671875,
-0.036773681640625,
0.0166473388671875,
-0.0047149658203125,
-0.006916046142578125,
0.013336181640625,
0.059844970703125,
-0.022369384765625,
-0.002155303955078125,
0.01401519775390625,
0.0193634033203125,
0.021636962890625,
-0.0037822723388671875,
-0.0017900466918945312,
0.010986328125,
0.021209716796875,
0.03204345703125,
0.013397216796875,
-0.01409912109375,
-0.0083770751953125,
0.01354217529296875,
0.000028431415557861328,
0.0305023193359375,
-0.0144195556640625,
0.0084228515625,
0.0035247802734375,
-0.01047515869140625,
0.03228759765625,
-0.0355224609375,
0.01422882080078125,
0.017120361328125,
0.00278472900390625,
-0.004306793212890625,
0.0179443359375,
-0.00917816162109375,
-0.00487518310546875,
-0.05377197265625,
0.01003265380859375,
-0.019927978515625,
0.006786346435546875,
-0.0240478515625,
-0.0028018951416015625,
-0.0390625,
-0.00545501708984375,
-0.003093719482421875,
0.053375244140625,
-0.02191162109375,
0.004489898681640625,
-0.002285003662109375,
-0.0108795166015625,
0.027099609375,
0.0253753662109375,
0.0112457275390625,
-0.0032634735107421875,
0.005268096923828125,
-0.0014057159423828125,
0.003208160400390625,
-0.0005450248718261719,
-0.0014810562133789062,
-0.016021728515625,
-0.0131072998046875,
-0.0032215118408203125,
-0.034332275390625,
0.00440216064453125,
-0.006542205810546875,
0.0068206787109375,
0.005504608154296875,
-0.00311279296875,
-0.01052093505859375,
-0.010162353515625,
-0.0103607177734375,
0.0159454345703125,
0.00586700439453125,
-0.00966644287109375,
-0.008453369140625,
-0.033477783203125,
0.00975799560546875,
-0.00785064697265625,
-0.0163116455078125,
-0.0261383056640625,
-0.0207366943359375,
0.012939453125,
0.0084075927734375,
0.016204833984375,
0.00746917724609375,
0.00537109375,
-0.005260467529296875,
-0.00010585784912109375,
-0.028106689453125,
0.005245208740234375,
-0.00743865966796875,
0.0180511474609375,
-0.0167388916015625,
0.03155517578125,
0.0279083251953125,
-0.01375579833984375,
0.01593017578125,
-0.032562255859375,
-0.0102691650390625,
-0.0002799034118652344,
-0.020904541015625,
0.028289794921875,
0.0199737548828125,
0.0262298583984375,
-0.00621795654296875,
0.00782012939453125,
0.005756378173828125,
-0.027587890625,
-0.0173187255859375,
-0.012908935546875,
-0.01285552978515625,
-0.016693115234375,
0.006591796875,
-0.01641845703125,
-0.0150604248046875,
-0.047576904296875,
0.0011415481567382812,
-0.0022640228271484375,
0.0287628173828125,
-0.00391387939453125,
0.008758544921875,
-0.0225372314453125,
0.01467132568359375,
0.01244354248046875,
0.01216888427734375,
-0.01259613037109375,
-0.0110321044921875,
0.004261016845703125,
-0.017730712890625,
0.0025730133056640625,
0.031036376953125,
0.00777435302734375,
0.0250091552734375,
-0.006015777587890625,
0.00983428955078125,
-0.0169525146484375,
0.01099395751953125,
-0.005580902099609375,
-0.0018453598022460938,
-0.04901123046875,
0.01287078857421875,
0.01345062255859375,
-0.0227813720703125,
0.017059326171875,
-0.01033782958984375,
0.0037784576416015625,
-0.019195556640625,
0.00391387939453125,
-0.02374267578125,
0.01323699951171875,
-0.014739990234375,
-0.0266265869140625,
-0.007106781005859375,
-0.0138092041015625,
0.0070648193359375,
0.002750396728515625,
0.008819580078125,
0.038482666015625,
0.01270294189453125,
0.00318145751953125,
-0.0036411285400390625,
0.000263214111328125,
0.00927734375,
-0.0112762451171875,
-0.006450653076171875,
-0.010711669921875,
-0.0214996337890625,
0.01166534423828125,
0.006343841552734375,
0.0168304443359375,
0.005279541015625,
-0.0012111663818359375,
-0.008575439453125,
0.00021505355834960938,
0.041534423828125,
0.01654052734375,
-0.00274658203125,
0.004489898681640625,
0.00933074951171875,
-0.00707244873046875,
0.0036468505859375,
0.02703857421875,
-0.0002453327178955078,
-0.0023651123046875,
-0.00943756103515625,
-0.006488800048828125,
-0.0040130615234375,
-0.0118255615234375,
-0.032440185546875,
0.0291748046875,
-0.0178985595703125,
0.0015344619750976562,
-0.00859832763671875,
0.0247650146484375,
-0.0384521484375,
0.025146484375,
-0.035614013671875,
-0.0440673828125,
-0.0227813720703125,
-0.0269012451171875,
-0.011749267578125,
-0.00963592529296875,
0.028900146484375,
0.0088653564453125,
-0.01430511474609375,
0.032867431640625,
0.0005927085876464844,
-0.0094146728515625,
0.032440185546875,
-0.0016450881958007812,
0.014984130859375,
0.01232147216796875,
-0.032745361328125,
-0.00839996337890625,
-0.024505615234375,
-0.01557159423828125,
0.0032806396484375,
0.0011348724365234375,
-0.01282501220703125,
-0.026702880859375,
-0.0081329345703125,
-0.013580322265625,
0.0345458984375,
-0.004932403564453125,
0.00894927978515625,
0.0231781005859375,
0.01885986328125,
-0.0156707763671875,
-0.017547607421875,
0.0267181396484375,
0.006237030029296875,
0.01174163818359375,
-0.033905029296875,
0.034393310546875,
0.044036865234375,
-0.0059661865234375,
0.003002166748046875,
0.0090179443359375,
0.0176239013671875,
-0.0038738250732421875,
-0.0128631591796875,
0.006839752197265625,
0.02801513671875,
-0.019134521484375,
0.0250396728515625,
-0.0207366943359375,
-0.001556396484375,
0.00909423828125,
-0.0274200439453125,
0.008056640625,
0.01873779296875,
-0.017913818359375,
-0.01473236083984375,
0.035400390625,
-0.006748199462890625,
-0.0111083984375,
-0.01351165771484375,
0.01331329345703125,
-0.0093536376953125,
-0.0162353515625,
0.004978179931640625,
-0.00508880615234375,
-0.00616455078125,
-0.0181884765625,
0.01038360595703125,
-0.0185546875,
-0.0239410400390625,
0.0113372802734375,
0.012603759765625,
0.0040283203125,
-0.011932373046875,
0.00867462158203125,
-0.0308074951171875,
-0.00647735595703125,
-0.0064849853515625,
0.0167388916015625,
0.000728607177734375,
-0.0126495361328125,
-0.0014171600341796875,
-0.0311737060546875,
-0.0215911865234375,
-0.0095672607421875,
0.0129547119140625,
-0.033050537109375,
0.0158843994140625,
0.00797271728515625,
-0.0277252197265625,
0.0004374980926513672,
-0.00403594970703125,
-0.0211334228515625,
-0.002166748046875,
-0.0220489501953125,
-0.005908966064453125,
0.0128326416015625,
-0.017333984375,
-0.034515380859375,
-0.0072174072265625,
-0.021697998046875,
-0.0101470947265625,
0.0017223358154296875,
-0.0274658203125,
-0.00228118896484375,
-0.0004496574401855469,
-0.0080718994140625,
-0.004512786865234375,
0.0019483566284179688,
-0.023101806640625,
0.00917816162109375,
-0.032440185546875,
0.0255889892578125,
-0.0137939453125,
0.0179443359375,
0.01111602783203125,
0.007659912109375,
-0.01023101806640625,
-0.004261016845703125,
0.007419586181640625,
0.004634857177734375,
-0.0003638267517089844,
-0.005580902099609375,
0.003154754638671875,
-0.01006317138671875,
-0.00751495361328125,
0.0205841064453125,
0.00833892822265625,
0.0023937225341796875,
-0.0304718017578125,
0.00899505615234375,
0.0015211105346679688,
-0.0093231201171875,
-0.0312042236328125,
-0.002216339111328125,
0.01568603515625,
-0.0018215179443359375,
-0.0037517547607421875,
-0.01117706298828125,
0.01485443115234375,
-0.04095458984375,
0.03729248046875,
0.01416015625,
-0.015350341796875,
0.0118865966796875,
-0.0038604736328125,
-0.012359619140625,
0.0250244140625,
-0.0073394775390625,
0.003139495849609375,
0.01837158203125,
0.005523681640625,
-0.0033779144287109375,
0.0191802978515625,
-0.0284576416015625,
-0.0019893646240234375,
0.0106658935546875,
-0.00482940673828125,
0.004199981689453125,
0.021331787109375,
0.033477783203125,
-0.006031036376953125,
0.0219879150390625,
0.044219970703125,
-0.01233673095703125,
-0.019775390625,
0.0035839080810546875,
-0.0027618408203125,
-0.0161590576171875,
-0.0299835205078125,
0.003345489501953125,
-0.0196380615234375,
0.0074920654296875,
-0.032745361328125,
-0.024169921875,
0.0028972625732421875,
-0.0224761962890625,
0.0095672607421875,
0.0242156982421875,
0.03228759765625,
0.00931549072265625,
-0.0019683837890625,
0.0270233154296875,
-0.0009374618530273438,
0.0258026123046875,
0.004596710205078125,
0.011383056640625,
-0.0111541748046875,
0.0020046234130859375,
-0.017974853515625,
-0.01367950439453125,
0.0137939453125,
0.0068511962890625,
0.01287078857421875,
-0.01267242431640625,
0.025299072265625,
0.0301361083984375,
0.00998687744140625,
-0.034637451171875,
-0.00379180908203125,
0.01479339599609375,
-0.0100555419921875,
-0.006099700927734375,
-0.0230560302734375,
0.0251922607421875,
-0.0091094970703125,
0.0025272369384765625,
-0.01331329345703125,
-0.00022661685943603516,
-0.027252197265625,
-0.021392822265625,
0.0240020751953125,
-0.04803466796875,
-0.040496826171875,
0.004322052001953125,
-0.013153076171875,
-0.00580596923828125,
-0.008544921875,
-0.0254364013671875,
0.01497650146484375,
0.0175323486328125,
-0.0189208984375,
0.006587982177734375,
-0.0017957687377929688,
0.006580352783203125,
-0.003833770751953125,
0.015625,
0.03326416015625,
0.00939178466796875,
-0.01000213623046875,
0.01556396484375,
0.0164642333984375,
0.00228118896484375,
0.035369873046875,
-0.0171966552734375,
-0.032684326171875,
0.003467559814453125,
-0.0107421875,
0.002880096435546875,
-0.00826263427734375,
0.015869140625,
0.006122589111328125,
0.008636474609375,
-0.01187896728515625,
0.0120849609375,
-0.0123443603515625,
-0.0256500244140625,
-0.006221771240234375,
0.038543701171875,
0.006591796875,
-0.01093292236328125,
-0.016571044921875,
0.01273345947265625,
-0.004932403564453125,
0.0011548995971679688,
0.0011358261108398438,
0.029449462890625,
0.0068206787109375,
0.019561767578125,
0.00731658935546875,
-0.014617919921875,
-0.00955963134765625,
0.01049041748046875,
-0.01499176025390625,
0.0182647705078125,
-0.0005078315734863281,
-0.028472900390625,
0.0124359130859375,
-0.0189208984375,
-0.0122222900390625,
-0.036102294921875,
-0.0072479248046875,
0.0269775390625,
0.0143585205078125,
-0.0027904510498046875,
-0.01473236083984375,
0.01349639892578125,
-0.028167724609375,
-0.0186614990234375,
0.00862884521484375,
-0.0296173095703125,
0.0004787445068359375,
-0.018646240234375,
-0.007701873779296875,
-0.006381988525390625,
-0.003326416015625,
-0.005126953125,
0.02447509765625,
0.0178985595703125,
-0.0302581787109375,
0.021331787109375,
0.01523590087890625,
-0.01428985595703125,
0.0237579345703125,
0.022918701171875,
0.0007147789001464844,
-0.00872039794921875,
0.0028858184814453125,
-0.004413604736328125,
-0.0087890625,
0.033050537109375,
-0.0010194778442382812,
0.0082550048828125,
-0.0146636962890625,
0.017120361328125,
-0.0006780624389648438,
-0.02099609375,
-0.00067138671875,
-0.0240020751953125,
-0.007335662841796875,
0.00981903076171875,
0.01047515869140625,
0.015899658203125,
-0.0111541748046875,
-0.0064849853515625,
0.0191192626953125,
-0.0233612060546875,
0.021697998046875,
-0.027587890625,
0.044769287109375,
0.007381439208984375,
-0.0149688720703125,
-0.00719451904296875,
-0.0013713836669921875,
0.030548095703125,
-0.01280975341796875,
0.002349853515625,
-0.02899169921875,
0.034271240234375,
-0.00478363037109375,
0.0195770263671875,
0.010528564453125,
-0.0122528076171875,
-0.0006394386291503906,
-0.037506103515625,
-0.01197052001953125,
0.0037441253662109375,
-0.0207977294921875,
0.0191192626953125,
0.0277252197265625,
0.005062103271484375,
-0.0325927734375,
0.0179290771484375,
-0.0202178955078125,
-0.01354217529296875,
0.0169219970703125,
0.0221710205078125,
-0.0007419586181640625,
-0.036773681640625,
-0.01384735107421875,
0.0026302337646484375,
-0.0029735565185546875,
-0.0271148681640625,
0.0012750625610351562,
0.004184722900390625,
-0.01153564453125,
-0.007358551025390625,
0.01021575927734375,
-0.0198974609375,
0.01025390625,
-0.0149688720703125,
-0.0053253173828125,
-0.023590087890625,
0.042327880859375,
0.01435089111328125,
0.019622802734375,
-0.01270294189453125,
0.0082855224609375,
0.0026073455810546875,
-0.0249786376953125,
0.002849578857421875,
0.0072784423828125,
-0.03802490234375,
-0.004108428955078125,
-0.012481689453125,
0.0179290771484375,
0.0188140869140625,
-0.01523590087890625,
-0.00208282470703125,
0.0035552978515625,
-0.01557159423828125,
0.0035610198974609375,
0.00769805908203125,
-0.029937744140625,
0.013153076171875,
-0.001491546630859375,
0.005657196044921875,
-0.027313232421875,
-0.0006399154663085938,
0.00415802001953125,
0.00362396240234375,
0.01192474365234375,
0.035064697265625,
0.023284912109375,
0.0267181396484375,
-0.0252685546875,
-0.02325439453125,
-0.0259857177734375,
0.013824462890625,
-0.0328369140625,
-0.01373291015625,
0.01094818115234375,
-0.0016222000122070312,
-0.0141143798828125,
0.0016107559204101562,
-0.0294189453125,
-0.025360107421875,
0.04852294921875,
0.00832366943359375,
0.00506591796875,
0.01348114013671875,
-0.0030002593994140625,
-0.0099945068359375,
0.0325927734375,
-0.00447845458984375,
0.00438690185546875,
-0.0044708251953125,
-0.03228759765625,
0.036346435546875,
0.004360198974609375,
-0.047027587890625,
-0.0166168212890625,
-0.014251708984375,
-0.0003516674041748047,
-0.00920867919921875,
0.0546875,
0.005252838134765625,
-0.0538330078125,
0.003662109375,
0.0177001953125,
-0.005847930908203125,
-0.0040435791015625,
-0.0059967041015625,
-0.0212554931640625,
-0.0237274169921875,
-0.01213836669921875,
-0.01482391357421875,
-0.006374359130859375,
0.019195556640625,
-0.018646240234375,
-0.0184173583984375,
-0.0187835693359375,
0.0180511474609375,
0.009368896484375,
-0.003772735595703125,
-0.0293426513671875,
-0.0206298828125,
-0.01113128662109375,
-0.0004088878631591797,
0.006256103515625,
0.0292510986328125,
-0.0240478515625,
-0.0165863037109375,
0.0244598388671875,
0.00033354759216308594,
0.00019550323486328125,
0.0253143310546875,
0.0030078887939453125,
-0.025726318359375,
-0.0282745361328125,
-0.003231048583984375,
0.00957489013671875,
0.003326416015625,
-0.0081939697265625,
-0.0228118896484375,
0.0005521774291992188,
0.04217529296875,
0.06475830078125,
-0.02069091796875,
-0.004245758056640625,
-0.01374053955078125,
0.0121307373046875,
0.00809478759765625,
0.00609588623046875,
0.0013217926025390625,
0.00396728515625,
0.001560211181640625,
-0.0088043212890625,
-0.0264129638671875,
0.012542724609375,
0.005290985107421875,
0.00661468505859375,
0.0089569091796875,
-0.00443267822265625,
-0.0076751708984375,
-0.010345458984375,
0.0009293556213378906,
-0.0194091796875,
-0.00957489013671875,
-0.0036144256591796875,
0.011627197265625
] |
ours_564
|
Let \( u=\frac{p}{q}, v=\frac{q}{r}, \) and \( w=\frac{r}{p} \). Clearly, \( u v w=1 \). We seek \( u+v+w \). Note that the two equations can be rewritten as
\[
\frac{(p+q)(q+r)(r+p)}{p q r}=\left(\frac{p+q}{q}\right)\left(\frac{q+r}{r}\right)\left(\frac{r+p}{p}\right)=(u+1)(v+1)(w+1)=24
\]
and
\[
\frac{(p-2 q)(q-2 r)(r-2 p)}{p q r}=\left(\frac{p-2 q}{q}\right)\left(\frac{q-2 r}{r}\right)\left(\frac{r-2 p}{p}\right)=(u-2)(v-2)(w-2)=10
\]
Expanding, we get \( u v w+u v+v w+w u+u+v+w+1=24 \) and \( u v w-2(u v+v w+w u)+4(u+v+w)-8=10 \). Adding twice the first equation to the second, we get \( 3 u v w+6(u+v+w)-6=58 \), so \( u+v+w=\frac{58+6-3}{6}=\frac{61}{6} \), giving an answer of \( 61+6=67 \).
\(\boxed{67}\)
|
67
|
{
"competition": "us_comps",
"dataset": "Ours",
"posts": null,
"source": "OMOSoln2.md"
}
|
Let \( p, q, r \) be real numbers satisfying
\[
\begin{gathered}
\frac{(p+q)(q+r)(r+p)}{p q r}=24 \\
\frac{(p-2 q)(q-2 r)(r-2 p)}{p q r}=10
\end{gathered}
\]
Given that \(\frac{p}{q}+\frac{q}{r}+\frac{r}{p}\) can be expressed in the form \(\frac{m}{n}\), where \(m, n\) are relatively prime positive integers, compute \(m+n\).
|
[
"/Mathematics/Algebra/AlgebraicEquations/AlgebraicExpression",
"/Mathematics/Algebra/AlgebraicEquations/SimultaneousEquations",
"/Mathematics/Algebra/AlgebraicIdentities/AlgebraicIdentity",
"/Mathematics/Algebra/GeneralAlgebra/Algebra"
] |
Introduce u=p/q, v=q/r, w=r/p (so uvw=1) and rewrite the given products as (u+1)(v+1)(w+1)=24 and (u-2)(v-2)(w-2)=10 to find u+v+w.
|
[
0.00006151199340820312,
0.005992889404296875,
-0.0109100341796875,
0.007236480712890625,
0.00042748451232910156,
0.01763916015625,
0.02154541015625,
0.034149169921875,
0.01050567626953125,
0.02398681640625,
0.0006299018859863281,
-0.01219940185546875,
-0.00592041015625,
-0.0003941059112548828,
-0.0305023193359375,
0.02557373046875,
-0.0244598388671875,
-0.0038051605224609375,
0.00290679931640625,
-0.0045928955078125,
-0.006160736083984375,
-0.0167388916015625,
-0.054656982421875,
0.00140380859375,
-0.0118865966796875,
-0.001506805419921875,
-0.01214599609375,
-0.02362060546875,
0.01168060302734375,
-0.016082763671875,
0.02392578125,
0.0017518997192382812,
-0.016357421875,
0.00933074951171875,
-0.003192901611328125,
0.01033782958984375,
0.0135345458984375,
-0.00664520263671875,
0.0016603469848632812,
-0.0260009765625,
-0.00885772705078125,
0.042633056640625,
-0.007625579833984375,
0.032562255859375,
-0.00847625732421875,
0.019561767578125,
0.0006361007690429688,
-0.00467681884765625,
-0.0142059326171875,
0.0171051025390625,
0.0021076202392578125,
0.003276824951171875,
-0.016693115234375,
-0.01030731201171875,
-0.0199432373046875,
-0.05615234375,
0.01552581787109375,
-0.006610870361328125,
-0.00476837158203125,
0.0100860595703125,
0.0003159046173095703,
-0.022552490234375,
0.0067596435546875,
-0.0311431884765625,
0.0005507469177246094,
0.0026149749755859375,
0.0290679931640625,
-0.043212890625,
0.0032138824462890625,
-0.004268646240234375,
0.0650634765625,
-0.0099029541015625,
0.018890380859375,
0.0189666748046875,
0.09112548828125,
-0.0009407997131347656,
-0.004352569580078125,
0.001003265380859375,
0.016326904296875,
0.0120849609375,
0.001033782958984375,
0.0310821533203125,
-0.0011243820190429688,
-0.032867431640625,
0.00637054443359375,
0.0145721435546875,
-0.005924224853515625,
0.00921630859375,
0.00133514404296875,
-0.006679534912109375,
0.004253387451171875,
0.00876617431640625,
-0.0180511474609375,
0.0257568359375,
0.009796142578125,
-0.0165252685546875,
-0.00539398193359375,
0.004730224609375,
-0.0106658935546875,
0.00731658935546875,
-0.0033435821533203125,
-0.00634765625,
0.023193359375,
-0.017913818359375,
-0.05126953125,
-0.0131683349609375,
0.00408935546875,
0.01279449462890625,
-0.0136260986328125,
-0.00392913818359375,
0.0093536376953125,
-0.0010585784912109375,
0.01412200927734375,
0.020782470703125,
0.009613037109375,
0.004657745361328125,
0.04229736328125,
0.01409912109375,
-0.001708984375,
-0.02569580078125,
-0.01087188720703125,
0.0258331298828125,
-0.022369384765625,
0.01629638671875,
0.0149078369140625,
-0.0106201171875,
0.0036258697509765625,
-0.0272674560546875,
0.0003399848937988281,
0.0101318359375,
0.00021338462829589844,
0.002536773681640625,
-0.0032024383544921875,
-0.0182952880859375,
-0.08221435546875,
0.014007568359375,
-0.004459381103515625,
0.005016326904296875,
-0.00577545166015625,
-0.00931549072265625,
0.01366424560546875,
-0.00566864013671875,
-0.0018281936645507812,
-0.0025577545166015625,
-0.00479888916015625,
-0.0049591064453125,
-0.0035762786865234375,
-0.004791259765625,
0.018524169921875,
-0.0065460205078125,
-0.0128631591796875,
-0.0138092041015625,
0.027008056640625,
-0.007793426513671875,
-0.00989532470703125,
0.01390838623046875,
0.0156402587890625,
0.004795074462890625,
0.01450347900390625,
0.0047454833984375,
0.01125335693359375,
0.0009870529174804688,
0.019256591796875,
-0.006778717041015625,
-0.0008616447448730469,
-0.0043487548828125,
-0.01503753662109375,
0.0217132568359375,
-0.0213470458984375,
0.0181121826171875,
0.002086639404296875,
0.0022678375244140625,
-0.02520751953125,
0.005496978759765625,
-0.01739501953125,
-0.00925445556640625,
-0.02325439453125,
0.03570556640625,
-0.007625579833984375,
0.00872802734375,
0.004791259765625,
-0.056304931640625,
-0.004268646240234375,
-0.002162933349609375,
-0.0086822509765625,
-0.0240325927734375,
0.00005519390106201172,
0.00891876220703125,
0.01898193359375,
0.0248260498046875,
-0.0447998046875,
0.0177154541015625,
-0.0084381103515625,
0.0125732421875,
-0.00850677490234375,
-0.005458831787109375,
-0.01445770263671875,
0.0124359130859375,
-0.0165557861328125,
0.016876220703125,
0.0034694671630859375,
-0.01007843017578125,
0.00746917724609375,
-0.00311279296875,
0.0080108642578125,
-0.01544189453125,
0.01050567626953125,
-0.0018301010131835938,
-0.01142120361328125,
0.0011053085327148438,
0.013397216796875,
0.0122222900390625,
0.003925323486328125,
-0.0028934478759765625,
-0.0076141357421875,
0.00699615478515625,
-0.0099945068359375,
-0.003543853759765625,
-0.01611328125,
0.00926971435546875,
0.0214385986328125,
-0.001125335693359375,
0.00846099853515625,
-0.01399993896484375,
0.00872802734375,
0.007343292236328125,
-0.0071258544921875,
-0.005615234375,
-0.00922393798828125,
0.006702423095703125,
-0.0024280548095703125,
-0.0015535354614257812,
-0.0012140274047851562,
0.00127410888671875,
0.0072784423828125,
-0.01447296142578125,
-0.036773681640625,
-0.0107421875,
0.01366424560546875,
-0.0023937225341796875,
0.045379638671875,
-0.006069183349609375,
-0.0032253265380859375,
-0.004547119140625,
-0.006687164306640625,
0.0045318603515625,
0.0081024169921875,
-0.008636474609375,
0.0006165504455566406,
-0.0077667236328125,
-0.01186370849609375,
0.0160064697265625,
0.002788543701171875,
-0.0070343017578125,
-0.0186004638671875,
-0.00246429443359375,
0.005382537841796875,
-0.0017461776733398438,
-0.0196990966796875,
0.027252197265625,
-0.0097198486328125,
-0.0311279296875,
0.00395965576171875,
-0.015838623046875,
-0.015960693359375,
0.0216522216796875,
0.035919189453125,
-0.003795623779296875,
0.01153564453125,
-0.003688812255859375,
0.0233001708984375,
-0.016937255859375,
-0.0177764892578125,
0.01407623291015625,
0.00885009765625,
0.0023708343505859375,
-0.0117645263671875,
0.009796142578125,
0.0227813720703125,
0.0045623779296875,
0.01617431640625,
-0.01088714599609375,
-0.04833984375,
0.01313018798828125,
-0.004459381103515625,
0.0305328369140625,
0.0257110595703125,
-0.0099945068359375,
-0.0088653564453125,
0.0086669921875,
0.01210784912109375,
-0.01396942138671875,
-0.010040283203125,
-0.0064544677734375,
0.06494140625,
-0.032623291015625,
-0.0030689239501953125,
0.0274658203125,
0.026702880859375,
0.0001569986343383789,
0.046539306640625,
-0.0022068023681640625,
-0.00787353515625,
-0.021575927734375,
0.0017833709716796875,
-0.00476837158203125,
0.004894256591796875,
-0.0137176513671875,
0.00255584716796875,
-0.004238128662109375,
0.024078369140625,
-0.0123138427734375,
0.004119873046875,
-0.003688812255859375,
-0.0207977294921875,
-0.048980712890625,
0.0019092559814453125,
0.0058746337890625,
-0.0277862548828125,
0.034820556640625,
0.0092620849609375,
-0.0010576248168945312,
-0.036285400390625,
0.0203094482421875,
0.03912353515625,
0.00359344482421875,
0.00030875205993652344,
0.0013036727905273438,
-0.0086669921875,
0.00045943260192871094,
-0.046142578125,
-0.0031147003173828125,
0.00323486328125,
-0.0287933349609375,
-0.001628875732421875,
0.0101776123046875,
0.0006337165832519531,
0.003448486328125,
-0.01335906982421875,
0.0065765380859375,
0.032501220703125,
-0.0271453857421875,
0.018310546875,
-0.0158233642578125,
-0.004718780517578125,
0.0091400146484375,
-0.0097503662109375,
0.0019283294677734375,
-0.012420654296875,
-0.035858154296875,
0.02117919921875,
0.00791168212890625,
0.03436279296875,
-0.005336761474609375,
-0.01070404052734375,
0.0148162841796875,
0.0088653564453125,
0.0214691162109375,
-0.00691986083984375,
0.010894775390625,
-0.00020503997802734375,
-0.00400543212890625,
-0.01617431640625,
-0.0304412841796875,
-0.006145477294921875,
0.0025653839111328125,
-0.0225982666015625,
0.01009368896484375,
-0.0194091796875,
0.0208282470703125,
0.002933502197265625,
0.0333251953125,
0.0200958251953125,
-0.0027866363525390625,
0.02069091796875,
0.0007262229919433594,
0.007144927978515625,
0.0113372802734375,
0.01491546630859375,
-0.001430511474609375,
0.01160430908203125,
0.003955841064453125,
-0.021484375,
0.00788116455078125,
-0.0013942718505859375,
0.01091766357421875,
-0.007598876953125,
-0.01084136962890625,
-0.046875,
0.019744873046875,
-0.00899505615234375,
-0.0005421638488769531,
-0.01096343994140625,
-0.0232391357421875,
-0.0038700103759765625,
-0.046722412109375,
0.0002999305725097656,
0.0088348388671875,
0.0093841552734375,
-0.0364990234375,
-0.023895263671875,
0.0162353515625,
-0.03240966796875,
-0.039337158203125,
-0.00528717041015625,
-0.0272674560546875,
-0.02813720703125,
0.0256805419921875,
-0.0307159423828125,
0.01141357421875,
0.0017795562744140625,
-0.0206146240234375,
-0.01445770263671875,
0.0004286766052246094,
-0.045166015625,
0.004425048828125,
0.0220489501953125,
0.005702972412109375,
-0.0100860595703125,
-0.007450103759765625,
-0.002033233642578125,
-0.03326416015625,
0.021575927734375,
-0.006404876708984375,
0.005184173583984375,
0.04779052734375,
-0.042633056640625,
0.0297088623046875,
-0.01442718505859375,
-0.01427459716796875,
0.02728271484375,
-0.001232147216796875,
-0.034332275390625,
0.00841522216796875,
0.005157470703125,
0.02703857421875,
0.0160675048828125,
0.01654052734375,
-0.01155853271484375,
0.01049041748046875,
-0.03424072265625,
-0.014862060546875,
0.00894927978515625,
0.0171661376953125,
-0.01035308837890625,
0.005413055419921875,
-0.002063751220703125,
-0.0017538070678710938,
-0.0010347366333007812,
-0.00974273681640625,
-0.006076812744140625,
-0.01324462890625,
0.011016845703125,
-0.0182037353515625,
-0.0031070709228515625,
0.0227203369140625,
0.0166168212890625,
-0.008575439453125,
-0.021728515625,
0.00986480712890625,
-0.00347900390625,
0.0030364990234375,
0.018524169921875,
0.0306243896484375,
-0.00708770751953125,
0.01451873779296875,
-0.0272674560546875,
0.03863525390625,
0.0227203369140625,
0.0108489990234375,
-0.017730712890625,
-0.014739990234375,
0.00687408447265625,
-0.0116729736328125,
-0.06671142578125,
0.024139404296875,
-0.0089874267578125,
0.022613525390625,
-0.0261993408203125,
0.0244293212890625,
0.03338623046875,
0.002880096435546875,
-0.048004150390625,
-0.04791259765625,
0.0033397674560546875,
0.0223388671875,
0.01123046875,
0.0122528076171875,
0.0187530517578125,
-0.0202789306640625,
0.0191497802734375,
0.07305908203125,
-0.0364990234375,
0.0010461807250976562,
-0.0239105224609375,
-0.00894927978515625,
0.01480865478515625,
0.0017213821411132812,
0.0016241073608398438,
-0.004817962646484375,
0.03704833984375,
-0.0316162109375,
-0.0028400421142578125,
-0.00911712646484375,
0.01074981689453125,
0.0132293701171875,
0.0296630859375,
0.0066986083984375,
0.00272369384765625,
-0.0170745849609375,
0.0171051025390625,
0.0156707763671875,
0.0285491943359375,
-0.029205322265625,
0.0149993896484375,
0.0233154296875,
0.0274505615234375,
-0.035308837890625,
0.004093170166015625,
0.02740478515625,
-0.0211639404296875,
0.021820068359375,
0.0164947509765625,
-0.00439453125,
0.04388427734375,
0.0294647216796875,
0.0016660690307617188,
0.00328826904296875,
-0.00009053945541381836,
0.0234375,
-0.0187530517578125,
-0.021514892578125,
-0.005451202392578125,
-0.01206207275390625,
-0.06591796875,
0.002513885498046875,
-0.02557373046875,
-0.0178375244140625,
0.019378662109375,
0.02069091796875,
0.0017881393432617188,
-0.0323486328125,
0.0301971435546875,
-0.01554107666015625,
-0.007755279541015625,
0.0179443359375,
-0.0031223297119140625,
0.025390625,
-0.0477294921875,
0.00849151611328125,
0.017303466796875,
0.01418304443359375,
-0.02203369140625,
0.003978729248046875,
0.014739990234375,
-0.00885009765625,
0.0007762908935546875,
0.0117034912109375,
0.0014715194702148438,
0.01374053955078125,
0.03985595703125,
-0.02227783203125,
0.0267333984375,
0.0168609619140625,
0.01200103759765625,
-0.0215911865234375,
0.003475189208984375,
-0.017303466796875,
0.01267242431640625,
-0.033447265625,
0.003505706787109375,
-0.0196990966796875,
-0.0286712646484375,
-0.01464080810546875,
0.060760498046875,
-0.01522064208984375,
-0.0061187744140625,
-0.0052490234375,
0.0599365234375,
-0.02001953125,
0.04046630859375,
0.01160430908203125,
0.018402099609375,
-0.0146331787109375,
0.0239715576171875,
0.0025482177734375,
-0.0009584426879882812,
-0.00482177734375,
0.007694244384765625,
-0.01312255859375,
-0.01580810546875,
-0.00018739700317382812,
0.0231475830078125,
-0.0160980224609375,
0.033721923828125,
-0.0160064697265625,
0.01276397705078125,
-0.002559661865234375,
-0.0096435546875,
0.011810302734375,
0.03155517578125,
0.01322174072265625,
-0.03497314453125,
0.041778564453125,
-0.023040771484375,
0.0079498291015625,
-0.0185699462890625,
0.0157470703125,
0.00911712646484375,
0.00762176513671875,
-0.0117034912109375,
-0.0187835693359375,
-0.0033245086669921875,
0.00937652587890625,
-0.0008292198181152344,
0.0149688720703125,
-0.0032501220703125,
-0.0021724700927734375,
0.0268707275390625,
-0.02301025390625,
0.0251617431640625,
-0.017852783203125,
-0.00652313232421875,
0.031494140625,
-0.0252685546875,
-0.00545501708984375,
-0.0014667510986328125,
-0.0146636962890625,
0.02911376953125,
0.006679534912109375,
-0.010467529296875,
0.0163116455078125,
-0.00791168212890625,
-0.0272216796875,
-0.0218963623046875,
-0.00147247314453125,
0.0122222900390625,
0.021270751953125,
-0.008697509765625,
-0.0015277862548828125,
0.01983642578125,
0.002956390380859375,
0.0350341796875,
-0.042877197265625,
-0.024993896484375,
0.0125579833984375,
0.004428863525390625,
0.0029354095458984375,
-0.035064697265625,
0.018280029296875,
-0.0279541015625,
-0.015869140625,
-0.00847625732421875,
0.024658203125,
-0.002696990966796875,
-0.020233154296875,
-0.0015211105346679688,
-0.019561767578125,
0.01690673828125,
-0.014923095703125,
0.0016689300537109375,
-0.0159759521484375,
0.032012939453125,
-0.002777099609375,
-0.048675537109375,
-0.01303863525390625,
0.017425537109375,
-0.0256500244140625,
0.030487060546875,
-0.0170745849609375,
0.01329803466796875,
-0.041778564453125,
0.0286407470703125,
0.0111236572265625,
-0.0184326171875,
0.011627197265625,
0.0006127357482910156,
-0.0185394287109375,
0.01543426513671875,
0.00591278076171875,
-0.000949859619140625,
0.017669677734375,
0.0115966796875,
-0.0023899078369140625,
0.0008244514465332031,
0.01158905029296875,
0.0101470947265625,
0.0199737548828125,
0.04547119140625,
0.0033969879150390625,
-0.023834228515625,
-0.0028533935546875,
-0.02447509765625,
-0.010009765625,
-0.0282135009765625,
-0.020721435546875,
0.0012655258178710938,
-0.01042938232421875,
-0.013641357421875,
-0.0296783447265625,
0.00595855712890625,
-0.021453857421875,
0.02587890625,
-0.00856781005859375,
-0.0195770263671875,
-0.003482818603515625,
0.004291534423828125,
0.0128021240234375,
-0.0204620361328125,
0.027191162109375,
-0.0186767578125,
-0.0213470458984375,
-0.032379150390625,
0.0117645263671875,
-0.0228271484375,
-0.0248870849609375,
-0.0246429443359375,
-0.0175323486328125,
0.00732421875,
0.0167083740234375,
-0.002544403076171875,
0.015869140625,
-0.00971221923828125,
-0.0079193115234375,
0.04583740234375,
0.0075836181640625,
-0.002681732177734375,
-0.025787353515625,
-0.006160736083984375,
0.0076141357421875,
0.0236358642578125,
0.0031490325927734375,
0.007183074951171875,
0.029327392578125,
0.0172576904296875,
-0.006671905517578125,
-0.0113983154296875,
-0.0228118896484375,
-0.023712158203125,
0.0195159912109375,
0.02764892578125,
0.00202178955078125,
0.007213592529296875,
0.0106964111328125,
0.007770538330078125,
-0.009033203125,
-0.00464630126953125,
-0.0251617431640625,
-0.01468658447265625,
-0.0140228271484375,
-0.0017795562744140625,
-0.0227203369140625,
-0.004123687744140625,
-0.049102783203125,
-0.0265655517578125,
-0.0003533363342285156,
-0.006061553955078125,
-0.0197601318359375,
0.00925445556640625,
0.01216888427734375,
0.0026569366455078125,
-0.0293426513671875,
0.009674072265625,
-0.006931304931640625,
0.01438140869140625,
-0.02130126953125,
-0.0227508544921875,
-0.03094482421875,
-0.053436279296875,
0.027435302734375,
-0.01812744140625,
0.00281524658203125,
-0.0222625732421875,
-0.01554107666015625,
-0.002040863037109375,
0.00922393798828125,
-0.05120849609375,
0.02001953125,
0.02862548828125,
0.0009298324584960938,
0.022796630859375,
0.0211181640625,
-0.003925323486328125,
-0.009918212890625,
0.00420379638671875,
0.005847930908203125,
-0.0210418701171875,
-0.0007076263427734375,
0.0203857421875,
-0.00608062744140625,
0.01263427734375,
-0.0026874542236328125,
0.0288543701171875,
0.003101348876953125,
0.0050506591796875,
-0.0073394775390625,
-0.0247344970703125,
-0.0188140869140625,
0.005588531494140625,
-0.0225830078125,
-0.024261474609375,
-0.0205535888671875,
-0.0010633468627929688,
-0.00055694580078125,
0.02484130859375,
0.0010709762573242188,
0.003955841064453125,
0.006679534912109375,
-0.02081298828125,
0.0252227783203125,
0.00881195068359375,
-0.033660888671875,
-0.0009436607360839844,
-0.006927490234375,
0.01349639892578125,
-0.00850677490234375,
-0.01250457763671875,
0.0181427001953125,
0.026092529296875,
0.031982421875,
0.0006842613220214844,
0.037139892578125,
0.01528167724609375,
-0.0252838134765625,
-0.01448822021484375,
-0.01025390625,
-0.0341796875,
0.0162811279296875,
0.02496337890625,
-0.007686614990234375,
0.0237884521484375,
-0.0167694091796875,
-0.02764892578125,
-0.0273590087890625,
-0.02362060546875,
-0.0010738372802734375,
0.00704193115234375,
-0.00493621826171875,
-0.006938934326171875,
0.005126953125,
-0.0035839080810546875,
0.0048675537109375,
0.0217437744140625,
0.026397705078125,
0.0145416259765625,
-0.0171356201171875,
0.005695343017578125,
0.0151519775390625,
0.00917816162109375,
-0.016143798828125,
0.01171875,
0.0022449493408203125,
-0.0400390625,
-0.019439697265625,
-0.032501220703125,
-0.0177459716796875,
0.0211181640625,
0.0027866363525390625,
-0.035003662109375,
0.0190887451171875,
0.005382537841796875,
-0.00423431396484375,
0.0196685791015625,
0.004024505615234375,
0.01739501953125,
-0.0004544258117675781,
0.01873779296875,
-0.039764404296875,
0.0440673828125,
-0.006496429443359375,
0.024322509765625,
-0.021026611328125,
0.004669189453125,
0.03057861328125,
0.0134735107421875,
0.045623779296875,
0.01751708984375,
0.045196533203125,
-0.0073089599609375,
-0.0282440185546875,
0.021087646484375,
-0.0219573974609375,
-0.0305023193359375,
-0.0335693359375,
0.00620269775390625,
0.0002009868621826172,
-0.0029621124267578125,
-0.00921630859375,
-0.0235748291015625,
-0.002140045166015625,
0.006214141845703125,
-0.01026153564453125,
-0.018310546875,
0.00029754638671875,
-0.004302978515625,
-0.01557159423828125,
-0.0162506103515625,
0.015625,
-0.00997161865234375,
-0.031463623046875,
-0.0007781982421875,
0.03216552734375,
0.014312744140625,
-0.0195159912109375,
-0.0127716064453125,
-0.0220794677734375,
-0.0200042724609375,
0.01166534423828125,
-0.019439697265625,
-0.00479888916015625,
-0.0345458984375,
-0.004642486572265625,
0.0152740478515625,
-0.005397796630859375,
0.0026645660400390625,
0.01340484619140625,
-0.00567626953125,
-0.03240966796875,
-0.00838470458984375,
0.01302337646484375,
0.0246429443359375,
-0.028594970703125,
-0.00848388671875,
-0.007049560546875,
0.0274505615234375,
-0.034698486328125,
-0.0083770751953125,
0.0193328857421875,
-0.03692626953125,
0.0166168212890625,
-0.0021686553955078125,
0.006221771240234375,
-0.02313232421875,
-0.03814697265625,
0.016571044921875,
0.0015287399291992188,
-0.0125732421875,
-0.017120361328125,
0.01102447509765625,
-0.01277923583984375,
-0.005641937255859375,
-0.0004673004150390625,
0.0086669921875,
-0.0007500648498535156,
0.04071044921875,
0.02490234375,
0.01113128662109375,
0.0231475830078125,
-0.00447845458984375,
0.0025310516357421875,
-0.007289886474609375,
-0.01392364501953125,
-0.0169525146484375,
0.0170440673828125,
-0.0179443359375,
-0.0152130126953125,
0.005878448486328125,
0.00144195556640625,
0.0092620849609375,
0.0103912353515625,
0.002269744873046875,
0.020477294921875,
-0.024871826171875,
-0.0196075439453125,
-0.0022411346435546875,
0.020538330078125,
0.0124359130859375,
0.0341796875,
0.01386260986328125,
0.0004303455352783203,
0.001987457275390625,
0.017822265625,
-0.0164337158203125,
-0.038116455078125,
0.0035266876220703125,
0.01390838623046875,
0.00850677490234375,
0.034515380859375,
0.0343017578125,
-0.0032978057861328125,
-0.06060791015625,
-0.01482391357421875,
-0.0169677734375,
-0.042236328125,
-0.001293182373046875,
-0.002422332763671875,
0.01413726806640625,
-0.006038665771484375,
0.02496337890625,
-0.006214141845703125,
0.02008056640625,
0.01322174072265625,
-0.0154571533203125,
-0.0131378173828125,
-0.003925323486328125,
0.003917694091796875,
-0.009429931640625,
-0.007415771484375,
-0.0022258758544921875,
0.001373291015625,
-0.0081787109375,
-0.004291534423828125,
0.005207061767578125,
0.016815185546875,
0.01140594482421875,
-0.00200653076171875,
0.0258026123046875,
0.009185791015625,
-0.005016326904296875,
-0.01220703125,
-0.0012006759643554688,
0.0125885009765625,
0.0044708251953125,
0.034698486328125,
-0.00321197509765625,
0.03607177734375,
0.003871917724609375,
0.0091400146484375,
-0.03887939453125,
0.01508331298828125,
0.005344390869140625,
-0.0234375,
-0.0015850067138671875,
-0.03173828125,
-0.0092620849609375,
0.0167083740234375,
-0.032012939453125,
-0.00860595703125,
0.019317626953125,
0.0247650146484375,
-0.00440216064453125,
-0.02020263671875,
0.00033020973205566406,
-0.041107177734375,
0.01470184326171875,
-0.02203369140625,
-0.0150299072265625,
-0.042388916015625,
0.05584716796875,
0.005970001220703125,
-0.0016546249389648438,
0.01235198974609375,
0.036956787109375,
0.0002741813659667969,
-0.005657196044921875,
-0.0013360977172851562,
-0.008392333984375,
0.04254150390625,
-0.0184173583984375,
0.00788116455078125,
-0.0022258758544921875,
-0.01064300537109375,
-0.01482391357421875,
0.0111083984375,
0.007232666015625,
0.0275421142578125,
0.0362548828125,
-0.0110931396484375,
-0.0092010498046875,
0.0008597373962402344,
0.0195159912109375,
-0.01189422607421875,
0.006656646728515625,
-0.032196044921875,
0.0291595458984375,
-0.0012874603271484375,
-0.0012807846069335938,
-0.015228271484375,
-0.02142333984375,
0.0183868408203125,
-0.030670166015625,
-0.0034885406494140625,
-0.0011463165283203125,
-0.0017147064208984375,
0.0006237030029296875,
-0.00015163421630859375,
0.00940704345703125,
-0.040679931640625,
0.0235595703125,
0.01412200927734375,
0.0157928466796875,
-0.0052642822265625,
-0.04473876953125,
0.0257415771484375,
0.01340484619140625,
0.0187530517578125,
-0.01374053955078125,
-0.0161590576171875,
-0.0027027130126953125,
-0.006992340087890625,
-0.00824737548828125,
0.009063720703125,
0.0047149658203125,
-0.0009074211120605469,
0.005290985107421875,
0.0026187896728515625,
0.0264739990234375,
-0.007305145263671875,
0.0091552734375,
-0.0275115966796875,
0.00568389892578125,
0.04742431640625,
0.0034999847412109375,
-0.03045654296875,
0.00750732421875,
0.00144195556640625,
-0.01611328125,
0.0158233642578125,
-0.00213623046875,
-0.0288543701171875,
-0.00937652587890625,
0.019622802734375,
0.0166473388671875,
0.0362548828125,
0.00501251220703125,
-0.008880615234375,
-0.0567626953125,
-0.0222015380859375,
0.0060577392578125,
-0.01629638671875,
0.01372528076171875,
0.0034160614013671875,
-0.006549835205078125,
0.00511932373046875,
0.031982421875,
0.01461029052734375,
0.007221221923828125,
-0.004581451416015625,
-0.00833892822265625,
0.00865936279296875,
0.029205322265625,
-0.0021610260009765625,
-0.002197265625,
-0.00995635986328125,
-0.00640869140625,
0.009124755859375,
-0.006458282470703125,
-0.023223876953125,
0.021087646484375,
-0.003894805908203125,
-0.0020923614501953125,
-0.0085906982421875,
0.023590087890625,
-0.00809478759765625,
-0.007183074951171875,
-0.035369873046875,
-0.04345703125,
-0.014068603515625,
0.033782958984375,
0.0245361328125,
-0.0086822509765625,
0.0094757080078125,
-0.0008568763732910156,
0.0115509033203125,
0.0031452178955078125,
-0.004444122314453125,
-0.0294647216796875,
-0.0014390945434570312,
0.007442474365234375,
0.0066375732421875,
0.00597381591796875,
-0.0236968994140625,
-0.0153045654296875,
0.0269622802734375,
-0.00408935546875,
0.006900787353515625,
0.0074615478515625,
0.0158538818359375,
-0.0264434814453125,
0.04400634765625,
-0.02740478515625,
-0.007305145263671875,
0.01512908935546875,
0.0154876708984375,
-0.0204315185546875,
0.006465911865234375,
-0.01465606689453125,
-0.00940704345703125,
-0.01418304443359375,
-0.0051116943359375,
-0.03125,
0.00528717041015625,
0.0284423828125,
-0.020721435546875,
-0.0037670135498046875,
0.015869140625,
-0.0299530029296875,
0.022247314453125,
-0.0323486328125,
-0.0104827880859375,
-0.0040740966796875,
0.027740478515625,
-0.0156097412109375,
-0.01544952392578125,
-0.01166534423828125,
0.010345458984375,
-0.02618408203125,
-0.0185699462890625,
-0.02349853515625,
-0.003459930419921875,
-0.0020389556884765625,
-0.032745361328125,
-0.0310516357421875,
-0.00701141357421875,
0.0276031494140625,
0.01279449462890625,
-0.0019893646240234375,
0.011810302734375,
0.00576019287109375,
0.0151519775390625,
-0.0027828216552734375,
-0.019378662109375,
0.01027679443359375,
-0.036590576171875,
0.04931640625,
-0.0130462646484375,
-0.002971649169921875,
0.0268707275390625,
-0.0181427001953125,
-0.0098419189453125,
-0.0006422996520996094,
0.018768310546875,
0.0224609375,
-0.01425933837890625,
-0.0119781494140625,
-0.01010894775390625,
0.0024585723876953125,
0.0275115966796875,
-0.0216522216796875,
0.005283355712890625,
0.0121917724609375,
0.0217437744140625,
0.0091400146484375,
0.006099700927734375,
0.0011243820190429688,
-0.016143798828125,
-0.016571044921875,
0.0040283203125,
-0.0047149658203125,
0.03680419921875,
-0.00750732421875,
0.01666259765625,
-0.00806427001953125,
-0.0311737060546875,
0.0085906982421875,
-0.01207733154296875,
-0.00814056396484375,
-0.03424072265625,
-0.027587890625,
0.0201416015625,
-0.0035552978515625,
0.0185394287109375,
0.001918792724609375,
0.003387451171875,
-0.0007796287536621094,
-0.03717041015625,
0.009765625,
-0.0173797607421875,
-0.0192413330078125,
-0.011077880859375,
-0.01358795166015625,
-0.0214691162109375,
0.00774383544921875,
-0.0013360977172851562,
-0.01177978515625,
-0.01192474365234375,
-0.01520538330078125,
0.017303466796875,
0.010223388671875,
0.0265960693359375,
0.0057830810546875,
0.0016374588012695312,
-0.00740814208984375,
0.018463134765625,
0.01222991943359375,
0.0075836181640625,
-0.01348876953125,
-0.02838134765625,
0.0149993896484375,
0.0007848739624023438,
-0.0086669921875,
0.007556915283203125,
0.03497314453125,
-0.0021820068359375,
-0.02484130859375,
-0.020416259765625,
-0.00372314453125,
0.018829345703125,
-0.0219879150390625,
0.006195068359375,
0.0222930908203125,
0.01242828369140625,
-0.004032135009765625,
0.0310821533203125,
-0.0028076171875,
-0.0175323486328125,
0.0162353515625,
0.00733184814453125,
0.032562255859375,
-0.0025157928466796875,
-0.00421142578125,
-0.0158538818359375,
0.0174560546875,
0.004306793212890625,
-0.0029697418212890625,
0.002353668212890625,
0.006053924560546875,
0.0021991729736328125,
-0.01224517822265625,
-0.0177001953125,
0.0046539306640625,
0.0236358642578125,
0.018157958984375,
0.0086212158203125,
0.03875732421875,
-0.00955963134765625,
0.0258331298828125,
0.00725555419921875,
-0.029510498046875,
-0.0005245208740234375,
-0.0214996337890625,
0.0252532958984375,
-0.005672454833984375,
0.002292633056640625,
-0.01462554931640625,
-0.0245819091796875,
-0.0166015625,
0.0144195556640625,
0.00263214111328125,
-0.0145721435546875,
-0.039642333984375,
-0.00743865966796875,
-0.04791259765625,
0.0171051025390625,
-0.01473236083984375,
0.00884246826171875,
0.000823974609375,
0.0306396484375,
-0.006805419921875,
-0.02001953125,
-0.036773681640625,
0.02337646484375,
-0.030792236328125,
-0.047210693359375,
0.0019073486328125,
-0.002197265625,
-0.0264129638671875,
0.00115203857421875,
-0.005237579345703125,
-0.037933349609375,
0.00003421306610107422,
-0.0012226104736328125,
0.0006718635559082031,
0.0289764404296875,
-0.0276031494140625,
-0.00809478759765625,
0.02496337890625,
0.009674072265625,
0.01522064208984375,
0.0077362060546875,
0.0172271728515625,
-0.00968170166015625,
-0.0002694129943847656,
-0.016204833984375,
0.040802001953125,
0.0216064453125,
0.0003757476806640625,
-0.016998291015625,
-0.008453369140625,
-0.026092529296875,
-0.01372528076171875,
-0.003841400146484375,
-0.018463134765625,
0.01763916015625,
-0.00948333740234375,
-0.0089569091796875,
-0.0217742919921875,
-0.01303863525390625,
0.0284423828125,
0.00417327880859375,
0.004642486572265625,
-0.006160736083984375,
-0.0184783935546875,
-0.0548095703125,
0.027496337890625,
0.0024871826171875,
-0.0170135498046875,
0.0064239501953125,
-0.01399993896484375,
-0.00850677490234375,
-0.00623321533203125,
0.0289764404296875,
-0.01180267333984375,
0.0179595947265625,
0.052093505859375,
-0.0008502006530761719,
-0.000682830810546875,
-0.0252227783203125,
-0.0071868896484375,
-0.0159759521484375,
-0.01395416259765625,
0.05078125,
0.032623291015625,
0.024322509765625,
0.001758575439453125,
-0.007686614990234375,
-0.025177001953125,
0.004451751708984375,
-0.0008955001831054688,
-0.005062103271484375,
-0.0280609130859375,
0.007396697998046875,
-0.01441192626953125,
-0.0296173095703125,
0.03399658203125,
-0.043731689453125,
0.025604248046875,
0.005336761474609375,
-0.004497528076171875,
0.0123138427734375,
0.0037937164306640625,
0.0179290771484375,
-0.0256195068359375,
0.0231475830078125,
-0.0110626220703125,
0.0036678314208984375,
0.01551055908203125,
0.004650115966796875,
0.0003094673156738281,
0.01554107666015625,
-0.0302581787109375,
0.0037136077880859375,
-0.0138397216796875,
-0.005336761474609375,
0.025238037109375,
-0.0024261474609375,
0.035491943359375,
0.046112060546875,
0.0214996337890625,
0.0212554931640625,
-0.0203857421875,
-0.01322174072265625,
0.020233154296875,
0.019622802734375,
-0.0243377685546875,
-0.00530242919921875,
0.0240478515625,
0.032928466796875,
-0.0194091796875,
0.019683837890625,
0.004436492919921875,
-0.01800537109375,
-0.027252197265625,
0.0218505859375,
0.022125244140625,
-0.0119476318359375,
0.00923919677734375,
0.0010423660278320312,
-0.00232696533203125,
-0.011749267578125,
-0.02056884765625,
0.016357421875,
-0.0104522705078125,
0.01806640625,
0.0197296142578125,
-0.01824951171875,
-0.023681640625,
0.0013427734375,
-0.003662109375,
-0.022003173828125,
-0.009979248046875,
-0.006656646728515625,
-0.0174407958984375,
0.01372528076171875,
-0.01435089111328125,
-0.00711822509765625,
0.055084228515625,
-0.009552001953125,
0.0018768310546875,
0.00853729248046875,
-0.0019254684448242188,
-0.0030803680419921875,
-0.0203704833984375,
0.001556396484375,
-0.01381683349609375,
-0.00859832763671875,
0.0193023681640625,
0.01239776611328125,
0.00882720947265625,
-0.03436279296875,
-0.0190582275390625,
-0.035614013671875,
0.0052490234375,
0.022216796875,
0.0035457611083984375,
0.007152557373046875,
-0.0263671875,
-0.046539306640625,
-0.0092010498046875,
-0.0282745361328125,
0.02642822265625,
-0.002521514892578125,
0.00276947021484375,
-0.0034942626953125,
0.0233001708984375,
-0.02996826171875,
-0.005283355712890625,
0.0238189697265625,
-0.016937255859375,
-0.0189666748046875,
0.00907135009765625,
-0.018646240234375,
-0.00521087646484375,
0.0017118453979492188,
-0.035614013671875,
-0.01244354248046875,
0.01361846923828125,
-0.018035888671875,
0.01502227783203125,
-0.0160980224609375,
-0.004116058349609375,
-0.0249786376953125,
0.004177093505859375,
0.006359100341796875,
0.006206512451171875,
-0.02508544921875,
0.0178680419921875,
-0.00634765625,
-0.00403594970703125,
-0.0008864402770996094,
0.001373291015625,
0.00699615478515625,
0.001705169677734375,
0.03570556640625,
-0.0114593505859375,
0.00171661376953125,
-0.00855255126953125,
0.04095458984375,
-0.004749298095703125,
-0.01447296142578125,
0.0205078125,
-0.0282745361328125,
0.00640106201171875,
-0.00010412931442260742,
-0.0157318115234375,
0.0033092498779296875,
0.0010557174682617188,
0.029266357421875,
0.0330810546875,
-0.016815185546875,
0.033294677734375,
-0.006160736083984375,
-0.01555633544921875,
-0.026763916015625,
-0.0164947509765625,
0.018463134765625,
0.046600341796875,
0.006103515625,
0.023345947265625,
-0.039306640625,
0.017852783203125,
0.012451171875,
-0.0154876708984375,
-0.0077972412109375,
0.00946044921875,
-0.01358795166015625,
-0.006633758544921875,
0.0285491943359375,
0.02130126953125,
-0.00018584728240966797,
0.007572174072265625,
0.0108489990234375,
0.009765625,
-0.00614166259765625,
-0.01397705078125,
-0.0102386474609375,
-0.00004118680953979492,
0.004985809326171875,
0.038482666015625,
0.0142059326171875,
-0.01154327392578125,
-0.01323699951171875,
0.026580810546875,
0.00531768798828125,
-0.0030517578125,
0.002483367919921875,
-0.006221771240234375,
0.04437255859375,
-0.01300048828125,
0.006587982177734375,
-0.01226806640625,
0.01235198974609375,
-0.002605438232421875,
0.011749267578125,
0.0290985107421875,
-0.06201171875,
0.0221099853515625,
-0.0377197265625,
0.0281524658203125,
0.028961181640625,
-0.0220489501953125,
-0.01035308837890625,
0.0163421630859375,
0.0018224716186523438,
-0.00321197509765625,
-0.0019855499267578125,
0.004970550537109375,
0.00818634033203125,
0.026580810546875,
-0.0023899078369140625,
-0.002643585205078125,
0.0099029541015625,
-0.0390625,
-0.018829345703125,
-0.020233154296875,
0.02105712890625,
0.000006318092346191406,
0.017730712890625,
-0.0005087852478027344,
0.028961181640625,
0.02593994140625,
-0.01727294921875,
0.016937255859375,
-0.006072998046875,
0.0021953582763671875,
0.003978729248046875,
-0.0128021240234375,
0.03106689453125,
-0.020599365234375,
-0.0250091552734375,
0.0225830078125,
-0.0191650390625,
-0.0107879638671875,
-0.01605224609375,
-0.0036907196044921875,
0.01537322998046875,
-0.0093231201171875,
0.0124053955078125,
-0.00872039794921875,
0.011566162109375,
0.0034923553466796875,
-0.0252685546875,
0.0239715576171875,
-0.0194854736328125,
0.00885772705078125,
0.00006967782974243164,
-0.0295562744140625,
0.01558685302734375,
-0.004070281982421875,
-0.00908660888671875,
-0.006130218505859375,
0.017913818359375,
0.01067352294921875,
0.0007572174072265625,
0.018096923828125,
-0.003452301025390625,
0.01318359375,
-0.01055908203125,
0.02001953125,
-0.0162811279296875,
0.0031223297119140625,
0.039337158203125,
0.0038814544677734375,
0.0174713134765625,
-0.0143585205078125,
0.0295867919921875,
-0.019134521484375,
-0.006237030029296875,
-0.0178070068359375,
0.004962921142578125,
0.01241302490234375,
-0.00852203369140625,
0.01751708984375,
-0.004688262939453125,
-0.0160369873046875,
-0.0271148681640625,
-0.031494140625,
0.00362396240234375,
-0.01105499267578125,
-0.0011348724365234375,
0.0132598876953125,
-0.0184478759765625,
-0.0012712478637695312,
0.0293426513671875,
-0.00917816162109375,
-0.0185089111328125,
-0.03826904296875,
0.005420684814453125,
0.01015472412109375,
0.004344940185546875,
0.0217437744140625,
-0.00484466552734375,
-0.00777435302734375,
0.00971221923828125,
-0.01434326171875,
0.030303955078125,
0.00983428955078125,
0.007663726806640625,
-0.0176544189453125,
0.021820068359375,
-0.01360321044921875,
-0.050323486328125,
0.0031948089599609375,
-0.017425537109375,
0.0247344970703125,
0.025115966796875,
-0.0123748779296875,
0.03143310546875,
-0.01082611083984375,
-0.0145721435546875,
0.019378662109375,
0.01499176025390625,
0.00946807861328125,
0.001163482666015625,
-0.015655517578125,
0.01403045654296875,
0.0231170654296875,
-0.0027217864990234375,
0.005016326904296875,
-0.02740478515625,
0.01276397705078125,
-0.0023975372314453125,
-0.0270233154296875,
-0.01375579833984375,
-0.004901885986328125,
-0.035919189453125,
-0.004825592041015625,
0.0227203369140625,
0.0009474754333496094,
0.0192718505859375,
-0.0265960693359375,
0.032379150390625,
-0.0218505859375,
-0.00927734375,
-0.0049591064453125,
0.00875091552734375,
-0.01238250732421875,
-0.0182647705078125,
-0.0038909912109375,
0.0079193115234375,
-0.01033782958984375,
-0.0019369125366210938,
0.0110931396484375,
0.0253448486328125,
-0.0037021636962890625,
-0.02716064453125,
0.0025177001953125,
0.0229339599609375,
0.0235137939453125,
0.007781982421875,
-0.005725860595703125,
-0.024688720703125,
0.01434326171875,
-0.00426483154296875,
-0.01409912109375,
0.0010738372802734375,
-0.01800537109375,
-0.0240631103515625,
-0.01316070556640625,
0.01117706298828125,
0.0234832763671875,
-0.0374755859375,
0.0210418701171875,
-0.00870513916015625,
-0.0380859375,
0.01446533203125,
0.00496673583984375,
-0.0203857421875,
0.0000073909759521484375,
-0.0215606689453125,
0.0200042724609375,
0.003429412841796875,
-0.0014066696166992188,
-0.0273284912109375,
0.0260009765625,
-0.0268402099609375,
0.0152740478515625,
0.0182647705078125,
-0.020721435546875,
0.0160064697265625,
-0.002777099609375,
0.0244598388671875,
-0.0082550048828125,
0.005855560302734375,
0.0018711090087890625,
-0.0265960693359375,
0.0023040771484375,
-0.01241302490234375,
-0.0303955078125,
0.0028247833251953125,
-0.032135009765625,
0.013153076171875,
-0.0098114013671875,
-0.009674072265625,
-0.01442718505859375,
-0.019287109375,
-0.0002846717834472656,
0.01247406005859375,
-0.0030345916748046875,
0.0243988037109375,
0.020050048828125,
0.0005321502685546875,
-0.0123443603515625,
-0.027313232421875,
0.0246734619140625,
-0.03411865234375,
-0.0187530517578125,
0.0157012939453125,
-0.00385284423828125,
-0.040924072265625,
0.0023212432861328125,
0.05792236328125,
-0.01053619384765625,
-0.0157623291015625,
-0.0140228271484375,
0.0013065338134765625,
-0.01287841796875,
-0.0187835693359375,
-0.0233917236328125,
-0.0005397796630859375,
-0.0289306640625,
0.0252685546875,
-0.01265716552734375,
-0.03125,
-0.00450897216796875,
-0.02178955078125,
0.0020046234130859375,
-0.028564453125,
-0.0004875659942626953,
0.054107666015625,
0.0059661865234375,
0.00795745849609375,
-0.0186309814453125,
-0.006603240966796875,
0.0152130126953125,
-0.0025386810302734375,
-0.0097198486328125,
-0.01421356201171875,
0.0010251998901367188,
-0.01959228515625,
-0.0075531005859375,
0.02056884765625,
0.0023212432861328125,
0.03515625,
0.01316070556640625,
-0.0285186767578125,
-0.0037746429443359375,
0.01004791259765625,
-0.01020050048828125,
0.0205841064453125,
0.0195465087890625,
-0.0139923095703125,
0.016021728515625,
0.01158905029296875,
-0.01418304443359375,
0.040802001953125,
-0.01506805419921875,
0.0258941650390625,
-0.030914306640625,
0.007480621337890625,
-0.017547607421875,
-0.0238037109375,
-0.030181884765625,
0.043670654296875,
0.0014772415161132812,
-0.005268096923828125,
0.01186370849609375,
0.01354217529296875,
0.0107879638671875,
-0.0014638900756835938,
-0.0048065185546875,
-0.03643798828125,
-0.0006756782531738281,
0.002185821533203125,
-0.037017822265625,
0.01171875,
-0.01470184326171875,
-0.0205230712890625,
0.0256195068359375,
0.025543212890625,
-0.002105712890625,
0.038543701171875,
-0.001739501953125,
0.0289154052734375,
-0.01023101806640625,
0.0054779052734375,
-0.0123138427734375,
0.041961669921875,
-0.001995086669921875,
0.031524658203125,
-0.0204925537109375,
0.01049041748046875,
0.0262908935546875,
0.0146942138671875,
0.0191650390625,
-0.0217437744140625,
-0.0183258056640625,
0.02276611328125,
-0.005126953125,
0.007190704345703125,
-0.037689208984375,
0.00669097900390625,
-0.036346435546875,
0.01233673095703125,
-0.0242156982421875,
0.01244354248046875,
-0.006275177001953125,
0.00844573974609375,
-0.021820068359375,
-0.019989013671875,
0.0005631446838378906,
-0.02178955078125,
0.00824737548828125,
-0.0033397674560546875,
-0.036346435546875,
0.010406494140625,
-0.0027027130126953125,
0.03656005859375,
-0.0206298828125,
-0.0062255859375,
-0.00508880615234375,
-0.01161956787109375,
0.025909423828125,
0.007305145263671875,
-0.0001811981201171875,
-0.01078033447265625,
0.005466461181640625,
-0.0220947265625,
0.0212860107421875,
-0.0212249755859375,
0.0184478759765625,
-0.00252532958984375,
0.020233154296875,
-0.037811279296875,
0.0433349609375,
0.00691986083984375,
-0.00789642333984375,
0.035369873046875,
0.0135955810546875,
0.01377105712890625,
0.0179443359375,
-0.011505126953125,
0.0191497802734375,
-0.005870819091796875,
-0.01212310791015625,
-0.012176513671875,
-0.011199951171875,
-0.021484375,
-0.01084136962890625,
-0.021148681640625,
0.002063751220703125,
0.01983642578125,
0.0005326271057128906,
-0.023223876953125,
0.020660400390625,
0.01812744140625,
0.0234527587890625,
-0.00209808349609375,
0.018829345703125,
-0.0244903564453125,
0.0027313232421875,
-0.0118255615234375,
-0.04168701171875,
-0.04693603515625,
-0.019134521484375,
0.01381683349609375,
0.0192413330078125,
-0.041748046875,
0.033477783203125,
-0.01010894775390625,
-0.0279998779296875,
0.022674560546875,
-0.0240936279296875,
0.009307861328125,
0.0124053955078125,
-0.019622802734375,
0.016998291015625,
0.036651611328125,
-0.0020198822021484375,
0.00011241436004638672,
0.0017690658569335938,
-0.0016889572143554688,
-0.02734375,
0.0003876686096191406,
0.0307159423828125,
-0.0288848876953125,
-0.00951385498046875,
-0.0031414031982421875,
0.00931549072265625,
0.026611328125,
0.01373291015625,
-0.0021266937255859375,
0.0224151611328125,
0.01885986328125,
-0.023895263671875,
-0.0018281936645507812,
0.01305389404296875,
0.0609130859375,
-0.00717926025390625,
-0.03375244140625,
-0.01322174072265625,
0.01366424560546875,
0.02593994140625,
-0.01322174072265625,
0.0106353759765625,
0.0238800048828125,
-0.0191192626953125,
0.015899658203125,
-0.001712799072265625,
-0.03143310546875,
0.01366424560546875,
-0.005340576171875,
-0.0088958740234375,
0.0002899169921875,
-0.01021575927734375,
0.033416748046875,
-0.02935791015625,
-0.006168365478515625,
-0.0175933837890625,
-0.007572174072265625,
-0.01476287841796875,
-0.018829345703125,
0.007717132568359375,
-0.0309295654296875,
0.00460052490234375,
0.006633758544921875,
-0.0021209716796875,
0.01495361328125,
-0.0015535354614257812,
0.02001953125,
-0.01312255859375,
-0.0007686614990234375,
0.0526123046875,
0.0193634033203125,
0.01448822021484375,
0.01326751708984375,
0.01540374755859375,
0.0210113525390625,
0.00370025634765625,
-0.00936126708984375,
-0.0020999908447265625,
-0.017791748046875,
0.0107879638671875,
0.0082550048828125,
-0.0130462646484375,
-0.0244598388671875,
0.034912109375,
0.017791748046875,
0.0014657974243164062,
0.023651123046875,
0.0007033348083496094,
0.01120758056640625,
0.019439697265625,
0.02667236328125,
-0.037445068359375,
-0.022216796875,
0.0128936767578125,
-0.0015621185302734375,
0.008331298828125,
0.0258636474609375,
0.0062255859375,
0.025604248046875,
0.0211029052734375,
-0.02154541015625,
-0.0006728172302246094,
0.0091705322265625,
-0.010162353515625,
0.01525115966796875,
0.01444244384765625,
0.00010269880294799805,
0.01788330078125,
-0.00188446044921875,
-0.0234832763671875,
-0.0046539306640625,
0.026275634765625,
-0.019744873046875,
-0.0159912109375,
0.06854248046875,
-0.003131866455078125,
0.02392578125,
-0.02947998046875,
0.007415771484375,
0.0160675048828125,
0.01480865478515625,
0.0077972412109375,
-0.0321044921875,
0.01311492919921875,
-0.00868988037109375,
0.038238525390625,
-0.02203369140625,
-0.03265380859375,
-0.011993408203125,
0.0285186767578125,
0.0234832763671875,
-0.005908966064453125,
-0.0079803466796875,
0.0018224716186523438,
0.0125579833984375,
0.01006317138671875,
-0.02032470703125,
-0.00693511962890625,
-0.007518768310546875,
-0.0136566162109375,
0.00824737548828125,
-0.01416778564453125,
0.0031871795654296875,
-0.03826904296875,
-0.030853271484375,
0.01605224609375,
0.0269775390625,
0.01139068603515625,
-0.015716552734375,
0.0308685302734375,
-0.019378662109375,
0.03460693359375,
0.024810791015625,
0.0155029296875,
-0.0186614990234375,
0.00942230224609375,
0.01666259765625,
0.0299072265625,
0.005443572998046875,
-0.0099029541015625,
-0.01045989990234375,
-0.0014591217041015625,
0.00174713134765625,
-0.0007081031799316406,
0.0262451171875,
-0.00879669189453125,
-0.0023670196533203125,
0.0158233642578125,
0.022308349609375,
-0.01934814453125,
-0.037872314453125,
-0.010650634765625,
-0.0142059326171875,
0.0049285888671875,
-0.004123687744140625,
-0.00957489013671875,
0.028533935546875,
0.01519012451171875,
0.03094482421875,
0.01331329345703125,
0.02020263671875,
0.0158843994140625,
0.0167999267578125,
0.0088653564453125,
0.02294921875,
0.00292205810546875,
-0.04547119140625,
-0.0190277099609375,
0.0004239082336425781,
-0.0157318115234375,
-0.0184783935546875,
0.04010009765625,
-0.00910186767578125,
0.0095367431640625,
-0.021392822265625,
0.02117919921875,
0.0291290283203125,
0.0189361572265625,
-0.00756072998046875,
0.0032196044921875,
-0.0007047653198242188,
-0.024749755859375,
-0.018035888671875,
0.003177642822265625,
0.0032634735107421875,
0.046478271484375,
0.007083892822265625,
0.01270294189453125,
0.01209259033203125,
-0.02484130859375,
0.01258087158203125,
-0.041748046875,
-0.0167999267578125,
0.0035858154296875,
0.04058837890625,
-0.00981903076171875,
0.00604248046875,
-0.016387939453125,
0.0092010498046875,
-0.0296630859375,
0.04620361328125,
-0.021270751953125,
0.01500701904296875,
0.003448486328125,
-0.0099029541015625,
-0.00811767578125,
-0.01448822021484375,
0.01256561279296875,
-0.017578125,
0.023162841796875,
-0.0026912689208984375,
-0.010711669921875,
-0.0017747879028320312,
0.0170440673828125,
0.01493072509765625,
-0.01004791259765625,
-0.0008220672607421875,
0.002552032470703125,
0.007801055908203125,
-0.0114898681640625,
-0.00507354736328125,
-0.0160064697265625,
-0.01464080810546875,
0.01114654541015625,
0.003582000732421875,
-0.007534027099609375,
0.01039886474609375,
-0.01129150390625,
0.0222930908203125,
-0.01290130615234375,
0.028564453125,
-0.0087127685546875,
-0.039276123046875,
0.00811004638671875,
-0.0212249755859375,
0.012603759765625,
0.01380157470703125,
-0.004611968994140625,
0.0166778564453125,
0.057952880859375,
0.01898193359375,
0.0295867919921875,
-0.004962921142578125,
0.00732421875,
0.01715087890625,
-0.003307342529296875,
0.01451873779296875,
0.004283905029296875,
0.00861358642578125,
0.006916046142578125,
-0.027252197265625,
-0.005535125732421875,
-0.000027894973754882812,
-0.0017490386962890625,
-0.0123138427734375,
-0.022979736328125,
0.007534027099609375,
-0.004825592041015625,
0.02740478515625,
-0.022613525390625,
0.057586669921875,
0.002368927001953125,
0.004878997802734375,
0.025909423828125,
-0.009979248046875,
0.00803375244140625,
-0.012298583984375,
-0.0193939208984375,
-0.01303863525390625,
-0.026641845703125,
0.0205230712890625,
0.01018524169921875,
0.004398345947265625,
0.025634765625,
0.0030307769775390625,
-0.01116943359375,
-0.00408172607421875,
0.0194854736328125,
0.0174407958984375,
0.00873565673828125,
0.016815185546875,
0.0019102096557617188,
-0.00901031494140625,
0.0020656585693359375,
0.0007205009460449219,
-0.00322723388671875,
-0.0113372802734375,
-0.0081024169921875,
-0.01268768310546875,
-0.01222991943359375,
-0.00006455183029174805,
0.0212554931640625,
-0.00919342041015625,
-0.036712646484375,
0.00860595703125,
0.0293426513671875,
0.0270843505859375,
-0.01776123046875,
0.01309967041015625,
-0.0206146240234375,
-0.007389068603515625,
0.030517578125,
0.005741119384765625,
-0.023193359375,
0.0180511474609375,
0.0165863037109375,
-0.019317626953125,
0.00949859619140625,
-0.050079345703125,
0.01309967041015625,
0.034149169921875,
0.0112762451171875,
0.017181396484375,
0.03802490234375,
0.034271240234375,
-0.01507568359375,
0.03741455078125,
0.062255859375,
0.00016927719116210938,
0.006923675537109375,
-0.0167388916015625,
-0.030120849609375,
0.0145721435546875,
-0.0164947509765625,
0.01019287109375,
0.00653839111328125,
0.03204345703125,
0.0323486328125,
-0.01055145263671875,
0.04833984375,
-0.006435394287109375,
-0.006786346435546875,
0.0035495758056640625,
-0.0233917236328125,
0.027191162109375,
-0.022186279296875,
-0.00853729248046875,
0.00023066997528076172,
0.01065826416015625,
0.007488250732421875,
-0.00408935546875,
-0.0140228271484375,
-0.0025081634521484375,
-0.0031147003173828125,
0.004283905029296875,
0.037261962890625,
0.00496673583984375,
0.0002415180206298828,
0.013092041015625,
-0.00013148784637451172,
0.0293731689453125,
-0.0144500732421875,
0.01654052734375,
0.0148773193359375,
0.014312744140625,
0.005855560302734375,
0.0163116455078125,
0.0010986328125,
-0.00989532470703125,
0.01325225830078125,
-0.0069580078125,
0.01519012451171875,
0.0211181640625,
0.0201873779296875,
0.0165252685546875,
-0.0129547119140625,
0.005725860595703125,
-0.01255035400390625,
0.0070037841796875,
-0.0048980712890625,
0.0115509033203125,
-0.00959014892578125,
-0.0019426345825195312,
-0.0236053466796875,
-0.01953125,
0.003604888916015625,
0.00797271728515625,
-0.0295562744140625,
0.03094482421875,
-0.0328369140625,
0.03350830078125,
-0.01012420654296875,
-0.0040740966796875,
0.0105438232421875,
-0.0012836456298828125,
0.05145263671875,
0.006847381591796875,
0.03094482421875,
-0.023040771484375,
-0.006011962890625,
-0.01424407958984375,
-0.0017938613891601562,
0.04095458984375,
0.032562255859375,
-0.0038967132568359375,
0.031402587890625,
0.00643157958984375,
0.03778076171875,
0.045013427734375,
-0.0177001953125,
0.0109405517578125,
0.030029296875,
0.034423828125,
0.0193023681640625,
-0.04620361328125,
0.019866943359375,
-0.0193939208984375,
-0.00787353515625,
0.0285797119140625,
0.0160980224609375,
-0.0216064453125,
-0.006870269775390625,
-0.0217742919921875,
0.0271453857421875,
0.0141754150390625,
0.0280609130859375,
0.0123748779296875,
0.003692626953125,
-0.0084381103515625,
0.001300811767578125,
0.0254058837890625,
0.004322052001953125,
0.021636962890625,
-0.0011129379272460938,
0.028564453125,
0.007350921630859375,
0.0007824897766113281,
-0.005802154541015625,
-0.01265716552734375,
-0.016265869140625,
0.01015472412109375,
0.01195526123046875,
-0.00506591796875,
0.03216552734375,
-0.0188446044921875,
-0.005985260009765625,
0.01016998291015625,
0.0268402099609375,
-0.01568603515625,
0.01214599609375,
-0.0231781005859375,
-0.0031585693359375,
-0.048309326171875,
-0.0245819091796875,
0.02825927734375,
-0.01177978515625,
-0.0099639892578125,
0.025177001953125,
-0.01317596435546875,
0.045745849609375,
-0.0257568359375,
-0.0299224853515625,
0.004215240478515625,
0.0215606689453125,
-0.0214080810546875,
-0.0183868408203125,
-0.006927490234375,
0.0120849609375,
-0.0014619827270507812,
0.002216339111328125,
-0.0026912689208984375,
0.0022029876708984375,
0.0164337158203125,
-0.03533935546875,
0.006710052490234375,
0.0084991455078125,
-0.007061004638671875,
-0.044342041015625,
0.0117034912109375,
-0.004604339599609375,
0.04229736328125,
0.0211944580078125,
-0.01396942138671875,
0.0208892822265625,
-0.00496673583984375,
-0.01727294921875,
0.01227569580078125,
0.0008077621459960938,
0.00006645917892456055,
0.037811279296875,
0.01180267333984375,
-0.0188140869140625,
-0.0234832763671875,
0.0078582763671875,
0.00313568115234375,
0.0108489990234375,
-0.027008056640625,
0.021331787109375,
-0.0043487548828125,
-0.01470184326171875,
-0.0245819091796875,
-0.02703857421875,
-0.0099945068359375,
0.025421142578125,
-0.0100250244140625,
-0.01071929931640625,
0.0059051513671875,
0.00327301025390625,
-0.01197052001953125,
0.0012331008911132812,
0.0262451171875,
-0.0087127685546875,
0.036590576171875,
-0.016357421875,
-0.0168609619140625,
-0.0322265625,
-0.07452392578125,
-0.025787353515625,
-0.06585693359375,
-0.0258636474609375,
-0.0149078369140625,
0.022979736328125,
-0.005268096923828125,
-0.0045318603515625,
0.0299224853515625,
-0.00383758544921875,
0.03619384765625,
0.02166748046875,
-0.01447296142578125,
-0.0163116455078125,
-0.05352783203125,
0.01044464111328125,
-0.03204345703125,
0.0082550048828125,
-0.037139892578125,
-0.045623779296875,
0.0073699951171875,
-0.016204833984375,
0.0157318115234375,
-0.0160675048828125,
-0.028472900390625,
-0.00952911376953125,
0.0003707408905029297,
0.0239715576171875,
-0.01203155517578125,
0.017303466796875,
0.0183258056640625,
-0.03216552734375,
0.0117340087890625,
-0.017578125,
0.01611328125,
-0.006366729736328125,
0.01192474365234375,
0.035919189453125,
-0.0184478759765625,
-0.0165863037109375,
-0.003948211669921875,
-0.011688232421875,
0.0284881591796875,
-0.0587158203125,
0.00569915771484375,
0.0009055137634277344,
0.005512237548828125,
0.017120361328125,
0.00716400146484375,
0.02655029296875,
0.0026645660400390625,
0.0296783447265625,
0.0006308555603027344,
-0.0028171539306640625,
-0.027191162109375,
0.006801605224609375,
0.0001863241195678711,
0.00435638427734375,
-0.00540924072265625,
0.01450347900390625,
0.00693511962890625,
-0.000051856040954589844,
0.01458740234375,
-0.012847900390625,
0.020416259765625,
0.00885772705078125,
0.0229949951171875,
0.0028820037841796875,
0.0029735565185546875,
0.0004661083221435547,
0.005916595458984375
] |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.